Finite Group Databasebeta

← C2×#19148572 #26004714

Subgroups — C2×#19148572 #26004714

Order 11008.

7142 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148572C2132yesmaximal, direct product factor
2C2×#14583609C211yesmaximal, characteristic, complemented
3C2×#14583609C211yesmaximal, characteristic, complemented
4C2×#14583602C212yesmaximal, complemented
5C2×#14583590C212yesmaximal, complemented
6C2×#14583590C212yesmaximal, complemented
7C2×#14583581C214yesmaximal, complemented
8C2×#14583552C211yesmaximal, characteristic, complemented
9C2×#14583552C212yesmaximal, complemented
10C2×#14583510C212yesmaximal, complemented
11C2×#14583497C214yesmaximal, complemented
12C2×#14583454C211yesmaximal, characteristic, complemented
13C2×#14583436C212yesmaximal, complemented
14C2×#14583436C211yesmaximal, characteristic, complemented
15C2×#125×D43C212yesmaximal, complemented
16C2×#14583381C212yesmaximal, complemented
17C2×C4×#10621902C211yesmaximal, characteristic, complemented
18C2×C43×#557C211yesmaximal, characteristic, complemented
19C22×#10621902C2211yescharacteristic
20C22×#10621902C2212yes—
21#14583609C22116yescomplemented
22#14583609C22116yescomplemented
23#14583602C22132yescomplemented
24#14583590C22132yescomplemented
25#14583590C22132yescomplemented
26#14583581C22164yescomplemented
27#14583552C22116yescomplemented
28#14583552C22132yescomplemented
29#14583510C22132yescomplemented
30#14583497C22164yescomplemented
31#14583454C22116yescomplemented
32C2×#13063325C2211yescharacteristic
33#14583436C22132yescomplemented
34#14583436C22116yescomplemented
35C2×#13063320C2212yes—
36C2×#13063320C2214yes—
37C2×#13063320C2214yes—
38C2×#13063319C2214yes—
39C2×#13063317C2212yes—
40C2×#13063317C2212yes—
41C2×#13063316C2211yescharacteristic
42C2×#13063316C2212yes—
43C2×#13063315C2214yes—
44C2×#13063315C2214yes—
45C2×#13063315C2214yes—
46#125×D43C22132yescomplemented
47C2×#13063314C2211yescharacteristic
48C2×#13063310C2214yes—
49C2×#13063310C2214yes—
50C2×#13063310C2214yes—
51C2×#13063310C2214yes—
52C2×#13063310C2212yes—
53C2×#13063305C2212yes—
54C2×#13063303C2214yes—
55C2×#13063303C2214yes—
56C2×#13063301C2212yes—
57C2×#13063301C2212yes—
58C2×#13063301C2212yes—
59C2×#13063301C2211yescharacteristic
60C2×#13063301C2212yes—
61C2×#13063300C2212yes—
62C2×#13063300C2214yes—
63C2×#13063300C2211yescharacteristic
64#14583381C22132yescomplemented
65C4×#10621902C22116yescomplemented
66C2×Q8×Dic43C2211yescharacteristic
67C2×Q8×Dic43C2212yes—
68C2×#13063290C2212yes—
69C2×C4×D172C2211yescharacteristic
70C2×C4×D172C2212yes—
71C2×C4×D172C2212yes—
72C2×C4×D172C2214yes—
73C2×C4×D172C2212yes—
74C2×C4×D172C2211yescharacteristic
75C2×C4×D172C2212yes—
76C2×#13063287C2211yescharacteristic
77C2×#13063287C2212yes—
78C2×#13063287C2214yes—
79C2×#13063283C2212yes—
80C2×#13063283C2211yescharacteristic
81C2×#13063283C2212yes—
82C2×#13063282C2214yes—
83C2×#13063282C2212yes—
84C2×#13063282C2214yes—
85C2×C4⋊C4×D43C2214yes—
86C2×C4⋊C4×D43C2212yes—
87C2×C4⋊C4×D43C2214yes—
88C2×C4⋊C4×D43C2212yes—
89C2×C4⋊C4×D43C2212yes—
90C2×C42×D43C2212yes—
91C2×C42×D43C2211yescharacteristic
92C43×#557C22116yescomplemented
93C2×C4⋊Q8×C43C2211yescharacteristic
94C2×C4⋊Q8×C43C2212yes—
95C2×#125×C43C2214yes—
96C2×#125×C43C2212yes—
97C2×C4×Q8×C43C2211yescharacteristic
98C2×C4×Q8×C43C2212yes—
99C2×C4×Q8×C43C2212yes—
100C2×C4×Q8×C43C2211yescharacteristic
101C2×#10621902—28no—
102C2×#10621902—216no—
103C2×#10621902C2318yes—
104C2×#10621902C23116yes—
105C22×Dic86C2312yes—
106C22×D172C2312yes—
107C22×D172C2314yes—
108C22×D172C2311yescharacteristic
109C22×D172C2312yes—
110C22×D172C2311yescharacteristic
111C22×C4×D43C2312yes—
112C22×C4×D43C2312yes—
113C22×C4×D43C2311yescharacteristic
114C22×C4×D43C2311yescharacteristic
115C22×C4×D43C2314yes—
116C22×C4×D43C2312yes—
117C22×C4×D43C2312yes—
118C22×C4×D43C2311yescharacteristic
119C22×C4×D43C2314yes—
120C22×C4×D43C2314yes—
121#13063325C2318yes—
122#13063320C23116yes—
123#13063320C23132yes—
124#13063320C23132yes—
125#13063319C23132yes—
126#13063317C23116yes—
127#13063317C23116yes—
128#13063316C2318yes—
129#13063316C23116yes—
130#13063315C23132yes—
131#13063315C23132yes—
132#13063315C23132yes—
133#13063314C2318yes—
134#13063310C23132yes—
135#13063310C23132yes—
136#13063310C23132yes—
137#13063310C23132yes—
138#13063310C23116yes—
139#13063305C23116yes—
140#13063303C23132yes—
141#13063303C23132yes—
142#13063301C23116yes—
143#13063301C23116yes—
144#13063301C23116yes—
145#13063301C2318yes—
146#13063301C23116yes—
147#13063300C23116yes—
148#13063300C23132yes—
149#13063300C2318yes—
150Q8×Dic43C2318yes—
151Q8×Dic43C23116yes—
152#13063290C23116yes—
153C4×D172C23116yes—
154C4×D172C2318yes—
155C4×D172C23116yes—
156C4×D172C2318yes—
157C4×D172C23116yes—
158C4×D172C23116yes—
159C4×D172C23132yes—
160#13063287C23132yes—
161#13063287C2318yes—
162#13063287C23116yes—
163#13063283C23116yes—
164#13063283C2318yes—
165#13063283C23116yes—
166#13063282C23132yes—
167#13063282C23132yes—
168#13063282C23116yes—
169C2×C4⋊Dic43C2311yescharacteristic
170C2×C4⋊Dic43C2312yes—
171C2×C4⋊Dic43C2312yes—
172C2×C4⋊Dic43C2312yes—
173C2×C4⋊Dic43C2314yes—
174C2×C4⋊Dic43C2311yescharacteristic
175C2×C4⋊Dic43C2312yes—
176C2×Dic43⋊C4C2314yes—
177C2×Dic43⋊C4C2312yes—
178C2×Dic43⋊C4C2314yes—
179C2×Dic43⋊C4C2314yes—
180C2×Dic43⋊C4C2314yes—
181C2×Dic43⋊C4C2314yes—
182C2×Dic43⋊C4C2312yes—
183C2×Dic43⋊C4C2314yes—
184C4⋊C4×D43C23132yes—
185C4⋊C4×D43C23116yes—
186C4⋊C4×D43C23116yes—
187C4⋊C4×D43C23116yes—
188C4⋊C4×D43C23132yes—
189C2×(C2×D43)⋊C4C2312yes—
190C2×(C2×D43)⋊C4C2312yes—
191C2×(C2×D43)⋊C4C2312yes—
192C2×(C2×D43)⋊C4C2314yes—
193C2×(C2×D43)⋊C4C2312yes—
194C2×(C2×D43)⋊C4C2314yes—
195C2×(C2×D43)⋊C4C2312yes—
196C2×(C2×D43)⋊C4C2312yes—
197C2×(C2×D43)⋊C4C2314yes—
198C2×(C2×D43)⋊C4C2314yes—
199C2×(C2×D43)⋊C4C2312yes—
200C2×(C2×D43)⋊C4C2312yes—
201C2×C4×Dic43C2311yescharacteristic
202C2×C4×Dic43C2312yes—
203C2×C4×Dic43C2311yescharacteristic
204C2×C4×Dic43C2311yescharacteristic
205C2×C4×Dic43C2312yes—
206C2×C4×Dic43C2314yes—
207C42×D43C23116yes—
208C42×D43C2318yes—
209C22×Q8×C43C2311yescharacteristic
210C22×Q8×C43C2311yescharacteristic
211C22×Q8×C43C2312yes—
212C4⋊Q8×C43C2318yes—
213C4⋊Q8×C43C23116yes—
214#125×C43C23132yes—
215#125×C43C23116yes—
216C4×Q8×C43C23116yes—
217C4×Q8×C43C23116yes—
218C4×Q8×C43C2318yes—
219C4×Q8×C43C2318yes—
220C2×C4⋊C4×C43C2311yescharacteristic
221C2×C4⋊C4×C43C2311yescharacteristic
222C2×C4⋊C4×C43C2314yes—
223C2×C4⋊C4×C43C2312yes—
224C2×C4⋊C4×C43C2312yes—
225C2×C4⋊C4×C43C2312yes—
226C2×C4⋊C4×C43C2314yes—
227C2×C4⋊C4×C43C2314yes—
228C2×C4⋊C4×C43C2312yes—
229C2×C42×C43C2312yes—
230C2×C42×C43C2314yes—
231C2×C42×C43C2311yescharacteristic
232C2×C42×C43C2312yes—
233C23×D43C2411yescharacteristic
234C23×D43C2412yes—
235C23×D43C2412yes—
236C2×Q8×C43—24no—
237C2×Q8×C43—28no—
238C2×Q8×C43—24no—
239C2×Q8×C43C2414yes—
240C2×Q8×C43C2418yes—
241C2×Q8×C43C2414yes—
242C22×C4×C43C2412yes—
243C22×C4×C43C2412yes—
244C22×C4×C43C2411yescharacteristic
245C22×C4×C43C2412yes—
246C22×C4×C43C2412yes—
247C22×C4×C43C2414yes—
248C22×C4×C43C2411yescharacteristic
249C22×C4×C43C2411yescharacteristic
250C22×Dic43C2411yescharacteristic
251C22×Dic43C2411yescharacteristic
252C22×Dic43C2411yescharacteristic
253C22×Dic43C2412yes—
254C22×Dic43C2414yes—
255C22×Dic43C2412yes—
256#10621902—232no—
257#10621902—264no—
258C2×D172—24no—
259C2×D172—28no—
260C2×D172—216no—
261C2×D172—44no—
262C2×D172#4118yes—
263C2×D172C24116yes—
264C2×D172C2418yes—
265C2×D172C2414yes—
266C2×D172C2418yes—
267C2×D172C2414yes—
268C2×C4×D43—24no—
269C2×C4×D43—28no—
270C2×C4×D43—28no—
271C2×C4×D43—24no—
272C2×C4×D43—28no—
273C2×C4×D43—216no—
274C2×C4×D43—48no—
275C2×C4×D43—44no—
276C2×C4×D43—48no—
277C2×C4×D43—42no—
278C2×C4×D43C2418yes—
279C2×C4×D43C2418yes—
280C2×C4×D43C2414yes—
281C2×C4×D43C2414yes—
282C2×C4×D43C24116yes—
283C2×C4×D43C2418yes—
284C2×C4×D43C2418yes—
285C2×C4×D43C2414yes—
286C2×C4×D43C24116yes—
287C2×C4×D43C24116yes—
288C2×Dic86—44no—
289C2×Dic86C2418yes—
290C4⋊C4×C43C2414yes—
291C4⋊C4×C43C2414yes—
292C4⋊C4×C43C24116yes—
293C4⋊C4×C43C2418yes—
294C4⋊C4×C43C2418yes—
295C4⋊C4×C43C2418yes—
296C4⋊C4×C43C24116yes—
297C4⋊C4×C43C24116yes—
298C4⋊C4×C43C2418yes—
299C42×C43C2418yes—
300C42×C43C24116yes—
301C42×C43C2414yes—
302C42×C43C2418yes—
303(C2×D43)⋊C4C2418yes—
304(C2×D43)⋊C4C2418yes—
305(C2×D43)⋊C4C2418yes—
306(C2×D43)⋊C4C24116yes—
307(C2×D43)⋊C4C2418yes—
308(C2×D43)⋊C4C24116yes—
309(C2×D43)⋊C4C2418yes—
310(C2×D43)⋊C4C2418yes—
311(C2×D43)⋊C4C24116yes—
312(C2×D43)⋊C4C24116yes—
313(C2×D43)⋊C4C2418yes—
314(C2×D43)⋊C4C2418yes—
315C4⋊Dic43C2414yes—
316C4⋊Dic43C2418yes—
317C4⋊Dic43C2418yes—
318C4⋊Dic43C2418yes—
319C4⋊Dic43C24116yes—
320C4⋊Dic43C2414yes—
321C4⋊Dic43C2418yes—
322Dic43⋊C4C24116yes—
323Dic43⋊C4C2418yes—
324Dic43⋊C4C24116yes—
325Dic43⋊C4C24116yes—
326Dic43⋊C4C24116yes—
327Dic43⋊C4C24116yes—
328Dic43⋊C4C2418yes—
329Dic43⋊C4C24116yes—
330C4×Dic43C2414yes—
331C4×Dic43C2418yes—
332C4×Dic43C2414yes—
333C4×Dic43C2414yes—
334C4×Dic43C2418yes—
335C4×Dic43C24116yes—
336C23×C43C2511yescharacteristic
337C22×D43—24no—
338C22×D43—24no—
339C22×D43—22no—
340C22×D43—24no—
341C22×D43—22no—
342C22×D43—24no—
343C22×D43—24no—
344C22×D43—22no—
345C22×D43C2×#4118yes—
346C22×D43C2512yes—
347C22×D43C2514yes—
348C22×D43C2514yes—
349Q8×C43—28no—
350Q8×C43—216no—
351Q8×C43—28no—
352C2×C4×C43—24no—
353C2×C4×C43—28no—
354C2×C4×C43—24no—
355C2×C4×C43—22no—
356C2×C4×C43—24no—
357C2×C4×C43—24no—
358C2×C4×C43C2×#4114yes—
359C2×C4×C432−1+414yes—
360C2×C4×C43C2514yes—
361C2×C4×C43C2518yes—
362C2×C4×C43C2514yes—
363C2×C4×C43C2512yes—
364C2×C4×C43C2514yes—
365C2×C4×C43C2514yes—
366C2×C4×C43C2512yes—
367C2×C4×C43C2512yes—
368C2×Dic43—22no—
369C2×Dic43—24no—
370C2×Dic43—22no—
371C2×Dic43—24no—
372C2×Dic43—28no—
373C2×Dic43—22no—
374C2×Dic43C2512yes—
375C2×Dic43C2512yes—
376C2×Dic43C2512yes—
377C2×Dic43C2514yes—
378C2×Dic43C2518yes—
379C2×Dic43C2514yes—
380D172—232no—
381D172—216no—
382D172—28no—
383D172—48no—
384D172C2×#41116yes—
385C4×D43—216no—
386C4×D43—232no—
387C4×D43—28no—
388C4×D43—216no—
389C4×D43—216no—
390C4×D43—28no—
391C4×D43—416no—
392C4×D43—416no—
393C4×D43—44no—
394C4×D43—48no—
395Dic86—48no—
396C2×#3515—431nomaximal, Sylow
397C22×C43C22×#4112yes—
398C22×C43C2×2−1+412yes—
399C22×C43#58512yes—
400C22×C43C2611yescharacteristic
401C2×D43—24no—
402C2×D43—24no—
403C2×D43—216no—
404C2×D43—22no—
405C2×D43—24no—
406C2×D43—22no—
407C2×D43—24no—
408C2×D43—24no—
409C2×D43—22no—
410C2×D43—44no—
411C2×D43—48no—
412C2×D43C22×#4118yes—
413C4×C43—24no—
414C4×C43—28no—
415C4×C43—24no—
416C4×C43—22no—
417C4×C43—24no—
418C4×C43—24no—
419C4×C43C22×#4114yes—
420C4×C43C2×2−1+414yes—
421Dic43—22no—
422Dic43—24no—
423Dic43—22no—
424Dic43—24no—
425Dic43—28no—
426Dic43—22no—
427#3515—4332no—
428C2×#557D4311yescharacteristic, complemented
429C2×#554—431no—
430C2×#554—431no—
431C2×#553—432no—
432C2×#552—434no—
433C2×#552—432no—
434C2×#552—432no—
435C2×#547—431no—
436C2×#547—432no—
437C2×#541—432no—
438C2×#539—434no—
439C2×#533—431no—
440C2×#529—431no—
441C2×#529—432no—
442C22×#125—432no—
443C2×#520—432no—
444C2×C4×#41—431no—
445C2×C43#351514yescomplemented
446C2×C43C23×#4111yescharacteristic
447C2×C43C22×2−1+411yescharacteristic
448C2×C43C2×#58511yescharacteristic
449D43—28no—
450D43—42no—
451D43—44no—
452C22×#41—431no—
453C22×#41—432no—
454#557C2×D43116yescomplemented
455#554—4316no—
456#554—4316no—
457#553—4332no—
458#552—4364no—
459#552—4332no—
460#552—4332no—
461#547—4316no—
462#547—4332no—
463#541—4332no—
464#539—4364no—
465#533—4316no—
466C2×C4⋊Q8—431no—
467C2×C4⋊Q8C2×D4311yescharacteristic
468C2×C4⋊Q8C2×D4312yes—
469#529—4332no—
470#529—4316no—
471C2×#126—434no—
472C2×#126—432no—
473C2×#126—434no—
474C2×#126—434no—
475C2×#125—4332no—
476C2×#125—431no—
477C2×#125—432no—
478C2×#125—434no—
479C2×#125—434no—
480C2×#125—434no—
481C2×#125—432no—
482C2×#125—432no—
483C2×#125C2×D4312yes—
484C2×#125C2×D4314yes—
485C2×#124—431no—
486C2×#123—432no—
487C2×#123—434no—
488C2×#123—434no—
489C2×#123—434no—
490C2×#123—434no—
491C2×C22⋊Q8—431no—
492C2×C22⋊Q8—432no—
493C2×C22⋊Q8—432no—
494C2×C22⋊Q8—432no—
495C2×C22⋊Q8—432no—
496C2×C22⋊Q8—434no—
497C2×C22⋊Q8—434no—
498C2×C22⋊Q8—432no—
499C2×#121—432no—
500C2×#121—431no—
501C2×#121—434no—
502#520—4332no—
503C4×#41—4316no—
504C2×C4×Q8—431no—
505C2×C4×Q8—432no—
506C2×C4×Q8—432no—
507C2×C4×Q8C2×D4311yescharacteristic
508C2×C4×Q8C2×D4312yes—
509C2×C4×Q8C2×D4312yes—
510C2×C4×Q8C2×D4311yescharacteristic
511C2×C4×D4—431no—
512C2×C4×D4—432no—
513C2×C4×D4—434no—
514C2×C4×D4—431no—
515C2×C4×D4—432no—
516C2×C4×D4—434no—
517C2×C4×D4—432no—
518C2×C4×D4—432no—
519C2×C4×D4—431no—
520C2×C4×D4—432no—
521C2×#117—431no—
522C2×#117—432no—
523C2×#117—432no—
524C2×#117—432no—
525C2×#117—434no—
526C2×#117—434no—
527C22×C4⋊C4—434no—
528C22×C4⋊C4—432no—
529C22×C4⋊C4—432no—
530C22×C4⋊C4—434no—
531C22×C4⋊C4—432no—
532C22×C42—432no—
533C22×C42—431no—
534C43C2×#351511yescharacteristic, complemented, Sylow
535C2×#41—438no—
536C2×#41—4316no—
537C2×#41—868no—
538C2×#41—8616no—
539C22×Q8—432no—
540C22×Q8C22×D4311yescharacteristic
541C22×Q8C22×D4312yes—
542C22×Q8C22×D4311yescharacteristic
543C22×D4—431no—
544C22×D4—431no—
545C22×D4—432no—
546C22×D4—434no—
547C22×D4—432no—
548C23×C4—434no—
549C23×C4—432no—
550C23×C4—432no—
551C23×C4—432no—
552C23×C4—431no—
553C23×C4—431no—
554C23×C4—434no—
555C23×C4—432no—
556C23×C4—434no—
557C23×C4—431no—
558C4⋊Q8—438no—
559C4⋊Q8C22×D4318yes—
560C4⋊Q8C22×D43116yes—
561#126—4332no—
562#126—4316no—
563#126—4332no—
564#126—4332no—
565#125—438no—
566#125—4316no—
567#125—4332no—
568#125—4332no—
569#125—4332no—
570#125—4316no—
571#125—4316no—
572#125C22×D43116yes—
573#125C22×D43132yes—
574#124—438no—
575#123—4316no—
576#123—4332no—
577#123—4332no—
578#123—4332no—
579#123—4332no—
580C22⋊Q8—438no—
581C22⋊Q8—4316no—
582C22⋊Q8—4316no—
583C22⋊Q8—4316no—
584C22⋊Q8—4316no—
585C22⋊Q8—4316no—
586C22⋊Q8—4332no—
587C22⋊Q8—4332no—
588#121—4316no—
589#121—438no—
590#121—4332no—
591C4×Q8—438no—
592C4×Q8—4316no—
593C4×Q8—4316no—
594C4×Q8C22×D4318yes—
595C4×Q8C22×D43116yes—
596C4×Q8C22×D43116yes—
597C4×Q8C22×D4318yes—
598C4×D4—438no—
599C4×D4—4316no—
600C4×D4—4332no—
601C4×D4—438no—
602C4×D4—4316no—
603C4×D4—4332no—
604C4×D4—4316no—
605C4×D4—4316no—
606C4×D4—438no—
607C4×D4—4316no—
608#117—438no—
609#117—4316no—
610#117—4316no—
611#117—4316no—
612#117—4332no—
613#117—4332no—
614C2×C4⋊C4—434no—
615C2×C4⋊C4—432no—
616C2×C4⋊C4—431no—
617C2×C4⋊C4—432no—
618C2×C4⋊C4—432no—
619C2×C4⋊C4—434no—
620C2×C4⋊C4—432no—
621C2×C4⋊C4—434no—
622C2×C4⋊C4—434no—
623C2×C4⋊C4—434no—
624C2×C4⋊C4—434no—
625C2×C4⋊C4—432no—
626C2×C4⋊C4—431no—
627C2×C4⋊C4—432no—
628C2×C4⋊C4—434no—
629C2×C4⋊C4—4332no—
630C2×C4⋊C4—4316no—
631C2×C4⋊C4—4316no—
632C2×C4⋊C4—4332no—
633C2×C4⋊C4—4316no—
634C2×C4⋊C4C22×D4311yescharacteristic
635C2×C4⋊C4C22×D4311yescharacteristic
636C2×C4⋊C4C22×D4312yes—
637C2×C4⋊C4C22×D4314yes—
638C2×C4⋊C4C22×D4314yes—
639C2×C4⋊C4C22×D4312yes—
640C2×C4⋊C4C22×D4312yes—
641C2×C4⋊C4C22×D4312yes—
642C2×C4⋊C4C22×D4314yes—
643C2×C22⋊C4—432no—
644C2×C22⋊C4—432no—
645C2×C22⋊C4—432no—
646C2×C22⋊C4—432no—
647C2×C22⋊C4—434no—
648C2×C22⋊C4—432no—
649C2×C22⋊C4—432no—
650C2×C22⋊C4—434no—
651C2×C22⋊C4—434no—
652C2×C22⋊C4—434no—
653C2×C22⋊C4—432no—
654C2×C22⋊C4—432no—
655C2×C42—432no—
656C2×C42—431no—
657C2×C42—434no—
658C2×C42—431no—
659C2×C42—432no—
660C2×C42—431no—
661C2×C42—4316no—
662C2×C42—438no—
663C2×C42C22×D4314yes—
664C2×C42C22×D4312yes—
665C2×C42C22×D4312yes—
666C2×C42C22×D4311yescharacteristic
667C24—432no—
668C24—431no—
669C24—432no—
670#41—8632no—
671#41—8664no—
672C2×Q8—24no—
673C2×Q8—28no—
674C2×Q8—24no—
675C2×Q8—438no—
676C2×Q8—1724no—
677C2×Q8C23×D4314yes—
678C2×Q8C23×D4318yes—
679C2×Q8C23×D4314yes—
680C2×D4—438no—
681C2×D4—434no—
682C2×D4—434no—
683C2×D4—438no—
684C2×D4—4316no—
685C2×D4—438no—
686C2×D4—868no—
687C2×D4—8616no—
688C2×D4—864no—
689C2×D4—1724no—
690C22×C4—431no—
691C22×C4—431no—
692C22×C4—431no—
693C22×C4—432no—
694C22×C4—434no—
695C22×C4—432no—
696C22×C4—438no—
697C22×C4—438no—
698C22×C4—434no—
699C22×C4—434no—
700C22×C4—4316no—
701C22×C4—438no—
702C22×C4—438no—
703C22×C4—434no—
704C22×C4—4316no—
705C22×C4—4316no—
706C22×C4—8616no—
707C22×C4—868no—
708C22×C4—868no—
709C22×C4—864no—
710C22×C4—868no—
711C22×C4—864no—
712C22×C4—1724no—
713C22×C4—1728no—
714C22×C4—1728no—
715C22×C4—1722no—
716C22×C4C23×D4312yes—
717C22×C4C23×D4311yescharacteristic
718C22×C4C23×D4314yes—
719C22×C4C23×D4312yes—
720C22×C4C23×D4312yes—
721C22×C4C23×D4312yes—
722C22×C4C23×D4311yescharacteristic
723C22×C4C23×D4311yescharacteristic
724C4⋊C4—4316no—
725C4⋊C4—438no—
726C4⋊C4—434no—
727C4⋊C4—438no—
728C4⋊C4—438no—
729C4⋊C4—4316no—
730C4⋊C4—438no—
731C4⋊C4—4316no—
732C4⋊C4—4316no—
733C4⋊C4—4316no—
734C4⋊C4—4316no—
735C4⋊C4—438no—
736C4⋊C4—434no—
737C4⋊C4—438no—
738C4⋊C4—4316no—
739C4⋊C4C23×D4314yes—
740C4⋊C4C23×D4314yes—
741C4⋊C4C23×D4318yes—
742C4⋊C4C23×D43116yes—
743C4⋊C4C23×D43116yes—
744C4⋊C4C23×D4318yes—
745C4⋊C4C23×D4318yes—
746C4⋊C4C23×D4318yes—
747C4⋊C4C23×D43116yes—
748C22⋊C4—438no—
749C22⋊C4—438no—
750C22⋊C4—438no—
751C22⋊C4—438no—
752C22⋊C4—4316no—
753C22⋊C4—438no—
754C22⋊C4—438no—
755C22⋊C4—4316no—
756C22⋊C4—4316no—
757C22⋊C4—4316no—
758C22⋊C4—438no—
759C22⋊C4—438no—
760C42—434no—
761C42—438no—
762C42—434no—
763C42—434no—
764C42—438no—
765C42—4316no—
766C42C23×D4318yes—
767C42C23×D4314yes—
768C42C23×D43116yes—
769C42C23×D4318yes—
770C23—438no—
771C23—434no—
772C23—432no—
773C23—434no—
774C23—864no—
775C23—864no—
776C23—862no—
777C23—864no—
778C23—862no—
779C23—864no—
780C23—864no—
781C23—862no—
782C23C24×D4311yescharacteristic
783Q8—28no—
784Q8—216no—
785Q8—28no—
786Q8—1728no—
787D4—4316no—
788D4—8616no—
789D4—8632no—
790D4—868no—
791D4—1728no—
792C2×C4—28no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—432no—
799C2×C4—432no—
800C2×C4—432no—
801C2×C4—434no—
802C2×C4—438no—
803C2×C4—434no—
804C2×C4—8616no—
805C2×C4—8632no—
806C2×C4—862no—
807C2×C4—864no—
808C2×C4—862no—
809C2×C4—864no—
810C2×C4—862no—
811C2×C4—868no—
812C2×C4—868no—
813C2×C4—8616no—
814C2×C4—8616no—
815C2×C4—868no—
816C2×C4—1728no—
817C2×C4—17216no—
818C2×C4—17216no—
819C2×C4—1724no—
820C2×C4#41×D4314yes—
821C2×C4#1306337314yes—
822C2×C4C24×D4314yes—
823C2×C4C24×D4312yes—
824C2×C4C24×D4314yes—
825C2×C4C24×D4318yes—
826C2×C4C24×D4314yes—
827C2×C4C24×D4314yes—
828C2×C4C24×D4312yes—
829C2×C4C24×D4312yes—
830C22—438no—
831C22—8616no—
832C22—864no—
833C22—864no—
834C22—862no—
835C22—864no—
836C22—862no—
837C22—864no—
838C22—864no—
839C22—862no—
840C22—1724no—
841C22—1728no—
842C22C2×#41×D4312yes—
843C22C2×#1306337312yes—
844C22#1458373612yes—
845C22C25×D4311yescharacteristic
846C4—24no—
847C4—28no—
848C4—24no—
849C4—24no—
850C4—24no—
851C4—22no—
852C4—862no—
853C4—864no—
854C4—862no—
855C4—864no—
856C4—862no—
857C4—868no—
858C4C2×#41×D4314yes—
859C4C2×#1306337314yes—
860C2—868no—
861C2—1722no—
862C2—1724no—
863C2#1914857214yesdirect product factor
864C2C22×#41×D4311yescharacteristic
865C2C22×#1306337311yescharacteristic
866C2C2×#1458373611yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#557C2
socleC23×C43C25
hypercenterC2×#557D43
hypocenterC43C2×#3515
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #19148572C2direct (N × H)
2. C2×#14583609C2semidirect
3. C2×#14583609C2semidirect
4. C2×#14583602C2semidirect
5. C2×#14583590C2semidirect
6. C2×#14583590C2semidirect
7. C2×#14583581C2semidirect
8. C2×#14583552C2semidirect
9. C2×#14583552C2semidirect
10. C2×#14583510C2semidirect
11. C2×#14583497C2semidirect
12. C2×#14583454C2semidirect
13. C2×#14583436C2semidirect
14. C2×#14583436C2semidirect
15. C2×#125×D43C2semidirect
16. C2×#14583381C2semidirect
17. C2×C4×#10621902C2semidirect
18. C2×C43×#557C2semidirect
21. #14583609C22semidirect
22. #14583609C22semidirect
23. #14583602C22semidirect
24. #14583590C22semidirect
25. #14583590C22semidirect
26. #14583581C22semidirect
27. #14583552C22semidirect
28. #14583552C22semidirect
29. #14583510C22semidirect
30. #14583497C22semidirect
31. #14583454C22semidirect
33. #14583436C22semidirect
34. #14583436C22semidirect
46. #125×D43C22semidirect
64. #14583381C22semidirect
65. C4×#10621902C22semidirect
92. C43×#557C22semidirect
428. C2×#557D43semidirect
445. C2×C43#3515semidirect
454. #557C2×D43semidirect
534. C43C2×#3515semidirect
863. C2#19148572direct (N × H)

Maximal subgroups

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

subgroupindex
#191485722
C2×#145836092
C2×#145836022
C2×#145835902
C2×#145835812
C2×#145835522
C2×#145835102
C2×#145834972
C2×#145834542
C2×#145834362
C2×#125×D432
C2×#145833812
C2×C4×#106219022
C2×C43×#5572
C2×#351543