Finite Group Databasebeta

← C2×#19148518 #26005099

Subgroups — C2×#19148518 #26005099

Order 11008.

7238 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148518C2132yesmaximal, direct product factor
2C2×#14583602C214yesmaximal, complemented
3C2×#14583600C214yesmaximal, complemented
4C2×#14583600C214yesmaximal, complemented
5C2×#14583581C214yesmaximal, complemented
6C2×#14583510C211yesmaximal, characteristic, complemented
7C2×#14583505C211yesmaximal, characteristic, complemented
8C2×#14583504C211yesmaximal, characteristic, complemented
9C2×#14583479C212yesmaximal, complemented
10C2×#14583450C211yesmaximal, characteristic, complemented
11C2×#14583436C212yesmaximal, complemented
12C2×#14583435C212yesmaximal, complemented
13C2×#125×D43C211yesmaximal, characteristic, complemented
14C2×#14583381C212yesmaximal, complemented
15C2×#14583367C211yesmaximal, characteristic, complemented
16C2×C43×#541C211yesmaximal, characteristic, complemented
17C22×#10621902C2212yes—
18C22×#10621898C2211yescharacteristic
19#14583602C22164yescomplemented
20#14583600C22164yescomplemented
21#14583600C22164yescomplemented
22#14583581C22164yescomplemented
23#14583510C22116yescomplemented
24#14583505C22116yescomplemented
25#14583504C22116yescomplemented
26#14583479C22132yescomplemented
27#14583450C22116yescomplemented
28C2×#13063322C2211yescharacteristic
29#14583436C22132yescomplemented
30#14583435C22132yescomplemented
31C2×#13063320C2214yes—
32C2×#13063320C2214yes—
33C2×#13063320C2214yes—
34C2×#13063317C2211yescharacteristic
35C2×#13063316C2212yes—
36C2×#13063315C2214yes—
37C2×#13063315C2214yes—
38#125×D43C22116yescomplemented
39C2×#13063314C2212yes—
40C2×#13063310C2214yes—
41C2×#13063310C2214yes—
42C2×#13063310C2214yes—
43C2×#13063309C2214yes—
44C2×#13063303C2214yes—
45C2×#13063301C2212yes—
46C2×#13063300C2214yes—
47C2×#13063300C2214yes—
48C2×#13063300C2212yes—
49C2×#13063300C2214yes—
50C2×#13063299C2212yes—
51C2×#13063298C2214yes—
52C2×#13063298C2214yes—
53C2×#13063298C2214yes—
54#14583381C22132yescomplemented
55#14583367C22116yescomplemented
56C2×Q8×Dic43C2212yes—
57C2×#13063290C2212yes—
58C2×C4×D172C2214yes—
59C2×C4×D172C2212yes—
60C2×C4×D172C2214yes—
61C2×#13063287C2212yes—
62C2×#13063287C2214yes—
63C2×#13063287C2214yes—
64C2×#13063287C2212yes—
65C2×(C22⋊D43)⋊C4C2214yes—
66C2×(C22⋊D43)⋊C4C2212yes—
67C2×(C22⋊D43)⋊C4C2212yes—
68C2×#13063283C2214yes—
69C2×#13063282C2211yescharacteristic
70C2×#13063282C2214yes—
71C2×#13063282C2214yes—
72C2×#13063282C2211yescharacteristic
73C2×C4⋊C4×D43C2214yes—
74C2×C4⋊C4×D43C2212yes—
75C2×C4⋊C4×D43C2214yes—
76C22×C4×Dic43C2211yescharacteristic
77C2×C42×D43C2211yescharacteristic
78C2×C42×D43C2211yescharacteristic
79C43×#541C22116yescomplemented
80C2×C4⋊Q8×C43C2211yescharacteristic
81C2×#126×C43C2214yes—
82C2×#125×C43C2214yes—
83C2×#125×C43C2211yescharacteristic
84C2×C22⋊Q8×C43C2212yes—
85C2×C4×Q8×C43C2212yes—
86C2×#117×C43C2211yescharacteristic
87C2×#10621902—216no—
88C2×#10621902C23116yes—
89C2×#10621898—28no—
90C2×#10621898C2318yes—
91C22×Dic86C2311yescharacteristic
92C22×D172C2311yescharacteristic
93C22×D172C2314yes—
94C22×D172C2312yes—
95C22×D172C2314yes—
96C22×D172C2314yes—
97C22×C22⋊D43C2311yescharacteristic
98C22×C22⋊D43C2311yescharacteristic
99C22×C22⋊D43C2314yes—
100C23×Dic43C2312yes—
101C22×C4×D43C2311yescharacteristic
102C22×C4×D43C2314yes—
103C22×C4×D43C2312yes—
104C22×C4×D43C2312yes—
105C22×C4×D43C2314yes—
106C22×C4×D43C2314yes—
107C22×C4×D43C2314yes—
108C22×C4×D43C2311yescharacteristic
109#13063322C2318yes—
110#13063320C23132yes—
111#13063320C23132yes—
112#13063320C23132yes—
113#13063317C2318yes—
114#13063316C23116yes—
115#13063315C23132yes—
116#13063315C23132yes—
117#13063314C23116yes—
118#13063310C23132yes—
119#13063310C23132yes—
120#13063310C23132yes—
121#13063309C23132yes—
122#13063303C23132yes—
123#13063301C23116yes—
124#13063300C23132yes—
125#13063300C23132yes—
126#13063300C23132yes—
127#13063300C23116yes—
128#13063299C23116yes—
129#13063298C23132yes—
130#13063298C23132yes—
131#13063298C23132yes—
132Q8×Dic43C23116yes—
133#13063290C23116yes—
134C4×D172C23132yes—
135C4×D172C23132yes—
136C4×D172C23116yes—
137#13063287C23132yes—
138#13063287C23132yes—
139#13063287C23116yes—
140#13063287C23116yes—
141(C22⋊D43)⋊C4C23116yes—
142(C22⋊D43)⋊C4C23116yes—
143(C22⋊D43)⋊C4C23132yes—
144#13063283C23132yes—
145#13063282C23132yes—
146#13063282C23132yes—
147#13063282C2318yes—
148#13063282C2318yes—
149C2×C4⋊Dic43C2314yes—
150C2×C4⋊Dic43C2312yes—
151C2×C4⋊Dic43C2314yes—
152C2×Dic43⋊C4C2312yes—
153C2×Dic43⋊C4C2314yes—
154C2×Dic43⋊C4C2314yes—
155C2×Dic43⋊C4C2314yes—
156C2×Dic43⋊C4C2312yes—
157C2×Dic43⋊C4C2314yes—
158C4⋊C4×D43C23132yes—
159C4⋊C4×D43C23132yes—
160C4⋊C4×D43C23116yes—
161C2×(C2×D43)⋊C4C2314yes—
162C2×(C2×D43)⋊C4C2312yes—
163C2×(C2×D43)⋊C4C2312yes—
164C2×(C2×D43)⋊C4C2314yes—
165C2×(C2×D43)⋊C4C2314yes—
166C2×(C2×D43)⋊C4C2314yes—
167C2×(C2×D43)⋊C4C2314yes—
168C2×(C2×D43)⋊C4C2314yes—
169C2×(C2×D43)⋊C4C2314yes—
170C2×C4×Dic43C2311yescharacteristic
171C2×C4×Dic43C2312yes—
172C2×C4×Dic43C2312yes—
173C2×C4×Dic43C2311yescharacteristic
174C2×C4×Dic43C2312yes—
175C2×C4×Dic43C2318yes—
176C2×C4×Dic43C2314yes—
177C42×D43C2318yes—
178C42×D43C2318yes—
179C22×Q8×C43C2312yes—
180C23×C4×C43C2311yescharacteristic
181C4⋊Q8×C43C2318yes—
182#126×C43C23132yes—
183#125×C43C23132yes—
184#125×C43C2318yes—
185C22⋊Q8×C43C23116yes—
186C4×Q8×C43C23116yes—
187#117×C43C2318yes—
188C2×C4⋊C4×C43C2312yes—
189C2×C4⋊C4×C43C2312yes—
190C2×C4⋊C4×C43C2314yes—
191C2×C4⋊C4×C43C2314yes—
192C2×C4⋊C4×C43C2314yes—
193C2×C4⋊C4×C43C2314yes—
194C2×C22⋊C4×C43C2312yes—
195C2×C22⋊C4×C43C2314yes—
196C2×C42×C43C2311yescharacteristic
197C2×C42×C43C2311yescharacteristic
198C2×C42×C43C2314yes—
199C24×C43C2411yescharacteristic
200C23×D43C2414yes—
201C23×D43C2411yescharacteristic
202C23×D43C2411yescharacteristic
203C2×Q8×C43—28no—
204C2×Q8×C43C2418yes—
205C22×C4×C43—24no—
206C22×C4×C43C2412yes—
207C22×C4×C43C2412yes—
208C22×C4×C43C2414yes—
209C22×C4×C43C2414yes—
210C22×C4×C43C2411yescharacteristic
211C22×C4×C43C2414yes—
212C22×C4×C43C2411yescharacteristic
213C2×C22⋊D43—24no—
214C2×C22⋊D43—24no—
215C2×C22⋊D43—48no—
216C2×C22⋊D43C2414yes—
217C2×C22⋊D43C2414yes—
218C2×C22⋊D43C24116yes—
219C22×Dic43—44no—
220C22×Dic43C2412yes—
221C22×Dic43C2412yes—
222C22×Dic43C2411yescharacteristic
223C22×Dic43C2414yes—
224C22×Dic43C2418yes—
225C22×Dic43C2411yescharacteristic
226#10621902—264no—
227#10621898—232no—
228C2×D172—28no—
229C2×D172—24no—
230C2×D172—216no—
231C2×D172—48no—
232C2×D172—48no—
233C2×D172C2414yes—
234C2×D172C24116yes—
235C2×D172C2418yes—
236C2×D172C24116yes—
237C2×D172C24116yes—
238C2×C4×D43—24no—
239C2×C4×D43—216no—
240C2×C4×D43—44no—
241C2×C4×D43—48no—
242C2×C4×D43—48no—
243C2×C4×D43—48no—
244C2×C4×D43—44no—
245C2×C4×D43#4118yes—
246C2×C4×D43C2414yes—
247C2×C4×D43C24116yes—
248C2×C4×D43C2418yes—
249C2×C4×D43C2418yes—
250C2×C4×D43C24116yes—
251C2×C4×D43C24116yes—
252C2×C4×D43C24116yes—
253C2×C4×D43C2414yes—
254C2×Dic86—24no—
255C2×Dic86C2414yes—
256C4⋊C4×C43C2418yes—
257C4⋊C4×C43C2418yes—
258C4⋊C4×C43C24116yes—
259C4⋊C4×C43C24116yes—
260C4⋊C4×C43C24116yes—
261C4⋊C4×C43C24116yes—
262C22⋊C4×C43C2418yes—
263C22⋊C4×C43C24116yes—
264C42×C43C2414yes—
265C42×C43C2414yes—
266C42×C43C24116yes—
267(C2×D43)⋊C4C24116yes—
268(C2×D43)⋊C4C2418yes—
269(C2×D43)⋊C4C2418yes—
270(C2×D43)⋊C4C24116yes—
271(C2×D43)⋊C4C24116yes—
272(C2×D43)⋊C4C24116yes—
273(C2×D43)⋊C4C24116yes—
274(C2×D43)⋊C4C24116yes—
275(C2×D43)⋊C4C24116yes—
276C4⋊Dic43C24116yes—
277C4⋊Dic43C2418yes—
278C4⋊Dic43C24116yes—
279Dic43⋊C4C2418yes—
280Dic43⋊C4C24116yes—
281Dic43⋊C4C24116yes—
282Dic43⋊C4C24116yes—
283Dic43⋊C4C2418yes—
284Dic43⋊C4C24116yes—
285C4×Dic43C2414yes—
286C4×Dic43C2418yes—
287C4×Dic43C2418yes—
288C4×Dic43C2414yes—
289C4×Dic43C2418yes—
290C4×Dic43C24116yes—
291C23×C43—22no—
292C23×C43—24no—
293C23×C43C2512yes—
294C23×C43C2511yescharacteristic
295C22×D43—24no—
296C22×D43—28no—
297C22×D43—22no—
298C22×D43—28no—
299C22×D43—24no—
300C22×D43—28no—
301C22×D43C2×#4114yes—
302C22×D43C2518yes—
303C22×D43C2512yes—
304C22×D43C2512yes—
305Q8×C43—216no—
306C2×C4×C43—22no—
307C2×C4×C43—28no—
308C2×C4×C43—24no—
309C2×C4×C43—28no—
310C2×C4×C43—24no—
311C2×C4×C43—28no—
312C2×C4×C43C2×#4114yes—
313C2×C4×C43C2512yes—
314C2×C4×C43C2514yes—
315C2×C4×C43C2518yes—
316C2×C4×C43C2514yes—
317C2×C4×C43C2518yes—
318C2×C4×C43C2512yes—
319C22⋊D43—28no—
320C22⋊D43—28no—
321C22⋊D43—416no—
322C2×Dic43—22no—
323C2×Dic43—24no—
324C2×Dic43—24no—
325C2×Dic43—28no—
326C2×Dic43—48no—
327C2×Dic43C2×#4114yes—
328C2×Dic43C2514yes—
329C2×Dic43C2514yes—
330C2×Dic43C2512yes—
331C2×Dic43C2518yes—
332C2×Dic43C2512yes—
333D172—28no—
334D172—232no—
335D172—216no—
336D172—416no—
337D172—416no—
338C4×D43—28no—
339C4×D43—232no—
340C4×D43—48no—
341C4×D43—416no—
342C4×D43—48no—
343C4×D43—416no—
344C4×D43—416no—
345C4×D43C2×#41116yes—
346Dic86—28no—
347C2×#3512—431nomaximal, Sylow
348C22×C43—22no—
349C22×C43—24no—
350C22×C43—44no—
351C22×C43C22×#4112yes—
352C22×C43#58514yes—
353C22×C43C2611yescharacteristic
354C2×D43—24no—
355C2×D43—28no—
356C2×D43—28no—
357C2×D43—22no—
358C2×D43—28no—
359C2×D43—24no—
360C2×D43—28no—
361C2×D43—416no—
362C2×D43—44no—
363C2×D43C22×#4114yes—
364C4×C43—22no—
365C4×C43—28no—
366C4×C43—24no—
367C4×C43—28no—
368C4×C43—24no—
369C4×C43C22×#4114yes—
370Dic43—22no—
371Dic43—24no—
372Dic43—24no—
373Dic43—28no—
374Dic43C22×#4114yes—
375#3512—4332no—
376C2×#553—434no—
377C2×#553—434no—
378C2×#553—434no—
379C2×#552—434no—
380C2×#541—431no—
381C2×#541D4311yescharacteristic, complemented
382C2×#540—431no—
383C2×#540—431no—
384C2×#537—432no—
385C2×#532—431no—
386C2×#529—432no—
387C2×#529—432no—
388C22×#125—431no—
389C2×#520—432no—
390C2×C4×#41—431no—
391C2×C43—42no—
392C2×C43#351214yescomplemented
393C2×C43C23×#4111yescharacteristic
394C2×C43C2×#58512yes—
395D43—24no—
396D43—48no—
397D43—42no—
398C22×#41—432no—
399C22×#41—431no—
400#553—4364no—
401#553—4364no—
402#553—4364no—
403#552—4364no—
404#541—4316no—
405#541C2×D43116yescomplemented
406#540—4316no—
407#540—4316no—
408#537—4332no—
409#532—4316no—
410C2×C4⋊Q8C2×D4311yescharacteristic
411C2×#127—431no—
412#529—4332no—
413#529—4332no—
414C2×#126—434no—
415C2×#126—434no—
416C2×#126—434no—
417C2×#126C2×D4314yes—
418C2×#125—4316no—
419C2×#125—432no—
420C2×#125—434no—
421C2×#125—434no—
422C2×#125—431no—
423C2×#125C2×D4311yescharacteristic
424C2×#125C2×D4314yes—
425C2×#124—432no—
426C2×#123—434no—
427C2×#123—434no—
428C2×#123—434no—
429C2×#123—434no—
430C2×C22⋊Q8—432no—
431C2×C22⋊Q8—434no—
432C2×C22⋊Q8C2×D4312yes—
433C2×#121—432no—
434C2×#121—432no—
435C2×#121—434no—
436C2×#121—434no—
437C2×#121—434no—
438C2×#121—434no—
439C2×#121—434no—
440C2×#121—434no—
441#520—4332no—
442C4×#41—4316no—
443C2×C4×Q8—432no—
444C2×C4×Q8—432no—
445C2×C4×Q8C2×D4312yes—
446C2×C4×D4—432no—
447C2×C4×D4—432no—
448C2×C4×D4—434no—
449C2×C4×D4—434no—
450C2×C4×D4—432no—
451C2×C4×D4—432no—
452C2×C4×D4—434no—
453C2×C4×D4—432no—
454C2×C4×D4—434no—
455C2×C4×D4—434no—
456C2×#117—434no—
457C2×#117—431no—
458C2×#117—431no—
459C2×#117—434no—
460C2×#117—434no—
461C2×#117C2×D4311yescharacteristic
462C22×C4⋊C4—432no—
463C22×C4⋊C4—434no—
464C22×C4⋊C4—434no—
465C22×C42—431no—
466C22×C42—431no—
467C22×C42—431no—
468C43C2×#351211yescharacteristic, complemented, Sylow
469C2×#41—4316no—
470C2×#41—438no—
471C2×#41—868no—
472C2×#41—8616no—
473C22×Q8—431no—
474C22×Q8C22×D4312yes—
475C22×D4—431no—
476C22×D4—431no—
477C22×D4—434no—
478C22×D4—431no—
479C22×D4—434no—
480C22×D4—432no—
481C22×D4—434no—
482C22×D4—434no—
483C23×C4—431no—
484C23×C4—432no—
485C23×C4—434no—
486C23×C4—431no—
487C23×C4—434no—
488C23×C4—432no—
489C23×C4—434no—
490C23×C4—434no—
491C23×C4—432no—
492C23×C4C22×D4311yescharacteristic
493C4⋊Q8C22×D4318yes—
494#127—438no—
495#126—4332no—
496#126—4332no—
497#126—4332no—
498#126C22×D43132yes—
499#125—4316no—
500#125—4332no—
501#125—4332no—
502#125—438no—
503#125C22×D4318yes—
504#125C22×D43132yes—
505#124—4316no—
506#123—4332no—
507#123—4332no—
508#123—4332no—
509#123—4332no—
510C22⋊Q8—4316no—
511C22⋊Q8—4332no—
512C22⋊Q8C22×D43116yes—
513#121—4316no—
514#121—4316no—
515#121—4332no—
516#121—4332no—
517#121—4332no—
518#121—4332no—
519#121—4332no—
520#121—4332no—
521C4×Q8—4316no—
522C4×Q8—4316no—
523C4×Q8C22×D43116yes—
524C4×D4—4316no—
525C4×D4—4316no—
526C4×D4—4332no—
527C4×D4—4332no—
528C4×D4—4316no—
529C4×D4—4316no—
530C4×D4—4332no—
531C4×D4—4316no—
532C4×D4—4332no—
533C4×D4—4332no—
534#117—4332no—
535#117—438no—
536#117—438no—
537#117—4332no—
538#117—4332no—
539#117C22×D4318yes—
540C2×C4⋊C4—432no—
541C2×C4⋊C4—434no—
542C2×C4⋊C4—434no—
543C2×C4⋊C4—434no—
544C2×C4⋊C4—432no—
545C2×C4⋊C4—434no—
546C2×C4⋊C4—434no—
547C2×C4⋊C4—432no—
548C2×C4⋊C4—434no—
549C2×C4⋊C4—4316no—
550C2×C4⋊C4—4332no—
551C2×C4⋊C4—4332no—
552C2×C4⋊C4C22×D4312yes—
553C2×C4⋊C4C22×D4314yes—
554C2×C4⋊C4C22×D4314yes—
555C2×C4⋊C4C22×D4314yes—
556C2×C4⋊C4C22×D4312yes—
557C2×C4⋊C4C22×D4314yes—
558C2×C22⋊C4—434no—
559C2×C22⋊C4—432no—
560C2×C22⋊C4—432no—
561C2×C22⋊C4—434no—
562C2×C22⋊C4—434no—
563C2×C22⋊C4—434no—
564C2×C22⋊C4—434no—
565C2×C22⋊C4—434no—
566C2×C22⋊C4—434no—
567C2×C22⋊C4C22×D4312yes—
568C2×C22⋊C4C22×D4314yes—
569C2×C42—431no—
570C2×C42—434no—
571C2×C42—432no—
572C2×C42—432no—
573C2×C42—432no—
574C2×C42—438no—
575C2×C42—431no—
576C2×C42—438no—
577C2×C42—438no—
578C2×C42C22×D4314yes—
579C2×C42C22×D4311yescharacteristic
580C2×C42C22×D4311yescharacteristic
581C24—431no—
582C24—434no—
583C24—431no—
584C24C23×D4311yescharacteristic
585#41—8632no—
586#41—8664no—
587C2×Q8—28no—
588C2×Q8—434no—
589C2×Q8—864no—
590C2×Q8C23×D4318yes—
591C2×D4—434no—
592C2×D4—434no—
593C2×D4—4316no—
594C2×D4—434no—
595C2×D4—4316no—
596C2×D4—438no—
597C2×D4—4316no—
598C2×D4—4316no—
599C2×D4—864no—
600C2×D4—8616no—
601C2×D4—864no—
602C2×D4—864no—
603C2×D4—868no—
604C2×D4—1728no—
605C2×D4—1728no—
606C2×D4—1728no—
607C22×C4—24no—
608C22×C4—431no—
609C22×C4—438no—
610C22×C4—434no—
611C22×C4—432no—
612C22×C4—432no—
613C22×C4—431no—
614C22×C4—434no—
615C22×C4—438no—
616C22×C4—434no—
617C22×C4—4316no—
618C22×C4—438no—
619C22×C4—438no—
620C22×C4—4316no—
621C22×C4—4316no—
622C22×C4—4316no—
623C22×C4—8616no—
624C22×C4—864no—
625C22×C4—1724no—
626C22×C4—1728no—
627C22×C4—1728no—
628C22×C4—1728no—
629C22×C4—1724no—
630C22×C4—1724no—
631C22×C4C23×D4314yes—
632C22×C4C23×D4311yescharacteristic
633C22×C4C23×D4312yes—
634C22×C4C23×D4314yes—
635C22×C4C23×D4312yes—
636C22×C4C23×D4314yes—
637C22×C4C23×D4311yescharacteristic
638C4⋊C4—438no—
639C4⋊C4—4316no—
640C4⋊C4—4316no—
641C4⋊C4—4316no—
642C4⋊C4—438no—
643C4⋊C4—4316no—
644C4⋊C4—4316no—
645C4⋊C4—438no—
646C4⋊C4—4316no—
647C4⋊C4C23×D4318yes—
648C4⋊C4C23×D43116yes—
649C4⋊C4C23×D43116yes—
650C4⋊C4C23×D43116yes—
651C4⋊C4C23×D4318yes—
652C4⋊C4C23×D43116yes—
653C22⋊C4—4316no—
654C22⋊C4—438no—
655C22⋊C4—438no—
656C22⋊C4—4316no—
657C22⋊C4—4316no—
658C22⋊C4—4316no—
659C22⋊C4—4316no—
660C22⋊C4—4316no—
661C22⋊C4—4316no—
662C22⋊C4C23×D4318yes—
663C22⋊C4C23×D43116yes—
664C42—434no—
665C42—434no—
666C42—438no—
667C42—438no—
668C42—438no—
669C42—4316no—
670C42C23×D4314yes—
671C42C23×D4314yes—
672C42C23×D43116yes—
673C23—22no—
674C23—24no—
675C23—434no—
676C23—432no—
677C23—438no—
678C23—432no—
679C23—864no—
680C23—868no—
681C23—862no—
682C23—868no—
683C23—864no—
684C23—868no—
685C23C24×D4312yes—
686C23C24×D4311yescharacteristic
687Q8—216no—
688Q8—868no—
689D4—868no—
690D4—8632no—
691D4—868no—
692D4—868no—
693D4—8616no—
694D4—17216no—
695D4—17216no—
696D4—17216no—
697C2×C4—22no—
698C2×C4—28no—
699C2×C4—24no—
700C2×C4—28no—
701C2×C4—24no—
702C2×C4—28no—
703C2×C4—434no—
704C2×C4—432no—
705C2×C4—4316no—
706C2×C4—434no—
707C2×C4—434no—
708C2×C4—432no—
709C2×C4—438no—
710C2×C4—8632no—
711C2×C4—862no—
712C2×C4—864no—
713C2×C4—864no—
714C2×C4—868no—
715C2×C4—868no—
716C2×C4—1728no—
717C2×C4—17216no—
718C2×C4—17216no—
719C2×C4—17216no—
720C2×C4—1728no—
721C2×C4—1728no—
722C2×C4#41×D4314yes—
723C2×C4C24×D4312yes—
724C2×C4C24×D4314yes—
725C2×C4C24×D4318yes—
726C2×C4C24×D4314yes—
727C2×C4C24×D4318yes—
728C2×C4C24×D4312yes—
729C22—22no—
730C22—24no—
731C22—44no—
732C22—434no—
733C22—864no—
734C22—868no—
735C22—868no—
736C22—862no—
737C22—868no—
738C22—864no—
739C22—868no—
740C22—17216no—
741C22—1724no—
742C22C2×#41×D4312yes—
743C22#1458373614yes—
744C22C25×D4311yescharacteristic
745C4—22no—
746C4—28no—
747C4—24no—
748C4—28no—
749C4—24no—
750C4—434no—
751C4—862no—
752C4—864no—
753C4—864no—
754C4—868no—
755C4C2×#41×D4314yes—
756C2—42no—
757C2—864no—
758C2—1728no—
759C2—1722no—
760C2#1914851814yesdirect product factor
761C2C22×#41×D4311yescharacteristic
762C2C2×#1458373612yes—
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#541C2
socleC23×C43C25
hypercenterC2×#541D43
hypocenterC43C2×#3512
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. #19148518C2direct (N × H)
2. C2×#14583602C2semidirect
3. C2×#14583600C2semidirect
4. C2×#14583600C2semidirect
5. C2×#14583581C2semidirect
6. C2×#14583510C2semidirect
7. C2×#14583505C2semidirect
8. C2×#14583504C2semidirect
9. C2×#14583479C2semidirect
10. C2×#14583450C2semidirect
11. C2×#14583436C2semidirect
12. C2×#14583435C2semidirect
13. C2×#125×D43C2semidirect
14. C2×#14583381C2semidirect
15. C2×#14583367C2semidirect
16. C2×C43×#541C2semidirect
19. #14583602C22semidirect
20. #14583600C22semidirect
21. #14583600C22semidirect
22. #14583581C22semidirect
23. #14583510C22semidirect
24. #14583505C22semidirect
25. #14583504C22semidirect
26. #14583479C22semidirect
27. #14583450C22semidirect
29. #14583436C22semidirect
30. #14583435C22semidirect
38. #125×D43C22semidirect
54. #14583381C22semidirect
55. #14583367C22semidirect
79. C43×#541C22semidirect
381. C2×#541D43semidirect
392. C2×C43#3512semidirect
405. #541C2×D43semidirect
468. C43C2×#3512semidirect
760. C2#19148518direct (N × H)

Maximal subgroups

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

subgroupindex
#191485182
C2×#145836022
C2×#145836002
C2×#145835812
C2×#145835102
C2×#145835052
C2×#145835042
C2×#145834792
C2×#145834502
C2×#145834362
C2×#145834352
C2×#125×D432
C2×#145833812
C2×#145833672
C2×C43×#5412
C2×#351243