Finite Group Databasebeta

← #35197415

Subgroups — #35197415

Order 20224.

7086 conjugacy classes of subgroups.

The subgroup lattice has 1538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777323C214yesmaximal, complemented
2#23777315C214yesmaximal, complemented
3#23777312C214yesmaximal, complemented
4#23777305C214yesmaximal, complemented
5#23777235C214yesmaximal, complemented
6#23777232C214yesmaximal, complemented
7#23777147C214yesmaximal, complemented
8#23777144C214yesmaximal, complemented
9#23777133C214yesmaximal, complemented
10#23777123C214yesmaximal, complemented
11#23777112C214yesmaximal, complemented
12#23777105C214yesmaximal, complemented
13#23776833C211yesmaximal, characteristic, complemented
14#23776824C212yesmaximal, complemented
15#23776823C211yesmaximal, characteristic, complemented
16#23776817C211yesmaximal, characteristic, complemented
17#23776816C212yesmaximal, complemented
18#544×D79C211yesmaximal, characteristic, complemented
19#23776732C212yesmaximal, complemented
20#537×D79C211yesmaximal, characteristic, complemented
21#23776599C212yesmaximal, complemented
22C2×#19099045C211yesmaximal, characteristic, complemented
23C79×#3461C211yesmaximal, characteristic, complemented
24C22×#11929625C2211yescharacteristic
25C2×#41×D79C2212yes—
26#19099285C2218yescomplemented
27#19099280C2218yescomplemented
28#19099276C2218yescomplemented
29#19099275C2218yescomplemented
30#19099269C2218yescomplemented
31#19099267C2218yescomplemented
32#19099266C2218yescomplemented
33#19099266C2214yescomplemented
34#19099264C2218yescomplemented
35#19099264C2218yescomplemented
36#19099264C2218yescomplemented
37#19099264C2218yescomplemented
38#19099263C2214yescomplemented
39#19099262C2218yescomplemented
40#19099258C2218yescomplemented
41#19099258C2218yescomplemented
42#19099257C2218yescomplemented
43#19099254C2214yescomplemented
44#19099251C2214yescomplemented
45#19099249C2218yescomplemented
46#19099246C2218yescomplemented
47#19099245C2218yescomplemented
48#19099245C2218yescomplemented
49#19099245C2218yescomplemented
50#19099240C2218yescomplemented
51#19099238C2218yescomplemented
52#19099238C2218yescomplemented
53#19099237C2218yescomplemented
54#19099225C2214yescomplemented
55#19099223C2218yescomplemented
56#19099221C2214yescomplemented
57#19099215C2218yescomplemented
58#19099211C2218yescomplemented
59#19099208C2214yescomplemented
60#19099206C2214yescomplemented
61#19099205C2218yescomplemented
62#19099194C2211yescharacteristic, complemented
63#19099193C2214yescomplemented
64#19099192C2214yescomplemented
65#19099191C2212yescomplemented
66#19099190C2214yescomplemented
67#19099187C2214yescomplemented
68#19099186C2214yescomplemented
69#19099186C2214yescomplemented
70#19099185C2214yescomplemented
71#19099185C2214yescomplemented
72#19099184C2214yescomplemented
73#19099182C2214yescomplemented
74#19099174C2214yescomplemented
75#19099173C2214yescomplemented
76#19099171C2214yescomplemented
77#19099169C2214yescomplemented
78#19099168C2214yescomplemented
79#19099166C2214yescomplemented
80#19099164C2214yescomplemented
81#19099160C2214yescomplemented
82#19099157C2218yescomplemented
83#19099153C2214yescomplemented
84#19099150C2214yescomplemented
85#19099146C2218yescomplemented
86#19099144C2211yescharacteristic
87#19099143C2214yescomplemented
88#19099143C2214yescomplemented
89#19099143C2214yescomplemented
90#19099142C2214yescomplemented
91#19099141C2212yes—
92#19099140C2214yes—
93#19099138C2214yes—
94#19099137C2212yescomplemented
95#19099132C2212yescomplemented
96#19099131C2214yes—
97#19099127C2212yescomplemented
98#19099124C2218yes—
99#19099118C2214yescomplemented
100#19099117C2214yescomplemented
101#19099115C2214yescomplemented
102#19099114C2214yescomplemented
103#19099114C2214yescomplemented
104#19099113C2214yescomplemented
105#19099112C2214yescomplemented
106#19099110C2214yescomplemented
107#19099108C2214yescomplemented
108C4⋊Q8×D79C2214yescomplemented
109#19099100C2214yescomplemented
110#19099100C2214yescomplemented
111#19099099C2214yescomplemented
112#19099099C2214yescomplemented
113#19099098C2214yescomplemented
114#19099097C2214yescomplemented
115#19099097C2214yescomplemented
116#19099092C2214yescomplemented
117#19099090C2218yescomplemented
118#125×D79C2214yescomplemented
119#19099076C2214yes—
120#19099076C2214yes—
121#19099076C2214yescomplemented
122#19099073C2214yescomplemented
123#19099072C2218yescomplemented
124#19099071C2218yescomplemented
125C22⋊Q8×D79C2214yes—
126C22⋊Q8×D79C2214yescomplemented
127#121×D79C2214yes—
128#121×D79C2214yescomplemented
129#19099045C2214yes—
130#19099045C2214yes—
131#19099045C2214yescomplemented
132#19099045C2212yescomplemented
133#19099045C2214yescomplemented
134#19099045C2212yescomplemented
135#19099042C2212yescomplemented
136#19099042C2212yescomplemented
137#19099042C2214yescomplemented
138#19099042C2214yescomplemented
139#19099039C2212yescomplemented
140#19099039C2212yescomplemented
141#19099035C2214yes—
142#19099035C2214yes—
143#19099035C2212yescomplemented
144#19099035C2212yescomplemented
145#41×Dic79C2212yescomplemented
146C4×#11929624C2214yescomplemented
147C4×#11929624C2212yescomplemented
148#19099031C2214yescomplemented
149#19099031C2212yescomplemented
150C2×Q8×Dic79C2211yescharacteristic, complemented
151C2×C4×D316C2212yes—
152C2×C4×D316C2211yescharacteristic, complemented
153C2×#14579123C2212yes—
154C2×#14579123C2211yescharacteristic, complemented
155C2×#14579118C2211yescharacteristic
156C2×#14579118C2212yescomplemented
157C2×#14579118C2214yescomplemented
158#117×D79C2212yes—
159#117×D79C2214yescomplemented
160C2×C4⋊C4×D79C2211yescharacteristic
161C2×C4⋊C4×D79C2212yescomplemented
162#544×C79C2211yescharacteristic, complemented
163#542×C79C2214yescomplemented
164#541×C79C2214yescomplemented
165#539×C79C2214yescomplemented
166#537×C79C2211yescharacteristic
167#536×C79C2212yescomplemented
168#533×C79C2214yescomplemented
169#529×C79C2214yescomplemented
170#529×C79C2214yescomplemented
171C4×#41×C79C2212yescomplemented
172C2×C4×Q8×C79C2211yescharacteristic, complemented
173C2×#11929625—28no—
174C2×#11929625C2314yes—
175C2×#11929625C2314yes—
176C2×#11929625C2312yes—
177C2×#11929625C2314yes—
178C2×#11929624C2312yes—
179C2×#11929624C2314yes—
180C2×#11929624C2318yes—
181C2×#11929623C2314yes—
182C2×#11929623C2312yes—
183C2×#11929623C2314yes—
184#41×D79—216no—
185C2×Q8×D79C2312yes—
186C2×Q8×D79C2314yes—
187C22×D316C2312yes—
188C22×D316C2311yescharacteristic
189C2×D4×D79C2314yes—
190C2×D4×D79C2312yes—
191C2×D4×D79C2314yes—
192C22×C4×D79C2312yes—
193C22×C4×D79C2314yes—
194C22×C4×D79C2312yes—
195C22×C4×D79C2312yes—
196C22×C4×D79C2312yes—
197C22×C4×D79C2311yescharacteristic
198#14579161C2314yes—
199#14579160C2314yes—
200#14579160C2314yes—
201#14579160C2318yes—
202#14579159C2314yes—
203#14579159C2318yes—
204#14579158C2314yes—
205#14579157C2314yes—
206#14579156C2318yes—
207#14579156C2318yes—
208#14579156C2318yes—
209#14579156C2318yes—
210#14579156C2318yes—
211#14579156C2318yes—
212#14579155C2318yes—
213#14579155C2318yes—
214#14579154C2318yes—
215#14579154C2318yes—
216#14579153C2314yes—
217#14579153C2314yes—
218#14579152C2318yes—
219#14579152C2314yes—
220#14579152C2314yes—
221#14579151C2318yes—
222#14579151C2318yes—
223#14579151C2318yes—
224#14579151C2318yes—
225#14579151C2318yes—
226#14579150C2314yes—
227#14579150C2314yes—
228#14579150C2318yes—
229#14579149C2314yes—
230#14579149C2318yes—
231#14579149C2314yes—
232#14579147C2318yes—
233#14579147C2318yes—
234#14579147C2318yes—
235#14579146C2318yes—
236#14579146C2318yes—
237#14579146C2318yes—
238#14579146C2318yes—
239#14579146C2318yes—
240#14579146C2318yes—
241#14579146C2318yes—
242#14579145C2318yes—
243#14579145C2318yes—
244#14579144C2318yes—
245#14579144C2318yes—
246#14579143C2318yes—
247#14579143C2318yes—
248#14579143C2318yes—
249#14579141C2314yes—
250#14579141C2318yes—
251#14579141C2314yes—
252#14579141C2314yes—
253#14579140C2314yes—
254#14579140C2314yes—
255#14579139C2318yes—
256#14579139C2318yes—
257#14579139C2318yes—
258#14579139C2318yes—
259#14579139C2318yes—
260#14579139C2318yes—
261#14579138C2318yes—
262#14579138C2318yes—
263#14579138C2318yes—
264#14579137C2314yes—
265#14579137C2314yes—
266#14579137C2314yes—
267#14579137C2314yes—
268#14579137C2314yes—
269#14579136C2314yes—
270#14579136C2314yes—
271#14579136C2314yes—
272#14579136C2314yes—
273#14579136C2318yes—
274#14579136C2318yes—
275#14579136C2318yes—
276#14579136C2314yes—
277#14579135C2314yes—
278#14579135C2314yes—
279#14579135C2314yes—
280#14579135C2314yes—
281#14579135C2318yes—
282#14579134C2318yes—
283#14579134C2318yes—
284#14579134C2318yes—
285#14579134C2318yes—
286#14579134C2318yes—
287#14579134C2318yes—
288#14579134C2318yes—
289#14579134C2318yes—
290#14579133C2318yes—
291#14579133C2318yes—
292#14579133C2318yes—
293#14579132C2314yes—
294#14579132C2314yes—
295#14579132C2314yes—
296#14579131C2318yes—
297#14579131C2318yes—
298#14579131C2318yes—
299#14579129C2318yes—
300Q8×Dic79C2314yes—
301Q8×Dic79C2312yes—
302Q8×Dic79C2314yes—
303Q8×Dic79C2312yes—
304C4×Dic158C2312yes—
305C4×Dic158C2312yes—
306C4×Dic158C2314yes—
307C4×Dic158C2314yes—
308C4×Dic158C2314yes—
309#14579126C2312yes—
310#14579126C2312yes—
311#14579126C2318yes—
312#14579126C2314yes—
313#14579126C2314yes—
314C4×D316C2314yes—
315C4×D316C2312yes—
316C4×D316C2314yes—
317C4×D316C2312yes—
318C4×D316C2314yes—
319C4×D316C2314yes—
320C4×D316C2314yes—
321C4×D316C2314yes—
322C4×D316C2314yes—
323C4×D316C2314yes—
324C4×D316C2318yes—
325C4×D316C2314yes—
326D4×Dic79C2314yes—
327D4×Dic79C2314yes—
328D4×Dic79C2312yes—
329D4×Dic79C2312yes—
330#14579123C2314yes—
331#14579123C2312yes—
332#14579123C2314yes—
333#14579123C2312yes—
334#14579123C2318yes—
335#14579123C2318yes—
336#14579123C2314yes—
337#14579123C2318yes—
338#14579123C2318yes—
339#14579123C2318yes—
340#14579123C2314yes—
341C4×C22⋊D79C2314yes—
342C4×C22⋊D79C2314yes—
343C4×C22⋊D79C2314yes—
344C4×C22⋊D79C2314yes—
345C4×C22⋊D79C2318yes—
346C4×C22⋊D79C2314yes—
347C4×C22⋊D79C2314yes—
348(C22⋊D79)⋊C4C2314yes—
349(C22⋊D79)⋊C4C2314yes—
350(C22⋊D79)⋊C4C2318yes—
351(C22⋊D79)⋊C4C2314yes—
352(C22⋊D79)⋊C4C2318yes—
353(C22⋊D79)⋊C4C2314yes—
354(C22⋊D79)⋊C4C2318yes—
355(C22⋊D79)⋊C4C2318yes—
356(C22⋊D79)⋊C4C2314yes—
357(C22⋊D79)⋊C4C2314yes—
358#14579120C2312yes—
359#14579120C2314yes—
360#14579119C2312yes—
361#14579119C2312yes—
362#14579119C2314yes—
363#14579119C2318yes—
364#14579119C2314yes—
365#14579119C2314yes—
366#14579119C2314yes—
367#14579118C2314yes—
368#14579118C2314yes—
369#14579118C2314yes—
370#14579118C2314yes—
371#14579118C2314yes—
372#14579118C2318yes—
373#14579118C2318yes—
374#14579118C2314yes—
375#14579118C2318yes—
376#14579118C2318yes—
377#14579118C2312yes—
378#14579118C2312yes—
379#14579118C2312yes—
380#14579118C2312yes—
381#14579118C2314yes—
382#14579117C2314yes—
383#14579117C2318yes—
384#14579117C2314yes—
385#14579117C2314yes—
386C2×C4⋊Dic79C2311yescharacteristic
387C2×C4⋊Dic79C2312yes—
388C2×Dic79⋊C4C2312yes—
389C2×Dic79⋊C4C2314yes—
390C2×Dic79⋊C4C2314yes—
391C2×Dic79⋊C4C2311yescharacteristic
392C2×Dic79⋊C4C2311yescharacteristic
393C4⋊C4×D79C2314yes—
394C4⋊C4×D79C2312yes—
395C4⋊C4×D79C2312yes—
396C4⋊C4×D79C2314yes—
397C4⋊C4×D79C2318yes—
398C4⋊C4×D79C2314yes—
399C4⋊C4×D79C2318yes—
400C4⋊C4×D79C2314yes—
401C4⋊C4×D79C2314yes—
402C4⋊C4×D79C2318yes—
403C4⋊C4×D79C2314yes—
404C2×(C2×D79)⋊C4C2312yes—
405C2×(C2×D79)⋊C4C2312yes—
406C2×(C2×D79)⋊C4C2314yes—
407C2×(C2×D79)⋊C4C2314yes—
408C2×(C2×D79)⋊C4C2311yescharacteristic
409C2×(C2×D79)⋊C4C2311yescharacteristic
410C22⋊C4×D79C2314yes—
411C22⋊C4×D79C2314yes—
412C22⋊C4×D79C2318yes—
413C22⋊C4×D79C2314yes—
414C2×C4×Dic79C2311yescharacteristic
415C2×C4×Dic79C2312yes—
416C2×C4×Dic79C2314yes—
417C42×D79C2314yes—
418C42×D79C2314yes—
419C42×D79C2314yes—
420C2×#41×C79C2312yes—
421C22×Q8×C79C2311yescharacteristic
422C4⋊Q8×C79C2314yes—
423C4⋊Q8×C79C2314yes—
424#126×C79C2318yes—
425#126×C79C2318yes—
426#125×C79C2314yes—
427#125×C79C2314yes—
428#125×C79C2318yes—
429#124×C79C2314yes—
430#124×C79C2314yes—
431#123×C79C2318yes—
432#123×C79C2318yes—
433C22⋊Q8×C79C2314yes—
434C22⋊Q8×C79C2314yes—
435C22⋊Q8×C79C2314yes—
436C22⋊Q8×C79C2314yes—
437C22⋊Q8×C79C2318yes—
438#121×C79C2314yes—
439#121×C79C2314yes—
440C4×Q8×C79C2314yes—
441C4×Q8×C79C2312yes—
442C4×Q8×C79C2314yes—
443C4×Q8×C79C2314yes—
444C4×Q8×C79C2312yes—
445C4×D4×C79C2314yes—
446C4×D4×C79C2312yes—
447C4×D4×C79C2314yes—
448C4×D4×C79C2314yes—
449C4×D4×C79C2312yes—
450#117×C79C2314yes—
451#117×C79C2312yes—
452#117×C79C2318yes—
453C2×C4⋊C4×C79C2311yescharacteristic
454C2×C4⋊C4×C79C2312yes—
455C2×C42×C79C2311yescharacteristic
456C2×C42×C79C2312yes—
457C2×C42×C79C2314yes—
458C23×D79C2414yes—
459C23×D79C2412yes—
460C23×D79C2411yescharacteristic
461#11929625—28no—
462#11929625—216no—
463#11929625—216no—
464#11929625—84no—
465#11929624—216no—
466#11929624—28no—
467#11929624—88no—
468#11929623—216no—
469#11929623—28no—
470#11929623—84no—
471C2×Dic158C2414yes—
472C2×Dic158C2412yes—
473C2×Dic158C2414yes—
474C2×Dic158C2418yes—
475Q8×D79—28no—
476Q8×D79—84no—
477C2×D316—28no—
478C2×D316—24no—
479C2×D316C2414yes—
480C2×D316C2412yes—
481C2×D316C2414yes—
482C2×D316C2414yes—
483C2×D316C2414yes—
484C2×D316C2418yes—
485C2×D316C2414yes—
486C2×D316C2418yes—
487C2×C22⋊D79C2414yes—
488C2×C22⋊D79C2414yes—
489C2×C22⋊D79C2414yes—
490C2×C22⋊D79C2418yes—
491C2×C22⋊D79C2418yes—
492C2×C22⋊D79C2418yes—
493D4×D79—28no—
494D4×D79—216no—
495D4×D79—84no—
496C22×Dic79C2414yes—
497C22×Dic79C2414yes—
498C22×Dic79C2411yescharacteristic
499C22×Dic79C2411yescharacteristic
500C22×Dic79C2412yes—
501C22×Dic79C2414yes—
502C22×Dic79C2411yescharacteristic
503C2×C4×D79—28no—
504C2×C4×D79—216no—
505C2×C4×D79—82no—
506C2×C4×D79—82no—
507C2×C4×D79—82no—
508C2×C4×D79#4118yescomplemented
509C2×C4×D79C2414yes—
510C2×C4×D79C2414yes—
511C2×C4×D79C2414yes—
512C2×C4×D79C2418yes—
513C2×C4×D79C2414yes—
514C2×C4×D79C2414yes—
515C2×C4×D79C2414yes—
516C2×C4×D79C2414yes—
517C2×C4×D79C2418yes—
518C2×C4×D79C2414yes—
519C2×C4×D79C2414yes—
520C2×C4×D79C2414yes—
521C2×C4×D79C2414yes—
522C2×C4×D79C2414yes—
523C2×C4×D79C2414yes—
524C2×C4×D79C2412yes—
525C2×C4×D79C2412yes—
526C4⋊Dic79C2414yes—
527C4⋊Dic79C2414yes—
528C4⋊Dic79C2414yes—
529C4⋊Dic79C2412yes—
530C4⋊Dic79C2412yes—
531C4⋊Dic79C2414yes—
532C4⋊Dic79C2414yes—
533C4⋊Dic79C2414yes—
534C4⋊Dic79C2418yes—
535C4⋊Dic79C2414yes—
536Dic79⋊C4C2412yes—
537Dic79⋊C4C2412yes—
538Dic79⋊C4C2418yes—
539Dic79⋊C4C2412yes—
540Dic79⋊C4C2414yes—
541Dic79⋊C4C2414yes—
542Dic79⋊C4C2418yes—
543Dic79⋊C4C2418yes—
544Dic79⋊C4C2418yes—
545Dic79⋊C4C2418yes—
546Dic79⋊C4C2412yes—
547Dic79⋊C4C2414yes—
548Dic79⋊C4C2414yes—
549Dic79⋊C4C2414yes—
550Dic79⋊C4C2414yes—
551Dic79⋊C4C2418yes—
552Dic79⋊C4C2418yes—
553C22⋊Dic79C2414yes—
554C22⋊Dic79C2414yes—
555C22⋊Dic79C2414yes—
556C22⋊Dic79C2418yes—
557(C2×D79)⋊C4C2411yescharacteristic
558(C2×D79)⋊C4C2412yes—
559(C2×D79)⋊C4C2414yes—
560(C2×D79)⋊C4C2414yes—
561(C2×D79)⋊C4C2418yes—
562(C2×D79)⋊C4C2418yes—
563(C2×D79)⋊C4C2411yescharacteristic
564(C2×D79)⋊C4C2411yescharacteristic
565(C2×D79)⋊C4C2412yes—
566(C2×D79)⋊C4C2414yes—
567(C2×D79)⋊C4C2414yes—
568(C2×D79)⋊C4C2411yescharacteristic
569(C2×D79)⋊C4C2414yes—
570(C2×D79)⋊C4C2414yes—
571(C2×D79)⋊C4C2418yes—
572(C2×D79)⋊C4C2414yes—
573(C2×D79)⋊C4C2414yes—
574(C2×D79)⋊C4C2418yes—
575(C2×D79)⋊C4C2418yes—
576(C2×D79)⋊C4C2418yes—
577(C2×D79)⋊C4C2418yes—
578(C2×D79)⋊C4C2418yes—
579(C2×D79)⋊C4C2418yes—
580C4×Dic79C2412yes—
581C4×Dic79C2414yes—
582C4×Dic79C2414yes—
583C4×Dic79C2414yes—
584C4×Dic79C2414yes—
585C4×Dic79C2414yes—
586C4×Dic79C2414yes—
587C4×Dic79C2414yes—
588C4×Dic79C2412yes—
589C4×Dic79C2418yes—
590C4×Dic79C2414yes—
591C4×Dic79C2414yes—
592#41×C79—28no—
593C2×Q8×C79—24no—
594C2×Q8×C79C2412yes—
595C2×Q8×C79C2414yes—
596C2×Q8×C79C2414yes—
597C2×D4×C79C2414yes—
598C2×D4×C79C2412yes—
599C2×D4×C79C2414yes—
600C22×C4×C79C2414yes—
601C22×C4×C79C2412yes—
602C22×C4×C79C2414yes—
603C22×C4×C79C2411yescharacteristic
604C22×C4×C79C2411yescharacteristic
605C22×C4×C79C2412yes—
606C22×C4×C79C2414yes—
607C22×C4×C79C2411yescharacteristic
608C4⋊C4×C79C2414yes—
609C4⋊C4×C79C2418yes—
610C4⋊C4×C79C2412yes—
611C4⋊C4×C79C2414yes—
612C4⋊C4×C79C2412yes—
613C4⋊C4×C79C2414yes—
614C4⋊C4×C79C2418yes—
615C4⋊C4×C79C2418yes—
616C4⋊C4×C79C2414yes—
617C4⋊C4×C79C2414yes—
618C4⋊C4×C79C2418yes—
619C22⋊C4×C79C2414yes—
620C22⋊C4×C79C2414yes—
621C22⋊C4×C79C2414yes—
622C22⋊C4×C79C2418yes—
623C22⋊C4×C79C2418yes—
624C22⋊C4×C79C2418yes—
625C42×C79C2412yes—
626C42×C79C2412yes—
627C42×C79C2414yes—
628C42×C79C2414yes—
629C42×C79C2414yes—
630C42×C79C2414yes—
631C42×C79C2414yes—
632C23×C79C2514yes—
633C23×C79C2511yescharacteristic
634C22×D79—24no—
635C22×D79—28no—
636C22×D79—41no—
637C22×D79—42no—
638C22×D79—41no—
639C22×D79—42no—
640C22×D79—44no—
641C22×D79—44no—
642C22×D79C2×#4114yes—
643C22×D79C2514yes—
644C22×D79C2514yes—
645C22×D79C2511yescharacteristic
646C22×D79C2511yescharacteristic
647Q8×C79—24no—
648Q8×C79—28no—
649Q8×C79—44no—
650D4×C79—28no—
651D4×C79—24no—
652D4×C79—44no—
653C2×C4×C79—24no—
654C2×C4×C79—28no—
655C2×C4×C79—41no—
656C2×C4×C79—42no—
657C2×C4×C79—44no—
658C2×C4×C79—41no—
659C2×C4×C79—44no—
660C2×C4×C79C2×#4114yes—
661C2×C4×C79C2511yescharacteristic
662C2×C4×C79C2514yes—
663C2×C4×C79C2514yes—
664C2×C4×C79C2514yes—
665C2×C4×C79C2512yes—
666C2×C4×C79C2514yes—
667C2×C4×C79C2511yescharacteristic
668C2×C4×C79C2514yes—
669C2×C4×C79C2512yes—
670C22⋊D79—28no—
671C22⋊D79—28no—
672C22⋊D79—28no—
673C22⋊D79—48no—
674C22⋊D79—48no—
675C22⋊D79—48no—
676C2×Dic79—28no—
677C2×Dic79—42no—
678C2×Dic79—41no—
679C2×Dic79—44no—
680C2×Dic79—41no—
681C2×Dic79—44no—
682C2×Dic79C2×#4114yes—
683C2×Dic79C2512yes—
684C2×Dic79C2511yescharacteristic
685C2×Dic79C2511yescharacteristic
686C2×Dic79C2514yes—
687C2×Dic79C2514yes—
688C2×Dic79C2514yes—
689C2×Dic79C2514yes—
690C2×Dic79C2512yes—
691D316—28no—
692D316—28no—
693D316—28no—
694D316—24no—
695D316—28no—
696D316—44no—
697D316—48no—
698D316—48no—
699C4×D79—28no—
700C4×D79—28no—
701C4×D79—28no—
702C4×D79—216no—
703C4×D79—44no—
704C4×D79—44no—
705C4×D79—44no—
706C4×D79—48no—
707C4×D79—44no—
708C4×D79—44no—
709C4×D79—44no—
710C4×D79—44no—
711C4×D79—44no—
712C4×D79—44no—
713C4×D79—44no—
714C4×D79C2×#4118yes—
715C4×D79C2×#4118yes—
716Dic158—24no—
717Dic158—28no—
718Dic158—44no—
719Dic158—48no—
720C22×C79—21no—
721C22×C79—21no—
722C22×C79—24no—
723C22×C79—24no—
724C22×C79—24no—
725C22×C79C22×#4112yes—
726C22×C79C2611yescharacteristic
727C2×D79—21no—
728C2×D79—21no—
729C2×D79—21no—
730C2×D79—21no—
731C2×D79—24no—
732C2×D79—24no—
733C2×D79—24no—
734C2×D79—24no—
735C2×D79—24no—
736C2×D79—24no—
737C2×D79—44no—
738C2×D79—48no—
739C2×D79—88no—
740C2×D79C22×#4112yes—
741C2×D79C22×#4112yes—
742C4×C79—24no—
743C4×C79—24no—
744C4×C79—22no—
745C4×C79—24no—
746C4×C79—24no—
747C4×C79—21no—
748C4×C79—21no—
749C4×C79—24no—
750C4×C79C22×#4114yes—
751Dic79—24no—
752Dic79—24no—
753Dic79—24no—
754Dic79—21no—
755Dic79—21no—
756Dic79—24no—
757Dic79—22no—
758Dic79C22×#4114yes—
759#62856—791nomaximal, Sylow
760C2×C79—22no—
761C2×C79—44no—
762C2×C79C23×#4111yescharacteristic
763C2×C79H(7,𝔽2)11yescharacteristic
764C2×C792−1+611yescharacteristic
765D79—22no—
766D79—22no—
767D79—44no—
768D79—44no—
769#3512—794no—
770#3512—794no—
771#3511—794no—
772#3511—794no—
773#3505—794no—
774#3505—794no—
775#3495—794no—
776#3495—794no—
777#3494—794no—
778#3494—794no—
779#3493—794no—
780#3492—794no—
781#3461—792no—
782#3461—791no—
783#3461D7911yescharacteristic, complemented
784#3460—791no—
785#3460—791no—
786#3460—792no—
787C2×#544—791no—
788#3449—792no—
789C2×#537—791no—
790#3428—792no—
791C2×#520—791no—
792C79#6285611yescharacteristic, complemented, Sylow
793C22×#41—792no—
794C22×#41—791no—
795#556—798no—
796#556—798no—
797#555—798no—
798#555—798no—
799#554—798no—
800#554—798no—
801#553—798no—
802#553—798no—
803#553—798no—
804#553—798no—
805#553—798no—
806#553—794no—
807#553—798no—
808#553—798no—
809#553—798no—
810#553—794no—
811#553—798no—
812#552—798no—
813#552—798no—
814#552—798no—
815#552—798no—
816#552—794no—
817#552—794no—
818#552—798no—
819#551—798no—
820#551—798no—
821#551—798no—
822#551—798no—
823#548—794no—
824#548—798no—
825#548—794no—
826#547—798no—
827#547—798no—
828#546—794no—
829#546—798no—
830#546—794no—
831#544—794no—
832#544—794no—
833#544—794no—
834#544—792no—
835#544—791no—
836#544C2×D7911yescharacteristic, complemented
837#542—794no—
838#542—794no—
839#542—794no—
840#542—794no—
841#542—794no—
842#542—794no—
843#542—794no—
844#542C2×D7914yescomplemented
845#541—794no—
846#541—794no—
847#541—794no—
848#541C2×D7914yescomplemented
849#540—794no—
850#540—794no—
851#540—794no—
852#540—794no—
853#539—798no—
854#539—794no—
855#539C2×D7914yescomplemented
856#538—794no—
857#538—794no—
858#538—798no—
859#537—792no—
860#537—794no—
861#537—794no—
862#537—794no—
863#537—794no—
864#537—794no—
865#537—791no—
866#537C2×D7911yescharacteristic
867#536—792no—
868#536—794no—
869#536C2×D7912yescomplemented
870#535—792no—
871#535—794no—
872#535—792no—
873#534—798no—
874#533—794no—
875#533—794no—
876#533—794no—
877#533C2×D7914yescomplemented
878#532—794no—
879#532—794no—
880#532—794no—
881#532—794no—
882#532—794no—
883#532—794no—
884C2×C4⋊Q8—794no—
885#529—794no—
886#529—794no—
887#529—798no—
888#529—794no—
889#529—794no—
890#529—794no—
891#529—794no—
892#529—794no—
893#529—794no—
894#529C2×D7914yescomplemented
895#529C2×D7914yescomplemented
896C2×#125—794no—
897#525—798no—
898#525—794no—
899#525—794no—
900#525—794no—
901#525—794no—
902#525—798no—
903C2×C22⋊Q8—794no—
904C2×C22⋊Q8—794no—
905C2×#121—794no—
906C2×#121—794no—
907#520—794no—
908#520—794no—
909#520—794no—
910#520—794no—
911#520—792no—
912#520—792no—
913#520—794no—
914#520—794no—
915#520—792no—
916#520—792no—
917#519—792no—
918#519—792no—
919#518—794no—
920#518—794no—
921#518—792no—
922#518—792no—
923C4×#41—792no—
924C4×#41—792no—
925C4×#41—794no—
926C4×#41—792no—
927C4×#41—794no—
928C4×#41C2×D7912yescomplemented
929C2×C4×Q8—791no—
930C2×C4×Q8C2×D7911yescharacteristic, complemented
931C2×C4×D4—791no—
932C2×C4×D4—792no—
933C2×C4×D4—791no—
934C2×C4×D4—792no—
935C2×#117—792no—
936C2×#117—794no—
937C2×#117—791no—
938C2×#117—792no—
939C2×#117—794no—
940C22×C4⋊C4—791no—
941C22×C4⋊C4—792no—
942C2×#41—794no—
943C2×#41—794no—
944C2×#41—792no—
945C2×#41—794no—
946C2×#41—794no—
947C2×#41—794no—
948C2×#41—792no—
949C2×#41—798no—
950C2×#41—792no—
951C2×#41—794no—
952C2×#41—1588no—
953C2×#41—15816no—
954C2×#41C22×D7912yes—
955C22×Q8—794no—
956C22×Q8—792no—
957C22×Q8C22×D7911yescharacteristic
958C22×D4—794no—
959C22×D4—794no—
960C22×D4—792no—
961C22×D4—792no—
962C22×D4—791no—
963C23×C4—791no—
964C23×C4—792no—
965C23×C4—792no—
966C23×C4—792no—
967C23×C4—792no—
968C23×C4—794no—
969C4⋊Q8—798no—
970C4⋊Q8—794no—
971C4⋊Q8—794no—
972C4⋊Q8—794no—
973C4⋊Q8—798no—
974C4⋊Q8—794no—
975C4⋊Q8C22×D7914yes—
976C4⋊Q8C22×D7914yes—
977#127—794no—
978#127—794no—
979#126—798no—
980#126—798no—
981#126—798no—
982#126—798no—
983#126—798no—
984#126—798no—
985#126—798no—
986#126—798no—
987#126—798no—
988#126—798no—
989#126C22×D7918yes—
990#126C22×D7918yes—
991#125—794no—
992#125—794no—
993#125—798no—
994#125—798no—
995#125—798no—
996#125—798no—
997#125—798no—
998#125—798no—
999#125—794no—
1000#125—794no—
1001#125C22×D7914yes—
1002#125C22×D7914yes—
1003#125C22×D7918yes—
1004#124—794no—
1005#124—794no—
1006#124—798no—
1007#124—798no—
1008#124—798no—
1009#124—798no—
1010#124—794no—
1011#124—794no—
1012#124—798no—
1013#124C22×D7914yes—
1014#124C22×D7914yes—
1015#123—798no—
1016#123—798no—
1017#123—798no—
1018#123—798no—
1019#123—798no—
1020#123—798no—
1021#123—798no—
1022#123—798no—
1023#123—798no—
1024#123—798no—
1025#123—798no—
1026#123—798no—
1027#123—798no—
1028#123—798no—
1029#123C22×D7918yes—
1030#123C22×D7918yes—
1031C22⋊Q8—794no—
1032C22⋊Q8—794no—
1033C22⋊Q8—794no—
1034C22⋊Q8—794no—
1035C22⋊Q8—794no—
1036C22⋊Q8—794no—
1037C22⋊Q8—794no—
1038C22⋊Q8—794no—
1039C22⋊Q8—798no—
1040C22⋊Q8—798no—
1041C22⋊Q8—794no—
1042C22⋊Q8—798no—
1043C22⋊Q8—798no—
1044C22⋊Q8—798no—
1045C22⋊Q8—794no—
1046C22⋊Q8—798no—
1047C22⋊Q8—798no—
1048C22⋊Q8—798no—
1049C22⋊Q8—798no—
1050C22⋊Q8—798no—
1051C22⋊Q8C22×D7914yes—
1052C22⋊Q8C22×D7914yes—
1053C22⋊Q8C22×D7914yes—
1054C22⋊Q8C22×D7914yes—
1055C22⋊Q8C22×D7918yes—
1056#121—798no—
1057#121—794no—
1058#121—798no—
1059#121—794no—
1060#121—794no—
1061#121—798no—
1062#121—794no—
1063#121—794no—
1064#121—794no—
1065#121—794no—
1066#121—798no—
1067#121—794no—
1068#121—794no—
1069#121—794no—
1070#121—794no—
1071#121—794no—
1072#121—798no—
1073#121—798no—
1074#121—798no—
1075#121—798no—
1076#121—798no—
1077#121—798no—
1078#121—798no—
1079#121—798no—
1080#121—798no—
1081#121—798no—
1082#121—798no—
1083#121C22×D7914yes—
1084#121C22×D7914yes—
1085#120—798no—
1086#120—798no—
1087#120—798no—
1088#120—798no—
1089C4×Q8—794no—
1090C4×Q8—794no—
1091C4×Q8—792no—
1092C4×Q8—792no—
1093C4×Q8—792no—
1094C4×Q8—792no—
1095C4×Q8—794no—
1096C4×Q8—794no—
1097C4×Q8—798no—
1098C4×Q8—792no—
1099C4×Q8—792no—
1100C4×Q8—794no—
1101C4×Q8—794no—
1102C4×Q8—794no—
1103C4×Q8C22×D7914yes—
1104C4×Q8C22×D7914yes—
1105C4×Q8C22×D7912yes—
1106C4×Q8C22×D7912yes—
1107C4×Q8C22×D7914yes—
1108C4×D4—794no—
1109C4×D4—794no—
1110C4×D4—792no—
1111C4×D4—792no—
1112C4×D4—794no—
1113C4×D4—794no—
1114C4×D4—794no—
1115C4×D4—794no—
1116C4×D4—794no—
1117C4×D4—794no—
1118C4×D4—798no—
1119C4×D4—794no—
1120C4×D4—794no—
1121C4×D4—798no—
1122C4×D4—798no—
1123C4×D4—792no—
1124C4×D4—792no—
1125C4×D4—794no—
1126C4×D4—794no—
1127C4×D4—798no—
1128C4×D4—798no—
1129C4×D4—798no—
1130C4×D4—794no—
1131C4×D4—794no—
1132C4×D4—794no—
1133C4×D4—794no—
1134C4×D4—794no—
1135C4×D4—794no—
1136C4×D4—798no—
1137C4×D4—798no—
1138C4×D4—798no—
1139C4×D4—798no—
1140C4×D4—794no—
1141C4×D4—794no—
1142C4×D4—794no—
1143C4×D4—794no—
1144C4×D4—794no—
1145C4×D4—794no—
1146C4×D4—792no—
1147C4×D4—792no—
1148C4×D4—794no—
1149C4×D4—794no—
1150C4×D4—798no—
1151C4×D4—794no—
1152C4×D4C22×D7914yes—
1153C4×D4C22×D7914yes—
1154C4×D4C22×D7912yes—
1155C4×D4C22×D7912yes—
1156C4×D4C22×D7914yes—
1157#117—792no—
1158#117—794no—
1159#117—792no—
1160#117—792no—
1161#117—794no—
1162#117—794no—
1163#117—794no—
1164#117—794no—
1165#117—798no—
1166#117—794no—
1167#117—794no—
1168#117—794no—
1169#117—798no—
1170#117—792no—
1171#117—792no—
1172#117—794no—
1173#117—792no—
1174#117—792no—
1175#117—794no—
1176#117—794no—
1177#117—794no—
1178#117—794no—
1179#117—794no—
1180#117—798no—
1181#117—798no—
1182#117—794no—
1183#117—798no—
1184#117—798no—
1185#117C22×D7912yes—
1186#117C22×D7914yes—
1187#117C22×D7918yes—
1188C2×C4⋊C4—791no—
1189C2×C4⋊C4—792no—
1190C2×C4⋊C4—791no—
1191C2×C4⋊C4—792no—
1192C2×C4⋊C4—791no—
1193C2×C4⋊C4—794no—
1194C2×C4⋊C4—794no—
1195C2×C4⋊C4—794no—
1196C2×C4⋊C4—794no—
1197C2×C4⋊C4—798no—
1198C2×C4⋊C4—798no—
1199C2×C4⋊C4—792no—
1200C2×C4⋊C4—792no—
1201C2×C4⋊C4—794no—
1202C2×C4⋊C4—794no—
1203C2×C4⋊C4—794no—
1204C2×C4⋊C4—794no—
1205C2×C4⋊C4—798no—
1206C2×C4⋊C4C22×D7911yescharacteristic
1207C2×C4⋊C4C22×D7912yes—
1208C2×C22⋊C4—791no—
1209C2×C22⋊C4—791no—
1210C2×C22⋊C4—792no—
1211C2×C22⋊C4—792no—
1212C2×C22⋊C4—794no—
1213C2×C22⋊C4—794no—
1214C2×C22⋊C4—794no—
1215C2×C22⋊C4—794no—
1216C2×C22⋊C4—794no—
1217C2×C22⋊C4—798no—
1218C2×C42—791no—
1219C2×C42—792no—
1220C2×C42—794no—
1221C2×C42—794no—
1222C2×C42—794no—
1223C2×C42—794no—
1224C2×C42C22×D7911yescharacteristic
1225C2×C42C22×D7912yes—
1226C2×C42C22×D7914yes—
1227C24—791no—
1228C24—794no—
1229C24—792no—
1230#41—28no—
1231#41—6328no—
1232#41—6324no—
1233#41—6324no—
1234#41—15816no—
1235#41—15816no—
1236#41—1588no—
1237#41—15816no—
1238#41—15816no—
1239#41—1588no—
1240#41—1588no—
1241C2×Q8—24no—
1242C2×Q8—794no—
1243C2×Q8—798no—
1244C2×Q8—794no—
1245C2×Q8—792no—
1246C2×Q8—6324no—
1247C2×Q8—1588no—
1248C2×Q8C23×D7912yes—
1249C2×Q8C23×D7914yes—
1250C2×Q8C23×D7914yes—
1251C2×D4—798no—
1252C2×D4—798no—
1253C2×D4—798no—
1254C2×D4—794no—
1255C2×D4—794no—
1256C2×D4—794no—
1257C2×D4—798no—
1258C2×D4—798no—
1259C2×D4—794no—
1260C2×D4—794no—
1261C2×D4—794no—
1262C2×D4—794no—
1263C2×D4—792no—
1264C2×D4—794no—
1265C2×D4—6324no—
1266C2×D4—1588no—
1267C2×D4—1588no—
1268C2×D4—15816no—
1269C2×D4—1584no—
1270C2×D4C23×D7914yes—
1271C2×D4C23×D7912yes—
1272C2×D4C23×D7914yes—
1273C22×C4—791no—
1274C22×C4—791no—
1275C22×C4—792no—
1276C22×C4—794no—
1277C22×C4—794no—
1278C22×C4—794no—
1279C22×C4—794no—
1280C22×C4—794no—
1281C22×C4—794no—
1282C22×C4—794no—
1283C22×C4—794no—
1284C22×C4—794no—
1285C22×C4—794no—
1286C22×C4—794no—
1287C22×C4—794no—
1288C22×C4—798no—
1289C22×C4—791no—
1290C22×C4—798no—
1291C22×C4—792no—
1292C22×C4—792no—
1293C22×C4—794no—
1294C22×C4—794no—
1295C22×C4—794no—
1296C22×C4—794no—
1297C22×C4—798no—
1298C22×C4—6322no—
1299C22×C4—6322no—
1300C22×C4—6322no—
1301C22×C4—1588no—
1302C22×C4—15816no—
1303C22×C4C23×D7912yes—
1304C22×C4C23×D7914yes—
1305C22×C4C23×D7911yescharacteristic
1306C22×C4C23×D7911yescharacteristic
1307C22×C4C23×D7912yes—
1308C22×C4C23×D7914yes—
1309C22×C4C23×D7914yes—
1310C22×C4C23×D7911yescharacteristic
1311C4⋊C4—792no—
1312C4⋊C4—792no—
1313C4⋊C4—798no—
1314C4⋊C4—792no—
1315C4⋊C4—792no—
1316C4⋊C4—794no—
1317C4⋊C4—794no—
1318C4⋊C4—794no—
1319C4⋊C4—794no—
1320C4⋊C4—794no—
1321C4⋊C4—794no—
1322C4⋊C4—798no—
1323C4⋊C4—798no—
1324C4⋊C4—798no—
1325C4⋊C4—798no—
1326C4⋊C4—798no—
1327C4⋊C4—798no—
1328C4⋊C4—794no—
1329C4⋊C4—794no—
1330C4⋊C4—794no—
1331C4⋊C4—792no—
1332C4⋊C4—792no—
1333C4⋊C4—794no—
1334C4⋊C4—794no—
1335C4⋊C4—794no—
1336C4⋊C4—798no—
1337C4⋊C4—794no—
1338C4⋊C4C23×D7914yes—
1339C4⋊C4C23×D7918yes—
1340C4⋊C4C23×D7912yes—
1341C4⋊C4C23×D7912yes—
1342C4⋊C4C23×D7914yes—
1343C4⋊C4C23×D7914yes—
1344C4⋊C4C23×D7914yes—
1345C4⋊C4C23×D7914yes—
1346C4⋊C4C23×D7918yes—
1347C4⋊C4C23×D7918yes—
1348C4⋊C4C23×D7918yes—
1349C22⋊C4—794no—
1350C22⋊C4—794no—
1351C22⋊C4—794no—
1352C22⋊C4—798no—
1353C22⋊C4—792no—
1354C22⋊C4—791no—
1355C22⋊C4—791no—
1356C22⋊C4—794no—
1357C22⋊C4—794no—
1358C22⋊C4—792no—
1359C22⋊C4—791no—
1360C22⋊C4—791no—
1361C22⋊C4—794no—
1362C22⋊C4—794no—
1363C22⋊C4—798no—
1364C22⋊C4—794no—
1365C22⋊C4—794no—
1366C22⋊C4—794no—
1367C22⋊C4—794no—
1368C22⋊C4—798no—
1369C22⋊C4—798no—
1370C22⋊C4—798no—
1371C22⋊C4—798no—
1372C22⋊C4—798no—
1373C22⋊C4—798no—
1374C22⋊C4—798no—
1375C22⋊C4—798no—
1376C22⋊C4C23×D7914yes—
1377C22⋊C4C23×D7914yes—
1378C22⋊C4C23×D7914yes—
1379C22⋊C4C23×D7918yes—
1380C22⋊C4C23×D7918yes—
1381C22⋊C4C23×D7918yes—
1382C42—792no—
1383C42—792no—
1384C42—794no—
1385C42—794no—
1386C42—794no—
1387C42—794no—
1388C42—798no—
1389C42—794no—
1390C42—794no—
1391C42—794no—
1392C42—794no—
1393C42—794no—
1394C42C23×D7912yes—
1395C42C23×D7914yes—
1396C42C23×D7912yes—
1397C42C23×D7914yes—
1398C42C23×D7914yes—
1399C42C23×D7914yes—
1400C42C23×D7914yes—
1401C23—3162no—
1402C23—3161no—
1403C23—3162no—
1404C23—3161no—
1405C23—3164no—
1406C23—3164no—
1407C23—794no—
1408C23—791no—
1409C23—791no—
1410C23—794no—
1411C23—794no—
1412C23—1588no—
1413C23—1584no—
1414C23C24×D7914yes—
1415C23C24×D7911yescharacteristic
1416Q8—28no—
1417Q8—24no—
1418Q8—44no—
1419Q8—3164no—
1420Q8—3168no—
1421Q8—1588no—
1422Q8—1584no—
1423D4—28no—
1424D4—24no—
1425D4—44no—
1426D4—3164no—
1427D4—3168no—
1428D4—3168no—
1429D4—3168no—
1430D4—3168no—
1431D4—3168no—
1432D4—1588no—
1433D4—1588no—
1434D4—1588no—
1435D4—1588no—
1436D4—1588no—
1437D4—1588no—
1438D4—1584no—
1439D4—1588no—
1440C2×C4—24no—
1441C2×C4—28no—
1442C2×C4—41no—
1443C2×C4—42no—
1444C2×C4—41no—
1445C2×C4—44no—
1446C2×C4—44no—
1447C2×C4—3164no—
1448C2×C4—3164no—
1449C2×C4—3168no—
1450C2×C4—3164no—
1451C2×C4—3164no—
1452C2×C4—3164no—
1453C2×C4—3164no—
1454C2×C4—3164no—
1455C2×C4—3164no—
1456C2×C4—3164no—
1457C2×C4—3164no—
1458C2×C4—3161no—
1459C2×C4—3162no—
1460C2×C4—3164no—
1461C2×C4—3161no—
1462C2×C4—3164no—
1463C2×C4—792no—
1464C2×C4—794no—
1465C2×C4—798no—
1466C2×C4—798no—
1467C2×C4—792no—
1468C2×C4—791no—
1469C2×C4—791no—
1470C2×C4—794no—
1471C2×C4—794no—
1472C2×C4—794no—
1473C2×C4—794no—
1474C2×C4—1588no—
1475C2×C4—15816no—
1476C2×C4—1588no—
1477C2×C4—1588no—
1478C2×C4—1588no—
1479C2×C4#41×D7914yes—
1480C2×C4C24×D7911yescharacteristic
1481C2×C4C24×D7912yes—
1482C2×C4C24×D7914yes—
1483C2×C4C24×D7914yes—
1484C2×C4C24×D7914yes—
1485C2×C4C24×D7914yes—
1486C2×C4C24×D7911yescharacteristic
1487C2×C4C24×D7914yes—
1488C2×C4C24×D7912yes—
1489C22—21no—
1490C22—21no—
1491C22—24no—
1492C22—24no—
1493C22—24no—
1494C22—3168no—
1495C22—3164no—
1496C22—792no—
1497C22—792no—
1498C22—6328no—
1499C22—1584no—
1500C22—1584no—
1501C22—1584no—
1502C22—1584no—
1503C22—1584no—
1504C22—1584no—
1505C22—1581no—
1506C22—1581no—
1507C22—1581no—
1508C22—1581no—
1509C22C2×#41×D7912yes—
1510C22C25×D7911yescharacteristic
1511C4—24no—
1512C4—24no—
1513C4—22no—
1514C4—24no—
1515C4—24no—
1516C4—21no—
1517C4—21no—
1518C4—24no—
1519C4—794no—
1520C4—1584no—
1521C4—1581no—
1522C4—1581no—
1523C4—1584no—
1524C4—1584no—
1525C4—1582no—
1526C4—1584no—
1527C4C2×#41×D7914yes—
1528C2—22no—
1529C2—44no—
1530C2—3164no—
1531C2—3164no—
1532C2—1582no—
1533C2—1582no—
1534C2C22×#41×D7911yescharacteristic
1535C2#2377821111yescharacteristic
1536C2#2377821211yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3461C2
hypercenter#3461D79
hypocenterC79#62856
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3461

Complements

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

NH ≅ G/Ntype
1. #23777323C2semidirect
2. #23777315C2semidirect
3. #23777312C2semidirect
4. #23777305C2semidirect
5. #23777235C2semidirect
6. #23777232C2semidirect
7. #23777147C2semidirect
8. #23777144C2semidirect
9. #23777133C2semidirect
10. #23777123C2semidirect
11. #23777112C2semidirect
12. #23777105C2semidirect
13. #23776833C2semidirect
14. #23776824C2semidirect
15. #23776823C2semidirect
16. #23776817C2semidirect
17. #23776816C2semidirect
18. #544×D79C2semidirect
19. #23776732C2semidirect
20. #537×D79C2semidirect
21. #23776599C2semidirect
22. C2×#19099045C2semidirect
23. C79×#3461C2semidirect
26. #19099285C22semidirect
27. #19099280C22semidirect
28. #19099276C22semidirect
29. #19099275C22semidirect
30. #19099269C22semidirect
31. #19099267C22semidirect
32. #19099266C22semidirect
33. #19099266C22semidirect
34. #19099264C22semidirect
35. #19099264C22semidirect
36. #19099264C22semidirect
37. #19099264C22semidirect
38. #19099263C22semidirect
39. #19099262C22semidirect
40. #19099258C22semidirect
41. #19099258C22semidirect
42. #19099257C22semidirect
43. #19099254C22semidirect
44. #19099251C22semidirect
45. #19099249C22semidirect
46. #19099246C22semidirect
47. #19099245C22semidirect
48. #19099245C22semidirect
49. #19099245C22semidirect
50. #19099240C22semidirect
51. #19099238C22semidirect
52. #19099238C22semidirect
53. #19099237C22semidirect
54. #19099225C22semidirect
55. #19099223C22semidirect
56. #19099221C22semidirect
57. #19099215C22semidirect
58. #19099211C22semidirect
59. #19099208C22semidirect
60. #19099206C22semidirect
61. #19099205C22semidirect
62. #19099194C22semidirect
63. #19099193C22semidirect
64. #19099192C22semidirect
65. #19099191C22semidirect
66. #19099190C22semidirect
67. #19099187C22semidirect
68. #19099186C22semidirect
69. #19099186C22semidirect
70. #19099185C22semidirect
71. #19099185C22semidirect
72. #19099184C22semidirect
73. #19099182C22semidirect
74. #19099174C22semidirect
75. #19099173C22semidirect
76. #19099171C22semidirect
77. #19099169C22semidirect
78. #19099168C22semidirect
79. #19099166C22semidirect
80. #19099164C22semidirect
81. #19099160C22semidirect
82. #19099157C22semidirect
83. #19099153C22semidirect
84. #19099150C22semidirect
85. #19099146C22semidirect
87. #19099143C22semidirect
88. #19099143C22semidirect
89. #19099143C22semidirect
90. #19099142C22semidirect
94. #19099137C22semidirect
95. #19099132C22semidirect
97. #19099127C22semidirect
99. #19099118C22semidirect
100. #19099117C22semidirect
101. #19099115C22semidirect
102. #19099114C22semidirect
103. #19099114C22semidirect
104. #19099113C22semidirect
105. #19099112C22semidirect
106. #19099110C22semidirect
107. #19099108C22semidirect
108. C4⋊Q8×D79C22semidirect
109. #19099100C22semidirect
110. #19099100C22semidirect
111. #19099099C22semidirect
112. #19099099C22semidirect
113. #19099098C22semidirect
114. #19099097C22semidirect
115. #19099097C22semidirect
116. #19099092C22semidirect
117. #19099090C22semidirect
118. #125×D79C22semidirect
121. #19099076C22semidirect
122. #19099073C22semidirect
123. #19099072C22semidirect
124. #19099071C22semidirect
126. C22⋊Q8×D79C22semidirect
128. #121×D79C22semidirect
131. #19099045C22semidirect
132. #19099045C22semidirect
133. #19099045C22semidirect
134. #19099045C22semidirect
135. #19099042C22semidirect
136. #19099042C22semidirect
137. #19099042C22semidirect
138. #19099042C22semidirect
139. #19099039C22semidirect
140. #19099039C22semidirect
143. #19099035C22semidirect
144. #19099035C22semidirect
145. #41×Dic79C22semidirect
146. C4×#11929624C22semidirect
147. C4×#11929624C22semidirect
148. #19099031C22semidirect
149. #19099031C22semidirect
150. C2×Q8×Dic79C22semidirect
152. C2×C4×D316C22semidirect
154. C2×#14579123C22semidirect
156. C2×#14579118C22semidirect
157. C2×#14579118C22semidirect
159. #117×D79C22semidirect
161. C2×C4⋊C4×D79C22semidirect
162. #544×C79C22semidirect
163. #542×C79C22semidirect
164. #541×C79C22semidirect
165. #539×C79C22semidirect
167. #536×C79C22semidirect
168. #533×C79C22semidirect
169. #529×C79C22semidirect
170. #529×C79C22semidirect
171. C4×#41×C79C22semidirect
172. C2×C4×Q8×C79C22semidirect
508. C2×C4×D79#41semidirect
783. #3461D79semidirect
792. C79#62856semidirect
836. #544C2×D79semidirect
844. #542C2×D79semidirect
848. #541C2×D79semidirect
855. #539C2×D79semidirect
869. #536C2×D79semidirect
877. #533C2×D79semidirect
894. #529C2×D79semidirect
895. #529C2×D79semidirect
928. C4×#41C2×D79semidirect
930. C2×C4×Q8C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237773232
#237773152
#237773122
#237773052
#237772352
#237772322
#237771472
#237771442
#237771332
#237771232
#237771122
#237771052
#237768332
#237768242
#237768232
#237768172
#237768162
#544×D792
#237767322
#537×D792
#237765992
C2×#190990452
C79×#34612
#6285679