Finite Group Databasebeta

← #33994574

Subgroups — #33994574

Order 18688.

7210 conjugacy classes of subgroups.

The subgroup lattice has 1220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623854C214yesmaximal, complemented
2#22623843C214yesmaximal, complemented
3#22623830C212yesmaximal, complemented
4#22623828C212yesmaximal, complemented
5#22623815C211yesmaximal, characteristic, complemented
6#22623808C211yesmaximal, characteristic, complemented
7#22623807C211yesmaximal, characteristic, complemented
8#22623797C214yesmaximal, complemented
9#22623784C214yesmaximal, complemented
10#22623771C218yesmaximal, complemented
11#22623531C214yesmaximal, complemented
12#22623523C214yesmaximal, complemented
13#22623496C218yesmaximal, complemented
14#22623322C214yesmaximal, complemented
15#22623263C212yesmaximal, complemented
16#22623228C214yesmaximal, complemented
17#533×D73C211yesmaximal, characteristic, complemented
18C2×#17989138C211yesmaximal, characteristic, complemented
19#22623133C212yesmaximal, complemented
20C4×#41×D73C211yesmaximal, characteristic, complemented
21C73×#3509C211yesmaximal, characteristic, complemented
22C22×#11924029C2212yes—
23C2×#41×D73C2211yescharacteristic
24#17989322C2214yescomplemented
25#17989322C2218yescomplemented
26#17989322C2214yescomplemented
27#17989319C2218yescomplemented
28#17989312C2214yescomplemented
29#17989311C2214yescomplemented
30#17989311C2218yescomplemented
31#17989309C2218yescomplemented
32#17989309C2218yescomplemented
33#17989300C2218yescomplemented
34#17989293C2218yescomplemented
35#17989290C2218yescomplemented
36#17989290C22116yescomplemented
37#17989288C22116yescomplemented
38#17989288C22116yescomplemented
39#17989281C2218yescomplemented
40#17989272C2218yescomplemented
41#17989269C22116yescomplemented
42#17989261C22116yescomplemented
43#17989260C22116yescomplemented
44#17989259C2214yescomplemented
45#17989258C2214yescomplemented
46#17989249C2218yescomplemented
47#17989247C2218yescomplemented
48#17989239C2218yescomplemented
49#17989233C2218yescomplemented
50#17989228C2218yescomplemented
51#17989210C2218yescomplemented
52#17989209C2218yescomplemented
53#17989198C2214yescomplemented
54#17989193C2214yescomplemented
55#17989192C2214yescomplemented
56#17989185C22116yescomplemented
57#17989176C22116yescomplemented
58#17989167C2218yescomplemented
59#17989162C2214yescomplemented
60#17989161C2212yes—
61#17989156C2212yes—
62#17989155C2214yescomplemented
63#17989151C2212yes—
64#17989148C2218yes—
65#17989144C2211yescharacteristic, complemented
66#17989143C2212yescomplemented
67#17989142C2214yescomplemented
68#17989142C2212yescomplemented
69#17989141C2214yescomplemented
70#17989140C2212yescomplemented
71#17989139C2214yescomplemented
72#17989138C2214yes—
73#17989138C2212yes—
74#17989138C2212yes—
75#17989138C2214yescomplemented
76#17989138C2214yescomplemented
77#17989138C2214yescomplemented
78#17989138C2212yescomplemented
79#17989138C2212yescomplemented
80#17989137C2214yescomplemented
81#17989136C2214yescomplemented
82C4⋊Q8×D73C2212yescomplemented
83C2×#14556588C2211yescharacteristic, complemented
84#17989124C2218yescomplemented
85#17989124C2218yescomplemented
86#17989123C2218yescomplemented
87#17989123C2218yescomplemented
88#17989122C22116yescomplemented
89#17989122C2218yescomplemented
90#17989122C2218yescomplemented
91#17989120C22116yescomplemented
92#125×D73C2212yescomplemented
93C2×#14556580C2212yescomplemented
94#17989100C2218yescomplemented
95#17989100C2218yescomplemented
96#17989099C2218yescomplemented
97#17989095C2218yes—
98C22⋊Q8×D73C2214yes—
99C2×#14556566C2214yes—
100#17989069C2218yescomplemented
101#17989069C2218yescomplemented
102#17989065C2212yescomplemented
103#17989061C2218yes—
104#17989061C2212yescomplemented
105#17989061C2212yescomplemented
106#41×Dic73C2211yescharacteristic
107C4×#11924029C2218yescomplemented
108C4×#11924029C2218yescomplemented
109C4×#11924029C2212yescomplemented
110C4×#11924029C2218yescomplemented
111C4×#11924028C2211yescharacteristic
112C4×#11924028C2212yescomplemented
113#17989055C2211yescharacteristic
114#17989055C2218yescomplemented
115#17989055C2212yescomplemented
116C4×#11924027C2214yes—
117C4×#11924027C2212yescomplemented
118C4×Q8×D73C2214yescomplemented
119C4×Q8×D73C2212yescomplemented
120C2×#14556553C2214yescomplemented
121C4×D4×D73C2214yes—
122C4×D4×D73C2212yescomplemented
123#117×D73C2212yes—
124#117×D73C2211yescharacteristic
125#117×D73C2218yescomplemented
126#117×D73C2212yescomplemented
127C2×C42×D73C2211yescharacteristic
128C2×C42×D73C2212yescomplemented
129#557×C73C2214yescomplemented
130#556×C73C2214yescomplemented
131#552×C73C2218yescomplemented
132#541×C73C2214yescomplemented
133#536×C73C2212yes—
134#533×C73C2211yescharacteristic, complemented
135#533×C73C2214yescomplemented
136C2×C4⋊Q8×C73C2211yescharacteristic, complemented
137#519×C73C2212yescomplemented
138C4×#41×C73C2211yescharacteristic
139C2×#11924029—216no—
140C2×#11924029C2314yes—
141C2×#11924029C2314yes—
142C2×#11924029C2314yes—
143C2×#11924029C2311yescharacteristic
144C2×#11924029C2314yes—
145C2×#11924029C2318yes—
146C2×#11924028C2311yescharacteristic
147C2×#11924028C2312yes—
148C2×#11924028C2318yes—
149C2×#11924027C2311yescharacteristic
150C2×#11924027C2312yes—
151#41×D73—28no—
152C2×Q8×D73C2311yescharacteristic
153C2×Q8×D73C2314yes—
154C22×D292C2312yes—
155C22×D292C2314yes—
156C22×D292C2314yes—
157C2×D4×D73C2312yes—
158C2×D4×D73C2311yescharacteristic
159C22×C4×D73C2312yes—
160C22×C4×D73C2314yes—
161C22×C4×D73C2312yes—
162C22×C4×D73C2314yes—
163C22×C4×D73C2311yescharacteristic
164#14556591C2312yes—
165#14556590C2314yes—
166#14556590C2314yes—
167#14556589C2314yes—
168#14556589C2314yes—
169#14556588C2312yes—
170#14556588C2312yes—
171#14556588C2314yes—
172#14556588C2314yes—
173#14556587C2314yes—
174#14556586C23116yes—
175#14556586C23116yes—
176#14556586C23116yes—
177#14556586C23116yes—
178#14556585C23116yes—
179#14556583C2312yes—
180#14556582C2314yes—
181#14556582C2318yes—
182#14556581C23116yes—
183#14556581C2318yes—
184#14556580C2314yes—
185#14556580C2318yes—
186#14556580C2314yes—
187#14556580C2318yes—
188#14556580C2314yes—
189#14556580C2314yes—
190#14556579C2318yes—
191#14556579C23116yes—
192#14556579C2314yes—
193#14556577C23116yes—
194#14556576C23116yes—
195#14556576C23116yes—
196#14556576C23116yes—
197#14556576C23116yes—
198#14556576C23116yes—
199#14556575C23116yes—
200#14556574C2318yes—
201#14556573C23116yes—
202#14556571C2314yes—
203#14556571C2318yes—
204#14556571C23116yes—
205#14556570C2314yes—
206#14556569C23116yes—
207#14556569C2318yes—
208#14556569C23116yes—
209#14556568C2318yes—
210#14556567C2314yes—
211#14556567C2318yes—
212#14556566C2318yes—
213#14556566C2318yes—
214#14556566C23116yes—
215#14556566C2318yes—
216#14556566C2318yes—
217#14556566C2318yes—
218#14556566C2318yes—
219#14556566C23116yes—
220#14556565C2318yes—
221#14556565C2318yes—
222#14556564C23116yes—
223#14556564C23116yes—
224#14556564C23116yes—
225#14556561C23116yes—
226#14556561C2318yes—
227#14556559C2318yes—
228Q8×Dic73C2314yes—
229Q8×Dic73C2318yes—
230Q8×Dic73C2312yes—
231Q8×Dic73C2318yes—
232C4×Dic146C2318yes—
233C4×Dic146C2314yes—
234C4×Dic146C2314yes—
235C4×Dic146C2312yes—
236#14556556C2318yes—
237#14556556C2314yes—
238#14556556C2318yes—
239#14556556C2314yes—
240#14556556C2312yes—
241C4×D292C2318yes—
242C4×D292C2318yes—
243C4×D292C23116yes—
244C4×D292C23116yes—
245C4×D292C2314yes—
246C4×D292C23116yes—
247C4×D292C2312yes—
248C4×D292C2318yes—
249D4×Dic73C2314yes—
250D4×Dic73C2312yes—
251#14556553C2318yes—
252#14556553C23116yes—
253#14556553C2318yes—
254#14556553C2318yes—
255#14556553C23116yes—
256#14556553C2318yes—
257#14556553C2318yes—
258#14556553C2318yes—
259#14556553C23116yes—
260#14556553C2318yes—
261#14556553C2314yes—
262#14556553C2312yes—
263C4×C22⋊D73C2314yes—
264C4×C22⋊D73C2314yes—
265C4×C22⋊D73C2314yes—
266#14556551C23116yes—
267#14556551C23116yes—
268#14556551C2314yes—
269#14556551C2314yes—
270#14556551C2314yes—
271#14556550C2312yes—
272#14556550C2312yes—
273#14556550C2318yes—
274#14556550C2311yescharacteristic
275#14556549C23116yes—
276#14556549C2314yes—
277#14556549C23116yes—
278#14556549C2314yes—
279#14556549C2318yes—
280#14556549C2312yes—
281#14556548C23116yes—
282#14556548C2314yes—
283#14556548C2312yes—
284#14556548C2312yes—
285#14556548C23116yes—
286#14556548C2312yes—
287#14556547C2314yes—
288#14556547C2314yes—
289#14556547C2312yes—
290C4⋊C4×D73C2314yes—
291C4⋊C4×D73C2314yes—
292C4⋊C4×D73C2314yes—
293C4⋊C4×D73C23116yes—
294C4⋊C4×D73C2318yes—
295C4⋊C4×D73C2312yes—
296C2×#11924005C2318yes—
297C22⋊C4×D73C2314yes—
298C22⋊C4×D73C2314yes—
299C22⋊C4×D73C2318yes—
300C22⋊C4×D73C2318yes—
301C22⋊C4×D73C2312yes—
302C2×C4×Dic73C2312yes—
303C2×C4×Dic73C2314yes—
304C2×C4×Dic73C2312yes—
305C2×C4×Dic73C2311yescharacteristic
306C42×D73C23116yes—
307C42×D73C2314yes—
308C42×D73C2314yes—
309C42×D73C2312yes—
310C42×D73C2311yescharacteristic
311C42×D73C2314yes—
312C42×D73C2312yes—
313C42×D73C2311yescharacteristic
314C42×D73C2311yescharacteristic
315C42×D73C2312yes—
316C42×D73C2312yes—
317C42×D73C2311yescharacteristic
318C42×D73C2312yes—
319C2×#41×C73C2311yescharacteristic
320C22×Q8×C73C2312yes—
321C4⋊Q8×C73C2312yes—
322C4⋊Q8×C73C2312yes—
323C4⋊Q8×C73C2312yes—
324C4⋊Q8×C73C2314yes—
325C4⋊Q8×C73C2314yes—
326#126×C73C23116yes—
327#125×C73C2318yes—
328#125×C73C23116yes—
329#125×C73C2312yes—
330#124×C73C2314yes—
331#123×C73C2318yes—
332C22⋊Q8×C73C2318yes—
333C22⋊Q8×C73C2318yes—
334C22⋊Q8×C73C2314yes—
335C4×Q8×C73C2318yes—
336C4×Q8×C73C2318yes—
337C4×Q8×C73C2314yes—
338C4×Q8×C73C2312yes—
339C4×Q8×C73C2318yes—
340C4×D4×C73C2314yes—
341C4×D4×C73C2312yes—
342#117×C73C2312yes—
343#117×C73C2312yes—
344#117×C73C2311yescharacteristic
345#117×C73C2318yes—
346#117×C73C2318yes—
347C2×C4⋊C4×C73C2314yes—
348C2×C42×C73C2311yescharacteristic
349C2×C42×C73C2312yes—
350C23×D73C2414yes—
351C23×D73C2412yes—
352C23×D73C2411yescharacteristic
353#11924029—24no—
354#11924029—216no—
355#11924029—216no—
356#11924029—216no—
357#11924029—216no—
358#11924029—416no—
359#11924028—24no—
360#11924028—28no—
361#11924028—416no—
362#11924027—28no—
363#11924027—24no—
364C2×Dic146C2414yes—
365C2×Dic146C2412yes—
366C2×Dic146C2411yescharacteristic
367C2×Dic146C2418yes—
368Q8×D73—24no—
369Q8×D73—48no—
370C2×D292—216no—
371C2×D292—28no—
372C2×D292—48no—
373C2×D292C2418yes—
374C2×D292C2418yes—
375C2×D292C2418yes—
376C2×D292C2414yes—
377C2×D292C2412yes—
378C2×D292C2414yes—
379C2×D292C2411yescharacteristic
380C2×D292C2418yes—
381C2×D292C24116yes—
382C2×C22⋊D73C2412yes—
383C2×C22⋊D73C2412yes—
384C2×C22⋊D73C2412yes—
385C2×C22⋊D73C24116yes—
386D4×D73—28no—
387D4×D73—24no—
388C22×Dic73C2412yes—
389C22×Dic73C2412yes—
390C22×Dic73C2414yes—
391C22×Dic73C2411yescharacteristic
392C2×C4×D73—216no—
393C2×C4×D73—28no—
394C2×C4×D73—44no—
395C2×C4×D73—48no—
396C2×C4×D73#4118yescomplemented
397C2×C4×D73C2412yes—
398C2×C4×D73C2412yes—
399C2×C4×D73C2412yes—
400C2×C4×D73C2412yes—
401C2×C4×D73C2418yes—
402C2×C4×D73C2414yes—
403C2×C4×D73C2412yes—
404C2×C4×D73C2418yes—
405C2×C4×D73C2414yes—
406C2×C4×D73C2412yes—
407C2×C4×D73C2412yes—
408C2×C4×D73C2414yes—
409C2×C4×D73C2418yes—
410C2×C4×D73C24116yes—
411C2×C4×D73C24116yes—
412C2×C4×D73C2411yescharacteristic
413C2×C4×D73C2411yescharacteristic
414C2×C4×D73C2411yescharacteristic
415C2×C4×D73C2411yescharacteristic
416C4⋊Dic73C2414yes—
417C4⋊Dic73C2418yes—
418C4⋊Dic73C2412yes—
419C4⋊Dic73C2414yes—
420C4⋊Dic73C2414yes—
421C4⋊Dic73C24116yes—
422#11924007C2414yes—
423#11924007C2418yes—
424#11924007C2414yes—
425#11924007C2414yes—
426#11924007C2418yes—
427#11924007C2418yes—
428#11924007C2418yes—
429#11924007C24116yes—
430C22⋊Dic73C2412yes—
431C22⋊Dic73C2414yes—
432C22⋊Dic73C2414yes—
433#11924005C2414yes—
434#11924005C2414yes—
435#11924005C2414yes—
436#11924005C2418yes—
437#11924005C24116yes—
438#11924005C24116yes—
439#11924005C24116yes—
440#11924005C24116yes—
441#11924005C24116yes—
442#11924005C24116yes—
443#11924005C24116yes—
444C4×Dic73C2414yes—
445C4×Dic73C2412yes—
446C4×Dic73C2411yescharacteristic
447C4×Dic73C2418yes—
448C4×Dic73C2412yes—
449C4×Dic73C2414yes—
450C4×Dic73C2412yes—
451C4×Dic73C2411yescharacteristic
452C4×Dic73C2414yes—
453C4×Dic73C2412yes—
454C4×Dic73C2412yes—
455C4×Dic73C2414yes—
456C4×Dic73C2412yes—
457C4×Dic73C24116yes—
458C4×Dic73C2414yes—
459#41×C73—24no—
460C2×Q8×C73—28no—
461C2×Q8×C73C2414yes—
462C2×Q8×C73C2414yes—
463C2×Q8×C73C2414yes—
464C2×Q8×C73C2411yescharacteristic
465C2×D4×C73C2412yes—
466C2×D4×C73C2411yescharacteristic
467C22×C4×C73C2412yes—
468C22×C4×C73C2414yes—
469C22×C4×C73C2412yes—
470C22×C4×C73C2414yes—
471C22×C4×C73C2411yescharacteristic
472C4⋊C4×C73C2418yes—
473C4⋊C4×C73C2418yes—
474C4⋊C4×C73C2414yes—
475C4⋊C4×C73C2412yes—
476C4⋊C4×C73C2414yes—
477C4⋊C4×C73C2414yes—
478C4⋊C4×C73C24116yes—
479C4⋊C4×C73C24116yes—
480C4⋊C4×C73C2418yes—
481C22⋊C4×C73C2412yes—
482C22⋊C4×C73C2414yes—
483C22⋊C4×C73C2414yes—
484C22⋊C4×C73C24116yes—
485C42×C73C2411yescharacteristic
486C42×C73C2412yes—
487C42×C73C2411yescharacteristic
488C42×C73C2414yes—
489C42×C73C2412yes—
490C42×C73C24116yes—
491C42×C73C2414yes—
492C23×C73C2512yes—
493C23×C73C2511yescharacteristic
494C22×D73—28no—
495C22×D73—24no—
496C22×D73—42no—
497C22×D73—44no—
498C22×D73—48no—
499C22×D73C2×#4114yes—
500C22×D73C2518yes—
501C22×D73C2512yes—
502C22×D73C2511yescharacteristic
503C22×D73C2511yescharacteristic
504Q8×C73—28no—
505Q8×C73—28no—
506Q8×C73—22no—
507Q8×C73—28no—
508D4×C73—24no—
509D4×C73—22no—
510C2×C4×C73—28no—
511C2×C4×C73—24no—
512C2×C4×C73—24no—
513C2×C4×C73—28no—
514C2×C4×C73C2×#4114yes—
515C2×C4×C73C2514yes—
516C2×C4×C73C2518yes—
517C2×C4×C73C2512yes—
518C2×C4×C73C2518yes—
519C2×C4×C73C2512yes—
520C2×C4×C73C2511yescharacteristic
521C2×C4×C73C2511yescharacteristic
522C2×C4×C73C2512yes—
523C22⋊D73—24no—
524C22⋊D73—24no—
525C22⋊D73—24no—
526C22⋊D73—416no—
527C2×Dic73—24no—
528C2×Dic73—42no—
529C2×Dic73—44no—
530C2×Dic73C2×#4114yes—
531C2×Dic73C2512yes—
532C2×Dic73C2514yes—
533C2×Dic73C2512yes—
534C2×Dic73C2512yes—
535C2×Dic73C2518yes—
536C2×Dic73C2511yescharacteristic
537C2×Dic73C2511yescharacteristic
538D292—24no—
539D292—216no—
540D292—216no—
541D292—22no—
542D292—28no—
543D292—28no—
544D292—216no—
545D292—48no—
546D292—416no—
547C4×D73—24no—
548C4×D73—24no—
549C4×D73—24no—
550C4×D73—24no—
551C4×D73—28no—
552C4×D73—24no—
553C4×D73—216no—
554C4×D73—216no—
555C4×D73—42no—
556C4×D73—44no—
557C4×D73—44no—
558C4×D73—42no—
559C4×D73—48no—
560C4×D73—416no—
561C4×D73—416no—
562C4×D73C2×#4114yes—
563C4×D73C2×#4114yes—
564C4×D73C2×#4114yes—
565C4×D73C2×#4114yes—
566Dic146—22no—
567Dic146—28no—
568Dic146—24no—
569Dic146—48no—
570C22×C73—22no—
571C22×C73—22no—
572C22×C73—24no—
573C22×C73C22×#4112yes—
574C22×C73C2611yescharacteristic
575C2×D73—22no—
576C2×D73—22no—
577C2×D73—28no—
578C2×D73—22no—
579C2×D73—24no—
580C2×D73—216no—
581C2×D73—44no—
582C2×D73—48no—
583C2×D73—88no—
584C2×D73C22×#4112yes—
585C2×D73C22×#4112yes—
586C4×C73—22no—
587C4×C73—28no—
588C4×C73—28no—
589C4×C73—24no—
590C4×C73—22no—
591C4×C73C22×#4112yes—
592C4×C73C22×#4112yes—
593C4×C73#58514yes—
594Dic73—22no—
595Dic73—28no—
596Dic73—22no—
597Dic73—24no—
598Dic73—22no—
599Dic73C22×#4112yes—
600Dic73C22×#4112yes—
601#62815—731nomaximal, Sylow
602C2×C73—22no—
603C2×C73—42no—
604C2×C73C23×#4111yescharacteristic
605C2×C73C2×#58512yes—
606D73—22no—
607D73—22no—
608D73—42no—
609D73—48no—
610#3512—734no—
611#3511—734no—
612#3510—732no—
613#3510—732no—
614#3509—731no—
615#3509D7311yescharacteristic, complemented
616#3508—731no—
617#3508—731no—
618#3507—734no—
619#3506—734no—
620#3505—738no—
621#3480—734no—
622#3480—734no—
623#3475—738no—
624#3455—734no—
625#3449—732no—
626#3444—734no—
627C2×#533—731no—
628C2×#532—731no—
629#3428—732no—
630C2×C4×#41—731no—
631C73#6281511yescharacteristic, complemented, Sylow
632C22×#41—731no—
633C22×#41—732no—
634#559—738no—
635#559—738no—
636#559—734no—
637#559—734no—
638#557—734no—
639#557C2×D7314yescomplemented
640#556—734no—
641#556—738no—
642#556—738no—
643#556—738no—
644#556C2×D7314yescomplemented
645#555—738no—
646#554—738no—
647#553—7316no—
648#553—7316no—
649#553—738no—
650#553—7316no—
651#553—738no—
652#552—7316no—
653#552—738no—
654#552C2×D7318yescomplemented
655#551—7316no—
656#551—7316no—
657#550—734no—
658#550—734no—
659#548—738no—
660#548—738no—
661#547—738no—
662#546—738no—
663#546—738no—
664#542—738no—
665#542—738no—
666#541—734no—
667#541C2×D7314yescomplemented
668#540—734no—
669#540—734no—
670#539—7316no—
671#538—7316no—
672#537—738no—
673#536—732no—
674#536—734no—
675#536C2×D7312yes—
676#535—732no—
677#535—734no—
678#535—732no—
679#534—738no—
680#533—732no—
681#533—734no—
682#533—732no—
683#533—734no—
684#533—734no—
685#533—732no—
686#533—731no—
687#533C2×D7311yescharacteristic, complemented
688#533C2×D7314yescomplemented
689#532—732no—
690#532—732no—
691#532—734no—
692#532—734no—
693#532—732no—
694#532—732no—
695#532—734no—
696#532—734no—
697#532—734no—
698#532—734no—
699C2×C4⋊Q8—732no—
700C2×C4⋊Q8C2×D7311yescharacteristic, complemented
701C2×#127—731no—
702#529—7316no—
703#529—738no—
704#529—738no—
705#529—7316no—
706#529—738no—
707#529—738no—
708#529—738no—
709#529—738no—
710C2×#125—732no—
711C2×#124—732no—
712#525—738no—
713#525—738no—
714#525—738no—
715#525—738no—
716C2×C22⋊Q8—734no—
717C2×#121—734no—
718#520—738no—
719#520—738no—
720#519—732no—
721#519C2×D7312yescomplemented
722#518—738no—
723#518—732no—
724#518—732no—
725C4×#41—731no—
726C4×#41—732no—
727C4×#41—738no—
728C4×#41—738no—
729C4×#41—738no—
730C4×#41—734no—
731C4×#41—732no—
732C4×#41—731no—
733C4×#41—732no—
734C4×#41—738no—
735C4×#41—731no—
736C4×#41—732no—
737C4×#41C2×D7311yescharacteristic
738C2×C4×Q8—732no—
739C2×C4×Q8—734no—
740C2×C4×D4—734no—
741C2×C4×D4—732no—
742C2×C4×D4—734no—
743C2×#117—731no—
744C2×#117—732no—
745C2×#117—732no—
746C2×#117—738no—
747C22×C42—731no—
748C22×C42—732no—
749C2×#41—738no—
750C2×#41—734no—
751C2×#41—731no—
752C2×#41—734no—
753C2×#41—734no—
754C2×#41—734no—
755C2×#41—732no—
756C2×#41—731no—
757C2×#41—738no—
758C2×#41—731no—
759C2×#41—732no—
760C2×#41—14616no—
761C2×#41—1468no—
762C2×#41C22×D7311yescharacteristic
763C22×Q8—734no—
764C22×Q8—731no—
765C22×Q8C22×D7312yes—
766C22×D4—732no—
767C22×D4—731no—
768C22×D4—734no—
769C22×D4—734no—
770C22×D4—732no—
771C23×C4—732no—
772C23×C4—734no—
773C23×C4—731no—
774C23×C4—734no—
775C23×C4—732no—
776C4⋊Q8—734no—
777C4⋊Q8—734no—
778C4⋊Q8—734no—
779C4⋊Q8—734no—
780C4⋊Q8—732no—
781C4⋊Q8C22×D7312yes—
782C4⋊Q8C22×D7312yes—
783C4⋊Q8C22×D7312yes—
784C4⋊Q8C22×D7314yes—
785C4⋊Q8C22×D7314yes—
786#127—734no—
787#127—732no—
788#127—732no—
789#127—734no—
790#127—734no—
791#126—7316no—
792#126—7316no—
793#126—7316no—
794#126—7316no—
795#126—7316no—
796#126C22×D73116yes—
797#125—734no—
798#125—738no—
799#125—738no—
800#125—7316no—
801#125—732no—
802#125C22×D7312yes—
803#125C22×D7318yes—
804#125C22×D73116yes—
805#124—734no—
806#124—734no—
807#124—738no—
808#124—738no—
809#124—734no—
810#124—734no—
811#124—7316no—
812#124—738no—
813#124—7316no—
814#124—734no—
815#124C22×D7314yes—
816#123—738no—
817#123—7316no—
818#123—7316no—
819#123—7316no—
820#123—7316no—
821#123—7316no—
822#123—7316no—
823#123—7316no—
824#123C22×D7318yes—
825C22⋊Q8—734no—
826C22⋊Q8—738no—
827C22⋊Q8—734no—
828C22⋊Q8—734no—
829C22⋊Q8—738no—
830C22⋊Q8—738no—
831C22⋊Q8—7316no—
832C22⋊Q8—7316no—
833C22⋊Q8—7316no—
834C22⋊Q8—738no—
835C22⋊Q8C22×D7314yes—
836C22⋊Q8C22×D7318yes—
837C22⋊Q8C22×D7318yes—
838#121—738no—
839#121—738no—
840#121—738no—
841#121—738no—
842#121—738no—
843#121—738no—
844#121—738no—
845#121—738no—
846#121—7316no—
847#121—7316no—
848#121—7316no—
849#121—7316no—
850#121—7316no—
851#120—738no—
852#120—7316no—
853#120—738no—
854C4×Q8—734no—
855C4×Q8—732no—
856C4×Q8—738no—
857C4×Q8—738no—
858C4×Q8—734no—
859C4×Q8—734no—
860C4×Q8—732no—
861C4×Q8—738no—
862C4×Q8—738no—
863C4×Q8—734no—
864C4×Q8—732no—
865C4×Q8—734no—
866C4×Q8—738no—
867C4×Q8C22×D7312yes—
868C4×Q8C22×D7314yes—
869C4×Q8C22×D7318yes—
870C4×Q8C22×D7318yes—
871C4×Q8C22×D7318yes—
872C4×D4—734no—
873C4×D4—732no—
874C4×D4—734no—
875C4×D4—734no—
876C4×D4—734no—
877C4×D4—738no—
878C4×D4—734no—
879C4×D4—732no—
880C4×D4—738no—
881C4×D4—738no—
882C4×D4—738no—
883C4×D4—7316no—
884C4×D4—738no—
885C4×D4—7316no—
886C4×D4—738no—
887C4×D4—7316no—
888C4×D4—738no—
889C4×D4—734no—
890C4×D4—734no—
891C4×D4—734no—
892C4×D4—7316no—
893C4×D4—7316no—
894C4×D4—734no—
895C4×D4—732no—
896C4×D4—7316no—
897C4×D4—738no—
898C4×D4—7316no—
899C4×D4—738no—
900C4×D4—7316no—
901C4×D4—738no—
902C4×D4C22×D7314yes—
903C4×D4C22×D7312yes—
904#117—731no—
905#117—732no—
906#117—732no—
907#117—738no—
908#117—732no—
909#117—734no—
910#117—734no—
911#117—7316no—
912#117—738no—
913#117—7316no—
914#117—732no—
915#117—734no—
916#117—734no—
917#117—732no—
918#117—732no—
919#117—732no—
920#117—734no—
921#117—7316no—
922#117—7316no—
923#117C22×D7311yescharacteristic
924#117C22×D7312yes—
925#117C22×D7312yes—
926#117C22×D7318yes—
927#117C22×D7318yes—
928C2×C4⋊C4—732no—
929C2×C4⋊C4—734no—
930C2×C4⋊C4—734no—
931C2×C4⋊C4—7316no—
932C2×C4⋊C4—738no—
933C2×C4⋊C4—734no—
934C2×C4⋊C4C22×D7314yes—
935C2×C22⋊C4—738no—
936C2×C22⋊C4—732no—
937C2×C22⋊C4—734no—
938C2×C22⋊C4—734no—
939C2×C22⋊C4—738no—
940C2×C22⋊C4—738no—
941C2×C42—732no—
942C2×C42—734no—
943C2×C42—731no—
944C2×C42—732no—
945C2×C42—732no—
946C2×C42—731no—
947C2×C42—734no—
948C2×C42—7316no—
949C2×C42—734no—
950C2×C42—732no—
951C2×C42—732no—
952C2×C42—734no—
953C2×C42—731no—
954C2×C42—732no—
955C2×C42—731no—
956C2×C42—732no—
957C2×C42—731no—
958C2×C42C22×D7311yescharacteristic
959C2×C42C22×D7312yes—
960C24—731no—
961C24—734no—
962C24—732no—
963#41—24no—
964#41—29216no—
965#41—29216no—
966#41—1468no—
967#41—1468no—
968#41—1464no—
969#41—14616no—
970#41—14616no—
971#41—14616no—
972#41—14616no—
973#41—1464no—
974#41—1464no—
975C2×Q8—28no—
976C2×Q8—2928no—
977C2×Q8—738no—
978C2×Q8—732no—
979C2×Q8—734no—
980C2×Q8—731no—
981C2×Q8—1464no—
982C2×Q8C23×D7314yes—
983C2×Q8C23×D7311yescharacteristic
984C2×Q8C23×D7314yes—
985C2×Q8C23×D7314yes—
986C2×D4—2928no—
987C2×D4—7316no—
988C2×D4—732no—
989C2×D4—732no—
990C2×D4—732no—
991C2×D4—7316no—
992C2×D4—738no—
993C2×D4—738no—
994C2×D4—732no—
995C2×D4—738no—
996C2×D4—734no—
997C2×D4—738no—
998C2×D4—734no—
999C2×D4—731no—
1000C2×D4—14616no—
1001C2×D4—1464no—
1002C2×D4—1468no—
1003C2×D4—1468no—
1004C2×D4C23×D7312yes—
1005C2×D4C23×D7311yescharacteristic
1006C22×C4—2924no—
1007C22×C4—2928no—
1008C22×C4—732no—
1009C22×C4—734no—
1010C22×C4—734no—
1011C22×C4—732no—
1012C22×C4—732no—
1013C22×C4—734no—
1014C22×C4—738no—
1015C22×C4—7316no—
1016C22×C4—7316no—
1017C22×C4—731no—
1018C22×C4—738no—
1019C22×C4—731no—
1020C22×C4—731no—
1021C22×C4—731no—
1022C22×C4—731no—
1023C22×C4—732no—
1024C22×C4—732no—
1025C22×C4—732no—
1026C22×C4—732no—
1027C22×C4—732no—
1028C22×C4—738no—
1029C22×C4—734no—
1030C22×C4—732no—
1031C22×C4—738no—
1032C22×C4—14616no—
1033C22×C4—1468no—
1034C22×C4C23×D7312yes—
1035C22×C4C23×D7312yes—
1036C22×C4C23×D7314yes—
1037C22×C4C23×D7314yes—
1038C22×C4C23×D7311yescharacteristic
1039C4⋊C4—734no—
1040C4⋊C4—738no—
1041C4⋊C4—734no—
1042C4⋊C4—738no—
1043C4⋊C4—734no—
1044C4⋊C4—738no—
1045C4⋊C4—738no—
1046C4⋊C4—7316no—
1047C4⋊C4—732no—
1048C4⋊C4—734no—
1049C4⋊C4—734no—
1050C4⋊C4—734no—
1051C4⋊C4—7316no—
1052C4⋊C4—738no—
1053C4⋊C4C23×D7312yes—
1054C4⋊C4C23×D7314yes—
1055C4⋊C4C23×D73116yes—
1056C4⋊C4C23×D7314yes—
1057C4⋊C4C23×D7314yes—
1058C4⋊C4C23×D7318yes—
1059C4⋊C4C23×D7318yes—
1060C4⋊C4C23×D7318yes—
1061C4⋊C4C23×D73116yes—
1062C22⋊C4—732no—
1063C22⋊C4—734no—
1064C22⋊C4—734no—
1065C22⋊C4—734no—
1066C22⋊C4—738no—
1067C22⋊C4—734no—
1068C22⋊C4—7316no—
1069C22⋊C4—7316no—
1070C22⋊C4—7316no—
1071C22⋊C4—734no—
1072C22⋊C4—7316no—
1073C22⋊C4—7316no—
1074C22⋊C4—7316no—
1075C22⋊C4—7316no—
1076C22⋊C4C23×D7312yes—
1077C22⋊C4C23×D7314yes—
1078C22⋊C4C23×D7314yes—
1079C22⋊C4C23×D73116yes—
1080C42—734no—
1081C42—732no—
1082C42—731no—
1083C42—732no—
1084C42—738no—
1085C42—732no—
1086C42—734no—
1087C42—734no—
1088C42—731no—
1089C42—732no—
1090C42—732no—
1091C42—734no—
1092C42—732no—
1093C42—7316no—
1094C42—734no—
1095C42C23×D7311yescharacteristic
1096C42C23×D7312yes—
1097C42C23×D7311yescharacteristic
1098C42C23×D7314yes—
1099C42C23×D7312yes—
1100C42C23×D73116yes—
1101C42C23×D7314yes—
1102C23—2922no—
1103C23—2924no—
1104C23—2928no—
1105C23—734no—
1106C23—731no—
1107C23—731no—
1108C23—738no—
1109C23—732no—
1110C23—1464no—
1111C23—1468no—
1112C23C24×D7312yes—
1113C23C24×D7311yescharacteristic
1114Q8—28no—
1115Q8—28no—
1116Q8—22no—
1117Q8—28no—
1118Q8—2928no—
1119Q8—1464no—
1120Q8—1462no—
1121Q8—1468no—
1122D4—24no—
1123D4—22no—
1124D4—2928no—
1125D4—29216no—
1126D4—29216no—
1127D4—1464no—
1128D4—14616no—
1129D4—14616no—
1130D4—1464no—
1131D4—1464no—
1132D4—1464no—
1133D4—1468no—
1134D4—1462no—
1135D4—1468no—
1136D4—14616no—
1137C2×C4—28no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—28no—
1141C2×C4—2924no—
1142C2×C4—2924no—
1143C2×C4—2922no—
1144C2×C4—2922no—
1145C2×C4—2928no—
1146C2×C4—29216no—
1147C2×C4—29216no—
1148C2×C4—2924no—
1149C2×C4—2922no—
1150C2×C4—734no—
1151C2×C4—731no—
1152C2×C4—731no—
1153C2×C4—734no—
1154C2×C4—734no—
1155C2×C4—734no—
1156C2×C4—734no—
1157C2×C4—734no—
1158C2×C4—732no—
1159C2×C4—732no—
1160C2×C4—732no—
1161C2×C4—738no—
1162C2×C4—1464no—
1163C2×C4—14616no—
1164C2×C4—14616no—
1165C2×C4—1464no—
1166C2×C4—1464no—
1167C2×C4—1464no—
1168C2×C4—1464no—
1169C2×C4—1464no—
1170C2×C4—1468no—
1171C2×C4#41×D7314yes—
1172C2×C4C24×D7314yes—
1173C2×C4C24×D7312yes—
1174C2×C4C24×D7318yes—
1175C2×C4C24×D7312yes—
1176C2×C4C24×D7318yes—
1177C2×C4C24×D7311yescharacteristic
1178C2×C4C24×D7311yescharacteristic
1179C2×C4C24×D7312yes—
1180C22—22no—
1181C22—22no—
1182C22—24no—
1183C22—2924no—
1184C22—2928no—
1185C22—5848no—
1186C22—732no—
1187C22—732no—
1188C22—1462no—
1189C22—1468no—
1190C22—14616no—
1191C22—1464no—
1192C22—1462no—
1193C22—1462no—
1194C22C2×#41×D7312yes—
1195C22C25×D7311yescharacteristic
1196C4—22no—
1197C4—28no—
1198C4—24no—
1199C4—22no—
1200C4—28no—
1201C4—732no—
1202C4—732no—
1203C4—1462no—
1204C4—1462no—
1205C4—1464no—
1206C4—1468no—
1207C4—1462no—
1208C4C2×#41×D7312yes—
1209C4C2×#41×D7312yes—
1210C4#1798942414yes—
1211C2—22no—
1212C2—42no—
1213C2—2922no—
1214C2—2928no—
1215C2—1462no—
1216C2—1462no—
1217C2C22×#41×D7311yescharacteristic
1218C2C2×#1798942412yes—
subgroupG/H
center, FrattiniC22C25×D73
commutator, socle, cosocleC22×C73C26
FittingC73×#3509C2
hypercenter#3509D73
hypocenterC73#62815
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #3509

Complements

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

NH ≅ G/Ntype
1. #22623854C2semidirect
2. #22623843C2semidirect
3. #22623830C2semidirect
4. #22623828C2semidirect
5. #22623815C2semidirect
6. #22623808C2semidirect
7. #22623807C2semidirect
8. #22623797C2semidirect
9. #22623784C2semidirect
10. #22623771C2semidirect
11. #22623531C2semidirect
12. #22623523C2semidirect
13. #22623496C2semidirect
14. #22623322C2semidirect
15. #22623263C2semidirect
16. #22623228C2semidirect
17. #533×D73C2semidirect
18. C2×#17989138C2semidirect
19. #22623133C2semidirect
20. C4×#41×D73C2semidirect
21. C73×#3509C2semidirect
24. #17989322C22semidirect
25. #17989322C22semidirect
26. #17989322C22semidirect
27. #17989319C22semidirect
28. #17989312C22semidirect
29. #17989311C22semidirect
30. #17989311C22semidirect
31. #17989309C22semidirect
32. #17989309C22semidirect
33. #17989300C22semidirect
34. #17989293C22semidirect
35. #17989290C22semidirect
36. #17989290C22semidirect
37. #17989288C22semidirect
38. #17989288C22semidirect
39. #17989281C22semidirect
40. #17989272C22semidirect
41. #17989269C22semidirect
42. #17989261C22semidirect
43. #17989260C22semidirect
44. #17989259C22semidirect
45. #17989258C22semidirect
46. #17989249C22semidirect
47. #17989247C22semidirect
48. #17989239C22semidirect
49. #17989233C22semidirect
50. #17989228C22semidirect
51. #17989210C22semidirect
52. #17989209C22semidirect
53. #17989198C22semidirect
54. #17989193C22semidirect
55. #17989192C22semidirect
56. #17989185C22semidirect
57. #17989176C22semidirect
58. #17989167C22semidirect
59. #17989162C22semidirect
62. #17989155C22semidirect
65. #17989144C22semidirect
66. #17989143C22semidirect
67. #17989142C22semidirect
68. #17989142C22semidirect
69. #17989141C22semidirect
70. #17989140C22semidirect
71. #17989139C22semidirect
75. #17989138C22semidirect
76. #17989138C22semidirect
77. #17989138C22semidirect
78. #17989138C22semidirect
79. #17989138C22semidirect
80. #17989137C22semidirect
81. #17989136C22semidirect
82. C4⋊Q8×D73C22semidirect
83. C2×#14556588C22semidirect
84. #17989124C22semidirect
85. #17989124C22semidirect
86. #17989123C22semidirect
87. #17989123C22semidirect
88. #17989122C22semidirect
89. #17989122C22semidirect
90. #17989122C22semidirect
91. #17989120C22semidirect
92. #125×D73C22semidirect
93. C2×#14556580C22semidirect
94. #17989100C22semidirect
95. #17989100C22semidirect
96. #17989099C22semidirect
100. #17989069C22semidirect
101. #17989069C22semidirect
102. #17989065C22semidirect
104. #17989061C22semidirect
105. #17989061C22semidirect
107. C4×#11924029C22semidirect
108. C4×#11924029C22semidirect
109. C4×#11924029C22semidirect
110. C4×#11924029C22semidirect
112. C4×#11924028C22semidirect
114. #17989055C22semidirect
115. #17989055C22semidirect
117. C4×#11924027C22semidirect
118. C4×Q8×D73C22semidirect
119. C4×Q8×D73C22semidirect
120. C2×#14556553C22semidirect
122. C4×D4×D73C22semidirect
125. #117×D73C22semidirect
126. #117×D73C22semidirect
128. C2×C42×D73C22semidirect
129. #557×C73C22semidirect
130. #556×C73C22semidirect
131. #552×C73C22semidirect
132. #541×C73C22semidirect
134. #533×C73C22semidirect
135. #533×C73C22semidirect
136. C2×C4⋊Q8×C73C22semidirect
137. #519×C73C22semidirect
396. C2×C4×D73#41semidirect
615. #3509D73semidirect
631. C73#62815semidirect
639. #557C2×D73semidirect
644. #556C2×D73semidirect
654. #552C2×D73semidirect
667. #541C2×D73semidirect
687. #533C2×D73semidirect
688. #533C2×D73semidirect
700. C2×C4⋊Q8C2×D73semidirect
721. #519C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226238542
#226238432
#226238302
#226238282
#226238152
#226238082
#226238072
#226237972
#226237842
#226237712
#226235312
#226235232
#226234962
#226233222
#226232632
#226232282
#533×D732
C2×#179891382
#226231332
C4×#41×D732
C73×#35092
#6281573