Finite Group Databasebeta

← #25119141

Subgroups — #25119141

Order 11008.

892 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144173C211yesmaximal, characteristic
2C2×#14583014C211yesmaximal, characteristic, complemented
3#19143316C211yesmaximal, characteristic, complemented
4C22×#13063260C211yesmaximal, characteristic, complemented
5#19135482C211yesmaximal, characteristic, complemented
6#19135340C211yesmaximal, characteristic, complemented
7#19135243C211yesmaximal, characteristic, complemented
8#19135240C211yesmaximal, characteristic, complemented
9#19134898C211yesmaximal, characteristic, complemented
10#19134897C211yesmaximal, characteristic, complemented
11#19134870C211yesmaximal, characteristic, complemented
12#19134869C211yesmaximal, characteristic, complemented
13#19134475C211yesmaximal, characteristic, complemented
14#19134369C211yesmaximal, characteristic, complemented
15C43×#2933C211yesmaximal, characteristic, complemented
16C2×#13063345C2211yescharacteristic
17C2×#13063331C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20#14583410C2211yescharacteristic
21#14583138C411yescharacteristic, complemented
22#14583138C411yescharacteristic, complemented
23#14583133C411yescharacteristic, complemented
24#14583133C411yescharacteristic, complemented
25#14583130C411yescharacteristic, complemented
26#14583130C411yescharacteristic, complemented
27#14583126C411yescharacteristic, complemented
28#14583126C411yescharacteristic, complemented
29#14583014—24no—
30#14582974—21no—
31#14582973—21no—
32#14582967—21no—
33(C22⋊D43)⋊C8—21no—
34C2×#13063260—24no—
35C2×#13063260C2211yescharacteristic
36C2×#13063260C2211yescharacteristic
37C2×#13063260C2211yescharacteristic
38C2×#13063260C2211yescharacteristic
39#14582935C2211yescharacteristic
40#14582925C2211yescharacteristic
41C2×#13063252C2211yescharacteristic
42C2×#13063252C2211yescharacteristic
43C2×#13063251C2211yescharacteristic
44C2×#13063251C2211yescharacteristic
45#14582895C2211yescharacteristic
46#14582893C2211yescharacteristic
47#14582865C2211yescharacteristic
48#14582854C2211yescharacteristic
49C2×C8×Dic43C2211yescharacteristic
50C2×C8×Dic43C2211yescharacteristic
51C4×C22⋊Dic43C2211yescharacteristic
52#14582660C2211yescharacteristic
53#14582660C2211yescharacteristic
54#14582658C2211yescharacteristic
55#14582658C2211yescharacteristic
56#14582653C2211yescharacteristic
57#14582653C2211yescharacteristic
58C2×#131×C43C2211yescharacteristic
59C22×M16×C43C2211yescharacteristic
60C43×#525C2211yescharacteristic
61C43×#436—21no—
62C43×#435—21no—
63C43×#435—21no—
64C8×D4×C43—21no—
65C43×#424C2211yescharacteristic
66C43×#408C2211yescharacteristic
67C2×C22⋊C8×C43C2211yescharacteristic
68C43×#405C2211yescharacteristic
69C2×#10621898C2311yescharacteristic
70#13063345—22no—
71#13063345—22no—
72C2×#10621885C2×C411yescharacteristic
73C2×#10621883C2×C411yescharacteristic
74C2×#10621884C2×C411yescharacteristic
75C2×#10621882C2×C411yescharacteristic
76#13063331—22no—
77#13063331—41no—
78C2×#10621877—21no—
79C2×#10621877—22no—
80C2×#10621877—41no—
81C2×#10621877C2311yescharacteristic
82C2×#10621877C2311yescharacteristic
83C2×#10621872—21no—
84C22×C43⋊C8—22no—
85C22×C43⋊C8—22no—
86C22×C43⋊C8—21no—
87C22×C43⋊C8C2×C411yescharacteristic
88C22×C43⋊C8C2×C411yescharacteristic
89C22×C43⋊C8C2×C411yescharacteristic
90C22×C43⋊C8C2×C411yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93C2×C8×D43—21no—
94#13063308—21no—
95#13063304C2×C411yescharacteristic
96#13063304C2×C411yescharacteristic
97#13063299C2×C411yescharacteristic
98#13063299C2×C411yescharacteristic
99#13063294—21no—
100C4×C22⋊D43—21no—
101C4×C22⋊D43—21no—
102#13063284C2311yescharacteristic
103C2×C22⋊Dic43—21no—
104C2×C4×Dic43C2311yescharacteristic
105C2×C4×Dic43C2311yescharacteristic
106#13063260—22no—
107#13063260—22no—
108#13063260—22no—
109#13063260D414yescomplemented
110#13063258C2×C411yescharacteristic
111#13063258C2×C411yescharacteristic
112#13063256C2×C411yescharacteristic
113#13063256C2×C411yescharacteristic
114Dic43⋊C8—21no—
115Dic43⋊C8—21no—
116#13063252—22no—
117#13063252—41no—
118#13063251—22no—
119#13063251—41no—
120#13063249C2×C411yescharacteristic
121#13063249C2×C411yescharacteristic
122#13063248C2×C411yescharacteristic
123#13063248C2×C411yescharacteristic
124#13063246C2×C411yescharacteristic
125#13063246C2×C411yescharacteristic
126#13063245C2×C411yescharacteristic
127#13063245C2×C411yescharacteristic
128(C2×D43)⋊C8—21no—
129(C2×D43)⋊C8—21no—
130#13063235—21no—
131C8×Dic43—21no—
132C8×Dic43—22no—
133C8×Dic43—22no—
134C43⋊#95—21no—
135C2×#41×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137#131×C43—22no—
138#131×C43—41no—
139C2×M16×C43—21no—
140C2×M16×C43—21no—
141C2×M16×C43—22no—
142C2×M16×C43—41no—
143C2×M16×C43C2311yescharacteristic
144C2×M16×C43C2311yescharacteristic
145C22×C8×C43—21no—
146C22×C8×C43—21no—
147C22×C8×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149#123×C43—21no—
150C22⋊Q8×C43C2×C411yescharacteristic
151C22⋊Q8×C43C2×C411yescharacteristic
152#121×C43C2×C411yescharacteristic
153#121×C43C2×C411yescharacteristic
154#120×C43—21no—
155C4×D4×C43—21no—
156C4×D4×C43—21no—
157#117×C43C2311yescharacteristic
158C4⋊C8×C43—21no—
159C4⋊C8×C43—21no—
160C22⋊C8×C43—21no—
161C22⋊C8×C43—21no—
162C22⋊C8×C43D411yescharacteristic
163C22⋊C8×C43D411yescharacteristic
164C22⋊C8×C43D411yescharacteristic
165C22⋊C8×C43D411yescharacteristic
166#97×C43—21no—
167C4×C8×C43—21no—
168C24×C43#4111yescharacteristic
169#41×C43—21no—
170#41×C43—21no—
171#41×C43—21no—
172#41×C43—21no—
173C2×Q8×C43C22×C411yescharacteristic
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43C22×C411yescharacteristic
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43C22×C411yescharacteristic
184C22×C4×C43C22×C411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43#4111yescharacteristic
188C22×C4×C43C2411yescharacteristic
189C2×C22⋊D43—21no—
190C2×C22⋊D43—21no—
191C2×C22⋊D43—21no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194#10621898—21no—
195#10621898—21no—
196#10621898—21no—
197#10621898—21no—
198C2×D172C22×C411yescharacteristic
199C2×C4×D43—21no—
200C2×Dic86C22×C411yescharacteristic
201M16×C43—21no—
202M16×C43—21no—
203M16×C43—21no—
204M16×C43—42no—
205M16×C43—42no—
206M16×C43C2×D412yes—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—42no—
214C2×C8×C43—42no—
215C2×C8×C43C2×D411yescharacteristic
216C2×C8×C43C2×D411yescharacteristic
217C2×C8×C43C2×D411yescharacteristic
218C2×C8×C43C2×D411yescharacteristic
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43C22×C411yescharacteristic
222C4⋊C4×C43C22×C411yescharacteristic
223C22⋊C4×C43—21no—
224C22⋊C4×C43—21no—
225C22⋊C4×C43—21no—
226C22⋊C4×C43—21no—
227C22⋊C4×C43—21no—
228C42×C43—21no—
229C22⋊Dic43—24no—
230C22⋊Dic43—21no—
231C22⋊Dic43—21no—
232C22⋊Dic43—21no—
233#10621885—22no—
234#10621884—22no—
235#10621883—22no—
236#10621882—22no—
237(C2×D43)⋊C4—21no—
238(C2×D43)⋊C4—21no—
239C4⋊Dic43C22×C411yescharacteristic
240C4⋊Dic43C22×C411yescharacteristic
241Dic43⋊C4—21no—
242Dic43⋊C4—21no—
243C4×Dic43—21no—
244C4×Dic43—21no—
245C4×Dic43—21no—
246C4×Dic43—21no—
247C4×Dic43—21no—
248#10621877—21no—
249#10621877—21no—
250#10621877—21no—
251#10621877—42no—
252#10621877C2×D412yes—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—22no—
257C2×C43⋊C8—22no—
258C2×C43⋊C8—22no—
259C2×C43⋊C8—22no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—42no—
262C2×C43⋊C8C22×C411yescharacteristic
263C2×C43⋊C8C22×C411yescharacteristic
264C2×C43⋊C8C22×C411yescharacteristic
265C2×C43⋊C8C22×C411yescharacteristic
266C2×C43⋊C8C2×D412yes—
267C2×C43⋊C8#4112yes—
268#10621872—42no—
269C8×D43—42no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—22no—
273C23×C43—21no—
274C23×C43—41no—
275C23×C43C4×D411yescharacteristic
276C23×C43C4×D411yescharacteristic
277C23×C43C2×#4111yescharacteristic
278C22×D43—21no—
279Q8×C43—21no—
280Q8×C43—21no—
281D4×C43—21no—
282D4×C43—21no—
283D4×C43—41no—
284D4×C43—41no—
285D4×C43—42no—
286D4×C43—81no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43C4×D411yescharacteristic
303C2×C4×C43C4×D411yescharacteristic
304C2×C4×C43C23×C411yescharacteristic
305C2×C4×C43C22×D411yescharacteristic
306C2×C4×C43C22×D411yescharacteristic
307C2×C4×C43C2×#4111yescharacteristic
308C2×C4×C43H(5,𝔽2)11yescharacteristic
309C2×C4×C432−1+411yescharacteristic
310C22⋊D43—41no—
311C22⋊D43—41no—
312C22⋊D43—42no—
313C22⋊D43—81no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323D172—21no—
324D172—21no—
325C4×D43—41no—
326C4×D43—41no—
327Dic86—21no—
328Dic86—21no—
329C8×C43—21no—
330C8×C43—21no—
331C8×C43—22no—
332C8×C43—21no—
333C8×C43—21no—
334C8×C43—41no—
335C43⋊C8—21no—
336C43⋊C8—21no—
337C43⋊C8—22no—
338C43⋊C8—41no—
339C43⋊C8C4×D412yes—
340C43⋊C8C4×D412yes—
341#23018—431nomaximal, Sylow
342C22×C43—21no—
343C22×C43—21no—
344C22×C43—21no—
345C22×C43—21no—
346C22×C43—21no—
347C22×C43—21no—
348C22×C43—21no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43#44312yescomplemented
355C22×C43C2×C4×D411yescharacteristic
356C22×C43#54811yescharacteristic
357C22×C43#55311yescharacteristic
358C2×D43—41no—
359C2×D43—41no—
360C2×D43—41no—
361C4×C43—21no—
362C4×C43—21no—
363C4×C43—41no—
364C4×C43—41no—
365C4×C43—41no—
366C4×C43C2×C4×D411yescharacteristic
367C4×C43#52011yescharacteristic
368C4×C43D4211yescharacteristic
369C4×C43#54711yescharacteristic
370Dic43—42no—
371Dic43—42no—
372Dic43—41no—
373Dic43—41no—
374Dic43—41no—
375#3050—431no—
376C2×#443—431no—
377#2933—431no—
378#2933D4311yescharacteristic, complemented
379C22×#108—431no—
380#1974—431no—
381#1945—431no—
382#1929—431no—
383#1929—431no—
384#1871—431no—
385#1871—431no—
386#1866—431no—
387#1866—431no—
388#1772—431no—
389C8×C22⋊C4—431no—
390C2×C43—21no—
391C2×C43—21no—
392C2×C43—22no—
393C2×C43—41no—
394C2×C43—81no—
395C2×C43#236111yescharacteristic
396C2×C43C2×#44311yescharacteristic
397C2×C43#295711yescharacteristic
398D43—81no—
399C2×#135—431no—
400C2×#131—431no—
401C2×#131C2×D4311yescharacteristic
402C22×M16—431no—
403C22×M16C2×D4311yescharacteristic
404C23×C8—431no—
405#525—431no—
406#525C2×D4311yescharacteristic
407#467—431no—
408#467—431no—
409#466—431no—
410#466—431no—
411#465—431no—
412#465—431no—
413#465—431no—
414#465—431no—
415#443—864no—
416#436—21no—
417#436—861no—
418#435—21no—
419#435—21no—
420#435—861no—
421#435—861no—
422C8×D4—21no—
423C8×D4—861no—
424C2×#108—431no—
425C2×#108—431no—
426C2×#108—431no—
427C2×#108—431no—
428C2×#108—864no—
429#427—431no—
430#424—431no—
431#424C2×D4311yescharacteristic
432C2×#104—431no—
433C2×#104—431no—
434C2×#104—431no—
435C2×#104—431no—
436#416—431no—
437#416—431no—
438#408—431no—
439#408C2×D4311yescharacteristic
440C2×C22⋊C8C2×D4311yescharacteristic
441#405—431no—
442#405C2×D4311yescharacteristic
443C2×C4×C8—431no—
444C2×C4×C8—431no—
445C4×C22⋊C4—431no—
446#339—431no—
447#339—431no—
448#339—431no—
449#339—431no—
450#336—431no—
451#336—431no—
452C43#2301811yescharacteristic, complemented, Sylow
453C2×#41—431no—
454C2×#41C22×D4311yescharacteristic
455C23×C4C22×D4311yescharacteristic
456#135—862no—
457#135—862no—
458C2×Q16—431no—
459C2×SD16—431no—
460C2×SD16—431no—
461C2×D8—431no—
462#131—22no—
463#131—41no—
464#131—862no—
465#131—1721no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—22no—
469C2×M16—41no—
470C2×M16—431no—
471C2×M16—431no—
472C2×M16—861no—
473C2×M16—861no—
474C2×M16—862no—
475C2×M16—1721no—
476C2×M16C22×D4311yescharacteristic
477C2×M16C22×D4311yescharacteristic
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—431no—
481C22×C8—431no—
482C22×C8—431no—
483C22×C8—431no—
484C22×C8—431no—
485C22×C8—431no—
486C22×C8—862no—
487C22×C8—862no—
488C22×C8—861no—
489C22×C8—861no—
490C22×C8C22×D4311yescharacteristic
491C22×C8C22×D4311yescharacteristic
492#123—21no—
493#123—861no—
494C22⋊Q8—431no—
495C22⋊Q8—431no—
496C22⋊Q8C4×D4311yescharacteristic
497C22⋊Q8C4×D4311yescharacteristic
498#121—431no—
499#121—431no—
500#121C4×D4311yescharacteristic
501#121C4×D4311yescharacteristic
502#120—21no—
503#120—861no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—861no—
507C4×D4—861no—
508#117—431no—
509#117C22×D4311yescharacteristic
510C2×C22⋊C4—861no—
511C2×C42—431no—
512C2×C42—431no—
513#108—434no—
514#108—862no—
515#108—862no—
516#108—862no—
517#107—431no—
518#107—431no—
519#106—431no—
520#106—431no—
521C4⋊C8—21no—
522C4⋊C8—21no—
523C4⋊C8—861no—
524C4⋊C8—861no—
525#104—862no—
526#104—862no—
527#104—1721no—
528#104—1721no—
529#103—431no—
530#103—431no—
531#103—431no—
532#103—431no—
533#102—431no—
534#102—431no—
535#102—431no—
536#102—431no—
537C22⋊C8—21no—
538C22⋊C8—21no—
539C22⋊C8—861no—
540C22⋊C8—861no—
541C22⋊C8C22⋊D4311yescharacteristic
542C22⋊C8C22⋊D4311yescharacteristic
543C22⋊C8C22⋊D4311yescharacteristic
544C22⋊C8C22⋊D4311yescharacteristic
545#97—21no—
546#97—861no—
547C4×C8—21no—
548C4×C8—862no—
549C4×C8—862no—
550C4×C8—861no—
551#95—861no—
552C24#1062189811yescharacteristic
553#41—21no—
554#41—21no—
555#41—21no—
556#41—21no—
557#41—861no—
558#41—861no—
559#41—861no—
560#41—861no—
561C2×Q8—431no—
562C2×Q8C2×C4×D4311yescharacteristic
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—431no—
567C2×D4—861no—
568C2×D4—861no—
569C2×D4—861no—
570C2×D4C2×C4×D4311yescharacteristic
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4C2×C4×D4311yescharacteristic
580C22×C4C2×C4×D4311yescharacteristic
581C22×C4#1062189811yescharacteristic
582C22×C4C2×C22⋊D4311yescharacteristic
583C22×C4C2×C22⋊D4311yescharacteristic
584C22×C4C23×D4311yescharacteristic
585Q16—862no—
586SD16—862no—
587SD16—862no—
588D8—862no—
589M16—21no—
590M16—21no—
591M16—21no—
592M16—42no—
593M16—42no—
594M16—432no—
595M16—861no—
596M16—861no—
597M16—861no—
598M16—1722no—
599M16—1722no—
600M16D4×D4312yes—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—42no—
608C2×C8—42no—
609C2×C8—431no—
610C2×C8—431no—
611C2×C8—432no—
612C2×C8—432no—
613C2×C8—431no—
614C2×C8—431no—
615C2×C8—862no—
616C2×C8—862no—
617C2×C8—862no—
618C2×C8—862no—
619C2×C8—861no—
620C2×C8—861no—
621C2×C8—861no—
622C2×C8—861no—
623C2×C8—1722no—
624C2×C8—1722no—
625C2×C8C2×C22⋊D4311yescharacteristic
626C2×C8C2×C22⋊D4311yescharacteristic
627C2×C8C2×C22⋊D4311yescharacteristic
628C2×C8C2×C22⋊D4311yescharacteristic
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—431no—
632C4⋊C4—431no—
633C4⋊C4—861no—
634C4⋊C4—861no—
635C4⋊C4C2×C4×D4311yescharacteristic
636C4⋊C4C2×C4×D4311yescharacteristic
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—864no—
643C22⋊C4—861no—
644C22⋊C4—861no—
645C22⋊C4—861no—
646C22⋊C4—861no—
647C22⋊C4—861no—
648C42—21no—
649C42—861no—
650C42—861no—
651C42—861no—
652C42—861no—
653C42—861no—
654C23—21no—
655C23—21no—
656C23—22no—
657C23—21no—
658C23—41no—
659C23—861no—
660C23C4×C22⋊D4311yescharacteristic
661C23C4×C22⋊D4311yescharacteristic
662C23C2×#1062189811yescharacteristic
663Q8—21no—
664Q8—21no—
665Q8—861no—
666Q8—861no—
667D4—21no—
668D4—21no—
669D4—41no—
670D4—41no—
671D4—42no—
672D4—81no—
673D4—861no—
674D4—861no—
675D4—3441no—
676D4—1721no—
677D4—1721no—
678D4—1722no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—861no—
697C2×C4—861no—
698C2×C4—861no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4C4×C22⋊D4311yescharacteristic
706C2×C4C4×C22⋊D4311yescharacteristic
707C2×C4C22×C4×D4311yescharacteristic
708C2×C4C2×D4×D4311yescharacteristic
709C2×C4C22×C22⋊D4311yescharacteristic
710C2×C4#41×D4311yescharacteristic
711C2×C4#1306337011yescharacteristic
712C2×C4#1306337211yescharacteristic
713C8—21no—
714C8—21no—
715C8—22no—
716C8—21no—
717C8—21no—
718C8—41no—
719C8—432no—
720C8—432no—
721C8—861no—
722C8—861no—
723C8—862no—
724C8—1721no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—1721no—
738C22—1721no—
739C22—1721no—
740C22#1458301412yescomplemented
741C22C2×C4×C22⋊D4311yescharacteristic
742C22#1458355811yescharacteristic
743C22#1458359811yescharacteristic
744C4—21no—
745C4—21no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—1722no—
750C4—1722no—
751C4—1721no—
752C4—1721no—
753C4—1721no—
754C4C4×D4×D4311yescharacteristic
755C4#1458337811yescharacteristic
756C4D4×C22⋊D4311yescharacteristic
757C4#1458354811yescharacteristic
758C2—21no—
759C2—21no—
760C2—22no—
761C2—41no—
762C2—81no—
763C2—3441no—
764C2#1913761211yescharacteristic
765C2C2×#1458301411yescharacteristic
766C2#1914351011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2933C2
socleC22×C43C2×C4×D4
prime radical#19144173C2
cosocleC22×C4×C43C24
hypercenter#2933D43
hypocenterC43#23018
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2933

Complements

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

NH ≅ G/Ntype
2. C2×#14583014C2semidirect
3. #19143316C2semidirect
4. C22×#13063260C2semidirect
5. #19135482C2semidirect
6. #19135340C2semidirect
7. #19135243C2semidirect
8. #19135240C2semidirect
9. #19134898C2semidirect
10. #19134897C2semidirect
11. #19134870C2semidirect
12. #19134869C2semidirect
13. #19134475C2semidirect
14. #19134369C2semidirect
15. C43×#2933C2semidirect
21. #14583138C4semidirect
22. #14583138C4semidirect
23. #14583133C4semidirect
24. #14583133C4semidirect
25. #14583130C4semidirect
26. #14583130C4semidirect
27. #14583126C4semidirect
28. #14583126C4semidirect
109. #13063260D4semidirect
354. C22×C43#443semidirect
378. #2933D43semidirect
452. C43#23018semidirect
740. C22#14583014semidirect

Maximal subgroups

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

subgroupindex
#191441732
C2×#145830142
#191433162
C22×#130632602
#191354822
#191353402
#191352432
#191352402
#191348982
#191348972
#191348702
#191348692
#191344752
#191343692
C43×#29332
#2301843