Finite Group Databasebeta

← #25112042

Subgroups — #25112042

Order 11008.

1498 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583558C211yesmaximal, characteristic
2C2×#14582896C211yesmaximal, characteristic, complemented
3C22×#13063250C211yesmaximal, characteristic, complemented
4#19137524C211yesmaximal, characteristic, complemented
5#19135525C211yesmaximal, characteristic, complemented
6#19135406C211yesmaximal, characteristic, complemented
7#19135023C211yesmaximal, characteristic, complemented
8#19135018C211yesmaximal, characteristic, complemented
9#19134910C211yesmaximal, characteristic, complemented
10#19134905C211yesmaximal, characteristic, complemented
11#19134611C211yesmaximal, characteristic, complemented
12#19134536C211yesmaximal, characteristic, complemented
13#19134531C211yesmaximal, characteristic, complemented
14C4×#13063250C211yesmaximal, characteristic, complemented
15C2×C8×D4×C43C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C23×Dic86C2211yescharacteristic
18#14583558—24no—
19#14583558C418yescomplemented
20C2×#13063313C2211yescharacteristic
21C2×#13063311—21no—
22C2×#13063304C2211yescharacteristic
23C2×#13063303—21no—
24C2×#13063299C2211yescharacteristic
25C2×#13063297—21no—
26C2×C4×Dic86C2211yescharacteristic
27C2×(C22⋊D43)⋊C4—21no—
28C2×#13063284C2211yescharacteristic
29C22×C4⋊Dic43C2211yescharacteristic
30#14582896—24no—
31C2×#13063250—24no—
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063250C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063250C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063247C2211yescharacteristic
42C2×#13063247C2211yescharacteristic
43C2×#13063247C2211yescharacteristic
44#14582792—21no—
45#14582785—21no—
46#14582779—21no—
47#14582765C2211yescharacteristic
48#14582759C2211yescharacteristic
49#14582759C2211yescharacteristic
50C4×C4⋊Dic43C2211yescharacteristic
51C22⋊C4×Dic43—21no—
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55#14582662C2211yescharacteristic
56C23×C8×C43C2211yescharacteristic
57C23×C8×C43C2211yescharacteristic
58C2×C4×D4×C43C2211yescharacteristic
59C8×D4×C43—24no—
60C2×C4⋊C8×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C2×C4×C8×C43C2211yescharacteristic
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—41no—
68C2×#10621898—41no—
69C2×#10621898C2×C414yescomplemented
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—
83C23×Dic43—21no—
84C22×C4×D43—21no—
85#13063313—22no—
86#13063313C2×C414yescomplemented
87#13063311—28no—
88#13063304—22no—
89#13063304C2×C414yescomplemented
90#13063303—28no—
91#13063299—22no—
92#13063299C2×C414yes—
93#13063297—28no—
94C4×Dic86—22no—
95C4×Dic86C2×C414yescomplemented
96(C22⋊D43)⋊C4—28no—
97#13063284—22no—
98#13063284—41no—
99C2×C4⋊Dic43—22no—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43—41no—
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C4⋊Dic43C2311yescharacteristic
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×C4×Dic43—21no—
117C2×C4×Dic43—21no—
118C2×C4×Dic43—21no—
119#13063250—22no—
120#13063250—22no—
121#13063250—22no—
122#13063250—22no—
123#13063250—22no—
124#13063250—41no—
125#13063250—41no—
126#13063250D414yescomplemented
127#13063247—22no—
128#13063247—22no—
129#13063247—41no—
130#13063247—41no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C43⋊#95—21no—
136C22×D4×C43D411yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C22×C8×C43—22no—
140C22×C8×C43—22no—
141C22×C8×C43—22no—
142C22×C8×C43—22no—
143C22×C8×C43—41no—
144C22×C8×C43—41no—
145C22×C8×C43C2311yescharacteristic
146C22×C8×C43C2311yescharacteristic
147C22×C8×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149C4×D4×C43C2×C414yes—
150C4×D4×C43D414yes—
151C2×C4⋊C4×C43D411yescharacteristic
152C2×C22⋊C4×C43D411yescharacteristic
153C2×C22⋊C4×C43D411yescharacteristic
154C2×C42×C43C2311yescharacteristic
155C4⋊C8×C43—22no—
156C22⋊C8×C43—22no—
157C22⋊C8×C43—22no—
158C4×C8×C43—22no—
159C24×C43C2×D411yescharacteristic
160C24×C43C2×D411yescharacteristic
161C23×D43—21no—
162C2×D4×C43—22no—
163C2×D4×C43—22no—
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×C43C22×C412yes—
174C22×C4×C43C22×C412yes—
175C22×C4×C43C2×D412yes—
176C22×C4×C43C2×D412yes—
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2411yescharacteristic
182C2×C22⋊D43—24no—
183C2×C22⋊D43—24no—
184C2×C22⋊D43—42no—
185C2×C22⋊D43—42no—
186C2×C22⋊D43—42no—
187C2×C22⋊D43—42no—
188C22×Dic43—24no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—42no—
197C22×Dic43—42no—
198C22×Dic43—42no—
199C22×Dic43—42no—
200C22×Dic43—81no—
201#10621898—28no—
202#10621898—44no—
203#10621898—44no—
204#10621898—44no—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172—21no—
210C2×D172C22×C412yes—
211C2×C4×D43—24no—
212C2×C4×D43—42no—
213C2×C4×D43—42no—
214C2×Dic86—21no—
215C2×Dic86—21no—
216C2×Dic86—21no—
217C2×Dic86—21no—
218C2×Dic86—21no—
219C2×Dic86—21no—
220C2×Dic86—21no—
221C2×Dic86—28no—
222C2×Dic86—24no—
223C2×Dic86—21no—
224C2×Dic86—44no—
225C2×Dic86—44no—
226C2×Dic86—44no—
227C2×Dic86—42no—
228C2×Dic86—42no—
229C2×Dic86C22×C412yes—
230C2×Dic86C22×C412yes—
231C2×Dic86C2×D412yes—
232C2×Dic86#4112yes—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—44no—
245C2×C8×C43—44no—
246C2×C8×C43C2×D412yes—
247C4⋊C4×C43C22⋊C414yes—
248C22⋊C4×C43C22⋊C414yes—
249C22⋊C4×C43C22⋊C414yes—
250C42×C43C22×C412yes—
251C42×C43C2×D412yes—
252C22⋊Dic43—24no—
253C22⋊Dic43—42no—
254C22⋊Dic43—42no—
255C22⋊Dic43—81no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—24no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—42no—
268C4⋊Dic43C22×C412yes—
269C4⋊Dic43C2×D412yes—
270Dic43⋊C4—24no—
271Dic43⋊C4—24no—
272C4×Dic43—24no—
273C4×Dic43—42no—
274C4×Dic43—81no—
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×C43C2×C22⋊C412yes—
286C23×C43C2×C22⋊C412yes—
287C23×C43#13512yes—
288C23×C43#13512yes—
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—28no—
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×C43C2×C22⋊C412yes—
315C2×C4×C43C2×C22⋊C412yes—
316C2×C4×C43C2×C22⋊C412yes—
317C2×C4×C43C2×C22⋊C412yes—
318C2×C4×C43C23×C411yescharacteristic
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C2×#4111yescharacteristic
322C2×C4×C43H(5,𝔽2)11yescharacteristic
323C2×C4×C43H(5,𝔽2)11yescharacteristic
324C22⋊D43—48no—
325C22⋊D43—48no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—48no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—84no—
349D172—22no—
350D172—22no—
351D172—41no—
352D172—41no—
353C4×D43—48no—
354Dic86—22no—
355Dic86—22no—
356Dic86—22no—
357Dic86—22no—
358Dic86—22no—
359Dic86—48no—
360Dic86—41no—
361Dic86—41no—
362Dic86C4×D414yes—
363C8×C43—22no—
364C8×C43—41no—
365C8×C43—41no—
366C8×C43—41no—
367#22416—431nomaximal, Sylow
368C22×C43—22no—
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—22no—
373C22×C43—22no—
374C22×C43—22no—
375C22×C43—22no—
376C22×C43—22no—
377C22×C43—41no—
378C22×C43—41no—
379C22×C43—41no—
380C22×C43—41no—
381C22×C43#41614yescomplemented
382C22×C43C22×C22⋊C411yescharacteristic
383C22×C43D4211yescharacteristic
384C22×C43#54611yescharacteristic
385C22×C43C2×#13511yescharacteristic
386C22×C43C2×#13511yescharacteristic
387C22×C43#57711yescharacteristic
388C22×C43#57811yescharacteristic
389C2×D43—42no—
390C2×D43—42no—
391C2×D43—42no—
392C2×D43—81no—
393C2×D43—81no—
394C2×D43—81no—
395C2×D43—81no—
396C4×C43—22no—
397C4×C43—22no—
398C4×C43—22no—
399C4×C43—22no—
400C4×C43C2×C4×D411yescharacteristic
401C4×C43#51811yescharacteristic
402C4×C43D4211yescharacteristic
403C4×C43#54611yescharacteristic
404Dic43—24no—
405Dic43—42no—
406Dic43—42no—
407Dic43—42no—
408Dic43—81no—
409Dic43—81no—
410Dic43—81no—
411C2×#548—431no—
412C2×C8×D4D4311yescharacteristic, complemented
413C2×#416—431no—
414C22×#103—431no—
415#2352—431no—
416#1983—431no—
417#1958—431no—
418#1893—431no—
419#1892—431no—
420#1874—431no—
421#1873—431no—
422#1805—431no—
423#1788—431no—
424#1787—431no—
425C4×#103—431no—
426C2×C43—24no—
427C2×C43—42no—
428C2×C43D4×C22⋊C411yescharacteristic
429C2×C43C2×#41611yescharacteristic
430C2×C43#289811yescharacteristic
431C2×C43#328211yescharacteristic
432C2×C43#328511yescharacteristic
433C2×C43#330011yescharacteristic
434C2×C43#330111yescharacteristic
435D43—82no—
436C22×#41—431no—
437C23×Q8—431no—
438C23×C8C2×D4311yescharacteristic
439C23×C8C2×D4311yescharacteristic
440#548—438no—
441#548—864no—
442C2×#124—431no—
443C2×#124—861no—
444C2×C22⋊Q8—431no—
445C2×C22⋊Q8—861no—
446C2×#121—431no—
447C2×#121—861no—
448C2×C4×Q8—431no—
449C2×C4×D4—861no—
450C2×C4×D4C2×D4311yescharacteristic
451C2×#117—431no—
452C22×C4⋊C4—431no—
453C8×D4—24no—
454C2×C4⋊C8C2×D4311yescharacteristic
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×#103—864no—
465C2×#102—431no—
466C2×#102—431no—
467C2×#102—431no—
468C2×#102—431no—
469C2×C22⋊C8C2×D4311yescharacteristic
470C2×C22⋊C8C2×D4311yescharacteristic
471C2×C4×C8C2×D4311yescharacteristic
472#388—861no—
473#387—861no—
474#386—861no—
475#382—431no—
476#380—431no—
477#380—431no—
478C4×C4⋊C4—431no—
479C4×C22⋊C4—861no—
480#340—431no—
481#340—431no—
482#340—431no—
483#340—431no—
484C43#2241611yescharacteristic, complemented, Sylow
485C2×#41—434no—
486C2×#41—862no—
487C2×#41—862no—
488C2×#41—862no—
489C2×#41—1721no—
490C2×#41—1721no—
491C22×Q8—434no—
492C22×Q8—431no—
493C22×Q8—431no—
494C22×Q8—862no—
495C22×Q8—862no—
496C22×Q8—861no—
497C22×Q8—862no—
498C22×Q8—1721no—
499C22×Q8—1721no—
500C22×D4—431no—
501C22×D4—861no—
502C22×D4—861no—
503C22×D4D17211yescharacteristic
504C23×C4—861no—
505C23×C4—861no—
506C23×C4—861no—
507C23×C4C22×D4311yescharacteristic
508C23×C4C22×D4311yescharacteristic
509C22×C8—22no—
510C22×C8—22no—
511C22×C8—22no—
512C22×C8—22no—
513C22×C8—41no—
514C22×C8—41no—
515C22×C8C22×D4311yescharacteristic
516C22×C8C22×D4311yescharacteristic
517C22×C8C22×D4311yescharacteristic
518C22×C8C22×D4311yescharacteristic
519#124—434no—
520#124—868no—
521#124—862no—
522C22⋊Q8—434no—
523C22⋊Q8—862no—
524C22⋊Q8—868no—
525#121—434no—
526#121—868no—
527#121—862no—
528C4×Q8—434no—
529C4×Q8—862no—
530C4×D4—868no—
531C4×D4C4×D4314yes—
532C4×D4C22⋊D4314yes—
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—431no—
540C2×C4⋊C4—862no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4—1721no—
545C2×C4⋊C4D17211yescharacteristic
546C2×C22⋊C4—861no—
547C2×C22⋊C4—861no—
548C2×C22⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4D17211yescharacteristic
554C2×C22⋊C4D17211yescharacteristic
555C2×C42—861no—
556C2×C42—861no—
557C2×C42—861no—
558C2×C42C22×D4311yescharacteristic
559C4⋊C8—22no—
560#103—434no—
561#103—862no—
562#103—862no—
563#103—862no—
564#103—862no—
565#103—862no—
566#103—1721no—
567#103—1721no—
568#102—862no—
569#102—862no—
570#102—1721no—
571#102—1721no—
572C22⋊C8—22no—
573C22⋊C8—22no—
574C4×C8—22no—
575#95—861no—
576#95—861no—
577#95—861no—
578#95—861no—
579#95—861no—
580C24—861no—
581C24C2×D17211yescharacteristic
582C24C2×D17211yescharacteristic
583#41—868no—
584#41—1724no—
585#41—1724no—
586#41—1724no—
587C2×Q8—432no—
588C2×Q8—432no—
589C2×Q8—432no—
590C2×Q8—432no—
591C2×Q8—868no—
592C2×Q8—864no—
593C2×Q8—861no—
594C2×Q8—861no—
595C2×Q8—861no—
596C2×Q8—861no—
597C2×Q8—861no—
598C2×Q8—861no—
599C2×Q8—861no—
600C2×Q8—861no—
601C2×Q8—1722no—
602C2×Q8—1722no—
603C2×Q8—1724no—
604C2×Q8—1724no—
605C2×Q8—1724no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—432no—
609C2×D4—864no—
610C2×D4—864no—
611C2×D4—861no—
612C2×D4—861no—
613C2×D4—861no—
614C2×D4—861no—
615C2×D4—861no—
616C2×D4—1722no—
617C2×D4—1722no—
618C2×D4—1722no—
619C2×D4—1722no—
620C2×D4(C2×D43)⋊C414yes—
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—861no—
630C22×C4—864no—
631C22×C4—861no—
632C22×C4—861no—
633C22×C4—861no—
634C22×C4—864no—
635C22×C4—861no—
636C22×C4—861no—
637C22×C4—861no—
638C22×C4—3441no—
639C22×C4—1722no—
640C22×C4—1722no—
641C22×C4—1722no—
642C22×C4—1722no—
643C22×C4—1722no—
644C22×C4—1722no—
645C22×C4C2×C4×D4312yes—
646C22×C4C2×C4×D4312yes—
647C22×C4C2×D17211yescharacteristic
648C22×C4C2×D17211yescharacteristic
649C22×C4C2×D17211yescharacteristic
650C22×C4C2×D17211yescharacteristic
651C22×C4C2×C22⋊D4312yes—
652C22×C4C2×C22⋊D4312yes—
653C22×C4C23×D4311yescharacteristic
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—44no—
666C2×C8—44no—
667C2×C8D4×D4312yes—
668C4⋊C4—432no—
669C4⋊C4—432no—
670C4⋊C4—864no—
671C4⋊C4—864no—
672C4⋊C4—861no—
673C4⋊C4—861no—
674C4⋊C4—861no—
675C4⋊C4—861no—
676C4⋊C4—861no—
677C4⋊C4—861no—
678C4⋊C4—861no—
679C4⋊C4—861no—
680C4⋊C4—1722no—
681C4⋊C4(C2×D43)⋊C414yes—
682C22⋊C4—864no—
683C22⋊C4—864no—
684C22⋊C4—864no—
685C22⋊C4—864no—
686C22⋊C4—3441no—
687C22⋊C4—1722no—
688C22⋊C4—1722no—
689C22⋊C4(C2×D43)⋊C414yes—
690C22⋊C4(C2×D43)⋊C414yes—
691C42—864no—
692C42—3441no—
693C42—1722no—
694C42C2×C4×D4312yes—
695C42C2×C22⋊D4312yes—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—862no—
707C23—1721no—
708C23—1721no—
709C23—1721no—
710C23—1721no—
711C23—1721no—
712C23—1721no—
713C23C2×(C2×D43)⋊C412yes—
714C23C2×(C2×D43)⋊C412yes—
715C23#1306334712yes—
716C23#1306334712yes—
717C23C22×D17211yescharacteristic
718Q8—434no—
719Q8—862no—
720Q8—862no—
721Q8—862no—
722Q8—862no—
723Q8—862no—
724Q8—1728no—
725Q8—1721no—
726Q8—1721no—
727D4—28no—
728D4—862no—
729D4—862no—
730D4—1728no—
731D4—1728no—
732D4—1721no—
733D4—1721no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
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—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—3444no—
757C2×C4—1728no—
758C2×C4—1728no—
759C2×C4—1721no—
760C2×C4—1721no—
761C2×C4—1721no—
762C2×C4—1721no—
763C2×C4—1721no—
764C2×C4—1721no—
765C2×C4—1721no—
766C2×C4—1721no—
767C2×C4—1721no—
768C2×C4—1721no—
769C2×C4—1721no—
770C2×C4—1721no—
771C2×C4—1721no—
772C2×C4—1721no—
773C2×C4—1721no—
774C2×C4C2×(C2×D43)⋊C412yes—
775C2×C4C2×(C2×D43)⋊C412yes—
776C2×C4C2×(C2×D43)⋊C412yes—
777C2×C4C2×(C2×D43)⋊C412yes—
778C2×C4C22×C4×D4311yescharacteristic
779C2×C4C2×D4×D4311yescharacteristic
780C2×C4C22×C22⋊D4311yescharacteristic
781C2×C4#41×D4311yescharacteristic
782C2×C4#1306337011yescharacteristic
783C2×C4#1306337111yescharacteristic
784C8—22no—
785C8—41no—
786C8—41no—
787C8—41no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—3441no—
802C22—3441no—
803C22—3441no—
804C22—3441no—
805C22—1722no—
806C22—1722no—
807C22—1722no—
808C22#1458289614yescomplemented
809C22C22×(C2×D43)⋊C411yescharacteristic
810C22D4×D17211yescharacteristic
811C22#1458354411yescharacteristic
812C22C2×#1306334711yescharacteristic
813C22C2×#1306334711yescharacteristic
814C22#1458371111yescharacteristic
815C22#1458371611yescharacteristic
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—864no—
821C4—3441no—
822C4—3441no—
823C4—3441no—
824C4—1722no—
825C4—1722no—
826C4—1722no—
827C4C4×D4×D4311yescharacteristic
828C4#1458337111yescharacteristic
829C4D4×C22⋊D4311yescharacteristic
830C4#1458353711yescharacteristic
831C2—24no—
832C2—42no—
833C2—3442no—
834C2D4×(C2×D43)⋊C411yescharacteristic
835C2C2×#1458289611yescharacteristic
836C2#1914312911yescharacteristic
837C2#1914630711yescharacteristic
838C2#1914633811yescharacteristic
839C2#1914648411yescharacteristic
840C2#1914649911yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C8×D4×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583558C2
cosocleC22×C4×C43C24
hypercenterC2×C8×D4D43
hypocenterC43#22416
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
2. C2×#14582896C2semidirect
3. C22×#13063250C2semidirect
4. #19137524C2semidirect
5. #19135525C2semidirect
6. #19135406C2semidirect
7. #19135023C2semidirect
8. #19135018C2semidirect
9. #19134910C2semidirect
10. #19134905C2semidirect
11. #19134611C2semidirect
12. #19134536C2semidirect
13. #19134531C2semidirect
14. C4×#13063250C2semidirect
15. C2×C8×D4×C43C2semidirect
19. #14583558C4semidirect
69. C2×#10621898C2×C4semidirect
86. #13063313C2×C4semidirect
89. #13063304C2×C4semidirect
95. C4×Dic86C2×C4semidirect
126. #13063250D4semidirect
381. C22×C43#416semidirect
412. C2×C8×D4D43semidirect
484. C43#22416semidirect
808. C22#14582896semidirect

Maximal subgroups

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

subgroupindex
C2×#145835582
C2×#145828962
C22×#130632502
#191375242
#191355252
#191354062
#191350232
#191350182
#191349102
#191349052
#191346112
#191345362
#191345312
C4×#130632502
C2×C8×D4×C432
#2241643