Finite Group Databasebeta

← C2×#19147674 #25977617

Subgroups — C2×#19147674 #25977617

Order 11008.

1938 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583621C211yesmaximal, characteristic, complemented
2C2×#14583618C211yesmaximal, characteristic, complemented
3#19147674C2116yesmaximal, direct product factor
4C2×#14583292C211yesmaximal, characteristic, complemented
5C2×#14583290C211yesmaximal, characteristic, complemented
6C2×#14583281C211yesmaximal, characteristic
7C2×#14583122C211yesmaximal, characteristic, complemented
8C2×#14583108C211yesmaximal, characteristic, complemented
9C2×#14583107C211yesmaximal, characteristic, complemented
10C2×#14583116C211yesmaximal, characteristic
11C2×#14583113C211yesmaximal, characteristic
12C2×#14583026C211yesmaximal, characteristic, complemented
13C2×#14583002C211yesmaximal, characteristic, complemented
14C2×#14582996C211yesmaximal, characteristic, complemented
15C2×C4×#10621885C211yesmaximal, characteristic, complemented
16C2×C43×#464C211yesmaximal, characteristic, complemented
17C22×Dic172C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621873C2211yescharacteristic
21C22×#10621883C2211yescharacteristic
22C22×#10621884C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24#14583621—24no—
25#14583621C2218yescomplemented
26#14583618—24no—
27#14583618C2218yescomplemented
28C2×#13063323C2211yescharacteristic
29C2×#13063323C2211yescharacteristic
30C2×#13063320—21no—
31C2×#13063319—21no—
32C2×#13063318—21no—
33C2×#13063318—21no—
34C2×#13063314C2211yescharacteristic
35C2×#13063313C2211yescharacteristic
36C2×#13063312C2211yescharacteristic
37C2×#13063303—21no—
38C2×#13063302—21no—
39C2×Q8×Dic43C2211yescharacteristic
40C2×C4×Dic86C2211yescharacteristic
41C2×C4×Dic86C2211yescharacteristic
42C2×#13063290C2211yescharacteristic
43C2×D4×Dic43C2211yescharacteristic
44C2×#13063287C2211yescharacteristic
45C2×#13063282—21no—
46C2×#13063281—21no—
47#14583292C2218yescomplemented
48#14583290C2218yescomplemented
49#14583281C2218yes—
50#14583122C2218yescomplemented
51#14583116C2218yes—
52#14583113C2218yes—
53#14583108C2218yescomplemented
54#14583107C2218yescomplemented
55#14583026C2218yescomplemented
56#14583002C2218yescomplemented
57#14582996C2218yescomplemented
58C4×#10621885C2218yescomplemented
59C2×#13063258C2211yescharacteristic
60C2×Dic43⋊C8C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×#13063250C2211yescharacteristic
63C2×#13063249C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×#13063235C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C4×C43⋊C8C2211yescharacteristic
69C22×Q16×C43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C2×#124×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic
73C43×#464C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C22×Dic86D411yescharacteristic
78C22×Dic86C2311yescharacteristic
79C22×Dic86C2311yescharacteristic
80C22×D172C2311yescharacteristic
81C23×Dic43—21no—
82C22×C4×D43—21no—
83C2×Dic172—42no—
84C2×Dic172C2314yes—
85C2×#10621885—24no—
86C2×#10621885—42no—
87C2×#10621885C2314yes—
88C2×#10621885C2314yes—
89C2×#10621873—42no—
90C2×#10621873C2314yes—
91C2×#10621883—24no—
92C2×#10621883C2314yes—
93C2×#10621884—24no—
94C2×#10621884C2314yes—
95C2×#10621882—42no—
96C2×#10621882C2314yes—
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2311yescharacteristic
99#13063323—22no—
100#13063323—22no—
101#13063323C2314yes—
102#13063323C2314yes—
103#13063320—28no—
104#13063319—28no—
105#13063318—28no—
106#13063318—28no—
107#13063314—22no—
108#13063314C2314yes—
109#13063313—22no—
110#13063313C2314yes—
111#13063312—22no—
112#13063312C2314yes—
113#13063303—28no—
114#13063302—28no—
115Q8×Dic43—22no—
116Q8×Dic43C2314yes—
117C4×Dic86—22no—
118C4×Dic86D414yes—
119C4×Dic86C2314yes—
120C4×Dic86C2314yes—
121#13063290—22no—
122#13063290C2314yes—
123D4×Dic43—22no—
124D4×Dic43C2314yes—
125#13063287—22no—
126#13063287C2314yes—
127#13063282—28no—
128#13063281—28no—
129C2×C4⋊Dic43—21no—
130C2×C4⋊Dic43D411yescharacteristic
131C2×C4⋊Dic43C2311yescharacteristic
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4D411yescharacteristic
139C2×Dic43⋊C4D411yescharacteristic
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43—21no—
142C2×C22⋊Dic43—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×C4×Dic43—21no—
149C2×C4×Dic43—21no—
150C2×C4×Dic43—21no—
151C2×C4×Dic43C2311yescharacteristic
152C2×C4×Dic43C2311yescharacteristic
153#13063258C2314yes—
154Dic43⋊C8C2314yes—
155Dic43⋊C8C2314yes—
156#13063250C2314yes—
157#13063249C2314yes—
158#13063248C2314yes—
159#13063247C2314yes—
160#13063235C2314yes—
161#13063235C2314yes—
162C4×C43⋊C8C2314yes—
163C22×Q8×C43C2311yescharacteristic
164C22×Q8×C43C2311yescharacteristic
165C22×D4×C43C2311yescharacteristic
166C2×Q16×C43—42no—
167C2×Q16×C43C2314yes—
168C2×SD16×C43—42no—
169C2×SD16×C43C2314yes—
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172#124×C43—22no—
173#124×C43C2314yes—
174C4×Q8×C43—22no—
175C4×Q8×C43C2314yes—
176C2×C4⋊C4×C43—21no—
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C42×C43—21no—
181C2×C42×C43C2311yescharacteristic
182C4⋊C8×C43C2314yes—
183#103×C43C2314yes—
184#102×C43C2314yes—
185C24×C43—21no—
186C23×D43—21no—
187C2×Q8×C43—21no—
188C2×Q8×C43—21no—
189C2×Q8×C43—22no—
190C2×Q8×C43—22no—
191C2×Q8×C43—22no—
192C2×Q8×C43—22no—
193C2×Q8×C43C2412yes—
194C2×Q8×C43C2412yes—
195C2×D4×C43—21no—
196C2×D4×C43—22no—
197C2×D4×C43—22no—
198C2×D4×C43C2412yes—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2411yescharacteristic
205C22×Dic43—24no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—44no—
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D411yescharacteristic
212C22×Dic43C2×D411yescharacteristic
213C22×Dic43C2×D411yescharacteristic
214C2×D172—21no—
215C2×D172—22no—
216C2×D172—22no—
217C2×D172C2412yes—
218C2×C4×D43—24no—
219C2×C4×D43—44no—
220C2×Dic86—22no—
221C2×Dic86—22no—
222C2×Dic86—22no—
223C2×Dic86—22no—
224C2×Dic86—21no—
225C2×Dic86—21no—
226C2×Dic86—42no—
227C2×Dic86C2×D414yes—
228C2×Dic86C2412yes—
229C2×Dic86C2412yes—
230Q16×C43—44no—
231SD16×C43—44no—
232C2×C8×C43—22no—
233C2×C8×C43—22no—
234C2×C8×C43C2412yes—
235C2×C8×C43C2412yes—
236C4⋊C4×C43—24no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43C2412yes—
239C22⋊C4×C43—24no—
240C22⋊C4×C43—24no—
241C42×C43—24no—
242C42×C43C2×D412yes—
243C42×C43C2412yes—
244C22⋊Dic43—24no—
245C22⋊Dic43—24no—
246C22⋊Dic43—24no—
247#10621885—28no—
248#10621885—44no—
249#10621884—28no—
250#10621883—28no—
251#10621882—44no—
252(C2×D43)⋊C4—24no—
253(C2×D43)⋊C4—24no—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—24no—
257C4⋊Dic43—21no—
258C4⋊Dic43—24no—
259C4⋊Dic43C2×D414yes—
260C4⋊Dic43C2412yes—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263Dic43⋊C4—24no—
264Dic43⋊C4—24no—
265Dic43⋊C4—24no—
266Dic43⋊C4—24no—
267Dic43⋊C4C2×D414yes—
268Dic43⋊C4C2×D414yes—
269C4×Dic43—24no—
270C4×Dic43—24no—
271C4×Dic43—24no—
272C4×Dic43C2×D412yes—
273C4×Dic43C2×D412yes—
274C4×Dic43C2412yes—
275C4×Dic43C2412yes—
276C2×C43⋊C8—22no—
277C2×C43⋊C8#4114yes—
278C2×C43⋊C8C2412yes—
279C2×C43⋊C8C2412yes—
280Dic172—44no—
281#10621873—44no—
282C23×C43—22no—
283C23×C43—42no—
284C23×C43—42no—
285C23×C43—42no—
286C23×C43C22×D411yescharacteristic
287C22×D43—22no—
288C22×D43—42no—
289C22×D43—42no—
290C22×D43—42no—
291Q8×C43—22no—
292Q8×C43—22no—
293Q8×C43—22no—
294Q8×C43—22no—
295Q8×C43—42no—
296Q8×C43—42no—
297D4×C43—22no—
298D4×C43—22no—
299D4×C43—42no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—42no—
306C2×C4×C43—42no—
307C2×C4×C43—42no—
308C2×C4×C43C22×D412yes—
309C2×C4×C43C22×D412yes—
310C2×C4×C43C22×D411yescharacteristic
311C2×C4×C43C2×#4112yes—
312C2×C4×C43H(5,𝔽2)12yes—
313C2×C4×C43C2511yescharacteristic
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—48no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43C22×D412yes—
326C2×Dic43C22×D412yes—
327C2×Dic43C22×D412yes—
328C2×Dic43C22×D412yes—
329D172—22no—
330D172—22no—
331D172—42no—
332C4×D43—48no—
333Dic86—22no—
334Dic86—22no—
335Dic86—22no—
336Dic86—22no—
337Dic86—44no—
338Dic86—42no—
339Dic86—42no—
340C8×C43—22no—
341C8×C43—22no—
342C43⋊C8—22no—
343C43⋊C8C2×#4114yes—
344C2×#3402—431nomaximal, Sylow
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—84no—
349C22×C43#55012yes—
350C22×C43#57512yes—
351C22×C43#57812yes—
352C22×C43C23×D411yescharacteristic
353C2×D43—42no—
354C2×D43—42no—
355C2×D43—42no—
356C2×D43—84no—
357C4×C43—22no—
358C4×C43—22no—
359C4×C43—42no—
360C4×C43—42no—
361C4×C43—42no—
362C4×C43#55012yes—
363C4×C43C22×#4111yescharacteristic
364C4×C43C2×H(5,𝔽2)11yescharacteristic
365Dic43—22no—
366Dic43—22no—
367Dic43—22no—
368Dic43—22no—
369Dic43—42no—
370Dic43—42no—
371Dic43—42no—
372C2×#556—431no—
373C2×#556—431no—
374#3402—4316no—
375C2×#497—431no—
376C2×#497—431no—
377C2×#495—431no—
378C2×#464—431no—
379C2×#464D4311yescharacteristic, complemented
380C2×#462—431no—
381C2×#462—431no—
382C2×#463—431no—
383C2×#463—431no—
384C2×#446—431no—
385C2×#440—431no—
386C2×#440—431no—
387C2×C4×Q16—431no—
388C2×C43—82no—
389C2×C43#340214yescomplemented
390C2×C43C2×#55011yescharacteristic
391C2×C43C2×#57511yescharacteristic
392C2×C43C2×#57811yescharacteristic
393D43—82no—
394C22×Q16—431no—
395C22×Q16—431no—
396C22×Q16—431no—
397C22×Q16C2×D4311yescharacteristic
398C22×SD16—431no—
399C22×SD16—431no—
400C22×SD16—431no—
401C22×SD16C2×D4311yescharacteristic
402C22×D8—431no—
403#556—438no—
404#556—438no—
405#556—864no—
406#556—864no—
407C2×C4⋊Q8—431no—
408C2×C4⋊Q8—431no—
409C2×#126—861no—
410C2×#126—861no—
411C2×#126—861no—
412C2×#126—861no—
413C2×#124—431no—
414C2×#124—431no—
415C2×#124—431no—
416C2×#124C2×D4311yescharacteristic
417C2×C22⋊Q8—861no—
418C2×C22⋊Q8—861no—
419C2×C4×Q8—431no—
420C2×C4×Q8—431no—
421C2×C4×Q8—431no—
422C2×C4×Q8—431no—
423C2×C4×Q8C2×D4311yescharacteristic
424C2×C4×D4—431no—
425C2×C4×D4—431no—
426C2×#117—861no—
427C2×#117—861no—
428#497—438no—
429#497—438no—
430#495—438no—
431#464—438no—
432#464C2×D4318yescomplemented
433#463—438no—
434#463—438no—
435#462—438no—
436#462—438no—
437#446—438no—
438#440—438no—
439#440—438no—
440C4×Q16—438no—
441C2×#107—431no—
442C2×C4⋊C8—431no—
443C2×C4⋊C8—431no—
444C2×C4⋊C8C2×D4311yescharacteristic
445C2×#103—431no—
446C2×#103—431no—
447C2×#103—431no—
448C2×#103C2×D4311yescharacteristic
449C2×#102—431no—
450C2×#102C2×D4311yescharacteristic
451C2×#97—431no—
452C2×#97—431no—
453C2×C4×C8—431no—
454C43C2×#340211yescharacteristic, complemented, Sylow
455C22×Q8—431no—
456C22×Q8—431no—
457C22×Q8—431no—
458C22×Q8C22×D4311yescharacteristic
459C22×Q8C22×D4311yescharacteristic
460C22×D4—431no—
461C22×D4C22×D4311yescharacteristic
462C23×C4—861no—
463C23×C4—861no—
464C2×Q16—42no—
465C2×Q16—434no—
466C2×Q16—434no—
467C2×Q16—434no—
468C2×Q16—864no—
469C2×Q16—1722no—
470C2×Q16—1722no—
471C2×Q16C22×D4314yes—
472C2×SD16—42no—
473C2×SD16—434no—
474C2×SD16—434no—
475C2×SD16—434no—
476C2×SD16—864no—
477C2×SD16—864no—
478C2×SD16—1722no—
479C2×SD16C22×D4314yes—
480C2×D8—434no—
481C2×D8—1722no—
482C22×C8—431no—
483C22×C8—431no—
484C22×C8C22×D4311yescharacteristic
485C22×C8C22×D4311yescharacteristic
486C4⋊Q8—434no—
487C4⋊Q8—434no—
488C4⋊Q8—862no—
489C4⋊Q8—862no—
490#126—868no—
491#126—868no—
492#126—868no—
493#126—868no—
494#124—22no—
495#124—434no—
496#124—434no—
497#124—434no—
498#124—862no—
499#124—862no—
500#124—862no—
501#124C22×D4314yes—
502C22⋊Q8—868no—
503C22⋊Q8—868no—
504C4×Q8—22no—
505C4×Q8—434no—
506C4×Q8—434no—
507C4×Q8—434no—
508C4×Q8—434no—
509C4×Q8—434no—
510C4×Q8—862no—
511C4×Q8—862no—
512C4×Q8—862no—
513C4×Q8C22×D4314yes—
514C4×D4—434no—
515C4×D4—434no—
516C4×D4—862no—
517C4×D4—862no—
518#117—868no—
519#117—868no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—431no—
523C2×C4⋊C4—431no—
524C2×C4⋊C4—431no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4—861no—
527C2×C4⋊C4—861no—
528C2×C4⋊C4—861no—
529C2×C4⋊C4—861no—
530C2×C4⋊C4—861no—
531C2×C4⋊C4—861no—
532C2×C4⋊C4C22×D4311yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4—861no—
542C2×C22⋊C4—861no—
543C2×C42—21no—
544C2×C42—431no—
545C2×C42—431no—
546C2×C42—861no—
547C2×C42—861no—
548C2×C42—861no—
549C2×C42C22×D4311yescharacteristic
550#107—434no—
551C4⋊C8—434no—
552C4⋊C8—434no—
553C4⋊C8C22×D4314yes—
554#103—434no—
555#103—434no—
556#103—434no—
557#103C22×D4314yes—
558#102—434no—
559#102C22×D4314yes—
560#97—434no—
561#97—434no—
562C4×C8—434no—
563C24—21no—
564C24—861no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—434no—
572C2×Q8—432no—
573C2×Q8—432no—
574C2×Q8—861no—
575C2×Q8—861no—
576C2×Q8—862no—
577C2×Q8—862no—
578C2×Q8—862no—
579C2×Q8—862no—
580C2×Q8—1722no—
581C2×Q8C23×D4312yes—
582C2×Q8C23×D4312yes—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—432no—
587C2×D4—861no—
588C2×D4—862no—
589C2×D4—862no—
590C2×D4C23×D4312yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—431no—
595C22×C4—431no—
596C22×C4—431no—
597C22×C4—431no—
598C22×C4—864no—
599C22×C4—864no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—1724no—
604C22×C4—1724no—
605C22×C4D4×D4311yescharacteristic
606C22×C4D4×D4311yescharacteristic
607C22×C4C23×D4311yescharacteristic
608Q16—44no—
609Q16—868no—
610Q16—1724no—
611Q16—1724no—
612SD16—44no—
613SD16—868no—
614SD16—868no—
615SD16—1724no—
616D8—1724no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—434no—
620C2×C8—432no—
621C2×C8—432no—
622C2×C8—862no—
623C2×C8C23×D4312yes—
624C2×C8C23×D4312yes—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—434no—
628C4⋊C4—434no—
629C4⋊C4—434no—
630C4⋊C4—432no—
631C4⋊C4—864no—
632C4⋊C4—864no—
633C4⋊C4—864no—
634C4⋊C4—864no—
635C4⋊C4—864no—
636C4⋊C4—864no—
637C4⋊C4—861no—
638C4⋊C4—864no—
639C4⋊C4C23×D4312yes—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—864no—
643C22⋊C4—864no—
644C22⋊C4—864no—
645C22⋊C4—864no—
646C22⋊C4—864no—
647C22⋊C4—864no—
648C22⋊C4—864no—
649C22⋊C4—864no—
650C42—24no—
651C42—432no—
652C42—432no—
653C42—432no—
654C42—432no—
655C42—864no—
656C42—864no—
657C42—864no—
658C42D4×D4312yes—
659C42C23×D4312yes—
660C23—22no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—862no—
665C23—1722no—
666C23—1722no—
667C23—1722no—
668C23C2×D4×D4311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—42no—
674Q8—42no—
675Q8—862no—
676Q8—862no—
677Q8—862no—
678Q8—862no—
679Q8—1724no—
680Q8—1722no—
681Q8—1722no—
682D4—22no—
683D4—22no—
684D4—42no—
685D4—862no—
686D4—862no—
687D4—1722no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—432no—
697C2×C4—432no—
698C2×C4—432no—
699C2×C4—432no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—862no—
707C2×C4—1728no—
708C2×C4—1728no—
709C2×C4—1722no—
710C2×C4—1722no—
711C2×C4—1722no—
712C2×C4C2×D4×D4312yes—
713C2×C4C2×D4×D4312yes—
714C2×C4C2×D4×D4311yescharacteristic
715C2×C4#41×D4312yes—
716C2×C4#1306337012yes—
717C2×C4C24×D4311yescharacteristic
718C8—22no—
719C8—22no—
720C8—434no—
721C8—862no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—3444no—
727C22—1722no—
728C22—1722no—
729C22—1722no—
730C22#1458356712yes—
731C22#1458369612yes—
732C22#1458371512yes—
733C22C22×D4×D4311yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—862no—
740C4—862no—
741C4—862no—
742C4—862no—
743C4—1722no—
744C4—1722no—
745C4—1722no—
746C4#1458356712yes—
747C4C2×#41×D4311yescharacteristic
748C4C2×#1306337011yescharacteristic
749C2—82no—
750C2—3442no—
751C2#1914767414yesdirect product factor
752C2C2×#1458356711yescharacteristic
753C2C2×#1458369611yescharacteristic
754C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#464C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
hypercenterC2×#464D43
hypocenterC43C2×#3402
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#14583621C2semidirect
2. C2×#14583618C2semidirect
3. #19147674C2direct (N × H)
4. C2×#14583292C2semidirect
5. C2×#14583290C2semidirect
7. C2×#14583122C2semidirect
8. C2×#14583108C2semidirect
9. C2×#14583107C2semidirect
12. C2×#14583026C2semidirect
13. C2×#14583002C2semidirect
14. C2×#14582996C2semidirect
15. C2×C4×#10621885C2semidirect
16. C2×C43×#464C2semidirect
25. #14583621C22semidirect
27. #14583618C22semidirect
47. #14583292C22semidirect
48. #14583290C22semidirect
50. #14583122C22semidirect
53. #14583108C22semidirect
54. #14583107C22semidirect
55. #14583026C22semidirect
56. #14583002C22semidirect
57. #14582996C22semidirect
58. C4×#10621885C22semidirect
73. C43×#464C22semidirect
379. C2×#464D43semidirect
389. C2×C43#3402semidirect
432. #464C2×D43semidirect
454. C43C2×#3402semidirect
751. C2#19147674direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836212
C2×#145836182
#191476742
C2×#145832922
C2×#145832902
C2×#145832812
C2×#145831222
C2×#145831082
C2×#145831072
C2×#145831162
C2×#145831132
C2×#145830262
C2×#145830022
C2×#145829962
C2×C4×#106218852
C2×C43×#4642
C2×#340243