Finite Group Databasebeta

← #32906029

Subgroups — #32906029

Order 18176.

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#22602259C214yesmaximal, complemented
2#22602241C214yesmaximal, complemented
3#22602235C212yesmaximal, complemented
4#22602231C212yesmaximal, complemented
5#22602227C211yesmaximal, characteristic, complemented
6#22602226C211yesmaximal, characteristic, complemented
7#22602214C211yesmaximal, characteristic, complemented
8#22602197C214yesmaximal, complemented
9#22602184C214yesmaximal, complemented
10#22602167C218yesmaximal, complemented
11#22601939C214yesmaximal, complemented
12#22601936C214yesmaximal, complemented
13#22601891C218yesmaximal, complemented
14#22601724C214yesmaximal, complemented
15#22601671C212yesmaximal, complemented
16#22601635C214yesmaximal, complemented
17#533×D71C211yesmaximal, characteristic, complemented
18C2×#17986547C211yesmaximal, characteristic, complemented
19#22601538C212yesmaximal, complemented
20C4×#41×D71C211yesmaximal, characteristic, complemented
21C71×#3508C211yesmaximal, characteristic, complemented
22C22×#11765864C2212yes—
23C2×#41×D71C2211yescharacteristic
24#17986735C2218yescomplemented
25#17986735C2214yescomplemented
26#17986732C2218yescomplemented
27#17986728C2214yescomplemented
28#17986727C2214yescomplemented
29#17986722C2214yescomplemented
30#17986719C2214yescomplemented
31#17986719C2218yescomplemented
32#17986718C2218yescomplemented
33#17986718C2218yescomplemented
34#17986713C2218yescomplemented
35#17986708C2218yescomplemented
36#17986699C2218yescomplemented
37#17986696C2218yescomplemented
38#17986696C22116yescomplemented
39#17986694C22116yescomplemented
40#17986692C22116yescomplemented
41#17986691C2218yescomplemented
42#17986689C2218yescomplemented
43#17986686C22116yescomplemented
44#17986680C22116yescomplemented
45#17986675C22116yescomplemented
46#17986669C2214yescomplemented
47#17986657C2218yescomplemented
48#17986656C2218yescomplemented
49#17986648C2218yescomplemented
50#17986643C2218yescomplemented
51#17986616C2218yescomplemented
52#17986614C2218yescomplemented
53#17986612C2214yescomplemented
54#17986611C2214yescomplemented
55#17986603C2214yescomplemented
56#17986592C22116yescomplemented
57#17986581C22116yescomplemented
58#17986578C2218yescomplemented
59#17986575C2212yes—
60#17986570C2212yes—
61#17986569C2214yescomplemented
62#17986566C2212yes—
63#17986562C2214yescomplemented
64#17986559C2218yes—
65#17986556C2214yescomplemented
66#17986556C2211yescharacteristic, complemented
67#17986555C2212yescomplemented
68#17986554C2214yescomplemented
69#17986554C2212yescomplemented
70#17986553C2214yescomplemented
71#17986552C2212yescomplemented
72#17986551C2214yescomplemented
73#17986548C2214yescomplemented
74#17986547C2212yes—
75#17986547C2214yes—
76#17986547C2212yes—
77#17986547C2212yescomplemented
78#17986547C2214yescomplemented
79#17986547C2212yescomplemented
80#17986547C2214yescomplemented
81#17986547C2214yescomplemented
82C2×#14556128C2211yescharacteristic, complemented
83C4⋊Q8×D71C2212yescomplemented
84#17986531C2218yescomplemented
85#17986531C2218yescomplemented
86#17986530C2218yescomplemented
87#17986530C2218yescomplemented
88#17986530C22116yescomplemented
89#17986528C2218yescomplemented
90#17986528C2218yescomplemented
91#17986526C22116yescomplemented
92#125×D71C2212yescomplemented
93C2×#14556115C2212yescomplemented
94#17986509C2218yescomplemented
95#17986509C2218yescomplemented
96#17986506C2218yescomplemented
97#17986505C2218yes—
98C22⋊Q8×D71C2214yes—
99C2×#14556099C2214yes—
100#17986478C2218yescomplemented
101#17986478C2218yescomplemented
102#17986476C2212yescomplemented
103#17986476C2212yescomplemented
104#17986474C2212yescomplemented
105#17986472C2218yes—
106#41×Dic71C2211yescharacteristic
107#41×Dic71C2218yescomplemented
108C4×#11765866C2212yescomplemented
109C4×#11765865C2211yescharacteristic
110C4×#11765865C2212yescomplemented
111#17986467C2211yescharacteristic
112#17986467C2212yescomplemented
113C4×#11765864C2214yes—
114C4×#11765864C2212yescomplemented
115C4×#11765864C2218yescomplemented
116C4×#11765864C2218yescomplemented
117C4×#11765864C2218yescomplemented
118C4×Q8×D71C2212yescomplemented
119C4×Q8×D71C2214yescomplemented
120C2×D4×Dic71C2214yescomplemented
121C4×D4×D71C2214yes—
122C4×D4×D71C2212yescomplemented
123C2×#14556084C2218yescomplemented
124#117×D71C2211yescharacteristic
125#117×D71C2212yes—
126#117×D71C2212yescomplemented
127C2×C42×D71C2211yescharacteristic
128C2×C42×D71C2212yescomplemented
129#559×C71C2214yescomplemented
130#550×C71C2214yescomplemented
131#546×C71C2218yescomplemented
132#540×C71C2214yescomplemented
133#535×C71C2212yes—
134#533×C71C2211yescharacteristic, complemented
135#532×C71C2214yescomplemented
136C2×#127×C71C2211yescharacteristic, complemented
137#518×C71C2212yescomplemented
138C4×#41×C71C2211yescharacteristic
139C2×#11765866C2311yescharacteristic
140C2×#11765865C2311yescharacteristic
141C2×#11765865C2312yes—
142C2×#11765864—216no—
143C2×#11765864C2314yes—
144C2×#11765864C2312yes—
145C2×#11765864C2311yescharacteristic
146C2×#11765864C2314yes—
147C2×#11765864C2314yes—
148C2×#11765864C2314yes—
149C2×#11765864C2318yes—
150#41×D71—28no—
151C22×Dic142C2312yes—
152C2×Q8×D71C2311yescharacteristic
153C2×Q8×D71C2314yes—
154C22×C22⋊D71C2314yes—
155C2×D4×D71C2311yescharacteristic
156C2×D4×D71C2312yes—
157C23×Dic71C2314yes—
158C22×C4×D71C2312yes—
159C22×C4×D71C2312yes—
160C22×C4×D71C2314yes—
161C22×C4×D71C2311yescharacteristic
162#14556128C2314yes—
163#14556128C2312yes—
164#14556128C2314yes—
165#14556128C2312yes—
166#14556128C2312yes—
167#14556127C2314yes—
168#14556127C2314yes—
169#14556126C2314yes—
170#14556126C2314yes—
171#14556124C2314yes—
172#14556123C23116yes—
173#14556121C23116yes—
174#14556121C23116yes—
175#14556121C23116yes—
176#14556121C23116yes—
177#14556121C23116yes—
178#14556120C2312yes—
179#14556120C2318yes—
180#14556119C23116yes—
181#14556119C2318yes—
182#14556119C2314yes—
183#14556118C23116yes—
184#14556118C2318yes—
185#14556116C2314yes—
186#14556115C2314yes—
187#14556115C2314yes—
188#14556115C23116yes—
189#14556115C2314yes—
190#14556115C2318yes—
191#14556115C2318yes—
192#14556115C2314yes—
193#14556114C23116yes—
194#14556112C2318yes—
195#14556111C23116yes—
196#14556110C23116yes—
197#14556110C23116yes—
198#14556109C2318yes—
199#14556109C23116yes—
200#14556109C23116yes—
201#14556109C23116yes—
202#14556108C2318yes—
203#14556108C2314yes—
204#14556107C2318yes—
205#14556107C23116yes—
206#14556107C2314yes—
207#14556107C2318yes—
208#14556106C2318yes—
209#14556105C23116yes—
210#14556105C23116yes—
211#14556105C2318yes—
212#14556104C2318yes—
213#14556104C2314yes—
214#14556101C23116yes—
215#14556100C23116yes—
216#14556100C23116yes—
217#14556099C2318yes—
218#14556099C23116yes—
219#14556099C2318yes—
220#14556099C2318yes—
221#14556099C2318yes—
222#14556099C2318yes—
223#14556099C2318yes—
224#14556097C2318yes—
225#14556096C23116yes—
226Q8×Dic71C2318yes—
227Q8×Dic71C2312yes—
228Q8×Dic71C2314yes—
229C4×Dic142C2318yes—
230C4×Dic142C2318yes—
231C4×Dic142C2314yes—
232C4×Dic142C2314yes—
233C4×Dic142C2318yes—
234C4×Dic142C2312yes—
235C4×Dic142C2318yes—
236#14556093C2318yes—
237#14556093C2314yes—
238#14556093C2312yes—
239#14556093C2314yes—
240#14556093C2318yes—
241#14556093C2318yes—
242C4×D284C2314yes—
243C4×D284C2312yes—
244D4×Dic71C2318yes—
245D4×Dic71C2318yes—
246D4×Dic71C2318yes—
247D4×Dic71C2318yes—
248D4×Dic71C2314yes—
249D4×Dic71C23116yes—
250D4×Dic71C2318yes—
251D4×Dic71C2312yes—
252D4×Dic71C2318yes—
253D4×Dic71C2318yes—
254D4×Dic71C23116yes—
255#14556090C2314yes—
256#14556090C2312yes—
257C4×C22⋊D71C23116yes—
258C4×C22⋊D71C2314yes—
259C4×C22⋊D71C2314yes—
260C4×C22⋊D71C2314yes—
261C4×C22⋊D71C23116yes—
262C4×C22⋊D71C23116yes—
263(C22⋊D71)⋊C4C23116yes—
264(C22⋊D71)⋊C4C23116yes—
265(C22⋊D71)⋊C4C2314yes—
266(C22⋊D71)⋊C4C2314yes—
267(C22⋊D71)⋊C4C2314yes—
268(C22⋊D71)⋊C4C23116yes—
269#14556087C2312yes—
270#14556087C2312yes—
271#14556087C23116yes—
272#14556087C2318yes—
273#14556087C2311yescharacteristic
274#14556086C2318yes—
275#14556086C2312yes—
276#14556086C2314yes—
277#14556086C2314yes—
278#14556085C2314yes—
279#14556085C2312yes—
280#14556085C2312yes—
281#14556085C2312yes—
282#14556084C2318yes—
283#14556084C2318yes—
284#14556084C23116yes—
285#14556084C23116yes—
286#14556084C2312yes—
287#14556084C2314yes—
288#14556084C2314yes—
289#14556084C23116yes—
290C2×C4⋊Dic71C2314yes—
291C2×Dic71⋊C4C23116yes—
292C4⋊C4×D71C2314yes—
293C4⋊C4×D71C2314yes—
294C4⋊C4×D71C2318yes—
295C4⋊C4×D71C2314yes—
296C4⋊C4×D71C2312yes—
297C2×C22⋊Dic71C2318yes—
298C2×C22⋊Dic71C2318yes—
299C22⋊C4×D71C2314yes—
300C22⋊C4×D71C2312yes—
301C22⋊C4×D71C2314yes—
302C2×C4×Dic71C2312yes—
303C2×C4×Dic71C2311yescharacteristic
304C2×C4×Dic71C2314yes—
305C2×C4×Dic71C2312yes—
306C2×C4×Dic71C23116yes—
307C42×D71C2311yescharacteristic
308C42×D71C2311yescharacteristic
309C42×D71C2312yes—
310C42×D71C2312yes—
311C42×D71C2311yescharacteristic
312C42×D71C2311yescharacteristic
313C42×D71C2312yes—
314C42×D71C2314yes—
315C42×D71C2314yes—
316C42×D71C2312yes—
317C42×D71C2312yes—
318C42×D71C2314yes—
319C2×#41×C71C2311yescharacteristic
320C2×#41×C71C2318yes—
321C22×D4×C71C2312yes—
322C22×D4×C71C2314yes—
323C4⋊Q8×C71C2312yes—
324#127×C71C2314yes—
325#127×C71C2312yes—
326#127×C71C2314yes—
327#127×C71C2312yes—
328#125×C71C2312yes—
329#124×C71C2314yes—
330#124×C71C2318yes—
331#123×C71C23116yes—
332C22⋊Q8×C71C2314yes—
333#121×C71C2318yes—
334#121×C71C23116yes—
335#121×C71C2318yes—
336#120×C71C2318yes—
337C4×Q8×C71C2312yes—
338C4×Q8×C71C2314yes—
339C4×D4×C71C2318yes—
340C4×D4×C71C2314yes—
341C4×D4×C71C2312yes—
342C4×D4×C71C2318yes—
343C4×D4×C71C2318yes—
344#117×C71C2312yes—
345#117×C71C2312yes—
346#117×C71C2311yescharacteristic
347C2×C22⋊C4×C71C2318yes—
348C2×C42×C71C2311yescharacteristic
349C2×C42×C71C2312yes—
350C23×D71C2412yes—
351C23×D71C2411yescharacteristic
352#11765866—24no—
353#11765865—24no—
354#11765865—28no—
355#11765864—28no—
356#11765864—24no—
357#11765864—216no—
358#11765864—216no—
359#11765864—216no—
360#11765864—216no—
361#11765864—416no—
362C2×Dic142—28no—
363C2×Dic142C2414yes—
364C2×Dic142C2412yes—
365C2×Dic142C2411yescharacteristic
366C2×Dic142C2414yes—
367C2×Dic142C2414yes—
368C2×Dic142C2418yes—
369Q8×D71—24no—
370Q8×D71—48no—
371C2×D284C2412yes—
372C2×D284C2411yescharacteristic
373C2×C22⋊D71—216no—
374C2×C22⋊D71C2412yes—
375C2×C22⋊D71C2412yes—
376C2×C22⋊D71C2412yes—
377C2×C22⋊D71C2418yes—
378C2×C22⋊D71C2418yes—
379C2×C22⋊D71C24116yes—
380D4×D71—28no—
381D4×D71—24no—
382C22×Dic71—216no—
383C22×Dic71C2412yes—
384C22×Dic71C2414yes—
385C22×Dic71C2418yes—
386C22×Dic71C2418yes—
387C22×Dic71C2412yes—
388C22×Dic71C2414yes—
389C22×Dic71C24116yes—
390C22×Dic71C2411yescharacteristic
391C2×C4×D71—28no—
392C2×C4×D71—44no—
393C2×C4×D71—48no—
394C2×C4×D71#4118yescomplemented
395C2×C4×D71C2412yes—
396C2×C4×D71C2412yes—
397C2×C4×D71C2412yes—
398C2×C4×D71C2414yes—
399C2×C4×D71C2412yes—
400C2×C4×D71C2412yes—
401C2×C4×D71C2414yes—
402C2×C4×D71C2412yes—
403C2×C4×D71C2412yes—
404C2×C4×D71C2414yes—
405C2×C4×D71C2418yes—
406C2×C4×D71C2411yescharacteristic
407C2×C4×D71C2411yescharacteristic
408C2×C4×D71C2411yescharacteristic
409C2×C4×D71C2411yescharacteristic
410C4⋊Dic71C2412yes—
411C4⋊Dic71C2414yes—
412C4⋊Dic71C2414yes—
413C4⋊Dic71C2414yes—
414C4⋊Dic71C2418yes—
415C4⋊Dic71C2418yes—
416C4⋊Dic71C2418yes—
417C4⋊Dic71C24116yes—
418Dic71⋊C4C2414yes—
419Dic71⋊C4C2418yes—
420Dic71⋊C4C2418yes—
421Dic71⋊C4C2414yes—
422Dic71⋊C4C2414yes—
423Dic71⋊C4C2418yes—
424Dic71⋊C4C2418yes—
425Dic71⋊C4C24116yes—
426Dic71⋊C4C24116yes—
427Dic71⋊C4C24116yes—
428C22⋊Dic71C2412yes—
429C22⋊Dic71C2414yes—
430C22⋊Dic71C2414yes—
431C22⋊Dic71C24116yes—
432C22⋊Dic71C24116yes—
433C22⋊Dic71C24116yes—
434C22⋊Dic71C24116yes—
435C22⋊Dic71C24116yes—
436(C2×D71)⋊C4C2414yes—
437(C2×D71)⋊C4C2418yes—
438(C2×D71)⋊C4C2414yes—
439(C2×D71)⋊C4C2414yes—
440(C2×D71)⋊C4C24116yes—
441C4×Dic71C2412yes—
442C4×Dic71C2411yescharacteristic
443C4×Dic71C2414yes—
444C4×Dic71C2414yes—
445C4×Dic71C2412yes—
446C4×Dic71C2412yes—
447C4×Dic71C2411yescharacteristic
448C4×Dic71C2414yes—
449C4×Dic71C2412yes—
450C4×Dic71C2412yes—
451C4×Dic71C2414yes—
452C4×Dic71C2412yes—
453C4×Dic71C2418yes—
454C4×Dic71C2414yes—
455C4×Dic71C24116yes—
456C4×Dic71C24116yes—
457C24×C71C2414yes—
458#41×C71—24no—
459#41×C71—416no—
460C2×Q8×C71C2411yescharacteristic
461C2×Q8×C71C2414yes—
462C2×D4×C71—28no—
463C2×D4×C71—48no—
464C2×D4×C71C2412yes—
465C2×D4×C71C2411yescharacteristic
466C2×D4×C71C2414yes—
467C2×D4×C71C2414yes—
468C2×D4×C71C2418yes—
469C2×D4×C71C24116yes—
470C2×D4×C71C2418yes—
471C22×C4×C71C2412yes—
472C22×C4×C71C2414yes—
473C22×C4×C71C2412yes—
474C22×C4×C71C24116yes—
475C22×C4×C71C2411yescharacteristic
476C4⋊C4×C71C2412yes—
477C4⋊C4×C71C2414yes—
478C4⋊C4×C71C2414yes—
479C4⋊C4×C71C2414yes—
480C4⋊C4×C71C2418yes—
481C22⋊C4×C71C2412yes—
482C22⋊C4×C71C2414yes—
483C22⋊C4×C71C24116yes—
484C22⋊C4×C71C2414yes—
485C22⋊C4×C71C24116yes—
486C42×C71C2411yescharacteristic
487C42×C71C2412yes—
488C42×C71C2411yescharacteristic
489C42×C71C2414yes—
490C42×C71C2412yes—
491C42×C71C2414yes—
492C23×C71—28no—
493C23×C71—48no—
494C23×C71C2518yes—
495C23×C71C2512yes—
496C23×C71C2511yescharacteristic
497C22×D71—24no—
498C22×D71—42no—
499C22×D71—44no—
500C22×D71C2×#4114yes—
501C22×D71C2512yes—
502C22×D71C2511yescharacteristic
503C22×D71C2511yescharacteristic
504Q8×C71—22no—
505Q8×C71—28no—
506D4×C71—24no—
507D4×C71—28no—
508D4×C71—28no—
509D4×C71—22no—
510D4×C71—216no—
511D4×C71—48no—
512D4×C71—416no—
513C2×C4×C71—24no—
514C2×C4×C71—24no—
515C2×C4×C71—28no—
516C2×C4×C71—416no—
517C2×C4×C71C2×#4114yes—
518C2×C4×C71C2512yes—
519C2×C4×C71C2514yes—
520C2×C4×C71C2512yes—
521C2×C4×C71C2518yes—
522C2×C4×C71C2511yescharacteristic
523C2×C4×C71C2511yescharacteristic
524C2×C4×C71C2512yes—
525C22⋊D71—24no—
526C22⋊D71—24no—
527C22⋊D71—216no—
528C22⋊D71—216no—
529C22⋊D71—24no—
530C22⋊D71—416no—
531C2×Dic71—28no—
532C2×Dic71—24no—
533C2×Dic71—216no—
534C2×Dic71—216no—
535C2×Dic71—42no—
536C2×Dic71—44no—
537C2×Dic71—416no—
538C2×Dic71C2×#4114yes—
539C2×Dic71C2514yes—
540C2×Dic71C2512yes—
541C2×Dic71C2512yes—
542C2×Dic71C2518yes—
543C2×Dic71C2518yes—
544C2×Dic71C2512yes—
545C2×Dic71C2511yescharacteristic
546C2×Dic71C2511yescharacteristic
547D284—24no—
548D284—22no—
549C4×D71—24no—
550C4×D71—24no—
551C4×D71—24no—
552C4×D71—24no—
553C4×D71—28no—
554C4×D71—24no—
555C4×D71—42no—
556C4×D71—44no—
557C4×D71—42no—
558C4×D71—44no—
559C4×D71—48no—
560C4×D71C2×#4114yes—
561C4×D71C2×#4114yes—
562C4×D71C2×#4114yes—
563C4×D71C2×#4114yes—
564Dic142—22no—
565Dic142—28no—
566Dic142—28no—
567Dic142—28no—
568Dic142—24no—
569Dic142—48no—
570C22×C71—22no—
571C22×C71—28no—
572C22×C71—22no—
573C22×C71—216no—
574C22×C71—24no—
575C22×C71—88no—
576C22×C71C22×#4112yes—
577C22×C71C2611yescharacteristic
578C2×D71—22no—
579C2×D71—22no—
580C2×D71—22no—
581C2×D71—24no—
582C2×D71—44no—
583C2×D71—48no—
584C2×D71C22×#4112yes—
585C2×D71C22×#4112yes—
586C4×C71—22no—
587C4×C71—28no—
588C4×C71—24no—
589C4×C71—22no—
590C4×C71C22×#4112yes—
591C4×C71C22×#4112yes—
592C4×C71#58514yes—
593Dic71—22no—
594Dic71—28no—
595Dic71—28no—
596Dic71—22no—
597Dic71—22no—
598Dic71—24no—
599Dic71C22×#4112yes—
600Dic71C22×#4112yes—
601#62815—711nomaximal, Sylow
602C2×C71—22no—
603C2×C71—42no—
604C2×C71—48no—
605C2×C71C23×#4111yescharacteristic
606C2×C71C2×#58512yes—
607D71—22no—
608D71—22no—
609D71—42no—
610#3512—714no—
611#3511—714no—
612#3510—712no—
613#3510—712no—
614#3509—711no—
615#3509—711no—
616#3508—711no—
617#3508D7111yescharacteristic, complemented
618#3507—714no—
619#3506—714no—
620#3505—718no—
621#3480—714no—
622#3480—714no—
623#3475—718no—
624#3455—714no—
625#3449—712no—
626#3444—714no—
627C2×#533—711no—
628C2×#532—711no—
629#3428—712no—
630C2×C4×#41—711no—
631C71#6281511yescharacteristic, complemented, Sylow
632C22×#41—711no—
633C22×#41—712no—
634#559—718no—
635#559—714no—
636#559—718no—
637#559C2×D7114yescomplemented
638#557—714no—
639#557—714no—
640#556—718no—
641#556—718no—
642#556—714no—
643#556—714no—
644#556—718no—
645#555—718no—
646#554—718no—
647#553—7116no—
648#553—7116no—
649#553—718no—
650#553—7116no—
651#553—718no—
652#552—7116no—
653#552—718no—
654#552—718no—
655#551—7116no—
656#551—7116no—
657#550—714no—
658#550C2×D7114yescomplemented
659#548—718no—
660#548—718no—
661#547—718no—
662#546—718no—
663#546C2×D7118yescomplemented
664#542—718no—
665#542—718no—
666#541—714no—
667#541—714no—
668#540—714no—
669#540C2×D7114yescomplemented
670#539—7116no—
671#538—7116no—
672#537—718no—
673#536—712no—
674#536—714no—
675#536—712no—
676#535—712no—
677#535—714no—
678#535C2×D7112yes—
679#534—718no—
680#533—712no—
681#533—714no—
682#533—712no—
683#533—714no—
684#533—714no—
685#533—712no—
686#533—711no—
687#533—714no—
688#533C2×D7111yescharacteristic, complemented
689#532—712no—
690#532—712no—
691#532—714no—
692#532—714no—
693#532—712no—
694#532—712no—
695#532—714no—
696#532—714no—
697#532—714no—
698#532C2×D7114yescomplemented
699C2×C4⋊Q8—712no—
700C2×C4⋊Q8—711no—
701C2×#127C2×D7111yescharacteristic, complemented
702#529—718no—
703#529—718no—
704#529—7116no—
705#529—718no—
706#529—718no—
707#529—7116no—
708#529—718no—
709#529—718no—
710C2×#125—712no—
711C2×#124—712no—
712#525—718no—
713#525—718no—
714#525—718no—
715#525—718no—
716C2×C22⋊Q8—714no—
717C2×#121—714no—
718#520—718no—
719#520—718no—
720#519—712no—
721#519—712no—
722#518—712no—
723#518—718no—
724#518C2×D7112yescomplemented
725C4×#41—711no—
726C4×#41—718no—
727C4×#41—712no—
728C4×#41—714no—
729C4×#41—712no—
730C4×#41—718no—
731C4×#41—718no—
732C4×#41—718no—
733C4×#41—711no—
734C4×#41—712no—
735C4×#41—711no—
736C4×#41—712no—
737C4×#41C2×D7111yescharacteristic
738C2×C4×Q8—712no—
739C2×C4×Q8—714no—
740C2×C4×D4—714no—
741C2×C4×D4—714no—
742C2×C4×D4—712no—
743C2×#117—711no—
744C2×#117—712no—
745C2×#117—712no—
746C2×#117—718no—
747C22×C42—711no—
748C22×C42—712no—
749C2×#41—711no—
750C2×#41—718no—
751C2×#41—712no—
752C2×#41—714no—
753C2×#41—711no—
754C2×#41—714no—
755C2×#41—714no—
756C2×#41—714no—
757C2×#41—711no—
758C2×#41—712no—
759C2×#41—14216no—
760C2×#41—1428no—
761C2×#41C22×D7111yescharacteristic
762C2×#41C22×D7118yes—
763C22×Q8—714no—
764C22×Q8—711no—
765C22×Q8—712no—
766C22×D4—714no—
767C22×D4—712no—
768C22×D4—711no—
769C22×D4C22×D7112yes—
770C22×D4C22×D7114yes—
771C23×C4—712no—
772C23×C4—714no—
773C23×C4—711no—
774C23×C4—714no—
775C23×C4—712no—
776C4⋊Q8—714no—
777C4⋊Q8—714no—
778C4⋊Q8—714no—
779C4⋊Q8—714no—
780C4⋊Q8—712no—
781C4⋊Q8—712no—
782C4⋊Q8—712no—
783C4⋊Q8—714no—
784C4⋊Q8—714no—
785C4⋊Q8C22×D7112yes—
786#127—714no—
787#127C22×D7112yes—
788#127C22×D7112yes—
789#127C22×D7114yes—
790#127C22×D7114yes—
791#126—7116no—
792#126—7116no—
793#126—7116no—
794#126—7116no—
795#126—7116no—
796#126—7116no—
797#125—714no—
798#125—718no—
799#125—718no—
800#125—7116no—
801#125—7116no—
802#125—712no—
803#125—718no—
804#125C22×D7112yes—
805#124—714no—
806#124—714no—
807#124—718no—
808#124—718no—
809#124—7116no—
810#124—714no—
811#124—714no—
812#124—7116no—
813#124—714no—
814#124C22×D7118yes—
815#124C22×D7114yes—
816#123—7116no—
817#123—718no—
818#123—7116no—
819#123—7116no—
820#123—7116no—
821#123—7116no—
822#123—7116no—
823#123—718no—
824#123C22×D71116yes—
825C22⋊Q8—714no—
826C22⋊Q8—718no—
827C22⋊Q8—714no—
828C22⋊Q8—718no—
829C22⋊Q8—718no—
830C22⋊Q8—7116no—
831C22⋊Q8—714no—
832C22⋊Q8—718no—
833C22⋊Q8—718no—
834C22⋊Q8—718no—
835C22⋊Q8—7116no—
836C22⋊Q8—7116no—
837C22⋊Q8C22×D7114yes—
838#121—718no—
839#121—718no—
840#121—718no—
841#121—718no—
842#121—718no—
843#121—718no—
844#121—7116no—
845#121—7116no—
846#121—7116no—
847#121—7116no—
848#121C22×D7118yes—
849#121C22×D7118yes—
850#121C22×D71116yes—
851#120—718no—
852#120—7116no—
853#120C22×D7118yes—
854C4×Q8—714no—
855C4×Q8—712no—
856C4×Q8—718no—
857C4×Q8—714no—
858C4×Q8—714no—
859C4×Q8—712no—
860C4×Q8—718no—
861C4×Q8—718no—
862C4×Q8—718no—
863C4×Q8—714no—
864C4×Q8—712no—
865C4×Q8—714no—
866C4×Q8—718no—
867C4×Q8—718no—
868C4×Q8—718no—
869C4×Q8—718no—
870C4×Q8C22×D7112yes—
871C4×Q8C22×D7114yes—
872C4×D4—718no—
873C4×D4—714no—
874C4×D4—712no—
875C4×D4—718no—
876C4×D4—718no—
877C4×D4—718no—
878C4×D4—718no—
879C4×D4—718no—
880C4×D4—7116no—
881C4×D4—7116no—
882C4×D4—718no—
883C4×D4—714no—
884C4×D4—714no—
885C4×D4—714no—
886C4×D4—7116no—
887C4×D4—7116no—
888C4×D4—7116no—
889C4×D4—714no—
890C4×D4—712no—
891C4×D4—714no—
892C4×D4—714no—
893C4×D4—714no—
894C4×D4—7116no—
895C4×D4—7116no—
896C4×D4—7116no—
897C4×D4—714no—
898C4×D4—712no—
899C4×D4C22×D7114yes—
900C4×D4C22×D7112yes—
901C4×D4C22×D7118yes—
902C4×D4C22×D7118yes—
903C4×D4C22×D7118yes—
904#117—711no—
905#117—712no—
906#117—712no—
907#117—718no—
908#117—7116no—
909#117—712no—
910#117—714no—
911#117—714no—
912#117—718no—
913#117—712no—
914#117—714no—
915#117—7116no—
916#117—714no—
917#117—718no—
918#117—718no—
919#117—7116no—
920#117—7116no—
921#117—712no—
922#117—712no—
923#117—712no—
924#117—714no—
925#117C22×D7111yescharacteristic
926#117C22×D7112yes—
927#117C22×D7112yes—
928C2×C4⋊C4—7116no—
929C2×C4⋊C4—714no—
930C2×C4⋊C4—712no—
931C2×C4⋊C4—714no—
932C2×C4⋊C4—714no—
933C2×C4⋊C4—718no—
934C2×C4⋊C4—714no—
935C2×C22⋊C4—718no—
936C2×C22⋊C4—718no—
937C2×C22⋊C4—712no—
938C2×C22⋊C4—714no—
939C2×C22⋊C4—714no—
940C2×C22⋊C4C22×D7118yes—
941C2×C42—7116no—
942C2×C42—712no—
943C2×C42—714no—
944C2×C42—711no—
945C2×C42—712no—
946C2×C42—712no—
947C2×C42—711no—
948C2×C42—714no—
949C2×C42—714no—
950C2×C42—712no—
951C2×C42—712no—
952C2×C42—714no—
953C2×C42—711no—
954C2×C42—712no—
955C2×C42—711no—
956C2×C42—712no—
957C2×C42—711no—
958C2×C42C22×D7111yescharacteristic
959C2×C42C22×D7112yes—
960C24—711no—
961C24—712no—
962C24C23×D7114yes—
963#41—24no—
964#41—416no—
965#41—28416no—
966#41—1428no—
967#41—1428no—
968#41—14216no—
969#41—14216no—
970#41—14216no—
971#41—14216no—
972#41—1424no—
973#41—1424no—
974#41—1424no—
975C2×Q8—2848no—
976C2×Q8—718no—
977C2×Q8—712no—
978C2×Q8—714no—
979C2×Q8—714no—
980C2×Q8—711no—
981C2×Q8—714no—
982C2×Q8—1424no—
983C2×Q8—1428no—
984C2×Q8C23×D7114yes—
985C2×Q8C23×D7111yescharacteristic
986C2×D4—28no—
987C2×D4—48no—
988C2×D4—7116no—
989C2×D4—712no—
990C2×D4—718no—
991C2×D4—712no—
992C2×D4—712no—
993C2×D4—718no—
994C2×D4—712no—
995C2×D4—711no—
996C2×D4—1424no—
997C2×D4—1428no—
998C2×D4—14216no—
999C2×D4C23×D7118yes—
1000C2×D4C23×D7112yes—
1001C2×D4C23×D7114yes—
1002C2×D4C23×D7111yescharacteristic
1003C2×D4C23×D7114yes—
1004C2×D4C23×D71116yes—
1005C2×D4C23×D7118yes—
1006C22×C4—2844no—
1007C22×C4—2848no—
1008C22×C4—712no—
1009C22×C4—714no—
1010C22×C4—7116no—
1011C22×C4—714no—
1012C22×C4—712no—
1013C22×C4—712no—
1014C22×C4—714no—
1015C22×C4—718no—
1016C22×C4—711no—
1017C22×C4—718no—
1018C22×C4—711no—
1019C22×C4—711no—
1020C22×C4—711no—
1021C22×C4—711no—
1022C22×C4—712no—
1023C22×C4—718no—
1024C22×C4—714no—
1025C22×C4—718no—
1026C22×C4—712no—
1027C22×C4—712no—
1028C22×C4—712no—
1029C22×C4—712no—
1030C22×C4—714no—
1031C22×C4—712no—
1032C22×C4—1428no—
1033C22×C4—14216no—
1034C22×C4C23×D7112yes—
1035C22×C4C23×D7114yes—
1036C22×C4C23×D7112yes—
1037C22×C4C23×D71116yes—
1038C22×C4C23×D7111yescharacteristic
1039C4⋊C4—714no—
1040C4⋊C4—718no—
1041C4⋊C4—714no—
1042C4⋊C4—718no—
1043C4⋊C4—7116no—
1044C4⋊C4—7116no—
1045C4⋊C4—714no—
1046C4⋊C4—718no—
1047C4⋊C4—718no—
1048C4⋊C4—7116no—
1049C4⋊C4—712no—
1050C4⋊C4—714no—
1051C4⋊C4—714no—
1052C4⋊C4—718no—
1053C4⋊C4—714no—
1054C4⋊C4—718no—
1055C4⋊C4—718no—
1056C4⋊C4—7116no—
1057C4⋊C4C23×D7114yes—
1058C4⋊C4C23×D7112yes—
1059C4⋊C4C23×D7114yes—
1060C4⋊C4C23×D7114yes—
1061C4⋊C4C23×D7118yes—
1062C22⋊C4—712no—
1063C22⋊C4—714no—
1064C22⋊C4—7116no—
1065C22⋊C4—7116no—
1066C22⋊C4—714no—
1067C22⋊C4—7116no—
1068C22⋊C4—7116no—
1069C22⋊C4—7116no—
1070C22⋊C4—714no—
1071C22⋊C4—718no—
1072C22⋊C4—714no—
1073C22⋊C4—714no—
1074C22⋊C4—7116no—
1075C22⋊C4C23×D7112yes—
1076C22⋊C4C23×D7114yes—
1077C22⋊C4C23×D7114yes—
1078C22⋊C4C23×D71116yes—
1079C22⋊C4C23×D71116yes—
1080C42—714no—
1081C42—712no—
1082C42—711no—
1083C42—712no—
1084C42—718no—
1085C42—712no—
1086C42—714no—
1087C42—714no—
1088C42—711no—
1089C42—712no—
1090C42—712no—
1091C42—714no—
1092C42—712no—
1093C42—7116no—
1094C42—7116no—
1095C42—714no—
1096C42C23×D7111yescharacteristic
1097C42C23×D7112yes—
1098C42C23×D7111yescharacteristic
1099C42C23×D7114yes—
1100C42C23×D7112yes—
1101C42C23×D7114yes—
1102C23—28no—
1103C23—48no—
1104C23—2842no—
1105C23—2844no—
1106C23—714no—
1107C23—711no—
1108C23—711no—
1109C23—712no—
1110C23—1424no—
1111C23C24×D7112yes—
1112C23C24×D7118yes—
1113C23C24×D7111yescharacteristic
1114Q8—22no—
1115Q8—28no—
1116Q8—2848no—
1117Q8—1424no—
1118Q8—1428no—
1119Q8—1422no—
1120Q8—1428no—
1121Q8—1428no—
1122D4—24no—
1123D4—28no—
1124D4—28no—
1125D4—22no—
1126D4—216no—
1127D4—48no—
1128D4—416no—
1129D4—28416no—
1130D4—1424no—
1131D4—1424no—
1132D4—1424no—
1133D4—14216no—
1134D4—14216no—
1135D4—1424no—
1136D4—1422no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—28no—
1140C2×C4—416no—
1141C2×C4—2844no—
1142C2×C4—2844no—
1143C2×C4—2842no—
1144C2×C4—2842no—
1145C2×C4—2848no—
1146C2×C4—2844no—
1147C2×C4—2842no—
1148C2×C4—28416no—
1149C2×C4—714no—
1150C2×C4—711no—
1151C2×C4—711no—
1152C2×C4—714no—
1153C2×C4—714no—
1154C2×C4—714no—
1155C2×C4—714no—
1156C2×C4—714no—
1157C2×C4—712no—
1158C2×C4—712no—
1159C2×C4—712no—
1160C2×C4—718no—
1161C2×C4—718no—
1162C2×C4—1424no—
1163C2×C4—1424no—
1164C2×C4—1424no—
1165C2×C4—14216no—
1166C2×C4—14216no—
1167C2×C4—1428no—
1168C2×C4—1424no—
1169C2×C4—1424no—
1170C2×C4—1424no—
1171C2×C4—1428no—
1172C2×C4#41×D7114yes—
1173C2×C4C24×D7114yes—
1174C2×C4C24×D7118yes—
1175C2×C4C24×D7112yes—
1176C2×C4C24×D7112yes—
1177C2×C4C24×D7111yescharacteristic
1178C2×C4C24×D7111yescharacteristic
1179C2×C4C24×D7112yes—
1180C22—22no—
1181C22—22no—
1182C22—28no—
1183C22—24no—
1184C22—216no—
1185C22—88no—
1186C22—2844no—
1187C22—2848no—
1188C22—712no—
1189C22—712no—
1190C22—1422no—
1191C22—1424no—
1192C22—1422no—
1193C22—1422no—
1194C22C2×#41×D7112yes—
1195C22C25×D7111yescharacteristic
1196C4—22no—
1197C4—24no—
1198C4—22no—
1199C4—28no—
1200C4—712no—
1201C4—712no—
1202C4—1422no—
1203C4—1428no—
1204C4—1422no—
1205C4—1424no—
1206C4—1428no—
1207C4—1422no—
1208C4C2×#41×D7112yes—
1209C4C2×#41×D7112yes—
1210C4#1798683414yes—
1211C2—22no—
1212C2—48no—
1213C2—42no—
1214C2—2842no—
1215C2—1422no—
1216C2—1422no—
1217C2C22×#41×D7111yescharacteristic
1218C2C2×#1798683412yes—
subgroupG/H
center, FrattiniC22C25×D71
commutator, socle, cosocleC22×C71C26
FittingC71×#3508C2
hypercenter#3508D71
hypocenterC71#62815
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #22602259C2semidirect
2. #22602241C2semidirect
3. #22602235C2semidirect
4. #22602231C2semidirect
5. #22602227C2semidirect
6. #22602226C2semidirect
7. #22602214C2semidirect
8. #22602197C2semidirect
9. #22602184C2semidirect
10. #22602167C2semidirect
11. #22601939C2semidirect
12. #22601936C2semidirect
13. #22601891C2semidirect
14. #22601724C2semidirect
15. #22601671C2semidirect
16. #22601635C2semidirect
17. #533×D71C2semidirect
18. C2×#17986547C2semidirect
19. #22601538C2semidirect
20. C4×#41×D71C2semidirect
21. C71×#3508C2semidirect
24. #17986735C22semidirect
25. #17986735C22semidirect
26. #17986732C22semidirect
27. #17986728C22semidirect
28. #17986727C22semidirect
29. #17986722C22semidirect
30. #17986719C22semidirect
31. #17986719C22semidirect
32. #17986718C22semidirect
33. #17986718C22semidirect
34. #17986713C22semidirect
35. #17986708C22semidirect
36. #17986699C22semidirect
37. #17986696C22semidirect
38. #17986696C22semidirect
39. #17986694C22semidirect
40. #17986692C22semidirect
41. #17986691C22semidirect
42. #17986689C22semidirect
43. #17986686C22semidirect
44. #17986680C22semidirect
45. #17986675C22semidirect
46. #17986669C22semidirect
47. #17986657C22semidirect
48. #17986656C22semidirect
49. #17986648C22semidirect
50. #17986643C22semidirect
51. #17986616C22semidirect
52. #17986614C22semidirect
53. #17986612C22semidirect
54. #17986611C22semidirect
55. #17986603C22semidirect
56. #17986592C22semidirect
57. #17986581C22semidirect
58. #17986578C22semidirect
61. #17986569C22semidirect
63. #17986562C22semidirect
65. #17986556C22semidirect
66. #17986556C22semidirect
67. #17986555C22semidirect
68. #17986554C22semidirect
69. #17986554C22semidirect
70. #17986553C22semidirect
71. #17986552C22semidirect
72. #17986551C22semidirect
73. #17986548C22semidirect
77. #17986547C22semidirect
78. #17986547C22semidirect
79. #17986547C22semidirect
80. #17986547C22semidirect
81. #17986547C22semidirect
82. C2×#14556128C22semidirect
83. C4⋊Q8×D71C22semidirect
84. #17986531C22semidirect
85. #17986531C22semidirect
86. #17986530C22semidirect
87. #17986530C22semidirect
88. #17986530C22semidirect
89. #17986528C22semidirect
90. #17986528C22semidirect
91. #17986526C22semidirect
92. #125×D71C22semidirect
93. C2×#14556115C22semidirect
94. #17986509C22semidirect
95. #17986509C22semidirect
96. #17986506C22semidirect
100. #17986478C22semidirect
101. #17986478C22semidirect
102. #17986476C22semidirect
103. #17986476C22semidirect
104. #17986474C22semidirect
107. #41×Dic71C22semidirect
108. C4×#11765866C22semidirect
110. C4×#11765865C22semidirect
112. #17986467C22semidirect
114. C4×#11765864C22semidirect
115. C4×#11765864C22semidirect
116. C4×#11765864C22semidirect
117. C4×#11765864C22semidirect
118. C4×Q8×D71C22semidirect
119. C4×Q8×D71C22semidirect
120. C2×D4×Dic71C22semidirect
122. C4×D4×D71C22semidirect
123. C2×#14556084C22semidirect
126. #117×D71C22semidirect
128. C2×C42×D71C22semidirect
129. #559×C71C22semidirect
130. #550×C71C22semidirect
131. #546×C71C22semidirect
132. #540×C71C22semidirect
134. #533×C71C22semidirect
135. #532×C71C22semidirect
136. C2×#127×C71C22semidirect
137. #518×C71C22semidirect
394. C2×C4×D71#41semidirect
617. #3508D71semidirect
631. C71#62815semidirect
637. #559C2×D71semidirect
658. #550C2×D71semidirect
663. #546C2×D71semidirect
669. #540C2×D71semidirect
688. #533C2×D71semidirect
698. #532C2×D71semidirect
701. C2×#127C2×D71semidirect
724. #518C2×D71semidirect

Maximal subgroups

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

subgroupindex
#226022592
#226022412
#226022352
#226022312
#226022272
#226022262
#226022142
#226021972
#226021842
#226021672
#226019392
#226019362
#226018912
#226017242
#226016712
#226016352
#533×D712
C2×#179865472
#226015382
C4×#41×D712
C71×#35082
#6281571