Finite Group Databasebeta

← #25112183

Subgroups — #25112183

Order 11008.

1458 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583560C211yesmaximal, characteristic
2C2×#14582968C211yesmaximal, characteristic, complemented
3C2×#14582894C211yesmaximal, characteristic, complemented
4#19137545C211yesmaximal, characteristic, complemented
5#19135524C211yesmaximal, characteristic, complemented
6#19135408C211yesmaximal, characteristic, complemented
7#19135033C211yesmaximal, characteristic, complemented
8#19135015C211yesmaximal, characteristic, complemented
9#19134917C211yesmaximal, characteristic, complemented
10#19134904C211yesmaximal, characteristic, complemented
11#19134598C211yesmaximal, characteristic, complemented
12#19134534C211yesmaximal, characteristic, complemented
13#19134530C211yesmaximal, characteristic, complemented
14#19134427C211yesmaximal, characteristic, complemented
15C2×C43×#419C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18#14583560—24no—
19#14583560C418yescomplemented
20C2×#13063314—21no—
21C2×#13063314C2211yescharacteristic
22C2×#13063301—21no—
23C2×#13063301C2211yescharacteristic
24C2×#13063299—21no—
25C2×#13063299C2211yescharacteristic
26C2×Q8×Dic43C2211yescharacteristic
27C2×C4×C22⋊D43—21no—
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×#13063283C2211yescharacteristic
30#14582968—24no—
31C2×Dic43⋊C8C2211yescharacteristic
32#14582894—24no—
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38C2×#13063247C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×#13063235C2211yescharacteristic
44#14582799—21no—
45#14582790—21no—
46#14582787—21no—
47#14582768C2211yescharacteristic
48#14582759C2211yescharacteristic
49#14582756C2211yescharacteristic
50C4⋊C4×Dic43C2211yescharacteristic
51C4×Dic43⋊C4—21no—
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56C23×Q8×C43C2211yescharacteristic
57C22×M16×C43C2211yescharacteristic
58C2×#117×C43C2211yescharacteristic
59C43×#419—24no—
60C2×#103×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#103×C43C2211yescharacteristic
63C2×#103×C43C2211yescharacteristic
64C2×#10621902—22no—
65C2×#10621902—22no—
66C2×#10621902—22no—
67C2×#10621902—41no—
68C2×#10621902—41no—
69C2×#10621902C2×C414yes—
70C22×D172—21no—
71C22×D172C2311yescharacteristic
72C22×C22⋊D43—21no—
73C22×C22⋊D43D411yescharacteristic
74C22×C4×D43—21no—
75C22×C4×D43C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C2×C8×D43—22no—
79C2×C8×D43—22no—
80C2×C8×D43—41no—
81#13063314—28no—
82#13063314—22no—
83#13063314C2×C414yes—
84#13063301—22no—
85#13063301—28no—
86#13063301C2×C414yes—
87#13063299—22no—
88#13063299—28no—
89#13063299C2×C414yes—
90Q8×Dic43—22no—
91Q8×Dic43C2×C414yes—
92C4×C22⋊D43—28no—
93C4×C22⋊D43C2×C414yes—
94C4×C22⋊D43D414yes—
95#13063283—22no—
96#13063283—41no—
97C2×C4⋊Dic43—21no—
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4D411yescharacteristic
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43D411yescharacteristic
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4D411yescharacteristic
114C2×C4×Dic43—21no—
115C2×C4×Dic43—21no—
116C2×C4×Dic43—21no—
117C2×C4×Dic43C2311yescharacteristic
118Dic43⋊C8—22no—
119#13063249—22no—
120#13063249—22no—
121#13063249—41no—
122#13063249—41no—
123#13063247—22no—
124#13063247—41no—
125#13063245—22no—
126#13063245—41no—
127C22⋊(C43⋊C8)—22no—
128(C2×D43)⋊C8—22no—
129#13063235—22no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C22×Q8×C43—22no—
134C22×Q8×C43—21no—
135C22×Q8×C43—22no—
136C22×Q8×C43—22no—
137C22×Q8×C43—41no—
138C22×Q8×C43—41no—
139C22×Q8×C43C2×C414yes—
140C22×Q8×C43C2311yescharacteristic
141C22×Q8×C43C2311yescharacteristic
142C23×C4×C43—21no—
143C23×C4×C43C2311yescharacteristic
144C2×M16×C43—22no—
145C2×M16×C43—22no—
146C2×M16×C43—41no—
147C22×C8×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149#117×C43—22no—
150#117×C43—41no—
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C22⋊C4×C43—21no—
154C2×C42×C43—21no—
155#103×C43—22no—
156#103×C43—22no—
157#103×C43—22no—
158#103×C43D414yescomplemented
159C24×C43C2×D411yescharacteristic
160C23×D43—21no—
161C23×D43C2×D411yescharacteristic
162C2×Q8×C43—24no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43—28no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—42no—
173C2×Q8×C43—42no—
174C2×Q8×C43—44no—
175C2×Q8×C43—44no—
176C2×Q8×C43—44no—
177C2×Q8×C43C22×C412yes—
178C2×Q8×C43C22×C412yes—
179C2×Q8×C43C2×D412yes—
180C2×Q8×C43#4112yes—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—24no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—42no—
191C22×C4×C43—42no—
192C22×C4×C43C22×C412yes—
193C22×C4×C43C2×D412yes—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—24no—
197C2×C22⋊D43—41no—
198C2×C22⋊D43—41no—
199C2×C22⋊D43—42no—
200C2×C22⋊D43—42no—
201C2×C22⋊D43C22⋊C414yes—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43C2×D411yescharacteristic
206C22×Dic43C2×D411yescharacteristic
207C22×Dic43C2×D411yescharacteristic
208#10621902—28no—
209#10621902—44no—
210#10621902—44no—
211#10621902—44no—
212C2×D172—21no—
213C2×D172—24no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172—42no—
219C2×D172—42no—
220C2×D172C22×C412yes—
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—24no—
226C2×C4×D43—42no—
227C2×C4×D43—42no—
228C2×C4×D43C22×C412yes—
229C2×C4×D43C2×D412yes—
230M16×C43—44no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43C2×D412yes—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43C2×D412yes—
241C22⋊C4×C43—42no—
242C42×C43—42no—
243C22⋊Dic43—81no—
244C22⋊Dic43C22⋊C414yes—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—42no—
250(C2×D43)⋊C4—81no—
251(C2×D43)⋊C4C22⋊C414yes—
252C4⋊Dic43—21no—
253C4⋊Dic43—24no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43C22×C412yes—
259Dic43⋊C4—24no—
260Dic43⋊C4—42no—
261Dic43⋊C4—81no—
262Dic43⋊C4C22⋊C414yes—
263C4×Dic43—24no—
264C4×Dic43—42no—
265C4×Dic43—42no—
266C4×Dic43C22×C412yes—
267C4×Dic43C2×D412yes—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273C2×C43⋊C8—21no—
274C8×D43—44no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43C2×C22⋊C412yes—
282C23×C43C22×D411yescharacteristic
283C22×D43—21no—
284C22×D43—21no—
285C22×D43—21no—
286C22×D43—21no—
287C22×D43—21no—
288C22×D43—21no—
289C22×D43—22no—
290C22×D43—41no—
291C22×D43—41no—
292C22×D43—41no—
293C22×D43—41no—
294C22×D43—41no—
295C22×D43—41no—
296C22×D43C2×C22⋊C412yes—
297Q8×C43—22no—
298Q8×C43—22no—
299Q8×C43—22no—
300Q8×C43—22no—
301Q8×C43—22no—
302Q8×C43—48no—
303Q8×C43—41no—
304Q8×C43—41no—
305Q8×C43C4×D414yes—
306C2×C4×C43—22no—
307C2×C4×C43—21no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—21no—
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—48no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43C2×C22⋊C412yes—
326C2×C4×C43C23×C411yescharacteristic
327C2×C4×C43C22×D411yescharacteristic
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C43C2×#4111yescharacteristic
330C2×C4×C43H(5,𝔽2)11yescharacteristic
331C2×C4×C43H(5,𝔽2)11yescharacteristic
332C22⋊D43—44no—
333C22⋊D43—48no—
334C2×Dic43—21no—
335C2×Dic43—21no—
336C2×Dic43—21no—
337C2×Dic43—21no—
338C2×Dic43—21no—
339C2×Dic43—21no—
340C2×Dic43—22no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43C2×C22⋊C412yes—
350C2×Dic43C2×C22⋊C412yes—
351C2×Dic43C2×C22⋊C412yes—
352D172—22no—
353D172—22no—
354D172—48no—
355D172—41no—
356D172—41no—
357C4×D43—22no—
358C4×D43—22no—
359C4×D43—22no—
360C4×D43—22no—
361C4×D43—48no—
362C8×C43—22no—
363C8×C43—41no—
364C43⋊C8—41no—
365C43⋊C8—41no—
366#22426—431nomaximal, Sylow
367C22×C43—22no—
368C22×C43—22no—
369C22×C43—22no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43C22×C22⋊C411yescharacteristic
375C22×C43D4211yescharacteristic
376C22×C43#54611yescharacteristic
377C22×C43#57511yescharacteristic
378C22×C43#57511yescharacteristic
379C22×C43#57711yescharacteristic
380C22×C43#57811yescharacteristic
381C2×D43—22no—
382C2×D43—22no—
383C2×D43—22no—
384C2×D43—41no—
385C2×D43—41no—
386C2×D43—41no—
387C2×D43—41no—
388C2×D43—42no—
389C2×D43—42no—
390C2×D43—42no—
391C2×D43—81no—
392C2×D43—81no—
393C2×D43—81no—
394C2×D43—81no—
395C4×C43—24no—
396C4×C43—22no—
397C4×C43—42no—
398C4×C43—42no—
399C4×C43—81no—
400C4×C43C2×C4×D411yescharacteristic
401C4×C43#51811yescharacteristic
402C4×C43D4211yescharacteristic
403C4×C43#54611yescharacteristic
404Dic43—22no—
405Dic43—22no—
406Dic43—22no—
407Dic43—42no—
408Dic43—81no—
409Dic43—81no—
410C2×#548—431no—
411C2×#435—431no—
412C2×#419D4311yescharacteristic, complemented
413C2×#416—431no—
414#2354—431no—
415#1983—431no—
416#1959—431no—
417#1895—431no—
418#1892—431no—
419#1875—431no—
420#1873—431no—
421#1803—431no—
422#1788—431no—
423#1787—431no—
424#1763—431no—
425C2×C43—42no—
426C2×C43D4×C22⋊C411yescharacteristic
427C2×C43#289611yescharacteristic
428C2×C43#289811yescharacteristic
429C2×C43#326911yescharacteristic
430C2×C43#327111yescharacteristic
431C2×C43#331311yescharacteristic
432C2×C43#332111yescharacteristic
433D43—42no—
434D43—82no—
435C22×#41—431no—
436C23×Q8C2×D4311yescharacteristic
437C22×M16C2×D4311yescharacteristic
438C23×C8—431no—
439#548—438no—
440#548—864no—
441C2×#124—431no—
442C2×#124—861no—
443C2×C22⋊Q8—431no—
444C2×C22⋊Q8—861no—
445C2×#121—431no—
446C2×#121—861no—
447C2×C4×Q8—431no—
448C2×C4×D4—431no—
449C2×C4×D4—861no—
450C2×#117—431no—
451C2×#117C2×D4311yescharacteristic
452#435—864no—
453C2×C4⋊C8—431no—
454#419—24no—
455#416—864no—
456C2×#103—431no—
457C2×#103—431no—
458C2×#103—431no—
459C2×#103—431no—
460C2×#103C2×D4311yescharacteristic
461C2×#103C2×D4311yescharacteristic
462C2×#103C2×D4311yescharacteristic
463C2×#103C2×D4311yescharacteristic
464C2×#102—431no—
465C2×#102—431no—
466C2×#102—431no—
467C2×#102—431no—
468C2×C22⋊C8—431no—
469C2×C22⋊C8—431no—
470C2×#97—431no—
471#390—861no—
472#388—861no—
473#388—861no—
474#384—431no—
475#380—431no—
476#380—431no—
477C4×C4⋊C4—431no—
478C4×C4⋊C4—861no—
479#340—431no—
480#340—431no—
481#340—431no—
482#340—431no—
483C43#2242611yescharacteristic, complemented, Sylow
484C2×#41—434no—
485C2×#41—862no—
486C2×#41—862no—
487C2×#41—862no—
488C2×#41—1721no—
489C2×#41—1721no—
490C22×Q8—21no—
491C22×Q8—22no—
492C22×Q8—22no—
493C22×Q8—22no—
494C22×Q8—41no—
495C22×Q8—41no—
496C22×Q8C4×D4314yes—
497C22×Q8C22×D4311yescharacteristic
498C22×Q8C22×D4311yescharacteristic
499C22×D4—431no—
500C22×D4—431no—
501C22×D4—861no—
502C22×D4—861no—
503C23×C4—21no—
504C23×C4—431no—
505C23×C4—861no—
506C23×C4C22×D4311yescharacteristic
507C2×M16—22no—
508C2×M16—22no—
509C2×M16—41no—
510C22×C8—431no—
511C22×C8—431no—
512C22×C8—862no—
513C22×C8—862no—
514C22×C8—1721no—
515C22×C8C22×D4311yescharacteristic
516C22×C8C22×D4311yescharacteristic
517#124—434no—
518#124—862no—
519#124—868no—
520C22⋊Q8—434no—
521C22⋊Q8—868no—
522C22⋊Q8—862no—
523#121—434no—
524#121—868no—
525#121—862no—
526C4×Q8—434no—
527C4×Q8—862no—
528C4×D4—434no—
529C4×D4—434no—
530C4×D4—868no—
531#117—22no—
532#117—41no—
533#117—862no—
534#117—1721no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—431no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4C22×D4311yescharacteristic
544C2×C4⋊C4C22×D4311yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—431no—
547C2×C22⋊C4—431no—
548C2×C22⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C42—21no—
556C2×C42—431no—
557C2×C42—861no—
558C2×C42—861no—
559C2×C42—861no—
560C4⋊C8—862no—
561#103—22no—
562#103—22no—
563#103—22no—
564#103—862no—
565#103—862no—
566#103—1721no—
567#103—1721no—
568#103C22⋊D4314yescomplemented
569#102—862no—
570#102—862no—
571#102—1721no—
572#102—1721no—
573C22⋊C8—862no—
574C22⋊C8—862no—
575#97—862no—
576#95—861no—
577#95—861no—
578#95—861no—
579C24—431no—
580C24—861no—
581C24D4×D4311yescharacteristic
582#41—868no—
583#41—1724no—
584#41—1724no—
585#41—1724no—
586C2×Q8—24no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—28no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—42no—
597C2×Q8—42no—
598C2×Q8—44no—
599C2×Q8—44no—
600C2×Q8—44no—
601C2×Q8C2×C4×D4312yes—
602C2×Q8C2×C4×D4312yes—
603C2×Q8#1062189812yes—
604C2×Q8C2×C22⋊D4312yes—
605C2×D4—434no—
606C2×D4—432no—
607C2×D4—864no—
608C2×D4—864no—
609C2×D4—861no—
610C2×D4—861no—
611C2×D4—861no—
612C2×D4—861no—
613C2×D4—861no—
614C2×D4—1722no—
615C2×D4—1722no—
616C2×D4—1721no—
617C2×D4—1721no—
618C2×D4—1722no—
619C2×D4—1722no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—24no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—431no—
632C22×C4—431no—
633C22×C4—431no—
634C22×C4—432no—
635C22×C4—432no—
636C22×C4—864no—
637C22×C4—861no—
638C22×C4—861no—
639C22×C4—861no—
640C22×C4—861no—
641C22×C4—861no—
642C22×C4—861no—
643C22×C4—861no—
644C22×C4—1722no—
645C22×C4—1722no—
646C22×C4C2×C4×D4312yes—
647C22×C4D4×D4311yescharacteristic
648C22×C4D4×D4312yes—
649C22×C4C23×D4311yescharacteristic
650M16—44no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—861no—
657C2×C8—861no—
658C2×C8—861no—
659C2×C8—861no—
660C2×C8—861no—
661C2×C8—861no—
662C2×C8—1724no—
663C2×C8C2×C22⋊D4312yes—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—434no—
668C4⋊C4—432no—
669C4⋊C4—864no—
670C4⋊C4—864no—
671C4⋊C4—861no—
672C4⋊C4—861no—
673C4⋊C4—861no—
674C4⋊C4—861no—
675C4⋊C4—861no—
676C4⋊C4—3441no—
677C4⋊C4—1722no—
678C4⋊C4C2×C22⋊D4312yes—
679C22⋊C4—42no—
680C22⋊C4—434no—
681C22⋊C4—434no—
682C22⋊C4—864no—
683C22⋊C4—864no—
684C22⋊C4—864no—
685C22⋊C4—864no—
686C22⋊C4—3441no—
687C22⋊C4—3441no—
688C22⋊C4—1722no—
689C42—42no—
690C42—432no—
691C42—432no—
692C42—864no—
693C42—1722no—
694C42—1722no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—432no—
702C23—861no—
703C23—861no—
704C23—861no—
705C23—861no—
706C23—861no—
707C23—861no—
708C23—862no—
709C23—1721no—
710C23—1721no—
711C23—1721no—
712C23—1721no—
713C23—1721no—
714C23—1721no—
715C23C22⋊C4×D4312yes—
716C23C2×D4×D4311yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—48no—
723Q8—41no—
724Q8—41no—
725Q8C4×C22⋊D4314yes—
726D4—862no—
727D4—862no—
728D4—1728no—
729D4—1724no—
730D4—1728no—
731D4—1721no—
732D4—1721no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—48no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—432no—
753C2×C4—432no—
754C2×C4—432no—
755C2×C4—861no—
756C2×C4—861no—
757C2×C4—861no—
758C2×C4—861no—
759C2×C4—861no—
760C2×C4—861no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—1728no—
767C2×C4—1721no—
768C2×C4—1721no—
769C2×C4—1721no—
770C2×C4—1721no—
771C2×C4—1721no—
772C2×C4—1721no—
773C2×C4—1721no—
774C2×C4—1721no—
775C2×C4C22⋊C4×D4312yes—
776C2×C4C22×C4×D4311yescharacteristic
777C2×C4C2×D4×D4311yescharacteristic
778C2×C4C22×C22⋊D4311yescharacteristic
779C2×C4C2×#1062189811yescharacteristic
780C2×C4#1306337011yescharacteristic
781C2×C4#1306337011yescharacteristic
782C8—22no—
783C8—41no—
784C8—1721no—
785C8—1721no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—862no—
794C22—862no—
795C22—862no—
796C22—3441no—
797C22—3441no—
798C22—3441no—
799C22—3441no—
800C22—1722no—
801C22—1722no—
802C22—1722no—
803C22—1721no—
804C22—1721no—
805C22—1721no—
806C22—1721no—
807C22C2×C22⋊C4×D4311yescharacteristic
808C22D4×C22⋊D4311yescharacteristic
809C22#1458353911yescharacteristic
810C22#1458369811yescharacteristic
811C22#1458369811yescharacteristic
812C22#1458370811yescharacteristic
813C22#1458371511yescharacteristic
814C4—22no—
815C4—24no—
816C4—42no—
817C4—42no—
818C4—81no—
819C4—862no—
820C4—862no—
821C4—862no—
822C4—3441no—
823C4—3441no—
824C4—1722no—
825C4C2×C4×C22⋊D4311yescharacteristic
826C4#1458337211yescharacteristic
827C4D4×C22⋊D4311yescharacteristic
828C4#1458353911yescharacteristic
829C2—42no—
830C2—3442no—
831C2—1722no—
832C2C22⋊C4×C22⋊D4311yescharacteristic
833C2#1914311311yescharacteristic
834C2#1914312711yescharacteristic
835C2#1914614411yescharacteristic
836C2#1914617411yescharacteristic
837C2#1914666211yescharacteristic
838C2#1914678211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#419C2
socleC23×C43C22×D4
prime radicalC2×#14583560C2
cosocleC22×C4×C43C24
hypercenterC2×#419D43
hypocenterC43#22426
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
2. C2×#14582968C2semidirect
3. C2×#14582894C2semidirect
4. #19137545C2semidirect
5. #19135524C2semidirect
6. #19135408C2semidirect
7. #19135033C2semidirect
8. #19135015C2semidirect
9. #19134917C2semidirect
10. #19134904C2semidirect
11. #19134598C2semidirect
12. #19134534C2semidirect
13. #19134530C2semidirect
14. #19134427C2semidirect
15. C2×C43×#419C2semidirect
19. #14583560C4semidirect
158. #103×C43D4semidirect
412. C2×#419D43semidirect
483. C43#22426semidirect
568. #103C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835602
C2×#145829682
C2×#145828942
#191375452
#191355242
#191354082
#191350332
#191350152
#191349172
#191349042
#191345982
#191345342
#191345302
#191344272
C2×C43×#4192
#2242643