Finite Group Databasebeta

← #25112176

Subgroups — #25112176

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×#14583558C211yesmaximal, characteristic
2C2×#14582971C211yesmaximal, characteristic, complemented
3C2×#14582907C211yesmaximal, characteristic, complemented
4C2×#14582893C211yesmaximal, characteristic, complemented
5#19135527C211yesmaximal, characteristic, complemented
6#19135409C211yesmaximal, characteristic, complemented
7#19135031C211yesmaximal, characteristic, complemented
8#19135016C211yesmaximal, characteristic, complemented
9#19134917C211yesmaximal, characteristic, complemented
10#19134907C211yesmaximal, characteristic, complemented
11#19134597C211yesmaximal, characteristic, complemented
12#19134533C211yesmaximal, characteristic, complemented
13#19134529C211yesmaximal, characteristic, complemented
14#19134428C211yesmaximal, characteristic, complemented
15C43×#2354C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C23×Dic86C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20#14583558—24no—
21#14583558C418yescomplemented
22C2×#13063313C2211yescharacteristic
23C2×#13063311—21no—
24C2×#13063304C2211yescharacteristic
25C2×#13063303—21no—
26C2×#13063299C2211yescharacteristic
27C2×#13063297—21no—
28C2×C4×Dic86C2211yescharacteristic
29C2×(C22⋊D43)⋊C4—21no—
30#14582971—24no—
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32#14582907—24no—
33#14582893—24no—
34C2×#13063248C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44C2×#13063245C2211yescharacteristic
45C2×#13063245C2211yescharacteristic
46C2×C22⋊(C43⋊C8)C2211yescharacteristic
47C2×C22⋊(C43⋊C8)C2211yescharacteristic
48C2×#13063236C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×#117×C43C2211yescharacteristic
55C2×#117×C43C2211yescharacteristic
56C43×#390—21no—
57C43×#388—21no—
58C43×#388—21no—
59C43×#384C2211yescharacteristic
60C43×#380C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C4×C4⋊C4×C43—21no—
63C4×C4⋊C4×C43C2211yescharacteristic
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—41no—
68C2×#10621898—41no—
69C2×#10621898C2×C414yes—
70C22×Dic86—22no—
71C22×Dic86—22no—
72C22×Dic86—22no—
73C22×Dic86—21no—
74C22×Dic86—41no—
75C22×Dic86—41no—
76C22×Dic86C2×C414yes—
77C22×Dic86C2311yescharacteristic
78C22×Dic86C2311yescharacteristic
79C22×D172C2311yescharacteristic
80C22×C22⋊D43—21no—
81C22×C22⋊D43—21no—
82C23×Dic43—21no—
83C22×C4×D43—21no—
84C2×#10621877—22no—
85C2×#10621877—22no—
86C2×#10621877—41no—
87C22×C43⋊C8—22no—
88C22×C43⋊C8—22no—
89C22×C43⋊C8—41no—
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93C22×C43⋊C8C2311yescharacteristic
94#13063313—22no—
95#13063313C2×C414yes—
96#13063311—28no—
97#13063304—22no—
98#13063304C2×C414yes—
99#13063303—28no—
100#13063299—22no—
101#13063299C2×C414yes—
102#13063297—28no—
103C4×Dic86—22no—
104C4×Dic86C2×C414yes—
105(C22⋊D43)⋊C4—28no—
106C2×C4⋊Dic43C2311yescharacteristic
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×C22⋊Dic43—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×C4×Dic43—21no—
114C4⋊(C43⋊C8)—22no—
115#13063248—22no—
116#13063248—22no—
117#13063248—22no—
118#13063248—22no—
119#13063248—22no—
120#13063248—41no—
121#13063248—41no—
122#13063248D414yescomplemented
123#13063245—22no—
124#13063245—22no—
125#13063245—41no—
126#13063245—41no—
127C22⋊(C43⋊C8)—22no—
128C22⋊(C43⋊C8)—22no—
129#13063236—22no—
130C22×D4×C43D411yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C4×D4×C43C2×C414yes—
134C4×D4×C43D414yes—
135#117×C43—22no—
136#117×C43—22no—
137#117×C43—41no—
138#117×C43—41no—
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43—21no—
141C2×C4⋊C4×C43D411yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C22⋊C4×C43—21no—
149C2×C22⋊C4×C43—21no—
150C2×C22⋊C4×C43D411yescharacteristic
151C2×C22⋊C4×C43D411yescharacteristic
152C2×C42×C43—21no—
153C2×C42×C43—21no—
154C2×C42×C43—21no—
155C2×C42×C43C2311yescharacteristic
156#95×C43—21no—
157#95×C43—21no—
158#95×C43—21no—
159C24×C43C2×D411yescharacteristic
160C24×C43C2×D411yescharacteristic
161C23×D43—21no—
162C2×D4×C43—41no—
163C2×D4×C43—41no—
164C2×D4×C43C22⋊C414yes—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43C22×C412yes—
178C22×C4×C43C22×C412yes—
179C22×C4×C43C2×D412yes—
180C22×C4×C43C2×D412yes—
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2411yescharacteristic
186C2×C22⋊D43—24no—
187C2×C22⋊D43—24no—
188C2×C22⋊D43—42no—
189C2×C22⋊D43—42no—
190C2×C22⋊D43—42no—
191C2×C22⋊D43—42no—
192C22×Dic43—24no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—42no—
197C22×Dic43—42no—
198#10621898—28no—
199#10621898—44no—
200#10621898—44no—
201#10621898—44no—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172C22×C412yes—
208C2×C4×D43—24no—
209C2×C4×D43—42no—
210C2×C4×D43—42no—
211C2×Dic86—21no—
212C2×Dic86—21no—
213C2×Dic86—21no—
214C2×Dic86—21no—
215C2×Dic86—21no—
216C2×Dic86—21no—
217C2×Dic86—21no—
218C2×Dic86—28no—
219C2×Dic86—24no—
220C2×Dic86—21no—
221C2×Dic86—44no—
222C2×Dic86—44no—
223C2×Dic86—44no—
224C2×Dic86—42no—
225C2×Dic86—42no—
226C2×Dic86C22×C412yes—
227C2×Dic86C22×C412yes—
228C2×Dic86C2×D412yes—
229C2×Dic86#4112yes—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—42no—
238C4⋊C4×C43—81no—
239C4⋊C4×C43C22⋊C414yes—
240C4⋊C4×C43C2×D412yes—
241C22⋊C4×C43—42no—
242C22⋊C4×C43—42no—
243C22⋊C4×C43—81no—
244C22⋊C4×C43—81no—
245C22⋊C4×C43C22⋊C414yes—
246C22⋊C4×C43C22⋊C414yes—
247C42×C43—42no—
248C42×C43—42no—
249C42×C43—42no—
250C42×C43C22×C412yes—
251C42×C43C2×D412yes—
252C22⋊Dic43—24no—
253(C2×D43)⋊C4—24no—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—24no—
256C4⋊Dic43—21no—
257C4⋊Dic43C22×C412yes—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260C4×Dic43—24no—
261#10621877—44no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273C2×C43⋊C8—44no—
274C2×C43⋊C8C2×D412yes—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43C2×C22⋊C412yes—
288C23×C43C2×C22⋊C412yes—
289C23×C43C22×D411yescharacteristic
290C22×D43—22no—
291C22×D43—41no—
292C22×D43—41no—
293C22×D43—41no—
294C22×D43—41no—
295C22×D43—41no—
296C22×D43—41no—
297D4×C43—44no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
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—22no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
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×C43—41no—
326C2×C4×C43C2×C22⋊C412yes—
327C2×C4×C43C2×C22⋊C412yes—
328C2×C4×C43C2×C22⋊C412yes—
329C2×C4×C43C2×C22⋊C412yes—
330C2×C4×C43C23×C411yescharacteristic
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43C2×#4111yescharacteristic
334C2×C4×C43H(5,𝔽2)11yescharacteristic
335C2×C4×C43H(5,𝔽2)11yescharacteristic
336C22⋊D43—48no—
337C22⋊D43—48no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—48no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348D172—22no—
349D172—22no—
350D172—41no—
351D172—41no—
352C4×D43—48no—
353Dic86—22no—
354Dic86—22no—
355Dic86—22no—
356Dic86—22no—
357Dic86—22no—
358Dic86—48no—
359Dic86—41no—
360Dic86—41no—
361Dic86C4×D414yes—
362C43⋊C8—22no—
363C43⋊C8—41no—
364C43⋊C8—41no—
365C43⋊C8—41no—
366#22426—431nomaximal, Sylow
367C22×C43—22no—
368C22×C43—22no—
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—22no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—41no—
378C22×C43—41no—
379C22×C43—41no—
380C22×C43—41no—
381C22×C43C22×C22⋊C411yescharacteristic
382C22×C43D4211yescharacteristic
383C22×C43#54611yescharacteristic
384C22×C43#57511yescharacteristic
385C22×C43#57511yescharacteristic
386C22×C43#57711yescharacteristic
387C22×C43#57811yescharacteristic
388C2×D43—42no—
389C2×D43—42no—
390C2×D43—42no—
391C2×D43—81no—
392C2×D43—81no—
393C2×D43—81no—
394C2×D43—81no—
395C4×C43—22no—
396C4×C43—22no—
397C4×C43—22no—
398C4×C43—22no—
399C4×C43—42no—
400C4×C43—81no—
401C4×C43—81no—
402C4×C43—81no—
403C4×C43C2×C4×D411yescharacteristic
404C4×C43#51811yescharacteristic
405C4×C43D4211yescharacteristic
406C4×C43#54611yescharacteristic
407Dic43—24no—
408Dic43—42no—
409Dic43—42no—
410C2×#548—431no—
411C2×#435—431no—
412C2×#419—431no—
413C2×#416—431no—
414#2354D4311yescharacteristic, complemented
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×C43—42no—
427C2×C43D4×C22⋊C411yescharacteristic
428C2×C43#289611yescharacteristic
429C2×C43#289811yescharacteristic
430C2×C43#326911yescharacteristic
431C2×C43#327111yescharacteristic
432C2×C43#331311yescharacteristic
433C2×C43#332111yescharacteristic
434D43—82no—
435C22×#41—431no—
436C23×Q8—431no—
437C22×M16—431no—
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—861no—
449C2×C4×D4C2×D4311yescharacteristic
450C2×#117C2×D4311yescharacteristic
451C2×#117C2×D4311yescharacteristic
452#435—864no—
453C2×C4⋊C8—431no—
454#419—864no—
455#416—864no—
456C2×#103—431no—
457C2×#103—431no—
458C2×#103—431no—
459C2×#103—431no—
460C2×#103—431no—
461C2×#103—431no—
462C2×#103—431no—
463C2×#103—431no—
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—21no—
472#388—21no—
473#388—21no—
474#384C2×D4311yescharacteristic
475#380C2×D4311yescharacteristic
476#380C2×D4311yescharacteristic
477C4×C4⋊C4—21no—
478C4×C4⋊C4C2×D4311yescharacteristic
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—434no—
491C22×Q8—431no—
492C22×Q8—431no—
493C22×Q8—862no—
494C22×Q8—862no—
495C22×Q8—862no—
496C22×Q8—861no—
497C22×Q8—1721no—
498C22×Q8—1721no—
499C22×D4—431no—
500C22×D4—861no—
501C22×D4—861no—
502C22×D4C22⋊D4311yescharacteristic
503C23×C4—861no—
504C23×C4—861no—
505C23×C4C22×D4311yescharacteristic
506C23×C4C22×D4311yescharacteristic
507C2×M16—862no—
508C2×M16—862no—
509C2×M16—1721no—
510C22×C8—431no—
511C22×C8—431no—
512C22×C8—431no—
513C22×C8—431no—
514C22×C8—862no—
515C22×C8—862no—
516C22×C8—1721no—
517#124—434no—
518#124—868no—
519#124—862no—
520C22⋊Q8—434no—
521C22⋊Q8—862no—
522C22⋊Q8—868no—
523#121—434no—
524#121—868no—
525#121—862no—
526C4×Q8—434no—
527C4×Q8—862no—
528C4×D4—868no—
529C4×D4C4×D4314yes—
530C4×D4D17214yes—
531#117—22no—
532#117—22no—
533#117—41no—
534#117—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4C22⋊D4311yescharacteristic
541C2×C4⋊C4C22×D4311yescharacteristic
542C2×C4⋊C4C22×D4311yescharacteristic
543C2×C4⋊C4C22×D4311yescharacteristic
544C2×C4⋊C4C22×D4311yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4C22⋊D4311yescharacteristic
554C2×C22⋊C4C22⋊D4311yescharacteristic
555C2×C42—21no—
556C2×C42—21no—
557C2×C42—21no—
558C2×C42—861no—
559C2×C42C22×D4311yescharacteristic
560C4⋊C8—862no—
561#103—434no—
562#103—862no—
563#103—862no—
564#103—862no—
565#103—862no—
566#103—862no—
567#103—1721no—
568#103—1721no—
569#102—862no—
570#102—862no—
571#102—1721no—
572#102—1721no—
573C22⋊C8—862no—
574C22⋊C8—862no—
575#97—862no—
576#95—21no—
577#95—21no—
578#95—21no—
579C24—861no—
580C24C2×C22⋊D4311yescharacteristic
581C24C2×C22⋊D4311yescharacteristic
582#41—868no—
583#41—1724no—
584#41—1724no—
585#41—1724no—
586C2×Q8—432no—
587C2×Q8—432no—
588C2×Q8—432no—
589C2×Q8—432no—
590C2×Q8—868no—
591C2×Q8—864no—
592C2×Q8—861no—
593C2×Q8—861no—
594C2×Q8—861no—
595C2×Q8—861no—
596C2×Q8—861no—
597C2×Q8—861no—
598C2×Q8—861no—
599C2×Q8—861no—
600C2×Q8—1722no—
601C2×Q8—1722no—
602C2×Q8—1724no—
603C2×Q8—1724no—
604C2×Q8—1724no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—432no—
608C2×D4—864no—
609C2×D4—864no—
610C2×D4—861no—
611C2×D4—861no—
612C2×D4—861no—
613C2×D4—861no—
614C2×D4—861no—
615C2×D4—1722no—
616C2×D4—1722no—
617C2×D4—1722no—
618C2×D4—1722no—
619C2×D4(C2×D43)⋊C414yes—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—861no—
633C22×C4—864no—
634C22×C4—861no—
635C22×C4—861no—
636C22×C4—864no—
637C22×C4—1722no—
638C22×C4—1722no—
639C22×C4—1722no—
640C22×C4—1722no—
641C22×C4C2×C4×D4312yes—
642C22×C4C2×C4×D4312yes—
643C22×C4C2×D17212yes—
644C22×C4C2×D17212yes—
645C22×C4C2×C22⋊D4311yescharacteristic
646C22×C4C2×C22⋊D4311yescharacteristic
647C22×C4C2×C22⋊D4311yescharacteristic
648C22×C4C2×C22⋊D4311yescharacteristic
649C22×C4C23×D4311yescharacteristic
650M16—1724no—
651C2×C8—432no—
652C2×C8—861no—
653C2×C8—861no—
654C2×C8—861no—
655C2×C8—861no—
656C2×C8—861no—
657C2×C8—861no—
658C2×C8—861no—
659C2×C8—861no—
660C2×C8—861no—
661C2×C8—861no—
662C2×C8—861no—
663C2×C8—1724no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—42no—
672C4⋊C4—81no—
673C4⋊C4—432no—
674C4⋊C4—864no—
675C4⋊C4—864no—
676C4⋊C4—861no—
677C4⋊C4(C2×D43)⋊C414yes—
678C4⋊C4D4×D4312yes—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—81no—
682C22⋊C4—81no—
683C22⋊C4—864no—
684C22⋊C4—864no—
685C22⋊C4—864no—
686C22⋊C4—864no—
687C22⋊C4(C2×D43)⋊C414yes—
688C22⋊C4(C2×D43)⋊C414yes—
689C42—42no—
690C42—42no—
691C42—42no—
692C42—864no—
693C42C2×C4×D4312yes—
694C42C2×D17212yes—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—862no—
708C23—1721no—
709C23—1721no—
710C23—1721no—
711C23—1721no—
712C23—1721no—
713C23—1721no—
714C23C2×(C2×D43)⋊C412yes—
715C23C2×(C2×D43)⋊C412yes—
716C23C22×C22⋊D4311yescharacteristic
717Q8—434no—
718Q8—862no—
719Q8—862no—
720Q8—862no—
721Q8—862no—
722Q8—862no—
723Q8—1728no—
724Q8—1721no—
725Q8—1721no—
726D4—44no—
727D4—862no—
728D4—862no—
729D4—1728no—
730D4—1728no—
731D4—1721no—
732D4—1721no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—1728no—
767C2×C4—1728no—
768C2×C4—1721no—
769C2×C4—1721no—
770C2×C4—1721no—
771C2×C4—1721no—
772C2×C4C2×(C2×D43)⋊C412yes—
773C2×C4C2×(C2×D43)⋊C412yes—
774C2×C4C2×(C2×D43)⋊C412yes—
775C2×C4C2×(C2×D43)⋊C412yes—
776C2×C4C22×C4×D4311yescharacteristic
777C2×C4C2×D4×D4311yescharacteristic
778C2×C4C22×D17211yescharacteristic
779C2×C4#41×D4311yescharacteristic
780C2×C4#1306337011yescharacteristic
781C2×C4#1306337111yescharacteristic
782C8—862no—
783C8—1721no—
784C8—1721no—
785C8—1721no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—3441no—
801C22—3441no—
802C22—3441no—
803C22—3441no—
804C22—1722no—
805C22—1722no—
806C22—1722no—
807C22C22×(C2×D43)⋊C411yescharacteristic
808C22D4×C22⋊D4311yescharacteristic
809C22#1458353711yescharacteristic
810C22#1458369711yescharacteristic
811C22#1458369711yescharacteristic
812C22#1458371011yescharacteristic
813C22#1458371411yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—42no—
819C4—81no—
820C4—81no—
821C4—81no—
822C4—864no—
823C4—1722no—
824C4—1722no—
825C4C4×D4×D4311yescharacteristic
826C4#1458337111yescharacteristic
827C4D4×D17211yescharacteristic
828C4#1458354411yescharacteristic
829C2—42no—
830C2—42no—
831C2—3442no—
832C2D4×(C2×D43)⋊C411yescharacteristic
833C2#1914311211yescharacteristic
834C2#1914312511yescharacteristic
835C2#1914614611yescharacteristic
836C2#1914617611yescharacteristic
837C2#1914665511yescharacteristic
838C2#1914677511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2354C2
socleC23×C43C22×D4
prime radicalC2×#14583558C2
cosocleC22×C4×C43C24
hypercenter#2354D43
hypocenterC43#22426
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. C2×#14582971C2semidirect
3. C2×#14582907C2semidirect
4. C2×#14582893C2semidirect
5. #19135527C2semidirect
6. #19135409C2semidirect
7. #19135031C2semidirect
8. #19135016C2semidirect
9. #19134917C2semidirect
10. #19134907C2semidirect
11. #19134597C2semidirect
12. #19134533C2semidirect
13. #19134529C2semidirect
14. #19134428C2semidirect
15. C43×#2354C2semidirect
21. #14583558C4semidirect
122. #13063248D4semidirect
414. #2354D43semidirect
483. C43#22426semidirect

Maximal subgroups

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

subgroupindex
C2×#145835582
C2×#145829712
C2×#145829072
C2×#145828932
#191355272
#191354092
#191350312
#191350162
#191349172
#191349072
#191345972
#191345332
#191345292
#191344282
C43×#23542
#2242643