Finite Group Databasebeta

← C2×#22602043 #32905388

Subgroups — C2×#22602043 #32905388

Order 18176.

7910 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602043C2132yesmaximal, direct product factor
2C2×#17986709C212yesmaximal, complemented
3C2×#17986704C212yesmaximal, complemented
4C2×#17986699C212yesmaximal, complemented
5C2×#17986693C212yesmaximal, complemented
6C2×#17986690C212yesmaximal, complemented
7C2×#17986688C212yesmaximal, complemented
8C2×#17986654C212yesmaximal, complemented
9C2×#17986650C212yesmaximal, complemented
10C2×#17986627C211yesmaximal, characteristic, complemented
11C2×#17986591C214yesmaximal, complemented
12C2×#17986577C211yesmaximal, characteristic, complemented
13C2×#17986511C211yesmaximal, characteristic, complemented
14C2×#17986508C214yesmaximal, complemented
15C2×#17986506C211yesmaximal, characteristic, complemented
16C2×#17986480C211yesmaximal, characteristic, complemented
17C22×C4⋊C4×D71C211yesmaximal, characteristic, complemented
18C2×#520×C71C211yesmaximal, characteristic, complemented
19C22×#11765865C2211yescharacteristic
20C22×#11765865C2214yes—
21C23×C4×D71C2211yescharacteristic
22C23×C4×D71C2212yes—
23#17986709C22132yescomplemented
24#17986704C22132yescomplemented
25#17986699C22132yescomplemented
26#17986693C22132yescomplemented
27#17986690C22132yescomplemented
28#17986688C22132yescomplemented
29#17986654C22132yescomplemented
30#17986650C22132yescomplemented
31#17986627C22116yescomplemented
32#17986591C22164yescomplemented
33#17986577C22116yescomplemented
34C2×#14556128C2212yescomplemented
35C2×#14556127C2212yescomplemented
36C2×#14556122C2214yescomplemented
37C2×#14556121C2214yescomplemented
38C2×#14556120C2212yescomplemented
39C2×#14556120C2214yescomplemented
40C2×#14556119C2212yescomplemented
41C2×#14556118C2214yescomplemented
42#17986511C22116yescomplemented
43#17986508C22164yescomplemented
44#17986506C22116yescomplemented
45C2×#14556113C2214yes—
46C2×#14556112C2212yes—
47C2×#14556111C2214yescomplemented
48C2×#14556110C2214yes—
49C2×#14556110C2214yescomplemented
50C2×#14556109C2212yes—
51C2×#14556108C2211yescharacteristic
52C2×#14556108C2211yescharacteristic
53C2×#14556107C2214yescomplemented
54C2×#14556107C2212yescomplemented
55C2×#14556106C2214yes—
56C2×#14556106C2214yescomplemented
57C2×#14556105C2214yes—
58C2×#14556104C2211yescharacteristic
59C2×#14556104C2211yescharacteristic
60C2×#14556104C2212yescomplemented
61C2×#14556103C2211yescharacteristic
62C2×#14556103C2211yescharacteristic
63C2×#14556102C2212yescomplemented
64C2×#14556101C2214yes—
65C2×#14556100C2214yes—
66C2×#14556099C2211yescharacteristic
67C2×#14556099C2211yescharacteristic
68C2×#14556099C2212yescomplemented
69C2×#14556098C2212yes—
70C2×#14556096C2212yes—
71#17986480C22116yescomplemented
72C2×#14556093C2212yescomplemented
73C2×C4×D284C2212yes—
74C2×C4×D284C2214yes—
75C2×C4×D284C2212yes—
76C2×#14556090C2212yescomplemented
77C2×C4×C22⋊D71C2214yes—
78C2×C4×C22⋊D71C2212yes—
79C2×C4×C22⋊D71C2212yes—
80C2×C4×C22⋊D71C2214yes—
81C2×#14556087C2211yescharacteristic
82C2×#14556086C2212yescomplemented
83C2×#14556085C2214yes—
84C22×C4⋊Dic71C2211yescharacteristic
85C22×Dic71⋊C4C2212yes—
86C2×C4⋊C4×D71C2212yes—
87C2×C4⋊C4×D71C2212yes—
88C2×C4⋊C4×D71C2212yes—
89C2×C4⋊C4×D71C2212yes—
90C2×C4⋊C4×D71C22116yescomplemented
91C2×C4⋊C4×D71C2212yescomplemented
92C22×#41×C71C2211yescharacteristic
93#520×C71C22116yescomplemented
94C2×C4×Q8×C71C2212yescomplemented
95C2×C4×D4×C71C2214yes—
96C2×C4×D4×C71C2212yescomplemented
97C2×#117×C71C2211yescharacteristic
98C2×#117×C71C2212yescomplemented
99C22×C4⋊C4×C71C2211yescharacteristic
100C22×C4⋊C4×C71C2212yescomplemented
101C24×D71C2311yescharacteristic
102C2×#11765865—28no—
103C2×#11765865—416no—
104C2×#11765865C2318yes—
105C2×#11765865C23132yes—
106C22×Dic142C2311yescharacteristic
107C22×Dic142C2314yes—
108C22×D284C2312yes—
109C22×D284C2311yescharacteristic
110C22×D284C2312yes—
111C22×C22⋊D71C2312yes—
112C22×C22⋊D71C2312yes—
113C22×C22⋊D71C2312yes—
114C22×C22⋊D71C2314yes—
115C23×Dic71C2311yescharacteristic
116C23×Dic71C2312yes—
117C22×C4×D71—28no—
118C22×C4×D71—48no—
119C22×C4×D71C2314yes—
120C22×C4×D71C2311yescharacteristic
121C22×C4×D71C2311yescharacteristic
122C22×C4×D71C2311yescharacteristic
123C22×C4×D71C2311yescharacteristic
124C22×C4×D71C2318yes—
125C22×C4×D71C2312yes—
126C22×C4×D71C2314yes—
127C22×C4×D71C23116yes—
128C22×C4×D71C2314yes—
129#14556128C23116yescomplemented
130#14556127C23116yescomplemented
131#14556122C23132yescomplemented
132#14556121C23132yescomplemented
133#14556120C23132yescomplemented
134#14556120C23116yescomplemented
135#14556119C23116yescomplemented
136#14556118C23132yescomplemented
137#14556113C23132yes—
138#14556112C23116yes—
139#14556111C23132yescomplemented
140#14556110C23132yes—
141#14556110C23132yescomplemented
142#14556109C23116yes—
143#14556108C2318yes—
144#14556108C2318yes—
145#14556107C23116yescomplemented
146#14556107C23132yescomplemented
147#14556106C23132yes—
148#14556106C23132yescomplemented
149#14556105C23132yes—
150#14556104C2318yes—
151#14556104C2318yes—
152#14556104C23116yescomplemented
153#14556103C2318yes—
154#14556103C2318yes—
155#14556102C23116yescomplemented
156#14556101C23132yes—
157#14556100C23132yes—
158#14556099C2318yes—
159#14556099C2318yes—
160#14556099C23116yescomplemented
161#14556098C23116yes—
162#14556096C23116yes—
163#14556093C23116yescomplemented
164C4×D284C23116yes—
165C4×D284C23132yes—
166C4×D284C23116yes—
167#14556090C23116yescomplemented
168C4×C22⋊D71C23132yes—
169C4×C22⋊D71C23116yes—
170C4×C22⋊D71C23116yes—
171C4×C22⋊D71C23132yes—
172#14556087C2318yes—
173#14556086C23116yescomplemented
174#14556085C23132yes—
175C2×C4⋊Dic71C2318yes—
176C2×C4⋊Dic71C2312yes—
177C2×C4⋊Dic71C2312yes—
178C2×C4⋊Dic71C2311yescharacteristic
179C2×C4⋊Dic71C2311yescharacteristic
180C2×C4⋊Dic71C2314yes—
181C2×C4⋊Dic71C2312yes—
182C2×C4⋊Dic71C2312yes—
183C2×Dic71⋊C4C23116yes—
184C2×Dic71⋊C4C2314yes—
185C2×Dic71⋊C4C2314yes—
186C2×Dic71⋊C4C2314yes—
187C2×Dic71⋊C4C2314yes—
188C2×Dic71⋊C4C2314yes—
189C2×Dic71⋊C4C2312yes—
190C2×Dic71⋊C4C2312yes—
191C2×Dic71⋊C4C2314yes—
192C4⋊C4×D71C23116yes—
193C4⋊C4×D71C23116yes—
194C4⋊C4×D71C23116yes—
195C4⋊C4×D71C23116yes—
196C4⋊C4×D71C23116yescomplemented
197C2×C22⋊Dic71C2312yes—
198C2×C22⋊Dic71C2312yes—
199C2×C22⋊Dic71C2312yes—
200C2×C22⋊Dic71C2314yes—
201C2×(C2×D71)⋊C4C2312yes—
202C2×(C2×D71)⋊C4C2312yes—
203C2×(C2×D71)⋊C4C2314yes—
204C2×(C2×D71)⋊C4C2312yes—
205C2×(C2×D71)⋊C4C2312yes—
206C2×(C2×D71)⋊C4C2314yes—
207C2×(C2×D71)⋊C4C2312yes—
208C2×(C2×D71)⋊C4C2312yes—
209C2×C4×Dic71C2314yes—
210C2×C4×Dic71C2312yes—
211C2×#41×C71—28no—
212C2×#41×C71C2318yes—
213C22×Q8×C71C2311yescharacteristic
214C22×D4×C71C2312yes—
215C22×D4×C71C2311yescharacteristic
216C23×C4×C71C2312yes—
217C23×C4×C71C2312yes—
218C23×C4×C71C2314yes—
219C23×C4×C71C2311yescharacteristic
220C4×Q8×C71C23116yescomplemented
221C4×D4×C71C23132yes—
222C4×D4×C71C23116yescomplemented
223#117×C71C2318yes—
224#117×C71C23116yescomplemented
225C2×C4⋊C4×C71C2312yes—
226C2×C4⋊C4×C71C2312yes—
227C2×C4⋊C4×C71C2318yes—
228C2×C4⋊C4×C71C2311yescharacteristic
229C2×C4⋊C4×C71C2314yes—
230C2×C4⋊C4×C71C2311yescharacteristic
231C2×C4⋊C4×C71C23116yescomplemented
232C2×C22⋊C4×C71C2312yes—
233C2×C22⋊C4×C71C2314yes—
234C2×C42×C71C2312yes—
235C2×C42×C71C2314yes—
236C23×D71—24no—
237C23×D71—24no—
238C23×D71—24no—
239C23×D71C2414yes—
240C23×D71C2412yes—
241C23×D71C2411yescharacteristic
242C23×D71C2411yescharacteristic
243#11765865—232no—
244#11765865—464no—
245C2×Dic142—24no—
246C2×Dic142—48no—
247C2×Dic142C2414yes—
248C2×Dic142C24116yes—
249C2×D284—28no—
250C2×D284—28no—
251C2×D284—24no—
252C2×D284C2418yes—
253C2×D284C2414yes—
254C2×D284C2418yes—
255C2×C22⋊D71—28no—
256C2×C22⋊D71—28no—
257C2×C22⋊D71—28no—
258C2×C22⋊D71—48no—
259C2×C22⋊D71C2418yes—
260C2×C22⋊D71C2418yes—
261C2×C22⋊D71C2418yes—
262C2×C22⋊D71C24116yes—
263C22×Dic71—24no—
264C22×Dic71—44no—
265C22×Dic71C2414yes—
266C22×Dic71C2411yescharacteristic
267C22×Dic71C2411yescharacteristic
268C22×Dic71C2414yes—
269C22×Dic71C2412yes—
270C22×Dic71C2412yes—
271C22×Dic71C2412yes—
272C22×Dic71C2418yes—
273C2×C4×D71—216no—
274C2×C4×D71—24no—
275C2×C4×D71—24no—
276C2×C4×D71—24no—
277C2×C4×D71—24no—
278C2×C4×D71—28no—
279C2×C4×D71—232no—
280C2×C4×D71—432no—
281C2×C4×D71—48no—
282C2×C4×D71—48no—
283C2×C4×D71C24116yes—
284C2×C4×D71C2414yes—
285C2×C4×D71C2414yes—
286C2×C4×D71C2414yes—
287C2×C4×D71C2414yes—
288C2×C4×D71C2418yes—
289C2×C4×D71C24116yes—
290C2×C4×D71C24116yes—
291C4⋊Dic71C2418yes—
292C4⋊Dic71C2418yes—
293C4⋊Dic71C2414yes—
294C4⋊Dic71C2414yes—
295C4⋊Dic71C24116yes—
296C4⋊Dic71C2418yes—
297C4⋊Dic71C2418yes—
298Dic71⋊C4C24116yes—
299Dic71⋊C4C24116yes—
300Dic71⋊C4C24116yes—
301Dic71⋊C4C24116yes—
302Dic71⋊C4C24116yes—
303Dic71⋊C4C2418yes—
304Dic71⋊C4C2418yes—
305Dic71⋊C4C24116yes—
306C22⋊Dic71C2418yes—
307C22⋊Dic71C2418yes—
308C22⋊Dic71C2418yes—
309C22⋊Dic71C24116yes—
310(C2×D71)⋊C4C2418yes—
311(C2×D71)⋊C4C2418yes—
312(C2×D71)⋊C4C24116yes—
313(C2×D71)⋊C4C2418yes—
314(C2×D71)⋊C4C2418yes—
315(C2×D71)⋊C4C24116yes—
316(C2×D71)⋊C4C2418yes—
317(C2×D71)⋊C4C2418yes—
318C4×Dic71C24116yes—
319C4×Dic71C2418yes—
320C24×C71C2412yes—
321C24×C71C2411yescharacteristic
322#41×C71—232no—
323C2×Q8×C71—24no—
324C2×Q8×C71C2414yes—
325C2×D4×C71—28no—
326C2×D4×C71—24no—
327C2×D4×C71C2418yes—
328C2×D4×C71C2414yes—
329C22×C4×C71—28no—
330C22×C4×C71—44no—
331C22×C4×C71—48no—
332C22×C4×C71#4118yescomplemented
333C22×C4×C71C2414yes—
334C22×C4×C71C2412yes—
335C22×C4×C71C2412yes—
336C22×C4×C71C2412yes—
337C22×C4×C71C2418yes—
338C22×C4×C71C2418yes—
339C22×C4×C71C24116yes—
340C22×C4×C71C2411yescharacteristic
341C22×C4×C71C2411yescharacteristic
342C22×C4×C71C2414yes—
343C4⋊C4×C71C2418yes—
344C4⋊C4×C71C2418yes—
345C4⋊C4×C71C2414yes—
346C4⋊C4×C71C24116yes—
347C4⋊C4×C71C2414yes—
348C22⋊C4×C71C2418yes—
349C22⋊C4×C71C24116yes—
350C42×C71C2418yes—
351C42×C71C24116yes—
352C23×C71—22no—
353C23×C71—22no—
354C23×C71—24no—
355C23×C71—24no—
356C23×C71—24no—
357C23×C71C2×#4114yes—
358C23×C71C2514yes—
359C23×C71C2512yes—
360C23×C71C2511yescharacteristic
361C22×D71—232no—
362C22×D71—28no—
363C22×D71—22no—
364C22×D71—22no—
365C22×D71—22no—
366C22×D71—22no—
367C22×D71—28no—
368C22×D71—28no—
369C22×D71—24no—
370C22×D71—24no—
371C22×D71—24no—
372C22×D71H(5,𝔽2)14yes—
373C22×D712−1+414yes—
374C22×D71C2514yes—
375C22×D71C2512yes—
376C22×D71C2512yes—
377Q8×C71—28no—
378D4×C71—216no—
379D4×C71—28no—
380C2×C4×C71—24no—
381C2×C4×C71—28no—
382C2×C4×C71—24no—
383C2×C4×C71—24no—
384C2×C4×C71—216no—
385C2×C4×C71—48no—
386C2×C4×C71—416no—
387C2×C4×C71C2×#4114yes—
388C2×C4×C71C2×#4114yes—
389C2×C4×C71C2×#41116yescomplemented
390C2×C4×C71C2514yes—
391C2×C4×C71C2514yes—
392C2×C4×C71C2518yes—
393C2×C4×C71C2514yes—
394C2×C4×C71C2512yes—
395C2×C4×C71C2512yes—
396C22⋊D71—216no—
397C22⋊D71—216no—
398C22⋊D71—216no—
399C22⋊D71—416no—
400C2×Dic71—28no—
401C2×Dic71—22no—
402C2×Dic71—22no—
403C2×Dic71—24no—
404C2×Dic71—28no—
405C2×Dic71—24no—
406C2×Dic71—24no—
407C2×Dic71—48no—
408C2×Dic71C2514yes—
409C2×Dic71C2514yes—
410C2×Dic71C2514yes—
411C2×Dic71C2512yes—
412C2×Dic71C2512yes—
413C2×Dic71C2518yes—
414D284—216no—
415D284—216no—
416D284—28no—
417C4×D71—232no—
418C4×D71—28no—
419C4×D71—28no—
420C4×D71—28no—
421C4×D71—28no—
422C4×D71—216no—
423C4×D71—416no—
424C4×D71—416no—
425Dic142—28no—
426Dic142—416no—
427C22×C71—22no—
428C22×C71—22no—
429C22×C71—28no—
430C22×C71—24no—
431C22×C71—24no—
432C22×C71—24no—
433C22×C71—48no—
434C22×C71C22×#4114yes—
435C22×C71C22×#4112yes—
436C22×C71C2×H(5,𝔽2)12yes—
437C22×C71C2×2−1+412yes—
438C22×C71C2611yescharacteristic
439C2×D71—232no—
440C2×D71—22no—
441C2×D71—22no—
442C2×D71—22no—
443C2×D71—22no—
444C2×D71—28no—
445C2×D71—28no—
446C2×D71—24no—
447C2×D71—24no—
448C2×D71—24no—
449C2×D71—48no—
450C2×D71C2×H(5,𝔽2)14yes—
451C2×D71C2×2−1+414yes—
452C4×C71—24no—
453C4×C71—24no—
454C4×C71—28no—
455C4×C71—24no—
456C4×C71C22×#4114yes—
457C4×C71C22×#4114yes—
458Dic71—24no—
459Dic71—22no—
460Dic71—22no—
461Dic71—24no—
462Dic71—28no—
463Dic71—24no—
464C2×#3492—711nomaximal, Sylow
465C2×C71—24no—
466C2×C71—44no—
467C2×C71#349214yescomplemented
468C2×C71C23×#4111yescharacteristic
469C2×C71C22×H(5,𝔽2)11yescharacteristic
470C2×C71C22×2−1+411yescharacteristic
471D71—24no—
472D71—24no—
473D71—44no—
474#3492—7132no—
475C2×#554—712no—
476C2×#554—712no—
477C2×#553—712no—
478C2×#553—712no—
479C2×#552—712no—
480C2×#552—712no—
481C2×#547—712no—
482C2×#547—712no—
483C2×#544—711no—
484C2×#539—714no—
485C2×#537—711no—
486C2×#525—711no—
487C2×#525—714no—
488C2×#525—711no—
489C2×#520—711no—
490C2×#520D7111yescharacteristic, complemented
491C23×C4⋊C4—711no—
492C71C2×#349211yescharacteristic, complemented, Sylow
493C22×#41—714no—
494C22×#41—711no—
495C22×#41C2×D7111yescharacteristic
496C24×C4—712no—
497C24×C4—711no—
498#554—7132no—
499#554—7132no—
500#553—7132no—
501#553—7132no—
502#552—7132no—
503#552—7132no—
504#547—7132no—
505#547—7132no—
506#544—7116no—
507#539—7164no—
508#537—7116no—
509C2×C4⋊Q8—712no—
510C2×C4⋊Q8—712no—
511C2×#126—714no—
512C2×#126—714no—
513C2×#125—714no—
514C2×#125—712no—
515C2×#125—714no—
516C2×#125—712no—
517#525—7116no—
518#525—7164no—
519#525—7116no—
520C2×#123—712no—
521C2×#123—714no—
522C2×#123—714no—
523C2×#123—712no—
524C2×#123—714no—
525C2×#123—714no—
526C2×C22⋊Q8—711no—
527C2×C22⋊Q8—711no—
528C2×C22⋊Q8—712no—
529C2×C22⋊Q8—712no—
530C2×C22⋊Q8—714no—
531C2×C22⋊Q8—711no—
532C2×C22⋊Q8—714no—
533C2×C22⋊Q8—711no—
534C2×C22⋊Q8—714no—
535C2×C22⋊Q8—714no—
536C2×#121—714no—
537C2×#121—711no—
538C2×#121—711no—
539C2×#121—712no—
540C2×#121—712no—
541C2×#121—711no—
542C2×#121—711no—
543C2×#121—714no—
544C2×#120—712no—
545C2×#120—712no—
546#520—7116no—
547#520C2×D71116yescomplemented
548C2×C4×Q8—712no—
549C2×C4×Q8C2×D7112yescomplemented
550C2×C4×D4—714no—
551C2×C4×D4—712no—
552C2×C4×D4—714no—
553C2×C4×D4—712no—
554C2×C4×D4—712no—
555C2×C4×D4—712no—
556C2×C4×D4—714no—
557C2×C4×D4—712no—
558C2×C4×D4C2×D7114yes—
559C2×C4×D4C2×D7112yescomplemented
560C2×#117—711no—
561C2×#117—712no—
562C2×#117—714no—
563C2×#117C2×D7111yescharacteristic
564C2×#117C2×D7112yescomplemented
565C22×C4⋊C4—711no—
566C22×C4⋊C4—712no—
567C22×C4⋊C4—712no—
568C22×C4⋊C4—712no—
569C22×C4⋊C4—712no—
570C22×C4⋊C4—712no—
571C22×C4⋊C4—7116no—
572C22×C4⋊C4—712no—
573C22×C4⋊C4C2×D7111yescharacteristic
574C22×C4⋊C4C2×D7112yescomplemented
575C25—711no—
576C2×#41—28no—
577C2×#41—28416no—
578C2×#41—7132no—
579C2×#41—718no—
580C2×#41—1428no—
581C2×#41C22×D7118yes—
582C22×Q8—714no—
583C22×Q8—711no—
584C22×Q8C22×D7111yescharacteristic
585C22×D4—714no—
586C22×D4—712no—
587C22×D4—712no—
588C22×D4—712no—
589C22×D4—712no—
590C22×D4—711no—
591C22×D4—712no—
592C22×D4C22×D7112yes—
593C22×D4C22×D7111yescharacteristic
594C23×C4—2848no—
595C23×C4—712no—
596C23×C4—714no—
597C23×C4—7116no—
598C23×C4—714no—
599C23×C4—711no—
600C23×C4—714no—
601C23×C4—711no—
602C23×C4—711no—
603C23×C4—711no—
604C23×C4—711no—
605C23×C4—718no—
606C23×C4—712no—
607C23×C4—1428no—
608C23×C4C22×D7112yes—
609C23×C4C22×D7112yes—
610C23×C4C22×D7114yes—
611C23×C4C22×D7111yescharacteristic
612C4⋊Q8—7116no—
613C4⋊Q8—7116no—
614#126—7132no—
615#126—7132no—
616#125—7132no—
617#125—7116no—
618#125—7132no—
619#125—7116no—
620#123—7116no—
621#123—7132no—
622#123—7132no—
623#123—7116no—
624#123—7132no—
625#123—7132no—
626C22⋊Q8—718no—
627C22⋊Q8—718no—
628C22⋊Q8—7116no—
629C22⋊Q8—7116no—
630C22⋊Q8—7132no—
631C22⋊Q8—718no—
632C22⋊Q8—7132no—
633C22⋊Q8—718no—
634C22⋊Q8—7132no—
635C22⋊Q8—7132no—
636#121—7132no—
637#121—718no—
638#121—718no—
639#121—7116no—
640#121—7116no—
641#121—718no—
642#121—718no—
643#121—7132no—
644#120—7116no—
645#120—7116no—
646C4×Q8—7116no—
647C4×Q8C22×D71116yescomplemented
648C4×D4—7132no—
649C4×D4—7116no—
650C4×D4—7132no—
651C4×D4—7116no—
652C4×D4—7116no—
653C4×D4—7116no—
654C4×D4—7132no—
655C4×D4—7116no—
656C4×D4C22×D71132yes—
657C4×D4C22×D71116yescomplemented
658#117—718no—
659#117—7116no—
660#117—7132no—
661#117C22×D7118yes—
662#117C22×D71116yescomplemented
663C2×C4⋊C4—712no—
664C2×C4⋊C4—712no—
665C2×C4⋊C4—714no—
666C2×C4⋊C4—714no—
667C2×C4⋊C4—718no—
668C2×C4⋊C4—7116no—
669C2×C4⋊C4—711no—
670C2×C4⋊C4—714no—
671C2×C4⋊C4—711no—
672C2×C4⋊C4—714no—
673C2×C4⋊C4—714no—
674C2×C4⋊C4—712no—
675C2×C4⋊C4—712no—
676C2×C4⋊C4—714no—
677C2×C4⋊C4—714no—
678C2×C4⋊C4—712no—
679C2×C4⋊C4—712no—
680C2×C4⋊C4—7116no—
681C2×C4⋊C4—7116no—
682C2×C4⋊C4—7116no—
683C2×C4⋊C4—7116no—
684C2×C4⋊C4—7116no—
685C2×C4⋊C4C22×D7112yes—
686C2×C4⋊C4C22×D7112yes—
687C2×C4⋊C4C22×D7118yes—
688C2×C4⋊C4C22×D7111yescharacteristic
689C2×C4⋊C4C22×D7114yes—
690C2×C4⋊C4C22×D7111yescharacteristic
691C2×C4⋊C4C22×D71116yescomplemented
692C2×C22⋊C4—712no—
693C2×C22⋊C4—714no—
694C2×C22⋊C4—712no—
695C2×C22⋊C4—712no—
696C2×C22⋊C4—712no—
697C2×C22⋊C4—712no—
698C2×C22⋊C4—714no—
699C2×C22⋊C4—712no—
700C2×C22⋊C4—712no—
701C2×C22⋊C4—714no—
702C2×C22⋊C4—712no—
703C2×C22⋊C4—712no—
704C2×C22⋊C4C22×D7112yes—
705C2×C22⋊C4C22×D7114yes—
706C2×C42—714no—
707C2×C42—712no—
708C2×C42C22×D7114yes—
709C2×C42C22×D7112yes—
710C24—711no—
711C24—711no—
712C24—714no—
713C24—712no—
714C24—1424no—
715C24—1424no—
716C24—1424no—
717C24C23×D7112yes—
718C24C23×D7111yescharacteristic
719#41—232no—
720#41—28464no—
721#41—14232no—
722C2×Q8—24no—
723C2×Q8—2848no—
724C2×Q8—7116no—
725C2×Q8—714no—
726C2×Q8—1424no—
727C2×Q8C23×D7114yes—
728C2×D4—28no—
729C2×D4—24no—
730C2×D4—2848no—
731C2×D4—7116no—
732C2×D4—718no—
733C2×D4—718no—
734C2×D4—718no—
735C2×D4—718no—
736C2×D4—714no—
737C2×D4—718no—
738C2×D4—1428no—
739C2×D4—1428no—
740C2×D4—1428no—
741C2×D4—1428no—
742C2×D4—1428no—
743C2×D4—1424no—
744C2×D4C23×D7118yes—
745C2×D4C23×D7114yes—
746C22×C4—28no—
747C22×C4—44no—
748C22×C4—48no—
749C22×C4—2848no—
750C22×C4—2848no—
751C22×C4—28432no—
752C22×C4—2844no—
753C22×C4—718no—
754C22×C4—7116no—
755C22×C4—7116no—
756C22×C4—714no—
757C22×C4—712no—
758C22×C4—712no—
759C22×C4—712no—
760C22×C4—711no—
761C22×C4—711no—
762C22×C4—714no—
763C22×C4—7116no—
764C22×C4—714no—
765C22×C4—714no—
766C22×C4—714no—
767C22×C4—714no—
768C22×C4—718no—
769C22×C4—14216no—
770C22×C4—1424no—
771C22×C4—1424no—
772C22×C4—1424no—
773C22×C4—1424no—
774C22×C4—1424no—
775C22×C4—1428no—
776C22×C4—14232no—
777C22×C4#1176586518yescomplemented
778C22×C4C23×D7118yes—
779C22×C4C23×D7114yes—
780C22×C4C23×D7112yes—
781C22×C4C23×D7112yes—
782C22×C4C23×D7112yes—
783C22×C4C23×D7118yes—
784C22×C4C23×D71116yes—
785C22×C4C23×D7111yescharacteristic
786C22×C4C23×D7111yescharacteristic
787C22×C4C23×D7114yes—
788C4⋊C4—7116no—
789C4⋊C4—7116no—
790C4⋊C4—7116no—
791C4⋊C4—7116no—
792C4⋊C4—7116no—
793C4⋊C4—718no—
794C4⋊C4—7116no—
795C4⋊C4—718no—
796C4⋊C4—718no—
797C4⋊C4—718no—
798C4⋊C4—714no—
799C4⋊C4—714no—
800C4⋊C4—718no—
801C4⋊C4—7116no—
802C4⋊C4—718no—
803C4⋊C4C23×D7118yes—
804C4⋊C4C23×D7118yes—
805C4⋊C4C23×D7114yes—
806C4⋊C4C23×D71116yes—
807C4⋊C4C23×D7114yes—
808C22⋊C4—718no—
809C22⋊C4—7116no—
810C22⋊C4—718no—
811C22⋊C4—718no—
812C22⋊C4—718no—
813C22⋊C4—718no—
814C22⋊C4—7116no—
815C22⋊C4—718no—
816C22⋊C4—718no—
817C22⋊C4—7116no—
818C22⋊C4—718no—
819C22⋊C4—718no—
820C22⋊C4C23×D7118yes—
821C22⋊C4C23×D71116yes—
822C42—7116no—
823C42—718no—
824C42C23×D71116yes—
825C42C23×D7118yes—
826C23—22no—
827C23—22no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—714no—
832C23—714no—
833C23—712no—
834C23—712no—
835C23—714no—
836C23—1428no—
837C23—1428no—
838C23—14232no—
839C23—1424no—
840C23—1424no—
841C23—1424no—
842C23—1428no—
843C23—1422no—
844C23—1422no—
845C23—1422no—
846C23—1422no—
847C23C2×#1176586514yes—
848C23C24×D7114yes—
849C23C24×D7112yes—
850C23C24×D7111yescharacteristic
851Q8—28no—
852Q8—28416no—
853Q8—1428no—
854D4—216no—
855D4—28no—
856D4—28416no—
857D4—14216no—
858D4—14216no—
859D4—14216no—
860D4—14216no—
861D4—14216no—
862D4—1428no—
863C2×C4—24no—
864C2×C4—28no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—216no—
868C2×C4—48no—
869C2×C4—416no—
870C2×C4—28416no—
871C2×C4—28416no—
872C2×C4—2848no—
873C2×C4—714no—
874C2×C4—714no—
875C2×C4—714no—
876C2×C4—712no—
877C2×C4—712no—
878C2×C4—718no—
879C2×C4—14232no—
880C2×C4—1428no—
881C2×C4—1422no—
882C2×C4—1422no—
883C2×C4—1424no—
884C2×C4—1428no—
885C2×C4—1424no—
886C2×C4—1424no—
887C2×C4—1428no—
888C2×C4—1428no—
889C2×C4—1428no—
890C2×C4—1428no—
891C2×C4—14216no—
892C2×C4C2×#1176586514yes—
893C2×C4C2×#1176586514yes—
894C2×C4C2×#11765865116yescomplemented
895C2×C4C24×D7118yes—
896C2×C4C24×D7114yes—
897C2×C4C24×D7114yes—
898C2×C4C24×D7114yes—
899C2×C4C24×D7112yes—
900C2×C4C24×D7112yes—
901C22—28no—
902C22—22no—
903C22—22no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—48no—
908C22—2848no—
909C22—714no—
910C22—714no—
911C22—14232no—
912C22—1424no—
913C22—1424no—
914C22—1424no—
915C22—1428no—
916C22—1428no—
917C22—1422no—
918C22—1422no—
919C22—1422no—
920C22—1422no—
921C22C22×#1176586514yes—
922C22C22×#1176586512yes—
923C22H(5,𝔽2)×D7112yes—
924C222−1+4×D7112yes—
925C22C25×D7111yescharacteristic
926C4—24no—
927C4—28no—
928C4—24no—
929C4—24no—
930C4—1422no—
931C4—1422no—
932C4—1424no—
933C4—1428no—
934C4—1424no—
935C4—1424no—
936C4C22×#1176586514yes—
937C4C22×#1176586514yes—
938C2—24no—
939C2—44no—
940C2—2844no—
941C2—1424no—
942C2—1424no—
943C2#2260204314yesdirect product factor
944C2C23×#1176586511yescharacteristic
945C2C2×H(5,𝔽2)×D7111yescharacteristic
946C2C2×2−1+4×D7111yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#520×C71C2
socleC23×C71C25
hypercenterC2×#520D71
hypocenterC71C2×#3492
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #22602043C2direct (N × H)
2. C2×#17986709C2semidirect
3. C2×#17986704C2semidirect
4. C2×#17986699C2semidirect
5. C2×#17986693C2semidirect
6. C2×#17986690C2semidirect
7. C2×#17986688C2semidirect
8. C2×#17986654C2semidirect
9. C2×#17986650C2semidirect
10. C2×#17986627C2semidirect
11. C2×#17986591C2semidirect
12. C2×#17986577C2semidirect
13. C2×#17986511C2semidirect
14. C2×#17986508C2semidirect
15. C2×#17986506C2semidirect
16. C2×#17986480C2semidirect
17. C22×C4⋊C4×D71C2semidirect
18. C2×#520×C71C2semidirect
23. #17986709C22semidirect
24. #17986704C22semidirect
25. #17986699C22semidirect
26. #17986693C22semidirect
27. #17986690C22semidirect
28. #17986688C22semidirect
29. #17986654C22semidirect
30. #17986650C22semidirect
31. #17986627C22semidirect
32. #17986591C22semidirect
33. #17986577C22semidirect
34. C2×#14556128C22semidirect
35. C2×#14556127C22semidirect
36. C2×#14556122C22semidirect
37. C2×#14556121C22semidirect
38. C2×#14556120C22semidirect
39. C2×#14556120C22semidirect
40. C2×#14556119C22semidirect
41. C2×#14556118C22semidirect
42. #17986511C22semidirect
43. #17986508C22semidirect
44. #17986506C22semidirect
47. C2×#14556111C22semidirect
49. C2×#14556110C22semidirect
53. C2×#14556107C22semidirect
54. C2×#14556107C22semidirect
56. C2×#14556106C22semidirect
60. C2×#14556104C22semidirect
63. C2×#14556102C22semidirect
68. C2×#14556099C22semidirect
71. #17986480C22semidirect
72. C2×#14556093C22semidirect
76. C2×#14556090C22semidirect
82. C2×#14556086C22semidirect
90. C2×C4⋊C4×D71C22semidirect
91. C2×C4⋊C4×D71C22semidirect
93. #520×C71C22semidirect
94. C2×C4×Q8×C71C22semidirect
96. C2×C4×D4×C71C22semidirect
98. C2×#117×C71C22semidirect
100. C22×C4⋊C4×C71C22semidirect
129. #14556128C23semidirect
130. #14556127C23semidirect
131. #14556122C23semidirect
132. #14556121C23semidirect
133. #14556120C23semidirect
134. #14556120C23semidirect
135. #14556119C23semidirect
136. #14556118C23semidirect
139. #14556111C23semidirect
141. #14556110C23semidirect
145. #14556107C23semidirect
146. #14556107C23semidirect
148. #14556106C23semidirect
152. #14556104C23semidirect
155. #14556102C23semidirect
160. #14556099C23semidirect
163. #14556093C23semidirect
167. #14556090C23semidirect
173. #14556086C23semidirect
196. C4⋊C4×D71C23semidirect
220. C4×Q8×C71C23semidirect
222. C4×D4×C71C23semidirect
224. #117×C71C23semidirect
231. C2×C4⋊C4×C71C23semidirect
332. C22×C4×C71#41semidirect
389. C2×C4×C71C2×#41semidirect
467. C2×C71#3492semidirect
490. C2×#520D71semidirect
492. C71C2×#3492semidirect
547. #520C2×D71semidirect
549. C2×C4×Q8C2×D71semidirect
559. C2×C4×D4C2×D71semidirect
564. C2×#117C2×D71semidirect
574. C22×C4⋊C4C2×D71semidirect
647. C4×Q8C22×D71semidirect
657. C4×D4C22×D71semidirect
662. #117C22×D71semidirect
691. C2×C4⋊C4C22×D71semidirect
777. C22×C4#11765865semidirect
894. C2×C4C2×#11765865semidirect
943. C2#22602043direct (N × H)

Maximal subgroups

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

subgroupindex
#226020432
C2×#179867092
C2×#179867042
C2×#179866992
C2×#179866932
C2×#179866902
C2×#179866882
C2×#179866542
C2×#179866502
C2×#179866272
C2×#179865912
C2×#179865772
C2×#179865112
C2×#179865082
C2×#179865062
C2×#179864802
C22×C4⋊C4×D712
C2×#520×C712
C2×#349271