Finite Group Databasebeta

← C2×#22602814 #32905082

Subgroups — C2×#22602814 #32905082

Order 18176.

7182 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602814C2132yesmaximal, direct product factor
2C2×#17986747C214yesmaximal, complemented
3C2×#17986734C211yesmaximal, characteristic, complemented
4C2×#17986734C212yesmaximal, complemented
5C2×#17986705C212yesmaximal, complemented
6C2×#17986671C211yesmaximal, characteristic, complemented
7C2×#17986664C211yesmaximal, characteristic, complemented
8C2×#17986661C212yesmaximal, complemented
9C2×#17986652C212yesmaximal, complemented
10C2×#17986621C212yesmaximal, complemented
11C2×#17986621C212yesmaximal, complemented
12C2×#17986605C212yesmaximal, complemented
13C2×#17986597C214yesmaximal, complemented
14C2×#17986574C212yesmaximal, complemented
15C2×#17986553C211yesmaximal, characteristic, complemented
16C2×#17986550C211yesmaximal, characteristic, complemented
17C2×#17986536C211yesmaximal, characteristic, complemented
18C2×#557×C71C211yesmaximal, characteristic, complemented
19C22×#11765866C2212yes—
20C22×#11765866C2212yes—
21C22×Q8×D71C2212yes—
22#17986747C22164yescomplemented
23#17986734C22132yescomplemented
24#17986734C22116yescomplemented
25#17986705C22132yescomplemented
26#17986671C22116yescomplemented
27#17986664C22116yescomplemented
28#17986661C22132yescomplemented
29#17986652C22132yescomplemented
30#17986621C22132yescomplemented
31#17986621C22132yescomplemented
32#17986605C22132yescomplemented
33#17986597C22164yescomplemented
34#17986574C22132yescomplemented
35#17986553C22116yescomplemented
36#17986550C22116yescomplemented
37C2×#14556127C2212yes—
38C2×#14556127C2211yescharacteristic
39C2×#14556126C2211yescharacteristic
40C2×#14556125C2211yescharacteristic
41C2×#14556125C2212yes—
42#17986536C22116yescomplemented
43C2×#14556123C2212yes—
44C2×#14556122C2214yes—
45C2×#14556119C2211yescharacteristic
46C2×#14556118C2212yes—
47C2×#14556117C2211yescharacteristic
48C2×#14556117C2212yes—
49C2×#14556117C2212yes—
50C2×#14556116C2212yes—
51C2×#14556116C2214yes—
52C2×#14556116C2214yes—
53C2×#14556113C2214yes—
54C2×#14556113C2214yes—
55C2×#14556113C2212yes—
56C2×#14556113C2214yes—
57C2×#14556113C2214yes—
58C2×#14556113C2214yes—
59C2×#14556113C2214yes—
60C2×#14556108C2211yescharacteristic
61C2×#14556108C2214yes—
62C2×#14556106C2214yes—
63C2×#14556106C2214yes—
64C2×#14556106C2214yes—
65C2×#14556106C2212yes—
66C2×#14556106C2214yes—
67C2×#14556104C2211yescharacteristic
68C2×#14556104C2212yes—
69C2×#14556104C2211yescharacteristic
70C2×#14556103C2214yes—
71C2×#14556103C2212yes—
72C2×#14556103C2214yes—
73C2×#14556103C2214yes—
74C2×#14556103C2211yescharacteristic
75C2×#14556103C2212yes—
76C2×#14556103C2212yes—
77C2×C4×Dic142C2211yescharacteristic
78C2×C4×Dic142C2212yes—
79C2×C4×D284C2212yes—
80C2×C4×D284C2212yes—
81C2×C4×D284C2214yes—
82C2×C4×D284C2211yescharacteristic
83C2×C4×D284C2212yes—
84C2×#14556090C2212yes—
85C2×#14556090C2212yes—
86C2×#14556090C2212yes—
87C2×#14556090C2212yes—
88C2×#14556085C2212yes—
89C2×#14556085C2212yes—
90C2×C4⋊C4×D71C2214yes—
91C2×C42×D71C2211yescharacteristic
92#557×C71C22116yescomplemented
93C2×C4⋊Q8×C71C2212yes—
94C2×C4⋊Q8×C71C2211yescharacteristic
95C2×#125×C71C2212yes—
96C2×#125×C71C2214yes—
97C2×C4×Q8×C71C2212yes—
98C2×C4×Q8×C71C2211yescharacteristic
99C2×C4×Q8×C71C2211yescharacteristic
100C2×C4×Q8×C71C2212yes—
101C2×#11765866—48no—
102C2×#11765866—48no—
103C2×#11765866C23116yes—
104C2×#11765866C23116yes—
105C22×Dic142C2311yescharacteristic
106C22×Dic142C2314yes—
107C22×Dic142C2312yes—
108C2×Q8×D71—48no—
109C2×Q8×D71C23116yes—
110C22×D284C2312yes—
111C22×D284C2311yescharacteristic
112C22×D284C2312yes—
113C22×D284C2314yes—
114C22×D284C2314yes—
115C22×D284C2312yes—
116C22×D284C2312yes—
117C22×D284C2314yes—
118C22×C4×D71C2312yes—
119C22×C4×D71C2311yescharacteristic
120C22×C4×D71C2311yescharacteristic
121C22×C4×D71C2314yes—
122C22×C4×D71C2314yes—
123C22×C4×D71C2314yes—
124C22×C4×D71C2311yescharacteristic
125C22×C4×D71C2314yes—
126#14556127C2318yes—
127#14556127C23116yes—
128#14556126C2318yes—
129#14556125C23116yes—
130#14556125C2318yes—
131#14556123C23116yes—
132#14556122C23132yes—
133#14556119C2318yes—
134#14556118C23116yes—
135#14556117C23116yes—
136#14556117C23116yes—
137#14556117C2318yes—
138#14556116C23116yes—
139#14556116C23132yes—
140#14556116C23132yes—
141#14556113C23132yes—
142#14556113C23132yes—
143#14556113C23132yes—
144#14556113C23132yes—
145#14556113C23132yes—
146#14556113C23132yes—
147#14556113C23116yes—
148#14556108C23132yes—
149#14556108C2318yes—
150#14556106C23132yes—
151#14556106C23132yes—
152#14556106C23132yes—
153#14556106C23132yes—
154#14556106C23116yes—
155#14556104C2318yes—
156#14556104C23116yes—
157#14556104C2318yes—
158#14556103C23132yes—
159#14556103C2318yes—
160#14556103C23116yes—
161#14556103C23132yes—
162#14556103C23132yes—
163#14556103C23116yes—
164#14556103C23116yes—
165C4×Dic142C2318yes—
166C4×Dic142C23116yes—
167C4×D284C23132yes—
168C4×D284C23116yes—
169C4×D284C23116yes—
170C4×D284C23116yes—
171C4×D284C2318yes—
172#14556090C23116yes—
173#14556090C23116yes—
174#14556090C23116yes—
175#14556090C23116yes—
176#14556085C23116yes—
177#14556085C23116yes—
178C2×C4⋊Dic71C2312yes—
179C2×C4⋊Dic71C2311yescharacteristic
180C2×C4⋊Dic71C2311yescharacteristic
181C2×C4⋊Dic71C2312yes—
182C2×Dic71⋊C4C2312yes—
183C2×Dic71⋊C4C2314yes—
184C2×Dic71⋊C4C2312yes—
185C2×Dic71⋊C4C2312yes—
186C2×Dic71⋊C4C2312yes—
187C2×Dic71⋊C4C2312yes—
188C2×Dic71⋊C4C2312yes—
189C2×Dic71⋊C4C2312yes—
190C4⋊C4×D71C23132yes—
191C2×(C2×D71)⋊C4C2312yes—
192C2×(C2×D71)⋊C4C2312yes—
193C2×(C2×D71)⋊C4C2312yes—
194C2×(C2×D71)⋊C4C2312yes—
195C2×(C2×D71)⋊C4C2314yes—
196C2×(C2×D71)⋊C4C2314yes—
197C2×(C2×D71)⋊C4C2314yes—
198C2×(C2×D71)⋊C4C2314yes—
199C2×(C2×D71)⋊C4C2312yes—
200C2×(C2×D71)⋊C4C2312yes—
201C2×(C2×D71)⋊C4C2314yes—
202C2×(C2×D71)⋊C4C2312yes—
203C2×(C2×D71)⋊C4C2314yes—
204C2×(C2×D71)⋊C4C2314yes—
205C2×C4×Dic71C2311yescharacteristic
206C2×C4×Dic71C2311yescharacteristic
207C2×C4×Dic71C2311yescharacteristic
208C2×C4×Dic71C2312yes—
209C42×D71C2318yes—
210C22×Q8×C71C2312yes—
211C22×Q8×C71C2311yescharacteristic
212C22×Q8×C71C2311yescharacteristic
213C4⋊Q8×C71C23116yes—
214C4⋊Q8×C71C2318yes—
215#125×C71C23132yes—
216#125×C71C23116yes—
217C4×Q8×C71C23116yes—
218C4×Q8×C71C23116yes—
219C4×Q8×C71C2318yes—
220C4×Q8×C71C2318yes—
221C2×C4⋊C4×C71C2311yescharacteristic
222C2×C4⋊C4×C71C2311yescharacteristic
223C2×C4⋊C4×C71C2312yes—
224C2×C4⋊C4×C71C2314yes—
225C2×C4⋊C4×C71C2312yes—
226C2×C4⋊C4×C71C2312yes—
227C2×C4⋊C4×C71C2314yes—
228C2×C4⋊C4×C71C2314yes—
229C2×C4⋊C4×C71C2312yes—
230C2×C42×C71C2312yes—
231C2×C42×C71C2314yes—
232C2×C42×C71C2311yescharacteristic
233C2×C42×C71C2312yes—
234C23×D71C2412yes—
235C23×D71C2411yescharacteristic
236C23×D71C2414yes—
237#11765866—432no—
238#11765866—432no—
239C2×Dic142—24no—
240C2×Dic142—48no—
241C2×Dic142—44no—
242C2×Dic142C2414yes—
243C2×Dic142C24116yes—
244C2×Dic142C2418yes—
245Q8×D71—432no—
246C2×D284—28no—
247C2×D284—24no—
248C2×D284—28no—
249C2×D284—44no—
250C2×D284—44no—
251C2×D284—48no—
252C2×D284—48no—
253C2×D284—48no—
254C2×D284C2418yes—
255C2×D284C2414yes—
256C2×D284C2418yes—
257C2×D284C24116yes—
258C2×D284C24116yes—
259C2×D284C2418yes—
260C2×D284C2418yes—
261C2×D284C24116yes—
262C22×Dic71C2411yescharacteristic
263C22×Dic71C2412yes—
264C22×Dic71C2412yes—
265C22×Dic71C2412yes—
266C22×Dic71C2411yescharacteristic
267C22×Dic71C2411yescharacteristic
268C2×C4×D71—28no—
269C2×C4×D71—24no—
270C2×C4×D71—24no—
271C2×C4×D71—48no—
272C2×C4×D71—42no—
273C2×C4×D71—48no—
274C2×C4×D71—48no—
275C2×C4×D71—48no—
276C2×C4×D71C2418yes—
277C2×C4×D71C2414yes—
278C2×C4×D71C2414yes—
279C2×C4×D71C24116yes—
280C2×C4×D71C24116yes—
281C2×C4×D71C24116yes—
282C2×C4×D71C2414yes—
283C2×C4×D71C24116yes—
284C4⋊Dic71C2418yes—
285C4⋊Dic71C2414yes—
286C4⋊Dic71C2414yes—
287C4⋊Dic71C2418yes—
288Dic71⋊C4C2418yes—
289Dic71⋊C4C24116yes—
290Dic71⋊C4C2418yes—
291Dic71⋊C4C2418yes—
292Dic71⋊C4C2418yes—
293Dic71⋊C4C2418yes—
294Dic71⋊C4C2418yes—
295Dic71⋊C4C2418yes—
296(C2×D71)⋊C4C2418yes—
297(C2×D71)⋊C4C2418yes—
298(C2×D71)⋊C4C2418yes—
299(C2×D71)⋊C4C2418yes—
300(C2×D71)⋊C4C24116yes—
301(C2×D71)⋊C4C24116yes—
302(C2×D71)⋊C4C24116yes—
303(C2×D71)⋊C4C24116yes—
304(C2×D71)⋊C4C2418yes—
305(C2×D71)⋊C4C2418yes—
306(C2×D71)⋊C4C24116yes—
307(C2×D71)⋊C4C2418yes—
308(C2×D71)⋊C4C24116yes—
309(C2×D71)⋊C4C24116yes—
310C4×Dic71C2414yes—
311C4×Dic71C2414yes—
312C4×Dic71C2414yes—
313C4×Dic71C2418yes—
314C2×Q8×C71—28no—
315C2×Q8×C71—24no—
316C2×Q8×C71—24no—
317C2×Q8×C71C2418yes—
318C2×Q8×C71C2414yes—
319C2×Q8×C71C2414yes—
320C22×C4×C71C2412yes—
321C22×C4×C71C2414yes—
322C22×C4×C71C2412yes—
323C22×C4×C71C2411yescharacteristic
324C22×C4×C71C2412yes—
325C22×C4×C71C2412yes—
326C22×C4×C71C2411yescharacteristic
327C22×C4×C71C2411yescharacteristic
328C4⋊C4×C71C2414yes—
329C4⋊C4×C71C2414yes—
330C4⋊C4×C71C2418yes—
331C4⋊C4×C71C24116yes—
332C4⋊C4×C71C2418yes—
333C4⋊C4×C71C2418yes—
334C4⋊C4×C71C24116yes—
335C4⋊C4×C71C24116yes—
336C4⋊C4×C71C2418yes—
337C42×C71C2418yes—
338C42×C71C24116yes—
339C42×C71C2414yes—
340C42×C71C2418yes—
341C23×C71C2511yescharacteristic
342C22×D71—24no—
343C22×D71—22no—
344C22×D71—28no—
345C22×D71—22no—
346C22×D71—24no—
347C22×D71—28no—
348C22×D71—22no—
349C22×D71—28no—
350C22×D71—24no—
351C22×D71C2514yes—
352C22×D71C2512yes—
353C22×D71C2518yes—
354Q8×C71—216no—
355Q8×C71—28no—
356Q8×C71—28no—
357C2×C4×C71—24no—
358C2×C4×C71—28no—
359C2×C4×C71—24no—
360C2×C4×C71—24no—
361C2×C4×C71—22no—
362C2×C4×C71—24no—
363C2×C4×C71H(5,𝔽2)14yes—
364C2×C4×C712−1+414yes—
365C2×C4×C71C2514yes—
366C2×C4×C71C2514yes—
367C2×C4×C71C2512yes—
368C2×C4×C71C2514yes—
369C2×C4×C71C2518yes—
370C2×C4×C71C2514yes—
371C2×C4×C71C2512yes—
372C2×C4×C71C2512yes—
373C2×Dic71—22no—
374C2×Dic71—24no—
375C2×Dic71—24no—
376C2×Dic71—22no—
377C2×Dic71—24no—
378C2×Dic71—22no—
379C2×Dic71C2512yes—
380C2×Dic71C2512yes—
381C2×Dic71C2512yes—
382C2×Dic71C2514yes—
383C2×Dic71C2514yes—
384C2×Dic71C2514yes—
385D284—216no—
386D284—28no—
387D284—216no—
388D284—416no—
389D284—48no—
390D284—48no—
391D284—416no—
392D284—416no—
393C4×D71—216no—
394C4×D71—28no—
395C4×D71—28no—
396C4×D71—44no—
397C4×D71—416no—
398C4×D71—416no—
399C4×D71—416no—
400C4×D71—416no—
401Dic142—28no—
402Dic142—416no—
403Dic142—48no—
404C22×C71C2×H(5,𝔽2)12yes—
405C22×C71C2×2−1+412yes—
406C22×C71#58512yes—
407C22×C71C2611yescharacteristic
408C2×D71—24no—
409C2×D71—22no—
410C2×D71—28no—
411C2×D71—22no—
412C2×D71—24no—
413C2×D71—28no—
414C2×D71—22no—
415C2×D71—28no—
416C2×D71—24no—
417C2×D71—48no—
418C2×D71—44no—
419C2×D71—416no—
420C4×C71—28no—
421C4×C71—24no—
422C4×C71—24no—
423C4×C71—24no—
424C4×C71—24no—
425C4×C71—22no—
426C4×C71C2×H(5,𝔽2)14yes—
427C4×C71C2×2−1+414yes—
428Dic71—24no—
429Dic71—24no—
430Dic71—22no—
431Dic71—22no—
432Dic71—22no—
433Dic71—24no—
434C2×#3554—711nomaximal, Sylow
435C2×C71#355414yescomplemented
436C2×C71C22×H(5,𝔽2)11yescharacteristic
437C2×C71C22×2−1+411yescharacteristic
438C2×C71C2×#58511yescharacteristic
439D71—44no—
440D71—42no—
441D71—48no—
442#3554—7132no—
443C2×#562—714no—
444C2×#559—712no—
445C2×#559—711no—
446C2×#557D7111yescharacteristic, complemented
447C2×#554—712no—
448C2×#550—711no—
449C2×D4×Q8—711no—
450C2×#548—712no—
451C2×#547—712no—
452C2×#542—712no—
453C2×#542—712no—
454C2×#540—712no—
455C2×#539—714no—
456C2×#536—712no—
457C2×#533—711no—
458C2×#532—711no—
459C2×#529—711no—
460C71C2×#355411yescharacteristic, complemented, Sylow
461C22×#41—712no—
462C22×#41—712no—
463C23×Q8—712no—
464#562—7164no—
465#559—7132no—
466#559—7116no—
467#557C2×D71116yescomplemented
468#554—7132no—
469#550—7116no—
470D4×Q8—7116no—
471#548—7132no—
472#547—7132no—
473#542—7132no—
474#542—7132no—
475#540—7132no—
476#539—7164no—
477#536—7132no—
478#533—7116no—
479#532—7116no—
480C2×C4⋊Q8—711no—
481C2×C4⋊Q8—711no—
482C2×C4⋊Q8—712no—
483C2×C4⋊Q8C2×D7111yescharacteristic
484C2×C4⋊Q8C2×D7112yes—
485C2×#127—711no—
486C2×#127—712no—
487#529—7116no—
488C2×#126—712no—
489C2×#126—714no—
490C2×#125—711no—
491C2×#125—712no—
492C2×#125C2×D7114yes—
493C2×#125C2×D7112yes—
494C2×#124—711no—
495C2×#124—712no—
496C2×#124—712no—
497C2×#124—712no—
498C2×#124—714no—
499C2×#124—714no—
500C2×#123—712no—
501C2×#123—714no—
502C2×#123—714no—
503C2×#123—714no—
504C2×#123—714no—
505C2×#123—714no—
506C2×#123—714no—
507C2×C22⋊Q8—711no—
508C2×C22⋊Q8—711no—
509C2×C22⋊Q8—712no—
510C2×C22⋊Q8—711no—
511C2×C22⋊Q8—712no—
512C2×C22⋊Q8—714no—
513C2×C22⋊Q8—714no—
514C2×C22⋊Q8—714no—
515C2×C22⋊Q8—714no—
516C2×C22⋊Q8—714no—
517C2×#121—711no—
518C2×#121—712no—
519C2×#121—712no—
520C2×#121—714no—
521C2×#121—714no—
522C2×#121—714no—
523C2×#121—712no—
524C2×C4×Q8—711no—
525C2×C4×Q8—712no—
526C2×C4×Q8C2×D7111yescharacteristic
527C2×C4×Q8C2×D7111yescharacteristic
528C2×C4×Q8C2×D7112yes—
529C2×C4×Q8C2×D7112yes—
530C2×C4×D4—712no—
531C2×C4×D4—712no—
532C2×C4×D4—712no—
533C2×C4×D4—712no—
534C2×C4×D4—712no—
535C2×C4×D4—711no—
536C2×C4×D4—714no—
537C2×C4×D4—712no—
538C2×C4×D4—712no—
539C2×#117—712no—
540C2×#117—712no—
541C22×C4⋊C4—714no—
542C22×C42—711no—
543C2×#41—2848no—
544C2×#41—2848no—
545C2×#41—7116no—
546C2×#41—7116no—
547C22×Q8—2848no—
548C22×Q8—7116no—
549C22×Q8—712no—
550C22×Q8—714no—
551C22×Q8—711no—
552C22×Q8C22×D7111yescharacteristic
553C22×Q8C22×D7112yes—
554C22×Q8C22×D7111yescharacteristic
555C22×D4—712no—
556C22×D4—712no—
557C22×D4—714no—
558C22×D4—714no—
559C22×D4—714no—
560C22×D4—712no—
561C22×D4—711no—
562C22×D4—712no—
563C23×C4—714no—
564C23×C4—714no—
565C23×C4—714no—
566C23×C4—714no—
567C23×C4—711no—
568C23×C4—711no—
569C23×C4—712no—
570C23×C4—711no—
571C4⋊Q8—718no—
572C4⋊Q8—718no—
573C4⋊Q8—7116no—
574C4⋊Q8C22×D7118yes—
575C4⋊Q8C22×D71116yes—
576#127—718no—
577#127—7116no—
578#126—7116no—
579#126—7132no—
580#125—718no—
581#125—7116no—
582#125C22×D71132yes—
583#125C22×D71116yes—
584#124—718no—
585#124—7116no—
586#124—7116no—
587#124—7116no—
588#124—7132no—
589#124—7132no—
590#123—7116no—
591#123—7132no—
592#123—7132no—
593#123—7132no—
594#123—7132no—
595#123—7132no—
596#123—7132no—
597C22⋊Q8—718no—
598C22⋊Q8—718no—
599C22⋊Q8—7116no—
600C22⋊Q8—718no—
601C22⋊Q8—7116no—
602C22⋊Q8—7132no—
603C22⋊Q8—7132no—
604C22⋊Q8—7132no—
605C22⋊Q8—7132no—
606C22⋊Q8—7132no—
607#121—718no—
608#121—7116no—
609#121—7116no—
610#121—7132no—
611#121—7132no—
612#121—7132no—
613#121—7116no—
614C4×Q8—718no—
615C4×Q8—7116no—
616C4×Q8C22×D7118yes—
617C4×Q8C22×D7118yes—
618C4×Q8C22×D71116yes—
619C4×Q8C22×D71116yes—
620C4×D4—7116no—
621C4×D4—7116no—
622C4×D4—7116no—
623C4×D4—7116no—
624C4×D4—7116no—
625C4×D4—718no—
626C4×D4—7132no—
627C4×D4—7116no—
628C4×D4—7116no—
629#117—7116no—
630#117—7116no—
631C2×C4⋊C4—712no—
632C2×C4⋊C4—712no—
633C2×C4⋊C4—714no—
634C2×C4⋊C4—712no—
635C2×C4⋊C4—712no—
636C2×C4⋊C4—712no—
637C2×C4⋊C4—712no—
638C2×C4⋊C4—711no—
639C2×C4⋊C4—712no—
640C2×C4⋊C4—711no—
641C2×C4⋊C4—712no—
642C2×C4⋊C4—712no—
643C2×C4⋊C4—7132no—
644C2×C4⋊C4C22×D7114yes—
645C2×C4⋊C4C22×D7111yescharacteristic
646C2×C4⋊C4C22×D7112yes—
647C2×C4⋊C4C22×D7112yes—
648C2×C4⋊C4C22×D7111yescharacteristic
649C2×C4⋊C4C22×D7112yes—
650C2×C4⋊C4C22×D7114yes—
651C2×C4⋊C4C22×D7114yes—
652C2×C4⋊C4C22×D7112yes—
653C2×C22⋊C4—712no—
654C2×C22⋊C4—712no—
655C2×C22⋊C4—712no—
656C2×C22⋊C4—712no—
657C2×C22⋊C4—712no—
658C2×C22⋊C4—712no—
659C2×C22⋊C4—714no—
660C2×C22⋊C4—714no—
661C2×C22⋊C4—714no—
662C2×C22⋊C4—714no—
663C2×C22⋊C4—714no—
664C2×C22⋊C4—712no—
665C2×C22⋊C4—714no—
666C2×C22⋊C4—714no—
667C2×C42—711no—
668C2×C42—712no—
669C2×C42—711no—
670C2×C42—711no—
671C2×C42—718no—
672C2×C42C22×D7112yes—
673C2×C42C22×D7112yes—
674C2×C42C22×D7111yescharacteristic
675C2×C42C22×D7114yes—
676C24—712no—
677C24—714no—
678C24—711no—
679#41—28432no—
680#41—28432no—
681C2×Q8—28no—
682C2×Q8—24no—
683C2×Q8—24no—
684C2×Q8—2848no—
685C2×Q8—2844no—
686C2×Q8—28432no—
687C2×Q8—718no—
688C2×Q8—7116no—
689C2×Q8—714no—
690C2×Q8—1424no—
691C2×Q8C23×D7114yes—
692C2×Q8C23×D7118yes—
693C2×Q8C23×D7114yes—
694C2×D4—2844no—
695C2×D4—2844no—
696C2×D4—2848no—
697C2×D4—2848no—
698C2×D4—2848no—
699C2×D4—718no—
700C2×D4—718no—
701C2×D4—7116no—
702C2×D4—7116no—
703C2×D4—7116no—
704C2×D4—718no—
705C2×D4—714no—
706C2×D4—718no—
707C2×D4—1428no—
708C2×D4—1428no—
709C2×D4—1424no—
710C22×C4—2848no—
711C22×C4—2842no—
712C22×C4—2848no—
713C22×C4—2848no—
714C22×C4—2848no—
715C22×C4—714no—
716C22×C4—7116no—
717C22×C4—7116no—
718C22×C4—7116no—
719C22×C4—7116no—
720C22×C4—711no—
721C22×C4—711no—
722C22×C4—711no—
723C22×C4—712no—
724C22×C4—712no—
725C22×C4—712no—
726C22×C4—714no—
727C22×C4—714no—
728C22×C4—718no—
729C22×C4—1428no—
730C22×C4—1424no—
731C22×C4—1424no—
732C22×C4C23×D7111yescharacteristic
733C22×C4C23×D7112yes—
734C22×C4C23×D7112yes—
735C22×C4C23×D7112yes—
736C22×C4C23×D7114yes—
737C22×C4C23×D7112yes—
738C22×C4C23×D7111yescharacteristic
739C22×C4C23×D7111yescharacteristic
740C4⋊C4—718no—
741C4⋊C4—7116no—
742C4⋊C4—718no—
743C4⋊C4—718no—
744C4⋊C4—718no—
745C4⋊C4—718no—
746C4⋊C4—718no—
747C4⋊C4—718no—
748C4⋊C4—718no—
749C4⋊C4—714no—
750C4⋊C4—718no—
751C4⋊C4—714no—
752C4⋊C4C23×D71116yes—
753C4⋊C4C23×D7114yes—
754C4⋊C4C23×D7118yes—
755C4⋊C4C23×D7118yes—
756C4⋊C4C23×D7114yes—
757C4⋊C4C23×D7118yes—
758C4⋊C4C23×D71116yes—
759C4⋊C4C23×D71116yes—
760C4⋊C4C23×D7118yes—
761C22⋊C4—718no—
762C22⋊C4—718no—
763C22⋊C4—718no—
764C22⋊C4—718no—
765C22⋊C4—718no—
766C22⋊C4—718no—
767C22⋊C4—7116no—
768C22⋊C4—7116no—
769C22⋊C4—7116no—
770C22⋊C4—7116no—
771C22⋊C4—7116no—
772C22⋊C4—718no—
773C22⋊C4—7116no—
774C22⋊C4—7116no—
775C42—714no—
776C42—714no—
777C42—714no—
778C42—718no—
779C42C23×D7114yes—
780C42C23×D7118yes—
781C42C23×D7118yes—
782C42C23×D71116yes—
783C23—714no—
784C23—718no—
785C23—712no—
786C23—1424no—
787C23—1428no—
788C23—1422no—
789C23—1422no—
790C23—1424no—
791C23—1428no—
792C23—1428no—
793C23—1422no—
794C23—1424no—
795C23C24×D7111yescharacteristic
796Q8—216no—
797Q8—28no—
798Q8—28no—
799Q8—28416no—
800Q8—2848no—
801Q8—1428no—
802D4—28416no—
803D4—28416no—
804D4—2848no—
805D4—2848no—
806D4—28416no—
807D4—14216no—
808D4—14216no—
809D4—1428no—
810C2×C4—24no—
811C2×C4—28no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—28416no—
817C2×C4—28416no—
818C2×C4—28416no—
819C2×C4—28416no—
820C2×C4—2844no—
821C2×C4—712no—
822C2×C4—712no—
823C2×C4—712no—
824C2×C4—714no—
825C2×C4—714no—
826C2×C4—714no—
827C2×C4—1422no—
828C2×C4—1424no—
829C2×C4—1424no—
830C2×C4—1422no—
831C2×C4—1424no—
832C2×C4—1422no—
833C2×C4—14216no—
834C2×C4—1428no—
835C2×C4—1428no—
836C2×C4#1455617414yes—
837C2×C4#1455617614yes—
838C2×C4C24×D7112yes—
839C2×C4C24×D7114yes—
840C2×C4C24×D7114yes—
841C2×C4C24×D7114yes—
842C2×C4C24×D7118yes—
843C2×C4C24×D7114yes—
844C2×C4C24×D7112yes—
845C2×C4C24×D7112yes—
846C22—2848no—
847C22—28416no—
848C22—2844no—
849C22—1424no—
850C22—1428no—
851C22—1422no—
852C22—1422no—
853C22—1424no—
854C22—1428no—
855C22—1428no—
856C22—1422no—
857C22—1424no—
858C22C2×#1455617412yes—
859C22C2×#1455617612yes—
860C22#1798683612yes—
861C22C25×D7111yescharacteristic
862C4—24no—
863C4—28no—
864C4—24no—
865C4—24no—
866C4—22no—
867C4—24no—
868C4—1422no—
869C4—1424no—
870C4—1424no—
871C4—1422no—
872C4—1424no—
873C4—1422no—
874C4C2×#1455617414yes—
875C4C2×#1455617614yes—
876C2—2844no—
877C2—2848no—
878C2—2842no—
879C2#2260281414yesdirect product factor
880C2C22×#1455617411yescharacteristic
881C2C22×#1455617611yescharacteristic
882C2C2×#1798683611yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#557×C71C2
socleC23×C71C25
hypercenterC2×#557D71
hypocenterC71C2×#3554
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #22602814C2direct (N × H)
2. C2×#17986747C2semidirect
3. C2×#17986734C2semidirect
4. C2×#17986734C2semidirect
5. C2×#17986705C2semidirect
6. C2×#17986671C2semidirect
7. C2×#17986664C2semidirect
8. C2×#17986661C2semidirect
9. C2×#17986652C2semidirect
10. C2×#17986621C2semidirect
11. C2×#17986621C2semidirect
12. C2×#17986605C2semidirect
13. C2×#17986597C2semidirect
14. C2×#17986574C2semidirect
15. C2×#17986553C2semidirect
16. C2×#17986550C2semidirect
17. C2×#17986536C2semidirect
18. C2×#557×C71C2semidirect
22. #17986747C22semidirect
23. #17986734C22semidirect
24. #17986734C22semidirect
25. #17986705C22semidirect
26. #17986671C22semidirect
27. #17986664C22semidirect
28. #17986661C22semidirect
29. #17986652C22semidirect
30. #17986621C22semidirect
31. #17986621C22semidirect
32. #17986605C22semidirect
33. #17986597C22semidirect
34. #17986574C22semidirect
35. #17986553C22semidirect
36. #17986550C22semidirect
42. #17986536C22semidirect
92. #557×C71C22semidirect
435. C2×C71#3554semidirect
446. C2×#557D71semidirect
460. C71C2×#3554semidirect
467. #557C2×D71semidirect
879. C2#22602814direct (N × H)

Maximal subgroups

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

subgroupindex
#226028142
C2×#179867472
C2×#179867342
C2×#179867052
C2×#179866712
C2×#179866642
C2×#179866612
C2×#179866522
C2×#179866212
C2×#179866052
C2×#179865972
C2×#179865742
C2×#179865532
C2×#179865502
C2×#179865362
C2×#557×C712
C2×#355471