Finite Group Databasebeta

← #14758246

Subgroups — #14758246

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic
2C2×#10622452C211yesmaximal, characteristic
3C2×#10622321C211yesmaximal, characteristic
4#13069556C211yesmaximal, characteristic, complemented
5#13069554C211yesmaximal, characteristic, complemented
6#13069554C211yesmaximal, characteristic, complemented
7#13069553C211yesmaximal, characteristic, complemented
8#13069551C211yesmaximal, characteristic, complemented
9#13069550C211yesmaximal, characteristic, complemented
10#13069550C211yesmaximal, characteristic, complemented
11#13068311C211yesmaximal, characteristic
12#13068311C211yesmaximal, characteristic
13#13068308C211yesmaximal, characteristic
14D11×#336C211yesmaximal, characteristic
15C11×#1985C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66999C411yescharacteristic
18C2×#66997C411yescharacteristic
19C22×#4313C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23#10623109—24no—
24#10623109—24no—
25C2×#66950C411yescharacteristic
26C2×#66949C411yescharacteristic
27C2×#66949C411yescharacteristic
28C2×#66942C411yescharacteristic
29C2×#66942C411yescharacteristic
30C2×#66941C411yescharacteristic
31C2×#66925C2211yescharacteristic
32C2×#66925C2211yescharacteristic
33C2×C42×D11C2211yescharacteristic
34C2×C4×Dic22C2211yescharacteristic
35C2×C4×Dic22C2211yescharacteristic
36C2×C4×Dic22C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#97C2211yescharacteristic
39C2×#66879C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic
42C2×C8×Dic11C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622452—24no—
46#10622321—24no—
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11C2×C411yescharacteristic
64C22×C4×D11C2×C411yescharacteristic
65C22×C4×D11C2×C411yescharacteristic
66C22×C4×D11C2311yescharacteristic
67C22×Dic22C2×C411yescharacteristic
68C22×Dic22C2×C411yescharacteristic
69C22×Dic22C2×C411yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C4×Q8×C11—22no—
75C4×Q8×C11—22no—
76C2×C11×C4⋊C4C2×C411yescharacteristic
77C2×C11×C4⋊C4C2×C411yescharacteristic
78C2×C11×C4⋊C4C2×C411yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82#66999—24no—
83#66997—24no—
84C2×(C2×D11)⋊C4C2×C411yescharacteristic
85C2×(C2×D11)⋊C4C2×C411yescharacteristic
86C2×(C2×D11)⋊C4C2×C411yescharacteristic
87C2×(C2×D11)⋊C4C2×C411yescharacteristic
88C2×C4⋊Dic11C2×C411yescharacteristic
89C2×C4⋊Dic11C2×C411yescharacteristic
90C2×C4⋊Dic11C2×C411yescharacteristic
91C2×Dic11⋊C4C2×C411yescharacteristic
92C2×Dic11⋊C4C2×C411yescharacteristic
93C2×Dic11⋊C4C2×C411yescharacteristic
94C2×Dic11⋊C4C2×C411yescharacteristic
95C2×Dic11⋊C4C2×C411yescharacteristic
96C2×Dic11⋊C4C2×C411yescharacteristic
97C2×Dic11⋊C4C2×C411yescharacteristic
98C2×Dic11⋊C4C2×C411yescharacteristic
99C2×Dic11⋊C4C2×C411yescharacteristic
100C2×Dic11⋊C4C2×C411yescharacteristic
101C2×C4×Dic11C2×C411yescharacteristic
102C2×C4×Dic11C2×C411yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C2×#4313—22no—
111C2×#4313—22no—
112C2×#4313—22no—
113C2×#4313—22no—
114C2×#4313—22no—
115C2×#4313Q814yescomplemented
116C2×C8×D11—22no—
117C2×C8×D11—22no—
118C2×C8×D11—22no—
119C2×C8×D11—22no—
120C2×C8×D11—22no—
121C2×C8×D11Q814yescomplemented
122#66950—24no—
123#66949—24no—
124#66949—24no—
125#66942—24no—
126#66942—24no—
127#66941—24no—
128#66925—22no—
129#66925—22no—
130#66925D414yes—
131#66925D414yes—
132C42×D11—22no—
133C42×D11—22no—
134C4×Dic22—22no—
135C4×Dic22—22no—
136C4×Dic22—22no—
137C4×Dic22—22no—
138C4×Dic22—22no—
139C4×Dic22—22no—
140C11×C4⋊C8—22no—
141C11×#97—22no—
142#66879—22no—
143Dic11⋊C8—22no—
144Dic11⋊C8—22no—
145C8×Dic11—22no—
146C4⋊(C11⋊C8)—22no—
147C4×C11⋊C8—22no—
148#21304—111nomaximal, Sylow
149C23×D11C22×C411yescharacteristic
150C2×Q8×C11—22no—
151C2×Q8×C11—22no—
152C2×Q8×C11—41no—
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C22×C411yescharacteristic
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C22×Dic11C22×C411yescharacteristic
161C22×Dic11C22×C411yescharacteristic
162C22×Dic11C22×C411yescharacteristic
163C22×Dic11C22×C411yescharacteristic
164C22×Dic11C22×C411yescharacteristic
165C22×Dic11C22×C411yescharacteristic
166C22×Dic11C22×C411yescharacteristic
167C2×C4×D11—22no—
168C2×C4×D11—22no—
169C2×C4×D11—22no—
170C2×C4×D11—22no—
171C2×C4×D11—41no—
172C2×C4×D11—41no—
173C2×C4×D11C2×D412yes—
174C2×C4×D11C2×D412yes—
175C2×C4×D11C2×Q812yes—
176C2×C4×D11C2×Q812yes—
177C2×C4×D11#4112yes—
178C2×C4×D11#4112yes—
179C2×Dic22—22no—
180C2×Dic22—22no—
181C2×Dic22—22no—
182C2×Dic22—22no—
183C2×Dic22—22no—
184C2×Dic22—22no—
185C2×Dic22—41no—
186C2×Dic22—41no—
187C2×Dic22—41no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11C2×Q812yes—
199C2×C8×C11C2×Q812yes—
200C11×C4⋊C4—22no—
201C11×C4⋊C4—22no—
202C11×C4⋊C4—22no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11—21no—
207C42×C11C2×D412yes—
208C42×C11C2×D412yes—
209(C2×D11)⋊C4—22no—
210(C2×D11)⋊C4—22no—
211(C2×D11)⋊C4C22⋊C414yes—
212(C2×D11)⋊C4C22⋊C414yes—
213C4⋊Dic11—22no—
214C4⋊Dic11—22no—
215C4⋊Dic11—22no—
216Dic11⋊C4—22no—
217Dic11⋊C4—22no—
218Dic11⋊C4—22no—
219Dic11⋊C4—22no—
220Dic11⋊C4—22no—
221Dic11⋊C4—22no—
222Dic11⋊C4—22no—
223Dic11⋊C4—22no—
224Dic11⋊C4C22⋊C414yes—
225Dic11⋊C4C22⋊C414yes—
226C4×Dic11—22no—
227C4×Dic11—22no—
228C4×Dic11—21no—
229C4×Dic11—21no—
230C4×Dic11—21no—
231C4×Dic11—21no—
232C4×Dic11C2×D412yes—
233C4×Dic11C2×D412yes—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8C2×Q812yes—
245C2×C11⋊C8C2×Q812yes—
246#4313—28no—
247#4313—44no—
248C8×D11—28no—
249C8×D11—44no—
250C2×#533—111no—
251C2×#424—111no—
252C2×#405—111no—
253#1985—111no—
254#1985—111no—
255#1985—111no—
256#1985D1111yescharacteristic, complemented
257#1984—111no—
258#1984—111no—
259#1984—111no—
260#1984—111no—
261#1729—111no—
262#1729—111no—
263#1728—111no—
264C2×#336—111no—
265C23×C11C23×C411yescharacteristic
266C22×D11—21no—
267C22×D11—21no—
268C22×D11—21no—
269C22×D11—21no—
270C22×D11C2×C22⋊C412yes—
271C22×D11C4×Q812yes—
272C22×D11C4×Q812yes—
273Q8×C11—44no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11C2×C22⋊C412yes—
290C2×C4×C11C2×C22⋊C412yes—
291C2×C4×C11#13112yes—
292C2×C4×C11C22×D411yescharacteristic
293C2×C4×C11C22×D411yescharacteristic
294C2×C4×C11C22×Q811yescharacteristic
295C2×C4×C11C22×Q811yescharacteristic
296C2×C4×C11C2×#4111yescharacteristic
297C2×C4×C11C2×#4111yescharacteristic
298C2×Dic11—21no—
299C2×Dic11—21no—
300C2×Dic11—21no—
301C2×Dic11—21no—
302C2×Dic11—21no—
303C2×Dic11—21no—
304C2×Dic11—21no—
305C2×Dic11—21no—
306C2×Dic11—21no—
307C2×Dic11—21no—
308C2×Dic11—21no—
309C2×Dic11—21no—
310C2×Dic11—21no—
311C2×Dic11—21no—
312C2×Dic11—21no—
313C2×Dic11C2×C22⋊C412yes—
314C2×Dic11C2×C22⋊C412yes—
315C2×Dic11C2×C22⋊C412yes—
316C2×Dic11C4×Q812yes—
317C2×Dic11C4×Q812yes—
318C2×Dic11#13112yes—
319C4×D11—44no—
320C4×D11—44no—
321C4×D11C22⋊Q814yes—
322C4×D11C22⋊Q814yes—
323C4×D11#12414yes—
324C4×D11C4⋊Q814yes—
325Dic22—44no—
326Dic22—44no—
327Dic22—44no—
328C8×C11—22no—
329C8×C11—22no—
330C8×C11—41no—
331C8×C11—41no—
332C11⋊C8—22no—
333C11⋊C8—22no—
334C11⋊C8—41no—
335C11⋊C8—41no—
336C22×M16—111no—
337C22×M16—111no—
338C23×C8—111no—
339C23×C8—111no—
340#533—224no—
341#533—224no—
342C2×C4⋊Q8—111no—
343C2×C4⋊Q8—111no—
344C2×#125—111no—
345C2×#125—111no—
346C2×C22⋊Q8—111no—
347C2×C22⋊Q8—111no—
348C2×C22⋊Q8—111no—
349C2×C22⋊Q8—111no—
350C2×C4×Q8—111no—
351C2×C4×Q8—111no—
352C2×C4×Q8—111no—
353C2×C4×Q8C2×D1111yescharacteristic
354C2×#117—111no—
355C2×#117—111no—
356C22×C42—111no—
357#424—224no—
358C2×C4⋊C8—111no—
359C2×C4⋊C8—111no—
360C2×C4⋊C8—111no—
361C2×C4⋊C8C2×D1111yescharacteristic
362#405—224no—
363C2×#97—111no—
364C2×#97C2×D1111yescharacteristic
365C2×C4×C8—111no—
366C2×C4×C8—111no—
367#336—111no—
368#336—111no—
369#336—111no—
370#336—111no—
371#336—111no—
372#336—111no—
373#336—111no—
374#336—111no—
375#336—111no—
376#336—111no—
377#336—111no—
378#336—111no—
379#336C2×D1111yescharacteristic
380#336C2×D1111yescharacteristic
381#336C2×D1111yescharacteristic
382#336C2×D1111yescharacteristic
383C22×C11C22×C22⋊C411yescharacteristic
384C22×C11C2×C4×Q811yescharacteristic
385C22×C11C2×C4×Q811yescharacteristic
386C22×C11C2×#13111yescharacteristic
387C22×C11C2×#13111yescharacteristic
388C22×C11#56811yescharacteristic
389C22×C11#56811yescharacteristic
390C2×D11—22no—
391C2×D11—22no—
392C2×D11—22no—
393C2×D11—22no—
394C2×D11—22no—
395C2×D11—22no—
396C2×D11#39114yes—
397C4×C11—22no—
398C4×C11—22no—
399C4×C11—22no—
400C4×C11—41no—
401C4×C11—41no—
402C4×C11—41no—
403C4×C11C2×C22⋊Q811yescharacteristic
404C4×C11C2×C22⋊Q811yescharacteristic
405C4×C11C2×#12411yescharacteristic
406C4×C11C2×C4⋊Q811yescharacteristic
407Dic11—22no—
408Dic11—22no—
409Dic11—22no—
410Dic11—41no—
411Dic11—41no—
412Dic11—41no—
413Dic11#39114yes—
414C22×Q8—111no—
415C22×Q8—111no—
416C22×Q8—111no—
417C22×Q8C4×D1111yescharacteristic
418C23×C4—111no—
419C23×C4—111no—
420C23×C4—111no—
421C2×M16—114no—
422C2×M16—222no—
423C2×M16—222no—
424C2×M16—222no—
425C2×M16—222no—
426C2×M16—222no—
427C22×C8—111no—
428C22×C8—111no—
429C22×C8—114no—
430C22×C8—111no—
431C22×C8—111no—
432C22×C8—222no—
433C22×C8—222no—
434C22×C8—222no—
435C22×C8—222no—
436C22×C8—222no—
437C22×C8C22×D1111yescharacteristic
438C22×C8C22×D1111yescharacteristic
439C22×C8C22×D1111yescharacteristic
440C22×C8C22×D1111yescharacteristic
441C4⋊Q8—224no—
442C4⋊Q8—224no—
443#125—224no—
444#125—224no—
445C22⋊Q8—224no—
446C22⋊Q8—224no—
447C22⋊Q8—224no—
448C22⋊Q8—224no—
449C4×Q8—22no—
450C4×Q8—22no—
451C4×Q8—222no—
452C4×Q8—222no—
453C4×Q8—222no—
454C4×Q8—222no—
455C4×Q8—222no—
456C4×Q8—222no—
457#117—114no—
458#117—114no—
459#117—222no—
460#117—222no—
461C2×C4⋊C4—111no—
462C2×C4⋊C4—111no—
463C2×C4⋊C4—111no—
464C2×C4⋊C4—111no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—111no—
472C2×C4⋊C4—111no—
473C2×C4⋊C4—111no—
474C2×C4⋊C4C4×D1111yescharacteristic
475C2×C4⋊C4C4×D1111yescharacteristic
476C2×C4⋊C4C4×D1111yescharacteristic
477C2×C22⋊C4—111no—
478C2×C22⋊C4—111no—
479C2×C22⋊C4—111no—
480C2×C22⋊C4—111no—
481C2×C42—111no—
482C2×C42—111no—
483C2×C42—111no—
484C2×C42—111no—
485C2×C42—111no—
486C2×C42—222no—
487C2×C42—222no—
488C2×C42C22×D1111yescharacteristic
489C2×C42C22×D1111yescharacteristic
490C2×C42C22×D1111yescharacteristic
491C4⋊C8—22no—
492C4⋊C8—222no—
493C4⋊C8—222no—
494C4⋊C8—222no—
495#97—22no—
496#97—222no—
497C4×C8—222no—
498C4×C8—222no—
499C2×C11C2×#39111yescharacteristic
500C2×C11#288011yescharacteristic
501C2×C11#288011yescharacteristic
502C2×C11#296011yescharacteristic
503C2×C11#296111yescharacteristic
504C2×C11#296211yescharacteristic
505C2×C11#296211yescharacteristic
506D11—24no—
507C24—111no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—41no—
511C2×Q8—222no—
512C2×Q8—222no—
513C2×Q8—222no—
514C2×Q8—222no—
515C2×Q8—222no—
516C2×Q8—222no—
517C2×Q8—441no—
518C2×Q8—441no—
519C2×Q8—441no—
520C22×C4—111no—
521C22×C4—112no—
522C22×C4—112no—
523C22×C4—112no—
524C22×C4—112no—
525C22×C4—112no—
526C22×C4—112no—
527C22×C4—111no—
528C22×C4—111no—
529C22×C4—111no—
530C22×C4—111no—
531C22×C4—111no—
532C22×C4—111no—
533C22×C4—222no—
534C22×C4—222no—
535C22×C4—222no—
536C22×C4—222no—
537C22×C4—441no—
538C22×C4—441no—
539C22×C4C2×C4×D1111yescharacteristic
540C22×C4C2×C4×D1111yescharacteristic
541C22×C4C2×C4×D1111yescharacteristic
542C22×C4C2×C4×D1111yescharacteristic
543C22×C4C2×C4×D1111yescharacteristic
544C22×C4C2×C4×D1111yescharacteristic
545C22×C4C23×D1111yescharacteristic
546M16—228no—
547M16—444no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—112no—
559C2×C8—112no—
560C2×C8—228no—
561C2×C8—221no—
562C2×C8—221no—
563C2×C8—221no—
564C2×C8—221no—
565C2×C8—221no—
566C2×C8—221no—
567C2×C8—221no—
568C2×C8—221no—
569C2×C8—221no—
570C2×C8—221no—
571C2×C8—444no—
572C2×C8Q8×D1112yes—
573C2×C8Q8×D1112yes—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—114no—
578C4⋊C4—114no—
579C4⋊C4—222no—
580C4⋊C4—222no—
581C4⋊C4—222no—
582C4⋊C4—222no—
583C4⋊C4—222no—
584C4⋊C4—222no—
585C4⋊C4—222no—
586C4⋊C4—222no—
587C4⋊C4—222no—
588C4⋊C4—222no—
589C4⋊C4—222no—
590C22⋊C4—114no—
591C22⋊C4—114no—
592C22⋊C4—222no—
593C22⋊C4—222no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—112no—
599C42—112no—
600C42—222no—
601C42—222no—
602C42—221no—
603C42—221no—
604C42—221no—
605C42—221no—
606C42D4×D1112yes—
607C42D4×D1112yes—
608C11#2130411yescharacteristic, complemented, Sylow
609C23—112no—
610C23—112no—
611C23—112no—
612C23—221no—
613C23—221no—
614C23—221no—
615C23—221no—
616C23C22×C4×D1111yescharacteristic
617Q8—44no—
618Q8—444no—
619Q8—444no—
620Q8—444no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—112no—
637C2×C4—112no—
638C2×C4—112no—
639C2×C4—114no—
640C2×C4—114no—
641C2×C4—114no—
642C2×C4—114no—
643C2×C4—112no—
644C2×C4—112no—
645C2×C4—112no—
646C2×C4—221no—
647C2×C4—221no—
648C2×C4—221no—
649C2×C4—221no—
650C2×C4—221no—
651C2×C4—221no—
652C2×C4—221no—
653C2×C4—221no—
654C2×C4—221no—
655C2×C4—221no—
656C2×C4—221no—
657C2×C4—221no—
658C2×C4—221no—
659C2×C4—221no—
660C2×C4—221no—
661C2×C4—444no—
662C2×C4—444no—
663C2×C4C22⋊C4×D1112yes—
664C2×C4C22⋊C4×D1112yes—
665C2×C4#6696012yes—
666C2×C4C2×D4×D1111yescharacteristic
667C2×C4C2×D4×D1111yescharacteristic
668C2×C4C2×Q8×D1111yescharacteristic
669C2×C4C2×Q8×D1111yescharacteristic
670C2×C4#41×D1111yescharacteristic
671C2×C4#41×D1111yescharacteristic
672C8—22no—
673C8—22no—
674C8—41no—
675C8—41no—
676C8—222no—
677C8—222no—
678C8—441no—
679C8—441no—
680C22—114no—
681C22—222no—
682C22—222no—
683C22—222no—
684C22—222no—
685C22—222no—
686C22—222no—
687C22C2×C22⋊C4×D1111yescharacteristic
688C22C4×Q8×D1111yescharacteristic
689C22C4×Q8×D1111yescharacteristic
690C22C2×#6696011yescharacteristic
691C22#1062327611yescharacteristic
692C22D11×#13111yescharacteristic
693C22#1062328111yescharacteristic
694C4—22no—
695C4—22no—
696C4—22no—
697C4—41no—
698C4—41no—
699C4—41no—
700C4—114no—
701C4—222no—
702C4—222no—
703C4—222no—
704C4—441no—
705C4—441no—
706C4—441no—
707C4D11×C22⋊Q811yescharacteristic
708C4D11×C22⋊Q811yescharacteristic
709C4D11×#12411yescharacteristic
710C4D11×C4⋊Q811yescharacteristic
711C2—224no—
712C2D11×#39111yescharacteristic
713C2#1307706411yescharacteristic
714C2#1307706611yescharacteristic
715C2#1307754711yescharacteristic
716C2#1307755211yescharacteristic
717C2#1307756111yescharacteristic
718C2#1307756411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1985C2
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1985D11
hypocenterC11#21304
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1985

Complements

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

NH ≅ G/Ntype
4. #13069556C2semidirect
5. #13069554C2semidirect
6. #13069554C2semidirect
7. #13069553C2semidirect
8. #13069551C2semidirect
9. #13069550C2semidirect
10. #13069550C2semidirect
15. C11×#1985C2semidirect
115. C2×#4313Q8semidirect
121. C2×C8×D11Q8semidirect
256. #1985D11semidirect
608. C11#21304semidirect

Maximal subgroups

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

subgroupindex
C2×#106231092
C2×#106224522
C2×#106223212
#130695562
#130695542
#130695532
#130695512
#130695502
#130683112
#130683082
D11×#3362
C11×#19852
#2130411