Finite Group Databasebeta

← #33994628

Subgroups — #33994628

Order 18688.

7242 conjugacy classes of subgroups.

The subgroup lattice has 1530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624225C214yesmaximal, complemented
2#22624218C214yesmaximal, complemented
3#22624177C214yesmaximal, complemented
4#22624154C214yesmaximal, complemented
5#22624138C218yesmaximal, complemented
6#22623977C214yesmaximal, complemented
7#22623971C214yesmaximal, complemented
8#22623760C214yesmaximal, complemented
9#22623728C214yesmaximal, complemented
10#22623686C212yesmaximal, complemented
11#22623684C212yesmaximal, complemented
12#22623640C211yesmaximal, characteristic, complemented
13#22623637C214yesmaximal, complemented
14#22623614C214yesmaximal, complemented
15#22623612C212yesmaximal, complemented
16#22623606C212yesmaximal, complemented
17#22623578C212yesmaximal, complemented
18#525×D73C212yesmaximal, complemented
19C22×#14556571C211yesmaximal, characteristic, complemented
20C73×#3492C211yesmaximal, characteristic, complemented
21C2×#14556638C2212yescomplemented
22C2×#41×D73C2212yescomplemented
23C23×Dic146C2211yescharacteristic, complemented
24C23×C4×D73C2211yescharacteristic
25#17989341C2218yescomplemented
26#17989339C2218yescomplemented
27#17989334C2218yescomplemented
28#17989333C2218yescomplemented
29#17989311C2214yescomplemented
30#17989305C2214yescomplemented
31#17989298C2214yescomplemented
32#17989295C2218yescomplemented
33#17989295C2218yescomplemented
34#17989294C2218yescomplemented
35#17989293C2218yescomplemented
36#17989292C2214yescomplemented
37#17989292C2214yescomplemented
38#17989289C2218yescomplemented
39#17989285C2214yescomplemented
40#17989283C2218yescomplemented
41#17989279C2218yescomplemented
42#17989277C2218yescomplemented
43#17989276C2214yescomplemented
44#17989275C2214yescomplemented
45#17989275C2214yescomplemented
46#17989272C2214yescomplemented
47#17989272C2214yescomplemented
48#17989266C2218yescomplemented
49#17989264C2218yescomplemented
50#17989262C2218yescomplemented
51#17989261C2218yescomplemented
52#17989260C2218yescomplemented
53#17989260C2218yescomplemented
54Q8×D292C2214yescomplemented
55D4×Dic146C2214yescomplemented
56D4×Dic146C2214yescomplemented
57#17989250C2214yescomplemented
58#17989250C2214yescomplemented
59#17989250C2214yescomplemented
60#17989249C2214yescomplemented
61#17989246C2214yescomplemented
62#17989246C2214yescomplemented
63#17989243C2214yescomplemented
64#17989243C2214yescomplemented
65#17989243C2214yescomplemented
66#17989241C2218yescomplemented
67#17989241C2214yescomplemented
68#17989239C2214yescomplemented
69#17989238C2214yescomplemented
70#17989237C2218yescomplemented
71#17989234C2214yescomplemented
72#17989232C2218yescomplemented
73#17989232C2214yescomplemented
74#17989229C2218yescomplemented
75#17989226C2218yescomplemented
76#17989225C2218yescomplemented
77#17989218C2211yescharacteristic, complemented
78#17989217C2218yescomplemented
79#17989215C2214yescomplemented
80#17989212C2214yes—
81#17989212C2218yescomplemented
82#17989211C2214yescomplemented
83#17989210C2218yescomplemented
84#17989203C2218yescomplemented
85#17989202C2214yescomplemented
86#17989200C2214yescomplemented
87#17989195C2214yescomplemented
88#17989185C2218yescomplemented
89#17989184C2214yescomplemented
90#17989181C2218yescomplemented
91#17989181C2218yescomplemented
92#17989181C2218yescomplemented
93#17989178C2218yescomplemented
94#17989177C2214yescomplemented
95#17989174C2214yescomplemented
96#17989173C2218yescomplemented
97#17989170C2218yescomplemented
98#17989168C2211yescharacteristic, complemented
99#17989168C2214yescomplemented
100#17989166C2214yescomplemented
101#17989165C2214yescomplemented
102#17989163C2212yescomplemented
103#17989163C2214yescomplemented
104#17989160C2214yescomplemented
105#17989159C2218yescomplemented
106#17989158C2212yescomplemented
107#17989145C2214yes—
108#17989142C2214yescomplemented
109#17989141C2214yescomplemented
110#17989122C2214yescomplemented
111#17989119C2214yescomplemented
112#17989100C2212yes—
113#17989100C2212yescomplemented
114#17989099C2212yes—
115#17989099C2214yescomplemented
116#17989098C2212yescomplemented
117#17989098C2214yescomplemented
118#17989097C2212yes—
119#17989097C2212yescomplemented
120#17989097C2214yescomplemented
121#17989096C2214yes—
122#17989096C2214yescomplemented
123#17989095C2214yes—
124#17989094C2212yes—
125#17989093C2218yescomplemented
126#17989093C2214yescomplemented
127#123×D73C2214yescomplemented
128C2×#14556571C2214yes—
129C2×#14556571C2212yescomplemented
130C2×#14556571C2212yescomplemented
131C2×#14556571C2214yescomplemented
132C2×#14556571C2214yescomplemented
133C2×#14556571C2214yescomplemented
134C2×#14556571C2214yescomplemented
135C2×#14556571C2214yescomplemented
136C22⋊Q8×D73C2212yes—
137C22⋊Q8×D73C2212yescomplemented
138C22⋊Q8×D73C2214yescomplemented
139#121×D73C2212yes—
140#121×D73C2212yescomplemented
141#120×D73C2214yes—
142#17989070C2214yescomplemented
143#17989068C2212yescomplemented
144#17989067C2214yescomplemented
145#17989064C2212yescomplemented
146#17989059C2218yes—
147C4×D4×D73C2214yes—
148C4×D4×D73C2214yescomplemented
149#117×D73C2212yescomplemented
150C22×C4⋊Dic73C2212yescomplemented
151C22×#11924005C2212yes—
152#554×C73C2214yescomplemented
153#553×C73C2214yescomplemented
154#552×C73C2214yescomplemented
155#547×C73C2214yescomplemented
156#544×C73C2211yescharacteristic, complemented
157#539×C73C2214yescomplemented
158#537×C73C2211yescharacteristic, complemented
159#525×C73C2212yescomplemented
160#525×C73C2214yescomplemented
161#520×C73C2212yescomplemented
162C22×C4⋊C4×C73C2211yescharacteristic, complemented
163C24×D73C2311yescharacteristic
164#14556638—48no—
165C2×#11924029C2312yes—
166C2×#11924028C2312yes—
167C2×#11924028C2314yes—
168C2×#11924028C2314yes—
169C2×#11924028C2314yescomplemented
170C2×#11924027C2314yes—
171C2×#11924027C2312yes—
172C2×#11924027C2318yes—
173C2×#11924027C2314yescomplemented
174#41×D73—48no—
175C22×Dic146—44no—
176C22×Dic146C2312yes—
177C22×Dic146C2312yes—
178C22×Dic146C2314yes—
179C22×Dic146C2314yes—
180C22×Dic146C2314yescomplemented
181C2×Q8×D73C2312yes—
182C2×Q8×D73C2314yescomplemented
183C2×D4×D73C2314yes—
184C2×D4×D73C2314yes—
185C2×D4×D73C2312yes—
186C2×D4×D73C2314yes—
187C23×Dic73C2311yescharacteristic
188C23×Dic73C2312yes—
189C22×C4×D73—44no—
190C22×C4×D73C2312yes—
191C22×C4×D73C2312yes—
192C22×C4×D73C2312yes—
193C22×C4×D73C2312yes—
194C22×C4×D73C2312yes—
195C22×C4×D73C2312yes—
196C22×C4×D73C2314yes—
197#14556591C2314yescomplemented
198#14556591C2318yescomplemented
199#14556590C2314yescomplemented
200#14556590C2318yescomplemented
201#14556590C2318yescomplemented
202#14556590C2318yescomplemented
203#14556589C2314yescomplemented
204#14556586C2318yes—
205#14556586C2318yes—
206#14556586C2318yes—
207#14556586C2318yescomplemented
208#14556586C2318yescomplemented
209#14556586C2318yescomplemented
210#14556585C2318yes—
211#14556584C2318yescomplemented
212#14556584C2318yescomplemented
213#14556583C2318yescomplemented
214#14556582C2318yescomplemented
215#14556582C2318yescomplemented
216#14556582C2318yescomplemented
217#14556582C2314yescomplemented
218#14556581C2318yescomplemented
219#14556581C2318yescomplemented
220#14556581C2318yescomplemented
221#14556580C2318yes—
222#14556579C2318yes—
223#14556579C2314yescomplemented
224#14556578C2314yescomplemented
225#14556577C2318yes—
226#14556577C2318yes—
227#14556577C2318yescomplemented
228#14556577C2318yescomplemented
229#14556576C2318yes—
230#14556576C2318yes—
231#14556576C2318yes—
232#14556576C2314yes—
233#14556576C2314yes—
234#14556576C2318yescomplemented
235#14556575C2318yes—
236#14556575C2318yes—
237#14556575C2314yes—
238#14556575C2318yescomplemented
239#14556575C2318yescomplemented
240#14556574C2314yes—
241#14556574C2318yes—
242#14556574C2318yes—
243#14556573C2318yes—
244#14556573C2314yes—
245#14556573C2314yes—
246#14556573C2318yescomplemented
247#14556573C2318yescomplemented
248#14556572C2318yes—
249#14556572C2314yes—
250#14556571C2314yes—
251#14556571C2314yes—
252#14556571C2312yes—
253#14556571C2314yes—
254#14556571C2312yes—
255#14556571C2314yes—
256#14556571C2318yes—
257#14556571C2318yes—
258#14556571C2318yes—
259#14556571C2314yes—
260#14556571C2314yes—
261#14556571C2314yes—
262#14556571C2314yes—
263#14556571C2318yes—
264#14556571C2318yes—
265#14556571C2314yescomplemented
266#14556571C2314yescomplemented
267#14556571C2314yescomplemented
268#14556571C2318yescomplemented
269#14556571C2318yescomplemented
270#14556570C2314yes—
271#14556570C2314yes—
272#14556570C2312yes—
273#14556570C2312yes—
274#14556570C2314yescomplemented
275#14556570C2314yescomplemented
276#14556570C2318yescomplemented
277#14556569C2318yes—
278#14556569C2318yes—
279#14556569C2314yes—
280#14556569C2314yes—
281#14556569C2318yescomplemented
282#14556569C2318yescomplemented
283#14556569C2318yescomplemented
284#14556568C2318yes—
285#14556568C2314yes—
286#14556568C2318yes—
287#14556568C2314yes—
288#14556568C2318yescomplemented
289#14556568C2318yescomplemented
290#14556568C2318yescomplemented
291#14556568C2318yescomplemented
292#14556567C2312yes—
293#14556567C2318yes—
294#14556567C2312yes—
295#14556567C2318yescomplemented
296#14556566C2312yes—
297#14556566C2312yes—
298#14556566C2318yes—
299#14556566C2314yescomplemented
300#14556565C2314yes—
301#14556565C2318yes—
302#14556565C2314yes—
303#14556565C2312yes—
304#14556565C2312yes—
305#14556565C2318yescomplemented
306#14556564C2318yes—
307#14556564C2314yes—
308#14556564C2314yes—
309#14556563C2318yes—
310#14556563C2314yes—
311#14556563C2318yes—
312#14556563C2318yes—
313#14556563C2314yes—
314#14556562C2312yes—
315#14556562C2312yes—
316#14556562C2318yescomplemented
317#14556561C2318yes—
318#14556561C2314yes—
319#14556561C2314yes—
320#14556561C2314yes—
321#14556560C2314yes—
322#14556559C2318yes—
323#14556559C2314yes—
324#14556559C2314yes—
325#14556559C2314yes—
326Q8×Dic73C2318yescomplemented
327C4×Dic146C2314yescomplemented
328C4×Dic146C2318yescomplemented
329C4×Dic146C2314yescomplemented
330#14556556C2314yescomplemented
331#14556556C2314yescomplemented
332#14556556C2314yescomplemented
333C4×D292C2318yes—
334C4×D292C2314yes—
335C4×D292C2314yes—
336C4×D292C2318yescomplemented
337D4×Dic73C2318yes—
338D4×Dic73C2314yes—
339D4×Dic73C2318yes—
340D4×Dic73C2314yes—
341D4×Dic73C2318yescomplemented
342#14556553C2318yes—
343#14556553C2314yes—
344#14556553C2314yes—
345#14556553C2314yescomplemented
346C4×C22⋊D73C2318yes—
347C4×C22⋊D73C2318yes—
348C4×C22⋊D73C2318yes—
349C4×C22⋊D73C2314yes—
350C4×C22⋊D73C2314yes—
351C4×C22⋊D73C2314yes—
352C4×C22⋊D73C2314yes—
353#14556551C2318yes—
354#14556551C2318yes—
355#14556551C2314yes—
356#14556551C2314yes—
357#14556551C2318yes—
358#14556551C2314yes—
359#14556551C2314yes—
360#14556550C2312yes—
361#14556550C2314yes—
362#14556550C2318yescomplemented
363#14556549C2318yes—
364#14556549C2312yes—
365#14556549C2312yes—
366#14556549C2318yescomplemented
367#14556549C2314yescomplemented
368#14556548C2318yes—
369#14556548C2314yes—
370#14556547C2318yes—
371#14556547C2314yes—
372C2×C4⋊Dic73C2314yes—
373C2×C4⋊Dic73C2314yes—
374C2×C4⋊Dic73C2314yes—
375C2×C4⋊Dic73C2314yes—
376C2×C4⋊Dic73C2318yes—
377C2×C4⋊Dic73C2318yescomplemented
378C4⋊C4×D73C2314yes—
379C4⋊C4×D73C2312yes—
380C4⋊C4×D73C2312yes—
381C4⋊C4×D73C2314yes—
382C4⋊C4×D73C2314yescomplemented
383C4⋊C4×D73C2318yescomplemented
384C2×#11924005C2314yes—
385C2×#11924005C2314yes—
386C2×#11924005C2318yes—
387C2×#11924005C2318yes—
388C2×#11924005C2314yes—
389C2×#11924005C2314yes—
390C22⋊C4×D73C2314yes—
391C22⋊C4×D73C2314yes—
392C22⋊C4×D73C2318yes—
393C22⋊C4×D73C2314yes—
394C22⋊C4×D73C2314yes—
395C22⋊C4×D73C2314yes—
396C42×D73C2314yes—
397C2×#41×C73C2312yes—
398C2×#41×C73C2314yes—
399C23×C4×C73C2311yescharacteristic
400C23×C4×C73C2312yes—
401C4⋊Q8×C73C2314yescomplemented
402#126×C73C2318yescomplemented
403#125×C73C2314yescomplemented
404#125×C73C2318yescomplemented
405#123×C73C2314yes—
406#123×C73C2318yes—
407#123×C73C2318yescomplemented
408C22⋊Q8×C73C2314yes—
409C22⋊Q8×C73C2312yes—
410C22⋊Q8×C73C2312yes—
411C22⋊Q8×C73C2314yes—
412C22⋊Q8×C73C2314yescomplemented
413C22⋊Q8×C73C2318yescomplemented
414#121×C73C2314yes—
415#121×C73C2314yes—
416#121×C73C2312yes—
417#121×C73C2312yes—
418#121×C73C2314yescomplemented
419#120×C73C2314yes—
420C4×Q8×C73C2314yescomplemented
421C4×D4×C73C2318yes—
422C4×D4×C73C2318yes—
423C4×D4×C73C2314yes—
424C4×D4×C73C2314yes—
425C4×D4×C73C2314yescomplemented
426#117×C73C2312yes—
427#117×C73C2314yes—
428#117×C73C2314yescomplemented
429C2×C4⋊C4×C73C2311yescharacteristic
430C2×C4⋊C4×C73C2312yes—
431C2×C4⋊C4×C73C2314yes—
432C2×C4⋊C4×C73C2311yescharacteristic
433C2×C4⋊C4×C73C2314yes—
434C2×C4⋊C4×C73C2314yescomplemented
435C23×D73—24no—
436C23×D73—42no—
437C23×D73—42no—
438C23×D73C2412yes—
439C23×D73C2412yes—
440C23×D73C2414yes—
441C23×D73C2411yescharacteristic
442C23×D73C2411yescharacteristic
443#11924029—44no—
444#11924028—28no—
445#11924028—48no—
446#11924028—48no—
447#11924028—48no—
448#11924027—44no—
449#11924027—48no—
450#11924027—48no—
451#11924027—416no—
452C2×Dic146—28no—
453C2×Dic146—48no—
454C2×Dic146—48no—
455C2×Dic146—48no—
456C2×Dic146—44no—
457C2×Dic146C2412yes—
458C2×Dic146C2414yes—
459C2×Dic146C2414yes—
460C2×Dic146C2414yes—
461C2×Dic146C2414yes—
462C2×Dic146C2418yes—
463C2×Dic146C2418yes—
464Q8×D73—44no—
465Q8×D73—48no—
466C2×D292C2414yes—
467C2×D292C2412yes—
468C2×D292C2414yes—
469C2×D292C2414yes—
470C2×D292C2414yes—
471C2×C22⋊D73C2414yes—
472C2×C22⋊D73C2414yes—
473C2×C22⋊D73C2414yes—
474C2×C22⋊D73C2414yes—
475C2×C22⋊D73C2414yes—
476C2×C22⋊D73C2414yes—
477C2×C22⋊D73C2418yes—
478C2×C22⋊D73C2414yes—
479D4×D73—216no—
480D4×D73—44no—
481D4×D73—48no—
482D4×D73—48no—
483C22×Dic73—42no—
484C22×Dic73—44no—
485C22×Dic73C2414yes—
486C22×Dic73C2412yes—
487C22×Dic73C2414yes—
488C22×Dic73C2414yes—
489C22×Dic73C2418yes—
490C22×Dic73C2411yescharacteristic
491C22×Dic73C2412yes—
492C22×Dic73C2411yescharacteristic
493C22×Dic73C2414yes—
494C2×C4×D73—28no—
495C2×C4×D73—44no—
496C2×C4×D73—44no—
497C2×C4×D73—44no—
498C2×C4×D73—44no—
499C2×C4×D73—48no—
500C2×C4×D73—44no—
501C2×C4×D73C2412yes—
502C2×C4×D73C2414yes—
503C2×C4×D73C2412yes—
504C2×C4×D73C2414yes—
505C2×C4×D73C2412yes—
506C2×C4×D73C2412yes—
507C2×C4×D73C2414yes—
508C2×C4×D73C2412yes—
509C2×C4×D73C2414yes—
510C2×C4×D73C2412yes—
511C2×C4×D73C2418yes—
512C2×C4×D73C2418yes—
513C2×C4×D73C2414yes—
514C2×C4×D73C2412yes—
515C2×C4×D73C2412yes—
516C4⋊Dic73C2412yes—
517C4⋊Dic73C2414yes—
518C4⋊Dic73C2412yes—
519C4⋊Dic73C2414yes—
520C4⋊Dic73C2418yes—
521C4⋊Dic73C2418yes—
522C4⋊Dic73C2418yes—
523C4⋊Dic73C2418yes—
524C4⋊Dic73C2414yes—
525C4⋊Dic73C2418yes—
526C4⋊Dic73C2418yes—
527C4⋊Dic73C2414yes—
528#11924007C2414yes—
529#11924007C2414yes—
530#11924007C2414yes—
531#11924007C2414yes—
532#11924007C2414yes—
533#11924007C2414yes—
534#11924007C2418yes—
535#11924007C2418yes—
536#11924007C2418yes—
537#11924007C2418yes—
538#11924007C2418yes—
539#11924007C2418yes—
540C22⋊Dic73C2414yes—
541C22⋊Dic73C2414yes—
542C22⋊Dic73C2414yes—
543C22⋊Dic73C2414yes—
544C22⋊Dic73C2414yes—
545C22⋊Dic73C2418yes—
546C22⋊Dic73C2418yes—
547#11924005C2414yes—
548#11924005C2418yes—
549#11924005C2414yes—
550#11924005C2414yes—
551#11924005C2414yes—
552#11924005C2414yes—
553#11924005C2414yes—
554#11924005C2414yes—
555#11924005C2414yes—
556#11924005C2414yes—
557#11924005C2414yes—
558#11924005C2418yes—
559#11924005C2418yes—
560#11924005C2418yes—
561#11924005C2418yes—
562#11924005C2418yes—
563#11924005C2418yes—
564#11924005C2418yes—
565C4×Dic73C2414yes—
566C4×Dic73C2414yes—
567C4×Dic73C2414yes—
568C4×Dic73C2418yes—
569C4×Dic73C2418yes—
570C4×Dic73C2418yes—
571C24×C73C2411yescharacteristic
572#41×C73—28no—
573#41×C73—48no—
574C2×Q8×C73C2412yes—
575C2×Q8×C73C2414yes—
576C2×D4×C73C2414yes—
577C2×D4×C73C2414yes—
578C2×D4×C73C2414yes—
579C2×D4×C73C2412yes—
580C2×D4×C73C2414yes—
581C22×C4×C73—24no—
582C22×C4×C73—44no—
583C22×C4×C73C2414yes—
584C22×C4×C73C2412yes—
585C22×C4×C73C2412yes—
586C22×C4×C73C2411yescharacteristic
587C22×C4×C73C2414yes—
588C22×C4×C73C2412yes—
589C22×C4×C73C2414yes—
590C22×C4×C73C2412yes—
591C22×C4×C73C2418yes—
592C22×C4×C73C2411yescharacteristic
593C4⋊C4×C73C2414yes—
594C4⋊C4×C73C2414yes—
595C4⋊C4×C73C2418yes—
596C4⋊C4×C73C2412yes—
597C4⋊C4×C73C2418yes—
598C4⋊C4×C73C2412yes—
599C4⋊C4×C73C2414yes—
600C4⋊C4×C73C2414yes—
601C4⋊C4×C73C2414yes—
602C4⋊C4×C73C2418yes—
603C4⋊C4×C73C2414yes—
604C22⋊C4×C73C2414yes—
605C22⋊C4×C73C2414yes—
606C22⋊C4×C73C2418yes—
607C22⋊C4×C73C2414yes—
608C22⋊C4×C73C2418yes—
609C22⋊C4×C73C2414yes—
610C22⋊C4×C73C2414yes—
611C42×C73C2418yes—
612C42×C73C2414yes—
613C23×C73—22no—
614C23×C73—22no—
615C23×C73—22no—
616C23×C73C2514yes—
617C23×C73C2511yescharacteristic
618C23×C73C2511yescharacteristic
619C23×C73C2511yescharacteristic
620C22×D73—24no—
621C22×D73—22no—
622C22×D73—24no—
623C22×D73—24no—
624C22×D73—24no—
625C22×D73—28no—
626C22×D73—41no—
627C22×D73—42no—
628C22×D73—41no—
629C22×D73—41no—
630C22×D73—42no—
631C22×D73—41no—
632C22×D73—44no—
633C22×D73—44no—
634C22×D73—416no—
635C22×D732−1+414yescomplemented
636C22×D73C2512yes—
637C22×D73C2514yes—
638C22×D73C2512yes—
639Q8×C73—24no—
640Q8×C73—44no—
641D4×C73—28no—
642D4×C73—28no—
643D4×C73—28no—
644D4×C73—24no—
645D4×C73—44no—
646C2×C4×C73—22no—
647C2×C4×C73—28no—
648C2×C4×C73—24no—
649C2×C4×C73—24no—
650C2×C4×C73—28no—
651C2×C4×C73—42no—
652C2×C4×C73—44no—
653C2×C4×C73—42no—
654C2×C4×C73—48no—
655C2×C4×C73H(5,𝔽2)14yes—
656C2×C4×C73C2514yes—
657C2×C4×C73C2514yes—
658C2×C4×C73C2514yes—
659C2×C4×C73C2514yes—
660C2×C4×C73C2512yes—
661C2×C4×C73C2514yes—
662C2×C4×C73C2512yes—
663C22⋊D73—28no—
664C22⋊D73—28no—
665C22⋊D73—28no—
666C22⋊D73—28no—
667C22⋊D73—44no—
668C22⋊D73—44no—
669C22⋊D73—44no—
670C22⋊D73—48no—
671C2×Dic73—24no—
672C2×Dic73—28no—
673C2×Dic73—41no—
674C2×Dic73—42no—
675C2×Dic73—41no—
676C2×Dic73—44no—
677C2×Dic73—44no—
678C2×Dic73—44no—
679C2×Dic73—48no—
680C2×Dic73C2514yes—
681C2×Dic73C2514yes—
682C2×Dic73C2512yes—
683C2×Dic73C2518yes—
684C2×Dic73C2514yes—
685C2×Dic73C2512yes—
686D292—28no—
687D292—24no—
688D292—44no—
689D292—44no—
690D292—44no—
691C4×D73—28no—
692C4×D73—24no—
693C4×D73—24no—
694C4×D73—24no—
695C4×D73—24no—
696C4×D73—28no—
697C4×D73—42no—
698C4×D73—42no—
699C4×D73—42no—
700C4×D73—42no—
701C4×D73—44no—
702C4×D73—44no—
703C4×D73—44no—
704C4×D73—48no—
705C4×D73—48no—
706Dic146—28no—
707Dic146—24no—
708Dic146—28no—
709Dic146—48no—
710Dic146—44no—
711Dic146—48no—
712Dic146—44no—
713C22×C73—28no—
714C22×C73—21no—
715C22×C73—21no—
716C22×C73—21no—
717C22×C73—21no—
718C22×C73—21no—
719C22×C73—21no—
720C22×C73—24no—
721C22×C73—24no—
722C22×C73—24no—
723C22×C73C2×H(5,𝔽2)12yes—
724C22×C73C2×2−1+412yes—
725C22×C73#58512yes—
726C22×C73C2611yescharacteristic
727C2×D73—22no—
728C2×D73—22no—
729C2×D73—22no—
730C2×D73—24no—
731C2×D73—24no—
732C2×D73—22no—
733C2×D73—24no—
734C2×D73—22no—
735C2×D73—44no—
736C2×D73—48no—
737C2×D73—48no—
738C2×D73—44no—
739C2×D73—88no—
740C2×D73C2×2−1+414yes—
741C4×C73—22no—
742C4×C73—24no—
743C4×C73—24no—
744C4×C73—24no—
745C4×C73—24no—
746C4×C73—24no—
747C4×C73C2×H(5,𝔽2)14yes—
748Dic73—28no—
749Dic73—24no—
750Dic73—22no—
751Dic73—22no—
752Dic73—24no—
753Dic73—24no—
754#62819—731nomaximal, Sylow
755C2×C73—22no—
756C2×C73—22no—
757C2×C73—22no—
758C2×C73—44no—
759C2×C73C22×H(5,𝔽2)11yescharacteristic
760C2×C73C22×2−1+411yescharacteristic
761C2×C73C2×#58511yescharacteristic
762D73—24no—
763D73—42no—
764D73—44no—
765#3541—734no—
766#3541—734no—
767#3538—734no—
768#3536—734no—
769#3535—738no—
770#3520—734no—
771#3520—734no—
772#3505—734no—
773#3501—734no—
774#3495—732no—
775#3495—732no—
776#3492—734no—
777#3492—731no—
778#3492D7311yescharacteristic, complemented
779#3490—734no—
780#3489—732no—
781#3489—732no—
782#3486—732no—
783C2×#525—732no—
784C22×C22⋊Q8—731no—
785C73#6281911yescharacteristic, complemented, Sylow
786C2×2−1+4—732no—
787C22×#41—732no—
788C23×Q8—731no—
789C24×C4—731no—
790#563—738no—
791#563—738no—
792#562—738no—
793#562—738no—
794#556—734no—
795#556—734no—
796#554—734no—
797#554—738no—
798#554—738no—
799#554—738no—
800#554—738no—
801#554—734no—
802#554—734no—
803#554C2×D7314yescomplemented
804#553—738no—
805#553—738no—
806#553—734no—
807#553C2×D7314yescomplemented
808#552—734no—
809#552—734no—
810#552—738no—
811#552—738no—
812#552—734no—
813#552—734no—
814#552—734no—
815#552C2×D7314yescomplemented
816#551—738no—
817#551—738no—
818#551—738no—
819#551—738no—
820#551—738no—
821#551—738no—
822D4×Q8—734no—
823D4×Q8—734no—
824D4×Q8—734no—
825D4×Q8—734no—
826D4×Q8—734no—
827D4×Q8—734no—
828#548—734no—
829#548—734no—
830#548—734no—
831#548—734no—
832#548—734no—
833#548—734no—
834#547—734no—
835#547—738no—
836#547—738no—
837#547—734no—
838#547—734no—
839#547C2×D7314yescomplemented
840#546—738no—
841#546—738no—
842#546—738no—
843#546—734no—
844#546—738no—
845#546—734no—
846#544—738no—
847#544—734no—
848#544—731no—
849#544C2×D7311yescharacteristic, complemented
850#543—734no—
851#543—738no—
852#542—734no—
853#542—738no—
854#542—738no—
855#542—734no—
856#541—734no—
857#541—734no—
858#539—738no—
859#539—738no—
860#539—738no—
861#539—738no—
862#539—738no—
863#539—734no—
864#539C2×D7314yescomplemented
865#538—738no—
866#538—734no—
867#538—734no—
868#538—738no—
869#537—734no—
870#537—734no—
871#537—731no—
872#537—734no—
873#537C2×D7311yescharacteristic, complemented
874#536—732no—
875#536—738no—
876#536—734no—
877#536—732no—
878#536—734no—
879#534—734no—
880#533—734no—
881#533—734no—
882#529—734no—
883#529—734no—
884#525—732no—
885#525—732no—
886#525—734no—
887#525—734no—
888#525—732no—
889#525—732no—
890#525—732no—
891#525—732no—
892#525—734no—
893#525—734no—
894#525—738no—
895#525—734no—
896#525—734no—
897#525—732no—
898#525—734no—
899#525C2×D7312yescomplemented
900#525C2×D7314yescomplemented
901C2×#123—734no—
902C2×C22⋊Q8—732no—
903C2×C22⋊Q8—732no—
904C2×C22⋊Q8—734no—
905C2×C22⋊Q8—732no—
906C2×C22⋊Q8—732no—
907C2×C22⋊Q8—734no—
908C2×C22⋊Q8—734no—
909C2×C22⋊Q8—734no—
910C2×C22⋊Q8—734no—
911C2×C22⋊Q8—734no—
912C2×C22⋊Q8—734no—
913C2×#121—732no—
914C2×#121—732no—
915C2×#120—734no—
916#520—734no—
917#520—734no—
918#520—732no—
919#520C2×D7312yescomplemented
920#519—732no—
921#518—738no—
922C2×C4×D4—734no—
923C2×C4×D4—734no—
924C2×#117—732no—
925C22×C4⋊C4—732no—
926C22×C4⋊C4C2×D7311yescharacteristic, complemented
927C22×C22⋊C4—732no—
928C25—731no—
9292−1+4—2928no—
930C2×#41—2928no—
931C2×#41—732no—
932C2×#41—734no—
933C2×#41—732no—
934C2×#41—738no—
935C2×#41—734no—
936C2×#41—734no—
937C2×#41—734no—
938C2×#41—734no—
939C2×#41—732no—
940C2×#41C22×D7312yes—
941C2×#41C22×D7314yes—
942C22×Q8—2924no—
943C22×Q8—732no—
944C22×Q8—734no—
945C22×Q8—732no—
946C22×Q8—734no—
947C22×Q8—734no—
948C22×Q8—734no—
949C22×Q8—732no—
950C22×D4—734no—
951C22×D4—734no—
952C22×D4—732no—
953C22×D4—734no—
954C23×C4—2924no—
955C23×C4—732no—
956C23×C4—731no—
957C23×C4—732no—
958C23×C4—732no—
959C23×C4—734no—
960C23×C4—732no—
961C23×C4—732no—
962C23×C4—732no—
963C23×C4—732no—
964C23×C4C22×D7311yescharacteristic
965C23×C4C22×D7312yes—
966C4⋊Q8—734no—
967C4⋊Q8—734no—
968C4⋊Q8—738no—
969C4⋊Q8—738no—
970C4⋊Q8—738no—
971C4⋊Q8—734no—
972C4⋊Q8—738no—
973C4⋊Q8C22×D7314yescomplemented
974#126—738no—
975#126—738no—
976#126—738no—
977#126—738no—
978#126—738no—
979#126—738no—
980#126—738no—
981#126—738no—
982#126—738no—
983#126C22×D7318yescomplemented
984#125—734no—
985#125—738no—
986#125—738no—
987#125—738no—
988#125—738no—
989#125—738no—
990#125—738no—
991#125—738no—
992#125C22×D7314yescomplemented
993#125C22×D7318yescomplemented
994#124—738no—
995#124—734no—
996#124—738no—
997#124—738no—
998#124—738no—
999#124—738no—
1000#124—734no—
1001#124—738no—
1002#123—734no—
1003#123—738no—
1004#123—734no—
1005#123—738no—
1006#123—738no—
1007#123—734no—
1008#123—734no—
1009#123—738no—
1010#123—738no—
1011#123—738no—
1012#123—738no—
1013#123—734no—
1014#123—734no—
1015#123—734no—
1016#123—738no—
1017#123—738no—
1018#123—738no—
1019#123—738no—
1020#123—738no—
1021#123—738no—
1022#123—738no—
1023#123C22×D7314yes—
1024#123C22×D7318yes—
1025#123C22×D7318yescomplemented
1026C22⋊Q8—732no—
1027C22⋊Q8—732no—
1028C22⋊Q8—738no—
1029C22⋊Q8—738no—
1030C22⋊Q8—732no—
1031C22⋊Q8—732no—
1032C22⋊Q8—734no—
1033C22⋊Q8—734no—
1034C22⋊Q8—734no—
1035C22⋊Q8—734no—
1036C22⋊Q8—738no—
1037C22⋊Q8—734no—
1038C22⋊Q8—734no—
1039C22⋊Q8—732no—
1040C22⋊Q8—734no—
1041C22⋊Q8—734no—
1042C22⋊Q8—738no—
1043C22⋊Q8—738no—
1044C22⋊Q8—734no—
1045C22⋊Q8—734no—
1046C22⋊Q8—734no—
1047C22⋊Q8—734no—
1048C22⋊Q8—738no—
1049C22⋊Q8—738no—
1050C22⋊Q8—732no—
1051C22⋊Q8—734no—
1052C22⋊Q8—734no—
1053C22⋊Q8—734no—
1054C22⋊Q8—734no—
1055C22⋊Q8—738no—
1056C22⋊Q8—738no—
1057C22⋊Q8—738no—
1058C22⋊Q8—734no—
1059C22⋊Q8—738no—
1060C22⋊Q8—738no—
1061C22⋊Q8—738no—
1062C22⋊Q8—738no—
1063C22⋊Q8—738no—
1064C22⋊Q8—734no—
1065C22⋊Q8—734no—
1066C22⋊Q8—738no—
1067C22⋊Q8—738no—
1068C22⋊Q8—738no—
1069C22⋊Q8—738no—
1070C22⋊Q8—738no—
1071C22⋊Q8—738no—
1072C22⋊Q8C22×D7312yes—
1073C22⋊Q8C22×D7312yes—
1074C22⋊Q8C22×D7314yes—
1075C22⋊Q8C22×D7314yes—
1076C22⋊Q8C22×D7314yescomplemented
1077C22⋊Q8C22×D7318yescomplemented
1078#121—732no—
1079#121—734no—
1080#121—732no—
1081#121—734no—
1082#121—738no—
1083#121—738no—
1084#121—738no—
1085#121—738no—
1086#121—732no—
1087#121—732no—
1088#121—734no—
1089#121—734no—
1090#121—738no—
1091#121—738no—
1092#121—732no—
1093#121—732no—
1094#121—734no—
1095#121—738no—
1096#121—734no—
1097#121—734no—
1098#121—738no—
1099#121C22×D7312yes—
1100#121C22×D7312yes—
1101#121C22×D7314yes—
1102#121C22×D7314yes—
1103#121C22×D7314yescomplemented
1104#120—734no—
1105#120—734no—
1106#120—734no—
1107#120—734no—
1108#120—738no—
1109#120—734no—
1110#120—734no—
1111#120—734no—
1112#120—738no—
1113#120C22×D7314yes—
1114C4×Q8—738no—
1115C4×Q8—734no—
1116C4×Q8—734no—
1117C4×Q8—734no—
1118C4×Q8—734no—
1119C4×Q8—734no—
1120C4×Q8—738no—
1121C4×Q8C22×D7314yescomplemented
1122C4×D4—734no—
1123C4×D4—734no—
1124C4×D4—738no—
1125C4×D4—738no—
1126C4×D4—738no—
1127C4×D4—734no—
1128C4×D4—734no—
1129C4×D4—734no—
1130C4×D4—734no—
1131C4×D4—738no—
1132C4×D4—738no—
1133C4×D4—738no—
1134C4×D4—734no—
1135C4×D4—734no—
1136C4×D4—738no—
1137C4×D4—734no—
1138C4×D4—734no—
1139C4×D4—734no—
1140C4×D4—734no—
1141C4×D4—734no—
1142C4×D4—738no—
1143C4×D4—738no—
1144C4×D4—738no—
1145C4×D4—734no—
1146C4×D4—734no—
1147C4×D4—738no—
1148C4×D4—738no—
1149C4×D4C22×D7314yes—
1150C4×D4C22×D7314yes—
1151C4×D4C22×D7318yes—
1152C4×D4C22×D7318yes—
1153C4×D4C22×D7314yescomplemented
1154#117—732no—
1155#117—734no—
1156#117—738no—
1157#117—732no—
1158#117—732no—
1159#117—738no—
1160#117—734no—
1161#117—738no—
1162#117—734no—
1163#117—738no—
1164#117—734no—
1165#117—738no—
1166#117C22×D7312yes—
1167#117C22×D7314yes—
1168#117C22×D7314yescomplemented
1169C2×C4⋊C4—734no—
1170C2×C4⋊C4—734no—
1171C2×C4⋊C4—734no—
1172C2×C4⋊C4—734no—
1173C2×C4⋊C4—738no—
1174C2×C4⋊C4—738no—
1175C2×C4⋊C4—732no—
1176C2×C4⋊C4—732no—
1177C2×C4⋊C4—734no—
1178C2×C4⋊C4—734no—
1179C2×C4⋊C4—734no—
1180C2×C4⋊C4—738no—
1181C2×C4⋊C4C22×D7311yescharacteristic
1182C2×C4⋊C4C22×D7311yescharacteristic
1183C2×C4⋊C4C22×D7312yes—
1184C2×C4⋊C4C22×D7314yes—
1185C2×C4⋊C4C22×D7314yes—
1186C2×C4⋊C4C22×D7314yescomplemented
1187C2×C22⋊C4—734no—
1188C2×C22⋊C4—734no—
1189C2×C22⋊C4—738no—
1190C2×C22⋊C4—734no—
1191C2×C22⋊C4—734no—
1192C2×C22⋊C4—738no—
1193C2×C22⋊C4—734no—
1194C2×C22⋊C4—734no—
1195C2×C22⋊C4—734no—
1196C2×C22⋊C4—734no—
1197C2×C22⋊C4—734no—
1198C2×C22⋊C4—738no—
1199C2×C42—734no—
1200C24—2922no—
1201C24—2922no—
1202C24—731no—
1203C24—734no—
1204C24—731no—
1205C24—732no—
1206C24—732no—
1207C24—1464no—
1208C24C23×D7311yescharacteristic
1209#41—28no—
1210#41—48no—
1211#41—2928no—
1212#41—2928no—
1213#41—2928no—
1214#41—2924no—
1215#41—2928no—
1216#41—2928no—
1217#41—29216no—
1218#41—2924no—
1219#41—1468no—
1220C2×Q8—2928no—
1221C2×Q8—2928no—
1222C2×Q8—2928no—
1223C2×Q8—2924no—
1224C2×Q8—2924no—
1225C2×Q8—2928no—
1226C2×Q8—734no—
1227C2×Q8—738no—
1228C2×Q8—734no—
1229C2×Q8—738no—
1230C2×Q8—734no—
1231C2×Q8—734no—
1232C2×Q8—732no—
1233C2×Q8—1468no—
1234C2×Q8C23×D7312yes—
1235C2×Q8C23×D7314yes—
1236C2×D4—2928no—
1237C2×D4—2928no—
1238C2×D4—2924no—
1239C2×D4—734no—
1240C2×D4—738no—
1241C2×D4—734no—
1242C2×D4—734no—
1243C2×D4—734no—
1244C2×D4—734no—
1245C2×D4—734no—
1246C2×D4—734no—
1247C2×D4—734no—
1248C2×D4—734no—
1249C2×D4—734no—
1250C2×D4—734no—
1251C2×D4—732no—
1252C2×D4—14616no—
1253C2×D4C23×D7314yes—
1254C2×D4C23×D7314yes—
1255C2×D4C23×D7314yes—
1256C2×D4C23×D7312yes—
1257C2×D4C23×D7314yes—
1258C22×C4—24no—
1259C22×C4—44no—
1260C22×C4—2924no—
1261C22×C4—2924no—
1262C22×C4—2924no—
1263C22×C4—2924no—
1264C22×C4—2924no—
1265C22×C4—2928no—
1266C22×C4—2922no—
1267C22×C4—2924no—
1268C22×C4—734no—
1269C22×C4—734no—
1270C22×C4—738no—
1271C22×C4—731no—
1272C22×C4—732no—
1273C22×C4—731no—
1274C22×C4—734no—
1275C22×C4—734no—
1276C22×C4—732no—
1277C22×C4—734no—
1278C22×C4—732no—
1279C22×C4—738no—
1280C22×C4—738no—
1281C22×C4—734no—
1282C22×C4—732no—
1283C22×C4—732no—
1284C22×C4—734no—
1285C22×C4—732no—
1286C22×C4—732no—
1287C22×C4—734no—
1288C22×C4—732no—
1289C22×C4—734no—
1290C22×C4—732no—
1291C22×C4—732no—
1292C22×C4—1468no—
1293C22×C4C23×D7314yes—
1294C22×C4C23×D7312yes—
1295C22×C4C23×D7312yes—
1296C22×C4C23×D7311yescharacteristic
1297C22×C4C23×D7314yes—
1298C22×C4C23×D7312yes—
1299C22×C4C23×D7314yes—
1300C22×C4C23×D7312yes—
1301C22×C4C23×D7318yes—
1302C22×C4C23×D7311yescharacteristic
1303C4⋊C4—734no—
1304C4⋊C4—734no—
1305C4⋊C4—734no—
1306C4⋊C4—734no—
1307C4⋊C4—734no—
1308C4⋊C4—734no—
1309C4⋊C4—738no—
1310C4⋊C4—738no—
1311C4⋊C4—738no—
1312C4⋊C4—738no—
1313C4⋊C4—738no—
1314C4⋊C4—738no—
1315C4⋊C4—738no—
1316C4⋊C4—738no—
1317C4⋊C4—732no—
1318C4⋊C4—734no—
1319C4⋊C4—738no—
1320C4⋊C4—738no—
1321C4⋊C4—734no—
1322C4⋊C4—732no—
1323C4⋊C4—734no—
1324C4⋊C4—738no—
1325C4⋊C4—734no—
1326C4⋊C4—738no—
1327C4⋊C4C23×D7314yes—
1328C4⋊C4C23×D7314yes—
1329C4⋊C4C23×D7312yes—
1330C4⋊C4C23×D7312yes—
1331C4⋊C4C23×D7314yes—
1332C4⋊C4C23×D7314yes—
1333C4⋊C4C23×D7314yes—
1334C4⋊C4C23×D7318yes—
1335C4⋊C4C23×D7318yes—
1336C4⋊C4C23×D7314yes—
1337C4⋊C4C23×D7318yes—
1338C22⋊C4—734no—
1339C22⋊C4—734no—
1340C22⋊C4—734no—
1341C22⋊C4—734no—
1342C22⋊C4—734no—
1343C22⋊C4—738no—
1344C22⋊C4—738no—
1345C22⋊C4—738no—
1346C22⋊C4—738no—
1347C22⋊C4—734no—
1348C22⋊C4—734no—
1349C22⋊C4—738no—
1350C22⋊C4—738no—
1351C22⋊C4—734no—
1352C22⋊C4—734no—
1353C22⋊C4—734no—
1354C22⋊C4—734no—
1355C22⋊C4—734no—
1356C22⋊C4—734no—
1357C22⋊C4—738no—
1358C22⋊C4—738no—
1359C22⋊C4—734no—
1360C22⋊C4—734no—
1361C22⋊C4—738no—
1362C22⋊C4—738no—
1363C22⋊C4C23×D7314yes—
1364C22⋊C4C23×D7314yes—
1365C22⋊C4C23×D7314yes—
1366C22⋊C4C23×D7318yes—
1367C22⋊C4C23×D7314yes—
1368C22⋊C4C23×D7314yes—
1369C22⋊C4C23×D7318yes—
1370C42—734no—
1371C42—734no—
1372C42—734no—
1373C42—738no—
1374C42—738no—
1375C42—738no—
1376C42C23×D7314yes—
1377C42C23×D7318yes—
1378C23—22no—
1379C23—22no—
1380C23—22no—
1381C23—29216no—
1382C23—2921no—
1383C23—2922no—
1384C23—2921no—
1385C23—2921no—
1386C23—2922no—
1387C23—2921no—
1388C23—2924no—
1389C23—2924no—
1390C23—734no—
1391C23—732no—
1392C23—732no—
1393C23—734no—
1394C23—1464no—
1395C23—1464no—
1396C23—1468no—
1397C23—1464no—
1398C23—1462no—
1399C23—1464no—
1400C23C24×D7314yes—
1401C23C24×D7311yescharacteristic
1402C23C24×D7311yescharacteristic
1403C23C24×D7311yescharacteristic
1404Q8—24no—
1405Q8—44no—
1406Q8—2928no—
1407Q8—2928no—
1408Q8—2924no—
1409Q8—2924no—
1410Q8—1468no—
1411Q8—1468no—
1412Q8—1464no—
1413D4—28no—
1414D4—28no—
1415D4—28no—
1416D4—24no—
1417D4—44no—
1418D4—2924no—
1419D4—2924no—
1420D4—2924no—
1421D4—2924no—
1422D4—2924no—
1423D4—2924no—
1424D4—2928no—
1425D4—1468no—
1426D4—1468no—
1427D4—1468no—
1428D4—1468no—
1429D4—1468no—
1430D4—1464no—
1431C2×C4—22no—
1432C2×C4—28no—
1433C2×C4—24no—
1434C2×C4—24no—
1435C2×C4—28no—
1436C2×C4—42no—
1437C2×C4—44no—
1438C2×C4—42no—
1439C2×C4—48no—
1440C2×C4—2922no—
1441C2×C4—2922no—
1442C2×C4—2922no—
1443C2×C4—2922no—
1444C2×C4—2924no—
1445C2×C4—2924no—
1446C2×C4—2924no—
1447C2×C4—2928no—
1448C2×C4—2928no—
1449C2×C4—2921no—
1450C2×C4—2922no—
1451C2×C4—2921no—
1452C2×C4—2924no—
1453C2×C4—2924no—
1454C2×C4—2924no—
1455C2×C4—2928no—
1456C2×C4—734no—
1457C2×C4—734no—
1458C2×C4—732no—
1459C2×C4—738no—
1460C2×C4—734no—
1461C2×C4—732no—
1462C2×C4—1468no—
1463C2×C4—1464no—
1464C2×C4—1468no—
1465C2×C4—1464no—
1466C2×C4—1464no—
1467C2×C4—1464no—
1468C2×C4—1464no—
1469C2×C4—1468no—
1470C2×C4#1455663714yes—
1471C2×C4C24×D7314yes—
1472C2×C4C24×D7314yes—
1473C2×C4C24×D7314yes—
1474C2×C4C24×D7314yes—
1475C2×C4C24×D7314yes—
1476C2×C4C24×D7312yes—
1477C2×C4C24×D7312yes—
1478C22—28no—
1479C22—21no—
1480C22—21no—
1481C22—21no—
1482C22—21no—
1483C22—21no—
1484C22—21no—
1485C22—24no—
1486C22—24no—
1487C22—24no—
1488C22—2924no—
1489C22—2928no—
1490C22—2928no—
1491C22—2924no—
1492C22—5848no—
1493C22—734no—
1494C22—1464no—
1495C22—1462no—
1496C22—1464no—
1497C22—1462no—
1498C22—1464no—
1499C22—1462no—
1500C22—1462no—
1501C22—1462no—
1502C22C2×#1455663712yes—
1503C222−1+4×D7312yes—
1504C22#1798942212yes—
1505C22C25×D7311yescharacteristic
1506C4—22no—
1507C4—24no—
1508C4—24no—
1509C4—24no—
1510C4—24no—
1511C4—24no—
1512C4—1462no—
1513C4—1462no—
1514C4—1464no—
1515C4—1468no—
1516C4—1464no—
1517C4—1464no—
1518C4C2×#1455663714yes—
1519C2—22no—
1520C2—22no—
1521C2—22no—
1522C2—44no—
1523C2—2922no—
1524C2—2924no—
1525C2—1464no—
1526C2C22×#1455663711yescharacteristic
1527C2C2×2−1+4×D7311yescharacteristic
1528C2C2×#1798942211yescharacteristic
subgroupG/H
center, FrattiniC22C25×D73
commutator, socle, cosocleC22×C73C26
FittingC73×#3492C2
hypercenter#3492D73
hypocenterC73#62819
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #3492

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #22624225C2semidirect
2. #22624218C2semidirect
3. #22624177C2semidirect
4. #22624154C2semidirect
5. #22624138C2semidirect
6. #22623977C2semidirect
7. #22623971C2semidirect
8. #22623760C2semidirect
9. #22623728C2semidirect
10. #22623686C2semidirect
11. #22623684C2semidirect
12. #22623640C2semidirect
13. #22623637C2semidirect
14. #22623614C2semidirect
15. #22623612C2semidirect
16. #22623606C2semidirect
17. #22623578C2semidirect
18. #525×D73C2semidirect
19. C22×#14556571C2semidirect
20. C73×#3492C2semidirect
21. C2×#14556638C22semidirect
22. C2×#41×D73C22semidirect
23. C23×Dic146C22semidirect
25. #17989341C22semidirect
26. #17989339C22semidirect
27. #17989334C22semidirect
28. #17989333C22semidirect
29. #17989311C22semidirect
30. #17989305C22semidirect
31. #17989298C22semidirect
32. #17989295C22semidirect
33. #17989295C22semidirect
34. #17989294C22semidirect
35. #17989293C22semidirect
36. #17989292C22semidirect
37. #17989292C22semidirect
38. #17989289C22semidirect
39. #17989285C22semidirect
40. #17989283C22semidirect
41. #17989279C22semidirect
42. #17989277C22semidirect
43. #17989276C22semidirect
44. #17989275C22semidirect
45. #17989275C22semidirect
46. #17989272C22semidirect
47. #17989272C22semidirect
48. #17989266C22semidirect
49. #17989264C22semidirect
50. #17989262C22semidirect
51. #17989261C22semidirect
52. #17989260C22semidirect
53. #17989260C22semidirect
54. Q8×D292C22semidirect
55. D4×Dic146C22semidirect
56. D4×Dic146C22semidirect
57. #17989250C22semidirect
58. #17989250C22semidirect
59. #17989250C22semidirect
60. #17989249C22semidirect
61. #17989246C22semidirect
62. #17989246C22semidirect
63. #17989243C22semidirect
64. #17989243C22semidirect
65. #17989243C22semidirect
66. #17989241C22semidirect
67. #17989241C22semidirect
68. #17989239C22semidirect
69. #17989238C22semidirect
70. #17989237C22semidirect
71. #17989234C22semidirect
72. #17989232C22semidirect
73. #17989232C22semidirect
74. #17989229C22semidirect
75. #17989226C22semidirect
76. #17989225C22semidirect
77. #17989218C22semidirect
78. #17989217C22semidirect
79. #17989215C22semidirect
81. #17989212C22semidirect
82. #17989211C22semidirect
83. #17989210C22semidirect
84. #17989203C22semidirect
85. #17989202C22semidirect
86. #17989200C22semidirect
87. #17989195C22semidirect
88. #17989185C22semidirect
89. #17989184C22semidirect
90. #17989181C22semidirect
91. #17989181C22semidirect
92. #17989181C22semidirect
93. #17989178C22semidirect
94. #17989177C22semidirect
95. #17989174C22semidirect
96. #17989173C22semidirect
97. #17989170C22semidirect
98. #17989168C22semidirect
99. #17989168C22semidirect
100. #17989166C22semidirect
101. #17989165C22semidirect
102. #17989163C22semidirect
103. #17989163C22semidirect
104. #17989160C22semidirect
105. #17989159C22semidirect
106. #17989158C22semidirect
108. #17989142C22semidirect
109. #17989141C22semidirect
110. #17989122C22semidirect
111. #17989119C22semidirect
113. #17989100C22semidirect
115. #17989099C22semidirect
116. #17989098C22semidirect
117. #17989098C22semidirect
119. #17989097C22semidirect
120. #17989097C22semidirect
122. #17989096C22semidirect
125. #17989093C22semidirect
126. #17989093C22semidirect
127. #123×D73C22semidirect
129. C2×#14556571C22semidirect
130. C2×#14556571C22semidirect
131. C2×#14556571C22semidirect
132. C2×#14556571C22semidirect
133. C2×#14556571C22semidirect
134. C2×#14556571C22semidirect
135. C2×#14556571C22semidirect
137. C22⋊Q8×D73C22semidirect
138. C22⋊Q8×D73C22semidirect
140. #121×D73C22semidirect
142. #17989070C22semidirect
143. #17989068C22semidirect
144. #17989067C22semidirect
145. #17989064C22semidirect
148. C4×D4×D73C22semidirect
149. #117×D73C22semidirect
150. C22×C4⋊Dic73C22semidirect
152. #554×C73C22semidirect
153. #553×C73C22semidirect
154. #552×C73C22semidirect
155. #547×C73C22semidirect
156. #544×C73C22semidirect
157. #539×C73C22semidirect
158. #537×C73C22semidirect
159. #525×C73C22semidirect
160. #525×C73C22semidirect
161. #520×C73C22semidirect
162. C22×C4⋊C4×C73C22semidirect
169. C2×#11924028C23semidirect
173. C2×#11924027C23semidirect
180. C22×Dic146C23semidirect
182. C2×Q8×D73C23semidirect
197. #14556591C23semidirect
198. #14556591C23semidirect
199. #14556590C23semidirect
200. #14556590C23semidirect
201. #14556590C23semidirect
202. #14556590C23semidirect
203. #14556589C23semidirect
207. #14556586C23semidirect
208. #14556586C23semidirect
209. #14556586C23semidirect
211. #14556584C23semidirect
212. #14556584C23semidirect
213. #14556583C23semidirect
214. #14556582C23semidirect
215. #14556582C23semidirect
216. #14556582C23semidirect
217. #14556582C23semidirect
218. #14556581C23semidirect
219. #14556581C23semidirect
220. #14556581C23semidirect
223. #14556579C23semidirect
224. #14556578C23semidirect
227. #14556577C23semidirect
228. #14556577C23semidirect
234. #14556576C23semidirect
238. #14556575C23semidirect
239. #14556575C23semidirect
246. #14556573C23semidirect
247. #14556573C23semidirect
265. #14556571C23semidirect
266. #14556571C23semidirect
267. #14556571C23semidirect
268. #14556571C23semidirect
269. #14556571C23semidirect
274. #14556570C23semidirect
275. #14556570C23semidirect
276. #14556570C23semidirect
281. #14556569C23semidirect
282. #14556569C23semidirect
283. #14556569C23semidirect
288. #14556568C23semidirect
289. #14556568C23semidirect
290. #14556568C23semidirect
291. #14556568C23semidirect
295. #14556567C23semidirect
299. #14556566C23semidirect
305. #14556565C23semidirect
316. #14556562C23semidirect
326. Q8×Dic73C23semidirect
327. C4×Dic146C23semidirect
328. C4×Dic146C23semidirect
329. C4×Dic146C23semidirect
330. #14556556C23semidirect
331. #14556556C23semidirect
332. #14556556C23semidirect
336. C4×D292C23semidirect
341. D4×Dic73C23semidirect
345. #14556553C23semidirect
362. #14556550C23semidirect
366. #14556549C23semidirect
367. #14556549C23semidirect
377. C2×C4⋊Dic73C23semidirect
382. C4⋊C4×D73C23semidirect
383. C4⋊C4×D73C23semidirect
401. C4⋊Q8×C73C23semidirect
402. #126×C73C23semidirect
403. #125×C73C23semidirect
404. #125×C73C23semidirect
407. #123×C73C23semidirect
412. C22⋊Q8×C73C23semidirect
413. C22⋊Q8×C73C23semidirect
418. #121×C73C23semidirect
420. C4×Q8×C73C23semidirect
425. C4×D4×C73C23semidirect
428. #117×C73C23semidirect
434. C2×C4⋊C4×C73C23semidirect
635. C22×D732−1+4semidirect
778. #3492D73semidirect
785. C73#62819semidirect
803. #554C2×D73semidirect
807. #553C2×D73semidirect
815. #552C2×D73semidirect
839. #547C2×D73semidirect
849. #544C2×D73semidirect
864. #539C2×D73semidirect
873. #537C2×D73semidirect
899. #525C2×D73semidirect
900. #525C2×D73semidirect
919. #520C2×D73semidirect
926. C22×C4⋊C4C2×D73semidirect
973. C4⋊Q8C22×D73semidirect
983. #126C22×D73semidirect
992. #125C22×D73semidirect
993. #125C22×D73semidirect
1025. #123C22×D73semidirect
1076. C22⋊Q8C22×D73semidirect
1077. C22⋊Q8C22×D73semidirect
1103. #121C22×D73semidirect
1121. C4×Q8C22×D73semidirect
1153. C4×D4C22×D73semidirect
1168. #117C22×D73semidirect
1186. C2×C4⋊C4C22×D73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226242252
#226242182
#226241772
#226241542
#226241382
#226239772
#226239712
#226237602
#226237282
#226236862
#226236842
#226236402
#226236372
#226236142
#226236122
#226236062
#226235782
#525×D732
C22×#145565712
C73×#34922
#6281973