Finite Group Databasebeta

← C2×#22602874 #32904819

Subgroups — C2×#22602874 #32904819

Order 18176.

7194 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602874C2132yesmaximal, direct product factor
2C2×#17986753C212yesmaximal, complemented
3C2×#17986747C212yesmaximal, complemented
4C2×#17986705C212yesmaximal, complemented
5C2×#17986702C212yesmaximal, complemented
6C2×#17986697C212yesmaximal, complemented
7C2×#17986650C214yesmaximal, complemented
8C2×#17986650C212yesmaximal, complemented
9C2×#17986629C212yesmaximal, complemented
10C2×#17986605C212yesmaximal, complemented
11C2×#17986597C214yesmaximal, complemented
12C2×#17986596C212yesmaximal, complemented
13C2×#17986580C212yesmaximal, complemented
14C2×#17986549C211yesmaximal, characteristic, complemented
15C2×#17986533C211yesmaximal, characteristic, complemented
16C22×#125×C71C211yesmaximal, characteristic, complemented
17C22×#11765865C2212yes—
18C22×#11765865C2214yes—
19#17986753C22132yescomplemented
20#17986747C22132yescomplemented
21#17986705C22132yescomplemented
22#17986702C22132yescomplemented
23#17986697C22132yescomplemented
24#17986650C22132yescomplemented
25#17986650C22164yescomplemented
26#17986629C22132yescomplemented
27#17986605C22132yescomplemented
28#17986597C22164yescomplemented
29#17986596C22132yescomplemented
30#17986580C22132yescomplemented
31#17986549C22116yescomplemented
32C2×#14556128C2211yescharacteristic
33C2×#14556127C2212yes—
34C2×#14556127C2214yes—
35C2×#14556125C2211yescharacteristic
36#17986533C22116yescomplemented
37C2×#14556123C2214yes—
38C2×#14556123C2214yes—
39C2×#14556122C2212yes—
40C2×#14556120C2211yescharacteristic
41C2×#14556119C2212yes—
42C2×#14556118C2214yes—
43C2×#14556116C2211yescharacteristic
44C2×#14556116C2212yes—
45C2×#14556113C2214yes—
46C2×#14556113C2214yes—
47C2×#14556113C2214yes—
48C2×#14556113C2214yes—
49C2×#14556113C2214yes—
50C2×#14556111C2212yes—
51C2×#14556111C2214yes—
52C2×#14556108C2214yes—
53C2×#14556108C2214yes—
54C2×#14556107C2211yescharacteristic
55C2×#14556106C2214yes—
56C2×#14556106C2214yes—
57C2×#14556106C2214yes—
58C2×#14556106C2214yes—
59C2×#14556103C2212yes—
60C2×#14556103C2214yes—
61C2×#14556103C2212yes—
62C2×#14556103C2214yes—
63C2×#14556103C2214yes—
64C2×#14556102C2212yes—
65C2×#14556102C2214yes—
66C2×#14556102C2211yescharacteristic
67C2×#14556102C2212yes—
68C2×C4×Dic142C2211yescharacteristic
69C2×C4×D284C2211yescharacteristic
70C2×C4×D284C2212yes—
71C2×C4×D284C2212yes—
72C2×#14556090C2214yes—
73C2×#14556090C2212yes—
74C2×#14556090C2212yes—
75C2×C4×C22⋊D71C2212yes—
76C2×C4×C22⋊D71C2214yes—
77C2×#14556086C2212yes—
78C2×#14556085C2212yes—
79C2×C4⋊C4×D71C2212yes—
80C2×C4⋊C4×D71C2214yes—
81C2×#125×C71C2212yes—
82C2×#125×C71C2212yes—
83C2×#125×C71C2212yes—
84C2×#125×C71C2212yes—
85C2×#125×C71C22116yescomplemented
86C22×C4⋊C4×C71C2211yescharacteristic
87C22×C4⋊C4×C71C2212yes—
88C22×C4⋊C4×C71C2211yescharacteristic
89C22×C4⋊C4×C71C2212yes—
90C22×C42×C71C2211yescharacteristic
91C2×#11765865—48no—
92C2×#11765865—416no—
93C2×#11765865C23132yes—
94C2×#11765865C23116yes—
95C22×Dic142C2314yes—
96C22×Dic142C2312yes—
97C22×Dic142C2311yescharacteristic
98C22×D284C2312yes—
99C22×D284C2314yes—
100C22×D284C2312yes—
101C22×D284C2314yes—
102C22×D284C2311yescharacteristic
103C22×D284C2312yes—
104C22×C22⋊D71C2314yes—
105C22×C22⋊D71C2312yes—
106C22×C4×D71C2312yes—
107C22×C4×D71C2314yes—
108C22×C4×D71C2314yes—
109C22×C4×D71C2314yes—
110C22×C4×D71C2314yes—
111#14556128C2318yes—
112#14556127C23116yes—
113#14556127C23132yes—
114#14556125C2318yes—
115#14556123C23132yes—
116#14556123C23132yes—
117#14556122C23116yes—
118#14556120C2318yes—
119#14556119C23116yes—
120#14556118C23132yes—
121#14556116C2318yes—
122#14556116C23116yes—
123#14556113C23132yes—
124#14556113C23132yes—
125#14556113C23132yes—
126#14556113C23132yes—
127#14556113C23132yes—
128#14556111C23132yes—
129#14556111C23116yes—
130#14556108C23132yes—
131#14556108C23132yes—
132#14556107C2318yes—
133#14556106C23132yes—
134#14556106C23132yes—
135#14556106C23132yes—
136#14556106C23132yes—
137#14556103C23132yes—
138#14556103C23132yes—
139#14556103C23116yes—
140#14556103C23132yes—
141#14556103C23116yes—
142#14556102C2318yes—
143#14556102C23116yes—
144#14556102C23132yes—
145#14556102C23116yes—
146C4×Dic142C2318yes—
147C4×D284C23116yes—
148C4×D284C2318yes—
149C4×D284C23116yes—
150#14556090C23132yes—
151#14556090C23116yes—
152#14556090C23116yes—
153C4×C22⋊D71C23132yes—
154C4×C22⋊D71C23116yes—
155#14556086C23116yes—
156#14556085C23116yes—
157C2×C4⋊Dic71C2312yes—
158C2×C4⋊Dic71C2314yes—
159C2×C4⋊Dic71C2312yes—
160C2×C4⋊Dic71C2311yescharacteristic
161C2×C4⋊Dic71C2311yescharacteristic
162C2×Dic71⋊C4C2312yes—
163C2×Dic71⋊C4C2314yes—
164C2×Dic71⋊C4C2314yes—
165C2×Dic71⋊C4C2312yes—
166C2×Dic71⋊C4C2312yes—
167C2×Dic71⋊C4C2314yes—
168C2×Dic71⋊C4C2312yes—
169C4⋊C4×D71C23132yes—
170C4⋊C4×D71C23116yes—
171C2×C22⋊Dic71C2312yes—
172C2×(C2×D71)⋊C4C2312yes—
173C2×(C2×D71)⋊C4C2312yes—
174C2×(C2×D71)⋊C4C2314yes—
175C2×(C2×D71)⋊C4C2314yes—
176C2×(C2×D71)⋊C4C2312yes—
177C2×(C2×D71)⋊C4C2312yes—
178C2×(C2×D71)⋊C4C2314yes—
179C2×(C2×D71)⋊C4C2314yes—
180C2×(C2×D71)⋊C4C2314yes—
181C2×(C2×D71)⋊C4C2314yes—
182C2×(C2×D71)⋊C4C2314yes—
183C2×C4×Dic71C2312yes—
184C2×C4×Dic71C2314yes—
185C23×C4×C71C2311yescharacteristic
186C23×C4×C71C2312yes—
187C23×C4×C71C2311yescharacteristic
188C23×C4×C71C2311yescharacteristic
189C23×C4×C71C2312yes—
190#125×C71C23116yes—
191#125×C71C23116yes—
192#125×C71C23116yes—
193#125×C71C23116yes—
194C2×C4⋊C4×C71C23116yes—
195C2×C4⋊C4×C71C2318yes—
196C2×C4⋊C4×C71C23116yes—
197C2×C4⋊C4×C71C2312yes—
198C2×C4⋊C4×C71C2314yes—
199C2×C4⋊C4×C71C2312yes—
200C2×C4⋊C4×C71C2314yes—
201C2×C4⋊C4×C71C2314yes—
202C2×C4⋊C4×C71C2314yes—
203C2×C4⋊C4×C71C2312yes—
204C2×C4⋊C4×C71C2312yes—
205C2×C4⋊C4×C71C2318yes—
206C2×C42×C71C2311yescharacteristic
207C2×C42×C71C2311yescharacteristic
208C2×C42×C71C2311yescharacteristic
209C2×C42×C71C2311yescharacteristic
210C2×C42×C71C2318yes—
211C23×D71C2412yes—
212C23×D71C2414yes—
213#11765865—464no—
214#11765865—432no—
215C2×Dic142—42no—
216C2×Dic142—48no—
217C2×Dic142—44no—
218C2×Dic142C24116yes—
219C2×Dic142C2418yes—
220C2×Dic142C2414yes—
221C2×D284—28no—
222C2×D284—48no—
223C2×D284—44no—
224C2×D284—42no—
225C2×D284—48no—
226C2×D284—44no—
227C2×D284C2418yes—
228C2×D284C24116yes—
229C2×D284C2418yes—
230C2×D284C24116yes—
231C2×D284C2414yes—
232C2×D284C2418yes—
233C2×C22⋊D71—216no—
234C2×C22⋊D71—28no—
235C2×C22⋊D71C2418yes—
236C2×C22⋊D71C24116yes—
237C22×Dic71C2414yes—
238C22×Dic71C2412yes—
239C22×Dic71C2412yes—
240C22×Dic71C2412yes—
241C2×C4×D71—28no—
242C2×C4×D71—48no—
243C2×C4×D71—48no—
244C2×C4×D71—48no—
245C2×C4×D71—48no—
246C2×C4×D71C2418yes—
247C2×C4×D71C24116yes—
248C2×C4×D71C24116yes—
249C2×C4×D71C24116yes—
250C2×C4×D71C24116yes—
251C4⋊Dic71C2418yes—
252C4⋊Dic71C24116yes—
253C4⋊Dic71C2418yes—
254C4⋊Dic71C2414yes—
255C4⋊Dic71C2414yes—
256Dic71⋊C4C2418yes—
257Dic71⋊C4C24116yes—
258Dic71⋊C4C24116yes—
259Dic71⋊C4C2418yes—
260Dic71⋊C4C2418yes—
261Dic71⋊C4C24116yes—
262Dic71⋊C4C2418yes—
263C22⋊Dic71C2418yes—
264(C2×D71)⋊C4C2418yes—
265(C2×D71)⋊C4C2418yes—
266(C2×D71)⋊C4C24116yes—
267(C2×D71)⋊C4C24116yes—
268(C2×D71)⋊C4C2418yes—
269(C2×D71)⋊C4C2418yes—
270(C2×D71)⋊C4C24116yes—
271(C2×D71)⋊C4C24116yes—
272(C2×D71)⋊C4C24116yes—
273(C2×D71)⋊C4C24116yes—
274(C2×D71)⋊C4C24116yes—
275C4×Dic71C2418yes—
276C4×Dic71C24116yes—
277C24×C71C2411yescharacteristic
278C22×C4×C71—24no—
279C22×C4×C71—28no—
280C22×C4×C71—24no—
281C22×C4×C71—44no—
282C22×C4×C71—42no—
283C22×C4×C71C2411yescharacteristic
284C22×C4×C71C2414yes—
285C22×C4×C71C2414yes—
286C22×C4×C71C2411yescharacteristic
287C22×C4×C71C2411yescharacteristic
288C22×C4×C71C2411yescharacteristic
289C22×C4×C71C2414yes—
290C22×C4×C71C2418yes—
291C22×C4×C71C2411yescharacteristic
292C22×C4×C71C2414yes—
293C22×C4×C71C2414yes—
294C22×C4×C71C2418yes—
295C22×C4×C71C2411yescharacteristic
296C4⋊C4×C71C2418yes—
297C4⋊C4×C71C24116yes—
298C4⋊C4×C71C2418yes—
299C4⋊C4×C71C24116yes—
300C4⋊C4×C71C24116yes—
301C4⋊C4×C71C24116yes—
302C4⋊C4×C71C2418yes—
303C4⋊C4×C71C2418yes—
304C42×C71C2414yes—
305C42×C71C2414yes—
306C42×C71C2414yes—
307C42×C71C2414yes—
308C23×C71—22no—
309C23×C71—22no—
310C23×C71H(5,𝔽2)14yes—
311C23×C71C2512yes—
312C23×C71C2511yescharacteristic
313C22×D71—24no—
314C22×D71—28no—
315C22×D71—24no—
316C22×D71—28no—
317C22×D71—28no—
318C22×D71—24no—
319C22×D71C2514yes—
320C22×D71C2518yes—
321C2×C4×C71—22no—
322C2×C4×C71—28no—
323C2×C4×C71—22no—
324C2×C4×C71—28no—
325C2×C4×C71—216no—
326C2×C4×C71—22no—
327C2×C4×C71—28no—
328C2×C4×C71—22no—
329C2×C4×C71—22no—
330C2×C4×C71—28no—
331C2×C4×C71—44no—
332C2×C4×C71—48no—
333C2×C4×C712−1+414yes—
334C2×C4×C71C2512yes—
335C2×C4×C71C2512yes—
336C2×C4×C71C2512yes—
337C2×C4×C71C2512yes—
338C2×C4×C71C2512yes—
339C2×C4×C71C2518yes—
340C2×C4×C71C2518yes—
341C2×C4×C71C2512yes—
342C22⋊D71—216no—
343C22⋊D71—232no—
344C2×Dic71—28no—
345C2×Dic71—24no—
346C2×Dic71—24no—
347C2×Dic71—24no—
348C2×Dic71C2514yes—
349C2×Dic71C2514yes—
350C2×Dic71C2514yes—
351C2×Dic71C2518yes—
352D284—216no—
353D284—44no—
354D284—416no—
355D284—48no—
356D284—48no—
357D284—416no—
358C4×D71—216no—
359C4×D71—416no—
360C4×D71—416no—
361C4×D71—416no—
362C4×D71—416no—
363Dic142—44no—
364Dic142—48no—
365Dic142—416no—
366C22×C71—22no—
367C22×C71—22no—
368C22×C71—28no—
369C22×C71C2×H(5,𝔽2)14yes—
370C22×C71C2×H(5,𝔽2)12yes—
371C22×C71C2×2−1+412yes—
372C22×C71#58512yes—
373C22×C71C2611yescharacteristic
374C2×D71—24no—
375C2×D71—28no—
376C2×D71—24no—
377C2×D71—28no—
378C2×D71—28no—
379C2×D71—24no—
380C2×D71—48no—
381C2×D71—416no—
382C4×C71—22no—
383C4×C71—28no—
384C4×C71—22no—
385C4×C71—22no—
386C4×C71—22no—
387C4×C71—28no—
388C4×C71—22no—
389C4×C71C2×2−1+414yes—
390Dic71—28no—
391Dic71—24no—
392Dic71—24no—
393Dic71—24no—
394C2×#3559—711nomaximal, Sylow
395C2×C71—24no—
396C2×C71#355914yescomplemented
397C2×C71C22×H(5,𝔽2)11yescharacteristic
398C2×C71C22×2−1+411yescharacteristic
399C2×C71C2×#58511yescharacteristic
400D71—44no—
401D71—48no—
402#3559—7132no—
403C2×#563—712no—
404C2×#562—712no—
405C2×#554—712no—
406C2×#553—712no—
407C2×#553—712no—
408C2×#547—714no—
409C2×#547—712no—
410C2×#544—712no—
411C2×#540—712no—
412C2×#539—714no—
413C2×#539—712no—
414C2×#537—712no—
415C2×#532—711no—
416C2×#529—711no—
417C22×#125D7111yescharacteristic, complemented
418C71C2×#355911yescharacteristic, complemented, Sylow
419C22×#41—712no—
420C22×#41—714no—
421#563—7132no—
422#562—7132no—
423#554—7132no—
424#553—7132no—
425#553—7132no—
426#547—7164no—
427#547—7132no—
428#544—7132no—
429#540—7132no—
430#539—7164no—
431#539—7132no—
432#537—7132no—
433#532—7116no—
434C2×C4⋊Q8—712no—
435C2×C4⋊Q8—714no—
436C2×C4⋊Q8—711no—
437C2×#127—711no—
438#529—7116no—
439C2×#126—714no—
440C2×#126—714no—
441C2×#126—712no—
442C2×#125—714no—
443C2×#125—712no—
444C2×#125—711no—
445C2×#125C2×D7112yes—
446C2×#125C2×D7112yes—
447C2×#125C2×D7112yes—
448C2×#125C2×D7112yes—
449C2×#125C2×D71116yescomplemented
450C2×#124—711no—
451C2×#124—712no—
452C2×#123—712no—
453C2×#123—714no—
454C2×#123—714no—
455C2×#123—714no—
456C2×#123—714no—
457C2×#123—714no—
458C2×#123—714no—
459C2×C22⋊Q8—711no—
460C2×C22⋊Q8—714no—
461C2×C22⋊Q8—714no—
462C2×C22⋊Q8—714no—
463C2×C22⋊Q8—714no—
464C2×C22⋊Q8—714no—
465C2×C22⋊Q8—714no—
466C2×#121—711no—
467C2×#121—712no—
468C2×#121—712no—
469C2×#121—714no—
470C2×#121—714no—
471C2×#121—714no—
472C2×#121—712no—
473C2×#121—714no—
474C2×#121—712no—
475C2×C4×Q8—711no—
476C2×C4×D4—712no—
477C2×C4×D4—714no—
478C2×C4×D4—714no—
479C2×C4×D4—712no—
480C2×C4×D4—712no—
481C2×C4×D4—711no—
482C2×C4×D4—712no—
483C2×C4×D4—712no—
484C2×#117—712no—
485C2×#117—712no—
486C22×C4⋊C4—714no—
487C22×C4⋊C4—712no—
488C22×C4⋊C4C2×D7112yes—
489C22×C4⋊C4C2×D7111yescharacteristic
490C22×C4⋊C4C2×D7112yes—
491C22×C4⋊C4C2×D7111yescharacteristic
492C22×C42C2×D7111yescharacteristic
493C2×#41—2848no—
494C2×#41—28416no—
495C2×#41—7116no—
496C2×#41—7132no—
497C22×Q8—711no—
498C22×Q8—714no—
499C22×Q8—712no—
500C22×D4—712no—
501C22×D4—714no—
502C22×D4—714no—
503C22×D4—711no—
504C22×D4—712no—
505C22×D4—714no—
506C22×D4—712no—
507C22×D4—712no—
508C23×C4—714no—
509C23×C4—714no—
510C23×C4—714no—
511C23×C4—714no—
512C23×C4—712no—
513C23×C4C22×D7112yes—
514C23×C4C22×D7111yescharacteristic
515C23×C4C22×D7111yescharacteristic
516C23×C4C22×D7112yes—
517C23×C4C22×D7111yescharacteristic
518C4⋊Q8—7116no—
519C4⋊Q8—7132no—
520C4⋊Q8—718no—
521#127—718no—
522#126—7132no—
523#126—7132no—
524#126—7116no—
525#125—7132no—
526#125—7116no—
527#125—718no—
528#125C22×D71116yes—
529#125C22×D71116yes—
530#125C22×D71116yes—
531#125C22×D71116yes—
532#124—718no—
533#124—7116no—
534#123—7116no—
535#123—7132no—
536#123—7132no—
537#123—7132no—
538#123—7132no—
539#123—7132no—
540#123—7132no—
541C22⋊Q8—718no—
542C22⋊Q8—7132no—
543C22⋊Q8—7132no—
544C22⋊Q8—7132no—
545C22⋊Q8—7132no—
546C22⋊Q8—7132no—
547C22⋊Q8—7132no—
548#121—718no—
549#121—7116no—
550#121—7116no—
551#121—7132no—
552#121—7132no—
553#121—7132no—
554#121—7116no—
555#121—7132no—
556#121—7116no—
557C4×Q8—718no—
558C4×D4—7116no—
559C4×D4—7132no—
560C4×D4—7132no—
561C4×D4—7116no—
562C4×D4—7116no—
563C4×D4—718no—
564C4×D4—7116no—
565C4×D4—7116no—
566#117—7116no—
567#117—7116no—
568C2×C4⋊C4—712no—
569C2×C4⋊C4—712no—
570C2×C4⋊C4—714no—
571C2×C4⋊C4—714no—
572C2×C4⋊C4—714no—
573C2×C4⋊C4—712no—
574C2×C4⋊C4—712no—
575C2×C4⋊C4—712no—
576C2×C4⋊C4—714no—
577C2×C4⋊C4—712no—
578C2×C4⋊C4—711no—
579C2×C4⋊C4—711no—
580C2×C4⋊C4—7132no—
581C2×C4⋊C4—7116no—
582C2×C4⋊C4C22×D7112yes—
583C2×C4⋊C4C22×D7114yes—
584C2×C4⋊C4C22×D7112yes—
585C2×C4⋊C4C22×D7114yes—
586C2×C4⋊C4C22×D7114yes—
587C2×C4⋊C4C22×D7114yes—
588C2×C4⋊C4C22×D7112yes—
589C2×C4⋊C4C22×D7112yes—
590C2×C4⋊C4C22×D71116yes—
591C2×C4⋊C4C22×D7118yes—
592C2×C4⋊C4C22×D71116yes—
593C2×C4⋊C4C22×D7118yes—
594C2×C22⋊C4—712no—
595C2×C22⋊C4—712no—
596C2×C22⋊C4—714no—
597C2×C22⋊C4—712no—
598C2×C22⋊C4—712no—
599C2×C22⋊C4—714no—
600C2×C22⋊C4—714no—
601C2×C22⋊C4—714no—
602C2×C22⋊C4—714no—
603C2×C22⋊C4—714no—
604C2×C22⋊C4—714no—
605C2×C22⋊C4—712no—
606C2×C42—712no—
607C2×C42—714no—
608C2×C42C22×D7111yescharacteristic
609C2×C42C22×D7111yescharacteristic
610C2×C42C22×D7111yescharacteristic
611C2×C42C22×D7111yescharacteristic
612C2×C42C22×D7118yes—
613C24—712no—
614C24—714no—
615C24C23×D7111yescharacteristic
616#41—28432no—
617#41—28464no—
618C2×Q8—2842no—
619C2×Q8—2848no—
620C2×Q8—2844no—
621C2×Q8—714no—
622C2×Q8—7116no—
623C2×Q8—718no—
624C2×D4—2848no—
625C2×D4—2844no—
626C2×D4—2842no—
627C2×D4—2848no—
628C2×D4—2844no—
629C2×D4—718no—
630C2×D4—7116no—
631C2×D4—7116no—
632C2×D4—714no—
633C2×D4—718no—
634C2×D4—7116no—
635C2×D4—718no—
636C2×D4—718no—
637C2×D4—1428no—
638C2×D4—14216no—
639C2×D4—1428no—
640C22×C4—24no—
641C22×C4—28no—
642C22×C4—24no—
643C22×C4—44no—
644C22×C4—42no—
645C22×C4—2848no—
646C22×C4—2848no—
647C22×C4—2848no—
648C22×C4—2848no—
649C22×C4—7116no—
650C22×C4—7116no—
651C22×C4—7116no—
652C22×C4—7116no—
653C22×C4—712no—
654C22×C4—712no—
655C22×C4—712no—
656C22×C4—714no—
657C22×C4—718no—
658C22×C4—1428no—
659C22×C4C23×D7114yes—
660C22×C4C23×D7114yes—
661C22×C4C23×D7118yes—
662C22×C4C23×D7114yes—
663C22×C4C23×D7111yescharacteristic
664C22×C4C23×D7111yescharacteristic
665C22×C4C23×D7111yescharacteristic
666C22×C4C23×D7111yescharacteristic
667C22×C4C23×D7111yescharacteristic
668C22×C4C23×D7114yes—
669C22×C4C23×D7114yes—
670C22×C4C23×D7118yes—
671C22×C4C23×D7111yescharacteristic
672C4⋊C4—718no—
673C4⋊C4—7116no—
674C4⋊C4—7116no—
675C4⋊C4—718no—
676C4⋊C4—718no—
677C4⋊C4—7116no—
678C4⋊C4—718no—
679C4⋊C4—718no—
680C4⋊C4—7116no—
681C4⋊C4—718no—
682C4⋊C4—714no—
683C4⋊C4—714no—
684C4⋊C4C23×D7118yes—
685C4⋊C4C23×D71116yes—
686C4⋊C4C23×D7118yes—
687C4⋊C4C23×D71116yes—
688C4⋊C4C23×D71116yes—
689C4⋊C4C23×D71116yes—
690C4⋊C4C23×D7118yes—
691C4⋊C4C23×D7118yes—
692C22⋊C4—718no—
693C22⋊C4—718no—
694C22⋊C4—7116no—
695C22⋊C4—718no—
696C22⋊C4—718no—
697C22⋊C4—7116no—
698C22⋊C4—7116no—
699C22⋊C4—7116no—
700C22⋊C4—7116no—
701C22⋊C4—7116no—
702C22⋊C4—7116no—
703C22⋊C4—718no—
704C42—718no—
705C42—7116no—
706C42C23×D7114yes—
707C42C23×D7114yes—
708C42C23×D7114yes—
709C42C23×D7114yes—
710C23—22no—
711C23—22no—
712C23—714no—
713C23—718no—
714C23—1424no—
715C23—1428no—
716C23—1424no—
717C23—1428no—
718C23—1428no—
719C23—1424no—
720C23#1455617414yes—
721C23C24×D7112yes—
722C23C24×D7111yescharacteristic
723Q8—28416no—
724Q8—2848no—
725Q8—2844no—
726D4—28416no—
727D4—2848no—
728D4—28416no—
729D4—2848no—
730D4—2844no—
731D4—14216no—
732D4—14232no—
733D4—14216no—
734C2×C4—22no—
735C2×C4—28no—
736C2×C4—22no—
737C2×C4—28no—
738C2×C4—216no—
739C2×C4—22no—
740C2×C4—28no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—28no—
744C2×C4—48no—
745C2×C4—44no—
746C2×C4—28416no—
747C2×C4—28416no—
748C2×C4—28416no—
749C2×C4—28416no—
750C2×C4—714no—
751C2×C4—714no—
752C2×C4—714no—
753C2×C4—718no—
754C2×C4—1428no—
755C2×C4—1424no—
756C2×C4—1424no—
757C2×C4—1424no—
758C2×C4—14216no—
759C2×C4#1455617614yes—
760C2×C4C24×D7118yes—
761C2×C4C24×D7112yes—
762C2×C4C24×D7112yes—
763C2×C4C24×D7112yes—
764C2×C4C24×D7112yes—
765C2×C4C24×D7112yes—
766C2×C4C24×D7118yes—
767C2×C4C24×D7112yes—
768C22—28no—
769C22—22no—
770C22—22no—
771C22—2848no—
772C22—28416no—
773C22—1424no—
774C22—1428no—
775C22—1424no—
776C22—1428no—
777C22—1428no—
778C22—1424no—
779C22C2×#1455617414yes—
780C22C2×#1455617412yes—
781C22C2×#1455617612yes—
782C22#1798683512yes—
783C22C25×D7111yescharacteristic
784C4—22no—
785C4—28no—
786C4—22no—
787C4—22no—
788C4—28no—
789C4—22no—
790C4—22no—
791C4—1428no—
792C4—1424no—
793C4—1424no—
794C4—1424no—
795C4C2×#1455617614yes—
796C2—24no—
797C2—2844no—
798C2—2848no—
799C2#2260287414yesdirect product factor
800C2C22×#1455617411yescharacteristic
801C2C22×#1455617611yescharacteristic
802C2C2×#1798683511yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC22×#125×C71C2
socleC23×C71C25
hypercenterC22×#125D71
hypocenterC71C2×#3559
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. #22602874C2direct (N × H)
2. C2×#17986753C2semidirect
3. C2×#17986747C2semidirect
4. C2×#17986705C2semidirect
5. C2×#17986702C2semidirect
6. C2×#17986697C2semidirect
7. C2×#17986650C2semidirect
8. C2×#17986650C2semidirect
9. C2×#17986629C2semidirect
10. C2×#17986605C2semidirect
11. C2×#17986597C2semidirect
12. C2×#17986596C2semidirect
13. C2×#17986580C2semidirect
14. C2×#17986549C2semidirect
15. C2×#17986533C2semidirect
16. C22×#125×C71C2semidirect
19. #17986753C22semidirect
20. #17986747C22semidirect
21. #17986705C22semidirect
22. #17986702C22semidirect
23. #17986697C22semidirect
24. #17986650C22semidirect
25. #17986650C22semidirect
26. #17986629C22semidirect
27. #17986605C22semidirect
28. #17986597C22semidirect
29. #17986596C22semidirect
30. #17986580C22semidirect
31. #17986549C22semidirect
36. #17986533C22semidirect
85. C2×#125×C71C22semidirect
396. C2×C71#3559semidirect
417. C22×#125D71semidirect
418. C71C2×#3559semidirect
449. C2×#125C2×D71semidirect
799. C2#22602874direct (N × H)

Maximal subgroups

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

subgroupindex
#226028742
C2×#179867532
C2×#179867472
C2×#179867052
C2×#179867022
C2×#179866972
C2×#179866502
C2×#179866292
C2×#179866052
C2×#179865972
C2×#179865962
C2×#179865802
C2×#179865492
C2×#179865332
C22×#125×C712
C2×#355971