Finite Group Databasebeta

← C2×#19146862 #25973465

Subgroups — C2×#19146862 #25973465

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×#14583587C211yesmaximal, characteristic, complemented
2C2×#14583557C211yesmaximal, characteristic
3#19146862C2116yesmaximal, direct product factor
4C2×#14583233C211yesmaximal, characteristic, complemented
5C2×#14583221C211yesmaximal, characteristic, complemented
6C2×#14583203C211yesmaximal, characteristic, complemented
7C2×#14583156C211yesmaximal, characteristic, complemented
8C2×#14583144C211yesmaximal, characteristic, complemented
9C2×#14583118C211yesmaximal, characteristic, complemented
10C2×#14583062C211yesmaximal, characteristic, complemented
11C2×#14583056C211yesmaximal, characteristic, complemented
12C2×C4×Dic172C211yesmaximal, characteristic, complemented
13C2×#14582978C211yesmaximal, characteristic, complemented
14C2×#14582897C211yesmaximal, characteristic, complemented
15C2×#14582906C211yesmaximal, characteristic, complemented
16C2×C43×#488C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C22×Dic172C2211yescharacteristic
20C22×#10621885C2211yescharacteristic
21C22×#10621883C2211yescharacteristic
22C22×#10621872C2211yescharacteristic
23C22×#10621872C2211yescharacteristic
24#14583587—24no—
25#14583587C2218yescomplemented
26#14583557—24no—
27#14583557C2218yes—
28C2×#13063320—21no—
29C2×#13063316—21no—
30C2×#13063311—21no—
31C2×#13063310—21no—
32C2×#13063305C2211yescharacteristic
33C2×#13063305C2211yescharacteristic
34C2×#13063302—21no—
35C2×#13063301C2211yescharacteristic
36C2×#13063298—21no—
37C2×#13063296C2211yescharacteristic
38C2×C4×Dic86C2211yescharacteristic
39C2×C4×Dic86C2211yescharacteristic
40C2×C4×D172C2211yescharacteristic
41C2×(C22⋊D43)⋊C4—21no—
42C2×#13063283—21no—
43C2×#13063283C2211yescharacteristic
44C2×C4⋊C4×D43C2211yescharacteristic
45#14583233C2218yescomplemented
46#14583221C2218yescomplemented
47#14583203C2218yescomplemented
48#14583156C2218yescomplemented
49#14583144C2218yescomplemented
50#14583118C2218yescomplemented
51#14583062C2218yescomplemented
52#14583056C2218yescomplemented
53C4×Dic172C2218yescomplemented
54#14582978C2218yescomplemented
55C2×#13063259C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×C4⋊(C43⋊C8)C2211yescharacteristic
59#14582906C2218yescomplemented
60#14582897C2218yescomplemented
61C2×#13063250C2211yescharacteristic
62C2×#13063250C2211yescharacteristic
63C2×#13063249C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063248C2211yescharacteristic
66C2×#13063246C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C2×#125×C43C2211yescharacteristic
70C2×#124×C43C2211yescharacteristic
71C43×#488C2218yescomplemented
72C2×#103×C43C2211yescharacteristic
73C2×#103×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C4×C8×C43C2211yescharacteristic
77C2×#10621900—22no—
78C2×#10621900—24no—
79C2×#10621900—42no—
80C2×#10621900C2314yes—
81C22×Dic86—21no—
82C22×Dic86C2311yescharacteristic
83C22×Dic86C2311yescharacteristic
84C2×Q8×D43—22no—
85C2×Q8×D43—24no—
86C2×Q8×D43—42no—
87C2×Q8×D43C2314yes—
88C22×D172D411yescharacteristic
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C23×Dic43—21no—
92C22×C4×D43—21no—
93C22×C4×D43—21no—
94C22×C4×D43C2311yescharacteristic
95C22×C4×D43C2311yescharacteristic
96C2×Dic172—24no—
97C2×Dic172C2314yes—
98C2×#10621885—42no—
99C2×#10621885C2314yes—
100C2×#10621883—42no—
101C2×#10621883C2314yes—
102C2×#10621872—42no—
103C2×#10621872—42no—
104C2×#10621872C2314yes—
105C2×#10621872C2314yes—
106C22×C43⋊C8C2311yescharacteristic
107C22×C43⋊C8C2311yescharacteristic
108#13063320—28no—
109#13063316—28no—
110#13063311—28no—
111#13063310—28no—
112#13063305—22no—
113#13063305—22no—
114#13063305C2314yes—
115#13063305C2314yes—
116#13063302—28no—
117#13063301—22no—
118#13063301C2314yes—
119#13063298—28no—
120#13063296—22no—
121#13063296C2314yes—
122C4×Dic86—22no—
123C4×Dic86—22no—
124C4×Dic86C2314yes—
125C4×Dic86C2314yes—
126C4×D172D414yes—
127C4×D172C2314yes—
128(C22⋊D43)⋊C4—28no—
129#13063283—22no—
130#13063283—28no—
131#13063283C2314yes—
132C2×C4⋊Dic43—21no—
133C2×C4⋊Dic43—21no—
134C2×C4⋊Dic43D411yescharacteristic
135C2×C4⋊Dic43C2311yescharacteristic
136C2×C4⋊Dic43C2311yescharacteristic
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×Dic43⋊C4—21no—
141C4⋊C4×D43—22no—
142C4⋊C4×D43C2314yes—
143C2×C22⋊Dic43—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4D411yescharacteristic
149C2×(C2×D43)⋊C4D411yescharacteristic
150C2×C4×Dic43—21no—
151C2×C4×Dic43—21no—
152C2×C4×Dic43—21no—
153#13063259C2314yes—
154#13063258C2314yes—
155#13063256C2314yes—
156C4⋊(C43⋊C8)C2314yes—
157#13063250C2314yes—
158#13063250C2314yes—
159#13063249C2314yes—
160#13063248C2314yes—
161#13063248C2314yes—
162#13063246C2314yes—
163(C2×D43)⋊C8C2314yes—
164(C2×D43)⋊C8C2314yes—
165C22×Q8×C43C2311yescharacteristic
166C22×D4×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169#125×C43—22no—
170#125×C43C2314yes—
171#124×C43—22no—
172#124×C43C2314yes—
173C2×C4⋊C4×C43—21no—
174C2×C4⋊C4×C43—21no—
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C22⋊C4×C43—21no—
178C2×C22⋊C4×C43—21no—
179C2×C42×C43C2311yescharacteristic
180#103×C43C2314yes—
181#103×C43C2314yes—
182#102×C43C2314yes—
183#102×C43C2314yes—
184C4×C8×C43C2314yes—
185C24×C43—21no—
186C23×D43C2×D411yescharacteristic
187C23×D43C2×D411yescharacteristic
188C2×Q8×C43—21no—
189C2×Q8×C43—22no—
190C2×Q8×C43—22no—
191C2×Q8×C43C2412yes—
192C2×D4×C43—21no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43C2412yes—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2411yescharacteristic
202C2×C22⋊D43—24no—
203C2×C22⋊D43—24no—
204C2×C22⋊D43—44no—
205C2×C22⋊D43—44no—
206C22×Dic43—24no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—44no—
212C22×Dic43C2×D411yescharacteristic
213C22×Dic43C2×D411yescharacteristic
214Q8×D43—28no—
215Q8×D43—44no—
216Q8×D43—48no—
217#10621900—28no—
218#10621900—44no—
219#10621900—48no—
220C2×D172—42no—
221C2×D172C2×D414yes—
222C2×C4×D43—22no—
223C2×C4×D43—22no—
224C2×C4×D43—22no—
225C2×C4×D43—22no—
226C2×C4×D43—24no—
227C2×C4×D43—24no—
228C2×C4×D43—44no—
229C2×C4×D43—44no—
230C2×C4×D43C2×D412yes—
231C2×C4×D43C2×D412yes—
232C2×C4×D43C2412yes—
233C2×C4×D43C2412yes—
234C2×Dic86—21no—
235C2×Dic86—22no—
236C2×Dic86—22no—
237C2×Dic86—22no—
238C2×Dic86—21no—
239C2×Dic86—24no—
240C2×Dic86—44no—
241C2×Dic86#4114yes—
242C2×Dic86C2412yes—
243C2×Dic86C2412yes—
244C2×C8×C43—22no—
245C2×C8×C43—22no—
246C2×C8×C43C2412yes—
247C2×C8×C43C2412yes—
248C4⋊C4×C43—24no—
249C4⋊C4×C43—24no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43C2412yes—
253C4⋊C4×C43C2412yes—
254C22⋊C4×C43—24no—
255C22⋊C4×C43—24no—
256C42×C43C2×D412yes—
257C42×C43C2412yes—
258C22⋊Dic43—24no—
259#10621885—44no—
260#10621883—44no—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—24no—
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4C2×D414yes—
266(C2×D43)⋊C4C2×D414yes—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43—24no—
270C4⋊Dic43—24no—
271C4⋊Dic43C2×D414yes—
272C4⋊Dic43C2412yes—
273C4⋊Dic43C2412yes—
274Dic43⋊C4—24no—
275Dic43⋊C4—24no—
276Dic43⋊C4—24no—
277Dic43⋊C4—24no—
278C4×Dic43—24no—
279C4×Dic43—24no—
280C4×Dic43—24no—
281C2×C43⋊C8—22no—
282C2×C43⋊C8—22no—
283C2×C43⋊C8C2412yes—
284C2×C43⋊C8C2412yes—
285Dic172—28no—
286#10621872—44no—
287#10621872—44no—
288C23×C43—22no—
289C23×C43—42no—
290C23×C43—42no—
291C23×C43—42no—
292C23×C43C22×D411yescharacteristic
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43C22×D412yes—
300C22×D43C22×D412yes—
301Q8×C43—22no—
302Q8×C43—22no—
303Q8×C43—42no—
304D4×C43—22no—
305D4×C43—22no—
306D4×C43—42no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—42no—
313C2×C4×C43—42no—
314C2×C4×C43—42no—
315C2×C4×C43C22×D412yes—
316C2×C4×C43C22×D412yes—
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43C2×#4112yes—
319C2×C4×C43H(5,𝔽2)12yes—
320C2×C4×C43C2511yescharacteristic
321C22⋊D43—48no—
322C22⋊D43—48no—
323C2×Dic43—24no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—48no—
331C2×Dic43—42no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43C22×D412yes—
335C2×Dic43C22×D412yes—
336D172—44no—
337C4×D43—24no—
338C4×D43—24no—
339C4×D43—22no—
340C4×D43—22no—
341C4×D43—22no—
342C4×D43—22no—
343C4×D43—48no—
344C4×D43—48no—
345Dic86—24no—
346Dic86—22no—
347Dic86—22no—
348Dic86—22no—
349Dic86—48no—
350Dic86—42no—
351Dic86C2×#4114yes—
352C8×C43—22no—
353C8×C43—22no—
354C43⋊C8—22no—
355C43⋊C8—22no—
356C2×#3327—431nomaximal, Sylow
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—84no—
361C22×C43#54612yes—
362C22×C43#57512yes—
363C22×C43#57812yes—
364C22×C43C23×D411yescharacteristic
365C2×D43—22no—
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—22no—
369C2×D43—22no—
370C2×D43—22no—
371C2×D43—44no—
372C2×D43—44no—
373C4×C43—22no—
374C4×C43—22no—
375C4×C43—42no—
376C4×C43—42no—
377C4×C43—42no—
378C4×C43#54612yes—
379C4×C43C22×#4111yescharacteristic
380C4×C43C2×H(5,𝔽2)11yescharacteristic
381Dic43—24no—
382Dic43—22no—
383Dic43—22no—
384Dic43—42no—
385Dic43—42no—
386Dic43—42no—
387C2×#552—431no—
388C2×#548—431no—
389#3327—4316no—
390C2×#488D4311yescharacteristic, complemented
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—82no—
404C2×C43#332714yescomplemented
405C2×C43C2×#54611yescharacteristic
406C2×C43C2×#57511yescharacteristic
407C2×C43C2×#57811yescharacteristic
408D43—42no—
409D43—42no—
410C22×#41—431no—
411C23×Q8—431no—
412C22×Q16—431no—
413C22×Q16—431no—
414C22×SD16—431no—
415C22×M16—431no—
416C22×M16—431no—
417#552—438no—
418#552—864no—
419#548—438no—
420#548—864no—
421C2×#126—861no—
422C2×#125—861no—
423C2×#125C2×D4311yescharacteristic
424C2×#124—861no—
425C2×#124C2×D4311yescharacteristic
426C2×#123—861no—
427C2×C22⋊Q8—431no—
428C2×C22⋊Q8—431no—
429C2×C22⋊Q8—431no—
430C2×C22⋊Q8—861no—
431C2×#121—431no—
432C2×#121—861no—
433C2×C4×Q8—431no—
434C2×C4×Q8—431no—
435C2×C4×D4—431no—
436C2×C4×D4—861no—
437C2×#117—431no—
438C2×#117—861no—
439C22×C4⋊C4—431no—
440#488C2×D4318yescomplemented
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×#103C2×D4311yescharacteristic
463C2×#103C2×D4311yescharacteristic
464C2×#102—431no—
465C2×#102C2×D4311yescharacteristic
466C2×#102C2×D4311yescharacteristic
467C2×C22⋊C8—431no—
468C2×C22⋊C8—431no—
469C2×C4×C8C2×D4311yescharacteristic
470C43C2×#332711yescharacteristic, complemented, Sylow
471C2×#41—434no—
472C2×#41—862no—
473C2×#41—864no—
474C2×#41—1722no—
475C22×Q8—434no—
476C22×Q8—431no—
477C22×Q8—431no—
478C22×Q8—861no—
479C22×Q8—862no—
480C22×Q8—864no—
481C22×Q8—1722no—
482C22×Q8C22×D4311yescharacteristic
483C22×D4—431no—
484C22×D4—861no—
485C22×D4—861no—
486C22×D4C22×D4311yescharacteristic
487C23×C4—431no—
488C23×C4—431no—
489C23×C4—861no—
490C23×C4—861no—
491C23×C4—861no—
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×C8C22×D4311yescharacteristic
505C22×C8C22×D4311yescharacteristic
506#126—868no—
507#125—22no—
508#125—868no—
509#125C22×D4314yes—
510#124—22no—
511#124—868no—
512#124C22×D4314yes—
513#123—868no—
514C22⋊Q8—434no—
515C22⋊Q8—434no—
516C22⋊Q8—434no—
517C22⋊Q8—868no—
518C22⋊Q8—862no—
519C22⋊Q8—862no—
520C22⋊Q8—862no—
521#121—434no—
522#121—868no—
523#121—862no—
524C4×Q8—434no—
525C4×Q8—434no—
526C4×Q8—862no—
527C4×Q8—862no—
528C4×D4—434no—
529C4×D4—434no—
530C4×D4—868no—
531#117—434no—
532#117—868no—
533#117—862no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—431no—
539C2×C4⋊C4—434no—
540C2×C4⋊C4—862no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4—861no—
545C2×C4⋊C4—861no—
546C2×C4⋊C4—861no—
547C2×C4⋊C4C22×D4311yescharacteristic
548C2×C4⋊C4C22×D4311yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—431no—
552C2×C22⋊C4—431no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4—861no—
558C2×C42—861no—
559C2×C42—861no—
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#103C22×D4314yes—
572#103C22×D4314yes—
573#102—434no—
574#102C22×D4314yes—
575#102C22×D4314yes—
576C22⋊C8—434no—
577C22⋊C8—434no—
578C4×C8C22×D4314yes—
579C24—21no—
580C24—431no—
581C24—431no—
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—864no—
592C2×Q8—861no—
593C2×Q8—861no—
594C2×Q8—862no—
595C2×Q8—868no—
596C2×Q8—862no—
597C2×Q8—862no—
598C2×Q8—1724no—
599C2×Q8—1724no—
600C2×Q8—1728no—
601C2×Q8C23×D4312yes—
602C2×D4—21no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—434no—
606C2×D4—864no—
607C2×D4—864no—
608C2×D4—1722no—
609C2×D4—1724no—
610C2×D4—1724no—
611C2×D4C23×D4312yes—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—431no—
616C22×C4—431no—
617C22×C4—432no—
618C22×C4—432no—
619C22×C4—432no—
620C22×C4—432no—
621C22×C4—864no—
622C22×C4—864no—
623C22×C4—864no—
624C22×C4—861no—
625C22×C4—862no—
626C22×C4—862no—
627C22×C4—862no—
628C22×C4—862no—
629C22×C4—861no—
630C22×C4—861no—
631C22×C4—861no—
632C22×C4—1724no—
633C22×C4—1724no—
634C22×C4—1724no—
635C22×C4D4×D4311yescharacteristic
636C22×C4D4×D4311yescharacteristic
637C22×C4C23×D4311yescharacteristic
638Q16—868no—
639Q16—1724no—
640SD16—1724no—
641M16—1724no—
642M16—1724no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—432no—
646C2×C8—432no—
647C2×C8—862no—
648C2×C8—862no—
649C2×C8C23×D4312yes—
650C2×C8C23×D4312yes—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—434no—
656C4⋊C4—432no—
657C4⋊C4—432no—
658C4⋊C4—864no—
659C4⋊C4—864no—
660C4⋊C4—864no—
661C4⋊C4—864no—
662C4⋊C4—861no—
663C4⋊C4—861no—
664C4⋊C4—864no—
665C4⋊C4—864no—
666C4⋊C4C23×D4312yes—
667C4⋊C4C23×D4312yes—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—434no—
671C22⋊C4—434no—
672C22⋊C4—864no—
673C22⋊C4—864no—
674C22⋊C4—864no—
675C22⋊C4—864no—
676C22⋊C4—864no—
677C42—864no—
678C42—864no—
679C42—864no—
680C42D4×D4312yes—
681C42C23×D4312yes—
682C23—22no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—432no—
687C23—432no—
688C23—862no—
689C23—862no—
690C23—862no—
691C23—862no—
692C23—862no—
693C23—862no—
694C23C2×D4×D4311yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—42no—
698Q8—434no—
699Q8—862no—
700Q8—864no—
701Q8—862no—
702Q8—862no—
703Q8—1728no—
704Q8—1722no—
705D4—22no—
706D4—22no—
707D4—42no—
708D4—1724no—
709D4—1728no—
710D4—1728no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—432no—
720C2×C4—432no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—864no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—864no—
730C2×C4—864no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—1728no—
735C2×C4—1728no—
736C2×C4—1728no—
737C2×C4—1722no—
738C2×C4—1722no—
739C2×C4—1722no—
740C2×C4C2×D4×D4312yes—
741C2×C4C2×D4×D4312yes—
742C2×C4C2×D4×D4311yescharacteristic
743C2×C4#41×D4312yes—
744C2×C4#1306337112yes—
745C2×C4C24×D4311yescharacteristic
746C8—22no—
747C8—22no—
748C8—862no—
749C8—862no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—84no—
754C22—862no—
755C22—862no—
756C22—862no—
757C22—862no—
758C22—862no—
759C22—862no—
760C22—1724no—
761C22—1724no—
762C22#1458354212yes—
763C22#1458369612yes—
764C22#1458371312yes—
765C22C22×D4×D4311yescharacteristic
766C4—22no—
767C4—22no—
768C4—42no—
769C4—42no—
770C4—42no—
771C4—862no—
772C4—862no—
773C4—864no—
774C4—1722no—
775C4—1722no—
776C4—1722no—
777C4#1458354212yes—
778C4C2×#41×D4311yescharacteristic
779C4C2×#1306337111yescharacteristic
780C2—82no—
781C2—1722no—
782C2—1722no—
783C2#1914686214yesdirect product factor
784C2C2×#1458354211yescharacteristic
785C2C2×#1458369611yescharacteristic
786C2C2×#1458371311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#488C2
socleC23×C43C22×D4
prime radicalC2×#14583557C2
hypercenterC2×#488D43
hypocenterC43C2×#3327
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#14583587C2semidirect
3. #19146862C2direct (N × H)
4. C2×#14583233C2semidirect
5. C2×#14583221C2semidirect
6. C2×#14583203C2semidirect
7. C2×#14583156C2semidirect
8. C2×#14583144C2semidirect
9. C2×#14583118C2semidirect
10. C2×#14583062C2semidirect
11. C2×#14583056C2semidirect
12. C2×C4×Dic172C2semidirect
13. C2×#14582978C2semidirect
14. C2×#14582897C2semidirect
15. C2×#14582906C2semidirect
16. C2×C43×#488C2semidirect
25. #14583587C22semidirect
45. #14583233C22semidirect
46. #14583221C22semidirect
47. #14583203C22semidirect
48. #14583156C22semidirect
49. #14583144C22semidirect
50. #14583118C22semidirect
51. #14583062C22semidirect
52. #14583056C22semidirect
53. C4×Dic172C22semidirect
54. #14582978C22semidirect
59. #14582906C22semidirect
60. #14582897C22semidirect
71. C43×#488C22semidirect
390. C2×#488D43semidirect
404. C2×C43#3327semidirect
440. #488C2×D43semidirect
470. C43C2×#3327semidirect
783. C2#19146862direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835872
C2×#145835572
#191468622
C2×#145832332
C2×#145832212
C2×#145832032
C2×#145831562
C2×#145831442
C2×#145831182
C2×#145830622
C2×#145830562
C2×C4×Dic1722
C2×#145829782
C2×#145828972
C2×#145829062
C2×C43×#4882
C2×#332743