Finite Group Databasebeta

← #25960578

Subgroups — #25960578

Order 11008.

2756 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583666C211yesmaximal, characteristic, complemented
2C22×#13063332C211yesmaximal, characteristic, complemented
3#19143339C213yesmaximal, complemented
4D4×#10621877C213yesmaximal, complemented
5#19143322C213yesmaximal, complemented
6#19143322C213yesmaximal, complemented
7#19143313C213yesmaximal, complemented
8#19143299C213yesmaximal, complemented
9#19143290C213yesmaximal, complemented
10C2×#14582971C213yesmaximal, complemented
11#19143163C211yesmaximal, characteristic, complemented
12#19143044C211yesmaximal, characteristic, complemented
13#19143044C211yesmaximal, characteristic, complemented
14#19143023C211yesmaximal, characteristic, complemented
15D4×#41×C43C211yesmaximal, characteristic
16#14583666—28no—
17C2×#13063332—28no—
18C2×#13063332C2211yescharacteristic
19C2×#13063332C2211yescharacteristic
20C2×#13063332C2211yescharacteristic
21C2×#13063332C2211yescharacteristic
22C2×#13063332C2213yescomplemented
23C2×#13063332C2213yescomplemented
24C2×#13063332C2213yescomplemented
25C2×#13063332C2213yescomplemented
26C22×#10621877C2213yescomplemented
27C22×#10621877C2213yescomplemented
28C22×#10621877C2213yescomplemented
29C23×C43⋊C8C2213yescomplemented
30#14582977C2216yescomplemented
31#14582977C2216yescomplemented
32#14582971C2211yescharacteristic
33#14582971C2213yes—
34#14582971C2213yescomplemented
35#14582971C2213yescomplemented
36#14582971C2213yescomplemented
37#14582971C2213yescomplemented
38#14582971C2213yescomplemented
39#14582971C2213yescomplemented
40#14582971C2216yescomplemented
41#14582971C2216yescomplemented
42#14582971C2216yescomplemented
43D4×C43⋊C8C2216yescomplemented
44D4×C43⋊C8C2216yescomplemented
45#14582926C2213yescomplemented
46#14582926C2213yescomplemented
47#14582923C2213yescomplemented
48C2×C4⋊(C43⋊C8)C2213yescomplemented
49#14582866C2213yescomplemented
50#14582866C2213yescomplemented
51#14582866C2213yescomplemented
52#14582866C2213yescomplemented
53#14582863C2213yescomplemented
54#14582863C2213yescomplemented
55C2×C22⋊(C43⋊C8)C2213yescomplemented
56C2×C22⋊(C43⋊C8)C2213yescomplemented
57#14582855C2213yescomplemented
58#14582855C2213yescomplemented
59C4×#10621877C2213yescomplemented
60C2×#13063236C2213yescomplemented
61C22×#41×C43C2211yescharacteristic
62C22×#41×C43C2211yescharacteristic
63C43×#550C411yescharacteristic
64D4×Q8×C43C411yescharacteristic
65C43×#548C411yescharacteristic
66C43×#548C411yescharacteristic
67C43×#547C413yes—
68C43×#546C413yes—
69C43×#546C413yes—
70D42×C43C413yes—
71C43×#532C2213yes—
72C43×#525C2213yes—
73C43×#525C2213yes—
74C4×#41×C43C2211yescharacteristic
75C2×C4×D4×C43C2213yes—
76#13063332—24no—
77#13063332—24no—
78#13063332—24no—
79#13063332—212no—
80#13063332—212no—
81#13063332—212no—
82#13063332—212no—
83#13063332D418yescomplemented
84C2×#10621877—212no—
85C2×#10621877—212no—
86C2×#10621877—212no—
87C2×#10621877C2313yes—
88C2×#10621877C2313yes—
89C2×#10621877C2313yes—
90C2×#10621877C2311yescharacteristic
91C2×#10621877C2313yes—
92C2×#10621877C2313yes—
93C2×#10621877C2313yes—
94C2×#10621877C2316yes—
95C2×#10621877C2313yes—
96C22×C43⋊C8—212no—
97C22×C43⋊C8C2313yes—
98C22×C43⋊C8C2313yes—
99C22×C43⋊C8C2313yes—
100C22×C43⋊C8C2311yescharacteristic
101C22×C43⋊C8C2313yes—
102C22×C43⋊C8C2313yes—
103C22×C43⋊C8C2313yes—
104C22×C43⋊C8C2316yes—
105C22×C43⋊C8C2313yes—
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2313yes—
108C4⋊(C43⋊C8)C2313yes—
109C4⋊(C43⋊C8)C2313yes—
110C4⋊(C43⋊C8)C2316yes—
111C22⋊(C43⋊C8)C2311yescharacteristic
112C22⋊(C43⋊C8)C2311yescharacteristic
113C22⋊(C43⋊C8)C2313yes—
114C22⋊(C43⋊C8)C2313yes—
115C22⋊(C43⋊C8)C2313yes—
116C22⋊(C43⋊C8)C2313yes—
117C22⋊(C43⋊C8)C2313yes—
118C22⋊(C43⋊C8)C2313yes—
119C22⋊(C43⋊C8)C2316yes—
120C22⋊(C43⋊C8)C2316yes—
121#13063236C2311yescharacteristic
122#13063236C2313yes—
123#13063236C2313yes—
124#13063236C2313yes—
125C4×C43⋊C8C2316yes—
126C2×#41×C43—24no—
127C2×#41×C43—24no—
128C2×#41×C43—24no—
129C2×#41×C43—24no—
130C2×#41×C43C2×C413yes—
131C2×#41×C43C2×C413yes—
132C2×#41×C43C2×C411yescharacteristic
133C2×#41×C43C2×C411yescharacteristic
134C2×#41×C43C2313yes—
135C2×#41×C43C2313yes—
136C2×#41×C43C2311yescharacteristic
137C22×Q8×C43C2×C411yescharacteristic
138C22×Q8×C43C2×C411yescharacteristic
139C22×D4×C43C2×C413yes—
140C22×D4×C43C2×C413yes—
141C22×D4×C43C2×C413yes—
142C23×C4×C43C2313yes—
143C23×C4×C43C2313yes—
144C4⋊Q8×C43C2×C413yes—
145#127×C43C2×C413yes—
146#124×C43C2×C413yes—
147#124×C43C2×C413yes—
148#123×C43C2×C416yes—
149#123×C43C2×C416yes—
150C22⋊Q8×C43C2×C413yes—
151C22⋊Q8×C43C2×C413yes—
152C22⋊Q8×C43C2×C413yes—
153C22⋊Q8×C43C2×C413yes—
154#121×C43C2×C413yes—
155#121×C43C2×C413yes—
156#121×C43C2×C413yes—
157#121×C43C2×C413yes—
158#121×C43C2×C416yes—
159#121×C43C2×C416yes—
160#120×C43C2×C416yes—
161#120×C43C2×C416yes—
162C4×Q8×C43C2×C411yescharacteristic
163C4×Q8×C43C2×C411yescharacteristic
164C4×D4×C43C2×C413yes—
165C4×D4×C43C2×C413yes—
166C4×D4×C43C2×C413yes—
167C4×D4×C43C2×C413yes—
168C4×D4×C43C2×C413yes—
169C4×D4×C43C2×C413yes—
170C4×D4×C43C2311yescharacteristic
171C4×D4×C43C2313yes—
172C4×D4×C43C2313yes—
173C4×D4×C43C2313yes—
174C4×D4×C43C2316yes—
175#117×C43C2313yes—
176C2×C4⋊C4×C43C2×C413yes—
177C2×C22⋊C4×C43C2×C413yes—
178C2×C22⋊C4×C43C2×C413yes—
179C2×C42×C43C2313yes—
180C24×C43C22×C413yes—
181C24×C43C22×C413yes—
182#41×C43—24no—
183#41×C43—24no—
184#41×C43—212no—
185#41×C43—212no—
186#41×C43—26no—
187#41×C43—26no—
188#41×C43—26no—
189#41×C43—26no—
190#41×C43C2×D414yes—
191#41×C43#4114yes—
192C2×Q8×C43—24no—
193C2×Q8×C43—24no—
194C2×Q8×C43C22×C413yes—
195C2×Q8×C43C22×C413yes—
196C2×Q8×C43C22×C411yescharacteristic
197C2×D4×C43—212no—
198C2×D4×C43—212no—
199C2×D4×C43—46no—
200C2×D4×C43C22×C411yescharacteristic
201C2×D4×C43C22×C413yes—
202C2×D4×C43C22×C416yes—
203C2×D4×C43C22×C416yes—
204C2×D4×C43C22×C413yes—
205C2×D4×C43C22×C413yes—
206C2×D4×C43C22×C413yes—
207C2×D4×C43C22×C413yes—
208C2×D4×C43C22×C416yes—
209C2×D4×C43C22×C413yes—
210C22×C4×C43—26no—
211C22×C4×C43—26no—
212C22×C4×C43—26no—
213C22×C4×C43—26no—
214C22×C4×C43C22×C413yes—
215C22×C4×C43C22×C413yes—
216C22×C4×C43C22×C413yes—
217C22×C4×C43C22×C413yes—
218C22×C4×C43C22×C413yes—
219C22×C4×C43C22×C413yes—
220C22×C4×C43C22×C413yes—
221C22×C4×C43C22×C413yes—
222C22×C4×C43C2411yescharacteristic
223C22×C4×C43C2411yescharacteristic
224C22×C4×C43C2413yes—
225C22×C4×C43C2413yes—
226C22×C4×C43C2413yes—
227C4⋊C4×C43C22×C411yescharacteristic
228C4⋊C4×C43C22×C413yes—
229C4⋊C4×C43C22×C413yes—
230C4⋊C4×C43C22×C413yes—
231C4⋊C4×C43C22×C413yes—
232C4⋊C4×C43C22×C413yes—
233C4⋊C4×C43C22×C416yes—
234C22⋊C4×C43C22×C411yescharacteristic
235C22⋊C4×C43C22×C411yescharacteristic
236C22⋊C4×C43C22×C413yes—
237C22⋊C4×C43C22×C413yes—
238C22⋊C4×C43C22×C413yes—
239C22⋊C4×C43C22×C413yes—
240C22⋊C4×C43C22×C413yes—
241C22⋊C4×C43C22×C413yes—
242C22⋊C4×C43C22×C416yes—
243C22⋊C4×C43C22×C416yes—
244C22⋊C4×C43C22×C416yes—
245C42×C43C22×C413yes—
246C42×C43C22×C413yes—
247C42×C43C2411yescharacteristic
248C42×C43C2413yes—
249#10621877—26no—
250#10621877—26no—
251#10621877—26no—
252#10621877—22no—
253#10621877—26no—
254#10621877—26no—
255#10621877—212no—
256#10621877—26no—
257#10621877C2×D4112yescomplemented
258C2×C43⋊C8—26no—
259C2×C43⋊C8—26no—
260C2×C43⋊C8—26no—
261C2×C43⋊C8—22no—
262C2×C43⋊C8—26no—
263C2×C43⋊C8—26no—
264C2×C43⋊C8—26no—
265C2×C43⋊C8—212no—
266C2×C43⋊C8C2×D4112yescomplemented
267C2×C43⋊C8C2413yes—
268C2×C43⋊C8C2411yescharacteristic
269C2×C43⋊C8C2411yescharacteristic
270C2×C43⋊C8C2411yescharacteristic
271C2×C43⋊C8C2413yes—
272C2×C43⋊C8C2413yes—
273C2×C43⋊C8C2413yes—
274C2×C43⋊C8C2411yescharacteristic
275C23×C43—26no—
276C23×C43—26no—
277C23×C43—26no—
278C23×C43—43no—
279C23×C43—43no—
280C23×C43—43no—
281C23×C43C23×C411yescharacteristic
282C23×C43C23×C413yes—
283C23×C43C23×C413yes—
284C23×C43C23×C413yes—
285C23×C43C23×C411yescharacteristic
286Q8×C43—26no—
287Q8×C43—26no—
288Q8×C43C4×D414yes—
289D4×C43—212no—
290D4×C43—212no—
291D4×C43—22no—
292D4×C43—26no—
293D4×C43—26no—
294D4×C43—26no—
295D4×C43—43no—
296D4×C43—43no—
297D4×C43—46no—
298D4×C43C4×D4112yes—
299C2×C4×C43—26no—
300C2×C4×C43—26no—
301C2×C4×C43—26no—
302C2×C4×C43—26no—
303C2×C4×C43—26no—
304C2×C4×C43—26no—
305C2×C4×C43—21no—
306C2×C4×C43—23no—
307C2×C4×C43—23no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—23no—
312C2×C4×C43—23no—
313C2×C4×C43—43no—
314C2×C4×C43—43no—
315C2×C4×C43C23×C411yescharacteristic
316C2×C4×C43C23×C411yescharacteristic
317C2×C4×C43C23×C413yes—
318C2×C4×C43C23×C413yes—
319C2×C4×C43C23×C411yescharacteristic
320C2×C4×C43C23×C411yescharacteristic
321C2×C4×C43C23×C413yes—
322C2×C4×C43C23×C413yes—
323C2×C4×C43C23×C413yes—
324C2×C4×C43C22×D416yes—
325C2×C4×C43C2×#4116yes—
326C2×C4×C43C2511yescharacteristic
327C43⋊C8—21no—
328C43⋊C8—23no—
329C43⋊C8—21no—
330C43⋊C8—23no—
331C43⋊C8—21no—
332C43⋊C8—23no—
333C43⋊C8C22×D412yes—
334C43⋊C8C22×D416yes—
335#60146—431nomaximal, Sylow
336C22×C43—21no—
337C22×C43—23no—
338C22×C43—21no—
339C22×C43—23no—
340C22×C43—21no—
341C22×C43—23no—
342C22×C43—23no—
343C22×C43—23no—
344C22×C43—21no—
345C22×C43—23no—
346C22×C43—21no—
347C22×C43—23no—
348C22×C43—23no—
349C22×C43—412no—
350C22×C43—86no—
351C22×C43C2×C4×D416yes—
352C22×C43#56812yescomplemented
353C22×C43C24×C411yescharacteristic
354C4×C43—21no—
355C4×C43—21no—
356C4×C43—23no—
357C4×C43—23no—
358C4×C43—21no—
359C4×C43—23no—
360C4×C43—21no—
361C4×C43—23no—
362C4×C43C2×C4×D416yes—
363C4×C43C23×D411yescharacteristic
364C4×C43C22×#4111yescharacteristic
365C2×#568—431no—
366C22×#131—431no—
367D4×#41D4311yescharacteristic
368#2935—433no—
369D4×M16—433no—
370#2933—433no—
371#2933—433no—
372#2932—433no—
373#2930—433no—
374#2929—433no—
375C2×#435—433no—
376#2906—431no—
377#2880—431no—
378#2880—431no—
379#2875—431no—
380C2×C43—22no—
381C2×C43—26no—
382C2×C43—43no—
383C2×C43—43no—
384C2×C43—41no—
385C2×C43C22×C4×D411yescharacteristic
386C2×C43C2×#56811yescharacteristic
387C2×C43#357311yescharacteristic
388C22×#41C2×D4311yescharacteristic
389C22×#41C2×D4311yescharacteristic
390#568—868no—
391C2×#131—431no—
392C2×#131—431no—
393C2×#131—431no—
394C2×#131—431no—
395C2×#131—433no—
396C2×#131—433no—
397C2×#131—433no—
398C2×#131—433no—
399C2×#131—868no—
400C22×M16—433no—
401C22×M16—433no—
402C22×M16—433no—
403C23×C8—433no—
404#550Dic4311yescharacteristic
405D4×Q8Dic4311yescharacteristic
406#548Dic4311yescharacteristic
407#548Dic4311yescharacteristic
408#547Dic4313yes—
409#546Dic4313yes—
410#546Dic4313yes—
411D42Dic4313yes—
412#532C2×D4313yes—
413#525C2×D4313yes—
414#525C2×D4313yes—
415C4×#41C2×D4311yescharacteristic
416C2×C4×D4C2×D4313yes—
417#436—436no—
418#436—436no—
419#435—431no—
420#435—433no—
421#435—433no—
422#435—433no—
423#435—433no—
424#435—433no—
425#435—433no—
426#435—433no—
427#435—436no—
428#435—436no—
429#435—436no—
430C8×D4—436no—
431C8×D4—436no—
432#424—433no—
433#424—433no—
434#423—433no—
435C2×C4⋊C8—433no—
436#408—433no—
437#408—433no—
438#408—433no—
439#408—433no—
440#407—433no—
441#407—433no—
442C2×C22⋊C8—433no—
443C2×C22⋊C8—433no—
444#405—433no—
445#405—433no—
446C4×M16—433no—
447C2×#97—433no—
448C43#6014611yescharacteristic, complemented, Sylow
449C2×#41—24no—
450C2×#41—24no—
451C2×#41—24no—
452C2×#41—24no—
453C2×#41C2×Dic4313yes—
454C2×#41C2×Dic4313yes—
455C2×#41C2×Dic4311yescharacteristic
456C2×#41C2×Dic4311yescharacteristic
457C2×#41C22×D4313yes—
458C2×#41C22×D4313yes—
459C2×#41C22×D4311yescharacteristic
460C22×Q8C2×Dic4311yescharacteristic
461C22×Q8C2×Dic4311yescharacteristic
462C22×D4C2×Dic4313yes—
463C22×D4C2×Dic4313yes—
464C22×D4C2×Dic4313yes—
465C23×C4C22×D4313yes—
466C23×C4C22×D4313yes—
467#131—438no—
468#131—8612no—
469#131—8612no—
470#131—8612no—
471#131—8612no—
472#131—864no—
473#131—864no—
474#131—864no—
475C2×M16—433no—
476C2×M16—431no—
477C2×M16—433no—
478C2×M16—433no—
479C2×M16—433no—
480C2×M16—433no—
481C2×M16—433no—
482C2×M16—436no—
483C2×M16—433no—
484C2×M16—8612no—
485C2×M16—8612no—
486C2×M16—8612no—
487C22×C8—433no—
488C22×C8—431no—
489C22×C8—433no—
490C22×C8—433no—
491C22×C8—433no—
492C22×C8—433no—
493C22×C8—433no—
494C22×C8—436no—
495C22×C8—433no—
496C22×C8—8612no—
497C4⋊Q8C2×Dic4313yes—
498#127C2×Dic4313yes—
499#124C2×Dic4313yes—
500#124C2×Dic4313yes—
501#123C2×Dic4316yes—
502#123C2×Dic4316yes—
503C22⋊Q8C2×Dic4313yes—
504C22⋊Q8C2×Dic4313yes—
505C22⋊Q8C2×Dic4313yes—
506C22⋊Q8C2×Dic4313yes—
507#121C2×Dic4313yes—
508#121C2×Dic4313yes—
509#121C2×Dic4313yes—
510#121C2×Dic4313yes—
511#121C2×Dic4316yes—
512#121C2×Dic4316yes—
513#120C2×Dic4316yes—
514#120C2×Dic4316yes—
515C4×Q8C2×Dic4311yescharacteristic
516C4×Q8C2×Dic4311yescharacteristic
517C4×D4C2×Dic4313yes—
518C4×D4C2×Dic4313yes—
519C4×D4C2×Dic4313yes—
520C4×D4C2×Dic4313yes—
521C4×D4C2×Dic4313yes—
522C4×D4C2×Dic4313yes—
523C4×D4C22×D4311yescharacteristic
524C4×D4C22×D4313yes—
525C4×D4C22×D4313yes—
526C4×D4C22×D4313yes—
527C4×D4C22×D4316yes—
528#117C22×D4313yes—
529C2×C4⋊C4C2×Dic4313yes—
530C2×C22⋊C4C2×Dic4313yes—
531C2×C22⋊C4C2×Dic4313yes—
532C2×C42C22×D4313yes—
533C4⋊C8—431no—
534C4⋊C8—433no—
535C4⋊C8—433no—
536C4⋊C8—433no—
537C4⋊C8—436no—
538C22⋊C8—431no—
539C22⋊C8—431no—
540C22⋊C8—433no—
541C22⋊C8—433no—
542C22⋊C8—433no—
543C22⋊C8—433no—
544C22⋊C8—433no—
545C22⋊C8—433no—
546C22⋊C8—436no—
547C22⋊C8—436no—
548#97—431no—
549#97—433no—
550#97—433no—
551#97—433no—
552C4×C8—436no—
553C24C22×Dic4313yes—
554C24C22×Dic4313yes—
555#41—24no—
556#41—24no—
557#41—212no—
558#41—212no—
559#41—26no—
560#41—26no—
561#41—26no—
562#41—26no—
563#41D4×D4314yes—
564#41#1062190014yes—
565C2×Q8—24no—
566C2×Q8—24no—
567C2×Q8C22×Dic4313yes—
568C2×Q8C22×Dic4313yes—
569C2×Q8C22×Dic4311yescharacteristic
570C2×D4—212no—
571C2×D4—212no—
572C2×D4—46no—
573C2×D4C22×Dic4311yescharacteristic
574C2×D4C22×Dic4313yes—
575C2×D4C22×Dic4316yes—
576C2×D4C22×Dic4316yes—
577C2×D4C22×Dic4313yes—
578C2×D4C22×Dic4313yes—
579C2×D4C22×Dic4313yes—
580C2×D4C22×Dic4313yes—
581C2×D4C22×Dic4316yes—
582C2×D4C22×Dic4313yes—
583C22×C4—26no—
584C22×C4—26no—
585C22×C4—26no—
586C22×C4—26no—
587C22×C4C22×Dic4313yes—
588C22×C4C22×Dic4313yes—
589C22×C4C22×Dic4313yes—
590C22×C4C22×Dic4313yes—
591C22×C4C22×Dic4313yes—
592C22×C4C22×Dic4313yes—
593C22×C4C22×Dic4313yes—
594C22×C4C22×Dic4313yes—
595C22×C4C23×D4311yescharacteristic
596C22×C4C23×D4313yes—
597C22×C4C23×D4313yes—
598C22×C4C23×D4311yescharacteristic
599C22×C4C23×D4313yes—
600M16—4312no—
601M16—862no—
602M16—866no—
603M16—866no—
604M16—866no—
605M16—8612no—
606M16—866no—
607M16—866no—
608M16—866no—
609C2×C8—4312no—
610C2×C8—433no—
611C2×C8—431no—
612C2×C8—433no—
613C2×C8—431no—
614C2×C8—431no—
615C2×C8—431no—
616C2×C8—433no—
617C2×C8—433no—
618C2×C8—862no—
619C2×C8—866no—
620C2×C8—866no—
621C2×C8—866no—
622C2×C8—8612no—
623C2×C8—866no—
624C2×C8—866no—
625C2×C8—866no—
626C4⋊C4C22×Dic4311yescharacteristic
627C4⋊C4C22×Dic4313yes—
628C4⋊C4C22×Dic4313yes—
629C4⋊C4C22×Dic4313yes—
630C4⋊C4C22×Dic4313yes—
631C4⋊C4C22×Dic4313yes—
632C4⋊C4C22×Dic4316yes—
633C22⋊C4C22×Dic4311yescharacteristic
634C22⋊C4C22×Dic4311yescharacteristic
635C22⋊C4C22×Dic4313yes—
636C22⋊C4C22×Dic4313yes—
637C22⋊C4C22×Dic4313yes—
638C22⋊C4C22×Dic4313yes—
639C22⋊C4C22×Dic4313yes—
640C22⋊C4C22×Dic4313yes—
641C22⋊C4C22×Dic4316yes—
642C22⋊C4C22×Dic4316yes—
643C22⋊C4C22×Dic4316yes—
644C42C22×Dic4313yes—
645C42C22×Dic4313yes—
646C42C23×D4313yes—
647C42C23×D4311yescharacteristic
648C23—26no—
649C23—26no—
650C23—26no—
651C23—43no—
652C23—43no—
653C23—43no—
654C23C23×Dic4311yescharacteristic
655C23C23×Dic4313yes—
656C23C23×Dic4313yes—
657C23C23×Dic4313yes—
658C23C23×Dic4311yescharacteristic
659Q8—26no—
660Q8—26no—
661Q8D4×Dic4314yes—
662D4—212no—
663D4—212no—
664D4—22no—
665D4—26no—
666D4—26no—
667D4—26no—
668D4—43no—
669D4—43no—
670D4—46no—
671D4D4×Dic43112yes—
672C2×C4—26no—
673C2×C4—26no—
674C2×C4—26no—
675C2×C4—26no—
676C2×C4—26no—
677C2×C4—26no—
678C2×C4—21no—
679C2×C4—23no—
680C2×C4—23no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—23no—
685C2×C4—23no—
686C2×C4—43no—
687C2×C4—43no—
688C2×C4C23×Dic4311yescharacteristic
689C2×C4C23×Dic4311yescharacteristic
690C2×C4C23×Dic4313yes—
691C2×C4C23×Dic4313yes—
692C2×C4C23×Dic4311yescharacteristic
693C2×C4C23×Dic4311yescharacteristic
694C2×C4C23×Dic4313yes—
695C2×C4C23×Dic4313yes—
696C2×C4C23×Dic4313yes—
697C2×C4C2×D4×D4316yes—
698C2×C4C2×#1062190016yes—
699C2×C4C24×D4311yescharacteristic
700C8—432no—
701C8—436no—
702C8—861no—
703C8—863no—
704C8—863no—
705C8—861no—
706C8—861no—
707C8—863no—
708C22—21no—
709C22—23no—
710C22—23no—
711C22—21no—
712C22—21no—
713C22—23no—
714C22—23no—
715C22—21no—
716C22—23no—
717C22—23no—
718C22—23no—
719C22—23no—
720C22—21no—
721C22—412no—
722C22—86no—
723C22C2×D4×Dic4316yes—
724C22#1458366612yescomplemented
725C22C24×Dic4311yescharacteristic
726C4—21no—
727C4—21no—
728C4—23no—
729C4—23no—
730C4—21no—
731C4—23no—
732C4—21no—
733C4—23no—
734C4C2×D4×Dic4316yes—
735C4C22×D4×D4311yescharacteristic
736C4C22×#1062190011yescharacteristic
737C2—22no—
738C2—26no—
739C2—43no—
740C2—41no—
741C2—43no—
742C2C22×D4×Dic4311yescharacteristic
743C2C2×#1458366611yescharacteristic
744C2#1914930711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D43
commutator, socleC22×C43C24×C4
Fitting, prime radicalD4×#41×C43C2
cosocleC2×C4×C43C25
hypercenterD4×#41D43
hypocenterC43#60146
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#14583666C2semidirect
2. C22×#13063332C2semidirect
3. #19143339C2semidirect
4. D4×#10621877C2semidirect
5. #19143322C2semidirect
6. #19143322C2semidirect
7. #19143313C2semidirect
8. #19143299C2semidirect
9. #19143290C2semidirect
10. C2×#14582971C2semidirect
11. #19143163C2semidirect
12. #19143044C2semidirect
13. #19143044C2semidirect
14. #19143023C2semidirect
22. C2×#13063332C22semidirect
23. C2×#13063332C22semidirect
24. C2×#13063332C22semidirect
25. C2×#13063332C22semidirect
26. C22×#10621877C22semidirect
27. C22×#10621877C22semidirect
28. C22×#10621877C22semidirect
29. C23×C43⋊C8C22semidirect
30. #14582977C22semidirect
31. #14582977C22semidirect
34. #14582971C22semidirect
35. #14582971C22semidirect
36. #14582971C22semidirect
37. #14582971C22semidirect
38. #14582971C22semidirect
39. #14582971C22semidirect
40. #14582971C22semidirect
41. #14582971C22semidirect
42. #14582971C22semidirect
43. D4×C43⋊C8C22semidirect
44. D4×C43⋊C8C22semidirect
45. #14582926C22semidirect
46. #14582926C22semidirect
47. #14582923C22semidirect
48. C2×C4⋊(C43⋊C8)C22semidirect
49. #14582866C22semidirect
50. #14582866C22semidirect
51. #14582866C22semidirect
52. #14582866C22semidirect
53. #14582863C22semidirect
54. #14582863C22semidirect
55. C2×C22⋊(C43⋊C8)C22semidirect
56. C2×C22⋊(C43⋊C8)C22semidirect
57. #14582855C22semidirect
58. #14582855C22semidirect
59. C4×#10621877C22semidirect
60. C2×#13063236C22semidirect
83. #13063332D4semidirect
257. #10621877C2×D4semidirect
266. C2×C43⋊C8C2×D4semidirect
352. C22×C43#568semidirect
448. C43#60146semidirect
724. C22#14583666semidirect

Maximal subgroups

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

subgroupindex
C2×#145836662
C22×#130633322
#191433392
D4×#106218772
#191433222
#191433132
#191432992
#191432902
C2×#145829712
#191431632
#191430442
#191430232
D4×#41×C432
#6014643