Finite Group Databasebeta

← C2×#22602423 #32905657

Subgroups — C2×#22602423 #32905657

Order 18176.

7758 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602423C2132yesmaximal, direct product factor
2C2×#17986734C211yesmaximal, characteristic, complemented
3C2×#17986731C212yesmaximal, complemented
4C2×Q8×Dic142C211yesmaximal, characteristic, complemented
5C2×#17986706C211yesmaximal, characteristic, complemented
6C2×#17986705C212yesmaximal, complemented
7C2×#17986670C211yesmaximal, characteristic, complemented
8C2×#17986658C212yesmaximal, complemented
9C2×#17986653C212yesmaximal, complemented
10C2×#17986647C214yesmaximal, complemented
11C2×#17986620C212yesmaximal, complemented
12C2×#17986615C214yesmaximal, complemented
13C2×#17986549C211yesmaximal, characteristic, complemented
14C2×#17986544C212yesmaximal, complemented
15C2×#17986535C212yesmaximal, complemented
16C2×#17986479C212yesmaximal, complemented
17C22×C4×Dic142C211yesmaximal, characteristic, complemented
18C2×#529×C71C211yesmaximal, characteristic, complemented
19C22×#11765865C2212yes—
20C22×#11765865C2212yes—
21C22×#11765864C2214yes—
22C23×Dic142C2211yescharacteristic
23#17986734C22116yescomplemented
24#17986731C22132yescomplemented
25Q8×Dic142C22116yescomplemented
26#17986706C22116yescomplemented
27#17986705C22132yescomplemented
28#17986670C22116yescomplemented
29#17986658C22132yescomplemented
30#17986653C22132yescomplemented
31#17986647C22164yescomplemented
32#17986620C22132yescomplemented
33#17986615C22164yescomplemented
34#17986549C22116yescomplemented
35#17986544C22132yescomplemented
36C2×#14556128C2212yes—
37C2×#14556128C2211yescharacteristic
38C2×#14556127C2214yes—
39C2×#14556127C2212yes—
40C2×#14556125C2211yescharacteristic
41C2×#14556124C2212yes—
42#17986535C22132yescomplemented
43C2×#14556123C2214yes—
44C2×#14556119C2212yes—
45C2×#14556117C2212yes—
46C2×#14556116C2212yes—
47C2×#14556116C2212yes—
48C2×#14556114C2214yes—
49C2×#14556114C2214yes—
50C2×#14556113C2214yes—
51C2×#14556112C2214yes—
52C2×#14556112C2214yes—
53C2×#14556110C2214yes—
54C2×#14556108C2214yes—
55C2×#14556107C2212yes—
56C2×#14556106C2214yes—
57C2×#14556106C2214yes—
58C2×#14556105C2214yes—
59C2×#14556102C2212yes—
60C2×#14556102C2212yes—
61C2×#14556102C2212yes—
62C2×#14556101C2214yes—
63C2×#14556100C2214yes—
64#17986479C22132yescomplemented
65C2×Q8×Dic71C2212yes—
66C2×C4×Dic142C2211yescharacteristic
67C2×C4×Dic142C2211yescharacteristic
68C2×C4×Dic142C2212yes—
69C2×C4×Dic142C2211yescharacteristic
70C2×C4×Dic142C2212yes—
71C2×C4×Dic142C2211yescharacteristic
72C2×C4×Dic142C2212yes—
73C2×C4×Dic142C22116yescomplemented
74C2×C4×D284C2212yes—
75C2×C4×D284C2212yes—
76C2×C4×D284C2212yes—
77C2×D4×Dic71C2212yes—
78C2×#14556090C2212yes—
79C2×#14556090C2212yes—
80C2×(C22⋊D71)⋊C4C2214yes—
81C2×(C22⋊D71)⋊C4C2214yes—
82C2×(C22⋊D71)⋊C4C2214yes—
83C2×#14556086C2214yes—
84C22×C4⋊Dic71C2211yescharacteristic
85C22×C4⋊Dic71C2212yes—
86C22×Dic71⋊C4C2212yes—
87C2×C4⋊C4×D71C2214yes—
88C22×C4×Dic71C2212yes—
89#529×C71C22116yescomplemented
90C2×#126×C71C2212yes—
91C2×#125×C71C2211yescharacteristic
92C2×#124×C71C2211yescharacteristic
93C2×#123×C71C2212yes—
94C2×C22⋊Q8×C71C2211yescharacteristic
95C2×#121×C71C2211yescharacteristic
96C2×C4×Q8×C71C2211yescharacteristic
97C2×C4×D4×C71C2212yes—
98C2×C4×D4×C71C2211yescharacteristic
99C2×#117×C71C2212yes—
100C22×C42×C71C2211yescharacteristic
101C2×#11765865—216no—
102C2×#11765865—48no—
103C2×#11765865C23116yes—
104C2×#11765865C23116yes—
105C2×#11765864—416no—
106C2×#11765864C23132yes—
107C22×Dic142—28no—
108C22×Dic142C2318yes—
109C22×Dic142C2312yes—
110C22×Dic142C2311yescharacteristic
111C22×Dic142C2314yes—
112C22×Dic142C2312yes—
113C22×Dic142C2311yescharacteristic
114C22×D284C2312yes—
115C22×D284C2312yes—
116C22×D284C2312yes—
117C22×C22⋊D71C2314yes—
118C22×C22⋊D71C2314yes—
119C22×C22⋊D71C2314yes—
120C23×Dic71C2312yes—
121C23×Dic71C2312yes—
122C23×Dic71C2314yes—
123C22×C4×D71C2314yes—
124C22×C4×D71C2314yes—
125C22×C4×D71C2314yes—
126#14556128C23116yes—
127#14556128C2318yes—
128#14556127C23132yes—
129#14556127C23116yes—
130#14556125C2318yes—
131#14556124C23116yes—
132#14556123C23132yes—
133#14556119C23116yes—
134#14556117C23116yes—
135#14556116C23116yes—
136#14556116C23116yes—
137#14556114C23132yes—
138#14556114C23132yes—
139#14556113C23132yes—
140#14556112C23132yes—
141#14556112C23132yes—
142#14556110C23132yes—
143#14556108C23132yes—
144#14556107C23116yes—
145#14556106C23132yes—
146#14556106C23132yes—
147#14556105C23132yes—
148#14556102C23116yes—
149#14556102C23116yes—
150#14556102C23116yes—
151#14556101C23132yes—
152#14556100C23132yes—
153Q8×Dic71C23116yes—
154C4×Dic142C23116yes—
155C4×Dic142C2318yes—
156C4×Dic142C23116yes—
157C4×Dic142C2318yes—
158C4×Dic142C23116yes—
159C4×Dic142C2318yes—
160C4×Dic142C2318yes—
161C4×D284C23116yes—
162C4×D284C23116yes—
163C4×D284C23116yes—
164D4×Dic71C23116yes—
165#14556090C23116yes—
166#14556090C23116yes—
167(C22⋊D71)⋊C4C23132yes—
168(C22⋊D71)⋊C4C23132yes—
169(C22⋊D71)⋊C4C23132yes—
170#14556086C23132yes—
171C2×C4⋊Dic71C2318yes—
172C2×C4⋊Dic71C23116yes—
173C2×C4⋊Dic71C2314yes—
174C2×C4⋊Dic71C2311yescharacteristic
175C2×C4⋊Dic71C2312yes—
176C2×C4⋊Dic71C2311yescharacteristic
177C2×C4⋊Dic71C2312yes—
178C2×C4⋊Dic71C2312yes—
179C2×C4⋊Dic71C2314yes—
180C2×Dic71⋊C4C23116yes—
181C2×Dic71⋊C4C2312yes—
182C2×Dic71⋊C4C2314yes—
183C2×Dic71⋊C4C2312yes—
184C2×Dic71⋊C4C2312yes—
185C2×Dic71⋊C4C2312yes—
186C2×Dic71⋊C4C2314yes—
187C4⋊C4×D71C23132yes—
188C2×C22⋊Dic71C2314yes—
189C2×(C2×D71)⋊C4C2314yes—
190C2×(C2×D71)⋊C4C2314yes—
191C2×(C2×D71)⋊C4C2314yes—
192C2×(C2×D71)⋊C4C2314yes—
193C2×(C2×D71)⋊C4C2314yes—
194C2×(C2×D71)⋊C4C2314yes—
195C2×C4×Dic71C2312yes—
196C2×C4×Dic71C2312yes—
197C2×C4×Dic71C2312yes—
198C2×C4×Dic71C2312yes—
199C2×C4×Dic71C23116yes—
200C2×C4×Dic71C2314yes—
201C22×Q8×C71C2311yescharacteristic
202C22×D4×C71C2312yes—
203C22×D4×C71C2311yescharacteristic
204C23×C4×C71C2311yescharacteristic
205C23×C4×C71C2311yescharacteristic
206C23×C4×C71C2312yes—
207C23×C4×C71C2311yescharacteristic
208#126×C71C23116yes—
209#125×C71C2318yes—
210#124×C71C2318yes—
211#123×C71C23116yes—
212C22⋊Q8×C71C2318yes—
213#121×C71C2318yes—
214C4×Q8×C71C2318yes—
215C4×D4×C71C23116yes—
216C4×D4×C71C2318yes—
217#117×C71C23116yes—
218C2×C4⋊C4×C71C2312yes—
219C2×C4⋊C4×C71C2312yes—
220C2×C4⋊C4×C71C2311yescharacteristic
221C2×C4⋊C4×C71C2312yes—
222C2×C4⋊C4×C71C2311yescharacteristic
223C2×C4⋊C4×C71C2312yes—
224C2×C22⋊C4×C71C2312yes—
225C2×C22⋊C4×C71C2312yes—
226C2×C22⋊C4×C71C2312yes—
227C2×C22⋊C4×C71C2312yes—
228C2×C22⋊C4×C71C2312yes—
229C2×C42×C71C2311yescharacteristic
230C2×C42×C71C2311yescharacteristic
231C2×C42×C71C2311yescharacteristic
232C2×C42×C71C2311yescharacteristic
233C2×C42×C71C2318yes—
234C2×C42×C71C2312yes—
235C23×D71C2414yes—
236#11765865—264no—
237#11765865—432no—
238#11765864—464no—
239C2×Dic142—24no—
240C2×Dic142—28no—
241C2×Dic142—232no—
242C2×Dic142—48no—
243C2×Dic142—44no—
244C2×Dic142#4118yescomplemented
245C2×Dic142C2418yes—
246C2×Dic142C2414yes—
247C2×Dic142C24116yes—
248C2×Dic142C2418yes—
249C2×Dic142C2414yes—
250C2×D284—28no—
251C2×D284—28no—
252C2×D284—44no—
253C2×D284C2418yes—
254C2×D284C2418yes—
255C2×D284C2418yes—
256C2×C22⋊D71—216no—
257C2×C22⋊D71—216no—
258C2×C22⋊D71—48no—
259C2×C22⋊D71C24116yes—
260C2×C22⋊D71C24116yes—
261C2×C22⋊D71C24116yes—
262C22×Dic71—28no—
263C22×Dic71—28no—
264C22×Dic71—48no—
265C22×Dic71C2412yes—
266C22×Dic71C2414yes—
267C22×Dic71C2412yes—
268C22×Dic71C2412yes—
269C22×Dic71C2418yes—
270C22×Dic71C2418yes—
271C22×Dic71C24116yes—
272C22×Dic71C2412yes—
273C2×C4×D71—216no—
274C2×C4×D71—48no—
275C2×C4×D71—48no—
276C2×C4×D71C24116yes—
277C2×C4×D71C24116yes—
278C2×C4×D71C24116yes—
279C4⋊Dic71C24116yes—
280C4⋊Dic71C2414yes—
281C4⋊Dic71C2418yes—
282C4⋊Dic71C2414yes—
283C4⋊Dic71C2418yes—
284C4⋊Dic71C2418yes—
285C4⋊Dic71C24116yes—
286Dic71⋊C4C2418yes—
287Dic71⋊C4C24116yes—
288Dic71⋊C4C2418yes—
289Dic71⋊C4C2418yes—
290Dic71⋊C4C2418yes—
291Dic71⋊C4C24116yes—
292C22⋊Dic71C24116yes—
293(C2×D71)⋊C4C24116yes—
294(C2×D71)⋊C4C24116yes—
295(C2×D71)⋊C4C24116yes—
296(C2×D71)⋊C4C24116yes—
297(C2×D71)⋊C4C24116yes—
298(C2×D71)⋊C4C24116yes—
299C4×Dic71C2418yes—
300C4×Dic71C2418yes—
301C4×Dic71C2418yes—
302C4×Dic71C2418yes—
303C4×Dic71C24116yes—
304C24×C71C2412yes—
305C24×C71C2411yescharacteristic
306C2×Q8×C71—24no—
307C2×Q8×C71C2414yes—
308C2×D4×C71—28no—
309C2×D4×C71—24no—
310C2×D4×C71C2418yes—
311C2×D4×C71C2414yes—
312C22×C4×C71—24no—
313C22×C4×C71—24no—
314C22×C4×C71—28no—
315C22×C4×C71—24no—
316C22×C4×C71C2411yescharacteristic
317C22×C4×C71C2412yes—
318C22×C4×C71C2412yes—
319C22×C4×C71C2411yescharacteristic
320C22×C4×C71C2411yescharacteristic
321C22×C4×C71C2414yes—
322C22×C4×C71C2414yes—
323C22×C4×C71C2418yes—
324C22×C4×C71C2411yescharacteristic
325C22×C4×C71C2414yes—
326C22×C4×C71C2412yes—
327C22×C4×C71C2411yescharacteristic
328C22×C4×C71C2411yescharacteristic
329C4⋊C4×C71C2418yes—
330C4⋊C4×C71C2418yes—
331C4⋊C4×C71C2414yes—
332C4⋊C4×C71C2418yes—
333C4⋊C4×C71C2414yes—
334C4⋊C4×C71C2418yes—
335C22⋊C4×C71C2418yes—
336C22⋊C4×C71C2418yes—
337C22⋊C4×C71C2418yes—
338C22⋊C4×C71C2418yes—
339C22⋊C4×C71C2418yes—
340C42×C71C2414yes—
341C42×C71C2414yes—
342C42×C71C2414yes—
343C42×C71C2414yes—
344C42×C71C2418yes—
345C23×C71—22no—
346C23×C71—22no—
347C23×C71—24no—
348C23×C71—24no—
349C23×C71—24no—
350C23×C71H(5,𝔽2)14yes—
351C23×C71C2514yes—
352C23×C71C2512yes—
353C23×C71C2511yescharacteristic
354C22×D71—28no—
355C22×D71—28no—
356C22×D71—28no—
357C22×D71C2518yes—
358Q8×C71—28no—
359D4×C71—216no—
360D4×C71—28no—
361C2×C4×C71—24no—
362C2×C4×C71—22no—
363C2×C4×C71—22no—
364C2×C4×C71—22no—
365C2×C4×C71—28no—
366C2×C4×C71—24no—
367C2×C4×C71—22no—
368C2×C4×C71—24no—
369C2×C4×C71—28no—
370C2×C4×C71—216no—
371C2×C4×C71—28no—
372C2×C4×C71C2×#4114yes—
373C2×C4×C712−1+414yes—
374C2×C4×C71C2512yes—
375C2×C4×C71C2512yes—
376C2×C4×C71C2512yes—
377C2×C4×C71C2512yes—
378C2×C4×C71C2514yes—
379C2×C4×C71C2514yes—
380C2×C4×C71C2514yes—
381C2×C4×C71C2512yes—
382C2×C4×C71C2512yes—
383C22⋊D71—232no—
384C22⋊D71—232no—
385C22⋊D71—416no—
386C2×Dic71—24no—
387C2×Dic71—24no—
388C2×Dic71—28no—
389C2×Dic71—24no—
390C2×Dic71—216no—
391C2×Dic71—216no—
392C2×Dic71—416no—
393C2×Dic71C2×#4118yes—
394C2×Dic71C2514yes—
395C2×Dic71C2514yes—
396C2×Dic71C2514yes—
397C2×Dic71C2518yes—
398C2×Dic71C2514yes—
399D284—216no—
400D284—216no—
401D284—48no—
402C4×D71—232no—
403C4×D71—416no—
404C4×D71—416no—
405Dic142—28no—
406Dic142—216no—
407Dic142—416no—
408Dic142—48no—
409Dic142C2×#41116yescomplemented
410C22×C71—22no—
411C22×C71—22no—
412C22×C71—28no—
413C22×C71—24no—
414C22×C71—24no—
415C22×C71—24no—
416C22×C71—48no—
417C22×C71C22×#4112yes—
418C22×C71C2×H(5,𝔽2)14yes—
419C22×C71C2×H(5,𝔽2)12yes—
420C22×C71C2×2−1+412yes—
421C22×C71C2611yescharacteristic
422C2×D71—28no—
423C2×D71—28no—
424C2×D71—28no—
425C2×D71—416no—
426C4×C71—22no—
427C4×C71—24no—
428C4×C71—24no—
429C4×C71—22no—
430C4×C71—22no—
431C4×C71—22no—
432C4×C71—24no—
433C4×C71C22×#4114yes—
434C4×C71C2×2−1+414yes—
435Dic71—24no—
436Dic71—28no—
437Dic71—24no—
438Dic71—24no—
439Dic71C22×#4118yes—
440C2×#3522—711nomaximal, Sylow
441C2×C71—24no—
442C2×C71—44no—
443C2×C71#352214yescomplemented
444C2×C71C23×#4111yescharacteristic
445C2×C71C22×H(5,𝔽2)11yescharacteristic
446C2×C71C22×2−1+411yescharacteristic
447D71—48no—
448#3522—7132no—
449C2×#559—712no—
450C2×#559—711no—
451C2×Q82—711no—
452C2×#554—712no—
453C2×#554—711no—
454C2×#550—711no—
455C2×#548—712no—
456C2×#547—714no—
457C2×#547—712no—
458C2×#542—714no—
459C2×#542—712no—
460C2×#532—711no—
461C2×#532—712no—
462C2×#529—712no—
463C2×#529D7111yescharacteristic, complemented
464C2×#520—712no—
465C22×C4×Q8—711no—
466C71C2×#352211yescharacteristic, complemented, Sylow
467C22×#41—714no—
468C22×#41—712no—
469C22×#41—712no—
470C23×Q8—711no—
471#559—7132no—
472#559—7116no—
473Q82—7116no—
474#554—7132no—
475#554—7116no—
476#550—7116no—
477#548—7132no—
478#547—7164no—
479#547—7132no—
480#542—7164no—
481#542—7132no—
482#532—7132no—
483#532—7116no—
484C2×C4⋊Q8—712no—
485C2×C4⋊Q8—714no—
486C2×C4⋊Q8—711no—
487C2×C4⋊Q8—712no—
488C2×#127—712no—
489C2×#127—711no—
490#529—7132no—
491#529C2×D71116yescomplemented
492C2×#126—714no—
493C2×#126C2×D7112yes—
494C2×#125—712no—
495C2×#125C2×D7111yescharacteristic
496C2×#124—712no—
497C2×#124—714no—
498C2×#124—714no—
499C2×#124—712no—
500C2×#124—712no—
501C2×#124C2×D7111yescharacteristic
502C2×#123—714no—
503C2×#123—714no—
504C2×#123—714no—
505C2×#123—714no—
506C2×#123C2×D7112yes—
507C2×C22⋊Q8—712no—
508C2×C22⋊Q8—714no—
509C2×C22⋊Q8—714no—
510C2×C22⋊Q8—714no—
511C2×C22⋊Q8—714no—
512C2×C22⋊Q8C2×D7111yescharacteristic
513C2×#121—714no—
514C2×#121—712no—
515C2×#121—712no—
516C2×#121—712no—
517C2×#121—714no—
518C2×#121C2×D7111yescharacteristic
519#520—7132no—
520C2×C4×Q8—712no—
521C2×C4×Q8—711no—
522C2×C4×Q8—712no—
523C2×C4×Q8—711no—
524C2×C4×Q8—711no—
525C2×C4×Q8—711no—
526C2×C4×Q8—712no—
527C2×C4×Q8—7116no—
528C2×C4×Q8—712no—
529C2×C4×Q8C2×D7111yescharacteristic
530C2×C4×D4—712no—
531C2×C4×D4—712no—
532C2×C4×D4—712no—
533C2×C4×D4—714no—
534C2×C4×D4—714no—
535C2×C4×D4—714no—
536C2×C4×D4—712no—
537C2×C4×D4—712no—
538C2×C4×D4—712no—
539C2×C4×D4C2×D7112yes—
540C2×C4×D4C2×D7111yescharacteristic
541C2×#117—714no—
542C2×#117C2×D7112yes—
543C22×C4⋊C4—712no—
544C22×C4⋊C4—711no—
545C22×C4⋊C4—712no—
546C22×C4⋊C4—714no—
547C22×C42—712no—
548C22×C42C2×D7111yescharacteristic
549C2×#41—2848no—
550C2×#41—28416no—
551C2×#41—7132no—
552C2×#41—7116no—
553C2×#41—7116no—
554C2×#41—14216no—
555C22×Q8—714no—
556C22×Q8—712no—
557C22×Q8—711no—
558C22×Q8—712no—
559C22×Q8—711no—
560C22×Q8—718no—
561C22×Q8—1428no—
562C22×Q8C22×D7111yescharacteristic
563C22×D4—714no—
564C22×D4—714no—
565C22×D4—714no—
566C22×D4—712no—
567C22×D4—712no—
568C22×D4—712no—
569C22×D4C22×D7111yescharacteristic
570C22×D4C22×D7112yes—
571C23×C4—714no—
572C23×C4—714no—
573C23×C4—714no—
574C23×C4—712no—
575C23×C4—712no—
576C23×C4—714no—
577C23×C4C22×D7111yescharacteristic
578C23×C4C22×D7112yes—
579C23×C4C22×D7111yescharacteristic
580C23×C4C22×D7111yescharacteristic
581C4⋊Q8—7116no—
582C4⋊Q8—7132no—
583C4⋊Q8—718no—
584C4⋊Q8—7116no—
585#127—7116no—
586#127—718no—
587#126—7132no—
588#126C22×D71116yes—
589#125—7116no—
590#125C22×D7118yes—
591#124—7116no—
592#124—7132no—
593#124—7132no—
594#124—7116no—
595#124—7116no—
596#124C22×D7118yes—
597#123—7132no—
598#123—7132no—
599#123—7132no—
600#123—7132no—
601#123C22×D71116yes—
602C22⋊Q8—7116no—
603C22⋊Q8—7132no—
604C22⋊Q8—7132no—
605C22⋊Q8—7132no—
606C22⋊Q8—7132no—
607C22⋊Q8C22×D7118yes—
608#121—7132no—
609#121—7116no—
610#121—7116no—
611#121—7116no—
612#121—7132no—
613#121C22×D7118yes—
614C4×Q8—7116no—
615C4×Q8—718no—
616C4×Q8—7116no—
617C4×Q8—718no—
618C4×Q8—718no—
619C4×Q8—718no—
620C4×Q8—7116no—
621C4×Q8—7116no—
622C4×Q8C22×D7118yes—
623C4×D4—7116no—
624C4×D4—7116no—
625C4×D4—7116no—
626C4×D4—7132no—
627C4×D4—7132no—
628C4×D4—7132no—
629C4×D4—7116no—
630C4×D4—7116no—
631C4×D4—7116no—
632C4×D4C22×D71116yes—
633C4×D4C22×D7118yes—
634#117—7132no—
635#117C22×D71116yes—
636C2×C4⋊C4—712no—
637C2×C4⋊C4—711no—
638C2×C4⋊C4—714no—
639C2×C4⋊C4—714no—
640C2×C4⋊C4—712no—
641C2×C4⋊C4—712no—
642C2×C4⋊C4—711no—
643C2×C4⋊C4—712no—
644C2×C4⋊C4—712no—
645C2×C4⋊C4—712no—
646C2×C4⋊C4—7116no—
647C2×C4⋊C4—718no—
648C2×C4⋊C4—7116no—
649C2×C4⋊C4—712no—
650C2×C4⋊C4—714no—
651C2×C4⋊C4—714no—
652C2×C4⋊C4—7132no—
653C2×C4⋊C4C22×D7112yes—
654C2×C4⋊C4C22×D7112yes—
655C2×C4⋊C4C22×D7111yescharacteristic
656C2×C4⋊C4C22×D7111yescharacteristic
657C2×C4⋊C4C22×D7112yes—
658C2×C4⋊C4C22×D7112yes—
659C2×C22⋊C4—714no—
660C2×C22⋊C4—714no—
661C2×C22⋊C4—714no—
662C2×C22⋊C4—714no—
663C2×C22⋊C4—714no—
664C2×C22⋊C4—714no—
665C2×C22⋊C4—714no—
666C2×C22⋊C4C22×D7112yes—
667C2×C22⋊C4C22×D7112yes—
668C2×C22⋊C4C22×D7112yes—
669C2×C22⋊C4C22×D7112yes—
670C2×C22⋊C4C22×D7112yes—
671C2×C42—712no—
672C2×C42—714no—
673C2×C42—712no—
674C2×C42—712no—
675C2×C42—712no—
676C2×C42—7116no—
677C2×C42C22×D7111yescharacteristic
678C2×C42C22×D7112yes—
679C2×C42C22×D7111yescharacteristic
680C2×C42C22×D7111yescharacteristic
681C2×C42C22×D7111yescharacteristic
682C2×C42C22×D7118yes—
683C24—714no—
684C24C23×D7112yes—
685C24C23×D7111yescharacteristic
686#41—28432no—
687#41—28464no—
688#41—14264no—
689C2×Q8—24no—
690C2×Q8—2844no—
691C2×Q8—2848no—
692C2×Q8—718no—
693C2×Q8—7116no—
694C2×Q8—718no—
695C2×Q8—714no—
696C2×Q8—718no—
697C2×Q8—714no—
698C2×Q8—1428no—
699C2×Q8—14232no—
700C2×Q8—1424no—
701C2×Q8C23×D7114yes—
702C2×D4—28no—
703C2×D4—24no—
704C2×D4—2844no—
705C2×D4—2848no—
706C2×D4—7116no—
707C2×D4—7116no—
708C2×D4—7116no—
709C2×D4—718no—
710C2×D4—718no—
711C2×D4—718no—
712C2×D4—14216no—
713C2×D4—14216no—
714C2×D4—1428no—
715C2×D4—1428no—
716C2×D4C23×D7114yes—
717C2×D4C23×D7118yes—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—28no—
721C22×C4—24no—
722C22×C4—2848no—
723C22×C4—2848no—
724C22×C4—2848no—
725C22×C4—7116no—
726C22×C4—7116no—
727C22×C4—7116no—
728C22×C4—712no—
729C22×C4—718no—
730C22×C4—718no—
731C22×C4—712no—
732C22×C4—712no—
733C22×C4—712no—
734C22×C4—714no—
735C22×C4—7116no—
736C22×C4—14216no—
737C22×C4—1428no—
738C22×C4—1428no—
739C22×C4C23×D7114yes—
740C22×C4C23×D7114yes—
741C22×C4C23×D7114yes—
742C22×C4C23×D7118yes—
743C22×C4C23×D7111yescharacteristic
744C22×C4C23×D7112yes—
745C22×C4C23×D7111yescharacteristic
746C22×C4C23×D7111yescharacteristic
747C22×C4C23×D7111yescharacteristic
748C22×C4C23×D7112yes—
749C22×C4C23×D7112yes—
750C22×C4C23×D7111yescharacteristic
751C22×C4C23×D7111yescharacteristic
752C4⋊C4—718no—
753C4⋊C4—7116no—
754C4⋊C4—718no—
755C4⋊C4—718no—
756C4⋊C4—718no—
757C4⋊C4—7116no—
758C4⋊C4—714no—
759C4⋊C4—7116no—
760C4⋊C4—718no—
761C4⋊C4—714no—
762C4⋊C4—718no—
763C4⋊C4—718no—
764C4⋊C4—7116no—
765C4⋊C4C23×D7118yes—
766C4⋊C4C23×D7118yes—
767C4⋊C4C23×D7114yes—
768C4⋊C4C23×D7114yes—
769C4⋊C4C23×D7118yes—
770C4⋊C4C23×D7118yes—
771C22⋊C4—7116no—
772C22⋊C4—7116no—
773C22⋊C4—7116no—
774C22⋊C4—7116no—
775C22⋊C4—7116no—
776C22⋊C4—7116no—
777C22⋊C4—7116no—
778C22⋊C4C23×D7118yes—
779C22⋊C4C23×D7118yes—
780C22⋊C4C23×D7118yes—
781C22⋊C4C23×D7118yes—
782C22⋊C4C23×D7118yes—
783C42—718no—
784C42—718no—
785C42—718no—
786C42—718no—
787C42—7116no—
788C42C23×D7114yes—
789C42C23×D7114yes—
790C42C23×D7114yes—
791C42C23×D7114yes—
792C42C23×D7118yes—
793C23—22no—
794C23—22no—
795C23—24no—
796C23—24no—
797C23—24no—
798C23—718no—
799C23—1428no—
800C23—1428no—
801C23—1428no—
802C23#1455617414yes—
803C23C24×D7114yes—
804C23C24×D7112yes—
805C23C24×D7111yescharacteristic
806Q8—28no—
807Q8—2848no—
808Q8—28416no—
809Q8—7116no—
810Q8—14216no—
811Q8—1428no—
812D4—216no—
813D4—28no—
814D4—2848no—
815D4—28416no—
816D4—14232no—
817D4—14232no—
818D4—14216no—
819D4—14216no—
820C2×C4—24no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—28no—
825C2×C4—24no—
826C2×C4—22no—
827C2×C4—24no—
828C2×C4—28no—
829C2×C4—216no—
830C2×C4—28no—
831C2×C4—28416no—
832C2×C4—28416no—
833C2×C4—28416no—
834C2×C4—718no—
835C2×C4—714no—
836C2×C4—714no—
837C2×C4—714no—
838C2×C4—714no—
839C2×C4—718no—
840C2×C4—14232no—
841C2×C4—14216no—
842C2×C4—1424no—
843C2×C4—1424no—
844C2×C4—1428no—
845C2×C4—1424no—
846C2×C4—14216no—
847C2×C4#41×D7114yes—
848C2×C4#1455617514yes—
849C2×C4C24×D7112yes—
850C2×C4C24×D7114yes—
851C2×C4C24×D7112yes—
852C2×C4C24×D7112yes—
853C2×C4C24×D7112yes—
854C2×C4C24×D7114yes—
855C2×C4C24×D7114yes—
856C2×C4C24×D7112yes—
857C2×C4C24×D7112yes—
858C22—22no—
859C22—22no—
860C22—28no—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—48no—
865C22—28416no—
866C22—1428no—
867C22—1428no—
868C22—1428no—
869C22C2×#41×D7112yes—
870C22C2×#1455617414yes—
871C22C2×#1455617412yes—
872C22C2×#1455617512yes—
873C22C25×D7111yescharacteristic
874C4—24no—
875C4—22no—
876C4—22no—
877C4—22no—
878C4—24no—
879C4—22no—
880C4—24no—
881C4—718no—
882C4—1424no—
883C4—1424no—
884C4—1428no—
885C4—1424no—
886C4C2×#41×D7114yes—
887C4C2×#1455617514yes—
888C2—24no—
889C2—44no—
890C2—2848no—
891C2#2260242314yesdirect product factor
892C2C22×#41×D7111yescharacteristic
893C2C22×#1455617411yescharacteristic
894C2C22×#1455617511yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#529×C71C2
socleC23×C71C25
hypercenterC2×#529D71
hypocenterC71C2×#3522
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #22602423C2direct (N × H)
2. C2×#17986734C2semidirect
3. C2×#17986731C2semidirect
4. C2×Q8×Dic142C2semidirect
5. C2×#17986706C2semidirect
6. C2×#17986705C2semidirect
7. C2×#17986670C2semidirect
8. C2×#17986658C2semidirect
9. C2×#17986653C2semidirect
10. C2×#17986647C2semidirect
11. C2×#17986620C2semidirect
12. C2×#17986615C2semidirect
13. C2×#17986549C2semidirect
14. C2×#17986544C2semidirect
15. C2×#17986535C2semidirect
16. C2×#17986479C2semidirect
17. C22×C4×Dic142C2semidirect
18. C2×#529×C71C2semidirect
23. #17986734C22semidirect
24. #17986731C22semidirect
25. Q8×Dic142C22semidirect
26. #17986706C22semidirect
27. #17986705C22semidirect
28. #17986670C22semidirect
29. #17986658C22semidirect
30. #17986653C22semidirect
31. #17986647C22semidirect
32. #17986620C22semidirect
33. #17986615C22semidirect
34. #17986549C22semidirect
35. #17986544C22semidirect
42. #17986535C22semidirect
64. #17986479C22semidirect
73. C2×C4×Dic142C22semidirect
89. #529×C71C22semidirect
244. C2×Dic142#41semidirect
409. Dic142C2×#41semidirect
443. C2×C71#3522semidirect
463. C2×#529D71semidirect
466. C71C2×#3522semidirect
491. #529C2×D71semidirect
891. C2#22602423direct (N × H)

Maximal subgroups

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

subgroupindex
#226024232
C2×#179867342
C2×#179867312
C2×Q8×Dic1422
C2×#179867062
C2×#179867052
C2×#179866702
C2×#179866582
C2×#179866532
C2×#179866472
C2×#179866202
C2×#179866152
C2×#179865492
C2×#179865442
C2×#179865352
C2×#179864792
C22×C4×Dic1422
C2×#529×C712
C2×#352271