Finite Group Databasebeta

← #35197461

Subgroups — #35197461

Order 20224.

10986 conjugacy classes of subgroups.

The subgroup lattice has 1626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099399C211yesmaximal, characteristic, complemented
2C2×2−1+4×D79C211yesmaximal, characteristic, complemented
3#23777191C212yesmaximal, complemented
4#23777186C216yesmaximal, complemented
5#23777184C212yesmaximal, complemented
6#23777179C216yesmaximal, complemented
7#23777081C211yesmaximal, characteristic, complemented
8#23777080C211yesmaximal, characteristic, complemented
9#23777078C213yesmaximal, complemented
10#23777076C213yesmaximal, complemented
11#23777075C213yesmaximal, complemented
12#23777073C211yesmaximal, characteristic, complemented
13#23777072C213yesmaximal, complemented
14#23777050C212yesmaximal, complemented
15#23777046C212yesmaximal, complemented
16#23777039C216yesmaximal, complemented
17#23777037C216yesmaximal, complemented
18#23776730C213yesmaximal, complemented
19#23776728C213yesmaximal, complemented
20C2×#19099136C213yesmaximal, complemented
21#536×D79C213yesmaximal, complemented
22#23776600C211yesmaximal, characteristic, complemented
23C79×#3489C211yesmaximal, characteristic, complemented
24#19099399—216no—
25C2×#14579209C2211yescharacteristic
26C2×#14579209C2213yescomplemented
27C2×#14579209C2212yescomplemented
28C2×#14579209C2211yescharacteristic, complemented
29C2×#14579208C2211yescharacteristic
30C2×#14579208C2213yescomplemented
31C2×#14579208C2211yescharacteristic, complemented
32C2×#14579208C2213yescomplemented
33C2×#14579208C2216yescomplemented
342−1+4×D79—216no—
35C2×#14579207C2213yes—
36C2×#14579207C2211yescharacteristic, complemented
37C2×#14579206C2213yes—
38C2×#14579206C2213yescomplemented
39C22×#11929624C2213yes—
40C22×#11929624C2213yescomplemented
41C2×#41×D79C2213yes—
42C2×#41×D79C2211yescharacteristic
43C2×#41×D79C2216yescomplemented
44C2×#41×D79C2211yescharacteristic, complemented
45C2×#41×D79C2213yescomplemented
46C2×#41×D79C2213yescomplemented
47C22×Q8×D79C2212yescomplemented
48C22×Q8×D79C2213yescomplemented
49Q8×D316C2212yescomplemented
50D4×Dic158C2216yescomplemented
51#19099228C2216yescomplemented
52Q8×C22⋊D79C2212yescomplemented
53Q8×C22⋊D79C2212yescomplemented
54#19099226C2216yescomplemented
55#19099226C2216yescomplemented
56#19099225C2212yescomplemented
57#19099224C2212yescomplemented
58#19099223C2216yescomplemented
59#19099222C2216yescomplemented
60#19099221C2216yescomplemented
61#19099220C2212yescomplemented
62#19099219C2216yescomplemented
63#19099218C2216yescomplemented
64#19099217C2216yescomplemented
65#19099216C2216yescomplemented
66#19099215C2216yescomplemented
67#19099215C2216yescomplemented
68#19099214C22112yescomplemented
69#19099213C22112yescomplemented
70#19099212C2216yescomplemented
71#19099212C2216yescomplemented
72#19099211C22112yescomplemented
73#19099211C22112yescomplemented
74#19099210C2216yescomplemented
75#19099209C2216yescomplemented
76#19099208C2216yescomplemented
77#19099207C2216yescomplemented
78#19099206C2216yescomplemented
79#19099205C22112yescomplemented
80#19099204C2216yescomplemented
81#19099203C22112yescomplemented
82#19099202C22112yescomplemented
83#19099201C2216yescomplemented
84#19099200C22112yescomplemented
85#19099144C2213yescomplemented
86#19099143C2213yescomplemented
87#19099143C2213yescomplemented
88#19099142C2213yescomplemented
89#19099142C2213yescomplemented
90#19099141C2213yescomplemented
91#19099141C2213yescomplemented
92#19099139C2213yescomplemented
93#19099138C2216yescomplemented
94#19099137C2213yescomplemented
95#19099136C2216yescomplemented
96#19099136C2216yescomplemented
97#19099136C2216yescomplemented
98#19099136C2216yescomplemented
99#19099136C2216yescomplemented
100#19099136C2216yescomplemented
101#19099136C2216yescomplemented
102#19099136C2213yescomplemented
103#19099136C2216yescomplemented
104#19099136C2213yescomplemented
105#19099135C2216yescomplemented
106#19099135C22112yescomplemented
107#19099134C2213yescomplemented
108#19099133C2216yescomplemented
109#19099129C2216yescomplemented
110#19099129C2213yescomplemented
111#19099129C2211yescharacteristic, complemented
112#19099128C2216yescomplemented
113#19099124C2216yescomplemented
114#19099123C2216yescomplemented
115#19099121C22112yescomplemented
116#19099110C2216yescomplemented
117#19099110C2216yescomplemented
118#19099108C22112yescomplemented
119C2×#14579160C2216yescomplemented
120C4⋊Q8×D79C2216yescomplemented
121C2×#14579147C2216yescomplemented
122#124×D79C2216yescomplemented
123#19099076C2216yescomplemented
124#19099076C2216yescomplemented
125#19099075C2213yescomplemented
126#19099074C2213yescomplemented
127#19099073C2216yescomplemented
128#19099073C2216yescomplemented
129#19099072C2216yescomplemented
130#19099072C2216yescomplemented
131#19099070C2213yescomplemented
132C2×#14579146C2216yescomplemented
133C2×#14579143C2216yescomplemented
134#123×D79C22112yescomplemented
135C2×#14579141C2213yescomplemented
136C2×#14579140C2213yescomplemented
137C2×#14579137C2213yescomplemented
138C22⋊Q8×D79C2216yescomplemented
139C22⋊Q8×D79C2216yescomplemented
140#19099046C2211yescharacteristic, complemented
141#19099044C2213yescomplemented
142#19099043C2213yescomplemented
143#19099039C2212yescomplemented
144#19099035C2216yescomplemented
145C4×#11929625C2212yescomplemented
146C4×#11929623C2216yescomplemented
147C2×#14579119C2213yescomplemented
148#117×D79C2213yescomplemented
149C2×2−1+4×C79C2211yescharacteristic, complemented
150C22×#41×C79C2211yescharacteristic, complemented
151D4×Q8×C79C2212yescomplemented
152#548×C79C2212yescomplemented
153#547×C79C2216yescomplemented
154#546×C79C2216yescomplemented
155#537×C79C2213yescomplemented
156#536×C79C2213yescomplemented
157#525×C79C2213yescomplemented
158C2×C22⋊Q8×C79C2213yescomplemented
159#520×C79C2211yescharacteristic, complemented
160#14579209—216no—
161#14579209—28no—
162#14579209—224no—
163#14579209—28no—
164#14579208—28no—
165#14579208—224no—
166#14579208—248no—
167#14579208—224no—
168#14579208—28no—
169#14579207—28no—
170#14579207—224no—
171#14579206—224no—
172#14579206—224no—
173C2×#11929625C2313yes—
174C2×#11929625C2313yes—
175C2×#11929625C2311yescharacteristic
176C2×#11929625C2313yes—
177C2×#11929625C2316yes—
178C2×#11929625C2311yescharacteristic
179C2×#11929624—224no—
180C2×#11929624—224no—
181C2×#11929624C2313yes—
182C2×#11929624C2311yescharacteristic
183C2×#11929624C2313yes—
184C2×#11929624C2313yes—
185C2×#11929624C2313yes—
186C2×#11929624C2313yes—
187C2×#11929624C2313yes—
188C2×#11929624C2313yes—
189C2×#11929624C2316yes—
190C2×#11929624C2313yes—
191C2×#11929624C2313yes—
192C2×#11929624C2313yes—
193C2×#11929624C2316yes—
194C2×#11929624C2313yes—
195C2×#11929624C23112yes—
196C2×#11929624C2316yes—
197C2×#11929624C2313yes—
198C2×#11929623C2313yes—
199C2×#11929623C2316yes—
200C2×#11929623C2313yes—
201C2×#11929623C2313yes—
202C2×#11929623C2316yes—
203C2×#11929623C2313yes—
204C2×#11929623C23112yes—
205C2×#11929623C2316yes—
206C2×#11929623C2316yes—
207C2×#11929623C2313yes—
208#41×D79—28no—
209#41×D79—224no—
210#41×D79—248no—
211#41×D79—224no—
212#41×D79—224no—
213#41×D79D4116yescomplemented
214C22×Dic158C2313yes—
215C22×Dic158C2313yes—
216C22×Dic158C2316yes—
217C22×Dic158C2316yes—
218C22×Dic158C2313yes—
219C2×Q8×D79—216no—
220C2×Q8×D79—224no—
221C2×Q8×D79C2313yes—
222C2×Q8×D79C2316yes—
223C2×Q8×D79C2316yes—
224C2×Q8×D79C2316yes—
225C2×Q8×D79C2313yes—
226C2×Q8×D79C2311yescharacteristic
227C2×Q8×D79C2313yes—
228C2×Q8×D79C2312yes—
229C2×Q8×D79C2316yes—
230C2×Q8×D79C2311yescharacteristic
231C22×D316C2313yes—
232C22×D316C2313yes—
233C22×C22⋊D79C2313yes—
234C22×C22⋊D79C2316yes—
235C22×C22⋊D79C2313yes—
236C2×D4×D79C2316yes—
237C2×D4×D79C2313yes—
238C2×D4×D79C2313yes—
239C2×D4×D79C2316yes—
240C2×D4×D79C2313yes—
241C2×D4×D79C2316yes—
242C2×D4×D79C2311yescharacteristic
243C2×D4×D79C2313yes—
244C22×C4×D79C2316yes—
245C22×C4×D79C2313yes—
246C22×C4×D79C2316yes—
247C22×C4×D79C2316yes—
248C22×C4×D79C2313yes—
249#14579161C2316yes—
250#14579160C23112yes—
251#14579160C2316yes—
252#14579160C23112yes—
253#14579160C23112yes—
254#14579160C2316yes—
255#14579159C2316yes—
256#14579159C2316yes—
257#14579157C2316yes—
258#14579157C2312yes—
259#14579150C2316yes—
260#14579149C2316yes—
261#14579148C2316yes—
262#14579147C2316yes—
263#14579147C23112yes—
264#14579147C23112yes—
265#14579147C23112yes—
266#14579147C2316yes—
267#14579147C2316yes—
268#14579147C2312yes—
269#14579146C2316yes—
270#14579146C23112yes—
271#14579146C23112yes—
272#14579146C23112yes—
273#14579146C2316yes—
274#14579146C23112yes—
275#14579145C23112yes—
276#14579145C2316yes—
277#14579144C23112yes—
278#14579144C2316yes—
279#14579143C2316yes—
280#14579143C23112yes—
281#14579143C23112yes—
282#14579143C23112yes—
283#14579143C23112yes—
284#14579143C2316yes—
285#14579142C23112yes—
286#14579142C2316yes—
287#14579141C2313yes—
288#14579141C2316yes—
289#14579141C2316yes—
290#14579141C2316yes—
291#14579141C2313yes—
292#14579141C2316yes—
293#14579140C2313yes—
294#14579140C2316yes—
295#14579140C2316yes—
296#14579140C2316yes—
297#14579140C2316yes—
298#14579140C2313yes—
299#14579139C23112yes—
300#14579139C23112yes—
301#14579139C2316yes—
302#14579139C2316yes—
303#14579138C2316yes—
304#14579138C2316yes—
305#14579138C23112yes—
306#14579138C23112yes—
307#14579137C2313yes—
308#14579137C2316yes—
309#14579137C2316yes—
310#14579137C2316yes—
311#14579137C2313yes—
312#14579137C2316yes—
313#14579136C2311yescharacteristic
314#14579136C2313yes—
315#14579136C2316yes—
316#14579136C2316yes—
317#14579136C2316yes—
318#14579135C2313yes—
319#14579135C2316yes—
320#14579135C2311yescharacteristic
321#14579135C23112yes—
322#14579134C2316yes—
323#14579134C2316yes—
324#14579134C2316yes—
325#14579134C2316yes—
326#14579134C2316yes—
327#14579134C2316yes—
328#14579133C23112yes—
329#14579133C23112yes—
330#14579133C2316yes—
331#14579133C2316yes—
332#14579132C2313yes—
333#14579132C2316yes—
334#14579132C2311yescharacteristic
335#14579132C2316yes—
336#14579132C2316yes—
337#14579131C23112yes—
338#14579131C2316yes—
339#14579131C2312yes—
340#14579131C2316yes—
341#14579130C2316yes—
342#14579129C23112yes—
343#14579129C2316yes—
344#14579129C2312yes—
345#14579129C2316yes—
346Q8×Dic79C2312yes—
347C4×Dic158C2316yes—
348#14579126C2316yes—
349C4×D316C2316yes—
350C4×D316C2316yes—
351C4×D316C2316yes—
352D4×Dic79C23112yes—
353D4×Dic79C2316yes—
354#14579123C2316yes—
355#14579123C23112yes—
356C4×C22⋊D79C2316yes—
357C4×C22⋊D79C23112yes—
358C4×C22⋊D79C2316yes—
359C4×C22⋊D79C2316yes—
360C4×C22⋊D79C2316yes—
361(C22⋊D79)⋊C4C23112yes—
362(C22⋊D79)⋊C4C23112yes—
363(C22⋊D79)⋊C4C23112yes—
364#14579120C2313yes—
365#14579119C2311yescharacteristic
366#14579119C2313yes—
367#14579119C2316yes—
368#14579119C2316yes—
369#14579119C2316yes—
370#14579118C2316yes—
371#14579117C2316yes—
372C2×C4⋊Dic79C2313yes—
373C2×C4⋊Dic79C2316yes—
374C2×Dic79⋊C4C2316yes—
375C2×Dic79⋊C4C2316yes—
376C4⋊C4×D79C2313yes—
377C4⋊C4×D79C2313yes—
378C4⋊C4×D79C23112yes—
379C4⋊C4×D79C23112yes—
380C2×C22⋊Dic79C2316yes—
381C2×(C2×D79)⋊C4C2316yes—
382C2×(C2×D79)⋊C4C2316yes—
383C2×(C2×D79)⋊C4C2316yes—
384C22⋊C4×D79C23112yes—
385C22⋊C4×D79C23112yes—
386C22⋊C4×D79C2316yes—
387C2×C4×Dic79C2316yes—
388C42×D79C2316yes—
3892−1+4×C79—28no—
390C2×#41×C79—28no—
391C2×#41×C79C2313yes—
392C2×#41×C79C2311yescharacteristic
393C2×#41×C79C2313yes—
394C2×#41×C79C2316yes—
395C2×#41×C79C2313yes—
396C2×#41×C79C2311yescharacteristic
397C22×Q8×C79C2313yes—
398C22×Q8×C79C2311yescharacteristic
399C22×Q8×C79C2312yes—
400C22×D4×C79C2313yes—
401C23×C4×C79C2313yes—
402C4⋊Q8×C79C2316yes—
403#124×C79C2316yes—
404#123×C79C23112yes—
405#123×C79C2316yes—
406C22⋊Q8×C79C2313yes—
407C22⋊Q8×C79C2316yes—
408C22⋊Q8×C79C2316yes—
409C22⋊Q8×C79C2316yes—
410C22⋊Q8×C79C2313yes—
411C22⋊Q8×C79C2316yes—
412#121×C79C2311yescharacteristic
413#121×C79C2313yes—
414#121×C79C23112yes—
415#121×C79C2316yes—
416#120×C79C2316yes—
417C4×Q8×C79C2312yes—
418C4×D4×C79C2316yes—
419C4×D4×C79C2316yes—
420C4×D4×C79C2316yes—
421#117×C79C2313yes—
422C2×C4⋊C4×C79C2313yes—
423C2×C4⋊C4×C79C2316yes—
424C2×C22⋊C4×C79C2316yes—
425C23×D79C2416yes—
426C23×D79C2413yes—
427C23×D79C2412yes—
428C23×D79C2413yes—
429#11929625—212no—
430#11929625—224no—
431#11929625—212no—
432#11929625—212no—
433#11929625—24no—
434#11929625C2×D418yes—
435#11929624—224no—
436#11929624—212no—
437#11929624—212no—
438#11929624—212no—
439#11929624—224no—
440#11929624—212no—
441#11929624—24no—
442#11929624—212no—
443#11929624—212no—
444#11929624—212no—
445#11929624—212no—
446#11929624—212no—
447#11929624—212no—
448#11929624—212no—
449#11929624—248no—
450#11929624—224no—
451#11929624C2×D4124yes—
452#11929623—224no—
453#11929623—224no—
454#11929623—212no—
455#11929623—212no—
456#11929623—212no—
457#11929623—212no—
458#11929623—224no—
459#11929623—224no—
460#11929623—248no—
461#11929623C2×D4124yes—
462C2×Dic158—224no—
463C2×Dic158—212no—
464C2×Dic158—224no—
465C2×Dic158—212no—
466C2×Dic158—212no—
467C2×Dic158C24112yes—
468C2×Dic158C2413yes—
469C2×Dic158C2416yes—
470C2×Dic158C2416yes—
471C2×Dic158C2413yes—
472C2×Dic158C2413yes—
473C2×Dic158C2413yes—
474C2×Dic158C2413yes—
475C2×Dic158C2411yescharacteristic
476C2×Dic158C2413yes—
477Q8×D79—224no—
478Q8×D79—212no—
479Q8×D79—224no—
480Q8×D79—224no—
481Q8×D79—212no—
482Q8×D79—224no—
483Q8×D79—212no—
484Q8×D79—28no—
485Q8×D79—24no—
486Q8×D79C2×D418yes—
487C2×D316—212no—
488C2×D316—212no—
489C2×D316C2411yescharacteristic
490C2×D316C2413yes—
491C2×D316C2416yes—
492C2×D316C2411yescharacteristic
493C2×D316C2413yes—
494C2×D316C2413yes—
495C2×D316C2413yes—
496C2×D316C2416yes—
497C2×D316C2412yes—
498C2×D316C2413yes—
499C2×C22⋊D79—212no—
500C2×C22⋊D79—212no—
501C2×C22⋊D79—224no—
502C2×C22⋊D79C2416yes—
503C2×C22⋊D79C2416yes—
504C2×C22⋊D79C2412yes—
505C2×C22⋊D79C2413yes—
506C2×C22⋊D79C2413yes—
507C2×C22⋊D79C2413yes—
508C2×C22⋊D79C2416yes—
509C2×C22⋊D79C2413yes—
510C2×C22⋊D79C2411yescharacteristic
511C2×C22⋊D79C2413yes—
512C2×C22⋊D79C2413yes—
513C2×C22⋊D79C2411yescharacteristic
514C2×C22⋊D79C2416yes—
515C2×C22⋊D79C2416yes—
516C2×C22⋊D79C2412yes—
517C2×C22⋊D79C2412yes—
518C2×C22⋊D79C2416yes—
519D4×D79—212no—
520D4×D79—24no—
521D4×D79—212no—
522D4×D79—224no—
523D4×D79—224no—
524D4×D79—212no—
525D4×D79—224no—
526D4×D79C2×D4124yes—
527C22×Dic79C2416yes—
528C22×Dic79C2416yes—
529C22×Dic79C2413yes—
530C22×Dic79C2416yes—
531C22×Dic79C2416yes—
532C22×Dic79C2413yes—
533C2×C4×D79—224no—
534C2×C4×D79—224no—
535C2×C4×D79—224no—
536C2×C4×D79—212no—
537C2×C4×D79C2×D4124yes—
538C2×C4×D79C2416yes—
539C2×C4×D79C24112yes—
540C2×C4×D79C2416yes—
541C2×C4×D79C2416yes—
542C2×C4×D79C2416yes—
543C2×C4×D79C2416yes—
544C2×C4×D79C2413yes—
545C2×C4×D79C2413yes—
546C2×C4×D79C2413yes—
547C2×C4×D79C2411yescharacteristic
548C2×C4×D79C2416yes—
549C2×C4×D79C2416yes—
550C2×C4×D79C2413yes—
551C2×C4×D79C2413yes—
552C2×C4×D79C2411yescharacteristic
553C2×C4×D79C2413yes—
554C4⋊Dic79C2411yescharacteristic
555C4⋊Dic79C2416yes—
556C4⋊Dic79C2413yes—
557C4⋊Dic79C24112yes—
558C4⋊Dic79C2416yes—
559C4⋊Dic79C2416yes—
560Dic79⋊C4C2416yes—
561Dic79⋊C4C2416yes—
562Dic79⋊C4C24112yes—
563Dic79⋊C4C24112yes—
564Dic79⋊C4C2416yes—
565Dic79⋊C4C2416yes—
566Dic79⋊C4C2416yes—
567Dic79⋊C4C2416yes—
568C22⋊Dic79C2416yes—
569C22⋊Dic79C24112yes—
570C22⋊Dic79C2416yes—
571C22⋊Dic79C2416yes—
572C22⋊Dic79C2412yes—
573C22⋊Dic79C2416yes—
574(C2×D79)⋊C4C2412yes—
575(C2×D79)⋊C4C2416yes—
576(C2×D79)⋊C4C2416yes—
577(C2×D79)⋊C4C2416yes—
578(C2×D79)⋊C4C24112yes—
579(C2×D79)⋊C4C24112yes—
580(C2×D79)⋊C4C2416yes—
581(C2×D79)⋊C4C2416yes—
582(C2×D79)⋊C4C24112yes—
583(C2×D79)⋊C4C2416yes—
584(C2×D79)⋊C4C2412yes—
585(C2×D79)⋊C4C2416yes—
586(C2×D79)⋊C4C2412yes—
587C4×Dic79C2412yes—
588C4×Dic79C2416yes—
589C4×Dic79C2416yes—
590C4×Dic79C24112yes—
591C24×C79C2413yes—
592#41×C79—24no—
593#41×C79—224no—
594#41×C79—212no—
595#41×C79—212no—
596#41×C79—212no—
597#41×C79C2×D418yes—
598C2×Q8×C79—28no—
599C2×Q8×C79—24no—
600C2×Q8×C79—212no—
601C2×Q8×C79C2413yes—
602C2×Q8×C79C2416yes—
603C2×Q8×C79C2413yes—
604C2×Q8×C79C2411yescharacteristic
605C2×D4×C79—212no—
606C2×D4×C79C2416yes—
607C2×D4×C79C2411yescharacteristic
608C2×D4×C79C2416yes—
609C2×D4×C79C2413yes—
610C2×D4×C79C2412yes—
611C2×D4×C79C2416yes—
612C2×D4×C79C2413yes—
613C22×C4×C79—212no—
614C22×C4×C79C2416yes—
615C22×C4×C79C2413yes—
616C22×C4×C79C2416yes—
617C22×C4×C79C2413yes—
618C22×C4×C79C2413yes—
619C22×C4×C79C2411yescharacteristic
620C22×C4×C79C2413yes—
621C22×C4×C79C2416yes—
622C22×C4×C79C2413yes—
623C4⋊C4×C79C2413yes—
624C4⋊C4×C79C2416yes—
625C4⋊C4×C79C2416yes—
626C4⋊C4×C79C24112yes—
627C4⋊C4×C79C2411yescharacteristic
628C4⋊C4×C79C2416yes—
629C22⋊C4×C79C2416yes—
630C22⋊C4×C79C24112yes—
631C22⋊C4×C79C2416yes—
632C22⋊C4×C79C2412yes—
633C22⋊C4×C79C2416yes—
634C22⋊C4×C79C2416yes—
635C42×C79C2416yes—
636C23×C79—26no—
637C23×C79—43no—
638C23×C79—43no—
639C23×C79C2513yes—
640C23×C79C2511yescharacteristic
641C23×C79C2512yes—
642C23×C79C2513yes—
643C22×D79—26no—
644C22×D79—24no—
645C22×D79—212no—
646C22×D79—43no—
647C22×D79—43no—
648C22×D79—42no—
649C22×D79—42no—
650C22×D79—46no—
651C22×D79—46no—
652C22×D79—43no—
653C22×D79—43no—
654C22×D79C22×D4112yes—
655C22×D79C2513yes—
656C22×D79C2511yescharacteristic
657C22×D79C2512yes—
658C22×D79C2511yescharacteristic
659C22×D79C2513yes—
660Q8×C79—26no—
661Q8×C79—212no—
662Q8×C79—26no—
663Q8×C79C22×D414yes—
664D4×C79—212no—
665D4×C79—212no—
666D4×C79—26no—
667D4×C79—22no—
668D4×C79—46no—
669D4×C79—42no—
670D4×C79C22×D4112yes—
671C2×C4×C79—212no—
672C2×C4×C79—26no—
673C2×C4×C79—26no—
674C2×C4×C79—212no—
675C2×C4×C79—26no—
676C2×C4×C79—22no—
677C2×C4×C79—26no—
678C2×C4×C79—46no—
679C2×C4×C79C22×D4112yes—
680C2×C4×C79C2516yes—
681C2×C4×C79C2512yes—
682C2×C4×C79C2516yes—
683C2×C4×C79C2513yes—
684C2×C4×C79C2511yescharacteristic
685C2×C4×C79C2513yes—
686C2×C4×C79C2511yescharacteristic
687C22⋊D79—212no—
688C22⋊D79—212no—
689C22⋊D79—26no—
690C22⋊D79—26no—
691C22⋊D79—212no—
692C22⋊D79—26no—
693C22⋊D79—22no—
694C22⋊D79—26no—
695C22⋊D79—26no—
696C22⋊D79—24no—
697C22⋊D79—22no—
698C22⋊D79—26no—
699C22⋊D79—42no—
700C22⋊D79—42no—
701C22⋊D79—46no—
702C22⋊D79—46no—
703C22⋊D79C22×D4124yes—
704C2×Dic79—26no—
705C2×Dic79—212no—
706C2×Dic79—212no—
707C2×Dic79—212no—
708C2×Dic79—46no—
709C2×Dic79C22×D4112yes—
710C2×Dic79C2516yes—
711C2×Dic79C2512yes—
712C2×Dic79C2516yes—
713C2×Dic79C2513yes—
714C2×Dic79C2511yescharacteristic
715C2×Dic79C2511yescharacteristic
716C2×Dic79C2513yes—
717D316—26no—
718D316—26no—
719D316—212no—
720D316—26no—
721D316—22no—
722D316—26no—
723D316—22no—
724D316—46no—
725D316—42no—
726D316C22×D4112yes—
727C4×D79—212no—
728C4×D79—212no—
729C4×D79—224no—
730C4×D79—26no—
731C4×D79—22no—
732C4×D79—26no—
733C4×D79—26no—
734C4×D79—212no—
735C4×D79—212no—
736C4×D79—212no—
737C4×D79—46no—
738C4×D79—46no—
739C4×D79C22×D4112yes—
740C4×D79C22×D4112yes—
741C4×D79C22×D414yes—
742C4×D79C22×D4112yes—
743Dic158—26no—
744Dic158—212no—
745Dic158—26no—
746Dic158—212no—
747Dic158—224no—
748Dic158—26no—
749Dic158—26no—
750Dic158—22no—
751Dic158—26no—
752Dic158C22×D4112yes—
753C22×C79—23no—
754C22×C79—23no—
755C22×C79—21no—
756C22×C79—22no—
757C22×C79—23no—
758C22×C79—22no—
759C22×C79—23no—
760C22×C79—21no—
761C22×C79—22no—
762C22×C79—23no—
763C22×C79—21no—
764C22×C79—86no—
765C22×C79C23×D416yes—
766C22×C79C2611yescharacteristic
767C2×D79—21no—
768C2×D79—21no—
769C2×D79—23no—
770C2×D79—23no—
771C2×D79—23no—
772C2×D79—21no—
773C2×D79—22no—
774C2×D79—22no—
775C2×D79—23no—
776C2×D79—21no—
777C2×D79—22no—
778C2×D79—21no—
779C2×D79—23no—
780C2×D79—412no—
781C2×D79—48no—
782C2×D79—812no—
783C2×D79—86no—
784C2×D79C23×D416yes—
785C2×D79C23×D412yes—
786C4×C79—21no—
787C4×C79—23no—
788C4×C79—26no—
789C4×C79—26no—
790C4×C79—22no—
791C4×C79C23×D412yes—
792C4×C79C23×D416yes—
793Dic79—23no—
794Dic79—21no—
795Dic79—26no—
796Dic79—22no—
797Dic79—26no—
798Dic79C23×D412yes—
799Dic79C23×D416yes—
800#62859—791nomaximal, Sylow
801C2×C79—26no—
802C2×C79—42no—
803C2×C79—43no—
804C2×C79—41no—
805C2×C79C24×D411yescharacteristic
806C2×C792−1+611yescharacteristic
807C2×C792−1+611yescharacteristic
808D79—22no—
809D79—26no—
810D79—42no—
811D79—43no—
812D79—41no—
813C2×#585—791no—
814C22×2−1+4—791no—
815#3500—792no—
816#3500—796no—
817#3499—792no—
818#3499—796no—
819#3489—791no—
820#3489—791no—
821#3489—793no—
822#3489—793no—
823#3489—793no—
824#3489—793no—
825#3489—791no—
826#3489D7911yescharacteristic, complemented
827#3486—792no—
828#3486—792no—
829#3485—796no—
830#3485—796no—
831#3449—793no—
832#3449—793no—
833C2×#536—793no—
834C2×#536—793no—
835#3428—791no—
836C79#6285911yescharacteristic, complemented, Sylow
837#585—15816no—
838C2×2−1+4—791no—
839C2×2−1+4—793no—
840C2×2−1+4—791no—
841C2×2−1+4—796no—
842C2×2−1+4—793no—
843C2×2−1+4—791no—
844C2×2−1+4—793no—
845C2×2−1+4—792no—
846C2×2−1+4—791no—
847C2×2−1+4—15816no—
848C2×2−1+4C2×D7911yescharacteristic, complemented
849C2×H(5,𝔽2)—793no—
850C2×H(5,𝔽2)—791no—
851C2×H(5,𝔽2)—793no—
852C2×H(5,𝔽2)—793no—
853C22×#41—791no—
854C22×#41—793no—
855C22×#41—796no—
856C22×#41—793no—
857C22×#41—793no—
858C22×#41—791no—
859C22×#41—793no—
860C22×#41—793no—
861C22×#41C2×D7911yescharacteristic, complemented
862C23×Q8—793no—
863C23×Q8—792no—
864D4×Q8—792no—
865D4×Q8—792no—
866D4×Q8—796no—
867D4×Q8—796no—
868D4×Q8—796no—
869D4×Q8—792no—
870D4×Q8—796no—
871D4×Q8C2×D7912yescomplemented
872#548—792no—
873#548—792no—
874#548—796no—
875#548—796no—
876#548—796no—
877#548—792no—
878#548—796no—
879#548C2×D7912yescomplemented
880#547—796no—
881#547—796no—
882#547—796no—
883#547—7912no—
884#547—7912no—
885#547—796no—
886#547—796no—
887#547—7912no—
888#547—796no—
889#547—796no—
890#547—7912no—
891#547C2×D7916yescomplemented
892#546—796no—
893#546—796no—
894#546—796no—
895#546—7912no—
896#546—796no—
897#546—7912no—
898#546—796no—
899#546—7912no—
900#546—796no—
901#546—796no—
902#546—7912no—
903#546C2×D7916yescomplemented
904#537—793no—
905#537—793no—
906#537—793no—
907#537—793no—
908#537—793no—
909#537—793no—
910#537—793no—
911#537C2×D7913yescomplemented
912#536—793no—
913#536—793no—
914#536—796no—
915#536—796no—
916#536—7912no—
917#536—796no—
918#536—793no—
919#536—796no—
920#536—793no—
921#536—796no—
922#536—796no—
923#536—796no—
924#536—796no—
925#536—796no—
926#536—796no—
927#536—796no—
928#536—793no—
929#536C2×D7913yescomplemented
930#535—793no—
931#535—791no—
932#535—796no—
933#535—796no—
934#534—796no—
935#534—7912no—
936#534—796no—
937#532—7912no—
938#532—796no—
939#532—796no—
940C2×C4⋊Q8—796no—
941C2×C4⋊Q8—796no—
942C2×#124—796no—
943C2×#124—796no—
944#525—793no—
945#525—793no—
946#525—796no—
947#525—796no—
948#525—796no—
949#525—796no—
950#525—796no—
951#525—796no—
952#525—793no—
953#525C2×D7913yescomplemented
954C2×#123—7912no—
955C2×#123—796no—
956C2×#123—796no—
957C2×C22⋊Q8—793no—
958C2×C22⋊Q8—793no—
959C2×C22⋊Q8—796no—
960C2×C22⋊Q8—796no—
961C2×C22⋊Q8—793no—
962C2×C22⋊Q8C2×D7913yescomplemented
963#520—791no—
964#520—793no—
965#520—793no—
966#520C2×D7911yescharacteristic, complemented
967#519—792no—
968#518—796no—
969C4×#41—792no—
970C4×#41—796no—
971C2×#117—793no—
972C2×#117—793no—
9732−1+4—28no—
9742−1+4—1588no—
9752−1+4—15816no—
9762−1+4—15824no—
9772−1+4—1588no—
9782−1+4—1588no—
9792−1+4—15848no—
9802−1+4—15824no—
9812−1+4—15824no—
9822−1+4—1588no—
983H(5,𝔽2)—15824no—
984H(5,𝔽2)—15824no—
985H(5,𝔽2)—15824no—
986H(5,𝔽2)—1588no—
987C2×#41—28no—
988C2×#41—7916no—
989C2×#41—791no—
990C2×#41—793no—
991C2×#41—793no—
992C2×#41—796no—
993C2×#41—793no—
994C2×#41—791no—
995C2×#41—793no—
996C2×#41—793no—
997C2×#41—793no—
998C2×#41—796no—
999C2×#41—796no—
1000C2×#41—796no—
1001C2×#41—7912no—
1002C2×#41—793no—
1003C2×#41—796no—
1004C2×#41—793no—
1005C2×#41—793no—
1006C2×#41—793no—
1007C2×#41—793no—
1008C2×#41—793no—
1009C2×#41—796no—
1010C2×#41—793no—
1011C2×#41—793no—
1012C2×#41—793no—
1013C2×#41—791no—
1014C2×#41—793no—
1015C2×#41—793no—
1016C2×#41—793no—
1017C2×#41—796no—
1018C2×#41—7912no—
1019C2×#41—793no—
1020C2×#41—796no—
1021C2×#41—793no—
1022C2×#41—15824no—
1023C2×#41—15824no—
1024C2×#41—15824no—
1025C2×#41—15824no—
1026C2×#41—15848no—
1027C2×#41—15824no—
1028C2×#41—1588no—
1029C2×#41C22×D7913yes—
1030C2×#41C22×D7913yes—
1031C2×#41C22×D7916yes—
1032C2×#41C22×D7913yes—
1033C2×#41C22×D7911yescharacteristic
1034C2×#41C22×D7911yescharacteristic
1035C22×Q8—791no—
1036C22×Q8—796no—
1037C22×Q8—796no—
1038C22×Q8—793no—
1039C22×Q8—793no—
1040C22×Q8—796no—
1041C22×Q8—796no—
1042C22×Q8—792no—
1043C22×Q8—793no—
1044C22×Q8—791no—
1045C22×Q8—793no—
1046C22×Q8—796no—
1047C22×Q8—793no—
1048C22×Q8—796no—
1049C22×Q8—793no—
1050C22×Q8—15824no—
1051C22×Q8—15816no—
1052C22×Q8C22×D7913yes—
1053C22×Q8C22×D7912yes—
1054C22×Q8C22×D7911yescharacteristic
1055C22×D4—793no—
1056C22×D4—793no—
1057C22×D4—793no—
1058C22×D4—796no—
1059C22×D4—796no—
1060C22×D4—793no—
1061C22×D4—796no—
1062C22×D4—791no—
1063C22×D4—796no—
1064C22×D4—793no—
1065C22×D4—793no—
1066C22×D4—793no—
1067C22×D4—793no—
1068C22×D4C22×D7913yes—
1069C23×C4—793no—
1070C23×C4—796no—
1071C23×C4—793no—
1072C23×C4—796no—
1073C23×C4—796no—
1074C23×C4C22×D7913yes—
1075C4⋊Q8—796no—
1076C4⋊Q8—796no—
1077C4⋊Q8—796no—
1078C4⋊Q8—7912no—
1079C4⋊Q8—796no—
1080C4⋊Q8—7912no—
1081C4⋊Q8—7912no—
1082C4⋊Q8—796no—
1083C4⋊Q8C22×D7916yes—
1084#127—796no—
1085#127—792no—
1086#124—796no—
1087#124—796no—
1088#124—796no—
1089#124—7912no—
1090#124—796no—
1091#124—7912no—
1092#124—7912no—
1093#124—796no—
1094#124—792no—
1095#124—796no—
1096#124C22×D7916yes—
1097#123—7912no—
1098#123—796no—
1099#123—7912no—
1100#123—796no—
1101#123—796no—
1102#123—7912no—
1103#123—796no—
1104#123—7912no—
1105#123—7912no—
1106#123—7912no—
1107#123—796no—
1108#123—7912no—
1109#123—796no—
1110#123—7912no—
1111#123—7912no—
1112#123—7912no—
1113#123—7912no—
1114#123—796no—
1115#123C22×D79112yes—
1116#123C22×D7916yes—
1117C22⋊Q8—793no—
1118C22⋊Q8—796no—
1119C22⋊Q8—793no—
1120C22⋊Q8—796no—
1121C22⋊Q8—796no—
1122C22⋊Q8—796no—
1123C22⋊Q8—796no—
1124C22⋊Q8—793no—
1125C22⋊Q8—793no—
1126C22⋊Q8—796no—
1127C22⋊Q8—796no—
1128C22⋊Q8—796no—
1129C22⋊Q8—793no—
1130C22⋊Q8—796no—
1131C22⋊Q8—793no—
1132C22⋊Q8—7912no—
1133C22⋊Q8—7912no—
1134C22⋊Q8—796no—
1135C22⋊Q8—796no—
1136C22⋊Q8—796no—
1137C22⋊Q8—796no—
1138C22⋊Q8—796no—
1139C22⋊Q8—7912no—
1140C22⋊Q8—7912no—
1141C22⋊Q8—796no—
1142C22⋊Q8—796no—
1143C22⋊Q8C22×D7913yes—
1144C22⋊Q8C22×D7916yes—
1145C22⋊Q8C22×D7913yes—
1146C22⋊Q8C22×D7916yes—
1147C22⋊Q8C22×D7916yes—
1148C22⋊Q8C22×D7916yes—
1149#121—791no—
1150#121—793no—
1151#121—796no—
1152#121—796no—
1153#121—796no—
1154#121—796no—
1155#121—796no—
1156#121—7912no—
1157#121—7912no—
1158#121—793no—
1159#121—791no—
1160#121—796no—
1161#121—7912no—
1162#121—791no—
1163#121—793no—
1164#121—796no—
1165#121—796no—
1166#121—796no—
1167#121—796no—
1168#121—796no—
1169#121—796no—
1170#121—796no—
1171#121—796no—
1172#121—796no—
1173#121C22×D7913yes—
1174#121C22×D7916yes—
1175#121C22×D7911yescharacteristic
1176#121C22×D79112yes—
1177#120—796no—
1178#120—796no—
1179#120—792no—
1180#120—7912no—
1181#120—796no—
1182#120—796no—
1183#120—792no—
1184#120—796no—
1185#120—7912no—
1186#120C22×D7916yes—
1187C4×Q8—792no—
1188C4×Q8—796no—
1189C4×Q8—796no—
1190C4×Q8C22×D7912yes—
1191C4×D4—796no—
1192C4×D4—7912no—
1193C4×D4—7912no—
1194C4×D4—796no—
1195C4×D4—796no—
1196C4×D4—796no—
1197C4×D4—796no—
1198C4×D4—796no—
1199C4×D4—7912no—
1200C4×D4—7912no—
1201C4×D4—7912no—
1202C4×D4—7912no—
1203C4×D4—796no—
1204C4×D4—796no—
1205C4×D4—796no—
1206C4×D4C22×D7916yes—
1207C4×D4C22×D7916yes—
1208C4×D4C22×D7916yes—
1209#117—793no—
1210#117—791no—
1211#117—793no—
1212#117—796no—
1213#117—796no—
1214#117—796no—
1215#117—796no—
1216#117—796no—
1217#117C22×D7913yes—
1218C2×C4⋊C4—793no—
1219C2×C4⋊C4—796no—
1220C2×C4⋊C4—796no—
1221C2×C4⋊C4—796no—
1222C2×C4⋊C4—793no—
1223C2×C4⋊C4—793no—
1224C2×C4⋊C4—7912no—
1225C2×C4⋊C4—7912no—
1226C2×C4⋊C4C22×D7913yes—
1227C2×C4⋊C4C22×D7916yes—
1228C2×C22⋊C4—796no—
1229C2×C22⋊C4—796no—
1230C2×C22⋊C4—796no—
1231C2×C22⋊C4—796no—
1232C2×C22⋊C4—796no—
1233C2×C22⋊C4—7912no—
1234C2×C22⋊C4—7912no—
1235C2×C22⋊C4C22×D7916yes—
1236C2×C42—796no—
1237C2×C42—796no—
1238C24—793no—
1239C24—796no—
1240C24—793no—
1241C24—792no—
1242C24C23×D7913yes—
1243#41—24no—
1244#41—212no—
1245#41—224no—
1246#41—212no—
1247#41—212no—
1248#41—798no—
1249#41—7924no—
1250#41—7924no—
1251#41—1584no—
1252#41—15812no—
1253#41—15812no—
1254#41—15812no—
1255#41—15812no—
1256#41—15812no—
1257#41—15812no—
1258#41—15812no—
1259#41—15824no—
1260#41—15824no—
1261#41—15812no—
1262#41—15848no—
1263#41—15824no—
1264#41—15812no—
1265#41—15824no—
1266#41—15812no—
1267#41—15824no—
1268#41—15812no—
1269#41—15812no—
1270#41—15812no—
1271#41—15824no—
1272#41—15848no—
1273#41—15812no—
1274#41—15812no—
1275#41—15824no—
1276#41—1584no—
1277#41—15812no—
1278#41—15824no—
1279#41—15812no—
1280#41—15812no—
1281#41D4×D7918yes—
1282C2×Q8—28no—
1283C2×Q8—24no—
1284C2×Q8—212no—
1285C2×Q8—798no—
1286C2×Q8—793no—
1287C2×Q8—793no—
1288C2×Q8—7912no—
1289C2×Q8—796no—
1290C2×Q8—793no—
1291C2×Q8—793no—
1292C2×Q8—793no—
1293C2×Q8—796no—
1294C2×Q8—793no—
1295C2×Q8—791no—
1296C2×Q8—15824no—
1297C2×Q8—15812no—
1298C2×Q8—15824no—
1299C2×Q8—15812no—
1300C2×Q8—15812no—
1301C2×Q8—15824no—
1302C2×Q8—15824no—
1303C2×Q8—15824no—
1304C2×Q8—15812no—
1305C2×Q8—15824no—
1306C2×Q8—15812no—
1307C2×Q8—1588no—
1308C2×Q8—1584no—
1309C2×Q8—15812no—
1310C2×Q8C23×D7913yes—
1311C2×Q8C23×D7916yes—
1312C2×Q8C23×D7913yes—
1313C2×Q8C23×D7911yescharacteristic
1314C2×D4—212no—
1315C2×D4—796no—
1316C2×D4—792no—
1317C2×D4—796no—
1318C2×D4—792no—
1319C2×D4—796no—
1320C2×D4—7924no—
1321C2×D4—796no—
1322C2×D4—796no—
1323C2×D4—793no—
1324C2×D4—791no—
1325C2×D4—793no—
1326C2×D4—793no—
1327C2×D4—796no—
1328C2×D4—793no—
1329C2×D4—793no—
1330C2×D4—793no—
1331C2×D4—791no—
1332C2×D4—792no—
1333C2×D4—796no—
1334C2×D4—792no—
1335C2×D4—793no—
1336C2×D4—796no—
1337C2×D4—793no—
1338C2×D4—791no—
1339C2×D4—791no—
1340C2×D4—793no—
1341C2×D4—793no—
1342C2×D4—793no—
1343C2×D4—15812no—
1344C2×D4—15812no—
1345C2×D4—1584no—
1346C2×D4—15812no—
1347C2×D4—15812no—
1348C2×D4—15824no—
1349C2×D4—15812no—
1350C2×D4—15824no—
1351C2×D4—15824no—
1352C2×D4—15824no—
1353C2×D4—15812no—
1354C2×D4—15812no—
1355C2×D4C23×D7916yes—
1356C2×D4C23×D7911yescharacteristic
1357C2×D4C23×D7916yes—
1358C2×D4C23×D7913yes—
1359C2×D4C23×D7916yes—
1360C2×D4C23×D7912yes—
1361C2×D4C23×D7913yes—
1362C22×C4—212no—
1363C22×C4—796no—
1364C22×C4—796no—
1365C22×C4—796no—
1366C22×C4—793no—
1367C22×C4—793no—
1368C22×C4—793no—
1369C22×C4—791no—
1370C22×C4—793no—
1371C22×C4—7924no—
1372C22×C4—796no—
1373C22×C4—793no—
1374C22×C4—796no—
1375C22×C4—796no—
1376C22×C4—7912no—
1377C22×C4—796no—
1378C22×C4—796no—
1379C22×C4—796no—
1380C22×C4—796no—
1381C22×C4—793no—
1382C22×C4—793no—
1383C22×C4—791no—
1384C22×C4—793no—
1385C22×C4—796no—
1386C22×C4—15824no—
1387C22×C4—15824no—
1388C22×C4—15824no—
1389C22×C4—15812no—
1390C22×C4C23×D7916yes—
1391C22×C4C23×D7913yes—
1392C22×C4C23×D7916yes—
1393C22×C4C23×D7913yes—
1394C22×C4C23×D7913yes—
1395C22×C4C23×D7913yes—
1396C22×C4C23×D7911yescharacteristic
1397C22×C4C23×D7916yes—
1398C22×C4C23×D7913yes—
1399C4⋊C4—796no—
1400C4⋊C4—7912no—
1401C4⋊C4—796no—
1402C4⋊C4—796no—
1403C4⋊C4—7912no—
1404C4⋊C4—796no—
1405C4⋊C4—796no—
1406C4⋊C4—796no—
1407C4⋊C4—791no—
1408C4⋊C4—793no—
1409C4⋊C4—7912no—
1410C4⋊C4—796no—
1411C4⋊C4—796no—
1412C4⋊C4—796no—
1413C4⋊C4C23×D7911yescharacteristic
1414C4⋊C4C23×D7916yes—
1415C4⋊C4C23×D7913yes—
1416C4⋊C4C23×D79112yes—
1417C4⋊C4C23×D7916yes—
1418C4⋊C4C23×D7916yes—
1419C22⋊C4—796no—
1420C22⋊C4—7912no—
1421C22⋊C4—796no—
1422C22⋊C4—796no—
1423C22⋊C4—792no—
1424C22⋊C4—796no—
1425C22⋊C4—796no—
1426C22⋊C4—792no—
1427C22⋊C4—796no—
1428C22⋊C4—7912no—
1429C22⋊C4—796no—
1430C22⋊C4—7912no—
1431C22⋊C4—796no—
1432C22⋊C4—796no—
1433C22⋊C4—7912no—
1434C22⋊C4—796no—
1435C22⋊C4—792no—
1436C22⋊C4—796no—
1437C22⋊C4—792no—
1438C22⋊C4C23×D7916yes—
1439C22⋊C4C23×D79112yes—
1440C22⋊C4C23×D7916yes—
1441C22⋊C4C23×D7916yes—
1442C22⋊C4C23×D7916yes—
1443C22⋊C4C23×D7912yes—
1444C42—796no—
1445C42—792no—
1446C42—7912no—
1447C42—796no—
1448C42C23×D7916yes—
1449C23—26no—
1450C23—43no—
1451C23—43no—
1452C23—3163no—
1453C23—3163no—
1454C23—3162no—
1455C23—3162no—
1456C23—3163no—
1457C23—3163no—
1458C23—3166no—
1459C23—3166no—
1460C23—7912no—
1461C23—791no—
1462C23—793no—
1463C23—793no—
1464C23—791no—
1465C23—792no—
1466C23—1584no—
1467C23—15812no—
1468C23—1586no—
1469C23C24×D7913yes—
1470C23C24×D7911yescharacteristic
1471C23C24×D7912yes—
1472C23C24×D7913yes—
1473Q8—26no—
1474Q8—212no—
1475Q8—26no—
1476Q8—7912no—
1477Q8—15812no—
1478Q8—15824no—
1479Q8—1582no—
1480Q8—1586no—
1481Q8—1586no—
1482Q8—1586no—
1483Q8—1586no—
1484Q8—15812no—
1485Q8—1586no—
1486Q8C2×D4×D7914yes—
1487D4—212no—
1488D4—212no—
1489D4—26no—
1490D4—22no—
1491D4—42no—
1492D4—46no—
1493D4—3162no—
1494D4—3166no—
1495D4—3166no—
1496D4—3166no—
1497D4—3162no—
1498D4—3162no—
1499D4—7924no—
1500D4—7912no—
1501D4—1582no—
1502D4—1586no—
1503D4—1586no—
1504D4—1586no—
1505D4—15812no—
1506D4—1582no—
1507D4—1586no—
1508D4—1586no—
1509D4—1586no—
1510D4—1584no—
1511D4—1582no—
1512D4—1586no—
1513D4—1586no—
1514D4—1586no—
1515D4—15812no—
1516D4—15812no—
1517D4—15812no—
1518D4—1586no—
1519D4—1582no—
1520D4C2×D4×D79112yes—
1521C2×C4—26no—
1522C2×C4—212no—
1523C2×C4—22no—
1524C2×C4—26no—
1525C2×C4—26no—
1526C2×C4—26no—
1527C2×C4—212no—
1528C2×C4—46no—
1529C2×C4—3166no—
1530C2×C4—3166no—
1531C2×C4—3166no—
1532C2×C4—791no—
1533C2×C4—793no—
1534C2×C4—7912no—
1535C2×C4—794no—
1536C2×C4—7912no—
1537C2×C4—7912no—
1538C2×C4—7912no—
1539C2×C4—796no—
1540C2×C4—792no—
1541C2×C4—796no—
1542C2×C4—791no—
1543C2×C4—793no—
1544C2×C4—15812no—
1545C2×C4—15812no—
1546C2×C4—15812no—
1547C2×C4—15812no—
1548C2×C4—15824no—
1549C2×C4—15812no—
1550C2×C4—15812no—
1551C2×C4—1586no—
1552C2×C4—15812no—
1553C2×C4—1586no—
1554C2×C4—1582no—
1555C2×C4—1586no—
1556C2×C4—1586no—
1557C2×C4—15812no—
1558C2×C4C2×D4×D79112yes—
1559C2×C4C24×D7916yes—
1560C2×C4C24×D7912yes—
1561C2×C4C24×D7916yes—
1562C2×C4C24×D7913yes—
1563C2×C4C24×D7911yescharacteristic
1564C2×C4C24×D7913yes—
1565C2×C4C24×D7911yescharacteristic
1566C22—23no—
1567C22—23no—
1568C22—21no—
1569C22—22no—
1570C22—23no—
1571C22—21no—
1572C22—22no—
1573C22—23no—
1574C22—22no—
1575C22—23no—
1576C22—21no—
1577C22—86no—
1578C22—31612no—
1579C22—3168no—
1580C22—792no—
1581C22—796no—
1582C22—6326no—
1583C22—63212no—
1584C22—1582no—
1585C22—1583no—
1586C22—1581no—
1587C22—1582no—
1588C22—1581no—
1589C22—1583no—
1590C22—1582no—
1591C22—1583no—
1592C22—1581no—
1593C22—1583no—
1594C22—1581no—
1595C22—1583no—
1596C22—1581no—
1597C22C22×D4×D7916yes—
1598C22C25×D7911yescharacteristic
1599C4—21no—
1600C4—23no—
1601C4—26no—
1602C4—22no—
1603C4—26no—
1604C4—792no—
1605C4—796no—
1606C4—1583no—
1607C4—1581no—
1608C4—1586no—
1609C4—1586no—
1610C4—1582no—
1611C4C22×D4×D7912yes—
1612C4C22×D4×D7916yes—
1613C2—26no—
1614C2—41no—
1615C2—43no—
1616C2—42no—
1617C2—3162no—
1618C2—3161no—
1619C2—3163no—
1620C2—1582no—
1621C2—1586no—
1622C2C23×D4×D7911yescharacteristic
1623C2#2377821211yescharacteristic
1624C2#2377821311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3489C2
hypercenter#3489D79
hypocenterC79#62859
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. C2×#19099399C2semidirect
2. C2×2−1+4×D79C2semidirect
3. #23777191C2semidirect
4. #23777186C2semidirect
5. #23777184C2semidirect
6. #23777179C2semidirect
7. #23777081C2semidirect
8. #23777080C2semidirect
9. #23777078C2semidirect
10. #23777076C2semidirect
11. #23777075C2semidirect
12. #23777073C2semidirect
13. #23777072C2semidirect
14. #23777050C2semidirect
15. #23777046C2semidirect
16. #23777039C2semidirect
17. #23777037C2semidirect
18. #23776730C2semidirect
19. #23776728C2semidirect
20. C2×#19099136C2semidirect
21. #536×D79C2semidirect
22. #23776600C2semidirect
23. C79×#3489C2semidirect
26. C2×#14579209C22semidirect
27. C2×#14579209C22semidirect
28. C2×#14579209C22semidirect
30. C2×#14579208C22semidirect
31. C2×#14579208C22semidirect
32. C2×#14579208C22semidirect
33. C2×#14579208C22semidirect
36. C2×#14579207C22semidirect
38. C2×#14579206C22semidirect
40. C22×#11929624C22semidirect
43. C2×#41×D79C22semidirect
44. C2×#41×D79C22semidirect
45. C2×#41×D79C22semidirect
46. C2×#41×D79C22semidirect
47. C22×Q8×D79C22semidirect
48. C22×Q8×D79C22semidirect
49. Q8×D316C22semidirect
50. D4×Dic158C22semidirect
51. #19099228C22semidirect
52. Q8×C22⋊D79C22semidirect
53. Q8×C22⋊D79C22semidirect
54. #19099226C22semidirect
55. #19099226C22semidirect
56. #19099225C22semidirect
57. #19099224C22semidirect
58. #19099223C22semidirect
59. #19099222C22semidirect
60. #19099221C22semidirect
61. #19099220C22semidirect
62. #19099219C22semidirect
63. #19099218C22semidirect
64. #19099217C22semidirect
65. #19099216C22semidirect
66. #19099215C22semidirect
67. #19099215C22semidirect
68. #19099214C22semidirect
69. #19099213C22semidirect
70. #19099212C22semidirect
71. #19099212C22semidirect
72. #19099211C22semidirect
73. #19099211C22semidirect
74. #19099210C22semidirect
75. #19099209C22semidirect
76. #19099208C22semidirect
77. #19099207C22semidirect
78. #19099206C22semidirect
79. #19099205C22semidirect
80. #19099204C22semidirect
81. #19099203C22semidirect
82. #19099202C22semidirect
83. #19099201C22semidirect
84. #19099200C22semidirect
85. #19099144C22semidirect
86. #19099143C22semidirect
87. #19099143C22semidirect
88. #19099142C22semidirect
89. #19099142C22semidirect
90. #19099141C22semidirect
91. #19099141C22semidirect
92. #19099139C22semidirect
93. #19099138C22semidirect
94. #19099137C22semidirect
95. #19099136C22semidirect
96. #19099136C22semidirect
97. #19099136C22semidirect
98. #19099136C22semidirect
99. #19099136C22semidirect
100. #19099136C22semidirect
101. #19099136C22semidirect
102. #19099136C22semidirect
103. #19099136C22semidirect
104. #19099136C22semidirect
105. #19099135C22semidirect
106. #19099135C22semidirect
107. #19099134C22semidirect
108. #19099133C22semidirect
109. #19099129C22semidirect
110. #19099129C22semidirect
111. #19099129C22semidirect
112. #19099128C22semidirect
113. #19099124C22semidirect
114. #19099123C22semidirect
115. #19099121C22semidirect
116. #19099110C22semidirect
117. #19099110C22semidirect
118. #19099108C22semidirect
119. C2×#14579160C22semidirect
120. C4⋊Q8×D79C22semidirect
121. C2×#14579147C22semidirect
122. #124×D79C22semidirect
123. #19099076C22semidirect
124. #19099076C22semidirect
125. #19099075C22semidirect
126. #19099074C22semidirect
127. #19099073C22semidirect
128. #19099073C22semidirect
129. #19099072C22semidirect
130. #19099072C22semidirect
131. #19099070C22semidirect
132. C2×#14579146C22semidirect
133. C2×#14579143C22semidirect
134. #123×D79C22semidirect
135. C2×#14579141C22semidirect
136. C2×#14579140C22semidirect
137. C2×#14579137C22semidirect
138. C22⋊Q8×D79C22semidirect
139. C22⋊Q8×D79C22semidirect
140. #19099046C22semidirect
141. #19099044C22semidirect
142. #19099043C22semidirect
143. #19099039C22semidirect
144. #19099035C22semidirect
145. C4×#11929625C22semidirect
146. C4×#11929623C22semidirect
147. C2×#14579119C22semidirect
148. #117×D79C22semidirect
149. C2×2−1+4×C79C22semidirect
150. C22×#41×C79C22semidirect
151. D4×Q8×C79C22semidirect
152. #548×C79C22semidirect
153. #547×C79C22semidirect
154. #546×C79C22semidirect
155. #537×C79C22semidirect
156. #536×C79C22semidirect
157. #525×C79C22semidirect
158. C2×C22⋊Q8×C79C22semidirect
159. #520×C79C22semidirect
213. #41×D79D4semidirect
826. #3489D79semidirect
836. C79#62859semidirect
848. C2×2−1+4C2×D79semidirect
861. C22×#41C2×D79semidirect
871. D4×Q8C2×D79semidirect
879. #548C2×D79semidirect
891. #547C2×D79semidirect
903. #546C2×D79semidirect
911. #537C2×D79semidirect
929. #536C2×D79semidirect
953. #525C2×D79semidirect
962. C2×C22⋊Q8C2×D79semidirect
966. #520C2×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190993992
C2×2−1+4×D792
#237771912
#237771862
#237771842
#237771792
#237770812
#237770802
#237770782
#237770762
#237770752
#237770732
#237770722
#237770502
#237770462
#237770392
#237770372
#237767302
#237767282
C2×#190991362
#536×D792
#237766002
C79×#34892
#6285979