Finite Group Databasebeta

← C2×#19146857 #25973460

Subgroups — C2×#19146857 #25973460

Order 11008.

2114 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583558C211yesmaximal, characteristic
2#19146857C2116yesmaximal, direct product factor
3C2×#14583256C211yesmaximal, characteristic, complemented
4C2×#14583234C211yesmaximal, characteristic, complemented
5C2×#14583223C211yesmaximal, characteristic, complemented
6C2×#14583203C211yesmaximal, characteristic, complemented
7C2×#14583155C211yesmaximal, characteristic, complemented
8C2×#14583147C211yesmaximal, characteristic, complemented
9C2×#14583121C211yesmaximal, characteristic, complemented
10C2×#14583059C211yesmaximal, characteristic, complemented
11C2×#14583054C211yesmaximal, characteristic, complemented
12C2×C4×#10621885C211yesmaximal, characteristic, complemented
13C2×#14582977C211yesmaximal, characteristic, complemented
14C2×#14582898C211yesmaximal, characteristic, complemented
15C2×#14582907C211yesmaximal, characteristic, complemented
16C2×C43×#552C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C23×Dic86C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621885C2211yescharacteristic
21C22×#10621884C2211yescharacteristic
22C22×#10621877C2211yescharacteristic
23C22×#10621877C2211yescharacteristic
24#14583558—24no—
25#14583558C2218yes—
26C2×#13063313C2211yescharacteristic
27C2×#13063311—21no—
28C2×#13063304C2211yescharacteristic
29C2×#13063303—21no—
30C2×#13063299C2211yescharacteristic
31C2×#13063297—21no—
32C2×C4×Dic86C2211yescharacteristic
33C2×(C22⋊D43)⋊C4—21no—
34#14583256C2218yescomplemented
35#14583234C2218yescomplemented
36#14583223C2218yescomplemented
37#14583203C2218yescomplemented
38#14583155C2218yescomplemented
39#14583147C2218yescomplemented
40#14583121C2218yescomplemented
41#14583059C2218yescomplemented
42#14583054C2218yescomplemented
43C4×#10621885C2218yescomplemented
44#14582977C2218yescomplemented
45C2×#13063258C2211yescharacteristic
46C2×#13063258C2211yescharacteristic
47C2×#13063256C2211yescharacteristic
48C2×C4⋊(C43⋊C8)C2211yescharacteristic
49#14582907C2218yescomplemented
50#14582898C2218yescomplemented
51C2×#13063249C2211yescharacteristic
52C2×#13063248C2211yescharacteristic
53C2×#13063248C2211yescharacteristic
54C2×#13063248C2211yescharacteristic
55C2×#13063248C2211yescharacteristic
56C2×#13063248C2211yescharacteristic
57C2×#13063248C2211yescharacteristic
58C2×#13063245C2211yescharacteristic
59C2×#13063245C2211yescharacteristic
60C2×#13063245C2211yescharacteristic
61C2×C22⋊(C43⋊C8)C2211yescharacteristic
62C2×C22⋊(C43⋊C8)C2211yescharacteristic
63C2×C4×C43⋊C8C2211yescharacteristic
64C43×#552—24no—
65C43×#552C2218yescomplemented
66C2×#126×C43—21no—
67C2×#125×C43—21no—
68C2×#125×C43C2211yescharacteristic
69C2×#123×C43—21no—
70C2×C22⋊Q8×C43C2211yescharacteristic
71C2×C22⋊Q8×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic
73C2×C4×D4×C43C2211yescharacteristic
74C2×#117×C43—21no—
75C2×#117×C43C2211yescharacteristic
76C22×C4⋊C4×C43C2211yescharacteristic
77C2×#10621898—22no—
78C2×#10621898—24no—
79C2×#10621898—42no—
80C2×#10621898C2314yes—
81C22×Dic86—24no—
82C22×Dic86—22no—
83C22×Dic86—21no—
84C22×Dic86—42no—
85C22×Dic86C2311yescharacteristic
86C22×Dic86C2314yes—
87C22×Dic86C2311yescharacteristic
88C22×D172C2311yescharacteristic
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C23×Dic43—21no—
92C22×C4×D43—21no—
93C2×#10621885—24no—
94C2×#10621885—42no—
95C2×#10621885C2314yes—
96C2×#10621885C2314yes—
97C2×#10621884—42no—
98C2×#10621884C2314yes—
99C2×#10621877—42no—
100C2×#10621877—42no—
101C2×#10621877C2314yes—
102C2×#10621877C2314yes—
103C22×C43⋊C8C2311yescharacteristic
104C22×C43⋊C8C2311yescharacteristic
105C22×C43⋊C8C2311yescharacteristic
106C22×C43⋊C8C2311yescharacteristic
107#13063313—22no—
108#13063313C2314yes—
109#13063311—28no—
110#13063304—22no—
111#13063304C2314yes—
112#13063303—28no—
113#13063299—22no—
114#13063299C2314yes—
115#13063297—28no—
116C4×Dic86—22no—
117C4×Dic86C2314yes—
118(C22⋊D43)⋊C4—28no—
119C2×C4⋊Dic43C2311yescharacteristic
120C2×Dic43⋊C4—21no—
121C2×Dic43⋊C4—21no—
122C2×C22⋊Dic43—21no—
123C2×(C2×D43)⋊C4—21no—
124C2×(C2×D43)⋊C4—21no—
125C2×(C2×D43)⋊C4—21no—
126C2×C4×Dic43—21no—
127#13063258C2314yes—
128#13063258C2314yes—
129#13063256C2314yes—
130C4⋊(C43⋊C8)C2314yes—
131#13063249C2314yes—
132#13063248C2314yes—
133#13063248C2314yes—
134#13063248C2314yes—
135#13063248C2314yes—
136#13063248C2314yes—
137#13063248C2314yes—
138#13063245C2314yes—
139#13063245C2314yes—
140#13063245C2314yes—
141C22⋊(C43⋊C8)C2314yes—
142C22⋊(C43⋊C8)C2314yes—
143C4×C43⋊C8C2314yes—
144C22×Q8×C43C2311yescharacteristic
145C22×D4×C43D411yescharacteristic
146C23×C4×C43—21no—
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149#126×C43—28no—
150#125×C43—28no—
151#125×C43—22no—
152#125×C43C2314yes—
153#123×C43—28no—
154C22⋊Q8×C43—22no—
155C22⋊Q8×C43—22no—
156C22⋊Q8×C43C2314yes—
157C22⋊Q8×C43C2314yes—
158C4×Q8×C43—22no—
159C4×Q8×C43C2314yes—
160C4×D4×C43D414yes—
161C4×D4×C43C2314yes—
162#117×C43—22no—
163#117×C43—28no—
164#117×C43C2314yes—
165C2×C4⋊C4×C43—21no—
166C2×C4⋊C4×C43—22no—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43—21no—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43D411yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C4⋊C4×C43C2314yes—
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C22⋊C4×C43—21no—
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C22⋊C4×C43D411yescharacteristic
181C2×C22⋊C4×C43D411yescharacteristic
182C2×C42×C43—21no—
183C2×C42×C43—21no—
184C2×C42×C43C2311yescharacteristic
185C24×C43C2×D411yescharacteristic
186C24×C43C2×D411yescharacteristic
187C23×D43—21no—
188C2×Q8×C43—21no—
189C2×Q8×C43—22no—
190C2×Q8×C43—22no—
191C2×Q8×C43C2412yes—
192C2×D4×C43—42no—
193C2×D4×C43C2×D414yes—
194C22×C4×C43—22no—
195C22×C4×C43—22no—
196C22×C4×C43—22no—
197C22×C4×C43—22no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—24no—
203C22×C4×C43—44no—
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D412yes—
209C22×C4×C43C2×D412yes—
210C22×C4×C43C2412yes—
211C22×C4×C43C2412yes—
212C22×C4×C43C2411yescharacteristic
213C2×C22⋊D43—24no—
214C2×C22⋊D43—24no—
215C2×C22⋊D43—44no—
216C2×C22⋊D43—44no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—24no—
221C22×Dic43—44no—
222#10621898—28no—
223#10621898—44no—
224#10621898—48no—
225C2×D172—21no—
226C2×D172—22no—
227C2×D172—22no—
228C2×D172C2412yes—
229C2×C4×D43—24no—
230C2×C4×D43—44no—
231C2×Dic86—21no—
232C2×Dic86—22no—
233C2×Dic86—22no—
234C2×Dic86—22no—
235C2×Dic86—28no—
236C2×Dic86—24no—
237C2×Dic86—21no—
238C2×Dic86—44no—
239C2×Dic86—48no—
240C2×Dic86—44no—
241C2×Dic86#4114yes—
242C2×Dic86C2412yes—
243C2×Dic86C2412yes—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—24no—
247C4⋊C4×C43—24no—
248C4⋊C4×C43—24no—
249C4⋊C4×C43—24no—
250C4⋊C4×C43—24no—
251C4⋊C4×C43—24no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43C2×D414yes—
254C4⋊C4×C43C2412yes—
255C4⋊C4×C43C2412yes—
256C4⋊C4×C43C2412yes—
257C22⋊C4×C43—24no—
258C22⋊C4×C43—24no—
259C22⋊C4×C43—24no—
260C22⋊C4×C43C2×D414yes—
261C22⋊C4×C43C2×D414yes—
262C42×C43—24no—
263C42×C43—24no—
264C42×C43C2×D412yes—
265C42×C43C2412yes—
266C22⋊Dic43—24no—
267#10621885—28no—
268#10621885—44no—
269#10621884—44no—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4—24no—
273C4⋊Dic43—21no—
274C4⋊Dic43C2412yes—
275Dic43⋊C4—24no—
276Dic43⋊C4—24no—
277C4×Dic43—24no—
278#10621877—44no—
279#10621877—44no—
280C2×C43⋊C8—22no—
281C2×C43⋊C8—22no—
282C2×C43⋊C8—22no—
283C2×C43⋊C8—22no—
284C2×C43⋊C8C2412yes—
285C2×C43⋊C8C2412yes—
286C2×C43⋊C8C2412yes—
287C2×C43⋊C8C2412yes—
288C23×C43—22no—
289C23×C43—22no—
290C23×C43—22no—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43C22×D412yes—
295C23×C43C22×D412yes—
296C23×C43C22×D411yescharacteristic
297C22×D43—22no—
298C22×D43—42no—
299C22×D43—42no—
300C22×D43—42no—
301Q8×C43—22no—
302Q8×C43—22no—
303Q8×C43—42no—
304D4×C43—44no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—24no—
310C2×C4×C43—24no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—48no—
320C2×C4×C43—42no—
321C2×C4×C43—42no—
322C2×C4×C43—42no—
323C2×C4×C43—42no—
324C2×C4×C43C22×D412yes—
325C2×C4×C43C22×D412yes—
326C2×C4×C43C22×D412yes—
327C2×C4×C43C22×D412yes—
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C43C2×#4112yes—
330C2×C4×C43H(5,𝔽2)12yes—
331C2×C4×C43C2511yescharacteristic
332C22⋊D43—48no—
333C22⋊D43—48no—
334C2×Dic43—24no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—48no—
339C2×Dic43—42no—
340C2×Dic43—42no—
341D172—22no—
342D172—22no—
343D172—42no—
344C4×D43—48no—
345Dic86—24no—
346Dic86—22no—
347Dic86—22no—
348Dic86—22no—
349Dic86—48no—
350Dic86—42no—
351Dic86C2×#4114yes—
352C43⋊C8—22no—
353C43⋊C8—22no—
354C43⋊C8—22no—
355C43⋊C8—22no—
356C2×#3327—431nomaximal, Sylow
357C22×C43—22no—
358C22×C43—22no—
359C22×C43—22no—
360C22×C43—22no—
361C22×C43—22no—
362C22×C43—22no—
363C22×C43—44no—
364C22×C43—44no—
365C22×C43#54612yes—
366C22×C43#57512yes—
367C22×C43#57812yes—
368C22×C43C23×D411yescharacteristic
369C2×D43—42no—
370C2×D43—42no—
371C2×D43—42no—
372C2×D43—84no—
373C4×C43—22no—
374C4×C43—22no—
375C4×C43—22no—
376C4×C43—22no—
377C4×C43—42no—
378C4×C43—42no—
379C4×C43—42no—
380C4×C43—42no—
381C4×C43#54612yes—
382C4×C43C22×#4111yescharacteristic
383C4×C43C2×H(5,𝔽2)11yescharacteristic
384Dic43—24no—
385Dic43—42no—
386Dic43—42no—
387C2×#552D4311yescharacteristic, complemented
388C2×#548—431no—
389#3327—4316no—
390C2×#488—431no—
391C2×#484—431no—
392C2×#482—431no—
393C2×#479—431no—
394C2×#470—431no—
395C2×#468—431no—
396C2×#464—431no—
397C2×#452—431no—
398C2×#451—431no—
399C2×C4×Q16—431no—
400C2×#436—431no—
401C2×#417—431no—
402C2×#419—431no—
403C2×C43—42no—
404C2×C43—42no—
405C2×C43#332714yescomplemented
406C2×C43C2×#54611yescharacteristic
407C2×C43C2×#57511yescharacteristic
408C2×C43C2×#57811yescharacteristic
409D43—82no—
410C22×#41—431no—
411C23×Q8—431no—
412C22×Q16—431no—
413C22×Q16—431no—
414C22×SD16—431no—
415C22×M16—431no—
416C22×M16—431no—
417#552—24no—
418#552C2×D4318yescomplemented
419#548—438no—
420#548—864no—
421C2×#126—21no—
422C2×#125—21no—
423C2×#125C2×D4311yescharacteristic
424C2×#124—431no—
425C2×#124—861no—
426C2×#123—21no—
427C2×C22⋊Q8—431no—
428C2×C22⋊Q8—861no—
429C2×C22⋊Q8C2×D4311yescharacteristic
430C2×C22⋊Q8C2×D4311yescharacteristic
431C2×#121—431no—
432C2×#121—861no—
433C2×C4×Q8—431no—
434C2×C4×Q8C2×D4311yescharacteristic
435C2×C4×D4—861no—
436C2×C4×D4C2×D4311yescharacteristic
437C2×#117—21no—
438C2×#117C2×D4311yescharacteristic
439C22×C4⋊C4C2×D4311yescharacteristic
440#488—438no—
441#484—438no—
442#482—438no—
443#479—438no—
444#470—438no—
445#468—438no—
446#464—438no—
447#452—438no—
448#451—438no—
449C4×Q16—438no—
450#436—438no—
451C2×#107—431no—
452C2×#107—431no—
453C2×#106—431no—
454C2×C4⋊C8—431no—
455#419—438no—
456#417—438no—
457C2×#103—431no—
458C2×#103—431no—
459C2×#103—431no—
460C2×#103—431no—
461C2×#103—431no—
462C2×#103—431no—
463C2×#103—431no—
464C2×#102—431no—
465C2×#102—431no—
466C2×#102—431no—
467C2×C22⋊C8—431no—
468C2×C22⋊C8—431no—
469C2×C4×C8—431no—
470C43C2×#332711yescharacteristic, complemented, Sylow
471C2×#41—434no—
472C2×#41—864no—
473C2×#41—862no—
474C2×#41—1722no—
475C22×Q8—431no—
476C22×Q8—431no—
477C22×Q8—434no—
478C22×Q8—864no—
479C22×Q8—861no—
480C22×Q8—862no—
481C22×Q8—1722no—
482C22×Q8C22×D4311yescharacteristic
483C22×D4—431no—
484C22×D4—861no—
485C22×D4—861no—
486C22×D4C22⋊D4311yescharacteristic
487C23×C4—21no—
488C23×C4—861no—
489C23×C4—861no—
490C23×C4C22×D4311yescharacteristic
491C23×C4C22×D4311yescharacteristic
492C2×Q16—434no—
493C2×Q16—434no—
494C2×Q16—864no—
495C2×Q16—1722no—
496C2×SD16—434no—
497C2×SD16—1722no—
498C2×M16—434no—
499C2×M16—434no—
500C2×M16—1722no—
501C2×M16—1722no—
502C22×C8—431no—
503C22×C8—431no—
504C22×C8—431no—
505C22×C8—431no—
506#126—28no—
507#125—28no—
508#125—22no—
509#125C22×D4314yes—
510#124—434no—
511#124—868no—
512#124—862no—
513#123—28no—
514C22⋊Q8—22no—
515C22⋊Q8—22no—
516C22⋊Q8—434no—
517C22⋊Q8—862no—
518C22⋊Q8—868no—
519C22⋊Q8C22×D4314yes—
520C22⋊Q8C22×D4314yes—
521#121—434no—
522#121—868no—
523#121—862no—
524C4×Q8—22no—
525C4×Q8—434no—
526C4×Q8—862no—
527C4×Q8C22×D4314yes—
528C4×D4—868no—
529C4×D4C22⋊D4314yes—
530C4×D4C22×D4314yes—
531#117—22no—
532#117—28no—
533#117C22×D4314yes—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—431no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4C22⋊D4311yescharacteristic
545C2×C4⋊C4C22×D4311yescharacteristic
546C2×C4⋊C4C22×D4311yescharacteristic
547C2×C4⋊C4C22×D4314yes—
548C2×C4⋊C4C22×D4311yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4C22⋊D4311yescharacteristic
557C2×C22⋊C4C22⋊D4311yescharacteristic
558C2×C42—21no—
559C2×C42—21no—
560C2×C42—861no—
561C2×C42C22×D4311yescharacteristic
562#107—434no—
563#107—434no—
564#106—434no—
565C4⋊C8—434no—
566#103—434no—
567#103—434no—
568#103—434no—
569#103—434no—
570#103—434no—
571#103—434no—
572#103—434no—
573#102—434no—
574#102—434no—
575#102—434no—
576C22⋊C8—434no—
577C22⋊C8—434no—
578C4×C8—434no—
579C24—861no—
580C24C2×C22⋊D4311yescharacteristic
581C24C2×C22⋊D4311yescharacteristic
582#41—868no—
583#41—1724no—
584#41—1728no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—434no—
589C2×Q8—432no—
590C2×Q8—432no—
591C2×Q8—868no—
592C2×Q8—861no—
593C2×Q8—864no—
594C2×Q8—861no—
595C2×Q8—862no—
596C2×Q8—862no—
597C2×Q8—862no—
598C2×Q8—1724no—
599C2×Q8—1724no—
600C2×Q8—1728no—
601C2×Q8C23×D4312yes—
602C2×D4—42no—
603C2×D4—432no—
604C2×D4—864no—
605C2×D4—864no—
606C2×D4—861no—
607C2×D4—862no—
608C2×D4—862no—
609C2×D4—1724no—
610C2×D4—1724no—
611C2×D4C2×C22⋊D4314yes—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—44no—
622C22×C4—861no—
623C22×C4—864no—
624C22×C4—861no—
625C22×C4—861no—
626C22×C4—864no—
627C22×C4—1724no—
628C22×C4—1724no—
629C22×C4C2×C22⋊D4312yes—
630C22×C4C2×C22⋊D4312yes—
631C22×C4C2×C22⋊D4311yescharacteristic
632C22×C4C2×C22⋊D4311yescharacteristic
633C22×C4C2×C22⋊D4311yescharacteristic
634C22×C4C2×C22⋊D4311yescharacteristic
635C22×C4C23×D4312yes—
636C22×C4C23×D4312yes—
637C22×C4C23×D4311yescharacteristic
638Q16—868no—
639Q16—1724no—
640SD16—1724no—
641M16—1724no—
642M16—1724no—
643C2×C8—432no—
644C2×C8—432no—
645C2×C8—432no—
646C2×C8—432no—
647C2×C8—862no—
648C2×C8—862no—
649C2×C8—862no—
650C2×C8—862no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—21no—
660C4⋊C4—432no—
661C4⋊C4—861no—
662C4⋊C4—864no—
663C4⋊C4—864no—
664C4⋊C4C2×C22⋊D4314yes—
665C4⋊C4C23×D4312yes—
666C4⋊C4C23×D4312yes—
667C4⋊C4C23×D4312yes—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—864no—
672C22⋊C4—864no—
673C22⋊C4—864no—
674C22⋊C4—864no—
675C22⋊C4C2×C22⋊D4314yes—
676C22⋊C4C2×C22⋊D4314yes—
677C42—24no—
678C42—24no—
679C42—864no—
680C42C2×C22⋊D4312yes—
681C42C23×D4312yes—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—862no—
689C23—1722no—
690C23—1722no—
691C23—1722no—
692C23C22×C22⋊D4312yes—
693C23C22×C22⋊D4312yes—
694C23C22×C22⋊D4311yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—42no—
698Q8—434no—
699Q8—862no—
700Q8—864no—
701Q8—862no—
702Q8—862no—
703Q8—1728no—
704Q8—1722no—
705D4—44no—
706D4—862no—
707D4—862no—
708D4—1728no—
709D4—1728no—
710D4—1722no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—48no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—862no—
731C2×C4—864no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—1728no—
735C2×C4—1728no—
736C2×C4—1722no—
737C2×C4—1722no—
738C2×C4C22×C22⋊D4312yes—
739C2×C4C22×C22⋊D4312yes—
740C2×C4C22×C22⋊D4312yes—
741C2×C4C22×C22⋊D4312yes—
742C2×C4C22×C22⋊D4311yescharacteristic
743C2×C4#41×D4312yes—
744C2×C4#1306337112yes—
745C2×C4C24×D4311yescharacteristic
746C8—862no—
747C8—862no—
748C8—862no—
749C8—862no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—44no—
758C22—3444no—
759C22—1722no—
760C22—1722no—
761C22—1722no—
762C22#1458353712yes—
763C22#1458369712yes—
764C22#1458371412yes—
765C22C23×C22⋊D4311yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—864no—
775C4—1722no—
776C4—1722no—
777C4#1458353712yes—
778C4C2×#41×D4311yescharacteristic
779C4C2×#1306337111yescharacteristic
780C2—42no—
781C2—42no—
782C2—3442no—
783C2#1914685714yesdirect product factor
784C2C2×#1458353711yescharacteristic
785C2C2×#1458369711yescharacteristic
786C2C2×#1458371411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#552C2
socleC23×C43C22×D4
prime radicalC2×#14583558C2
hypercenterC2×#552D43
hypocenterC43C2×#3327
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #19146857C2direct (N × H)
3. C2×#14583256C2semidirect
4. C2×#14583234C2semidirect
5. C2×#14583223C2semidirect
6. C2×#14583203C2semidirect
7. C2×#14583155C2semidirect
8. C2×#14583147C2semidirect
9. C2×#14583121C2semidirect
10. C2×#14583059C2semidirect
11. C2×#14583054C2semidirect
12. C2×C4×#10621885C2semidirect
13. C2×#14582977C2semidirect
14. C2×#14582898C2semidirect
15. C2×#14582907C2semidirect
16. C2×C43×#552C2semidirect
34. #14583256C22semidirect
35. #14583234C22semidirect
36. #14583223C22semidirect
37. #14583203C22semidirect
38. #14583155C22semidirect
39. #14583147C22semidirect
40. #14583121C22semidirect
41. #14583059C22semidirect
42. #14583054C22semidirect
43. C4×#10621885C22semidirect
44. #14582977C22semidirect
49. #14582907C22semidirect
50. #14582898C22semidirect
65. C43×#552C22semidirect
387. C2×#552D43semidirect
405. C2×C43#3327semidirect
418. #552C2×D43semidirect
470. C43C2×#3327semidirect
783. C2#19146857direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835582
#191468572
C2×#145832562
C2×#145832342
C2×#145832232
C2×#145832032
C2×#145831552
C2×#145831472
C2×#145831212
C2×#145830592
C2×#145830542
C2×C4×#106218852
C2×#145829772
C2×#145828982
C2×#145829072
C2×C43×#5522
C2×#332743