Finite Group Databasebeta

← #14770292

Subgroups — #14770292

Order 2816.

1064 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic
2C2×#10622314C211yesmaximal, characteristic, complemented
3C2×#10622443C211yesmaximal, characteristic, complemented
4#13069554C211yesmaximal, characteristic, complemented
5#13069553C211yesmaximal, characteristic, complemented
6#13069550C211yesmaximal, characteristic, complemented
7#13069550C211yesmaximal, characteristic, complemented
8#13069550C211yesmaximal, characteristic, complemented
9#13068599C211yesmaximal, characteristic
10#13068597C211yesmaximal, characteristic
11#13068595C211yesmaximal, characteristic
12#13068385C211yesmaximal, characteristic
13#13068381C211yesmaximal, characteristic
14#13068373C211yesmaximal, characteristic
15C11×#1985C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66999C411yescharacteristic
18C2×#66997C411yescharacteristic
19#10623109—24no—
20#10623109—24no—
21C2×#66950C411yescharacteristic
22C2×#66949C411yescharacteristic
23C2×#66949C411yescharacteristic
24C2×#66942C411yescharacteristic
25C2×#66942C411yescharacteristic
26C2×#66941C411yescharacteristic
27C2×#66925C2211yescharacteristic
28C2×#66925C2211yescharacteristic
29C2×C42×D11C2211yescharacteristic
30C2×C4×Dic22C2211yescharacteristic
31C2×C4×Dic22C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C2×C11×C4⋊C8C2211yescharacteristic
34C2×C11×#97C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×(C2×D11)⋊C8C2211yescharacteristic
39C2×#66879C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic
42C2×Dic11⋊C8C2211yescharacteristic
43C2×Dic11⋊C8C2211yescharacteristic
44C2×C8×Dic11C2211yescharacteristic
45C2×C8×Dic11C2211yescharacteristic
46C2×C8×Dic11C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622443—24no—
50#10622314—24no—
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
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
110#66950—24no—
111#66949—24no—
112#66949—24no—
113#66942—24no—
114#66942—24no—
115#66941—24no—
116#66925—22no—
117#66925—22no—
118#66925—22no—
119#66925—22no—
120C42×D11—22no—
121C42×D11—22no—
122C4×Dic22—22no—
123C4×Dic22—22no—
124C4×Dic22—22no—
125C4×Dic22—22no—
126C4×Dic22D414yes—
127C4×Dic22D414yes—
128C11×C4⋊C8—22no—
129C11×#97—22no—
130(C2×D11)⋊C8—22no—
131(C2×D11)⋊C8—22no—
132(C2×D11)⋊C8—22no—
133(C2×D11)⋊C8Q814yescomplemented
134#66879—22no—
135Dic11⋊C8—22no—
136Dic11⋊C8—22no—
137Dic11⋊C8—22no—
138Dic11⋊C8—22no—
139C8×Dic11—22no—
140C8×Dic11—22no—
141C8×Dic11—22no—
142C4⋊(C11⋊C8)—22no—
143C4×C11⋊C8—22no—
144#22509—111nomaximal, Sylow
145C23×D11C22×C411yescharacteristic
146C2×Q8×C11—22no—
147C2×Q8×C11—22no—
148C2×Q8×C11—41no—
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C22×Dic11C22×C411yescharacteristic
157C22×Dic11C22×C411yescharacteristic
158C22×Dic11C22×C411yescharacteristic
159C22×Dic11C22×C411yescharacteristic
160C22×Dic11C22×C411yescharacteristic
161C22×Dic11C22×C411yescharacteristic
162C22×Dic11C22×C411yescharacteristic
163C2×C4×D11—22no—
164C2×C4×D11—22no—
165C2×C4×D11—22no—
166C2×C4×D11—22no—
167C2×C4×D11—22no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—41no—
173C2×C4×D11C2×Q812yes—
174C2×C4×D11#4112yes—
175C2×Dic22—22no—
176C2×Dic22—22no—
177C2×Dic22—22no—
178C2×Dic22—22no—
179C2×Dic22—22no—
180C2×Dic22—22no—
181C2×Dic22—22no—
182C2×Dic22—41no—
183C2×Dic22C22⋊C414yes—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
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×C11C2×Q812yes—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—22no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11C2×D412yes—
204C42×C11C2×D412yes—
205(C2×D11)⋊C4—22no—
206(C2×D11)⋊C4—22no—
207(C2×D11)⋊C4—22no—
208(C2×D11)⋊C4—22no—
209C4⋊Dic11—22no—
210C4⋊Dic11—22no—
211C4⋊Dic11C22⋊C414yes—
212Dic11⋊C4—22no—
213Dic11⋊C4—22no—
214Dic11⋊C4—22no—
215Dic11⋊C4—22no—
216Dic11⋊C4—22no—
217Dic11⋊C4—22no—
218Dic11⋊C4—22no—
219Dic11⋊C4—22no—
220Dic11⋊C4C22⋊C414yes—
221Dic11⋊C4C22⋊C414yes—
222C4×Dic11—22no—
223C4×Dic11—22no—
224C4×Dic11—21no—
225C4×Dic11—21no—
226C4×Dic11C2×D412yes—
227C4×Dic11C2×D412yes—
228C4×Dic11C2×D412yes—
229C4×Dic11C2×D412yes—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
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⋊C8C2×Q812yes—
242C2×#533—111no—
243C2×#446—111no—
244C2×C8×Q8—111no—
245#1985—111no—
246#1985D1111yescharacteristic, complemented
247#1984—111no—
248#1984—111no—
249#1984—111no—
250#1984—111no—
251#1798—111no—
252#1798—111no—
253#1797—111no—
254#1750—111no—
255#1750—111no—
256C4×C22⋊C8—111no—
257C23×C11C23×C411yescharacteristic
258C22×D11—21no—
259C22×D11—21no—
260C22×D11—21no—
261C22×D11—21no—
262C22×D11—21no—
263C22×D11—21no—
264C22×D11C4×Q812yes—
265Q8×C11—44no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
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×C11C2×C22⋊C412yes—
282C2×C4×C11C2×C22⋊C412yes—
283C2×C4×C11#13112yes—
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C22×Q811yescharacteristic
287C2×C4×C11C2×#4111yescharacteristic
288C2×C4×C112−1+411yescharacteristic
289C2×C4×C112−1+411yescharacteristic
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—21no—
299C2×Dic11—21no—
300C2×Dic11—21no—
301C2×Dic11—21no—
302C2×Dic11—21no—
303C2×Dic11—21no—
304C2×Dic11C2×C22⋊C412yes—
305C2×Dic11C2×C22⋊C412yes—
306C2×Dic11C2×C22⋊C412yes—
307C2×Dic11C2×C22⋊C412yes—
308C2×Dic11C4×Q812yes—
309C2×Dic11#13112yes—
310C2×Dic11#13112yes—
311C4×D11—22no—
312C4×D11—22no—
313C4×D11—22no—
314C4×D11—22no—
315C4×D11—44no—
316C4×D11—44no—
317Dic22—28no—
318Dic22—44no—
319Dic22—44no—
320C8×C11—22no—
321C8×C11—41no—
322C8×C11—41no—
323C8×C11—41no—
324C11⋊C8—22no—
325C11⋊C8—41no—
326C11⋊C8—41no—
327C11⋊C8—41no—
328#533—224no—
329#533—224no—
330C2×C4⋊Q8—111no—
331C2×C4⋊Q8—111no—
332C2×#125—111no—
333C2×#125—111no—
334C2×C22⋊Q8—111no—
335C2×C22⋊Q8—111no—
336C2×C22⋊Q8—111no—
337C2×C22⋊Q8—111no—
338C2×C4×Q8—111no—
339C2×C4×Q8—111no—
340C2×C4×Q8—111no—
341C2×C4×Q8C2×D1111yescharacteristic
342C2×#117—111no—
343C2×#117—111no—
344C22×C42—111no—
345#446—224no—
346C8×Q8—224no—
347C2×C4⋊C8—111no—
348C2×C4⋊C8—111no—
349C2×C4⋊C8—111no—
350C2×C4⋊C8—111no—
351C2×C4⋊C8—111no—
352C2×C4⋊C8C2×D1111yescharacteristic
353C2×C22⋊C8—111no—
354C2×C22⋊C8—111no—
355C2×C22⋊C8—111no—
356C2×C22⋊C8—111no—
357C2×#97—111no—
358C2×#97C2×D1111yescharacteristic
359C2×C4×C8—111no—
360C2×C4×C8—111no—
361C2×C4×C8—111no—
362C2×C4×C8—111no—
363#336—111no—
364#336—111no—
365#336—111no—
366#336—111no—
367#336—111no—
368#336—111no—
369#336—111no—
370#336—111no—
371#336C2×D1111yescharacteristic
372#336C2×D1111yescharacteristic
373#336C2×D1111yescharacteristic
374#336C2×D1111yescharacteristic
375C22×C11C22×C22⋊C411yescharacteristic
376C22×C11C2×C4×Q811yescharacteristic
377C22×C11#51911yescharacteristic
378C22×C11C2×#13111yescharacteristic
379C22×C11C2×#13111yescharacteristic
380C22×C11C2×#13111yescharacteristic
381C22×C11#56811yescharacteristic
382C2×D11—22no—
383C2×D11—22no—
384C2×D11—22no—
385C2×D11—41no—
386C2×D11—41no—
387C2×D11—41no—
388C2×D11—41no—
389C4×C11—22no—
390C4×C11—22no—
391C4×C11—22no—
392C4×C11—41no—
393C4×C11—41no—
394C4×C11—41no—
395C4×C11#54811yescharacteristic
396C4×C11#54811yescharacteristic
397C4×C11D4×Q811yescharacteristic
398C4×C11D4×Q811yescharacteristic
399Dic11—22no—
400Dic11—22no—
401Dic11—22no—
402Dic11—22no—
403Dic11—41no—
404Dic11—41no—
405Dic11#40814yes—
406C22×Q8—111no—
407C22×Q8—111no—
408C22×Q8—111no—
409C22×Q8C4×D1111yescharacteristic
410C23×C4—111no—
411C23×C4—111no—
412C23×C4—111no—
413C22×C8—111no—
414C22×C8—111no—
415C22×C8—111no—
416C22×C8—111no—
417C22×C8C22×D1111yescharacteristic
418C22×C8C22×D1111yescharacteristic
419C22×C8C22×D1111yescharacteristic
420C22×C8C22×D1111yescharacteristic
421C4⋊Q8—224no—
422C4⋊Q8—224no—
423#125—224no—
424#125—224no—
425C22⋊Q8—224no—
426C22⋊Q8—224no—
427C22⋊Q8—224no—
428C22⋊Q8—224no—
429C4×Q8—22no—
430C4×Q8—22no—
431C4×Q8—114no—
432C4×Q8—114no—
433C4×Q8—222no—
434C4×Q8—222no—
435C4×Q8—222no—
436C4×Q8—222no—
437#117—222no—
438#117—222no—
439#117—222no—
440#117—222no—
441C2×C4⋊C4—111no—
442C2×C4⋊C4—111no—
443C2×C4⋊C4—111no—
444C2×C4⋊C4—111no—
445C2×C4⋊C4—111no—
446C2×C4⋊C4—111no—
447C2×C4⋊C4—111no—
448C2×C4⋊C4—111no—
449C2×C4⋊C4—111no—
450C2×C4⋊C4—111no—
451C2×C4⋊C4—111no—
452C2×C4⋊C4—111no—
453C2×C4⋊C4—111no—
454C2×C4⋊C4C4×D1111yescharacteristic
455C2×C4⋊C4C4×D1111yescharacteristic
456C2×C4⋊C4C4×D1111yescharacteristic
457C2×C22⋊C4—111no—
458C2×C22⋊C4—111no—
459C2×C22⋊C4—111no—
460C2×C22⋊C4—111no—
461C2×C42—111no—
462C2×C42—111no—
463C2×C42—111no—
464C2×C42—111no—
465C2×C42—111no—
466C2×C42—222no—
467C2×C42—222no—
468C2×C42C22×D1111yescharacteristic
469C2×C42C22×D1111yescharacteristic
470C2×C42C22×D1111yescharacteristic
471C4⋊C8—22no—
472C4⋊C8—222no—
473C4⋊C8—222no—
474C4⋊C8—222no—
475C4⋊C8—222no—
476C4⋊C8—222no—
477C22⋊C8—114no—
478C22⋊C8—222no—
479C22⋊C8—222no—
480C22⋊C8—222no—
481#97—22no—
482#97—222no—
483C4×C8—222no—
484C4×C8—222no—
485C4×C8—222no—
486C4×C8—222no—
487C2×C11Q8×C22⋊C411yescharacteristic
488C2×C11C2×#40811yescharacteristic
489C2×C11#288011yescharacteristic
490C2×C11#296011yescharacteristic
491C2×C11#296211yescharacteristic
492C2×C11#298511yescharacteristic
493C2×C11#298611yescharacteristic
494D11—42no—
495C24—111no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—41no—
499C2×Q8—114no—
500C2×Q8—222no—
501C2×Q8—222no—
502C2×Q8—222no—
503C2×Q8—222no—
504C2×Q8—222no—
505C2×Q8—222no—
506C2×Q8—222no—
507C2×Q8—441no—
508C22×C4—111no—
509C22×C4—111no—
510C22×C4—111no—
511C22×C4—111no—
512C22×C4—111no—
513C22×C4—112no—
514C22×C4—112no—
515C22×C4—111no—
516C22×C4—111no—
517C22×C4—222no—
518C22×C4—222no—
519C22×C4—222no—
520C22×C4—222no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—221no—
525C22×C4—222no—
526C22×C4—441no—
527C22×C4C2×C4×D1111yescharacteristic
528C22×C4C2×C4×D1111yescharacteristic
529C22×C4C2×C4×D1111yescharacteristic
530C22×C4C2×C4×D1111yescharacteristic
531C22×C4C2×C4×D1111yescharacteristic
532C22×C4C2×C4×D1111yescharacteristic
533C22×C4C23×D1111yescharacteristic
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—112no—
546C2×C8—221no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—221no—
553C2×C8—221no—
554C2×C8—221no—
555C2×C8—221no—
556C2×C8—221no—
557C2×C8Q8×D1112yes—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—114no—
562C4⋊C4—114no—
563C4⋊C4—114no—
564C4⋊C4—222no—
565C4⋊C4—222no—
566C4⋊C4—222no—
567C4⋊C4—222no—
568C4⋊C4—222no—
569C4⋊C4—222no—
570C4⋊C4—222no—
571C4⋊C4—222no—
572C4⋊C4—222no—
573C4⋊C4—222no—
574C22⋊C4—222no—
575C22⋊C4—222no—
576C22⋊C4—222no—
577C22⋊C4—222no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—112no—
583C42—112no—
584C42—112no—
585C42—112no—
586C42—222no—
587C42—222no—
588C42—221no—
589C42—221no—
590C42D4×D1112yes—
591C42D4×D1112yes—
592C11#2250911yescharacteristic, complemented, Sylow
593C23—112no—
594C23—221no—
595C23—221no—
596C23—221no—
597C23—221no—
598C23—221no—
599C23—221no—
600C23C22×C4×D1111yescharacteristic
601Q8—44no—
602Q8—228no—
603Q8—444no—
604Q8—444no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—112no—
621C2×C4—112no—
622C2×C4—112no—
623C2×C4—112no—
624C2×C4—112no—
625C2×C4—112no—
626C2×C4—112no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—221no—
631C2×C4—221no—
632C2×C4—221no—
633C2×C4—221no—
634C2×C4—221no—
635C2×C4—222no—
636C2×C4—222no—
637C2×C4—222no—
638C2×C4—222no—
639C2×C4—221no—
640C2×C4—221no—
641C2×C4—221no—
642C2×C4—221no—
643C2×C4—221no—
644C2×C4—221no—
645C2×C4—444no—
646C2×C4—444no—
647C2×C4C22⋊C4×D1112yes—
648C2×C4C22⋊C4×D1112yes—
649C2×C4#6696012yes—
650C2×C4C2×D4×D1111yescharacteristic
651C2×C4C2×D4×D1111yescharacteristic
652C2×C4C2×Q8×D1111yescharacteristic
653C2×C4#6704011yescharacteristic
654C2×C4#41×D1111yescharacteristic
655C2×C4#6704311yescharacteristic
656C8—22no—
657C8—41no—
658C8—41no—
659C8—41no—
660C8—222no—
661C8—441no—
662C8—441no—
663C8—441no—
664C22—222no—
665C22—222no—
666C22—222no—
667C22—441no—
668C22—441no—
669C22—441no—
670C22—441no—
671C22C2×C22⋊C4×D1111yescharacteristic
672C22C4×Q8×D1111yescharacteristic
673C22#1062310311yescharacteristic
674C22C2×#6696011yescharacteristic
675C22#1062327611yescharacteristic
676C22D11×#13111yescharacteristic
677C22D11×#13111yescharacteristic
678C4—22no—
679C4—22no—
680C4—22no—
681C4—41no—
682C4—41no—
683C4—41no—
684C4—114no—
685C4—222no—
686C4—222no—
687C4—222no—
688C4—222no—
689C4—441no—
690C4—441no—
691C4#1062316311yescharacteristic
692C4#1062316411yescharacteristic
693C4#1062320811yescharacteristic
694C4#1062325811yescharacteristic
695C2—442no—
696C2#1307145011yescharacteristic
697C2D11×#40811yescharacteristic
698C2#1307706611yescharacteristic
699C2#1307754711yescharacteristic
700C2#1307756111yescharacteristic
701C2#1307770911yescharacteristic
702C2#1307771411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1985C2
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1985D11
hypocenterC11#22509
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1985

Complements

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

NH ≅ G/Ntype
2. C2×#10622314C2semidirect
3. C2×#10622443C2semidirect
4. #13069554C2semidirect
5. #13069553C2semidirect
6. #13069550C2semidirect
7. #13069550C2semidirect
8. #13069550C2semidirect
15. C11×#1985C2semidirect
133. (C2×D11)⋊C8Q8semidirect
246. #1985D11semidirect
592. C11#22509semidirect

Maximal subgroups

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

subgroupindex
C2×#106231092
C2×#106223142
C2×#106224432
#130695542
#130695532
#130695502
#130685992
#130685972
#130685952
#130683852
#130683812
#130683732
C11×#19852
#2250911