Finite Group Databasebeta

← C2×#19145228 #25966413

Subgroups — C2×#19145228 #25966413

Order 11008.

1970 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583520C211yesmaximal, characteristic, complemented
2#19145228C2116yesmaximal, direct product factor
3C2×#14583302C211yesmaximal, characteristic, complemented
4C2×#14583281C211yesmaximal, characteristic, complemented
5C2×#14583261C211yesmaximal, characteristic, complemented
6C2×#14583258C211yesmaximal, characteristic, complemented
7C2×#14583147C211yesmaximal, characteristic, complemented
8C2×#14583143C211yesmaximal, characteristic, complemented
9C2×#14583138C211yesmaximal, characteristic, complemented
10C2×#14583133C211yesmaximal, characteristic
11C2×#14582999C211yesmaximal, characteristic, complemented
12C2×#14582997C211yesmaximal, characteristic, complemented
13C2×C4×#10621885C211yesmaximal, characteristic, complemented
14C2×C4×#10621882C211yesmaximal, characteristic, complemented
15C2×#14582855C211yesmaximal, characteristic, complemented
16C2×C43×#542C211yesmaximal, characteristic, complemented
17C22×#10621885C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21C22×#10621877C2211yescharacteristic
22C23×C43⋊C8C2211yescharacteristic
23#14583520—24no—
24#14583520C2218yescomplemented
25C2×#13063325C2211yescharacteristic
26C2×#13063320—21no—
27C2×#13063313C2211yescharacteristic
28C2×#13063311—21no—
29C2×#13063307—21no—
30C2×#13063304C2211yescharacteristic
31C2×#13063303—21no—
32C2×#13063299C2211yescharacteristic
33C2×C4×Dic86C2211yescharacteristic
34C2×C4×D172C2211yescharacteristic
35#14583302C2218yescomplemented
36#14583281C2218yescomplemented
37#14583261C2218yescomplemented
38#14583258C2218yescomplemented
39#14583147C2218yescomplemented
40#14583143C2218yescomplemented
41#14583138C2218yescomplemented
42#14583133C2218yes—
43#14582999C2218yescomplemented
44#14582997C2218yescomplemented
45C4×#10621885C2218yescomplemented
46C4×#10621882C2218yescomplemented
47C2×#13063258C2211yescharacteristic
48C2×#13063258C2211yescharacteristic
49C2×#13063258C2211yescharacteristic
50C2×#13063258C2211yescharacteristic
51C2×#13063249C2211yescharacteristic
52C2×#13063249C2211yescharacteristic
53C2×#13063248C2211yescharacteristic
54C2×#13063248C2211yescharacteristic
55C2×#13063246C2211yescharacteristic
56C2×#13063246C2211yescharacteristic
57C2×#13063245C2211yescharacteristic
58C2×#13063245C2211yescharacteristic
59#14582855C2218yescomplemented
60C2×#13063236C2211yescharacteristic
61C2×#13063236C2211yescharacteristic
62C2×C4×C43⋊C8C2211yescharacteristic
63C2×C4×C43⋊C8C2211yescharacteristic
64C43×#542—24no—
65C43×#542C2218yescomplemented
66C2×C4⋊Q8×C43C2211yescharacteristic
67C2×#126×C43—21no—
68C2×#124×C43—21no—
69C2×#124×C43C2211yescharacteristic
70C2×#123×C43—21no—
71C2×C22⋊Q8×C43—21no—
72C2×C22⋊Q8×C43C2211yescharacteristic
73C2×#121×C43C2211yescharacteristic
74C2×C4×Q8×C43C2211yescharacteristic
75C2×C4×D4×C43C2211yescharacteristic
76C2×#117×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C22×D172C2311yescharacteristic
80C22×C22⋊D43—21no—
81C22×C4×D43—21no—
82C2×#10621885—24no—
83C2×#10621885C2314yes—
84C2×#10621883—24no—
85C2×#10621883C2314yes—
86C2×#10621884—24no—
87C2×#10621884C2314yes—
88C2×#10621882—24no—
89C2×#10621882C2314yes—
90C2×#10621877—24no—
91C2×#10621877C2314yes—
92C22×C43⋊C8—24no—
93C22×C43⋊C8C2311yescharacteristic
94C22×C43⋊C8C2311yescharacteristic
95C22×C43⋊C8C2314yes—
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98#13063325—22no—
99#13063325C2314yes—
100#13063320—28no—
101#13063313—22no—
102#13063313C2314yes—
103#13063311—28no—
104#13063307—28no—
105#13063304—22no—
106#13063304C2314yes—
107#13063303—28no—
108#13063299—22no—
109#13063299C2314yes—
110C4×Dic86—22no—
111C4×Dic86C2314yes—
112C4×D172—22no—
113C4×D172C2314yes—
114C2×C4⋊Dic43—21no—
115C2×C4⋊Dic43C2311yescharacteristic
116C2×C4⋊Dic43C2311yescharacteristic
117C2×Dic43⋊C4—21no—
118C2×Dic43⋊C4—21no—
119C2×C22⋊Dic43—21no—
120C2×(C2×D43)⋊C4—21no—
121C2×(C2×D43)⋊C4—21no—
122C2×(C2×D43)⋊C4—21no—
123C2×(C2×D43)⋊C4—21no—
124C2×C4×Dic43—21no—
125#13063258C2314yes—
126#13063258C2314yes—
127#13063258C2314yes—
128#13063258C2314yes—
129#13063249C2314yes—
130#13063249C2314yes—
131#13063248C2314yes—
132#13063248C2314yes—
133#13063246C2314yes—
134#13063246C2314yes—
135#13063245C2314yes—
136#13063245C2314yes—
137#13063236C2314yes—
138#13063236C2314yes—
139C4×C43⋊C8C2314yes—
140C4×C43⋊C8C2314yes—
141C22×Q8×C43—21no—
142C22×Q8×C43C2311yescharacteristic
143C22×D4×C43—21no—
144C22×D4×C43C2311yescharacteristic
145C23×C4×C43—21no—
146C23×C4×C43C2311yescharacteristic
147C4⋊Q8×C43—22no—
148C4⋊Q8×C43C2314yes—
149#126×C43—28no—
150#124×C43—28no—
151#124×C43—22no—
152#124×C43C2314yes—
153#123×C43—28no—
154C22⋊Q8×C43—22no—
155C22⋊Q8×C43—28no—
156C22⋊Q8×C43C2314yes—
157#121×C43—22no—
158#121×C43C2314yes—
159C4×Q8×C43—22no—
160C4×Q8×C43C2314yes—
161C4×D4×C43—22no—
162C4×D4×C43C2314yes—
163#117×C43D414yes—
164#117×C43C2314yes—
165C2×C4⋊C4×C43—21no—
166C2×C4⋊C4×C43—21no—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43D411yescharacteristic
169C2×C4⋊C4×C43D411yescharacteristic
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C22⋊C4×C43—21no—
173C2×C22⋊C4×C43—21no—
174C2×C22⋊C4×C43—21no—
175C2×C22⋊C4×C43—21no—
176C2×C22⋊C4×C43—21no—
177C2×C22⋊C4×C43D411yescharacteristic
178C2×C22⋊C4×C43D411yescharacteristic
179C2×C42×C43—21no—
180C2×C42×C43C2311yescharacteristic
181C2×C42×C43C2311yescharacteristic
182C24×C43—21no—
183C24×C43C2×D411yescharacteristic
184C23×D43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—24no—
187C2×Q8×C43—22no—
188C2×Q8×C43—22no—
189C2×Q8×C43—82no—
190C2×Q8×C43C2412yes—
191C2×D4×C43—21no—
192C2×D4×C43—24no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43—82no—
196C2×D4×C43C2412yes—
197C22×C4×C43—22no—
198C22×C4×C43—22no—
199C22×C4×C43—24no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—82no—
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2×D412yes—
210C22×C4×C43C2412yes—
211C22×C4×C43C2411yescharacteristic
212C2×C22⋊D43—24no—
213C2×C22⋊D43—82no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C2×D172—21no—
218C2×D172—22no—
219C2×D172—22no—
220C2×D172C2412yes—
221C2×C4×D43—24no—
222C2×C4×D43—82no—
223C2×Dic86—22no—
224C2×Dic86—22no—
225C2×Dic86—21no—
226C2×Dic86—24no—
227C2×Dic86—82no—
228C2×Dic86C2412yes—
229C4⋊C4×C43—24no—
230C4⋊C4×C43—24no—
231C4⋊C4×C43—24no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43C2×D414yes—
235C4⋊C4×C43C2×D414yes—
236C4⋊C4×C43C2412yes—
237C4⋊C4×C43C2412yes—
238C22⋊C4×C43—24no—
239C22⋊C4×C43—24no—
240C22⋊C4×C43—24no—
241C22⋊C4×C43—24no—
242C22⋊C4×C43—24no—
243C22⋊C4×C43C2×D414yes—
244C22⋊C4×C43C2×D414yes—
245C42×C43—24no—
246C42×C43C2×D412yes—
247C42×C43C2×D412yes—
248C42×C43C2412yes—
249C42×C43C2412yes—
250C22⋊Dic43—24no—
251#10621885—28no—
252#10621884—28no—
253#10621883—28no—
254#10621882—28no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—24no—
259C4⋊Dic43—24no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43C2412yes—
263C4⋊Dic43C2412yes—
264Dic43⋊C4—24no—
265Dic43⋊C4—24no—
266C4×Dic43—24no—
267#10621877—28no—
268C2×C43⋊C8—22no—
269C2×C43⋊C8—22no—
270C2×C43⋊C8—28no—
271C2×C43⋊C8#4114yes—
272C2×C43⋊C8#4114yes—
273C2×C43⋊C8C2412yes—
274C2×C43⋊C8C2412yes—
275C2×C43⋊C8C2412yes—
276C2×C43⋊C8C2412yes—
277C23×C43—22no—
278C23×C43—22no—
279C23×C43—22no—
280C23×C43—22no—
281C23×C43—42no—
282C23×C43—42no—
283C23×C43—42no—
284C23×C43C22×D412yes—
285C23×C43C22×D411yescharacteristic
286C22×D43—22no—
287C22×D43—42no—
288C22×D43—42no—
289C22×D43—42no—
290Q8×C43—22no—
291Q8×C43—22no—
292Q8×C43—42no—
293Q8×C43—84no—
294D4×C43—22no—
295D4×C43—22no—
296D4×C43—42no—
297D4×C43—84no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—24no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—42no—
310C2×C4×C43—42no—
311C2×C4×C43—42no—
312C2×C4×C43—84no—
313C2×C4×C43C22×D412yes—
314C2×C4×C43C22×D412yes—
315C2×C4×C43C22×D412yes—
316C2×C4×C43C22×D412yes—
317C2×C4×C43C22×D412yes—
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C2×#4112yes—
320C2×C4×C43C2×#4112yes—
321C2×C4×C43C2511yescharacteristic
322C22⋊D43—84no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43—42no—
329D172—22no—
330D172—22no—
331D172—42no—
332C4×D43—84no—
333Dic86—22no—
334Dic86—22no—
335Dic86—42no—
336Dic86—84no—
337C43⋊C8—22no—
338C43⋊C8—22no—
339C43⋊C8C2×#4114yes—
340C43⋊C8C2×#4114yes—
341C2×#3175—431nomaximal, Sylow
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—44no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—84no—
350C22×C43#53212yes—
351C22×C43#57612yes—
352C22×C43#57812yes—
353C22×C43C23×D411yescharacteristic
354C2×D43—42no—
355C2×D43—42no—
356C2×D43—42no—
357C2×D43—84no—
358C4×C43—22no—
359C4×C43—22no—
360C4×C43—22no—
361C4×C43—22no—
362C4×C43—22no—
363C4×C43—42no—
364C4×C43—42no—
365C4×C43—42no—
366C4×C43#53212yes—
367C4×C43C22×#4111yescharacteristic
368C4×C43C22×#4111yescharacteristic
369Dic43—42no—
370Dic43—42no—
371Dic43—42no—
372C2×#542—431no—
373C2×#542D4311yescharacteristic, complemented
374#3175—4316no—
375C2×#500—431no—
376C2×#495—431no—
377C2×#489—431no—
378C2×#489—431no—
379C2×#468—431no—
380C2×#468—431no—
381C2×#467—431no—
382C2×#466—431no—
383C2×#440—431no—
384C2×#440—431no—
385C2×C4×Q16—431no—
386C2×C4×D8—431no—
387C2×#405—431no—
388C2×C43—42no—
389C2×C43—82no—
390C2×C43#317514yescomplemented
391C2×C43C2×#53211yescharacteristic
392C2×C43C2×#57611yescharacteristic
393C2×C43C2×#57811yescharacteristic
394D43—82no—
395C22×Q16—431no—
396C22×SD16—431no—
397C22×SD16—431no—
398C22×D8—431no—
399C22×M16—431no—
400C23×C8—431no—
401#542—24no—
402#542—438no—
403#542—864no—
404#542C2×D4318yescomplemented
405C2×C4⋊Q8—431no—
406C2×C4⋊Q8C2×D4311yescharacteristic
407C2×#126—21no—
408C2×#126—861no—
409C2×#124—21no—
410C2×#124—431no—
411C2×#124—861no—
412C2×#124C2×D4311yescharacteristic
413C2×#123—21no—
414C2×#123—861no—
415C2×C22⋊Q8—21no—
416C2×C22⋊Q8—431no—
417C2×C22⋊Q8—861no—
418C2×C22⋊Q8C2×D4311yescharacteristic
419C2×#121—431no—
420C2×#121C2×D4311yescharacteristic
421C2×C4×Q8—431no—
422C2×C4×Q8C2×D4311yescharacteristic
423C2×C4×D4—431no—
424C2×C4×D4C2×D4311yescharacteristic
425C2×#117C2×D4311yescharacteristic
426#500—438no—
427#495—438no—
428#489—438no—
429#489—438no—
430#468—438no—
431#468—438no—
432#467—438no—
433#466—438no—
434#440—438no—
435#440—438no—
436C4×Q16—438no—
437C4×D8—438no—
438C2×#107—431no—
439C2×#107—431no—
440C2×#107—431no—
441C2×#107—431no—
442C2×#103—431no—
443C2×#103—431no—
444C2×#103—431no—
445C2×#103—431no—
446C2×#102—431no—
447C2×#102—431no—
448C2×#102—431no—
449C2×#102—431no—
450#405—438no—
451C2×#97—431no—
452C2×#97—431no—
453C2×C4×C8—431no—
454C2×C4×C8—431no—
455C43C2×#317511yescharacteristic, complemented, Sylow
456C22×Q8—21no—
457C22×Q8—431no—
458C22×Q8—861no—
459C22×Q8C22×D4311yescharacteristic
460C22×D4—21no—
461C22×D4—431no—
462C22×D4—861no—
463C22×D4C22×D4311yescharacteristic
464C23×C4—21no—
465C23×C4—861no—
466C23×C4C22×D4311yescharacteristic
467C2×Q16—434no—
468C2×Q16—864no—
469C2×SD16—434no—
470C2×SD16—434no—
471C2×SD16—864no—
472C2×SD16—864no—
473C2×D8—434no—
474C2×D8—864no—
475C2×M16—434no—
476C2×M16—864no—
477C22×C8—431no—
478C22×C8—431no—
479C22×C8—431no—
480C22×C8—434no—
481C22×C8—431no—
482C22×C8—864no—
483C4⋊Q8—22no—
484C4⋊Q8—434no—
485C4⋊Q8—862no—
486C4⋊Q8C22×D4314yes—
487#126—28no—
488#126—868no—
489#124—28no—
490#124—22no—
491#124—434no—
492#124—868no—
493#124—862no—
494#124C22×D4314yes—
495#123—28no—
496#123—868no—
497C22⋊Q8—22no—
498C22⋊Q8—28no—
499C22⋊Q8—434no—
500C22⋊Q8—862no—
501C22⋊Q8—868no—
502C22⋊Q8C22×D4314yes—
503#121—22no—
504#121—434no—
505#121—862no—
506#121C22×D4314yes—
507C4×Q8—22no—
508C4×Q8—434no—
509C4×Q8—862no—
510C4×Q8C22×D4314yes—
511C4×D4—22no—
512C4×D4—434no—
513C4×D4—862no—
514C4×D4C22×D4314yes—
515#117C22⋊D4314yes—
516#117C22×D4314yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4C22⋊D4311yescharacteristic
526C2×C4⋊C4C22⋊D4311yescharacteristic
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C4⋊C4C22×D4311yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4C22⋊D4311yescharacteristic
540C2×C22⋊C4C22⋊D4311yescharacteristic
541C2×C42—21no—
542C2×C42—861no—
543C2×C42C22×D4311yescharacteristic
544C2×C42C22×D4311yescharacteristic
545#107—434no—
546#107—434no—
547#107—434no—
548#107—434no—
549#103—434no—
550#103—434no—
551#103—434no—
552#103—434no—
553#102—434no—
554#102—434no—
555#102—434no—
556#102—434no—
557#97—434no—
558#97—434no—
559C4×C8—434no—
560C4×C8—434no—
561C24—21no—
562C24—861no—
563C24C2×C22⋊D4311yescharacteristic
564C2×Q8—21no—
565C2×Q8—24no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—82no—
569C2×Q8—432no—
570C2×Q8—864no—
571C2×Q8—861no—
572C2×Q8—862no—
573C2×Q8—862no—
574C2×Q8—3442no—
575C2×Q8C23×D4312yes—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—82no—
581C2×D4—432no—
582C2×D4—864no—
583C2×D4—861no—
584C2×D4—862no—
585C2×D4—862no—
586C2×D4—3442no—
587C2×D4C23×D4312yes—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—24no—
594C22×C4—82no—
595C22×C4—861no—
596C22×C4—861no—
597C22×C4—861no—
598C22×C4—864no—
599C22×C4—3442no—
600C22×C4C2×C22⋊D4312yes—
601C22×C4C2×C22⋊D4311yescharacteristic
602C22×C4C2×C22⋊D4311yescharacteristic
603C22×C4C2×C22⋊D4311yescharacteristic
604C22×C4C2×C22⋊D4311yescharacteristic
605C22×C4C2×C22⋊D4311yescharacteristic
606C22×C4C23×D4312yes—
607C22×C4C23×D4311yescharacteristic
608Q16—868no—
609SD16—868no—
610SD16—868no—
611D8—868no—
612M16—868no—
613C2×C8—434no—
614C2×C8—434no—
615C2×C8—432no—
616C2×C8—432no—
617C2×C8—432no—
618C2×C8—432no—
619C2×C8—868no—
620C2×C8—862no—
621C2×C8—862no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—432no—
628C4⋊C4—432no—
629C4⋊C4—861no—
630C4⋊C4—861no—
631C4⋊C4—864no—
632C4⋊C4—864no—
633C4⋊C4—864no—
634C4⋊C4C2×C22⋊D4314yes—
635C4⋊C4C2×C22⋊D4314yes—
636C4⋊C4C23×D4312yes—
637C4⋊C4C23×D4312yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—864no—
644C22⋊C4—864no—
645C22⋊C4—864no—
646C22⋊C4—864no—
647C22⋊C4—864no—
648C22⋊C4C2×C22⋊D4314yes—
649C22⋊C4C2×C22⋊D4314yes—
650C42—24no—
651C42—864no—
652C42C2×C22⋊D4312yes—
653C42C2×C22⋊D4312yes—
654C42C23×D4312yes—
655C42C23×D4312yes—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—862no—
664C23—1722no—
665C23—1722no—
666C23—1722no—
667C23C22×C22⋊D4312yes—
668C23C22×C22⋊D4311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—84no—
673Q8—862no—
674Q8—862no—
675Q8—3444no—
676Q8—1722no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—84no—
681D4—862no—
682D4—862no—
683D4—3444no—
684D4—1722no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—84no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—3444no—
704C2×C4—1722no—
705C2×C4—1722no—
706C2×C4—1722no—
707C2×C4C22×C22⋊D4312yes—
708C2×C4C22×C22⋊D4312yes—
709C2×C4C22×C22⋊D4312yes—
710C2×C4C22×C22⋊D4312yes—
711C2×C4C22×C22⋊D4312yes—
712C2×C4C22×C22⋊D4311yescharacteristic
713C2×C4#41×D4312yes—
714C2×C4#41×D4312yes—
715C2×C4C24×D4311yescharacteristic
716C8—434no—
717C8—434no—
718C8—862no—
719C8—862no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—3444no—
729C22—1722no—
730C22—1722no—
731C22—1722no—
732C22#1458344512yes—
733C22#1458370212yes—
734C22#1458371412yes—
735C22C23×C22⋊D4311yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—22no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—1722no—
745C4—1722no—
746C4—1722no—
747C4#1458344512yes—
748C4C2×#41×D4311yescharacteristic
749C4C2×#41×D4311yescharacteristic
750C2—42no—
751C2—82no—
752C2—3442no—
753C2#1914522814yesdirect product factor
754C2C2×#1458344511yescharacteristic
755C2C2×#1458370211yescharacteristic
756C2C2×#1458371411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#542C2
socleC23×C43C22×D4
prime radicalC2×#14583133C2
hypercenterC2×#542D43
hypocenterC43C2×#3175
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#14583520C2semidirect
2. #19145228C2direct (N × H)
3. C2×#14583302C2semidirect
4. C2×#14583281C2semidirect
5. C2×#14583261C2semidirect
6. C2×#14583258C2semidirect
7. C2×#14583147C2semidirect
8. C2×#14583143C2semidirect
9. C2×#14583138C2semidirect
11. C2×#14582999C2semidirect
12. C2×#14582997C2semidirect
13. C2×C4×#10621885C2semidirect
14. C2×C4×#10621882C2semidirect
15. C2×#14582855C2semidirect
16. C2×C43×#542C2semidirect
24. #14583520C22semidirect
35. #14583302C22semidirect
36. #14583281C22semidirect
37. #14583261C22semidirect
38. #14583258C22semidirect
39. #14583147C22semidirect
40. #14583143C22semidirect
41. #14583138C22semidirect
43. #14582999C22semidirect
44. #14582997C22semidirect
45. C4×#10621885C22semidirect
46. C4×#10621882C22semidirect
59. #14582855C22semidirect
65. C43×#542C22semidirect
373. C2×#542D43semidirect
390. C2×C43#3175semidirect
404. #542C2×D43semidirect
455. C43C2×#3175semidirect
753. C2#19145228direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835202
#191452282
C2×#145833022
C2×#145832812
C2×#145832612
C2×#145832582
C2×#145831472
C2×#145831432
C2×#145831382
C2×#145831332
C2×#145829992
C2×#145829972
C2×C4×#106218852
C2×C4×#106218822
C2×#145828552
C2×C43×#5422
C2×#317543