Finite Group Databasebeta

← C2×#19146887 #25973492

Subgroups — C2×#19146887 #25973492

Order 11008.

2146 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583612C211yesmaximal, characteristic
2C2×#14583562C211yesmaximal, characteristic, complemented
3#19146887C2116yesmaximal, direct product factor
4C2×#14583248C211yesmaximal, characteristic, complemented
5C2×#14583243C211yesmaximal, characteristic, complemented
6C2×#14583193C211yesmaximal, characteristic, complemented
7C2×#14583147C211yesmaximal, characteristic, complemented
8C2×#14583146C211yesmaximal, characteristic, complemented
9C2×#14583103C211yesmaximal, characteristic, complemented
10C2×#14583040C211yesmaximal, characteristic, complemented
11C2×#14583039C211yesmaximal, characteristic, complemented
12C2×#14582986C211yesmaximal, characteristic, complemented
13C2×#14582974C211yesmaximal, characteristic, complemented
14C2×#14582907C211yesmaximal, characteristic, complemented
15C2×#14582906C211yesmaximal, characteristic, complemented
16C2×C43×#485C211yesmaximal, characteristic, complemented
17C23×Dic86C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621873C2211yescharacteristic
21C22×#10621884C2211yescharacteristic
22C22×#10621877C2211yescharacteristic
23C22×#10621872C2211yescharacteristic
24#14583612—24no—
25#14583612C2218yes—
26#14583562—24no—
27#14583562C2218yescomplemented
28C2×#13063324—21no—
29C2×#13063324C2211yescharacteristic
30C2×#13063323C2211yescharacteristic
31C2×#13063313—21no—
32C2×#13063311—21no—
33C2×#13063305C2211yescharacteristic
34C2×#13063303—21no—
35C2×#13063302—21no—
36C2×#13063300C2211yescharacteristic
37C2×#13063299C2211yescharacteristic
38C2×#13063298—21no—
39C2×#13063290C2211yescharacteristic
40C2×#13063287C2211yescharacteristic
41C2×C4×C22⋊D43C2211yescharacteristic
42C2×(C22⋊D43)⋊C4—21no—
43C2×#13063283C2211yescharacteristic
44C2×#13063282—21no—
45#14583248C2218yescomplemented
46#14583243C2218yescomplemented
47#14583193C2218yescomplemented
48#14583147C2218yescomplemented
49#14583146C2218yescomplemented
50#14583103C2218yescomplemented
51#14583040C2218yescomplemented
52#14583039C2218yescomplemented
53#14582986C2218yescomplemented
54#14582974C2218yescomplemented
55C2×#13063258C2211yescharacteristic
56C2×Dic43⋊C8C2211yescharacteristic
57#14582907C2218yescomplemented
58#14582906C2218yescomplemented
59C2×#13063250C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063248C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C2×C22⋊Q8×C43C2211yescharacteristic
70C2×#117×C43C2211yescharacteristic
71C43×#485C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C22×Dic86—24no—
78C22×Dic86—22no—
79C22×Dic86—21no—
80C22×Dic86—21no—
81C22×Dic86—21no—
82C22×Dic86—42no—
83C22×Dic86C2311yescharacteristic
84C22×Dic86C2314yes—
85C22×Dic86C2311yescharacteristic
86C2×Q8×D43—22no—
87C2×Q8×D43—24no—
88C2×Q8×D43—42no—
89C2×Q8×D43C2314yes—
90C22×D172—21no—
91C22×D172C2311yescharacteristic
92C22×C22⋊D43—21no—
93C22×C22⋊D43D411yescharacteristic
94C23×Dic43—21no—
95C22×C4×D43—21no—
96C22×C4×D43—21no—
97C22×C4×D43C2311yescharacteristic
98C2×#10621873—24no—
99C2×#10621873—42no—
100C2×#10621873C2314yes—
101C2×#10621873C2314yes—
102C2×#10621884—42no—
103C2×#10621884C2314yes—
104C2×#10621877—42no—
105C2×#10621877C2314yes—
106C2×#10621872—42no—
107C2×#10621872C2314yes—
108C22×C43⋊C8C2311yescharacteristic
109C22×C43⋊C8C2311yescharacteristic
110#13063324—28no—
111#13063324—22no—
112#13063324C2314yes—
113#13063323—22no—
114#13063323C2314yes—
115#13063313—28no—
116#13063311—28no—
117#13063305—22no—
118#13063305C2314yes—
119#13063303—28no—
120#13063302—28no—
121#13063300—22no—
122#13063300C2314yes—
123#13063299—22no—
124#13063299C2314yes—
125#13063298—28no—
126#13063290—22no—
127#13063290C2314yes—
128#13063287—22no—
129#13063287C2314yes—
130C4×C22⋊D43D414yes—
131C4×C22⋊D43C2314yes—
132(C22⋊D43)⋊C4—28no—
133#13063283—22no—
134#13063283C2314yes—
135#13063282—28no—
136C2×C4⋊Dic43—21no—
137C2×C4⋊Dic43C2311yescharacteristic
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×Dic43⋊C4—21no—
141C2×Dic43⋊C4—21no—
142C2×Dic43⋊C4D411yescharacteristic
143C2×C22⋊Dic43D411yescharacteristic
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4D411yescharacteristic
150C2×C4×Dic43—21no—
151C2×C4×Dic43—21no—
152C2×C4×Dic43C2311yescharacteristic
153#13063258C2314yes—
154Dic43⋊C8C2314yes—
155#13063250C2314yes—
156#13063250C2314yes—
157#13063249C2314yes—
158#13063248C2314yes—
159#13063248C2314yes—
160#13063248C2314yes—
161#13063248C2314yes—
162#13063245C2314yes—
163(C2×D43)⋊C8C2314yes—
164C8×Dic43C2314yes—
165C22×Q8×C43C2311yescharacteristic
166C23×C4×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C22⋊Q8×C43—22no—
170C22⋊Q8×C43C2314yes—
171#117×C43—22no—
172#117×C43C2314yes—
173C2×C4⋊C4×C43—21no—
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C22⋊C4×C43—21no—
178C2×C22⋊C4×C43—21no—
179C2×C42×C43—21no—
180#107×C43C2314yes—
181#106×C43C2314yes—
182#103×C43C2314yes—
183#103×C43C2314yes—
184C22⋊C8×C43C2314yes—
185C24×C43C2×D411yescharacteristic
186C23×D43—21no—
187C23×D43C2×D411yescharacteristic
188C2×Q8×C43—21no—
189C2×Q8×C43—22no—
190C2×Q8×C43—22no—
191C2×Q8×C43C2412yes—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D412yes—
200C22×C4×C43C2412yes—
201C22×C4×C43C2411yescharacteristic
202C2×C22⋊D43—24no—
203C2×C22⋊D43—24no—
204C2×C22⋊D43—82no—
205C2×C22⋊D43C2×D414yes—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—24no—
210C22×Dic43—44no—
211C22×Dic43C2×D411yescharacteristic
212C22×Dic43C2×D411yescharacteristic
213C22×Dic43C2×D411yescharacteristic
214Q8×D43—28no—
215Q8×D43—44no—
216Q8×D43—48no—
217C2×D172—21no—
218C2×D172—24no—
219C2×D172—22no—
220C2×D172—22no—
221C2×D172—82no—
222C2×D172C2412yes—
223C2×C4×D43—22no—
224C2×C4×D43—22no—
225C2×C4×D43—24no—
226C2×C4×D43—24no—
227C2×C4×D43—44no—
228C2×C4×D43—44no—
229C2×C4×D43C2×D412yes—
230C2×C4×D43C2412yes—
231C2×Dic86—21no—
232C2×Dic86—22no—
233C2×Dic86—22no—
234C2×Dic86—22no—
235C2×Dic86—28no—
236C2×Dic86—24no—
237C2×Dic86—21no—
238C2×Dic86—24no—
239C2×Dic86—24no—
240C2×Dic86—44no—
241C2×Dic86—48no—
242C2×Dic86—44no—
243C2×Dic86—44no—
244C2×Dic86—82no—
245C2×Dic86#4114yes—
246C2×Dic86C2412yes—
247C2×Dic86C2412yes—
248C2×C8×C43—22no—
249C2×C8×C43—22no—
250C2×C8×C43C2412yes—
251C2×C8×C43C2412yes—
252C4⋊C4×C43—24no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43C2412yes—
257C4⋊C4×C43C2412yes—
258C4⋊C4×C43C2412yes—
259C22⋊C4×C43—24no—
260C22⋊C4×C43—24no—
261C42×C43—24no—
262C22⋊Dic43C2×D414yes—
263#10621884—44no—
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4C2×D414yes—
270C4⋊Dic43—21no—
271C4⋊Dic43—24no—
272C4⋊Dic43C2412yes—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275Dic43⋊C4—24no—
276Dic43⋊C4—24no—
277Dic43⋊C4C2×D414yes—
278C4×Dic43—24no—
279C4×Dic43—24no—
280C4×Dic43C2×D412yes—
281C4×Dic43C2412yes—
282#10621877—44no—
283C2×C43⋊C8—22no—
284C2×C43⋊C8—22no—
285C2×C43⋊C8C2412yes—
286C2×C43⋊C8C2412yes—
287#10621873—28no—
288#10621873—44no—
289#10621872—44no—
290C23×C43—22no—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43C22×D412yes—
294C23×C43C22×D411yescharacteristic
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—42no—
300C22×D43—42no—
301C22×D43—42no—
302C22×D43C22×D412yes—
303Q8×C43—22no—
304Q8×C43—22no—
305Q8×C43—42no—
306C2×C4×C43—22no—
307C2×C4×C43—24no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—42no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43C22×D412yes—
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C2×#4112yes—
321C2×C4×C43H(5,𝔽2)12yes—
322C2×C4×C43C2511yescharacteristic
323C22⋊D43—28no—
324C22⋊D43—84no—
325C2×Dic43—24no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—48no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43#13714yes—
335C2×Dic43C22×D412yes—
336C2×Dic43C22×D412yes—
337C2×Dic43C22×D412yes—
338D172—22no—
339D172—22no—
340D172—42no—
341D172—84no—
342C4×D43—24no—
343C4×D43—22no—
344C4×D43—22no—
345C4×D43—48no—
346C4×D43—48no—
347Dic86—24no—
348Dic86—22no—
349Dic86—22no—
350Dic86—22no—
351Dic86—48no—
352Dic86—48no—
353Dic86—42no—
354Dic86—84no—
355Dic86C2×#4114yes—
356C8×C43—22no—
357C8×C43—22no—
358C43⋊C8—22no—
359C43⋊C8—22no—
360C2×#3329—431nomaximal, Sylow
361C22×C43—22no—
362C22×C43—22no—
363C22×C43—22no—
364C22×C43—44no—
365C22×C43#54612yes—
366C22×C43C2×#13712yes—
367C22×C43#57712yes—
368C22×C43C23×D411yescharacteristic
369C2×D43—22no—
370C2×D43—22no—
371C2×D43—22no—
372C2×D43—44no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—84no—
377C4×C43—22no—
378C4×C43—42no—
379C4×C43—42no—
380C4×C43—42no—
381C4×C43—42no—
382C4×C43#54612yes—
383C4×C43C22×#4111yescharacteristic
384C4×C43C2×H(5,𝔽2)11yescharacteristic
385Dic43—24no—
386Dic43—22no—
387Dic43—22no—
388Dic43—42no—
389Dic43—42no—
390Dic43C2×#13714yes—
391C2×#555—431no—
392C2×D4×Q8—431no—
393#3329—4316no—
394C2×#487—431no—
395C2×#485—431no—
396C2×#485D4311yescharacteristic, complemented
397C2×#477—431no—
398C2×#468—431no—
399C2×#468—431no—
400C2×#461—431no—
401C2×#448—431no—
402C2×#448—431no—
403C2×C4×SD16—431no—
404C2×#436—431no—
405C2×#419—431no—
406C2×#419—431no—
407C2×C43—42no—
408C2×C43#332914yescomplemented
409C2×C43C2×#54611yescharacteristic
410C2×C43C22×#13711yescharacteristic
411C2×C43C2×#57711yescharacteristic
412D43—42no—
413D43—82no—
414C23×Q8—431no—
415C23×Q8—431no—
416C22×SD16—431no—
417C22×SD16—431no—
418C22×SD16—431no—
419C22×M16—431no—
420C22×M16—431no—
421#555—438no—
422#555—864no—
423D4×Q8—438no—
424D4×Q8—864no—
425C2×C4⋊Q8—431no—
426C2×C4⋊Q8—431no—
427C2×C4⋊Q8—861no—
428C2×#124—861no—
429C2×#124—861no—
430C2×C22⋊Q8—431no—
431C2×C22⋊Q8—861no—
432C2×C22⋊Q8—861no—
433C2×C22⋊Q8C2×D4311yescharacteristic
434C2×#121—431no—
435C2×#121—431no—
436C2×#121—861no—
437C2×C4×Q8—431no—
438C2×C4×D4—431no—
439C2×C4×D4—431no—
440C2×C4×D4—861no—
441C2×#117—431no—
442C2×#117—861no—
443C2×#117C2×D4311yescharacteristic
444#487—438no—
445#485—438no—
446#485C2×D4318yescomplemented
447#477—438no—
448#468—438no—
449#468—438no—
450#461—438no—
451#448—438no—
452#448—438no—
453C4×SD16—438no—
454#436—438no—
455C2×#107—431no—
456C2×#107C2×D4311yescharacteristic
457C2×#106C2×D4311yescharacteristic
458C2×C4⋊C8—431no—
459#419—438no—
460#419—438no—
461C2×#103—431no—
462C2×#103—431no—
463C2×#103—431no—
464C2×#103—431no—
465C2×#103—431no—
466C2×#103—431no—
467C2×#103—431no—
468C2×#103C2×D4311yescharacteristic
469C2×#103C2×D4311yescharacteristic
470C2×#102—431no—
471C2×C22⋊C8—431no—
472C2×C22⋊C8C2×D4311yescharacteristic
473C2×C4×C8—431no—
474C43C2×#332911yescharacteristic, complemented, Sylow
475C22×Q8—434no—
476C22×Q8—431no—
477C22×Q8—431no—
478C22×Q8—434no—
479C22×Q8—861no—
480C22×Q8—861no—
481C22×Q8—864no—
482C22×Q8—862no—
483C22×Q8—861no—
484C22×Q8—862no—
485C22×Q8—864no—
486C22×Q8—1722no—
487C22×Q8—1722no—
488C22×Q8C22×D4311yescharacteristic
489C22×D4—431no—
490C22×D4—431no—
491C22×D4—861no—
492C22×D4—861no—
493C23×C4—431no—
494C23×C4—861no—
495C23×C4—861no—
496C23×C4—861no—
497C23×C4C22×D4311yescharacteristic
498C2×SD16—434no—
499C2×SD16—434no—
500C2×SD16—434no—
501C2×SD16—864no—
502C2×SD16—1722no—
503C2×SD16—1722no—
504C2×M16—434no—
505C2×M16—434no—
506C2×M16—1722no—
507C2×M16—1722no—
508C22×C8—431no—
509C22×C8—431no—
510C22×C8C22×D4311yescharacteristic
511C22×C8C22×D4311yescharacteristic
512C4⋊Q8—434no—
513C4⋊Q8—434no—
514C4⋊Q8—862no—
515C4⋊Q8—862no—
516C4⋊Q8—868no—
517#124—868no—
518#124—868no—
519C22⋊Q8—22no—
520C22⋊Q8—434no—
521C22⋊Q8—868no—
522C22⋊Q8—868no—
523C22⋊Q8—862no—
524C22⋊Q8C22×D4314yes—
525#121—434no—
526#121—434no—
527#121—868no—
528#121—862no—
529#121—862no—
530C4×Q8—434no—
531C4×Q8—862no—
532C4×D4—434no—
533C4×D4—434no—
534C4×D4—434no—
535C4×D4—862no—
536C4×D4—868no—
537#117—22no—
538#117—434no—
539#117—868no—
540#117—862no—
541#117C22×D4314yes—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—431no—
544C2×C4⋊C4—431no—
545C2×C4⋊C4—861no—
546C2×C4⋊C4—861no—
547C2×C4⋊C4—861no—
548C2×C4⋊C4—861no—
549C2×C4⋊C4—861no—
550C2×C4⋊C4C22×D4311yescharacteristic
551C2×C4⋊C4C22×D4311yescharacteristic
552C2×C4⋊C4C22×D4311yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—431no—
556C2×C22⋊C4—431no—
557C2×C22⋊C4—861no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C42—21no—
563C2×C42—431no—
564C2×C42—861no—
565C2×C42—861no—
566#107—434no—
567#107C22×D4314yes—
568#106C22×D4314yes—
569C4⋊C8—434no—
570#103—434no—
571#103—434no—
572#103—434no—
573#103—434no—
574#103—434no—
575#103—434no—
576#103—434no—
577#103C22×D4314yes—
578#103C22×D4314yes—
579#102—434no—
580C22⋊C8—434no—
581C22⋊C8C22×D4314yes—
582C4×C8—434no—
583C24—431no—
584C24—861no—
585C24D4×D4311yescharacteristic
586C2×Q8—21no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—434no—
590C2×Q8—432no—
591C2×Q8—432no—
592C2×Q8—864no—
593C2×Q8—864no—
594C2×Q8—868no—
595C2×Q8—861no—
596C2×Q8—864no—
597C2×Q8—861no—
598C2×Q8—862no—
599C2×Q8—868no—
600C2×Q8—862no—
601C2×Q8—862no—
602C2×Q8—3442no—
603C2×Q8—1724no—
604C2×Q8—1724no—
605C2×Q8—1728no—
606C2×Q8—1724no—
607C2×Q8—1724no—
608C2×Q8—1728no—
609C2×Q8C23×D4312yes—
610C2×D4—434no—
611C2×D4—432no—
612C2×D4—864no—
613C2×D4—864no—
614C2×D4—864no—
615C2×D4—861no—
616C2×D4—862no—
617C2×D4—862no—
618C2×D4—3442no—
619C2×D4—3442no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—431no—
627C22×C4—431no—
628C22×C4—431no—
629C22×C4—432no—
630C22×C4—432no—
631C22×C4—864no—
632C22×C4—864no—
633C22×C4—861no—
634C22×C4—862no—
635C22×C4—862no—
636C22×C4—864no—
637C22×C4—861no—
638C22×C4—861no—
639C22×C4—1724no—
640C22×C4—1724no—
641C22×C4—1724no—
642C22×C4D4×D4312yes—
643C22×C4D4×D4311yescharacteristic
644C22×C4C23×D4312yes—
645C22×C4C23×D4311yescharacteristic
646SD16—868no—
647SD16—1724no—
648SD16—1724no—
649M16—1724no—
650M16—1724no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—432no—
654C2×C8—432no—
655C2×C8—862no—
656C2×C8—862no—
657C2×C8C23×D4312yes—
658C2×C8C23×D4312yes—
659C4⋊C4—24no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—434no—
664C4⋊C4—432no—
665C4⋊C4—864no—
666C4⋊C4—864no—
667C4⋊C4—864no—
668C4⋊C4—864no—
669C4⋊C4—864no—
670C4⋊C4—861no—
671C4⋊C4C23×D4312yes—
672C4⋊C4C23×D4312yes—
673C4⋊C4C23×D4312yes—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—434no—
677C22⋊C4—434no—
678C22⋊C4—864no—
679C22⋊C4—864no—
680C22⋊C4—864no—
681C22⋊C4—864no—
682C22⋊C4—864no—
683C42—24no—
684C42—432no—
685C42—432no—
686C42—864no—
687C42—864no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—432no—
692C23—862no—
693C23—862no—
694C23—862no—
695C23—862no—
696C23—1722no—
697C23—1722no—
698C23—1722no—
699C23C2×D4×D4312yes—
700C23C2×D4×D4311yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—42no—
704Q8—434no—
705Q8—862no—
706Q8—864no—
707Q8—862no—
708Q8—862no—
709Q8—3444no—
710Q8—1728no—
711Q8—1728no—
712Q8—1722no—
713D4—868no—
714D4—862no—
715D4—862no—
716D4—3444no—
717D4—3444no—
718D4—1722no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—434no—
732C2×C4—432no—
733C2×C4—432no—
734C2×C4—432no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—864no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—864no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—1728no—
745C2×C4—1728no—
746C2×C4—1728no—
747C2×C4—1722no—
748C2×C4—1722no—
749C2×C4C2×D4×D4312yes—
750C2×C4C2×D4×D4311yescharacteristic
751C2×C4#41×D4312yes—
752C2×C4#1306337112yes—
753C2×C4C24×D4311yescharacteristic
754C8—22no—
755C8—22no—
756C8—862no—
757C8—862no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—44no—
762C22—862no—
763C22—862no—
764C22—862no—
765C22—3444no—
766C22—1722no—
767C22—1722no—
768C22—1722no—
769C22—1724no—
770C22#1458354112yes—
771C22#137×D4312yes—
772C22#1458370612yes—
773C22C22×D4×D4311yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—434no—
780C4—862no—
781C4—864no—
782C4—862no—
783C4—1722no—
784C4—1722no—
785C4#1458354112yes—
786C4C2×#41×D4311yescharacteristic
787C4C2×#1306337111yescharacteristic
788C2—42no—
789C2—3442no—
790C2—1722no—
791C2#1914688714yesdirect product factor
792C2C2×#1458354111yescharacteristic
793C2C2×#137×D4311yescharacteristic
794C2C2×#1458370611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#485C2
socleC23×C43C22×D4
prime radicalC2×#14583612C2
hypercenterC2×#485D43
hypocenterC43C2×#3329
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
2. C2×#14583562C2semidirect
3. #19146887C2direct (N × H)
4. C2×#14583248C2semidirect
5. C2×#14583243C2semidirect
6. C2×#14583193C2semidirect
7. C2×#14583147C2semidirect
8. C2×#14583146C2semidirect
9. C2×#14583103C2semidirect
10. C2×#14583040C2semidirect
11. C2×#14583039C2semidirect
12. C2×#14582986C2semidirect
13. C2×#14582974C2semidirect
14. C2×#14582907C2semidirect
15. C2×#14582906C2semidirect
16. C2×C43×#485C2semidirect
27. #14583562C22semidirect
45. #14583248C22semidirect
46. #14583243C22semidirect
47. #14583193C22semidirect
48. #14583147C22semidirect
49. #14583146C22semidirect
50. #14583103C22semidirect
51. #14583040C22semidirect
52. #14583039C22semidirect
53. #14582986C22semidirect
54. #14582974C22semidirect
57. #14582907C22semidirect
58. #14582906C22semidirect
71. C43×#485C22semidirect
396. C2×#485D43semidirect
408. C2×C43#3329semidirect
446. #485C2×D43semidirect
474. C43C2×#3329semidirect
791. C2#19146887direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836122
C2×#145835622
#191468872
C2×#145832482
C2×#145832432
C2×#145831932
C2×#145831472
C2×#145831462
C2×#145831032
C2×#145830402
C2×#145830392
C2×#145829862
C2×#145829742
C2×#145829072
C2×#145829062
C2×C43×#4852
C2×#332943