Finite Group Databasebeta

← #14759885

Subgroups — #14759885

Order 2816.

1058 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622449C211yesmaximal, characteristic, complemented
2C2×#10622343C211yesmaximal, characteristic, complemented
3C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
4C2×#10622302C211yesmaximal, characteristic, complemented
5#13071860C211yesmaximal, characteristic
6#13069412C211yesmaximal, characteristic, complemented
7#13069336C211yesmaximal, characteristic, complemented
8#13069222C211yesmaximal, characteristic, complemented
9#13068907C211yesmaximal, characteristic, complemented
10#13068905C211yesmaximal, characteristic, complemented
11#13068599C211yesmaximal, characteristic, complemented
12#13068482C211yesmaximal, characteristic, complemented
13#13068394C211yesmaximal, characteristic, complemented
14#13068391C211yesmaximal, characteristic, complemented
15C11×#1923C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊D11C2211yescharacteristic
17C2×C4×C22⋊D11C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×#66925C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28C4×C11×C22⋊C4C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×C8×Dic11C2211yescharacteristic
41#10622573C411yescharacteristic
42#10622572C411yescharacteristic
43#10622572C411yescharacteristic
44#10622561C411yescharacteristic
45C4×(C2×D11)⋊C4C2211yescharacteristic
46C4×Dic11⋊C4C2211yescharacteristic
47C2×#66867C2211yescharacteristic
48C2×#66867C2211yescharacteristic
49#10622449—24no—
50#10622343—24no—
51(C22⋊D11)⋊C8—24no—
52#10622302—24no—
53#10622289C411yescharacteristic
54#10622288C411yescharacteristic
55#10622285C411yescharacteristic
56#10622270C411yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11C2×C411yescharacteristic
65C22×C22⋊D11C2×C411yescharacteristic
66C22×D44C2×C411yescharacteristic
67C22×C4×D11C2311yescharacteristic
68C22×C4×D11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C2×C11×C22⋊C4C2×C411yescharacteristic
74C2×C11×C22⋊C4C2×C411yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11C2×C411yescharacteristic
78C2×C22⋊Dic11C2×C411yescharacteristic
79C4×C22⋊D11—22no—
80C4×C22⋊D11—22no—
81C4×C22⋊D11—22no—
82C4×C22⋊D11—22no—
83C2×(C2×D11)⋊C4C2×C411yescharacteristic
84C2×(C2×D11)⋊C4C2×C411yescharacteristic
85C2×(C2×D11)⋊C4C2×C411yescharacteristic
86C2×(C2×D11)⋊C4C2×C411yescharacteristic
87C2×(C2×D11)⋊C4C2×C411yescharacteristic
88C2×(C2×D11)⋊C4C2×C411yescharacteristic
89C2×(C2×D11)⋊C4C2×C411yescharacteristic
90C2×(C2×D11)⋊C4C2×C411yescharacteristic
91C2×C4⋊Dic11C2×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×C4×Dic11C2311yescharacteristic
99C2×C4×Dic11C2311yescharacteristic
100C22×C11⋊C8—22no—
101C22×C11⋊C8—22no—
102C22×C11⋊C8—22no—
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C2×#4313—22no—
108C2×#4313—22no—
109C2×#4313D414yescomplemented
110C2×C8×D11—22no—
111C2×C8×D11—22no—
112C2×C8×D11—22no—
113C2×C8×D11—22no—
114C2×C8×D11—22no—
115C2×C8×D11—22no—
116C4×D44—22no—
117C4×D44—22no—
118#66925—22no—
119#66925—22no—
120C11×C4⋊C8—22no—
121C11×C22⋊C8—22no—
122C11×C22⋊C8—22no—
123C4×C8×C11—22no—
124C11×#95C2×C411yescharacteristic
125C11×#95C2×C411yescharacteristic
126C11⋊#95C2×C411yescharacteristic
127C11⋊#95C2×C411yescharacteristic
128C11⋊#95C2×C411yescharacteristic
129C11⋊#95C2×C411yescharacteristic
130C22⋊(C11⋊C8)—22no—
131(C2×D11)⋊C8—22no—
132(C2×D11)⋊C8—22no—
133(C2×D11)⋊C8—22no—
134(C2×D11)⋊C8—22no—
135(C2×D11)⋊C8—22no—
136#66879—22no—
137#66879—22no—
138Dic11⋊C8—22no—
139Dic11⋊C8—22no—
140Dic11⋊C8—22no—
141C8×Dic11D414yescomplemented
142#66867—22no—
143#66867—22no—
144#21492—111nomaximal, Sylow
145C24×C11C22×C411yescharacteristic
146C23×D11C22×C411yescharacteristic
147C23×D11C22×C411yescharacteristic
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×C11C22×C411yescharacteristic
155C22×C4×C11C22×C411yescharacteristic
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—22no—
161C2×C22⋊D11—22no—
162C2×C22⋊D11—22no—
163C2×C22⋊D11—22no—
164C2×C22⋊D11—22no—
165C2×C22⋊D11—41no—
166C22×Dic11C22×C411yescharacteristic
167C22×Dic11C22×C411yescharacteristic
168C22×Dic11C22×C411yescharacteristic
169C22×Dic11C22×C411yescharacteristic
170C22×Dic11C22×C411yescharacteristic
171C22×Dic11C22×C411yescharacteristic
172C2×D44—22no—
173C2×D44—22no—
174C2×D44—41no—
175C2×C4×D11—21no—
176C2×C4×D11—21no—
177C2×C4×D11—21no—
178C2×C4×D11—21no—
179C2×C4×D11—21no—
180C2×C4×D11—21no—
181C2×C4×D11—21no—
182C2×C4×D11—21no—
183C2×C4×D11—21no—
184C2×C4×D11—21no—
185C2×C4×D11C2×D412yes—
186C2×C4×D11#4112yes—
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×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11C2×D412yes—
198C2×C8×C11C2×D412yes—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—41no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—21no—
205C22⋊Dic11—22no—
206C22⋊Dic11—22no—
207(C2×D11)⋊C4—22no—
208(C2×D11)⋊C4—22no—
209(C2×D11)⋊C4—22no—
210(C2×D11)⋊C4—22no—
211(C2×D11)⋊C4—22no—
212(C2×D11)⋊C4—22no—
213(C2×D11)⋊C4—22no—
214(C2×D11)⋊C4—41no—
215C4⋊Dic11—22no—
216Dic11⋊C4—22no—
217Dic11⋊C4—22no—
218Dic11⋊C4—22no—
219Dic11⋊C4—22no—
220Dic11⋊C4—41no—
221Dic11⋊C4—41no—
222C4×Dic11—21no—
223C4×Dic11—21no—
224C4×Dic11C2×D412yes—
225C4×Dic11#4112yes—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—44no—
235C2×C11⋊C8C2×D412yes—
236C2×C11⋊C8C2×D412yes—
237C2×C11⋊C8#4112yes—
238C2×C11⋊C8#4112yes—
239#4313—28no—
240C8×D11—28no—
241C8×D11—44no—
242C2×#435—111no—
243C2×#435—111no—
244C2×C8×D4—111no—
245C2×#405—111no—
246#2392—111no—
247#1955—111no—
248#1940—111no—
249#1923—111no—
250#1923D1111yescharacteristic, complemented
251#1869—111no—
252#1869—111no—
253#1798—111no—
254#1770—111no—
255#1752—111no—
256#1752—111no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11#13112yes—
264C23×C11C23×C411yescharacteristic
265C22×D11—21no—
266C22×D11—21no—
267C22×D11—21no—
268C22×D11—21no—
269C22×D11—21no—
270C22×D11—21no—
271C22×D11—21no—
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—21no—
277C22×D11C4×D412yes—
278C22×D11#13112yes—
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×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11C22×D411yescharacteristic
299C2×C4×C11C22×D411yescharacteristic
300C2×C4×C11C2×#4111yescharacteristic
301C2×C4×C11C2×#4111yescharacteristic
302C2×C4×C11C2×#4111yescharacteristic
303C2×C4×C11C2×#4111yescharacteristic
304C22⋊D11—28no—
305C22⋊D11—44no—
306C2×Dic11—21no—
307C2×Dic11—21no—
308C2×Dic11—21no—
309C2×Dic11—21no—
310C2×Dic11—21no—
311C2×Dic11—21no—
312C2×Dic11—21no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11C4×D412yes—
322C2×Dic11C4×D412yes—
323C2×Dic11C4×D412yes—
324D44—44no—
325C4×D11—22no—
326C4×D11—22no—
327C4×D11—22no—
328C4×D11—22no—
329C4×D11—41no—
330C4×D11—41no—
331C4×D11—41no—
332C4×D11—41no—
333C8×C11—22no—
334C8×C11—22no—
335C8×C11—41no—
336C8×C11—41no—
337C11⋊C8—22no—
338C11⋊C8—41no—
339C11⋊C8—41no—
340C11⋊C8#12114yes—
341C22×M16—111no—
342C23×C8—111no—
343C23×C8—111no—
344C23×C8—111no—
345C2×C4×D4—111no—
346C2×C4×D4—111no—
347C2×C4×D4—111no—
348C2×#117—111no—
349#435—224no—
350#435—224no—
351C8×D4—224no—
352C2×C4⋊C8—111no—
353C2×C4⋊C8—111no—
354C2×C4⋊C8—111no—
355C2×C4⋊C8C2×D1111yescharacteristic
356C2×C22⋊C8—111no—
357C2×C22⋊C8—111no—
358C2×C22⋊C8—111no—
359C2×C22⋊C8—111no—
360C2×C22⋊C8—111no—
361C2×C22⋊C8—111no—
362C2×C22⋊C8C2×D1111yescharacteristic
363C2×C22⋊C8C2×D1111yescharacteristic
364#405—224no—
365C2×#97—111no—
366C2×#97—111no—
367C2×#97—111no—
368C2×#97—111no—
369C2×C4×C8—111no—
370C2×C4×C8C2×D1111yescharacteristic
371#398—111no—
372#397—111no—
373#396—111no—
374#396—111no—
375#394—111no—
376#394—111no—
377#394—111no—
378#392—111no—
379C4×C4⋊C4—111no—
380C4×C22⋊C4—111no—
381C4×C22⋊C4C2×D1111yescharacteristic
382#336—111no—
383#336—111no—
384#336—111no—
385#336—111no—
386#336C2×D1111yescharacteristic
387#336C2×D1111yescharacteristic
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11C2×C4×D411yescharacteristic
396C22×C11C2×C4×D411yescharacteristic
397C22×C11C4×#4111yescharacteristic
398C22×C11C2×#13111yescharacteristic
399C22×C11C2×#13111yescharacteristic
400C22×C11#56811yescharacteristic
401C22×C11#56811yescharacteristic
402C2×D11—22no—
403C2×D11—22no—
404C2×D11—22no—
405C2×D11—22no—
406C2×D11—22no—
407C2×D11—22no—
408C2×D11—41no—
409C2×D11—41no—
410C2×D11—41no—
411C2×D11—41no—
412C2×D11—41no—
413C2×D11—41no—
414C2×D11—41no—
415C2×D11—41no—
416C4×C11—41no—
417C4×C11—41no—
418C4×C11—41no—
419C4×C11—41no—
420C4×C11—41no—
421C4×C11C2×#12111yescharacteristic
422C4×C11#52511yescharacteristic
423C4×C11#52911yescharacteristic
424C4×C11#53211yescharacteristic
425Dic11—22no—
426Dic11—22no—
427Dic11—22no—
428Dic11—41no—
429Dic11—41no—
430Dic11—41no—
431C22×D4—111no—
432C22×D4—111no—
433C22×D4—111no—
434C23×C4—111no—
435C23×C4—111no—
436C23×C4C22×D1111yescharacteristic
437C2×M16—114no—
438C2×M16—222no—
439C2×M16—222no—
440C22×C8—111no—
441C22×C8—111no—
442C22×C8—111no—
443C22×C8—111no—
444C22×C8—222no—
445C22×C8—222no—
446C22×C8—222no—
447C22×C8—222no—
448C22×C8—222no—
449C22×C8—222no—
450C22×C8—222no—
451C22×C8—222no—
452C22×C8—222no—
453C22×C8C22×D1111yescharacteristic
454C22×C8C22×D1111yescharacteristic
455C22×C8C22×D1111yescharacteristic
456C22×C8C22×D1111yescharacteristic
457C4×D4—222no—
458C4×D4—222no—
459C4×D4—222no—
460C4×D4—222no—
461C4×D4—222no—
462C4×D4—222no—
463#117—222no—
464#117—222no—
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×C22⋊C4—111no—
473C2×C22⋊C4—111no—
474C2×C22⋊C4—111no—
475C2×C22⋊C4—111no—
476C2×C22⋊C4—111no—
477C2×C22⋊C4—111no—
478C2×C22⋊C4—111no—
479C2×C22⋊C4—111no—
480C2×C22⋊C4—111no—
481C2×C22⋊C4—111no—
482C2×C22⋊C4C4×D1111yescharacteristic
483C2×C22⋊C4C4×D1111yescharacteristic
484C2×C42—111no—
485C2×C42—111no—
486C2×C42C22×D1111yescharacteristic
487C2×C42C22×D1111yescharacteristic
488C4⋊C8—22no—
489C4⋊C8—222no—
490C4⋊C8—222no—
491C4⋊C8—222no—
492C22⋊C8—22no—
493C22⋊C8—22no—
494C22⋊C8—222no—
495C22⋊C8—222no—
496C22⋊C8—222no—
497C22⋊C8—222no—
498C22⋊C8—222no—
499C22⋊C8—222no—
500#97—222no—
501#97—222no—
502#97—222no—
503#97—222no—
504C4×C8—22no—
505C4×C8—114no—
506#95—111no—
507#95—111no—
508#95—111no—
509#95—111no—
510#95C4×D1111yescharacteristic
511#95C4×D1111yescharacteristic
512C2×C11—42no—
513C2×C11C4×#12111yescharacteristic
514C2×C11#292911yescharacteristic
515C2×C11#293211yescharacteristic
516C2×C11#293311yescharacteristic
517C2×C11#293311yescharacteristic
518C2×C11#296811yescharacteristic
519C2×C11#296811yescharacteristic
520D11—42no—
521D11—42no—
522C24—111no—
523C24—111no—
524C24C2×C4×D1111yescharacteristic
525C2×D4—222no—
526C2×D4—222no—
527C2×D4—222no—
528C2×D4—222no—
529C2×D4—222no—
530C2×D4—222no—
531C2×D4—222no—
532C2×D4—441no—
533C2×D4—441no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—111no—
541C22×C4—111no—
542C22×C4—111no—
543C22×C4—112no—
544C22×C4—112no—
545C22×C4—111no—
546C22×C4—111no—
547C22×C4—111no—
548C22×C4—221no—
549C22×C4—221no—
550C22×C4—221no—
551C22×C4—221no—
552C22×C4—221no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—221no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4C2×C4×D1111yescharacteristic
559C22×C4C2×C4×D1111yescharacteristic
560C22×C4C2×C4×D1111yescharacteristic
561C22×C4C2×C4×D1111yescharacteristic
562C22×C4C2×C4×D1111yescharacteristic
563C22×C4C23×D1111yescharacteristic
564M16—228no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—112no—
576C2×C8—112no—
577C2×C8—112no—
578C2×C8—112no—
579C2×C8—228no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C2×C8—221no—
588C2×C8—444no—
589C2×C8—444no—
590C2×C8D4×D1112yes—
591C2×C8D4×D1112yes—
592C4⋊C4—222no—
593C4⋊C4—222no—
594C4⋊C4—222no—
595C4⋊C4—222no—
596C4⋊C4—222no—
597C4⋊C4—441no—
598C4⋊C4—441no—
599C22⋊C4—22no—
600C22⋊C4—41no—
601C22⋊C4—222no—
602C22⋊C4—222no—
603C22⋊C4—222no—
604C22⋊C4—222no—
605C22⋊C4—222no—
606C22⋊C4—222no—
607C22⋊C4—222no—
608C22⋊C4—222no—
609C22⋊C4—222no—
610C22⋊C4—441no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—112no—
616C42—112no—
617C42—221no—
618C42—221no—
619C11#2149211yescharacteristic, complemented, Sylow
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—112no—
627C23—112no—
628C23—221no—
629C23—221no—
630C23—221no—
631C23—221no—
632C23—221no—
633C23—221no—
634C23—221no—
635C23—221no—
636C23—221no—
637C23—221no—
638C23—221no—
639C23—221no—
640C23#6695412yes—
641C23C22×C4×D1111yescharacteristic
642D4—228no—
643D4—444no—
644D4—444no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—112no—
665C2×C4—112no—
666C2×C4—112no—
667C2×C4—221no—
668C2×C4—221no—
669C2×C4—221no—
670C2×C4—221no—
671C2×C4—221no—
672C2×C4—221no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—222no—
677C2×C4—221no—
678C2×C4—221no—
679C2×C4—221no—
680C2×C4—221no—
681C2×C4—221no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—221no—
685C2×C4—221no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—441no—
690C2×C4C2×D4×D1111yescharacteristic
691C2×C4C2×D4×D1111yescharacteristic
692C2×C4#41×D1111yescharacteristic
693C2×C4#41×D1111yescharacteristic
694C2×C4#41×D1111yescharacteristic
695C2×C4#41×D1111yescharacteristic
696C8—22no—
697C8—22no—
698C8—41no—
699C8—41no—
700C8—114no—
701C8—222no—
702C8—441no—
703C8—441no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—222no—
712C22—222no—
713C22—222no—
714C22—222no—
715C22—222no—
716C22—222no—
717C22—441no—
718C22—441no—
719C22—441no—
720C22—441no—
721C22—441no—
722C22—441no—
723C22—441no—
724C22—441no—
725C22#1062305311yescharacteristic
726C22C4×D4×D1111yescharacteristic
727C22C4×D4×D1111yescharacteristic
728C22C2×#6695411yescharacteristic
729C22#1062327611yescharacteristic
730C22D11×#13111yescharacteristic
731C22#1062328111yescharacteristic
732C4—41no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—222no—
738C4—222no—
739C4—222no—
740C4—441no—
741C4—441no—
742C4—441no—
743C4D11×#12111yescharacteristic
744C4#1062318711yescharacteristic
745C4#1062319911yescharacteristic
746C4#1062323711yescharacteristic
747C2—42no—
748C2—442no—
749C2—442no—
750C2#1307112811yescharacteristic
751C2#1307730511yescharacteristic
752C2#1307733011yescharacteristic
753C2#1307733611yescharacteristic
754C2#1307734511yescharacteristic
755C2#1307760511yescharacteristic
756C2#1307760811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1923C2
prime radical#10622573C4
cosocleC22×C4×C11C24
hypercenter#1923D11
hypocenterC11#21492
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. C2×#10622449C2semidirect
2. C2×#10622343C2semidirect
3. C2×(C22⋊D11)⋊C8C2semidirect
4. C2×#10622302C2semidirect
6. #13069412C2semidirect
7. #13069336C2semidirect
8. #13069222C2semidirect
9. #13068907C2semidirect
10. #13068905C2semidirect
11. #13068599C2semidirect
12. #13068482C2semidirect
13. #13068394C2semidirect
14. #13068391C2semidirect
15. C11×#1923C2semidirect
109. C2×#4313D4semidirect
141. C8×Dic11D4semidirect
250. #1923D11semidirect
619. C11#21492semidirect

Maximal subgroups

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

subgroupindex
C2×#106224492
C2×#106223432
C2×(C22⋊D11)⋊C82
C2×#106223022
#130718602
#130694122
#130693362
#130692222
#130689072
#130689052
#130685992
#130684822
#130683942
#130683912
C11×#19232
#2149211