Finite Group Databasebeta

← C2×#22602155 #32905782

Subgroups — C2×#22602155 #32905782

Order 18176.

7478 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602155C2132yesmaximal, direct product factor
2C2×#17986729C212yesmaximal, complemented
3C2×#17986726C212yesmaximal, complemented
4C2×#17986705C212yesmaximal, complemented
5C2×#17986703C214yesmaximal, complemented
6C2×#17986664C212yesmaximal, complemented
7C2×#17986662C214yesmaximal, complemented
8C2×#17986629C212yesmaximal, complemented
9C2×#17986627C211yesmaximal, characteristic, complemented
10C2×#17986626C212yesmaximal, complemented
11C2×#17986555C212yesmaximal, complemented
12C2×#17986552C211yesmaximal, characteristic, complemented
13C22×#14556127C211yesmaximal, characteristic, complemented
14C2×C4⋊Q8×D71C212yesmaximal, complemented
15C2×#17986480C211yesmaximal, characteristic
16C2×#17986479C211yesmaximal, characteristic
17C2×#17986467C211yesmaximal, characteristic
18C2×#544×C71C211yesmaximal, characteristic, complemented
19C22×#11765865C2211yescharacteristic
20C23×Dic142C2212yes—
21C22×Q8×D71C2214yes—
22#17986729C22132yescomplemented
23#17986726C22132yescomplemented
24#17986705C22132yescomplemented
25#17986703C22164yescomplemented
26#17986664C22132yescomplemented
27#17986662C22164yescomplemented
28#17986629C22132yescomplemented
29#17986627C22116yescomplemented
30#17986626C22132yescomplemented
31#17986555C22132yescomplemented
32#17986552C22116yescomplemented
33C2×#14556128C2212yes—
34C2×#14556127C2212yes—
35C2×#14556127C2212yes—
36C2×#14556127C2214yes—
37C2×#14556127C2214yes—
38C2×#14556127C2212yes—
39C2×#14556127C2211yescharacteristic
40C2×#14556127C2212yes—
41C2×#14556127C2212yes—
42C2×#14556127C2211yescharacteristic
43C2×#14556127C22116yescomplemented
44C2×#14556126C2214yes—
45C2×#14556126C2214yes—
46C4⋊Q8×D71C22132yescomplemented
47C2×#14556120C2212yes—
48C2×#14556119C2211yescharacteristic
49C2×#14556119C2212yes—
50C2×#14556119C2211yescharacteristic
51C2×#14556118C2214yes—
52C2×#14556118C2214yes—
53C2×#14556108C2214yes—
54C2×#14556106C2214yes—
55C2×#14556106C2214yes—
56C2×#14556106C2214yes—
57C2×#14556106C2214yes—
58C2×#14556105C2214yes—
59C2×#14556105C2212yes—
60C2×#14556105C2212yes—
61C2×#14556104C2214yes—
62#17986480C22116yes—
63#17986479C22116yes—
64#17986467C22116yes—
65C2×C4×Dic142C2212yes—
66C2×C4×Dic142C2212yes—
67C2×C4×Dic142C2212yes—
68C2×#14556093C2211yescharacteristic
69C2×#14556093C2211yescharacteristic
70C2×#14556093C2212yes—
71C2×#14556093C2214yes—
72C2×#14556093C2214yes—
73C2×C4×D284C2212yes—
74C2×#14556090C2211yescharacteristic
75C2×#14556090C2211yescharacteristic
76C2×#14556090C2212yes—
77C2×C4×C22⋊D71C2214yes—
78C2×(C22⋊D71)⋊C4C2212yes—
79C2×(C22⋊D71)⋊C4C2212yes—
80C2×(C22⋊D71)⋊C4C2214yes—
81C2×#14556087C2211yescharacteristic
82C2×#14556086C2212yes—
83C2×#14556086C2212yes—
84C2×#14556085C2212yes—
85C22×C4⋊Dic71C2211yescharacteristic
86C22×Dic71⋊C4C2212yes—
87C2×C4⋊C4×D71C2212yes—
88C2×C4⋊C4×D71C2212yes—
89C2×C4⋊C4×D71C2214yes—
90C22×C4×Dic71C2211yescharacteristic
91C2×C42×D71C2212yes—
92#544×C71C22116yescomplemented
93C2×C4⋊Q8×C71C2212yes—
94C2×C4⋊Q8×C71C2212yes—
95C2×#125×C71C2212yes—
96C2×#125×C71C2212yes—
97C2×C22⋊Q8×C71C2214yes—
98C2×#117×C71C2211yescharacteristic
99C2×#117×C71C2211yescharacteristic
100C22×C4⋊C4×C71C2211yescharacteristic
101C2×#11765865Q8116yescomplemented
102C2×#11765865C2318yes—
103C22×Dic142—48no—
104C22×Dic142C2312yes—
105C22×Dic142C2314yes—
106C22×Dic142C2312yes—
107C22×Dic142C2314yes—
108C22×Dic142C23116yes—
109C22×Dic142C2314yes—
110C22×Dic142C2311yescharacteristic
111C2×Q8×D71—416no—
112C2×Q8×D71C23132yes—
113C22×D284C2311yescharacteristic
114C22×C22⋊D71C2312yes—
115C23×Dic71C2311yescharacteristic
116C23×Dic71C2311yescharacteristic
117C23×Dic71C2312yes—
118C22×C4×D71C2312yes—
119C22×C4×D71C2312yes—
120C22×C4×D71C2314yes—
121C22×C4×D71C2314yes—
122C22×C4×D71C2312yes—
123#14556128C23116yes—
124#14556127C23116yes—
125#14556127C23116yes—
126#14556127C23132yes—
127#14556127C23132yes—
128#14556127C23116yes—
129#14556127C23116yes—
130#14556127C2318yes—
131#14556127C23116yes—
132#14556127C2318yes—
133#14556126C23132yes—
134#14556126C23132yes—
135#14556120C23116yes—
136#14556119C2318yes—
137#14556119C23116yes—
138#14556119C2318yes—
139#14556118C23132yes—
140#14556118C23132yes—
141#14556108C23132yes—
142#14556106C23132yes—
143#14556106C23132yes—
144#14556106C23132yes—
145#14556106C23132yes—
146#14556105C23132yes—
147#14556105C23116yes—
148#14556105C23116yes—
149#14556104C23132yes—
150C4×Dic142C23116yes—
151C4×Dic142C23116yes—
152C4×Dic142C23116yes—
153#14556093C23132yes—
154#14556093C23132yes—
155#14556093C2318yes—
156#14556093C2318yes—
157#14556093C23116yes—
158C4×D284C23116yes—
159#14556090C2318yes—
160#14556090C23116yes—
161#14556090C2318yes—
162C4×C22⋊D71C23132yes—
163(C22⋊D71)⋊C4C23116yes—
164(C22⋊D71)⋊C4C23132yes—
165(C22⋊D71)⋊C4C23116yes—
166#14556087C2318yes—
167#14556086C23116yes—
168#14556086C23116yes—
169#14556085C23116yes—
170C2×C4⋊Dic71C2318yes—
171C2×C4⋊Dic71C2311yescharacteristic
172C2×C4⋊Dic71C2312yes—
173C2×C4⋊Dic71C2314yes—
174C2×C4⋊Dic71C2312yes—
175C2×C4⋊Dic71C2311yescharacteristic
176C2×C4⋊Dic71C2312yes—
177C2×C4⋊Dic71C2312yes—
178C2×Dic71⋊C4C23116yes—
179C2×Dic71⋊C4C2312yes—
180C2×Dic71⋊C4C2314yes—
181C2×Dic71⋊C4C2314yes—
182C2×Dic71⋊C4C2314yes—
183C2×Dic71⋊C4C2314yes—
184C2×Dic71⋊C4C2312yes—
185C2×Dic71⋊C4C2312yes—
186C2×Dic71⋊C4C2312yes—
187C2×Dic71⋊C4C2314yes—
188C2×Dic71⋊C4C2314yes—
189C2×Dic71⋊C4C2312yes—
190C2×Dic71⋊C4C2312yes—
191C4⋊C4×D71C23116yes—
192C4⋊C4×D71C23116yes—
193C4⋊C4×D71C23132yes—
194C2×C22⋊Dic71C2312yes—
195C2×(C2×D71)⋊C4C2312yes—
196C2×(C2×D71)⋊C4C2312yes—
197C2×(C2×D71)⋊C4C2314yes—
198C2×(C2×D71)⋊C4C2314yes—
199C2×C4×Dic71C2311yescharacteristic
200C2×C4×Dic71C2312yes—
201C2×C4×Dic71C2312yes—
202C2×C4×Dic71C2311yescharacteristic
203C2×C4×Dic71C2311yescharacteristic
204C2×C4×Dic71C2311yescharacteristic
205C2×C4×Dic71C2318yes—
206C2×C4×Dic71C2314yes—
207C2×C4×Dic71C2314yes—
208C2×C4×Dic71C2312yes—
209C42×D71C23116yes—
210C22×Q8×C71C2314yes—
211C23×C4×C71C2312yes—
212C23×C4×C71C2311yescharacteristic
213C4⋊Q8×C71C23116yes—
214C4⋊Q8×C71C23116yes—
215#125×C71C23116yes—
216#125×C71C23116yes—
217C22⋊Q8×C71C23132yes—
218#117×C71C2318yes—
219#117×C71C2318yes—
220C2×C4⋊C4×C71C2312yes—
221C2×C4⋊C4×C71C2312yes—
222C2×C4⋊C4×C71C2318yes—
223C2×C4⋊C4×C71C2311yescharacteristic
224C2×C4⋊C4×C71C2311yescharacteristic
225C2×C4⋊C4×C71C2311yescharacteristic
226C2×C4⋊C4×C71C2311yescharacteristic
227C2×C4⋊C4×C71C2314yes—
228C2×C4⋊C4×C71C2314yes—
229C2×C4⋊C4×C71C2314yes—
230C2×C22⋊C4×C71C2312yes—
231C2×C22⋊C4×C71C2312yes—
232C2×C42×C71C2312yes—
233C2×C42×C71C2312yes—
234C23×D71C2412yes—
235#11765865C2×Q8164yescomplemented
236C2×Dic142—28no—
237C2×Dic142—216no—
238C2×Dic142—28no—
239C2×Dic142—432no—
240C2×Dic142—48no—
241C2×Dic142—48no—
242C2×Dic142C2×Q818yescomplemented
243C2×Dic142C2418yes—
244C2×Dic142C24116yes—
245C2×Dic142C2418yes—
246C2×Dic142C24116yes—
247C2×Dic142C24116yes—
248C2×Dic142C2414yes—
249Q8×D71—464no—
250C2×D284C2×Q818yescomplemented
251C2×D284C2414yes—
252C2×C22⋊D71C2×Q8116yescomplemented
253C2×C22⋊D71C2418yes—
254C22×Dic71—24no—
255C22×Dic71—24no—
256C22×Dic71—44no—
257C22×Dic71C2412yes—
258C22×Dic71C2414yes—
259C22×Dic71C2411yescharacteristic
260C22×Dic71C2414yes—
261C22×Dic71C2411yescharacteristic
262C22×Dic71C2414yes—
263C22×Dic71C2412yes—
264C22×Dic71C2418yes—
265C22×Dic71C2412yes—
266C22×Dic71C2411yescharacteristic
267C22×Dic71C2411yescharacteristic
268C2×C4×D71—28no—
269C2×C4×D71—28no—
270C2×C4×D71—48no—
271C2×C4×D71—48no—
272C2×C4×D71C2×Q8116yescomplemented
273C2×C4×D71C2418yes—
274C2×C4×D71C2418yes—
275C2×C4×D71C24116yes—
276C2×C4×D71C24116yes—
277C2×C4×D71C2418yes—
278C4⋊Dic71C2414yes—
279C4⋊Dic71C2418yes—
280C4⋊Dic71C24116yes—
281C4⋊Dic71C2418yes—
282C4⋊Dic71C2414yes—
283C4⋊Dic71C2418yes—
284C4⋊Dic71C2418yes—
285Dic71⋊C4C2418yes—
286Dic71⋊C4C24116yes—
287Dic71⋊C4C24116yes—
288Dic71⋊C4C24116yes—
289Dic71⋊C4C24116yes—
290Dic71⋊C4C2418yes—
291Dic71⋊C4C2418yes—
292Dic71⋊C4C2418yes—
293Dic71⋊C4C24116yes—
294Dic71⋊C4C24116yes—
295Dic71⋊C4C2418yes—
296Dic71⋊C4C2418yes—
297C22⋊Dic71C2418yes—
298(C2×D71)⋊C4C2418yes—
299(C2×D71)⋊C4C2418yes—
300(C2×D71)⋊C4C24116yes—
301(C2×D71)⋊C4C24116yes—
302C4×Dic71C2414yes—
303C4×Dic71C2418yes—
304C4×Dic71C2418yes—
305C4×Dic71C2414yes—
306C4×Dic71C2414yes—
307C4×Dic71C2414yes—
308C4×Dic71C24116yes—
309C4×Dic71C24116yes—
310C4×Dic71C2418yes—
311C24×C71C2411yescharacteristic
312C2×Q8×C71—48no—
313C2×Q8×C71C24116yes—
314C22×C4×C71—44no—
315C22×C4×C71C2×Q818yescomplemented
316C22×C4×C71C2412yes—
317C22×C4×C71C2412yes—
318C22×C4×C71C2414yes—
319C22×C4×C71C2412yes—
320C22×C4×C71C2412yes—
321C22×C4×C71C2418yes—
322C22×C4×C71C2411yescharacteristic
323C22×C4×C71C2411yescharacteristic
324C22×C4×C71C2414yes—
325C4⋊C4×C71C2418yes—
326C4⋊C4×C71C2418yes—
327C4⋊C4×C71C2414yes—
328C4⋊C4×C71C2414yes—
329C4⋊C4×C71C2414yes—
330C4⋊C4×C71C2414yes—
331C4⋊C4×C71C24116yes—
332C4⋊C4×C71C24116yes—
333C4⋊C4×C71C24116yes—
334C22⋊C4×C71C2418yes—
335C22⋊C4×C71C2418yes—
336C42×C71C2418yes—
337C42×C71C2418yes—
338C23×C71—22no—
339C23×C71—22no—
340C23×C71C22×Q814yes—
341C23×C71C2512yes—
342C23×C71C2511yescharacteristic
343C22×D71—24no—
344C22×D71—24no—
345C22×D71C22×Q818yes—
346C22×D71C2514yes—
347Q8×C71—416no—
348C2×C4×C71—28no—
349C2×C4×C71—24no—
350C2×C4×C71—24no—
351C2×C4×C71—24no—
352C2×C4×C71—24no—
353C2×C4×C71—48no—
354C2×C4×C71C22×Q814yes—
355C2×C4×C71C22×Q814yes—
356C2×C4×C71C22×Q8116yescomplemented
357C2×C4×C71C2514yes—
358C2×C4×C71C2514yes—
359C2×C4×C71C2514yes—
360C2×C4×C71C2514yes—
361C2×C4×C71C2518yes—
362C2×C4×C71C2512yes—
363C2×C4×C71C2512yes—
364C22⋊D71C22×Q8132yescomplemented
365C2×Dic71—24no—
366C2×Dic71—28no—
367C2×Dic71—22no—
368C2×Dic71—22no—
369C2×Dic71—24no—
370C2×Dic71—28no—
371C2×Dic71—28no—
372C2×Dic71—48no—
373C2×Dic71C22×Q818yes—
374C2×Dic71H(5,𝔽2)14yes—
375C2×Dic712−1+414yes—
376C2×Dic71C2514yes—
377C2×Dic71C2512yes—
378C2×Dic71C2512yes—
379C2×Dic71C2518yes—
380C2×Dic71C2514yes—
381C2×Dic71C2514yes—
382C2×Dic71C2512yes—
383C2×Dic71C2512yes—
384D284C22×Q8116yescomplemented
385C4×D71—216no—
386C4×D71—216no—
387C4×D71—416no—
388C4×D71—416no—
389C4×D71C22×Q8132yescomplemented
390Dic142—216no—
391Dic142—232no—
392Dic142—216no—
393Dic142—416no—
394Dic142—416no—
395Dic142C22×Q8116yescomplemented
396C22×C71—22no—
397C22×C71—22no—
398C22×C71—28no—
399C22×C71C23×Q814yes—
400C22×C71C23×Q812yes—
401C22×C71C2×H(5,𝔽2)12yes—
402C22×C71C2×2−1+412yes—
403C22×C71C2611yescharacteristic
404C2×D71—24no—
405C2×D71—24no—
406C2×D71—216no—
407C2×D71C23×Q818yes—
408C4×C71—28no—
409C4×C71—24no—
410C4×C71—24no—
411C4×C71—24no—
412C4×C71—24no—
413C4×C71C23×Q814yes—
414C4×C71C23×Q814yes—
415Dic71—24no—
416Dic71—28no—
417Dic71—22no—
418Dic71—24no—
419Dic71—22no—
420Dic71C23×Q818yes—
421Dic71C2×H(5,𝔽2)14yes—
422Dic71C2×2−1+414yes—
423C2×#3503—711nomaximal, Sylow
424C2×C71—24no—
425C2×C71#350314yescomplemented
426C2×C71C24×Q811yescharacteristic
427C2×C71C22×H(5,𝔽2)11yescharacteristic
428C2×C71C22×2−1+411yescharacteristic
429D71—28no—
430#3503—7132no—
431C2×Q82—712no—
432C2×#557—712no—
433C2×#554—712no—
434C2×#554—714no—
435C2×D4×Q8—712no—
436C2×D4×Q8—714no—
437C2×#544—712no—
438C2×#544—712no—
439C2×#544—711no—
440C2×#544D7111yescharacteristic, complemented
441C2×#533—712no—
442C2×#533—711no—
443C22×C4⋊Q8—712no—
444C22×C4⋊Q8—711no—
445C2×#520—711no—
446C2×#520—711no—
447C2×C4×#41—711no—
448C71C2×#350311yescharacteristic, complemented, Sylow
449C22×#41—711no—
450C23×Q8—714no—
451C23×Q8—712no—
452Q82—7132no—
453#557—7132no—
454#554—7132no—
455#554—7164no—
456D4×Q8—7132no—
457D4×Q8—7164no—
458#544—7132no—
459#544—7132no—
460#544—7116no—
461#544C2×D71116yescomplemented
462#533—7132no—
463#533—7116no—
464C2×C4⋊Q8—714no—
465C2×C4⋊Q8—714no—
466C2×C4⋊Q8—7132no—
467C2×C4⋊Q8—711no—
468C2×C4⋊Q8—712no—
469C2×C4⋊Q8—712no—
470C2×C4⋊Q8—714no—
471C2×C4⋊Q8—712no—
472C2×C4⋊Q8—712no—
473C2×C4⋊Q8—7116no—
474C2×C4⋊Q8—711no—
475C2×C4⋊Q8—714no—
476C2×C4⋊Q8—712no—
477C2×C4⋊Q8—712no—
478C2×C4⋊Q8C2×D7112yes—
479C2×C4⋊Q8C2×D7112yes—
480C2×#125—711no—
481C2×#125—711no—
482C2×#125—714no—
483C2×#125—714no—
484C2×#125—712no—
485C2×#125—712no—
486C2×#125C2×D7112yes—
487C2×#125C2×D7112yes—
488C2×C22⋊Q8—714no—
489C2×C22⋊Q8—714no—
490C2×C22⋊Q8—714no—
491C2×C22⋊Q8—714no—
492C2×C22⋊Q8—714no—
493C2×C22⋊Q8—714no—
494C2×C22⋊Q8—712no—
495C2×C22⋊Q8—712no—
496C2×C22⋊Q8—714no—
497C2×C22⋊Q8C2×D7114yes—
498#520—7116no—
499#520—7116no—
500C4×#41—7116no—
501C2×C4×Q8—711no—
502C2×C4×Q8—711no—
503C2×C4×Q8—712no—
504C2×C4×Q8—714no—
505C2×C4×Q8—714no—
506C2×C4×Q8—712no—
507C2×C4×Q8—712no—
508C2×C4×Q8—712no—
509C2×C4×D4—714no—
510C2×C4×D4—711no—
511C2×C4×D4—711no—
512C2×C4×D4—712no—
513C2×C4×D4—712no—
514C2×C4×D4—712no—
515C2×C4×D4—714no—
516C2×C4×D4—712no—
517C2×#117—711no—
518C2×#117—712no—
519C2×#117—712no—
520C2×#117—712no—
521C2×#117C2×D7111yescharacteristic
522C2×#117C2×D7111yescharacteristic
523C22×C4⋊C4—711no—
524C22×C4⋊C4—712no—
525C22×C4⋊C4—712no—
526C22×C4⋊C4—712no—
527C22×C4⋊C4—714no—
528C22×C4⋊C4C2×D7111yescharacteristic
529C22×C42—711no—
530C22×C42—712no—
531C2×#41—7116no—
532C2×#41—718no—
533C22×Q8—2848no—
534C22×Q8—28416no—
535C22×Q8—7132no—
536C22×Q8—714no—
537C22×Q8—714no—
538C22×Q8—7116no—
539C22×Q8—711no—
540C22×Q8—712no—
541C22×Q8—714no—
542C22×Q8—712no—
543C22×Q8C22×D7114yes—
544C22×D4—712no—
545C22×D4—711no—
546C23×C4—712no—
547C23×C4—714no—
548C23×C4—714no—
549C23×C4—712no—
550C23×C4—711no—
551C23×C4—711no—
552C23×C4—712no—
553C23×C4—712no—
554C23×C4C22×D7112yes—
555C23×C4C22×D7111yescharacteristic
556C4⋊Q8—7132no—
557C4⋊Q8—7132no—
558C4⋊Q8—718no—
559C4⋊Q8—7116no—
560C4⋊Q8—7116no—
561C4⋊Q8—7132no—
562C4⋊Q8—7116no—
563C4⋊Q8—7116no—
564C4⋊Q8—718no—
565C4⋊Q8—7132no—
566C4⋊Q8—7116no—
567C4⋊Q8—7116no—
568C4⋊Q8C22×D71116yes—
569C4⋊Q8C22×D71116yes—
570#125—718no—
571#125—718no—
572#125—7132no—
573#125—7132no—
574#125—7116no—
575#125—7116no—
576#125C22×D71116yes—
577#125C22×D71116yes—
578C22⋊Q8—7132no—
579C22⋊Q8—7132no—
580C22⋊Q8—7132no—
581C22⋊Q8—7132no—
582C22⋊Q8—7132no—
583C22⋊Q8—7132no—
584C22⋊Q8—7116no—
585C22⋊Q8—7116no—
586C22⋊Q8—7132no—
587C22⋊Q8C22×D71132yes—
588C4×Q8—718no—
589C4×Q8—718no—
590C4×Q8—7116no—
591C4×Q8—7132no—
592C4×Q8—7132no—
593C4×Q8—7116no—
594C4×Q8—7116no—
595C4×Q8—7116no—
596C4×D4—7132no—
597C4×D4—718no—
598C4×D4—718no—
599C4×D4—7116no—
600C4×D4—7116no—
601C4×D4—7116no—
602C4×D4—7132no—
603C4×D4—7116no—
604#117—718no—
605#117—7116no—
606#117—7116no—
607#117—7116no—
608#117C22×D7118yes—
609#117C22×D7118yes—
610C2×C4⋊C4—712no—
611C2×C4⋊C4—711no—
612C2×C4⋊C4—714no—
613C2×C4⋊C4—712no—
614C2×C4⋊C4—714no—
615C2×C4⋊C4—714no—
616C2×C4⋊C4—712no—
617C2×C4⋊C4—718no—
618C2×C4⋊C4—714no—
619C2×C4⋊C4—714no—
620C2×C4⋊C4—7116no—
621C2×C4⋊C4—711no—
622C2×C4⋊C4—712no—
623C2×C4⋊C4—712no—
624C2×C4⋊C4—712no—
625C2×C4⋊C4—714no—
626C2×C4⋊C4—712no—
627C2×C4⋊C4—712no—
628C2×C4⋊C4—712no—
629C2×C4⋊C4—714no—
630C2×C4⋊C4—712no—
631C2×C4⋊C4—7116no—
632C2×C4⋊C4—7116no—
633C2×C4⋊C4—7132no—
634C2×C4⋊C4C22×D7111yescharacteristic
635C2×C4⋊C4C22×D7112yes—
636C2×C4⋊C4C22×D7114yes—
637C2×C4⋊C4C22×D7112yes—
638C2×C4⋊C4C22×D7118yes—
639C2×C4⋊C4C22×D7111yescharacteristic
640C2×C4⋊C4C22×D7111yescharacteristic
641C2×C4⋊C4C22×D7111yescharacteristic
642C2×C4⋊C4C22×D7114yes—
643C2×C4⋊C4C22×D7114yes—
644C2×C22⋊C4—712no—
645C2×C22⋊C4—714no—
646C2×C22⋊C4—712no—
647C2×C22⋊C4—712no—
648C2×C22⋊C4—714no—
649C2×C22⋊C4C22×D7112yes—
650C2×C22⋊C4C22×D7112yes—
651C2×C42—711no—
652C2×C42—714no—
653C2×C42—714no—
654C2×C42—712no—
655C2×C42—712no—
656C2×C42—712no—
657C2×C42—711no—
658C2×C42—711no—
659C2×C42—718no—
660C2×C42—711no—
661C2×C42—7116no—
662C2×C42C22×D7112yes—
663C2×C42C22×D7112yes—
664C24—712no—
665C24C23×D7111yescharacteristic
666#41—7164no—
667C2×Q8—48no—
668C2×Q8—2848no—
669C2×Q8—2848no—
670C2×Q8—28432no—
671C2×Q8—28464no—
672C2×Q8—718no—
673C2×Q8—7116no—
674C2×Q8—7116no—
675C2×Q8—714no—
676C2×Q8—718no—
677C2×Q8—7116no—
678C2×Q8—718no—
679C2×Q8—14216no—
680C2×Q8—1428no—
681C2×Q8—1428no—
682C2×Q8C23×D71116yes—
683C2×D4—7116no—
684C2×D4—718no—
685C2×D4—718no—
686C2×D4—714no—
687C22×C4—44no—
688C22×C4—2848no—
689C22×C4—2848no—
690C22×C4—2844no—
691C22×C4—718no—
692C22×C4—7116no—
693C22×C4—7116no—
694C22×C4—712no—
695C22×C4—711no—
696C22×C4—711no—
697C22×C4—7116no—
698C22×C4—718no—
699C22×C4—714no—
700C22×C4—714no—
701C22×C4—712no—
702C22×C4—711no—
703C22×C4—711no—
704C22×C4—712no—
705C22×C4—714no—
706C22×C4—718no—
707C22×C4—718no—
708C22×C4—1428no—
709C22×C4—1428no—
710C22×C4—1424no—
711C22×C4—1424no—
712C22×C4Q8×D7118yescomplemented
713C22×C4C23×D7112yes—
714C22×C4C23×D7112yes—
715C22×C4C23×D7112yes—
716C22×C4C23×D7114yes—
717C22×C4C23×D7112yes—
718C22×C4C23×D7118yes—
719C22×C4C23×D7111yescharacteristic
720C22×C4C23×D7111yescharacteristic
721C22×C4C23×D7114yes—
722C4⋊C4—7116no—
723C4⋊C4—718no—
724C4⋊C4—7116no—
725C4⋊C4—7116no—
726C4⋊C4—7116no—
727C4⋊C4—718no—
728C4⋊C4—718no—
729C4⋊C4—718no—
730C4⋊C4—7116no—
731C4⋊C4—718no—
732C4⋊C4—718no—
733C4⋊C4—7116no—
734C4⋊C4—714no—
735C4⋊C4—718no—
736C4⋊C4—718no—
737C4⋊C4—7116no—
738C4⋊C4—714no—
739C4⋊C4—718no—
740C4⋊C4—718no—
741C4⋊C4C23×D7114yes—
742C4⋊C4C23×D7118yes—
743C4⋊C4C23×D71116yes—
744C4⋊C4C23×D7118yes—
745C4⋊C4C23×D7114yes—
746C4⋊C4C23×D7114yes—
747C4⋊C4C23×D7114yes—
748C4⋊C4C23×D71116yes—
749C4⋊C4C23×D71116yes—
750C22⋊C4—718no—
751C22⋊C4—7116no—
752C22⋊C4—718no—
753C22⋊C4—718no—
754C22⋊C4—7116no—
755C22⋊C4C23×D7118yes—
756C22⋊C4C23×D7118yes—
757C42—714no—
758C42—714no—
759C42—718no—
760C42—718no—
761C42—714no—
762C42—714no—
763C42—7116no—
764C42—7116no—
765C42—718no—
766C42C23×D7118yes—
767C42C23×D7118yes—
768C23—22no—
769C23—22no—
770C23—718no—
771C23—714no—
772C23—1424no—
773C23—1424no—
774C23C2×Q8×D7114yes—
775C23C24×D7112yes—
776C23C24×D7111yescharacteristic
777Q8—416no—
778Q8—28416no—
779Q8—28416no—
780Q8—7116no—
781Q8—14232no—
782Q8—14216no—
783Q8—14216no—
784D4—7132no—
785D4—7116no—
786C2×C4—28no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—48no—
792C2×C4—28416no—
793C2×C4—28416no—
794C2×C4—2848no—
795C2×C4—718no—
796C2×C4—714no—
797C2×C4—714no—
798C2×C4—714no—
799C2×C4—712no—
800C2×C4—712no—
801C2×C4—7132no—
802C2×C4—714no—
803C2×C4—712no—
804C2×C4—712no—
805C2×C4—714no—
806C2×C4—718no—
807C2×C4—14216no—
808C2×C4—14216no—
809C2×C4—1428no—
810C2×C4—1428no—
811C2×C4—1424no—
812C2×C4—1428no—
813C2×C4—1422no—
814C2×C4—1422no—
815C2×C4—1424no—
816C2×C4C2×Q8×D7114yes—
817C2×C4C2×Q8×D7114yes—
818C2×C4C2×Q8×D71116yescomplemented
819C2×C4C24×D7114yes—
820C2×C4C24×D7114yes—
821C2×C4C24×D7114yes—
822C2×C4C24×D7118yes—
823C2×C4C24×D7114yes—
824C2×C4C24×D7112yes—
825C2×C4C24×D7112yes—
826C22—22no—
827C22—22no—
828C22—28no—
829C22—718no—
830C22—1424no—
831C22—1424no—
832C22—14216no—
833C22C22×Q8×D7114yes—
834C22C22×Q8×D7112yes—
835C22H(5,𝔽2)×D7112yes—
836C222−1+4×D7112yes—
837C22C25×D7111yescharacteristic
838C4—28no—
839C4—24no—
840C4—24no—
841C4—24no—
842C4—24no—
843C4—718no—
844C4—714no—
845C4—714no—
846C4—1424no—
847C4—1428no—
848C4—1422no—
849C4—1422no—
850C4—1424no—
851C4C22×Q8×D7114yes—
852C4C22×Q8×D7114yes—
853C2—24no—
854C2—1428no—
855C2#2260215514yesdirect product factor
856C2C23×Q8×D7111yescharacteristic
857C2C2×H(5,𝔽2)×D7111yescharacteristic
858C2C2×2−1+4×D7111yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#544×C71C2
socleC23×C71C25
prime radicalC22×#11765865C22
hypercenterC2×#544D71
hypocenterC71C2×#3503
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #22602155C2direct (N × H)
2. C2×#17986729C2semidirect
3. C2×#17986726C2semidirect
4. C2×#17986705C2semidirect
5. C2×#17986703C2semidirect
6. C2×#17986664C2semidirect
7. C2×#17986662C2semidirect
8. C2×#17986629C2semidirect
9. C2×#17986627C2semidirect
10. C2×#17986626C2semidirect
11. C2×#17986555C2semidirect
12. C2×#17986552C2semidirect
13. C22×#14556127C2semidirect
14. C2×C4⋊Q8×D71C2semidirect
18. C2×#544×C71C2semidirect
22. #17986729C22semidirect
23. #17986726C22semidirect
24. #17986705C22semidirect
25. #17986703C22semidirect
26. #17986664C22semidirect
27. #17986662C22semidirect
28. #17986629C22semidirect
29. #17986627C22semidirect
30. #17986626C22semidirect
31. #17986555C22semidirect
32. #17986552C22semidirect
43. C2×#14556127C22semidirect
46. C4⋊Q8×D71C22semidirect
92. #544×C71C22semidirect
101. C2×#11765865Q8semidirect
235. #11765865C2×Q8semidirect
242. C2×Dic142C2×Q8semidirect
250. C2×D284C2×Q8semidirect
252. C2×C22⋊D71C2×Q8semidirect
272. C2×C4×D71C2×Q8semidirect
315. C22×C4×C71C2×Q8semidirect
356. C2×C4×C71C22×Q8semidirect
364. C22⋊D71C22×Q8semidirect
384. D284C22×Q8semidirect
389. C4×D71C22×Q8semidirect
395. Dic142C22×Q8semidirect
425. C2×C71#3503semidirect
440. C2×#544D71semidirect
448. C71C2×#3503semidirect
461. #544C2×D71semidirect
712. C22×C4Q8×D71semidirect
818. C2×C4C2×Q8×D71semidirect
855. C2#22602155direct (N × H)

Maximal subgroups

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

subgroupindex
#226021552
C2×#179867292
C2×#179867262
C2×#179867052
C2×#179867032
C2×#179866642
C2×#179866622
C2×#179866292
C2×#179866272
C2×#179866262
C2×#179865552
C2×#179865522
C22×#145561272
C2×C4⋊Q8×D712
C2×#179864802
C2×#179864792
C2×#179864672
C2×#544×C712
C2×#350371