Finite Group Databasebeta

← C2×#22602770 #32905064

Subgroups — C2×#22602770 #32905064

Order 18176.

7086 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602770C2132yesmaximal, direct product factor
2C2×#17986751C214yesmaximal, complemented
3C2×#17986728C211yesmaximal, characteristic, complemented
4C2×#17986707C212yesmaximal, complemented
5C2×#17986693C212yesmaximal, complemented
6C2×Q8×D284C212yesmaximal, complemented
7C2×#17986664C211yesmaximal, characteristic, complemented
8C2×#17986657C212yesmaximal, complemented
9C2×#17986653C211yesmaximal, characteristic, complemented
10C2×#17986627C212yesmaximal, complemented
11C2×#17986622C212yesmaximal, complemented
12C2×#17986607C212yesmaximal, complemented
13C2×#17986590C214yesmaximal, complemented
14C2×#17986569C212yesmaximal, complemented
15C2×C4⋊Q8×D71C211yesmaximal, characteristic, complemented
16C2×#17986536C211yesmaximal, characteristic, complemented
17C2×#17986531C211yesmaximal, characteristic, complemented
18C2×#556×C71C211yesmaximal, characteristic, complemented
19C22×#11765864C2212yes—
20C22×Q8×D71C2212yes—
21C22×Q8×D71C2212yes—
22#17986751C22164yescomplemented
23#17986728C22116yescomplemented
24#17986707C22132yescomplemented
25#17986693C22132yescomplemented
26Q8×D284C22132yescomplemented
27#17986664C22116yescomplemented
28#17986657C22132yescomplemented
29#17986653C22116yescomplemented
30#17986627C22132yescomplemented
31#17986622C22132yescomplemented
32#17986607C22132yescomplemented
33#17986590C22164yescomplemented
34#17986569C22132yescomplemented
35C2×#14556128C2214yes—
36C2×#14556128C2211yescharacteristic
37C2×#14556128C2212yes—
38C2×#14556127C2212yes—
39C2×#14556127C2212yes—
40C2×#14556127C2212yes—
41C2×#14556126C2212yes—
42C4⋊Q8×D71C22116yescomplemented
43#17986536C22116yescomplemented
44#17986531C22116yescomplemented
45C2×#14556123C2212yes—
46C2×#14556123C2214yes—
47C2×#14556122C2214yes—
48C2×#14556121C2212yes—
49C2×#14556120C2214yes—
50C2×#14556119C2211yescharacteristic
51C2×#14556119C2212yes—
52C2×#14556119C2211yescharacteristic
53C2×#14556119C2214yes—
54C2×#14556118C2214yes—
55C2×#14556117C2211yescharacteristic
56C2×#14556115C2211yescharacteristic
57C2×#14556114C2214yes—
58C2×#14556113C2212yes—
59C2×#14556112C2214yes—
60C2×#14556110C2214yes—
61C2×#14556110C2212yes—
62C2×#14556110C2214yes—
63C2×#14556108C2212yes—
64C2×#14556108C2211yescharacteristic
65C2×#14556108C2214yes—
66C2×#14556108C2214yes—
67C2×#14556106C2214yes—
68C2×#14556105C2214yes—
69C2×#14556105C2214yes—
70C2×#14556105C2214yes—
71C2×#14556104C2212yes—
72C2×#14556104C2211yescharacteristic
73C2×#14556103C2211yescharacteristic
74C2×#14556102C2212yes—
75C2×#14556101C2214yes—
76C2×#14556099C2211yescharacteristic
77C2×Q8×Dic71C2212yes—
78C2×C4×Dic142C2212yes—
79C2×C4×Dic142C2211yescharacteristic
80C2×C4×D284C2211yescharacteristic
81C2×C4×D284C2212yes—
82C2×C4×D284C2214yes—
83C2×#14556090C2212yes—
84C2×C4×C22⋊D71C2212yes—
85C2×(C22⋊D71)⋊C4C2214yes—
86C2×#14556087C2212yes—
87C2×#14556085C2212yes—
88C22×C4⋊Dic71C2212yes—
89C2×C4⋊C4×D71C2212yes—
90C2×C4⋊C4×D71C2212yes—
91C2×C42×D71C2211yescharacteristic
92#556×C71C22116yescomplemented
93C2×C4⋊Q8×C71C2211yescharacteristic
94C2×#126×C71C2214yes—
95C2×#124×C71C2212yes—
96C2×C22⋊Q8×C71C2212yes—
97C2×C4×Q8×C71C2212yes—
98C2×C4×Q8×C71C2211yescharacteristic
99C2×C4×D4×C71C2211yescharacteristic
100C2×#117×C71C2212yes—
101C2×#11765864—48no—
102C2×#11765864C23116yes—
103C22×Dic142C2311yescharacteristic
104C22×Dic142C2312yes—
105C22×Dic142C2314yes—
106C22×Dic142C2314yes—
107C2×Q8×D71—48no—
108C2×Q8×D71—48no—
109C2×Q8×D71C23116yes—
110C2×Q8×D71C23116yes—
111C22×D284C2311yescharacteristic
112C22×D284C2312yes—
113C22×C22⋊D71C2312yes—
114C22×C22⋊D71C2314yes—
115C23×Dic71C2314yes—
116C22×C4×D71C2311yescharacteristic
117C22×C4×D71C2312yes—
118C22×C4×D71C2311yescharacteristic
119C22×C4×D71C2311yescharacteristic
120C22×C4×D71C2314yes—
121C22×C4×D71C2314yes—
122#14556128C23116yes—
123#14556128C23132yes—
124#14556128C2318yes—
125#14556127C23116yes—
126#14556127C23116yes—
127#14556127C23116yes—
128#14556126C23116yes—
129#14556123C23132yes—
130#14556123C23116yes—
131#14556122C23132yes—
132#14556121C23116yes—
133#14556120C23132yes—
134#14556119C23132yes—
135#14556119C2318yes—
136#14556119C2318yes—
137#14556119C23116yes—
138#14556118C23132yes—
139#14556117C2318yes—
140#14556115C2318yes—
141#14556114C23132yes—
142#14556113C23116yes—
143#14556112C23132yes—
144#14556110C23132yes—
145#14556110C23132yes—
146#14556110C23116yes—
147#14556108C23132yes—
148#14556108C23116yes—
149#14556108C23132yes—
150#14556108C2318yes—
151#14556106C23132yes—
152#14556105C23132yes—
153#14556105C23132yes—
154#14556105C23132yes—
155#14556104C23116yes—
156#14556104C2318yes—
157#14556103C2318yes—
158#14556102C23116yes—
159#14556101C23132yes—
160#14556099C2318yes—
161Q8×Dic71C23116yes—
162C4×Dic142C23116yes—
163C4×Dic142C2318yes—
164C4×D284C23132yes—
165C4×D284C2318yes—
166C4×D284C23116yes—
167#14556090C23116yes—
168C4×C22⋊D71C23116yes—
169(C22⋊D71)⋊C4C23132yes—
170#14556087C23116yes—
171#14556085C23116yes—
172C2×C4⋊Dic71C23116yes—
173C2×C4⋊Dic71C2312yes—
174C2×C4⋊Dic71C2312yes—
175C2×C4⋊Dic71C2311yescharacteristic
176C2×C4⋊Dic71C2314yes—
177C2×C4⋊Dic71C2312yes—
178C2×C4⋊Dic71C2312yes—
179C2×C4⋊Dic71C2312yes—
180C2×C4⋊Dic71C2314yes—
181C2×C4⋊Dic71C2311yescharacteristic
182C2×C4⋊Dic71C2314yes—
183C2×Dic71⋊C4C2314yes—
184C2×Dic71⋊C4C2314yes—
185C2×Dic71⋊C4C2312yes—
186C2×Dic71⋊C4C2312yes—
187C2×Dic71⋊C4C2314yes—
188C2×Dic71⋊C4C2312yes—
189C2×Dic71⋊C4C2314yes—
190C2×Dic71⋊C4C2312yes—
191C4⋊C4×D71C23116yes—
192C4⋊C4×D71C23116yes—
193C2×C22⋊Dic71C2312yes—
194C2×C22⋊Dic71C2312yes—
195C2×C22⋊Dic71C2312yes—
196C2×(C2×D71)⋊C4C2312yes—
197C2×(C2×D71)⋊C4C2312yes—
198C2×(C2×D71)⋊C4C2312yes—
199C2×(C2×D71)⋊C4C2312yes—
200C2×(C2×D71)⋊C4C2314yes—
201C2×(C2×D71)⋊C4C2314yes—
202C2×(C2×D71)⋊C4C2312yes—
203C2×(C2×D71)⋊C4C2312yes—
204C2×C4×Dic71C2311yescharacteristic
205C2×C4×Dic71C2311yescharacteristic
206C2×C4×Dic71C2311yescharacteristic
207C2×C4×Dic71C2312yes—
208C2×C4×Dic71C2314yes—
209C42×D71C2318yes—
210C22×Q8×C71C2312yes—
211C22×Q8×C71C2311yescharacteristic
212C22×D4×C71C2311yescharacteristic
213C23×C4×C71C2312yes—
214C4⋊Q8×C71C2318yes—
215#126×C71C23132yes—
216#124×C71C23116yes—
217C22⋊Q8×C71C23116yes—
218C4×Q8×C71C23116yes—
219C4×Q8×C71C2318yes—
220C4×D4×C71C2318yes—
221#117×C71C23116yes—
222C2×C4⋊C4×C71C2311yescharacteristic
223C2×C4⋊C4×C71C2312yes—
224C2×C4⋊C4×C71C2311yescharacteristic
225C2×C4⋊C4×C71C2314yes—
226C2×C4⋊C4×C71C2312yes—
227C2×C4⋊C4×C71C2312yes—
228C2×C22⋊C4×C71C2314yes—
229C2×C22⋊C4×C71C2312yes—
230C2×C22⋊C4×C71C2314yes—
231C2×C42×C71C2314yes—
232C2×C42×C71C2311yescharacteristic
233C2×C42×C71C2312yes—
234C23×D71C2412yes—
235C23×D71C2411yescharacteristic
236#11765864—432no—
237C2×Dic142—24no—
238C2×Dic142—28no—
239C2×Dic142—48no—
240C2×Dic142—48no—
241C2×Dic142C2414yes—
242C2×Dic142C2418yes—
243C2×Dic142C24116yes—
244C2×Dic142C24116yes—
245Q8×D71—432no—
246Q8×D71—432no—
247C2×D284—28no—
248C2×D284—24no—
249C2×D284C2414yes—
250C2×D284C2418yes—
251C2×C22⋊D71—28no—
252C2×C22⋊D71—48no—
253C2×C22⋊D71C2418yes—
254C2×C22⋊D71C24116yes—
255C22×Dic71—48no—
256C22×Dic71C2412yes—
257C22×Dic71C2412yes—
258C22×Dic71C2414yes—
259C22×Dic71C2411yescharacteristic
260C22×Dic71C2411yescharacteristic
261C22×Dic71C2411yescharacteristic
262C22×Dic71C2412yes—
263C22×Dic71C24116yes—
264C2×C4×D71—24no—
265C2×C4×D71—24no—
266C2×C4×D71—28no—
267C2×C4×D71—24no—
268C2×C4×D71—48no—
269C2×C4×D71—48no—
270C2×C4×D71C2414yes—
271C2×C4×D71C2418yes—
272C2×C4×D71C2414yes—
273C2×C4×D71C2414yes—
274C2×C4×D71C24116yes—
275C2×C4×D71C24116yes—
276C4⋊Dic71C2418yes—
277C4⋊Dic71C2418yes—
278C4⋊Dic71C2414yes—
279C4⋊Dic71C24116yes—
280C4⋊Dic71C2418yes—
281C4⋊Dic71C2418yes—
282C4⋊Dic71C2418yes—
283C4⋊Dic71C24116yes—
284C4⋊Dic71C2414yes—
285C4⋊Dic71C24116yes—
286Dic71⋊C4C24116yes—
287Dic71⋊C4C24116yes—
288Dic71⋊C4C2418yes—
289Dic71⋊C4C2418yes—
290Dic71⋊C4C24116yes—
291Dic71⋊C4C2418yes—
292Dic71⋊C4C24116yes—
293Dic71⋊C4C2418yes—
294C22⋊Dic71C2418yes—
295C22⋊Dic71C2418yes—
296C22⋊Dic71C2418yes—
297(C2×D71)⋊C4C2418yes—
298(C2×D71)⋊C4C2418yes—
299(C2×D71)⋊C4C2418yes—
300(C2×D71)⋊C4C2418yes—
301(C2×D71)⋊C4C24116yes—
302(C2×D71)⋊C4C24116yes—
303(C2×D71)⋊C4C2418yes—
304(C2×D71)⋊C4C2418yes—
305C4×Dic71C2414yes—
306C4×Dic71C2414yes—
307C4×Dic71C2414yes—
308C4×Dic71C2418yes—
309C4×Dic71C24116yes—
310C24×C71C2412yes—
311C2×Q8×C71—28no—
312C2×Q8×C71—24no—
313C2×Q8×C71C2418yes—
314C2×Q8×C71C2414yes—
315C2×D4×C71—24no—
316C2×D4×C71C2414yes—
317C22×C4×C71—28no—
318C22×C4×C71C2414yes—
319C22×C4×C71C2411yescharacteristic
320C22×C4×C71C2412yes—
321C22×C4×C71C2412yes—
322C22×C4×C71C2412yes—
323C22×C4×C71C2418yes—
324C22×C4×C71C2411yescharacteristic
325C22×C4×C71C2411yescharacteristic
326C4⋊C4×C71C2414yes—
327C4⋊C4×C71C2418yes—
328C4⋊C4×C71C2414yes—
329C4⋊C4×C71C24116yes—
330C4⋊C4×C71C2418yes—
331C4⋊C4×C71C2418yes—
332C22⋊C4×C71C24116yes—
333C22⋊C4×C71C2418yes—
334C22⋊C4×C71C24116yes—
335C42×C71C24116yes—
336C42×C71C2414yes—
337C42×C71C2418yes—
338C23×C71—24no—
339C23×C71—24no—
340C23×C71—24no—
341C23×C71C2514yes—
342C23×C71C2511yescharacteristic
343C22×D71—22no—
344C22×D71—22no—
345C22×D71—24no—
346C22×D71—24no—
347C22×D71—24no—
348C22×D712−1+414yes—
349C22×D71C2514yes—
350C22×D71C2512yes—
351Q8×C71—216no—
352Q8×C71—28no—
353D4×C71—28no—
354C2×C4×C71—28no—
355C2×C4×C71—24no—
356C2×C4×C71—24no—
357C2×C4×C71—22no—
358C2×C4×C71—24no—
359C2×C4×C71—216no—
360C2×C4×C71H(5,𝔽2)14yes—
361C2×C4×C712−1+414yes—
362C2×C4×C71C2514yes—
363C2×C4×C71C2514yes—
364C2×C4×C71C2512yes—
365C2×C4×C71C2514yes—
366C2×C4×C71C2518yes—
367C2×C4×C71C2512yes—
368C2×C4×C71C2512yes—
369C22⋊D71—216no—
370C22⋊D71—416no—
371C2×Dic71—24no—
372C2×Dic71—22no—
373C2×Dic71—24no—
374C2×Dic71—28no—
375C2×Dic71—22no—
376C2×Dic71—22no—
377C2×Dic71—24no—
378C2×Dic71—416no—
379C2×Dic71C2514yes—
380C2×Dic71C2512yes—
381C2×Dic71C2512yes—
382C2×Dic71C2512yes—
383C2×Dic71C2514yes—
384C2×Dic71C2518yes—
385C2×Dic71C2514yes—
386D284—216no—
387D284—28no—
388C4×D71—28no—
389C4×D71—28no—
390C4×D71—216no—
391C4×D71—28no—
392C4×D71—416no—
393C4×D71—416no—
394Dic142—28no—
395Dic142—216no—
396Dic142—416no—
397Dic142—416no—
398C22×C71—24no—
399C22×C71—24no—
400C22×C71—24no—
401C22×C71—48no—
402C22×C71C2×H(5,𝔽2)12yes—
403C22×C71C2×2−1+412yes—
404C22×C71C2×2−1+412yes—
405C22×C71C2611yescharacteristic
406C2×D71—22no—
407C2×D71—22no—
408C2×D71—28no—
409C2×D71—24no—
410C2×D71—24no—
411C2×D71—24no—
412C2×D71—48no—
413C2×D71C2×2−1+414yes—
414C4×C71—28no—
415C4×C71—22no—
416C4×C71—24no—
417C4×C71—24no—
418C4×C71—24no—
419C4×C71C2×H(5,𝔽2)14yes—
420C4×C71C2×2−1+414yes—
421Dic71—24no—
422Dic71—28no—
423Dic71—22no—
424Dic71—24no—
425Dic71—22no—
426Dic71—22no—
427Dic71—24no—
428C2×#3552—711nomaximal, Sylow
429C2×C71—44no—
430C2×C71#355214yescomplemented
431C2×C71C22×H(5,𝔽2)11yescharacteristic
432C2×C71C22×2−1+411yescharacteristic
433C2×C71C22×2−1+411yescharacteristic
434D71—24no—
435D71—44no—
436#3552—7132no—
437C2×#563—714no—
438C2×#557—711no—
439C2×#556D7111yescharacteristic, complemented
440C2×#554—712no—
441C2×#553—712no—
442C2×D4×Q8—711no—
443C2×D4×Q8—712no—
444C2×#548—712no—
445C2×#547—711no—
446C2×#544—712no—
447C2×#542—712no—
448C2×#541—712no—
449C2×#539—714no—
450C2×#536—712no—
451C22×C4⋊Q8—711no—
452C2×#529—711no—
453C2×#529—711no—
454C71C2×#355211yescharacteristic, complemented, Sylow
455C22×#41—712no—
456C23×Q8—712no—
457C23×Q8—712no—
458#563—7164no—
459#557—7116no—
460#556C2×D71116yescomplemented
461#554—7132no—
462#553—7132no—
463D4×Q8—7116no—
464D4×Q8—7132no—
465#548—7132no—
466#547—7116no—
467#544—7132no—
468#542—7132no—
469#541—7132no—
470#539—7164no—
471#536—7132no—
472C2×C4⋊Q8—712no—
473C2×C4⋊Q8—7116no—
474C2×C4⋊Q8—712no—
475C2×C4⋊Q8—712no—
476C2×C4⋊Q8—712no—
477C2×C4⋊Q8—711no—
478C2×C4⋊Q8—712no—
479C2×C4⋊Q8—714no—
480C2×C4⋊Q8C2×D7111yescharacteristic
481#529—7116no—
482#529—7116no—
483C2×#126—712no—
484C2×#126—714no—
485C2×#126—712no—
486C2×#126—714no—
487C2×#126C2×D7114yes—
488C2×#125—711no—
489C2×#125—711no—
490C2×#125—714no—
491C2×#125—714no—
492C2×#125—712no—
493C2×#125—714no—
494C2×#124—711no—
495C2×#124—711no—
496C2×#124—714no—
497C2×#124C2×D7112yes—
498C2×#123—712no—
499C2×#123—712no—
500C2×#123—714no—
501C2×#123—714no—
502C2×#123—714no—
503C2×C22⋊Q8—711no—
504C2×C22⋊Q8—712no—
505C2×C22⋊Q8—711no—
506C2×C22⋊Q8—714no—
507C2×C22⋊Q8—714no—
508C2×C22⋊Q8—712no—
509C2×C22⋊Q8—714no—
510C2×C22⋊Q8—714no—
511C2×C22⋊Q8—714no—
512C2×C22⋊Q8—714no—
513C2×C22⋊Q8C2×D7112yes—
514C2×#121—711no—
515C2×#121—712no—
516C2×#121—711no—
517C2×#121—714no—
518C2×C4×Q8—712no—
519C2×C4×Q8—711no—
520C2×C4×Q8—712no—
521C2×C4×Q8C2×D7111yescharacteristic
522C2×C4×Q8C2×D7112yes—
523C2×C4×D4—712no—
524C2×C4×D4—712no—
525C2×C4×D4—714no—
526C2×C4×D4—711no—
527C2×C4×D4—712no—
528C2×C4×D4—714no—
529C2×C4×D4C2×D7111yescharacteristic
530C2×#117—712no—
531C2×#117—712no—
532C2×#117C2×D7112yes—
533C22×C4⋊C4—712no—
534C22×C4⋊C4—712no—
535C22×C4⋊C4—712no—
536C22×C42—711no—
537C2×#41—2848no—
538C2×#41—7116no—
539C22×Q8—2848no—
540C22×Q8—2848no—
541C22×Q8—7116no—
542C22×Q8—7116no—
543C22×Q8—714no—
544C22×Q8—714no—
545C22×Q8—711no—
546C22×Q8—712no—
547C22×Q8C22×D7111yescharacteristic
548C22×Q8C22×D7112yes—
549C22×D4—714no—
550C22×D4—712no—
551C22×D4—712no—
552C22×D4—711no—
553C22×D4C22×D7111yescharacteristic
554C23×C4—714no—
555C23×C4—714no—
556C23×C4—714no—
557C23×C4—711no—
558C23×C4—711no—
559C23×C4—712no—
560C23×C4—711no—
561C23×C4C22×D7112yes—
562C4⋊Q8—7116no—
563C4⋊Q8—7116no—
564C4⋊Q8—7116no—
565C4⋊Q8—7116no—
566C4⋊Q8—718no—
567C4⋊Q8—7116no—
568C4⋊Q8—7132no—
569C4⋊Q8C22×D7118yes—
570#126—7116no—
571#126—7132no—
572#126—7116no—
573#126—7132no—
574#126C22×D71132yes—
575#125—718no—
576#125—718no—
577#125—7132no—
578#125—7132no—
579#125—7116no—
580#125—7132no—
581#124—718no—
582#124—718no—
583#124—7132no—
584#124C22×D71116yes—
585#123—7116no—
586#123—7116no—
587#123—7132no—
588#123—7132no—
589#123—7132no—
590C22⋊Q8—718no—
591C22⋊Q8—7116no—
592C22⋊Q8—718no—
593C22⋊Q8—7132no—
594C22⋊Q8—7132no—
595C22⋊Q8—7116no—
596C22⋊Q8—7132no—
597C22⋊Q8—7132no—
598C22⋊Q8—7132no—
599C22⋊Q8—7132no—
600C22⋊Q8C22×D71116yes—
601#121—718no—
602#121—7116no—
603#121—718no—
604#121—7132no—
605C4×Q8—7116no—
606C4×Q8—718no—
607C4×Q8—7116no—
608C4×Q8C22×D7118yes—
609C4×Q8C22×D71116yes—
610C4×D4—7116no—
611C4×D4—7116no—
612C4×D4—7132no—
613C4×D4—718no—
614C4×D4—7116no—
615C4×D4—7132no—
616C4×D4C22×D7118yes—
617#117—7116no—
618#117—7116no—
619#117C22×D71116yes—
620C2×C4⋊C4—711no—
621C2×C4⋊C4—712no—
622C2×C4⋊C4—714no—
623C2×C4⋊C4—714no—
624C2×C4⋊C4—714no—
625C2×C4⋊C4—712no—
626C2×C4⋊C4—7116no—
627C2×C4⋊C4—712no—
628C2×C4⋊C4—712no—
629C2×C4⋊C4—712no—
630C2×C4⋊C4—712no—
631C2×C4⋊C4—714no—
632C2×C4⋊C4—712no—
633C2×C4⋊C4—714no—
634C2×C4⋊C4—712no—
635C2×C4⋊C4—711no—
636C2×C4⋊C4—714no—
637C2×C4⋊C4—714no—
638C2×C4⋊C4—712no—
639C2×C4⋊C4—7116no—
640C2×C4⋊C4—7116no—
641C2×C4⋊C4C22×D7112yes—
642C2×C4⋊C4C22×D7112yes—
643C2×C4⋊C4C22×D7111yescharacteristic
644C2×C4⋊C4C22×D7111yescharacteristic
645C2×C4⋊C4C22×D7114yes—
646C2×C4⋊C4C22×D7112yes—
647C2×C22⋊C4—712no—
648C2×C22⋊C4—712no—
649C2×C22⋊C4—712no—
650C2×C22⋊C4—712no—
651C2×C22⋊C4—712no—
652C2×C22⋊C4—712no—
653C2×C22⋊C4—712no—
654C2×C22⋊C4—714no—
655C2×C22⋊C4—714no—
656C2×C22⋊C4—712no—
657C2×C22⋊C4—712no—
658C2×C22⋊C4C22×D7114yes—
659C2×C22⋊C4C22×D7114yes—
660C2×C22⋊C4C22×D7112yes—
661C2×C42—711no—
662C2×C42—711no—
663C2×C42—712no—
664C2×C42—714no—
665C2×C42—711no—
666C2×C42—718no—
667C2×C42C22×D7112yes—
668C2×C42C22×D7114yes—
669C2×C42C22×D7111yescharacteristic
670C24—711no—
671C24—712no—
672C24C23×D7112yes—
673#41—28432no—
674C2×Q8—28no—
675C2×Q8—24no—
676C2×Q8—2848no—
677C2×Q8—2848no—
678C2×Q8—28432no—
679C2×Q8—28432no—
680C2×Q8—7116no—
681C2×Q8—7116no—
682C2×Q8—714no—
683C2×Q8—718no—
684C2×Q8—1424no—
685C2×Q8—1428no—
686C2×Q8C23×D7114yes—
687C2×Q8C23×D7118yes—
688C2×D4—24no—
689C2×D4—2848no—
690C2×D4—7116no—
691C2×D4—718no—
692C2×D4—718no—
693C2×D4—714no—
694C2×D4—1428no—
695C2×D4—1428no—
696C2×D4—1424no—
697C2×D4C23×D7114yes—
698C22×C4—28no—
699C22×C4—2848no—
700C22×C4—2848no—
701C22×C4—2848no—
702C22×C4—7116no—
703C22×C4—7116no—
704C22×C4—7116no—
705C22×C4—712no—
706C22×C4—711no—
707C22×C4—711no—
708C22×C4—711no—
709C22×C4—712no—
710C22×C4—714no—
711C22×C4—712no—
712C22×C4—714no—
713C22×C4—714no—
714C22×C4—714no—
715C22×C4—718no—
716C22×C4—1424no—
717C22×C4—1424no—
718C22×C4—1428no—
719C22×C4—1424no—
720C22×C4C23×D7118yes—
721C22×C4C23×D7112yes—
722C22×C4C23×D7111yescharacteristic
723C22×C4C23×D7112yes—
724C22×C4C23×D7112yes—
725C22×C4C23×D7114yes—
726C22×C4C23×D7111yescharacteristic
727C22×C4C23×D7111yescharacteristic
728C4⋊C4—7116no—
729C4⋊C4—7116no—
730C4⋊C4—718no—
731C4⋊C4—718no—
732C4⋊C4—7116no—
733C4⋊C4—718no—
734C4⋊C4—7116no—
735C4⋊C4—718no—
736C4⋊C4—714no—
737C4⋊C4—718no—
738C4⋊C4—7116no—
739C4⋊C4—718no—
740C4⋊C4—718no—
741C4⋊C4—718no—
742C4⋊C4—718no—
743C4⋊C4—7116no—
744C4⋊C4—714no—
745C4⋊C4—7116no—
746C4⋊C4C23×D7118yes—
747C4⋊C4C23×D7118yes—
748C4⋊C4C23×D7114yes—
749C4⋊C4C23×D7114yes—
750C4⋊C4C23×D71116yes—
751C4⋊C4C23×D7118yes—
752C22⋊C4—718no—
753C22⋊C4—718no—
754C22⋊C4—718no—
755C22⋊C4—718no—
756C22⋊C4—718no—
757C22⋊C4—718no—
758C22⋊C4—718no—
759C22⋊C4—7116no—
760C22⋊C4—7116no—
761C22⋊C4—718no—
762C22⋊C4—718no—
763C22⋊C4C23×D71116yes—
764C22⋊C4C23×D71116yes—
765C22⋊C4C23×D7118yes—
766C42—714no—
767C42—714no—
768C42—714no—
769C42—718no—
770C42—7116no—
771C42C23×D7114yes—
772C42C23×D7118yes—
773C42C23×D71116yes—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—714no—
778C23—712no—
779C23—714no—
780C23—1424no—
781C23—1424no—
782C23—1424no—
783C23—1422no—
784C23—1422no—
785C23C24×D7114yes—
786C23C24×D7111yescharacteristic
787Q8—216no—
788Q8—28no—
789Q8—28416no—
790Q8—28416no—
791Q8—1428no—
792Q8—14216no—
793D4—28no—
794D4—28416no—
795D4—14216no—
796D4—14216no—
797D4—1428no—
798C2×C4—28no—
799C2×C4—22no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—216no—
804C2×C4—28416no—
805C2×C4—28416no—
806C2×C4—28416no—
807C2×C4—714no—
808C2×C4—712no—
809C2×C4—712no—
810C2×C4—712no—
811C2×C4—714no—
812C2×C4—718no—
813C2×C4—714no—
814C2×C4—1428no—
815C2×C4—1424no—
816C2×C4—1428no—
817C2×C4—1424no—
818C2×C4—1422no—
819C2×C4—1422no—
820C2×C4—1424no—
821C2×C4—1422no—
822C2×C4—1428no—
823C2×C4—14216no—
824C2×C4—1428no—
825C2×C4#1455617414yes—
826C2×C4#1455617514yes—
827C2×C4C24×D7114yes—
828C2×C4C24×D7112yes—
829C2×C4C24×D7114yes—
830C2×C4C24×D7114yes—
831C2×C4C24×D7118yes—
832C2×C4C24×D7112yes—
833C2×C4C24×D7112yes—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—48no—
838C22—2848no—
839C22—714no—
840C22—1424no—
841C22—1424no—
842C22—1424no—
843C22—1428no—
844C22—1422no—
845C22—1422no—
846C22C2×#1455617412yes—
847C222−1+4×D7112yes—
848C22C2×#1455617512yes—
849C22C25×D7111yescharacteristic
850C4—28no—
851C4—22no—
852C4—24no—
853C4—24no—
854C4—24no—
855C4—1424no—
856C4—1428no—
857C4—1424no—
858C4—1422no—
859C4—1422no—
860C4—1424no—
861C4—1422no—
862C4C2×#1455617414yes—
863C4C2×#1455617514yes—
864C2—44no—
865C2—2844no—
866C2—1424no—
867C2#2260277014yesdirect product factor
868C2C22×#1455617411yescharacteristic
869C2C2×2−1+4×D7111yescharacteristic
870C2C22×#1455617511yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#556×C71C2
socleC23×C71C25
hypercenterC2×#556D71
hypocenterC71C2×#3552
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #22602770C2direct (N × H)
2. C2×#17986751C2semidirect
3. C2×#17986728C2semidirect
4. C2×#17986707C2semidirect
5. C2×#17986693C2semidirect
6. C2×Q8×D284C2semidirect
7. C2×#17986664C2semidirect
8. C2×#17986657C2semidirect
9. C2×#17986653C2semidirect
10. C2×#17986627C2semidirect
11. C2×#17986622C2semidirect
12. C2×#17986607C2semidirect
13. C2×#17986590C2semidirect
14. C2×#17986569C2semidirect
15. C2×C4⋊Q8×D71C2semidirect
16. C2×#17986536C2semidirect
17. C2×#17986531C2semidirect
18. C2×#556×C71C2semidirect
22. #17986751C22semidirect
23. #17986728C22semidirect
24. #17986707C22semidirect
25. #17986693C22semidirect
26. Q8×D284C22semidirect
27. #17986664C22semidirect
28. #17986657C22semidirect
29. #17986653C22semidirect
30. #17986627C22semidirect
31. #17986622C22semidirect
32. #17986607C22semidirect
33. #17986590C22semidirect
34. #17986569C22semidirect
42. C4⋊Q8×D71C22semidirect
43. #17986536C22semidirect
44. #17986531C22semidirect
92. #556×C71C22semidirect
430. C2×C71#3552semidirect
439. C2×#556D71semidirect
454. C71C2×#3552semidirect
460. #556C2×D71semidirect
867. C2#22602770direct (N × H)

Maximal subgroups

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

subgroupindex
#226027702
C2×#179867512
C2×#179867282
C2×#179867072
C2×#179866932
C2×Q8×D2842
C2×#179866642
C2×#179866572
C2×#179866532
C2×#179866272
C2×#179866222
C2×#179866072
C2×#179865902
C2×#179865692
C2×C4⋊Q8×D712
C2×#179865362
C2×#179865312
C2×#556×C712
C2×#355271