Finite Group Databasebeta

← C2×#22602244 #32905820

Subgroups — C2×#22602244 #32905820

Order 18176.

7758 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602244C2132yesmaximal, direct product factor
2C2×#17986722C211yesmaximal, characteristic, complemented
3C2×#17986712C212yesmaximal, complemented
4C2×#17986707C212yesmaximal, complemented
5C2×#17986700C214yesmaximal, complemented
6C2×#17986661C212yesmaximal, complemented
7C2×#17986657C212yesmaximal, complemented
8C2×#17986653C211yesmaximal, characteristic, complemented
9C2×#17986652C211yesmaximal, characteristic, complemented
10C2×#17986615C214yesmaximal, complemented
11C2×#17986579C212yesmaximal, complemented
12C2×#17986553C212yesmaximal, complemented
13C2×#17986548C212yesmaximal, complemented
14C2×#17986546C211yesmaximal, characteristic, complemented
15C2×C4⋊Q8×D71C211yesmaximal, characteristic, complemented
16C2×#17986479C212yesmaximal, complemented
17C2×C4×#11765866C211yesmaximal, characteristic, complemented
18C2×#556×C71C211yesmaximal, characteristic, complemented
19C22×#11765866C2211yescharacteristic
20C22×#11765866C2212yes—
21C22×#11765865C2212yes—
22C22×#11765864C2212yes—
23C22×Q8×D71C2212yes—
24#17986722C22116yescomplemented
25#17986712C22132yescomplemented
26#17986707C22132yescomplemented
27#17986700C22164yescomplemented
28#17986661C22132yescomplemented
29#17986657C22132yescomplemented
30#17986653C22116yescomplemented
31#17986652C22116yescomplemented
32#17986615C22164yescomplemented
33#17986579C22132yescomplemented
34#17986553C22132yescomplemented
35#17986548C22132yescomplemented
36#17986546C22116yescomplemented
37C2×#14556128C2211yescharacteristic
38C2×#14556127C2212yes—
39C2×#14556127C2212yes—
40C2×#14556127C2211yescharacteristic
41C2×#14556126C2212yes—
42C4⋊Q8×D71C22116yescomplemented
43C2×#14556124C2211yescharacteristic
44C2×#14556123C2214yes—
45C2×#14556118C2214yes—
46C2×#14556116C2212yes—
47C2×#14556116C2214yes—
48C2×#14556114C2214yes—
49C2×#14556114C2212yes—
50C2×#14556113C2214yes—
51C2×#14556112C2214yes—
52C2×#14556108C2212yes—
53C2×#14556108C2214yes—
54C2×#14556106C2214yes—
55C2×#14556105C2214yes—
56C2×#14556104C2212yes—
57C2×#14556104C2212yes—
58C2×#14556103C2212yes—
59C2×#14556103C2211yescharacteristic
60C2×#14556103C2214yes—
61C2×#14556102C2212yes—
62C2×#14556101C2214yes—
63C2×#14556101C2212yes—
64C2×#14556101C2214yes—
65C2×#14556101C2214yes—
66C2×#14556099C2211yescharacteristic
67#17986479C22132yescomplemented
68C4×#11765866C22116yescomplemented
69C2×Q8×Dic71C2211yescharacteristic
70C2×C4×Dic142C2214yes—
71C2×C4×Dic142C2212yes—
72C2×C4×D284C2211yescharacteristic
73C2×C4×D284C2212yes—
74C2×C4×D284C2214yes—
75C2×C4×D284C2211yescharacteristic
76C2×#14556090C2212yes—
77C2×#14556090C2211yescharacteristic
78C2×C4×C22⋊D71C2212yes—
79C2×(C22⋊D71)⋊C4C2214yes—
80C2×(C22⋊D71)⋊C4C2214yes—
81C2×(C22⋊D71)⋊C4C2214yes—
82C2×#14556086C2211yescharacteristic
83C2×#14556086C2212yes—
84C2×#14556086C2212yes—
85C2×#14556085C2214yes—
86C22×C4⋊Dic71C2212yes—
87C2×C4⋊C4×D71C2212yes—
88C2×C4⋊C4×D71C2212yes—
89C2×C4⋊C4×D71C2212yes—
90C2×C42×D71C2211yescharacteristic
91C2×C42×D71C2212yes—
92#556×C71C22116yescomplemented
93C2×C4⋊Q8×C71C2211yescharacteristic
94C2×#126×C71C2214yes—
95C2×#124×C71C2212yes—
96C2×C22⋊Q8×C71C2212yes—
97C2×C4×Q8×C71C2211yescharacteristic
98C2×C4×Q8×C71C2212yes—
99C2×C4×D4×C71C2211yescharacteristic
100C2×#117×C71C2212yes—
101C2×#11765866—28no—
102C2×#11765866—48no—
103C2×#11765866C2318yes—
104C2×#11765866C23116yes—
105C2×#11765865—216no—
106C2×#11765865C23116yes—
107C2×#11765864—48no—
108C2×#11765864C23116yes—
109C22×Dic142C2312yes—
110C22×Dic142C2312yes—
111C22×Dic142C2314yes—
112C2×Q8×D71—48no—
113C2×Q8×D71C23116yes—
114C22×D284C2312yes—
115C22×D284C2311yescharacteristic
116C22×D284C2312yes—
117C22×D284C2311yescharacteristic
118C22×D284C2314yes—
119C22×C22⋊D71C2312yes—
120C22×C22⋊D71C2312yes—
121C22×C22⋊D71C2312yes—
122C22×C22⋊D71C2314yes—
123C23×Dic71C2314yes—
124C22×C4×D71C2311yescharacteristic
125C22×C4×D71C2312yes—
126C22×C4×D71C2312yes—
127C22×C4×D71C2312yes—
128C22×C4×D71C2311yescharacteristic
129C22×C4×D71C2312yes—
130C22×C4×D71C2314yes—
131C22×C4×D71C2314yes—
132C22×C4×D71C2311yescharacteristic
133#14556128C2318yes—
134#14556127C23116yes—
135#14556127C23116yes—
136#14556127C2318yes—
137#14556126C23116yes—
138#14556124C2318yes—
139#14556123C23132yes—
140#14556118C23132yes—
141#14556116C23132yes—
142#14556116C23116yes—
143#14556114C23116yes—
144#14556114C23132yes—
145#14556113C23132yes—
146#14556112C23132yes—
147#14556108C23132yes—
148#14556108C23116yes—
149#14556106C23132yes—
150#14556105C23132yes—
151#14556104C23116yes—
152#14556104C23116yes—
153#14556103C23116yes—
154#14556103C23132yes—
155#14556103C2318yes—
156#14556102C23116yes—
157#14556101C23132yes—
158#14556101C23132yes—
159#14556101C23116yes—
160#14556101C23132yes—
161#14556099C2318yes—
162Q8×Dic71C2318yes—
163C4×Dic142C23132yes—
164C4×Dic142C23116yes—
165C4×D284C2318yes—
166C4×D284C2318yes—
167C4×D284C23116yes—
168C4×D284C23132yes—
169#14556090C23116yes—
170#14556090C2318yes—
171C4×C22⋊D71C23116yes—
172(C22⋊D71)⋊C4C23132yes—
173(C22⋊D71)⋊C4C23132yes—
174(C22⋊D71)⋊C4C23132yes—
175#14556086C23116yes—
176#14556086C23116yes—
177#14556086C2318yes—
178#14556085C23132yes—
179C2×C4⋊Dic71C23116yes—
180C2×C4⋊Dic71C2311yescharacteristic
181C2×C4⋊Dic71C2312yes—
182C2×C4⋊Dic71C2312yes—
183C2×C4⋊Dic71C2314yes—
184C2×C4⋊Dic71C2312yes—
185C2×C4⋊Dic71C2311yescharacteristic
186C2×Dic71⋊C4C2314yes—
187C2×Dic71⋊C4C2314yes—
188C2×Dic71⋊C4C2314yes—
189C2×Dic71⋊C4C2312yes—
190C2×Dic71⋊C4C2314yes—
191C4⋊C4×D71C23116yes—
192C4⋊C4×D71C23116yes—
193C4⋊C4×D71C23116yes—
194C2×C22⋊Dic71C2312yes—
195C2×(C2×D71)⋊C4C2314yes—
196C2×(C2×D71)⋊C4C2314yes—
197C2×(C2×D71)⋊C4C2312yes—
198C2×(C2×D71)⋊C4C2314yes—
199C2×(C2×D71)⋊C4C2312yes—
200C2×(C2×D71)⋊C4C2312yes—
201C2×(C2×D71)⋊C4C2314yes—
202C2×(C2×D71)⋊C4C2312yes—
203C2×(C2×D71)⋊C4C2312yes—
204C2×C4×Dic71C2311yescharacteristic
205C2×C4×Dic71C2312yes—
206C2×C4×Dic71C2311yescharacteristic
207C2×C4×Dic71C2312yes—
208C2×C4×Dic71C2311yescharacteristic
209C2×C4×Dic71C2314yes—
210C42×D71C2318yes—
211C42×D71C23116yes—
212C22×Q8×C71C2312yes—
213C22×Q8×C71C2311yescharacteristic
214C22×D4×C71C2311yescharacteristic
215C23×C4×C71C2312yes—
216C4⋊Q8×C71C2318yes—
217#126×C71C23132yes—
218#124×C71C23116yes—
219C22⋊Q8×C71C23116yes—
220C4×Q8×C71C23116yes—
221C4×Q8×C71C2318yes—
222C4×D4×C71C2318yes—
223#117×C71C23116yes—
224C2×C4⋊C4×C71C2311yescharacteristic
225C2×C4⋊C4×C71C2312yes—
226C2×C4⋊C4×C71C2311yescharacteristic
227C2×C4⋊C4×C71C2314yes—
228C2×C4⋊C4×C71C2312yes—
229C2×C4⋊C4×C71C2312yes—
230C2×C22⋊C4×C71C2314yes—
231C2×C22⋊C4×C71C2312yes—
232C2×C22⋊C4×C71C2314yes—
233C2×C42×C71C2314yes—
234C2×C42×C71C2311yescharacteristic
235C2×C42×C71C2312yes—
236C23×D71C2412yes—
237C23×D71C2412yes—
238C23×D71C2411yescharacteristic
239#11765866—232no—
240#11765866—432no—
241#11765865—264no—
242#11765864—432no—
243C2×Dic142—28no—
244C2×Dic142—28no—
245C2×Dic142—48no—
246C2×Dic142C2418yes—
247C2×Dic142C2418yes—
248C2×Dic142C24116yes—
249Q8×D71—432no—
250C2×D284—28no—
251C2×D284—28no—
252C2×D284—24no—
253C2×D284—24no—
254C2×D284—48no—
255C2×D284C2418yes—
256C2×D284C2414yes—
257C2×D284C2418yes—
258C2×D284C2414yes—
259C2×D284C24116yes—
260C2×C22⋊D71—28no—
261C2×C22⋊D71—28no—
262C2×C22⋊D71—28no—
263C2×C22⋊D71—48no—
264C2×C22⋊D71C2418yes—
265C2×C22⋊D71C2418yes—
266C2×C22⋊D71C2418yes—
267C2×C22⋊D71C24116yes—
268C22×Dic71—48no—
269C22×Dic71C2412yes—
270C22×Dic71C2414yes—
271C22×Dic71C2412yes—
272C22×Dic71C2411yescharacteristic
273C22×Dic71C24116yes—
274C22×Dic71C2411yescharacteristic
275C22×Dic71C2411yescharacteristic
276C2×C4×D71—28no—
277C2×C4×D71—24no—
278C2×C4×D71—28no—
279C2×C4×D71—28no—
280C2×C4×D71—24no—
281C2×C4×D71—28no—
282C2×C4×D71—48no—
283C2×C4×D71—48no—
284C2×C4×D71#4118yescomplemented
285C2×C4×D71C2414yes—
286C2×C4×D71C2418yes—
287C2×C4×D71C2418yes—
288C2×C4×D71C2418yes—
289C2×C4×D71C2414yes—
290C2×C4×D71C2418yes—
291C2×C4×D71C24116yes—
292C2×C4×D71C24116yes—
293C2×C4×D71C2414yes—
294C4⋊Dic71C2414yes—
295C4⋊Dic71C2418yes—
296C4⋊Dic71C2418yes—
297C4⋊Dic71C24116yes—
298C4⋊Dic71C2418yes—
299C4⋊Dic71C2414yes—
300Dic71⋊C4C24116yes—
301Dic71⋊C4C24116yes—
302Dic71⋊C4C24116yes—
303Dic71⋊C4C2418yes—
304Dic71⋊C4C24116yes—
305C22⋊Dic71C2418yes—
306(C2×D71)⋊C4C24116yes—
307(C2×D71)⋊C4C24116yes—
308(C2×D71)⋊C4C2418yes—
309(C2×D71)⋊C4C24116yes—
310(C2×D71)⋊C4C2418yes—
311(C2×D71)⋊C4C2418yes—
312(C2×D71)⋊C4C24116yes—
313(C2×D71)⋊C4C2418yes—
314(C2×D71)⋊C4C2418yes—
315C4×Dic71C2414yes—
316C4×Dic71C2418yes—
317C4×Dic71C2414yes—
318C4×Dic71C2418yes—
319C4×Dic71C2414yes—
320C4×Dic71C24116yes—
321C24×C71C2412yes—
322C2×Q8×C71—24no—
323C2×Q8×C71—28no—
324C2×Q8×C71C2418yes—
325C2×Q8×C71C2414yes—
326C2×D4×C71—24no—
327C2×D4×C71C2414yes—
328C22×C4×C71—28no—
329C22×C4×C71C2414yes—
330C22×C4×C71C2412yes—
331C22×C4×C71C2412yes—
332C22×C4×C71C2411yescharacteristic
333C22×C4×C71C2412yes—
334C22×C4×C71C2418yes—
335C22×C4×C71C2411yescharacteristic
336C22×C4×C71C2411yescharacteristic
337C4⋊C4×C71C2414yes—
338C4⋊C4×C71C2418yes—
339C4⋊C4×C71C2414yes—
340C4⋊C4×C71C24116yes—
341C4⋊C4×C71C2418yes—
342C4⋊C4×C71C2418yes—
343C22⋊C4×C71C24116yes—
344C22⋊C4×C71C2418yes—
345C22⋊C4×C71C24116yes—
346C42×C71C24116yes—
347C42×C71C2414yes—
348C42×C71C2418yes—
349C23×C71—24no—
350C23×C71—24no—
351C23×C71—24no—
352C23×C71C2514yes—
353C23×C71C2511yescharacteristic
354C22×D71—22no—
355C22×D71—22no—
356C22×D71—24no—
357C22×D71—24no—
358C22×D71—24no—
359C22×D71—24no—
360C22×D71—24no—
361C22×D71—24no—
362C22×D71C2×#4114yes—
363C22×D71C2514yes—
364C22×D71C2514yes—
365C22×D71C2512yes—
366Q8×C71—28no—
367Q8×C71—216no—
368D4×C71—28no—
369C2×C4×C71—24no—
370C2×C4×C71—24no—
371C2×C4×C71—28no—
372C2×C4×C71—24no—
373C2×C4×C71—22no—
374C2×C4×C71—216no—
375C2×C4×C71C2×#4114yes—
376C2×C4×C71H(5,𝔽2)14yes—
377C2×C4×C71C2514yes—
378C2×C4×C71C2514yes—
379C2×C4×C71C2512yes—
380C2×C4×C71C2514yes—
381C2×C4×C71C2518yes—
382C2×C4×C71C2512yes—
383C2×C4×C71C2512yes—
384C22⋊D71—216no—
385C22⋊D71—216no—
386C22⋊D71—216no—
387C22⋊D71—416no—
388C2×Dic71—24no—
389C2×Dic71—24no—
390C2×Dic71—22no—
391C2×Dic71—28no—
392C2×Dic71—416no—
393C2×Dic71C2×#4114yes—
394C2×Dic712−1+414yes—
395C2×Dic71C2512yes—
396C2×Dic71C2514yes—
397C2×Dic71C2514yes—
398C2×Dic71C2518yes—
399C2×Dic71C2512yes—
400C2×Dic71C2512yes—
401D284—216no—
402D284—216no—
403D284—28no—
404D284—28no—
405D284—416no—
406C4×D71—216no—
407C4×D71—28no—
408C4×D71—216no—
409C4×D71—216no—
410C4×D71—28no—
411C4×D71—216no—
412C4×D71—416no—
413C4×D71—416no—
414C4×D71C2×#41116yescomplemented
415Dic142—216no—
416Dic142—216no—
417Dic142—416no—
418C22×C71—24no—
419C22×C71—24no—
420C22×C71—24no—
421C22×C71—48no—
422C22×C71C22×#4112yes—
423C22×C71C2×H(5,𝔽2)12yes—
424C22×C71C2×2−1+412yes—
425C22×C71C2611yescharacteristic
426C2×D71—22no—
427C2×D71—22no—
428C2×D71—28no—
429C2×D71—24no—
430C2×D71—24no—
431C2×D71—24no—
432C2×D71—24no—
433C2×D71—24no—
434C2×D71—24no—
435C2×D71—48no—
436C2×D71—48no—
437C2×D71C22×#4114yes—
438C4×C71—24no—
439C4×C71—24no—
440C4×C71—28no—
441C4×C71—24no—
442C4×C71—22no—
443C4×C71C22×#4114yes—
444C4×C71C2×H(5,𝔽2)14yes—
445Dic71—24no—
446Dic71—28no—
447Dic71—22no—
448Dic71—24no—
449Dic71C22×#4114yes—
450Dic71C2×2−1+414yes—
451C2×#3511—711nomaximal, Sylow
452C2×C71—44no—
453C2×C71#351114yescomplemented
454C2×C71C23×#4111yescharacteristic
455C2×C71C22×H(5,𝔽2)11yescharacteristic
456C2×C71C22×2−1+411yescharacteristic
457D71—24no—
458D71—44no—
459D71—44no—
460#3511—7132no—
461C2×#556—711no—
462C2×#556D7111yescharacteristic, complemented
463C2×#555—712no—
464C2×#554—712no—
465C2×#553—714no—
466C2×#548—712no—
467C2×#548—712no—
468C2×#547—711no—
469C2×#547—711no—
470C2×#542—714no—
471C2×#537—712no—
472C2×#533—712no—
473C2×#532—712no—
474C2×#532—711no—
475C22×C4⋊Q8—711no—
476C2×#520—712no—
477C2×C4×#41—711no—
478C71C2×#351111yescharacteristic, complemented, Sylow
479C22×#41—712no—
480C22×#41—711no—
481C22×#41—712no—
482C22×#41—712no—
483C23×Q8—712no—
484#556—7116no—
485#556C2×D71116yescomplemented
486#555—7132no—
487#554—7132no—
488#553—7164no—
489#548—7132no—
490#548—7132no—
491#547—7116no—
492#547—7116no—
493#542—7164no—
494#537—7132no—
495#533—7132no—
496#532—7132no—
497#532—7116no—
498C2×C4⋊Q8—712no—
499C2×C4⋊Q8—7116no—
500C2×C4⋊Q8—712no—
501C2×C4⋊Q8—712no—
502C2×C4⋊Q8—711no—
503C2×C4⋊Q8—711no—
504C2×C4⋊Q8C2×D7111yescharacteristic
505C2×#127—711no—
506C2×#126—714no—
507C2×#126C2×D7114yes—
508C2×#125—714no—
509C2×#124—712no—
510C2×#124—714no—
511C2×#124—712no—
512C2×#124—714no—
513C2×#124C2×D7112yes—
514C2×#123—714no—
515C2×#123—714no—
516C2×C22⋊Q8—712no—
517C2×C22⋊Q8—712no—
518C2×C22⋊Q8—714no—
519C2×C22⋊Q8—712no—
520C2×C22⋊Q8—714no—
521C2×C22⋊Q8—714no—
522C2×C22⋊Q8C2×D7112yes—
523C2×#121—711no—
524C2×#121—712no—
525C2×#121—711no—
526C2×#121—712no—
527C2×#121—714no—
528C2×#121—714no—
529C2×#121—712no—
530C2×#121—714no—
531C2×#121—714no—
532#520—7132no—
533C4×#41—7116no—
534C2×C4×Q8—711no—
535C2×C4×Q8—714no—
536C2×C4×Q8—712no—
537C2×C4×Q8C2×D7111yescharacteristic
538C2×C4×Q8C2×D7112yes—
539C2×C4×D4—712no—
540C2×C4×D4—712no—
541C2×C4×D4—711no—
542C2×C4×D4—714no—
543C2×C4×D4—714no—
544C2×C4×D4—714no—
545C2×C4×D4—711no—
546C2×C4×D4—712no—
547C2×C4×D4—714no—
548C2×C4×D4—711no—
549C2×C4×D4C2×D7111yescharacteristic
550C2×#117—711no—
551C2×#117—712no—
552C2×#117—712no—
553C2×#117—714no—
554C2×#117C2×D7112yes—
555C22×C4⋊C4—712no—
556C22×C4⋊C4—712no—
557C22×C4⋊C4—712no—
558C22×C4⋊C4—712no—
559C22×C42—711no—
560C22×C42—712no—
561C2×#41—2848no—
562C2×#41—2848no—
563C2×#41—7116no—
564C2×#41—718no—
565C2×#41—7116no—
566C2×#41—7116no—
567C2×#41—14216no—
568C2×#41—1428no—
569C22×Q8—2848no—
570C22×Q8—7116no—
571C22×Q8—714no—
572C22×Q8—712no—
573C22×Q8—712no—
574C22×Q8C22×D7111yescharacteristic
575C22×Q8C22×D7112yes—
576C22×D4—714no—
577C22×D4—712no—
578C22×D4—712no—
579C22×D4—712no—
580C22×D4—714no—
581C22×D4—712no—
582C22×D4—712no—
583C22×D4—711no—
584C22×D4—711no—
585C22×D4C22×D7111yescharacteristic
586C23×C4—714no—
587C23×C4—714no—
588C23×C4—714no—
589C23×C4—711no—
590C23×C4—711no—
591C23×C4—712no—
592C23×C4—712no—
593C23×C4—712no—
594C23×C4—711no—
595C23×C4—712no—
596C23×C4C22×D7112yes—
597C4⋊Q8—7116no—
598C4⋊Q8—7116no—
599C4⋊Q8—7116no—
600C4⋊Q8—718no—
601C4⋊Q8—718no—
602C4⋊Q8C22×D7118yes—
603#127—718no—
604#126—7132no—
605#126C22×D71132yes—
606#125—7132no—
607#124—7116no—
608#124—7132no—
609#124—7116no—
610#124—7132no—
611#124C22×D71116yes—
612#123—7132no—
613#123—7132no—
614C22⋊Q8—7116no—
615C22⋊Q8—7116no—
616C22⋊Q8—7132no—
617C22⋊Q8—7116no—
618C22⋊Q8—7132no—
619C22⋊Q8—7132no—
620C22⋊Q8C22×D71116yes—
621#121—718no—
622#121—7116no—
623#121—718no—
624#121—7116no—
625#121—7132no—
626#121—7132no—
627#121—7116no—
628#121—7132no—
629#121—7132no—
630C4×Q8—718no—
631C4×Q8—7132no—
632C4×Q8—7116no—
633C4×Q8C22×D7118yes—
634C4×Q8C22×D71116yes—
635C4×D4—7116no—
636C4×D4—7116no—
637C4×D4—718no—
638C4×D4—7132no—
639C4×D4—7132no—
640C4×D4—7132no—
641C4×D4—718no—
642C4×D4—7116no—
643C4×D4—7132no—
644C4×D4—718no—
645C4×D4C22×D7118yes—
646#117—718no—
647#117—7116no—
648#117—7116no—
649#117—7132no—
650#117C22×D71116yes—
651C2×C4⋊C4—711no—
652C2×C4⋊C4—712no—
653C2×C4⋊C4—714no—
654C2×C4⋊C4—714no—
655C2×C4⋊C4—714no—
656C2×C4⋊C4—714no—
657C2×C4⋊C4—7116no—
658C2×C4⋊C4—712no—
659C2×C4⋊C4—712no—
660C2×C4⋊C4—712no—
661C2×C4⋊C4—711no—
662C2×C4⋊C4—714no—
663C2×C4⋊C4—7116no—
664C2×C4⋊C4—7116no—
665C2×C4⋊C4—7116no—
666C2×C4⋊C4C22×D7112yes—
667C2×C4⋊C4C22×D7112yes—
668C2×C4⋊C4C22×D7111yescharacteristic
669C2×C4⋊C4C22×D7112yes—
670C2×C4⋊C4C22×D7111yescharacteristic
671C2×C4⋊C4C22×D7114yes—
672C2×C22⋊C4—712no—
673C2×C22⋊C4—712no—
674C2×C22⋊C4—714no—
675C2×C22⋊C4—712no—
676C2×C22⋊C4—712no—
677C2×C22⋊C4—714no—
678C2×C22⋊C4—714no—
679C2×C22⋊C4—714no—
680C2×C22⋊C4—712no—
681C2×C22⋊C4—712no—
682C2×C22⋊C4C22×D7114yes—
683C2×C22⋊C4C22×D7114yes—
684C2×C22⋊C4C22×D7112yes—
685C2×C42—712no—
686C2×C42—714no—
687C2×C42—711no—
688C2×C42—712no—
689C2×C42—711no—
690C2×C42—711no—
691C2×C42—718no—
692C2×C42—7116no—
693C2×C42C22×D7114yes—
694C2×C42C22×D7111yescharacteristic
695C2×C42C22×D7112yes—
696C24—711no—
697C24—712no—
698C24—712no—
699C24C23×D7112yes—
700#41—28432no—
701#41—28432no—
702#41—14264no—
703#41—14232no—
704C2×Q8—24no—
705C2×Q8—28no—
706C2×Q8—2848no—
707C2×Q8—28432no—
708C2×Q8—7116no—
709C2×Q8—718no—
710C2×Q8—718no—
711C2×Q8—1428no—
712C2×Q8—1428no—
713C2×Q8C23×D7114yes—
714C2×Q8C23×D7118yes—
715C2×D4—24no—
716C2×D4—2848no—
717C2×D4—2848no—
718C2×D4—7116no—
719C2×D4—718no—
720C2×D4—718no—
721C2×D4—718no—
722C2×D4—7116no—
723C2×D4—718no—
724C2×D4—718no—
725C2×D4—714no—
726C2×D4—714no—
727C2×D4—1428no—
728C2×D4—1428no—
729C2×D4—1428no—
730C2×D4—1428no—
731C2×D4—1428no—
732C2×D4—1424no—
733C2×D4—1424no—
734C2×D4C23×D7114yes—
735C22×C4—28no—
736C22×C4—2848no—
737C22×C4—2848no—
738C22×C4—2848no—
739C22×C4—7116no—
740C22×C4—7116no—
741C22×C4—7116no—
742C22×C4—711no—
743C22×C4—711no—
744C22×C4—718no—
745C22×C4—714no—
746C22×C4—711no—
747C22×C4—712no—
748C22×C4—712no—
749C22×C4—714no—
750C22×C4—714no—
751C22×C4—718no—
752C22×C4—718no—
753C22×C4—714no—
754C22×C4—718no—
755C22×C4—718no—
756C22×C4—1428no—
757C22×C4—1424no—
758C22×C4—1428no—
759C22×C4—1428no—
760C22×C4—1424no—
761C22×C4—1428no—
762C22×C4C23×D7118yes—
763C22×C4C23×D7112yes—
764C22×C4C23×D7111yescharacteristic
765C22×C4C23×D7112yes—
766C22×C4C23×D7112yes—
767C22×C4C23×D7114yes—
768C22×C4C23×D7111yescharacteristic
769C22×C4C23×D7111yescharacteristic
770C4⋊C4—7116no—
771C4⋊C4—7116no—
772C4⋊C4—7116no—
773C4⋊C4—718no—
774C4⋊C4—7116no—
775C4⋊C4—714no—
776C4⋊C4—718no—
777C4⋊C4—7116no—
778C4⋊C4—718no—
779C4⋊C4—718no—
780C4⋊C4—714no—
781C4⋊C4C23×D7118yes—
782C4⋊C4C23×D7118yes—
783C4⋊C4C23×D7114yes—
784C4⋊C4C23×D7118yes—
785C4⋊C4C23×D7114yes—
786C4⋊C4C23×D71116yes—
787C22⋊C4—718no—
788C22⋊C4—718no—
789C22⋊C4—7116no—
790C22⋊C4—718no—
791C22⋊C4—718no—
792C22⋊C4—7116no—
793C22⋊C4—7116no—
794C22⋊C4—7116no—
795C22⋊C4—718no—
796C22⋊C4—718no—
797C22⋊C4C23×D71116yes—
798C22⋊C4C23×D71116yes—
799C22⋊C4C23×D7118yes—
800C42—714no—
801C42—718no—
802C42—714no—
803C42—718no—
804C42—714no—
805C42—7116no—
806C42C23×D7114yes—
807C42C23×D7118yes—
808C42C23×D71116yes—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—714no—
813C23—712no—
814C23—714no—
815C23—714no—
816C23—1424no—
817C23—1424no—
818C23—1424no—
819C23—1424no—
820C23—1424no—
821C23—1424no—
822C23—1422no—
823C23—1422no—
824C23C24×D7114yes—
825C23C24×D7111yescharacteristic
826Q8—28no—
827Q8—216no—
828Q8—28416no—
829Q8—14216no—
830Q8—14216no—
831D4—28no—
832D4—28416no—
833D4—28416no—
834D4—14216no—
835D4—14216no—
836D4—14216no—
837D4—14216no—
838D4—14216no—
839D4—1428no—
840D4—1428no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—28no—
844C2×C4—24no—
845C2×C4—22no—
846C2×C4—216no—
847C2×C4—28416no—
848C2×C4—28416no—
849C2×C4—28416no—
850C2×C4—714no—
851C2×C4—714no—
852C2×C4—712no—
853C2×C4—712no—
854C2×C4—7116no—
855C2×C4—712no—
856C2×C4—714no—
857C2×C4—714no—
858C2×C4—718no—
859C2×C4—14216no—
860C2×C4—14216no—
861C2×C4—1428no—
862C2×C4—1424no—
863C2×C4—1424no—
864C2×C4—1428no—
865C2×C4—1422no—
866C2×C4—14216no—
867C2×C4—1428no—
868C2×C4—14216no—
869C2×C4#41×D7114yes—
870C2×C4#1455617414yes—
871C2×C4C24×D7114yes—
872C2×C4C24×D7112yes—
873C2×C4C24×D7114yes—
874C2×C4C24×D7114yes—
875C2×C4C24×D7118yes—
876C2×C4C24×D7112yes—
877C2×C4C24×D7112yes—
878C22—24no—
879C22—24no—
880C22—24no—
881C22—48no—
882C22—2848no—
883C22—2848no—
884C22—714no—
885C22—1424no—
886C22—1424no—
887C22—1424no—
888C22—1424no—
889C22—1424no—
890C22—1424no—
891C22—1428no—
892C22—1422no—
893C22—1422no—
894C22C2×#41×D7112yes—
895C22C2×#1455617412yes—
896C222−1+4×D7112yes—
897C22C25×D7111yescharacteristic
898C4—24no—
899C4—24no—
900C4—28no—
901C4—24no—
902C4—22no—
903C4—714no—
904C4—714no—
905C4—1424no—
906C4—1424no—
907C4—1428no—
908C4—1422no—
909C4C2×#41×D7114yes—
910C4C2×#1455617414yes—
911C2—44no—
912C2—2844no—
913C2—2844no—
914C2—1424no—
915C2#2260224414yesdirect product factor
916C2C22×#41×D7111yescharacteristic
917C2C22×#1455617411yescharacteristic
918C2C2×2−1+4×D7111yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#556×C71C2
socleC23×C71C25
hypercenterC2×#556D71
hypocenterC71C2×#3511
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #22602244C2direct (N × H)
2. C2×#17986722C2semidirect
3. C2×#17986712C2semidirect
4. C2×#17986707C2semidirect
5. C2×#17986700C2semidirect
6. C2×#17986661C2semidirect
7. C2×#17986657C2semidirect
8. C2×#17986653C2semidirect
9. C2×#17986652C2semidirect
10. C2×#17986615C2semidirect
11. C2×#17986579C2semidirect
12. C2×#17986553C2semidirect
13. C2×#17986548C2semidirect
14. C2×#17986546C2semidirect
15. C2×C4⋊Q8×D71C2semidirect
16. C2×#17986479C2semidirect
17. C2×C4×#11765866C2semidirect
18. C2×#556×C71C2semidirect
24. #17986722C22semidirect
25. #17986712C22semidirect
26. #17986707C22semidirect
27. #17986700C22semidirect
28. #17986661C22semidirect
29. #17986657C22semidirect
30. #17986653C22semidirect
31. #17986652C22semidirect
32. #17986615C22semidirect
33. #17986579C22semidirect
34. #17986553C22semidirect
35. #17986548C22semidirect
36. #17986546C22semidirect
42. C4⋊Q8×D71C22semidirect
67. #17986479C22semidirect
68. C4×#11765866C22semidirect
92. #556×C71C22semidirect
284. C2×C4×D71#41semidirect
414. C4×D71C2×#41semidirect
453. C2×C71#3511semidirect
462. C2×#556D71semidirect
478. C71C2×#3511semidirect
485. #556C2×D71semidirect
915. C2#22602244direct (N × H)

Maximal subgroups

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

subgroupindex
#226022442
C2×#179867222
C2×#179867122
C2×#179867072
C2×#179867002
C2×#179866612
C2×#179866572
C2×#179866532
C2×#179866522
C2×#179866152
C2×#179865792
C2×#179865532
C2×#179865482
C2×#179865462
C2×C4⋊Q8×D712
C2×#179864792
C2×C4×#117658662
C2×#556×C712
C2×#351171