Finite Group Databasebeta

← C2×#19148576 #26004710

Subgroups — C2×#19148576 #26004710

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#19148576C2132yesmaximal, direct product factor
2C2×#14583627C211yesmaximal, characteristic, complemented
3C2×#14583610C211yesmaximal, characteristic, complemented
4C2×#14583599C212yesmaximal, complemented
5C2×#14583587C212yesmaximal, complemented
6C2×#14583584C212yesmaximal, complemented
7C2×#14583583C214yesmaximal, complemented
8C2×#14583554C211yesmaximal, characteristic, complemented
9C2×#14583551C212yesmaximal, complemented
10C2×#14583509C212yesmaximal, complemented
11C2×#14583495C214yesmaximal, complemented
12C2×#14583454C211yesmaximal, characteristic, complemented
13C2×#14583431C211yesmaximal, characteristic, complemented
14C2×#14583431C212yesmaximal, complemented
15C2×#125×D43C212yesmaximal, complemented
16C2×#14583380C212yesmaximal, complemented
17C2×C4×#10621902C211yesmaximal, characteristic, complemented
18C2×C43×#554C211yesmaximal, characteristic, complemented
19C22×#10621902C2211yescharacteristic
20C22×#10621898C2212yes—
21#14583627C22116yescomplemented
22#14583610C22116yescomplemented
23#14583599C22132yescomplemented
24#14583587C22132yescomplemented
25#14583584C22132yescomplemented
26#14583583C22164yescomplemented
27#14583554C22116yescomplemented
28#14583551C22132yescomplemented
29#14583509C22132yescomplemented
30#14583495C22164yescomplemented
31#14583454C22116yescomplemented
32C2×#13063325C2211yescharacteristic
33C2×#13063323C2212yes—
34#14583431C22116yescomplemented
35#14583431C22132yescomplemented
36C2×#13063320C2214yes—
37C2×#13063318C2212yes—
38C2×#13063318C2214yes—
39C2×#13063318C2214yes—
40C2×#13063317C2212yes—
41C2×#13063316C2211yescharacteristic
42C2×#13063316C2212yes—
43C2×#13063316C2214yes—
44C2×#13063316C2212yes—
45C2×#13063315C2214yes—
46C2×#13063315C2214yes—
47C2×#13063315C2214yes—
48#125×D43C22132yescomplemented
49C2×#13063312C2211yescharacteristic
50C2×#13063310C2214yes—
51C2×#13063308C2214yes—
52C2×#13063307C2214yes—
53C2×#13063307C2214yes—
54C2×#13063307C2212yes—
55C2×#13063305C2212yes—
56C2×#13063305C2211yescharacteristic
57C2×#13063305C2212yes—
58C2×#13063304C2212yes—
59C2×#13063301C2214yes—
60C2×#13063301C2212yes—
61C2×#13063298C2214yes—
62C2×#13063296C2212yes—
63C2×#13063296C2211yescharacteristic
64#14583380C22132yescomplemented
65C4×#10621902C22116yescomplemented
66C2×Q8×Dic43C2211yescharacteristic
67C2×Q8×Dic43C2212yes—
68C2×C4×Dic86C2212yes—
69C2×C4×Dic86C2211yescharacteristic
70C2×#13063290C2212yes—
71C2×#13063290C2212yes—
72C2×C4×D172C2211yescharacteristic
73C2×C4×D172C2212yes—
74C2×#13063287C2211yescharacteristic
75C2×#13063287C2212yes—
76C2×#13063287C2212yes—
77C2×C4×C22⋊D43C2214yes—
78C2×C4×C22⋊D43C2214yes—
79C2×C4×C22⋊D43C2212yes—
80C2×#13063284C2212yes—
81C2×#13063284C2214yes—
82C2×#13063283C2212yes—
83C2×#13063283C2211yescharacteristic
84C2×#13063283C2214yes—
85C2×#13063283C2212yes—
86C2×C4⋊C4×D43C2214yes—
87C2×C4⋊C4×D43C2214yes—
88C2×C4⋊C4×D43C2212yes—
89C2×C4⋊C4×D43C2212yes—
90C2×C42×D43C2212yes—
91C2×C42×D43C2211yescharacteristic
92C43×#554C22116yescomplemented
93C2×C4⋊Q8×C43C2211yescharacteristic
94C2×#125×C43C2212yes—
95C2×C22⋊Q8×C43C2212yes—
96C2×C22⋊Q8×C43C2214yes—
97C2×C4×Q8×C43C2211yescharacteristic
98C2×C4×D4×C43C2211yescharacteristic
99C2×C4×D4×C43C2212yes—
100C22×C4⋊C4×C43C2212yes—
101C2×#10621902—28no—
102C2×#10621902C2318yes—
103C2×#10621898—216no—
104C2×#10621898C23116yes—
105C22×Dic86C2312yes—
106C22×Dic86C2311yescharacteristic
107C22×D172C2312yes—
108C22×D172C2311yescharacteristic
109C22×C22⋊D43C2314yes—
110C22×C22⋊D43C2312yes—
111C22×C4×D43C2312yes—
112C22×C4×D43C2312yes—
113C22×C4×D43C2311yescharacteristic
114C22×C4×D43C2311yescharacteristic
115C22×C4×D43C2314yes—
116C22×C4×D43C2312yes—
117C22×C4×D43C2311yescharacteristic
118C22×C4×D43C2314yes—
119#13063325C2318yes—
120#13063323C23116yes—
121#13063320C23132yes—
122#13063318C23116yes—
123#13063318C23132yes—
124#13063318C23132yes—
125#13063317C23116yes—
126#13063316C23132yes—
127#13063316C23116yes—
128#13063316C2318yes—
129#13063316C23116yes—
130#13063315C23132yes—
131#13063315C23132yes—
132#13063315C23132yes—
133#13063312C2318yes—
134#13063310C23132yes—
135#13063308C23132yes—
136#13063307C23132yes—
137#13063307C23132yes—
138#13063307C23116yes—
139#13063305C23116yes—
140#13063305C2318yes—
141#13063305C23116yes—
142#13063304C23116yes—
143#13063301C23132yes—
144#13063301C23116yes—
145#13063298C23132yes—
146#13063296C23116yes—
147#13063296C2318yes—
148Q8×Dic43C23116yes—
149Q8×Dic43C2318yes—
150C4×Dic86C23116yes—
151C4×Dic86C2318yes—
152#13063290C23116yes—
153#13063290C23116yes—
154C4×D172C2318yes—
155C4×D172C23116yes—
156#13063287C23116yes—
157#13063287C2318yes—
158#13063287C23116yes—
159C4×C22⋊D43C23132yes—
160C4×C22⋊D43C23116yes—
161C4×C22⋊D43C23132yes—
162#13063284C23132yes—
163#13063284C23116yes—
164#13063283C23116yes—
165#13063283C23132yes—
166#13063283C2318yes—
167#13063283C23116yes—
168C2×C4⋊Dic43C2312yes—
169C2×C4⋊Dic43C2311yescharacteristic
170C2×C4⋊Dic43C2312yes—
171C2×C4⋊Dic43C2314yes—
172C2×C4⋊Dic43C2312yes—
173C2×C4⋊Dic43C2311yescharacteristic
174C2×C4⋊Dic43C2312yes—
175C2×C4⋊Dic43C2314yes—
176C2×C4⋊Dic43C2312yes—
177C2×Dic43⋊C4C2312yes—
178C2×Dic43⋊C4C2314yes—
179C2×Dic43⋊C4C2314yes—
180C2×Dic43⋊C4C2314yes—
181C2×Dic43⋊C4C2314yes—
182C2×Dic43⋊C4C2314yes—
183C2×Dic43⋊C4C2312yes—
184C2×Dic43⋊C4C2314yes—
185C4⋊C4×D43C23116yes—
186C4⋊C4×D43C23132yes—
187C4⋊C4×D43C23116yes—
188C4⋊C4×D43C23132yes—
189C2×C22⋊Dic43C2312yes—
190C2×C22⋊Dic43C2312yes—
191C2×C22⋊Dic43C2312yes—
192C2×C22⋊Dic43C2314yes—
193C2×(C2×D43)⋊C4C2312yes—
194C2×(C2×D43)⋊C4C2314yes—
195C2×(C2×D43)⋊C4C2312yes—
196C2×(C2×D43)⋊C4C2312yes—
197C2×(C2×D43)⋊C4C2314yes—
198C2×(C2×D43)⋊C4C2312yes—
199C2×C4×Dic43C2311yescharacteristic
200C2×C4×Dic43C2312yes—
201C2×C4×Dic43C2311yescharacteristic
202C2×C4×Dic43C2311yescharacteristic
203C2×C4×Dic43C2312yes—
204C2×C4×Dic43C2314yes—
205C2×C4×Dic43C2314yes—
206C2×C4×Dic43C2312yes—
207C42×D43C23116yes—
208C42×D43C2318yes—
209C22×Q8×C43C2311yescharacteristic
210C22×Q8×C43C2312yes—
211C22×D4×C43C2311yescharacteristic
212C23×C4×C43C2312yes—
213C23×C4×C43C2314yes—
214C4⋊Q8×C43C2318yes—
215#125×C43C23116yes—
216C22⋊Q8×C43C23132yes—
217C22⋊Q8×C43C23116yes—
218C4×Q8×C43C2318yes—
219C4×D4×C43C2318yes—
220C4×D4×C43C23116yes—
221C2×C4⋊C4×C43C2311yescharacteristic
222C2×C4⋊C4×C43C2314yes—
223C2×C4⋊C4×C43C2312yes—
224C2×C4⋊C4×C43C23116yes—
225C2×C4⋊C4×C43C2311yescharacteristic
226C2×C4⋊C4×C43C2312yes—
227C2×C4⋊C4×C43C2312yes—
228C2×C4⋊C4×C43C2314yes—
229C2×C22⋊C4×C43C2314yes—
230C2×C22⋊C4×C43C2312yes—
231C2×C42×C43C2312yes—
232C2×C42×C43C2311yescharacteristic
233C24×C43C2412yes—
234C23×D43C2411yescharacteristic
235C23×D43C2412yes—
236C2×Q8×C43—24no—
237C2×Q8×C43—44no—
238C2×Q8×C43C2414yes—
239C2×Q8×C43C2418yes—
240C2×D4×C43—24no—
241C2×D4×C43C2414yes—
242C22×C4×C43—28no—
243C22×C4×C43—48no—
244C22×C4×C43C2412yes—
245C22×C4×C43C2411yescharacteristic
246C22×C4×C43C2412yes—
247C22×C4×C43C2412yes—
248C22×C4×C43C2414yes—
249C22×C4×C43C2418yes—
250C22×C4×C43C24116yes—
251C22×C4×C43C2411yescharacteristic
252C22×C4×C43C2411yescharacteristic
253C2×C22⋊D43—216no—
254C2×C22⋊D43—44no—
255C2×C22⋊D43C24116yes—
256C2×C22⋊D43C2418yes—
257C22×Dic43C2411yescharacteristic
258C22×Dic43C2411yescharacteristic
259C22×Dic43C2411yescharacteristic
260C22×Dic43C2412yes—
261C22×Dic43C2412yes—
262C22×Dic43C2414yes—
263C22×Dic43C2412yes—
264#10621902—232no—
265#10621898—264no—
266C2×D172—28no—
267C2×D172#4118yes—
268C2×D172C2418yes—
269C2×D172C2414yes—
270C2×C4×D43—24no—
271C2×C4×D43—28no—
272C2×C4×D43—24no—
273C2×C4×D43—216no—
274C2×C4×D43—28no—
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×D43C2414yes—
285C2×C4×D43C24116yes—
286C2×Dic86—28no—
287C2×Dic86—24no—
288C2×Dic86C2418yes—
289C2×Dic86C2414yes—
290C4⋊C4×C43C2414yes—
291C4⋊C4×C43C24116yes—
292C4⋊C4×C43C2418yes—
293C4⋊C4×C43C2414yes—
294C4⋊C4×C43C2418yes—
295C4⋊C4×C43C2418yes—
296C4⋊C4×C43C24116yes—
297C22⋊C4×C43C24116yes—
298C22⋊C4×C43C2418yes—
299C42×C43C2418yes—
300C42×C43C2414yes—
301C22⋊Dic43C2418yes—
302C22⋊Dic43C2418yes—
303C22⋊Dic43C2418yes—
304C22⋊Dic43C24116yes—
305(C2×D43)⋊C4C2418yes—
306(C2×D43)⋊C4C24116yes—
307(C2×D43)⋊C4C2418yes—
308(C2×D43)⋊C4C2418yes—
309(C2×D43)⋊C4C24116yes—
310(C2×D43)⋊C4C2418yes—
311C4⋊Dic43C2418yes—
312C4⋊Dic43C2414yes—
313C4⋊Dic43C2418yes—
314C4⋊Dic43C24116yes—
315C4⋊Dic43C2418yes—
316C4⋊Dic43C2414yes—
317C4⋊Dic43C2418yes—
318C4⋊Dic43C24116yes—
319C4⋊Dic43C2418yes—
320Dic43⋊C4C2418yes—
321Dic43⋊C4C24116yes—
322Dic43⋊C4C24116yes—
323Dic43⋊C4C24116yes—
324Dic43⋊C4C24116yes—
325Dic43⋊C4C24116yes—
326Dic43⋊C4C2418yes—
327Dic43⋊C4C24116yes—
328C4×Dic43C2414yes—
329C4×Dic43C2418yes—
330C4×Dic43C2414yes—
331C4×Dic43C2414yes—
332C4×Dic43C2418yes—
333C4×Dic43C24116yes—
334C4×Dic43C24116yes—
335C4×Dic43C2418yes—
336C23×C43—24no—
337C23×C43—24no—
338C23×C43—24no—
339C23×C43C2514yes—
340C23×C43C2511yescharacteristic
341C22×D43—24no—
342C22×D43—24no—
343C22×D43—22no—
344C22×D43—22no—
345C22×D43—22no—
346C22×D43C2×#4118yes—
347C22×D43C2512yes—
348C22×D43C2514yes—
349Q8×C43—28no—
350Q8×C43—48no—
351D4×C43—28no—
352C2×C4×C43—24no—
353C2×C4×C43—24no—
354C2×C4×C43—24no—
355C2×C4×C43—28no—
356C2×C4×C43—22no—
357C2×C4×C43—216no—
358C2×C4×C43—416no—
359C2×C4×C43C2×#4114yes—
360C2×C4×C432−1+414yes—
361C2×C4×C43C2514yes—
362C2×C4×C43C2514yes—
363C2×C4×C43C2512yes—
364C2×C4×C43C2518yes—
365C2×C4×C43C2514yes—
366C2×C4×C43C2512yes—
367C2×C4×C43C2512yes—
368C22⋊D43—232no—
369C22⋊D43—48no—
370C2×Dic43—28no—
371C2×Dic43—22no—
372C2×Dic43—24no—
373C2×Dic43—22no—
374C2×Dic43—24no—
375C2×Dic43—22no—
376C2×Dic43—24no—
377C2×Dic43C2512yes—
378C2×Dic43C2512yes—
379C2×Dic43C2512yes—
380C2×Dic43C2514yes—
381C2×Dic43C2518yes—
382C2×Dic43C2514yes—
383C2×Dic43C2514yes—
384D172—216no—
385D172C2×#41116yes—
386C4×D43—232no—
387C4×D43—216no—
388C4×D43—28no—
389C4×D43—216no—
390C4×D43—28no—
391C4×D43—48no—
392C4×D43—44no—
393C4×D43—416no—
394Dic86—216no—
395Dic86—28no—
396C2×#3515—431nomaximal, Sylow
397C22×C43—24no—
398C22×C43—24no—
399C22×C43—24no—
400C22×C43—48no—
401C22×C43C22×#4112yes—
402C22×C43C2×2−1+412yes—
403C22×C43#58512yes—
404C22×C43C2611yescharacteristic
405C2×D43—24no—
406C2×D43—24no—
407C2×D43—216no—
408C2×D43—22no—
409C2×D43—22no—
410C2×D43—22no—
411C2×D43—44no—
412C2×D43C22×#4118yes—
413C4×C43—24no—
414C4×C43—24no—
415C4×C43—24no—
416C4×C43—28no—
417C4×C43—22no—
418C4×C43C22×#4114yes—
419C4×C43C2×2−1+414yes—
420Dic43—28no—
421Dic43—22no—
422Dic43—24no—
423Dic43—22no—
424Dic43—24no—
425Dic43—22no—
426Dic43—24no—
427#3515—4332no—
428C2×#557—431no—
429C2×#554—431no—
430C2×#554D4311yescharacteristic, complemented
431C2×#553—432no—
432C2×#552—432no—
433C2×#552—434no—
434C2×#552—432no—
435C2×#547—432no—
436C2×#547—431no—
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—44no—
446C2×C43#351514yescomplemented
447C2×C43C23×#4111yescharacteristic
448C2×C43C22×2−1+411yescharacteristic
449C2×C43C2×#58511yescharacteristic
450D43—28no—
451D43—42no—
452C22×#41—431no—
453C22×#41—432no—
454#557—4316no—
455#554—4316no—
456#554C2×D43116yescomplemented
457#553—4332no—
458#552—4332no—
459#552—4364no—
460#552—4332no—
461#547—4332no—
462#547—4316no—
463#541—4332no—
464#539—4364no—
465#533—4316no—
466C2×C4⋊Q8—432no—
467C2×C4⋊Q8—431no—
468C2×C4⋊Q8C2×D4311yescharacteristic
469#529—4332no—
470#529—4316no—
471C2×#126—434no—
472C2×#126—434no—
473C2×#126—432no—
474C2×#126—434no—
475C2×#125—4332no—
476C2×#125—431no—
477C2×#125—432no—
478C2×#125—434no—
479C2×#125—434no—
480C2×#125—434no—
481C2×#125—434no—
482C2×#125—432no—
483C2×#125—432no—
484C2×#125C2×D4312yes—
485C2×#124—431no—
486C2×#123—434no—
487C2×#123—434no—
488C2×#123—432no—
489C2×#123—434no—
490C2×#123—434no—
491C2×C22⋊Q8—432no—
492C2×C22⋊Q8—434no—
493C2×C22⋊Q8—432no—
494C2×C22⋊Q8—431no—
495C2×C22⋊Q8—432no—
496C2×C22⋊Q8—432no—
497C2×C22⋊Q8C2×D4314yes—
498C2×C22⋊Q8C2×D4312yes—
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×Q8—432no—
508C2×C4×Q8—432no—
509C2×C4×Q8—431no—
510C2×C4×Q8C2×D4311yescharacteristic
511C2×C4×D4—434no—
512C2×C4×D4—434no—
513C2×C4×D4—432no—
514C2×C4×D4—431no—
515C2×C4×D4—432no—
516C2×C4×D4—432no—
517C2×C4×D4—431no—
518C2×C4×D4—432no—
519C2×C4×D4C2×D4311yescharacteristic
520C2×C4×D4C2×D4312yes—
521C2×#117—432no—
522C2×#117—434no—
523C2×#117—431no—
524C2×#117—432no—
525C2×#117—434no—
526C2×#117—432no—
527C22×C4⋊C4—434no—
528C22×C4⋊C4—434no—
529C22×C4⋊C4—432no—
530C22×C4⋊C4—432no—
531C22×C4⋊C4C2×D4312yes—
532C22×C42—432no—
533C22×C42—431no—
534C43C2×#351511yescharacteristic, complemented, Sylow
535C2×#41—438no—
536C2×#41—4316no—
537C2×#41—8616no—
538C2×#41—868no—
539C22×Q8—431no—
540C22×Q8—432no—
541C22×Q8C22×D4311yescharacteristic
542C22×Q8C22×D4312yes—
543C22×D4—434no—
544C22×D4—432no—
545C22×D4—431no—
546C22×D4—432no—
547C22×D4C22×D4311yescharacteristic
548C23×C4—434no—
549C23×C4—432no—
550C23×C4—432no—
551C23×C4—431no—
552C23×C4—431no—
553C23×C4—434no—
554C23×C4—432no—
555C23×C4—431no—
556C23×C4C22×D4312yes—
557C23×C4C22×D4314yes—
558C4⋊Q8—4316no—
559C4⋊Q8—438no—
560C4⋊Q8C22×D4318yes—
561#126—4332no—
562#126—4332no—
563#126—4316no—
564#126—4332no—
565#125—438no—
566#125—4316no—
567#125—4332no—
568#125—4332no—
569#125—4332no—
570#125—4332no—
571#125—4316no—
572#125—4316no—
573#125C22×D43116yes—
574#124—438no—
575#123—4332no—
576#123—4332no—
577#123—4316no—
578#123—4332no—
579#123—4332no—
580C22⋊Q8—4316no—
581C22⋊Q8—4332no—
582C22⋊Q8—4316no—
583C22⋊Q8—438no—
584C22⋊Q8—4316no—
585C22⋊Q8—4316no—
586C22⋊Q8C22×D43132yes—
587C22⋊Q8C22×D43116yes—
588#121—4316no—
589#121—438no—
590#121—4332no—
591C4×Q8—438no—
592C4×Q8—4316no—
593C4×Q8—4316no—
594C4×Q8—4316no—
595C4×Q8—4316no—
596C4×Q8—438no—
597C4×Q8C22×D4318yes—
598C4×D4—4332no—
599C4×D4—4332no—
600C4×D4—4316no—
601C4×D4—438no—
602C4×D4—4316no—
603C4×D4—4316no—
604C4×D4—438no—
605C4×D4—4316no—
606C4×D4C22×D4318yes—
607C4×D4C22×D43116yes—
608#117—4316no—
609#117—4332no—
610#117—438no—
611#117—4316no—
612#117—4332no—
613#117—4316no—
614C2×C4⋊C4—432no—
615C2×C4⋊C4—432no—
616C2×C4⋊C4—431no—
617C2×C4⋊C4—432no—
618C2×C4⋊C4—434no—
619C2×C4⋊C4—434no—
620C2×C4⋊C4—434no—
621C2×C4⋊C4—434no—
622C2×C4⋊C4—434no—
623C2×C4⋊C4—434no—
624C2×C4⋊C4—432no—
625C2×C4⋊C4—431no—
626C2×C4⋊C4—432no—
627C2×C4⋊C4—434no—
628C2×C4⋊C4—432no—
629C2×C4⋊C4—432no—
630C2×C4⋊C4—434no—
631C2×C4⋊C4—4332no—
632C2×C4⋊C4—4332no—
633C2×C4⋊C4—4316no—
634C2×C4⋊C4—4316no—
635C2×C4⋊C4C22×D4311yescharacteristic
636C2×C4⋊C4C22×D4314yes—
637C2×C4⋊C4C22×D4312yes—
638C2×C4⋊C4C22×D4314yes—
639C2×C4⋊C4C22×D4311yescharacteristic
640C2×C4⋊C4C22×D4312yes—
641C2×C4⋊C4C22×D43116yes—
642C2×C4⋊C4C22×D4312yes—
643C2×C22⋊C4—432no—
644C2×C22⋊C4—432no—
645C2×C22⋊C4—432no—
646C2×C22⋊C4—434no—
647C2×C22⋊C4—432no—
648C2×C22⋊C4—434no—
649C2×C22⋊C4—432no—
650C2×C22⋊C4—432no—
651C2×C22⋊C4—434no—
652C2×C22⋊C4—432no—
653C2×C22⋊C4C22×D4314yes—
654C2×C22⋊C4C22×D4312yes—
655C2×C42—432no—
656C2×C42—431no—
657C2×C42—434no—
658C2×C42—434no—
659C2×C42—431no—
660C2×C42—432no—
661C2×C42—432no—
662C2×C42—431no—
663C2×C42—4316no—
664C2×C42—438no—
665C2×C42C22×D4312yes—
666C2×C42C22×D4311yescharacteristic
667C24—432no—
668C24—431no—
669C24C23×D4312yes—
670#41—8664no—
671#41—8632no—
672C2×Q8—24no—
673C2×Q8—44no—
674C2×Q8—434no—
675C2×Q8—438no—
676C2×Q8—868no—
677C2×Q8—864no—
678C2×Q8C23×D4314yes—
679C2×Q8C23×D4318yes—
680C2×D4—24no—
681C2×D4—4316no—
682C2×D4—438no—
683C2×D4—438no—
684C2×D4—434no—
685C2×D4—438no—
686C2×D4—868no—
687C2×D4—8616no—
688C2×D4—1724no—
689C2×D4C23×D4314yes—
690C22×C4—28no—
691C22×C4—48no—
692C22×C4—431no—
693C22×C4—431no—
694C22×C4—431no—
695C22×C4—432no—
696C22×C4—432no—
697C22×C4—434no—
698C22×C4—432no—
699C22×C4—438no—
700C22×C4—438no—
701C22×C4—434no—
702C22×C4—434no—
703C22×C4—4316no—
704C22×C4—438no—
705C22×C4—434no—
706C22×C4—4316no—
707C22×C4—8616no—
708C22×C4—868no—
709C22×C4—864no—
710C22×C4—868no—
711C22×C4—864no—
712C22×C4—1724no—
713C22×C4—1728no—
714C22×C4—1722no—
715C22×C4C23×D4318yes—
716C22×C4C23×D4312yes—
717C22×C4C23×D4311yescharacteristic
718C22×C4C23×D4312yes—
719C22×C4C23×D4314yes—
720C22×C4C23×D4312yes—
721C22×C4C23×D43116yes—
722C22×C4C23×D4311yescharacteristic
723C22×C4C23×D4311yescharacteristic
724C4⋊C4—438no—
725C4⋊C4—438no—
726C4⋊C4—434no—
727C4⋊C4—438no—
728C4⋊C4—4316no—
729C4⋊C4—4316no—
730C4⋊C4—4316no—
731C4⋊C4—4316no—
732C4⋊C4—4316no—
733C4⋊C4—4316no—
734C4⋊C4—438no—
735C4⋊C4—434no—
736C4⋊C4—438no—
737C4⋊C4—4316no—
738C4⋊C4—438no—
739C4⋊C4—438no—
740C4⋊C4—4316no—
741C4⋊C4C23×D4314yes—
742C4⋊C4C23×D43116yes—
743C4⋊C4C23×D4318yes—
744C4⋊C4C23×D43116yes—
745C4⋊C4C23×D4314yes—
746C4⋊C4C23×D4318yes—
747C4⋊C4C23×D4318yes—
748C22⋊C4—438no—
749C22⋊C4—438no—
750C22⋊C4—438no—
751C22⋊C4—4316no—
752C22⋊C4—438no—
753C22⋊C4—4316no—
754C22⋊C4—438no—
755C22⋊C4—438no—
756C22⋊C4—4316no—
757C22⋊C4—438no—
758C22⋊C4C23×D43116yes—
759C22⋊C4C23×D4318yes—
760C42—434no—
761C42—438no—
762C42—434no—
763C42—434no—
764C42—438no—
765C42—4316no—
766C42—4316no—
767C42—438no—
768C42C23×D4318yes—
769C42C23×D4314yes—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—438no—
774C23—434no—
775C23—432no—
776C23—864no—
777C23—864no—
778C23—862no—
779C23—862no—
780C23—862no—
781C23C24×D4314yes—
782C23C24×D4311yescharacteristic
783Q8—28no—
784Q8—48no—
785Q8—8616no—
786Q8—868no—
787D4—28no—
788D4—4316no—
789D4—8616no—
790D4—8632no—
791D4—1728no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—216no—
798C2×C4—416no—
799C2×C4—432no—
800C2×C4—432no—
801C2×C4—432no—
802C2×C4—434no—
803C2×C4—434no—
804C2×C4—438no—
805C2×C4—434no—
806C2×C4—8632no—
807C2×C4—8616no—
808C2×C4—862no—
809C2×C4—868no—
810C2×C4—862no—
811C2×C4—864no—
812C2×C4—864no—
813C2×C4—862no—
814C2×C4—864no—
815C2×C4—868no—
816C2×C4—8616no—
817C2×C4—868no—
818C2×C4—1728no—
819C2×C4—17216no—
820C2×C4—1724no—
821C2×C4#41×D4314yes—
822C2×C4#1306337314yes—
823C2×C4C24×D4314yes—
824C2×C4C24×D4312yes—
825C2×C4C24×D4314yes—
826C2×C4C24×D4318yes—
827C2×C4C24×D4314yes—
828C2×C4C24×D4312yes—
829C2×C4C24×D4312yes—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—48no—
834C22—438no—
835C22—8616no—
836C22—864no—
837C22—864no—
838C22—862no—
839C22—862no—
840C22—862no—
841C22—1724no—
842C22C2×#41×D4312yes—
843C22C2×#1306337312yes—
844C22#1458373412yes—
845C22C25×D4311yescharacteristic
846C4—24no—
847C4—24no—
848C4—24no—
849C4—28no—
850C4—22no—
851C4—862no—
852C4—868no—
853C4—862no—
854C4—864no—
855C4—864no—
856C4—862no—
857C4—864no—
858C4C2×#41×D4314yes—
859C4C2×#1306337314yes—
860C2—44no—
861C2—868no—
862C2—1722no—
863C2#1914857614yesdirect product factor
864C2C22×#41×D4311yescharacteristic
865C2C22×#1306337311yescharacteristic
866C2C2×#1458373411yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#554C2
socleC23×C43C25
hypercenterC2×#554D43
hypocenterC43C2×#3515
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #19148576C2direct (N × H)
2. C2×#14583627C2semidirect
3. C2×#14583610C2semidirect
4. C2×#14583599C2semidirect
5. C2×#14583587C2semidirect
6. C2×#14583584C2semidirect
7. C2×#14583583C2semidirect
8. C2×#14583554C2semidirect
9. C2×#14583551C2semidirect
10. C2×#14583509C2semidirect
11. C2×#14583495C2semidirect
12. C2×#14583454C2semidirect
13. C2×#14583431C2semidirect
14. C2×#14583431C2semidirect
15. C2×#125×D43C2semidirect
16. C2×#14583380C2semidirect
17. C2×C4×#10621902C2semidirect
18. C2×C43×#554C2semidirect
21. #14583627C22semidirect
22. #14583610C22semidirect
23. #14583599C22semidirect
24. #14583587C22semidirect
25. #14583584C22semidirect
26. #14583583C22semidirect
27. #14583554C22semidirect
28. #14583551C22semidirect
29. #14583509C22semidirect
30. #14583495C22semidirect
31. #14583454C22semidirect
34. #14583431C22semidirect
35. #14583431C22semidirect
48. #125×D43C22semidirect
64. #14583380C22semidirect
65. C4×#10621902C22semidirect
92. C43×#554C22semidirect
430. C2×#554D43semidirect
446. C2×C43#3515semidirect
456. #554C2×D43semidirect
534. C43C2×#3515semidirect
863. C2#19148576direct (N × H)

Maximal subgroups

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

subgroupindex
#191485762
C2×#145836272
C2×#145836102
C2×#145835992
C2×#145835872
C2×#145835842
C2×#145835832
C2×#145835542
C2×#145835512
C2×#145835092
C2×#145834952
C2×#145834542
C2×#145834312
C2×#125×D432
C2×#145833802
C2×C4×#106219022
C2×C43×#5542
C2×#351543