Finite Group Databasebeta

← #14813264

Subgroups — #14813264

Order 2816.

1008 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622580C211yesmaximal, characteristic, complemented
2C22×#66871C211yesmaximal, characteristic, complemented
3#13072056C211yesmaximal, characteristic
4#13070145C211yesmaximal, characteristic, complemented
5#13070088C211yesmaximal, characteristic, complemented
6#13070042C211yesmaximal, characteristic, complemented
7#13069798C211yesmaximal, characteristic, complemented
8#13069236C211yesmaximal, characteristic, complemented
9#13069187C211yesmaximal, characteristic, complemented
10#13069042C211yesmaximal, characteristic, complemented
11#13068933C211yesmaximal, characteristic, complemented
12#13068909C211yesmaximal, characteristic, complemented
13#13068804C211yesmaximal, characteristic, complemented
14#13068803C211yesmaximal, characteristic, complemented
15D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11—21no—
17C2×C4×D4×C11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×#66992—21no—
21C2×#66983C2211yescharacteristic
22C2×#66983C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C23×C11⋊C8C2211yescharacteristic
25C11×#389—21no—
26C11×#385—21no—
27C11×#385—21no—
28C11×#384C2211yescharacteristic
29C11×#380C2211yescharacteristic
30C11×#380C2211yescharacteristic
31C4×C11×C4⋊C4C2211yescharacteristic
32#10622825C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36#10622607—21no—
37#10622580—24no—
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66871—24no—
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622574—21no—
50#10622571—21no—
51#10622552C2211yescharacteristic
52#10622541C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D4×C11D411yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—21no—
67C22×C22⋊D11—21no—
68C23×Dic11—21no—
69C22×D44C2311yescharacteristic
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—44no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—41no—
80C2×C11×C4⋊C4—41no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4D411yescharacteristic
89C2×C11×C22⋊C4D411yescharacteristic
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92C2×C22⋊Dic11—21no—
93#66992—44no—
94#66983—22no—
95#66983—22no—
96#66983—22no—
97#66983—41no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—41no—
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×Dic11⋊C4—21no—
109C22×C11⋊C8—22no—
110C22×C11⋊C8—22no—
111C22×C11⋊C8—22no—
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C11×#95—21no—
117C11×#95—21no—
118C11×#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C22⋊(C11⋊C8)—22no—
122C22⋊(C11⋊C8)—22no—
123C22⋊(C11⋊C8)—22no—
124#66873—22no—
125#66873—22no—
126#66873—22no—
127#66873—41no—
128#66871—22no—
129#66871—22no—
130#66871—22no—
131#66871—22no—
132#66871—41no—
133#66871D414yescomplemented
134#26126—111nomaximal, Sylow
135C24×C11C2×D411yescharacteristic
136C24×C11C2×D411yescharacteristic
137C23×D11—21no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11D814yes—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11—81no—
160C22×C4×C11—81no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11#4112yes—
166C22×C4×C11#4112yes—
167C22×C4×C11C2411yescharacteristic
168C2×C22⋊D11—42no—
169C2×C22⋊D11—42no—
170C2×C22⋊D11—42no—
171C2×C22⋊D11—42no—
172C2×C22⋊D11—42no—
173C2×C22⋊D11—81no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—42no—
178C22×Dic11—42no—
179C22×Dic11—81no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44—21no—
185C2×D44—21no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—42no—
195C11×C4⋊C4—42no—
196C11×C4⋊C4—42no—
197C11×C4⋊C4—81no—
198C11×C4⋊C4C2×D412yes—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—42no—
202C11×C22⋊C4—42no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—42no—
206C22⋊Dic11—42no—
207(C2×D11)⋊C4—42no—
208(C2×D11)⋊C4—42no—
209(C2×D11)⋊C4—42no—
210(C2×D11)⋊C4—81no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—42no—
217C4⋊Dic11C2×D412yes—
218Dic11⋊C4—42no—
219C2×C11⋊C8—28no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8C2×D412yes—
231C2×C11⋊C8#4112yes—
232C2×#480—111no—
233C22×#107—111no—
234#2416—111no—
235D4×C4⋊C4D1111yescharacteristic, complemented
236#2093—111no—
237#2083—111no—
238#2075—111no—
239#2033—111no—
240#1925—111no—
241#1918—111no—
242#1893—111no—
243#1874—111no—
244#1869—111no—
245#1852—111no—
246#1852—111no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11#12312yes—
258C23×C11C2×D812yes—
259C23×C11C2×D812yes—
260C23×C11#13712yes—
261C23×C11C22×D411yescharacteristic
262C22×D11—41no—
263C22×D11—41no—
264C22×D11—41no—
265C22×D11—41no—
266C22×D11—41no—
267C22×D11—41no—
268C22×D11—41no—
269D4×C11—28no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—22no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—84no—
301C2×C4×C11—84no—
302C2×C4×C11#12312yes—
303C2×C4×C11C2×D812yes—
304C2×C4×C11C22×D411yescharacteristic
305C2×C4×C11C2×#4111yescharacteristic
306C2×C4×C11C2×#4111yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11H(5,𝔽2)11yescharacteristic
309C2×C4×C112−1+411yescharacteristic
310C22⋊D11—84no—
311C22⋊D11—84no—
312C2×Dic11—22no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—84no—
322D44—41no—
323D44—41no—
324D44—41no—
325D44—41no—
326C11⋊C8—22no—
327C11⋊C8—22no—
328C11⋊C8—41no—
329C11⋊C8—41no—
330C23×C8—111no—
331C2×#121—111no—
332C2×#121—111no—
333C2×#121—221no—
334C2×C4×D4—21no—
335C2×C4×D4C2×D1111yescharacteristic
336C22×C4⋊C4—111no—
337C22×C4⋊C4C2×D1111yescharacteristic
338C22×C4⋊C4C2×D1111yescharacteristic
339#480—224no—
340C2×#107—111no—
341C2×#107—111no—
342C2×#107—111no—
343C2×#107—111no—
344C2×#107—111no—
345C2×#107—111no—
346C2×#107—224no—
347C2×#102—111no—
348C2×#102—111no—
349C2×#102—111no—
350C2×#102—111no—
351C2×C22⋊C8—111no—
352C2×C22⋊C8—111no—
353C2×C22⋊C8—111no—
354#396—221no—
355#394—221no—
356#390—111no—
357#389—21no—
358#389—111no—
359#386—221no—
360#385—21no—
361#385—21no—
362#384C2×D1111yescharacteristic
363#380—111no—
364#380C2×D1111yescharacteristic
365#380C2×D1111yescharacteristic
366C4×C4⋊C4C2×D1111yescharacteristic
367#340—111no—
368#340—111no—
369#340—111no—
370#340—111no—
371#340—111no—
372#340—111no—
373#336—111no—
374#336—111no—
375C22×C11—22no—
376C22×C11—22no—
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—22no—
380C22×C11—22no—
381C22×C11—22no—
382C22×C11—22no—
383C22×C11—22no—
384C22×C11—41no—
385C22×C11—41no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11#48014yescomplemented
389C22×C11C2×#12311yescharacteristic
390C22×C11D4211yescharacteristic
391C22×C11#54711yescharacteristic
392C22×C11C22×D811yescharacteristic
393C22×C11C2×#13711yescharacteristic
394C22×C11#57611yescharacteristic
395C22×C11#57811yescharacteristic
396C2×D11—81no—
397C2×D11—81no—
398C2×D11—81no—
399C2×D11—81no—
400C2×D11—81no—
401C2×D11—81no—
402C2×D11—81no—
403C4×C11—22no—
404C4×C11—22no—
405C4×C11—41no—
406C4×C11—41no—
407C4×C11—42no—
408C4×C11—81no—
409C4×C11—81no—
410C4×C11—81no—
411C4×C11#52511yescharacteristic
412C4×C11#53911yescharacteristic
413C4×C11#54811yescharacteristic
414C4×C11#55311yescharacteristic
415Dic11—42no—
416Dic11—81no—
417Dic11—81no—
418C22×D4—111no—
419C22×D4—221no—
420C22×D4—221no—
421C22×D4C22⋊D1111yescharacteristic
422C23×C4—21no—
423C23×C4—21no—
424C23×C4—221no—
425C23×C4C22×D1111yescharacteristic
426C23×C4C22×D1111yescharacteristic
427C22×C8—111no—
428C22×C8—111no—
429C22×C8—111no—
430C22×C8—111no—
431C22×C8—222no—
432C22×C8—222no—
433C22×C8—222no—
434#121—222no—
435#121—222no—
436#121—222no—
437#121—441no—
438#121—444no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—44no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—41no—
449C2×C4⋊C4—41no—
450C2×C4⋊C4—111no—
451C2×C4⋊C4—111no—
452C2×C4⋊C4—111no—
453C2×C4⋊C4—222no—
454C2×C4⋊C4—221no—
455C2×C4⋊C4—221no—
456C2×C4⋊C4—441no—
457C2×C4⋊C4C22⋊D1111yescharacteristic
458C2×C4⋊C4C22×D1111yescharacteristic
459C2×C4⋊C4C22×D1111yescharacteristic
460C2×C4⋊C4C22×D1111yescharacteristic
461C2×C4⋊C4C22×D1111yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—221no—
465C2×C22⋊C4—221no—
466C2×C22⋊C4—221no—
467C2×C22⋊C4—221no—
468C2×C22⋊C4—221no—
469C2×C22⋊C4C22⋊D1111yescharacteristic
470C2×C22⋊C4C22⋊D1111yescharacteristic
471C2×C42—21no—
472C2×C42C22×D1111yescharacteristic
473#107—114no—
474#107—222no—
475#107—222no—
476#107—222no—
477#107—222no—
478#107—441no—
479#102—222no—
480#102—222no—
481#102—222no—
482#102—441no—
483C22⋊C8—222no—
484C22⋊C8—222no—
485C22⋊C8—222no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—221no—
490#95—221no—
491C2×C11—24no—
492C2×C11—42no—
493C2×C11#244311yescharacteristic
494C2×C11C2×#48011yescharacteristic
495C2×C11#309811yescharacteristic
496C2×C11#327011yescharacteristic
497C2×C11D4×D811yescharacteristic
498C2×C11#333411yescharacteristic
499C2×C11#334611yescharacteristic
500D11—161no—
501C24—221no—
502C24C2×C22⋊D1111yescharacteristic
503C24C2×C22⋊D1111yescharacteristic
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—221no—
507C2×D4—221no—
508C2×D4—221no—
509C2×D4—221no—
510C2×D4—221no—
511C2×D4—221no—
512C2×D4—442no—
513C2×D4—442no—
514C2×D4—442no—
515C2×D4—442no—
516C2×D4—442no—
517C2×D4—881no—
518C2×D4#432314yes—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—81no—
538C22×C4—81no—
539C22×C4—221no—
540C22×C4—221no—
541C22×C4—221no—
542C22×C4—442no—
543C22×C4—442no—
544C22×C4—881no—
545C22×C4#433912yes—
546C22×C4#433912yes—
547C22×C4C2×C22⋊D1111yescharacteristic
548C22×C4C2×C22⋊D1111yescharacteristic
549C22×C4C2×C22⋊D1111yescharacteristic
550C22×C4C2×C22⋊D1111yescharacteristic
551C22×C4C23×D1111yescharacteristic
552C2×C8—112no—
553C2×C8—112no—
554C2×C8—228no—
555C2×C8—221no—
556C2×C8—221no—
557C2×C8—221no—
558C2×C8—221no—
559C2×C8—221no—
560C2×C8—221no—
561C2×C8—221no—
562C2×C8—221no—
563C2×C8—221no—
564C2×C8—221no—
565C4⋊C4—22no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—81no—
577C4⋊C4—112no—
578C4⋊C4—221no—
579C4⋊C4—221no—
580C4⋊C4—221no—
581C4⋊C4—221no—
582C4⋊C4—221no—
583C4⋊C4—442no—
584C4⋊C4—442no—
585C4⋊C4D4×D1112yes—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—442no—
591C22⋊C4—442no—
592C22⋊C4—442no—
593C22⋊C4—442no—
594C22⋊C4—881no—
595C42—21no—
596C42—21no—
597C42—42no—
598C11#2612611yescharacteristic, complemented, Sylow
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—441no—
610C23—441no—
611C23—441no—
612C23—441no—
613C23—441no—
614C23—441no—
615C23—441no—
616C23#6698212yes—
617C23C2×#432312yes—
618C23C2×#432312yes—
619C23#6699512yes—
620C23C22×C22⋊D1111yescharacteristic
621D4—28no—
622D4—441no—
623D4—441no—
624D4—441no—
625D4—441no—
626D4—884no—
627D4—884no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—84no—
659C2×C4—84no—
660C2×C4—222no—
661C2×C4—441no—
662C2×C4—441no—
663C2×C4—441no—
664C2×C4—441no—
665C2×C4—441no—
666C2×C4—441no—
667C2×C4—441no—
668C2×C4—441no—
669C2×C4—884no—
670C2×C4#6698212yes—
671C2×C4C2×#432312yes—
672C2×C4C2×#433911yescharacteristic
673C2×C4C2×#433911yescharacteristic
674C2×C4C2×D4×D1111yescharacteristic
675C2×C4#6703711yescharacteristic
676C2×C4#41×D1111yescharacteristic
677C2×C4#6704311yescharacteristic
678C8—222no—
679C8—222no—
680C8—441no—
681C8—441no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—881no—
696C22—881no—
697C22—881no—
698C22—881no—
699C22—881no—
700C22—881no—
701C22—881no—
702C22#1062258014yescomplemented
703C22C2×#6698211yescharacteristic
704C22C22×#432311yescharacteristic
705C22D4×C22⋊D1111yescharacteristic
706C22C2×#6699511yescharacteristic
707C22#1062335511yescharacteristic
708C22#1062336611yescharacteristic
709C22#1062336911yescharacteristic
710C4—22no—
711C4—22no—
712C4—41no—
713C4—41no—
714C4—42no—
715C4—81no—
716C4—81no—
717C4—81no—
718C4—442no—
719C4—881no—
720C4—881no—
721C4#1062307111yescharacteristic
722C4#1062307811yescharacteristic
723C4#1062308311yescharacteristic
724C4#1062309511yescharacteristic
725C2—24no—
726C2—42no—
727C2—1761no—
728C2#1307234511yescharacteristic
729C2C2×#1062258011yescharacteristic
730C2#1307859411yescharacteristic
731C2#1308018711yescharacteristic
732C2D4×#432311yescharacteristic
733C2#1308095911yescharacteristic
734C2#1308109511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingD4×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radical#13072056C2
hypercenterD4×C4⋊C4D11
hypocenterC11#26126
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622580C2semidirect
2. C22×#66871C2semidirect
4. #13070145C2semidirect
5. #13070088C2semidirect
6. #13070042C2semidirect
7. #13069798C2semidirect
8. #13069236C2semidirect
9. #13069187C2semidirect
10. #13069042C2semidirect
11. #13068933C2semidirect
12. #13068909C2semidirect
13. #13068804C2semidirect
14. #13068803C2semidirect
15. D4×C11×C4⋊C4C2semidirect
133. #66871D4semidirect
235. D4×C4⋊C4D11semidirect
388. C22×C11#480semidirect
598. C11#26126semidirect
702. C22#10622580semidirect

Maximal subgroups

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

subgroupindex
C2×#106225802
C22×#668712
#130720562
#130701452
#130700882
#130700422
#130697982
#130692362
#130691872
#130690422
#130689332
#130689092
#130688042
#130688032
D4×C11×C4⋊C42
#2612611