Finite Group Databasebeta

← #25113162

Subgroups — #25113162

Order 11008.

1014 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583605C211yesmaximal, characteristic
2M16×Dic86C211yesmaximal, characteristic, complemented
3#19143546C211yesmaximal, characteristic, complemented
4#19135589C211yesmaximal, characteristic, complemented
5#19135586C211yesmaximal, characteristic, complemented
6#19135586C211yesmaximal, characteristic, complemented
7#19135582C211yesmaximal, characteristic, complemented
8#19135582C211yesmaximal, characteristic, complemented
9#19134586C211yesmaximal, characteristic
10#19134586C211yesmaximal, characteristic
11#19134584C211yesmaximal, characteristic
12C4×#13063241C211yesmaximal, characteristic
13#19134386C211yesmaximal, characteristic
14#19134386C211yesmaximal, characteristic
15C43×#1998C211yesmaximal, characteristic, complemented
16#14583605—21no—
17#14583605—21no—
18#14583605—21no—
19#14583605—21no—
20#14583605—21no—
21#14583605—21no—
22#14583605—21no—
23#14583605—21no—
24C2×#13063324C2211yescharacteristic
25C2×#13063316C2211yescharacteristic
26C2×#13063305C412yes—
27C2×#13063303C412yes—
28C2×#13063303C412yes—
29C2×C4×Dic86C2211yescharacteristic
30C2×C4×D172C2211yescharacteristic
31C2×#13063287C2211yescharacteristic
32C2×#13063287C2211yescharacteristic
33C2×C4⋊C4×D43C412yes—
34#14583029—21no—
35#14583028—21no—
36#14583028—21no—
37#14583027—21no—
38#14583027—21no—
39#14583026—21no—
40C8×Dic86—21no—
41#14583023—21no—
42#14582923C2211yescharacteristic
43#14582922C2211yescharacteristic
44#14582922C2211yescharacteristic
45#14582922C2211yescharacteristic
46#14582922C2211yescharacteristic
47C2×#13063241C2211yescharacteristic
48C2×#13063241C2211yescharacteristic
49C2×#13063241C2211yescharacteristic
50C2×#13063241C2211yescharacteristic
51C4×#10621877C2211yescharacteristic
52M16×Dic43C2211yescharacteristic
53M16×Dic43C2211yescharacteristic
54M16×Dic43C2211yescharacteristic
55M16×Dic43C2211yescharacteristic
56#14582668C2211yescharacteristic
57#14582668C2211yescharacteristic
58#14582668C2211yescharacteristic
59#14582668C2211yescharacteristic
60#14582667C2211yescharacteristic
61#14582667C2211yescharacteristic
62#14582667C2211yescharacteristic
63#14582667C2211yescharacteristic
64C2×#125×C43C2211yescharacteristic
65C43×#423C2211yescharacteristic
66C4×M16×C43C2211yescharacteristic
67C43×#343C2211yescharacteristic
68C43×#343C2211yescharacteristic
69C43×#343C2211yescharacteristic
70C43×#343C2211yescharacteristic
71C22×Dic86C2×C412yes—
72C22×Dic86C2×C411yescharacteristic
73C22×D172C2311yescharacteristic
74C22×C4×D43C2×C412yes—
75C22×C4×D43C2×C412yes—
76C22×C4×D43C2×C412yes—
77C2×#10621877C2311yescharacteristic
78C2×#10621877C2311yescharacteristic
79C2×#10621877C2311yescharacteristic
80C2×#10621877C2311yescharacteristic
81#13063324—21no—
82#13063324—21no—
83#13063324—21no—
84#13063324—21no—
85#13063316—21no—
86#13063316—21no—
87#13063316—21no—
88#13063316—21no—
89#13063305—22no—
90#13063305—22no—
91#13063305—22no—
92#13063305—22no—
93#13063303—22no—
94#13063303—22no—
95#13063303—22no—
96#13063303—22no—
97#13063303—22no—
98#13063303—22no—
99#13063303—22no—
100#13063303—22no—
101C4×Dic86D411yescharacteristic
102C4×Dic86D411yescharacteristic
103C4×Dic86D411yescharacteristic
104C4×Dic86D411yescharacteristic
105C4×Dic86D411yescharacteristic
106C4×Dic86D411yescharacteristic
107C4×Dic86D411yescharacteristic
108C4×Dic86D411yescharacteristic
109C4×D172—21no—
110C4×D172—21no—
111C4×D172—21no—
112C4×D172—21no—
113#13063287—21no—
114#13063287—21no—
115#13063287—21no—
116#13063287—21no—
117#13063287—21no—
118#13063287—21no—
119#13063287—21no—
120#13063287—21no—
121C2×C4⋊Dic43C2×C412yes—
122C2×C4⋊Dic43C2×C411yescharacteristic
123C2×C4⋊Dic43C2311yescharacteristic
124C2×Dic43⋊C4C2×C412yes—
125C2×Dic43⋊C4C2×C412yes—
126C2×Dic43⋊C4C2×C411yescharacteristic
127C2×Dic43⋊C4C2×C411yescharacteristic
128C4⋊C4×D43—22no—
129C4⋊C4×D43—22no—
130C4⋊C4×D43—22no—
131C4⋊C4×D43—22no—
132C2×(C2×D43)⋊C4C2×C412yes—
133C2×(C2×D43)⋊C4C2×C412yes—
134C2×(C2×D43)⋊C4C2×C412yes—
135C2×C4×Dic43C2311yescharacteristic
136C2×C4×Dic43C2311yescharacteristic
137C4⋊(C43⋊C8)—21no—
138C4⋊(C43⋊C8)—21no—
139Dic43⋊C8—21no—
140Dic43⋊C8—21no—
141Dic43⋊C8—21no—
142Dic43⋊C8—21no—
143Dic43⋊C8—21no—
144Dic43⋊C8—21no—
145Dic43⋊C8—21no—
146Dic43⋊C8—21no—
147#13063241—22no—
148#13063241—22no—
149#13063241—22no—
150#13063241Q814yescomplemented
151#13063236—21no—
152#13063235—21no—
153#13063235—21no—
154#13063235—21no—
155#13063235—21no—
156C4×C43⋊C8—21no—
157C8×Dic43—21no—
158C8×Dic43—21no—
159C8×Dic43—21no—
160C8×Dic43—21no—
161C2×M16×C43C2311yescharacteristic
162C2×M16×C43C2311yescharacteristic
163C2×M16×C43C2311yescharacteristic
164C2×M16×C43C2311yescharacteristic
165#125×C43—21no—
166#125×C43—21no—
167#125×C43—21no—
168#125×C43—21no—
169C2×C4⋊C4×C43C2×C412yes—
170C2×C4⋊C4×C43C2×C412yes—
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C42×C43C2311yescharacteristic
174C4⋊C8×C43—21no—
175C4⋊C8×C43—21no—
176#97×C43—21no—
177C4×C8×C43—21no—
178C23×D43C22×C412yes—
179C22×C4×C43C22×C412yes—
180C22×C4×C43C22×C412yes—
181C22×C4×C43C22×C411yescharacteristic
182C22×C4×C43C22×C411yescharacteristic
183C22×C4×C43C2411yescharacteristic
184C22×Dic43C22×C411yescharacteristic
185C22×Dic43C22×C412yes—
186C22×Dic43C22×C411yescharacteristic
187C22×Dic43C22×C411yescharacteristic
188C22×Dic43C22×C411yescharacteristic
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172—21no—
193C2×D172C2×Q812yes—
194C2×D172#4112yes—
195C2×C4×D43—22no—
196C2×C4×D43—22no—
197C2×C4×D43—22no—
198C2×C4×D43—22no—
199C2×C4×D43—22no—
200C2×C4×D43—22no—
201C2×C4×D43—44no—
202C2×C4×D43—82no—
203C2×C4×D43—82no—
204C2×Dic86—22no—
205C2×Dic86—22no—
206C2×Dic86—42no—
207C2×Dic86—82no—
208C2×Dic86C22⋊C411yescharacteristic
209C2×Dic86C22⋊C411yescharacteristic
210C2×Dic86C22⋊C411yescharacteristic
211C2×Dic86C22⋊C411yescharacteristic
212M16×C43—21no—
213M16×C43—21no—
214M16×C43—21no—
215M16×C43—21no—
216M16×C43—21no—
217M16×C43—21no—
218M16×C43—21no—
219M16×C43C2×Q812yes—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C4⋊C4×C43—22no—
225C4⋊C4×C43—22no—
226C4⋊C4×C43—22no—
227C4⋊C4×C43—22no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C42×C43C2×D411yescharacteristic
233C42×C43C2×D411yescharacteristic
234C42×C43C2×D411yescharacteristic
235C42×C43C2×D411yescharacteristic
236(C2×D43)⋊C4—22no—
237(C2×D43)⋊C4—22no—
238(C2×D43)⋊C4—22no—
239(C2×D43)⋊C4—22no—
240(C2×D43)⋊C4—22no—
241(C2×D43)⋊C4—22no—
242C4⋊Dic43—21no—
243C4⋊Dic43—21no—
244C4⋊Dic43—22no—
245C4⋊Dic43—22no—
246C4⋊Dic43C22⋊C411yescharacteristic
247C4⋊Dic43C22⋊C411yescharacteristic
248C4⋊Dic43C22⋊C411yescharacteristic
249C4⋊Dic43C22⋊C411yescharacteristic
250Dic43⋊C4—22no—
251Dic43⋊C4—22no—
252Dic43⋊C4—22no—
253Dic43⋊C4—22no—
254Dic43⋊C4C22⋊C411yescharacteristic
255Dic43⋊C4C22⋊C411yescharacteristic
256Dic43⋊C4C22⋊C411yescharacteristic
257Dic43⋊C4C22⋊C411yescharacteristic
258Dic43⋊C4C22⋊C411yescharacteristic
259Dic43⋊C4C22⋊C411yescharacteristic
260Dic43⋊C4C22⋊C411yescharacteristic
261Dic43⋊C4C22⋊C411yescharacteristic
262C4×Dic43C2×D411yescharacteristic
263C4×Dic43C2×D411yescharacteristic
264C4×Dic43C2×D411yescharacteristic
265C4×Dic43C2×D411yescharacteristic
266C4×Dic43C2×D411yescharacteristic
267C4×Dic43C2×D411yescharacteristic
268C4×Dic43C2×D411yescharacteristic
269C4×Dic43C2×D411yescharacteristic
270#10621877—21no—
271#10621877—21no—
272#10621877—21no—
273#10621877—21no—
274#10621877—21no—
275#10621877—21no—
276#10621877—21no—
277#10621877C2×Q812yes—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C23×C43C23×C411yescharacteristic
283C22×D43—22no—
284C22×D43—22no—
285C22×D43—42no—
286C22×D43—42no—
287C22×D43C4×Q814yes—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—42no—
293C2×C4×C43—42no—
294C2×C4×C43C2×C22⋊C411yescharacteristic
295C2×C4×C43C2×C22⋊C411yescharacteristic
296C2×C4×C43C2×C22⋊C411yescharacteristic
297C2×C4×C43C2×C22⋊C411yescharacteristic
298C2×C4×C43C22×D411yescharacteristic
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C22×Q811yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C432−1+411yescharacteristic
303C2×C4×C432−1+411yescharacteristic
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—42no—
310C2×Dic43C2×C22⋊C411yescharacteristic
311C2×Dic43C2×C22⋊C411yescharacteristic
312C2×Dic43C2×C22⋊C411yescharacteristic
313C2×Dic43C2×C22⋊C411yescharacteristic
314C2×Dic43C2×C22⋊C411yescharacteristic
315C2×Dic43C2×C22⋊C411yescharacteristic
316C2×Dic43C2×C22⋊C411yescharacteristic
317C2×Dic43C2×C22⋊C411yescharacteristic
318D172—22no—
319D172—22no—
320D172—22no—
321D172—22no—
322C4×D43—44no—
323C4×D43—44no—
324C4×D43—82no—
325C4×D43—82no—
326C4×D43—82no—
327C4×D43—82no—
328Dic86—22no—
329Dic86—22no—
330Dic86—41no—
331Dic86—41no—
332Dic86—82no—
333Dic86—82no—
334C8×C43—22no—
335C8×C43—41no—
336C8×C43—41no—
337C8×C43—41no—
338C43⋊C8—22no—
339C43⋊C8—41no—
340C43⋊C8—41no—
341C43⋊C8—41no—
342#22515—431nomaximal, Sylow
343C22×C43—21no—
344C22×C43—21no—
345C22×C43C22×C22⋊C411yescharacteristic
346C22×C43C2×C4×Q811yescharacteristic
347C22×C43#51911yescharacteristic
348C2×D43—24no—
349C2×D43—44no—
350C2×D43—42no—
351C2×D43—42no—
352C2×D43—44no—
353C4×C43—21no—
354C4×C43—21no—
355C4×C43—21no—
356C4×C43—21no—
357C4×C43—42no—
358C4×C43—42no—
359C4×C43#54811yescharacteristic
360C4×C43#54811yescharacteristic
361C4×C43D4×Q811yescharacteristic
362C4×C43D4×Q811yescharacteristic
363Dic43—21no—
364Dic43—21no—
365Dic43—21no—
366Dic43—21no—
367Dic43—21no—
368Dic43—21no—
369Dic43—21no—
370Dic43—42no—
371Dic43#41312yes—
372C2×#554—431no—
373Q8×M16—431no—
374Q8×M16—431no—
375#1998—431no—
376#1998—431no—
377#1998—431no—
378#1998D4311yescharacteristic, complemented
379#1997—431no—
380#1997—431no—
381#1800—431no—
382#1800—431no—
383#1800—431no—
384C4×#100—431no—
385C4×#100—431no—
386C4×#100—431no—
387C2×C43—21no—
388C2×C43—21no—
389C2×C43Q8×C22⋊C411yescharacteristic
390C2×C43C2×#41311yescharacteristic
391C2×C43#288811yescharacteristic
392D43—44no—
393#554—861no—
394#554—861no—
395#554—861no—
396#554—861no—
397#554—861no—
398#554—861no—
399#554—861no—
400#554—861no—
401C2×C4⋊Q8—431no—
402C2×#125—431no—
403C2×#125C2×D4311yescharacteristic
404C2×C22⋊Q8—432no—
405C2×C22⋊Q8—432no—
406C2×C22⋊Q8—432no—
407C2×C4×Q8—431no—
408C2×C4×D4—431no—
409C2×C4×D4—431no—
410C2×C4×D4—431no—
411C22×C4⋊C4—432no—
412#446—861no—
413#446—861no—
414#446—861no—
415#446—861no—
416#446—861no—
417#446—861no—
418C8×Q8—861no—
419C8×Q8—861no—
420#423—431no—
421#423—431no—
422#423—431no—
423#423—431no—
424#423—431no—
425#423C2×D4311yescharacteristic
426C2×#100—431no—
427C2×#100—431no—
428C2×#100—431no—
429C2×#100—431no—
430C4×M16—431no—
431C4×M16—431no—
432C4×M16—431no—
433C4×M16—431no—
434C4×M16—431no—
435C4×M16C2×D4311yescharacteristic
436#343—431no—
437#343—431no—
438#343—431no—
439#343—431no—
440#343—431no—
441#343—431no—
442#343—431no—
443#343—431no—
444#343C2×D4311yescharacteristic
445#343C2×D4311yescharacteristic
446#343C2×D4311yescharacteristic
447#343C2×D4311yescharacteristic
448C43#2251511yescharacteristic, complemented, Sylow
449C22×Q8—431no—
450C22×Q8—432no—
451C22×D4—431no—
452C23×C4—432no—
453C23×C4—432no—
454C23×C4—432no—
455C2×M16—431no—
456C2×M16—431no—
457C2×M16—431no—
458C2×M16—431no—
459C2×M16C22×D4311yescharacteristic
460C2×M16C22×D4311yescharacteristic
461C2×M16C22×D4311yescharacteristic
462C2×M16C22×D4311yescharacteristic
463C4⋊Q8—861no—
464C4⋊Q8—861no—
465C4⋊Q8—861no—
466C4⋊Q8—861no—
467#125—21no—
468#125—21no—
469#125—21no—
470#125—21no—
471#125—861no—
472#125—861no—
473#125—861no—
474#125—861no—
475C22⋊Q8—862no—
476C22⋊Q8—862no—
477C22⋊Q8—862no—
478C22⋊Q8—862no—
479C22⋊Q8—862no—
480C22⋊Q8—862no—
481C22⋊Q8—862no—
482C22⋊Q8—862no—
483C22⋊Q8—862no—
484C22⋊Q8—862no—
485C22⋊Q8—862no—
486C22⋊Q8—862no—
487C4×Q8—431no—
488C4×Q8—431no—
489C4×Q8—431no—
490C4×Q8—431no—
491C4×Q8—431no—
492C4×Q8—431no—
493C4×Q8—431no—
494C4×Q8—431no—
495C4×D4—861no—
496C4×D4—861no—
497C4×D4—861no—
498C4×D4—861no—
499C4×D4—861no—
500C4×D4—861no—
501C4×D4—861no—
502C4×D4—861no—
503C4×D4—861no—
504C4×D4—861no—
505C4×D4—861no—
506C4×D4—861no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—431no—
510C2×C4⋊C4—432no—
511C2×C4⋊C4—432no—
512C2×C4⋊C4—432no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—862no—
515C2×C4⋊C4—862no—
516C2×C4⋊C4—862no—
517C2×C4⋊C4—862no—
518C2×C4⋊C4C4×D4312yes—
519C2×C4⋊C4C4×D4312yes—
520C2×C4⋊C4C22×D4311yescharacteristic
521C2×C4⋊C4C22×D4311yescharacteristic
522C2×C22⋊C4—432no—
523C2×C22⋊C4—432no—
524C2×C22⋊C4—432no—
525C2×C42—431no—
526C2×C42—431no—
527C2×C42C22×D4311yescharacteristic
528C4⋊C8—21no—
529C4⋊C8—21no—
530C4⋊C8—861no—
531C4⋊C8—861no—
532C4⋊C8—861no—
533C4⋊C8—861no—
534C4⋊C8—861no—
535C4⋊C8—861no—
536C4⋊C8—861no—
537C4⋊C8—861no—
538C4⋊C8—861no—
539C4⋊C8—861no—
540#100—434no—
541#100—862no—
542#100—862no—
543#100—862no—
544#97—21no—
545#97—861no—
546#97—861no—
547#97—861no—
548#97—861no—
549#97—861no—
550C4×C8—21no—
551C4×C8—861no—
552C4×C8—861no—
553C4×C8—861no—
554C4×C8—861no—
555C4×C8—861no—
556C24—432no—
557C2×Q8—431no—
558C2×Q8—431no—
559C2×Q8—431no—
560C2×Q8—431no—
561C2×Q8—862no—
562C2×Q8—862no—
563C2×Q8—3442no—
564C2×Q8—1722no—
565C2×D4—432no—
566C2×D4—432no—
567C2×D4—861no—
568C2×D4—861no—
569C2×D4—861no—
570C2×D4—861no—
571C22×C4—431no—
572C22×C4—431no—
573C22×C4—431no—
574C22×C4—431no—
575C22×C4—432no—
576C22×C4—862no—
577C22×C4—862no—
578C22×C4—862no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—862no—
582C22×C4—3442no—
583C22×C4—3442no—
584C22×C4—1724no—
585C22×C4C2×C4×D4312yes—
586C22×C4C2×C4×D4312yes—
587C22×C4C2×C4×D4311yescharacteristic
588C22×C4C2×C4×D4311yescharacteristic
589C22×C4C23×D4311yescharacteristic
590M16—21no—
591M16—21no—
592M16—21no—
593M16—21no—
594M16—21no—
595M16—21no—
596M16—21no—
597M16—432no—
598M16—861no—
599M16—861no—
600M16—861no—
601M16—861no—
602M16—861no—
603M16—861no—
604M16—861no—
605M16Q8×D4312yes—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8—861no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—431no—
623C4⋊C4—431no—
624C4⋊C4—431no—
625C4⋊C4—431no—
626C4⋊C4—431no—
627C4⋊C4—431no—
628C4⋊C4—431no—
629C4⋊C4—431no—
630C4⋊C4—431no—
631C4⋊C4—431no—
632C4⋊C4—431no—
633C4⋊C4—431no—
634C4⋊C4—862no—
635C4⋊C4—862no—
636C4⋊C4—862no—
637C4⋊C4—862no—
638C4⋊C4—862no—
639C4⋊C4—862no—
640C4⋊C4—861no—
641C4⋊C4—861no—
642C22⋊C4—862no—
643C22⋊C4—862no—
644C22⋊C4—862no—
645C22⋊C4—862no—
646C22⋊C4—862no—
647C22⋊C4—862no—
648C42—431no—
649C42—431no—
650C42—431no—
651C42—431no—
652C42—431no—
653C42—431no—
654C42—431no—
655C42—431no—
656C42D4×D4311yescharacteristic
657C42D4×D4311yescharacteristic
658C42D4×D4311yescharacteristic
659C42D4×D4311yescharacteristic
660C23—434no—
661C23—862no—
662C23—862no—
663C23—1722no—
664C23—1722no—
665C23C22×C4×D4311yescharacteristic
666Q8—862no—
667Q8—862no—
668Q8—3442no—
669Q8—3442no—
670Q8—1721no—
671Q8—1721no—
672D4—862no—
673D4—862no—
674D4—862no—
675D4—862no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—431no—
683C2×C4—431no—
684C2×C4—431no—
685C2×C4—431no—
686C2×C4—431no—
687C2×C4—431no—
688C2×C4—431no—
689C2×C4—431no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—3442no—
693C2×C4—3442no—
694C2×C4—3442no—
695C2×C4—3442no—
696C2×C4—1724no—
697C2×C4—1724no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4—1722no—
702C2×C4C22⋊C4×D4311yescharacteristic
703C2×C4C22⋊C4×D4311yescharacteristic
704C2×C4C22⋊C4×D4311yescharacteristic
705C2×C4C22⋊C4×D4311yescharacteristic
706C2×C4C2×D4×D4311yescharacteristic
707C2×C4C2×D4×D4311yescharacteristic
708C2×C4C2×Q8×D4311yescharacteristic
709C2×C4#41×D4311yescharacteristic
710C2×C4#1306337211yescharacteristic
711C2×C4#1306337311yescharacteristic
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—862no—
717C8—1721no—
718C8—1721no—
719C8—1721no—
720C22—21no—
721C22—21no—
722C22—864no—
723C22—1724no—
724C22—1724no—
725C22—1722no—
726C22—1722no—
727C22C2×C22⋊C4×D4311yescharacteristic
728C22C4×Q8×D4311yescharacteristic
729C22#1458337511yescharacteristic
730C4—21no—
731C4—21no—
732C4—21no—
733C4—21no—
734C4—42no—
735C4—42no—
736C4—432no—
737C4—861no—
738C4—861no—
739C4—861no—
740C4—861no—
741C4—861no—
742C4—861no—
743C4—861no—
744C4—1722no—
745C4#1458355711yescharacteristic
746C4#1458355911yescharacteristic
747C4#1458356211yescharacteristic
748C4#1458356411yescharacteristic
749C2—21no—
750C2—21no—
751C2—1724no—
752C2#1913742911yescharacteristic
753C2#413×D4311yescharacteristic
754C2#1914307211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1998C2
socleC22×C43C22×C22⋊C4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1998D43
hypocenterC43#22515
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1998

Complements

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

NH ≅ G/Ntype
2. M16×Dic86C2semidirect
3. #19143546C2semidirect
4. #19135589C2semidirect
5. #19135586C2semidirect
6. #19135586C2semidirect
7. #19135582C2semidirect
8. #19135582C2semidirect
15. C43×#1998C2semidirect
150. #13063241Q8semidirect
378. #1998D43semidirect
448. C43#22515semidirect

Maximal subgroups

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

subgroupindex
C2×#145836052
M16×Dic862
#191435462
#191355892
#191355862
#191355822
#191345862
#191345842
C4×#130632412
#191343862
C43×#19982
#2251543