Finite Group Databasebeta

← #14780044

Subgroups — #14780044

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071860C211yesmaximal, characteristic
2#13069413C211yesmaximal, characteristic, complemented
3#13069408C211yesmaximal, characteristic, complemented
4#13069231C211yesmaximal, characteristic, complemented
5#13069221C211yesmaximal, characteristic, complemented
6#13069178C211yesmaximal, characteristic, complemented
7#13069170C211yesmaximal, characteristic, complemented
8#13068908C211yesmaximal, characteristic, complemented
9#13068908C211yesmaximal, characteristic, complemented
10#13068907C211yesmaximal, characteristic, complemented
11#13068905C211yesmaximal, characteristic, complemented
12#13068795C211yesmaximal, characteristic, complemented
13#13068686C211yesmaximal, characteristic, complemented
14#13068597C211yesmaximal, characteristic, complemented
15C11×#1850C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C2×C4×C22⋊D11C2211yescharacteristic
18C2×C4×C22⋊D11C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×#66925C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C4×C11×C22⋊C4C2211yescharacteristic
26C2×C22⋊(C11⋊C8)C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622573C411yescharacteristic
38#10622572C411yescharacteristic
39#10622572C411yescharacteristic
40#10622561C411yescharacteristic
41C4×(C2×D11)⋊C4C2211yescharacteristic
42C4×Dic11⋊C4C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45#10622289C411yescharacteristic
46#10622288C411yescharacteristic
47#10622285C411yescharacteristic
48#10622270C411yescharacteristic
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11C2×C411yescharacteristic
61C22×C22⋊D11C2×C411yescharacteristic
62C22×D44C2×C411yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×C4×D11C2311yescharacteristic
65C22×C8×C11—41no—
66C22×C8×C11—41no—
67C22×C8×C11—41no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C2×C11×C22⋊C4C2×C411yescharacteristic
73C2×C11×C22⋊C4C2×C411yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11C2×C411yescharacteristic
77C2×C22⋊Dic11C2×C411yescharacteristic
78C4×C22⋊D11—41no—
79C4×C22⋊D11—41no—
80C4×C22⋊D11—41no—
81C4×C22⋊D11—41no—
82C2×(C2×D11)⋊C4C2×C411yescharacteristic
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×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×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C2×C8×D11—41no—
104C2×C8×D11—41no—
105C2×C8×D11—41no—
106C4×D44—41no—
107C4×D44—41no—
108#66925—41no—
109#66925—41no—
110C11×C4⋊C8—41no—
111C11×C4⋊C8—41no—
112C11×C22⋊C8—41no—
113C11×#95C2×C411yescharacteristic
114C11×#95C2×C411yescharacteristic
115C11⋊#95C2×C411yescharacteristic
116C11⋊#95C2×C411yescharacteristic
117C11⋊#95C2×C411yescharacteristic
118C11⋊#95C2×C411yescharacteristic
119C22⋊(C11⋊C8)—41no—
120C22⋊(C11⋊C8)—41no—
121(C2×D11)⋊C8—41no—
122(C2×D11)⋊C8—41no—
123(C2×D11)⋊C8—41no—
124(C2×D11)⋊C8—41no—
125(C2×D11)⋊C8—41no—
126(C2×D11)⋊C8—41no—
127(C2×D11)⋊C8—41no—
128Dic11⋊C8—41no—
129C8×Dic11—41no—
130C4⋊(C11⋊C8)—41no—
131#66867—41no—
132#23330—111nomaximal, Sylow
133C24×C11C22×C411yescharacteristic
134C23×D11C22×C411yescharacteristic
135C23×D11C22×C411yescharacteristic
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11C22×C411yescharacteristic
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C2×C22⋊D11—22no—
149C2×C22⋊D11—22no—
150C2×C22⋊D11—22no—
151C2×C22⋊D11—22no—
152C2×C22⋊D11—41no—
153C2×C22⋊D11—41no—
154C22×Dic11C22×C411yescharacteristic
155C22×Dic11C22×C411yescharacteristic
156C22×Dic11C22×C411yescharacteristic
157C22×Dic11C22×C411yescharacteristic
158C22×Dic11C22×C411yescharacteristic
159C22×Dic11C22×C411yescharacteristic
160C2×D44—22no—
161C2×D44—41no—
162C2×D44—41no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C4×D11—21no—
174C2×C4×D11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—44no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—41no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C22⋊Dic11—41no—
195C22⋊Dic11—41no—
196(C2×D11)⋊C4—22no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—41no—
199(C2×D11)⋊C4—41no—
200(C2×D11)⋊C4—41no—
201(C2×D11)⋊C4—41no—
202(C2×D11)⋊C4—41no—
203(C2×D11)⋊C4—41no—
204C4⋊Dic11—41no—
205Dic11⋊C4—22no—
206Dic11⋊C4—41no—
207Dic11⋊C4—41no—
208Dic11⋊C4—41no—
209Dic11⋊C4—41no—
210Dic11⋊C4—41no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
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—
227C8×D11—44no—
228#2392—111no—
229#1955—111no—
230#1954—111no—
231#1924—111no—
232#1923—111no—
233#1917—111no—
234#1916—111no—
235#1869—111no—
236#1869—111no—
237#1869—111no—
238#1869—111no—
239#1850—111no—
240#1850D1111yescharacteristic, complemented
241#1818—111no—
242#1798—111no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11#13112yes—
250C23×C11C23×C411yescharacteristic
251C22×D11—21no—
252C22×D11—21no—
253C22×D11—21no—
254C22×D11—21no—
255C22×D11—21no—
256C22×D11—21no—
257C22×D11—21no—
258C22×D11—21no—
259C22×D11—21no—
260C22×D11—21no—
261C22×D11—21no—
262C22×D11—21no—
263C22×D11—21no—
264C22×D11#13112yes—
265C2×C4×C11—21no—
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—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11H(5,𝔽2)11yescharacteristic
285C2×C4×C11H(5,𝔽2)11yescharacteristic
286C2×C4×C11H(5,𝔽2)11yescharacteristic
287C2×C4×C11H(5,𝔽2)11yescharacteristic
288C2×C4×C11H(5,𝔽2)11yescharacteristic
289C2×C4×C112−1+411yescharacteristic
290C22⋊D11—44no—
291C22⋊D11—44no—
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×Dic11—21no—
305C2×Dic11—21no—
306C2×Dic11—21no—
307C2×Dic11—21no—
308C2×Dic11—21no—
309C2×Dic11#13112yes—
310D44—44no—
311C4×D11—41no—
312C4×D11—41no—
313C4×D11—41no—
314C4×D11—41no—
315C4×D11—41no—
316C4×D11—41no—
317C4×D11—41no—
318C4×D11—41no—
319C8×C11—41no—
320C8×C11—41no—
321C8×C11—41no—
322C8×C11—41no—
323C11⋊C8—41no—
324C11⋊C8—41no—
325C11⋊C8—41no—
326C11⋊C8—41no—
327C23×C8—111no—
328C23×C8C2×D1111yescharacteristic
329C2×C4×D4—111no—
330C2×C4×D4—111no—
331C2×C4×D4—111no—
332C2×#117—111no—
333C2×C4⋊C8—111no—
334C2×C4⋊C8—111no—
335C2×C4⋊C8C2×D1111yescharacteristic
336C2×C4⋊C8C2×D1111yescharacteristic
337C2×C22⋊C8—111no—
338C2×C22⋊C8—111no—
339C2×C22⋊C8—111no—
340C2×C22⋊C8—111no—
341C2×C22⋊C8—111no—
342C2×C22⋊C8—111no—
343C2×C22⋊C8—111no—
344C2×C22⋊C8—111no—
345C2×C22⋊C8—111no—
346C2×C22⋊C8C2×D1111yescharacteristic
347C2×#97—111no—
348C2×C4×C8—111no—
349#398—111no—
350#397—111no—
351#396—111no—
352#396—111no—
353#394—111no—
354#394—111no—
355#394—111no—
356#392—111no—
357C4×C4⋊C4—111no—
358C4×C22⋊C4—111no—
359C4×C22⋊C4C2×D1111yescharacteristic
360#336—111no—
361#336—111no—
362#336—111no—
363#336—111no—
364#336—111no—
365#336—111no—
366#336—111no—
367#336—111no—
368#336C2×D1111yescharacteristic
369#336C2×D1111yescharacteristic
370C22×C11—22no—
371C22×C11—22no—
372C22×C11—22no—
373C22×C11—41no—
374C22×C11—41no—
375C22×C11—41no—
376C22×C11—41no—
377C22×C11#51811yescharacteristic
378C22×C11#51811yescharacteristic
379C22×C11#52011yescharacteristic
380C22×C11C2×#13111yescharacteristic
381C22×C11C2×#13111yescharacteristic
382C22×C11C2×#13111yescharacteristic
383C22×C11#56811yescharacteristic
384C2×D11—22no—
385C2×D11—22no—
386C2×D11—22no—
387C2×D11—41no—
388C2×D11—41no—
389C2×D11—41no—
390C2×D11—41no—
391C2×D11—41no—
392C2×D11—41no—
393C2×D11—41no—
394C2×D11—41no—
395C2×D11—41no—
396C2×D11—41no—
397C2×D11—41no—
398C4×C11—41no—
399C4×C11—41no—
400C4×C11—41no—
401C4×C11—41no—
402C4×C11—41no—
403C4×C11#56011yescharacteristic
404C4×C11#56011yescharacteristic
405C4×C11#56211yescharacteristic
406C4×C11#56211yescharacteristic
407Dic11—22no—
408Dic11—41no—
409Dic11—41no—
410Dic11—41no—
411Dic11—41no—
412Dic11—41no—
413C22×D4—111no—
414C22×D4—111no—
415C22×D4—111no—
416C23×C4—111no—
417C23×C4—111no—
418C23×C4C22×D1111yescharacteristic
419C22×C8—41no—
420C22×C8—41no—
421C22×C8—41no—
422C22×C8—111no—
423C22×C8—111no—
424C22×C8—111no—
425C22×C8—111no—
426C22×C8—441no—
427C22×C8—441no—
428C22×C8—441no—
429C22×C8C22×D1111yescharacteristic
430C22×C8C22×D1111yescharacteristic
431C22×C8C22×D1111yescharacteristic
432C22×C8C22×D1111yescharacteristic
433C4×D4—441no—
434C4×D4—441no—
435C4×D4—441no—
436C4×D4—441no—
437C4×D4—441no—
438C4×D4—441no—
439#117—441no—
440#117—441no—
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×C22⋊C4—111no—
449C2×C22⋊C4—111no—
450C2×C22⋊C4—111no—
451C2×C22⋊C4—111no—
452C2×C22⋊C4—111no—
453C2×C22⋊C4—111no—
454C2×C22⋊C4—111no—
455C2×C22⋊C4—111no—
456C2×C22⋊C4—111no—
457C2×C22⋊C4—111no—
458C2×C22⋊C4C4×D1111yescharacteristic
459C2×C22⋊C4C4×D1111yescharacteristic
460C2×C42—111no—
461C2×C42—111no—
462C2×C42C22×D1111yescharacteristic
463C2×C42C22×D1111yescharacteristic
464C4⋊C8—41no—
465C4⋊C8—41no—
466C4⋊C8—441no—
467C4⋊C8—441no—
468C22⋊C8—41no—
469C22⋊C8—441no—
470C22⋊C8—441no—
471C22⋊C8—441no—
472C22⋊C8—441no—
473C22⋊C8—441no—
474C22⋊C8—441no—
475C22⋊C8—441no—
476C22⋊C8—441no—
477C22⋊C8—441no—
478#97—441no—
479C4×C8—441no—
480#95—111no—
481#95—111no—
482#95—111no—
483#95—111no—
484#95C4×D1111yescharacteristic
485#95C4×D1111yescharacteristic
486C2×C11—42no—
487C2×C11#237711yescharacteristic
488C2×C11#297611yescharacteristic
489C2×C11#297711yescharacteristic
490C2×C11#297711yescharacteristic
491C2×C11#298111yescharacteristic
492C2×C11#299211yescharacteristic
493C2×C11#299411yescharacteristic
494D11—42no—
495D11—81no—
496C24—111no—
497C24—111no—
498C24C2×C4×D1111yescharacteristic
499C2×D4—222no—
500C2×D4—222no—
501C2×D4—222no—
502C2×D4—222no—
503C2×D4—222no—
504C2×D4—441no—
505C2×D4—441no—
506C2×D4—441no—
507C2×D4—441no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—111no—
515C22×C4—111no—
516C22×C4—111no—
517C22×C4—111no—
518C22×C4—111no—
519C22×C4—111no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—221no—
525C22×C4—221no—
526C22×C4—221no—
527C22×C4—221no—
528C22×C4—221no—
529C22×C4—221no—
530C22×C4—221no—
531C22×C4—221no—
532C22×C4C2×C4×D1111yescharacteristic
533C22×C4C2×C4×D1111yescharacteristic
534C22×C4C2×C4×D1111yescharacteristic
535C22×C4C2×C4×D1111yescharacteristic
536C22×C4C2×C4×D1111yescharacteristic
537C22×C4C23×D1111yescharacteristic
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—44no—
551C2×C8—221no—
552C2×C8—221no—
553C2×C8—221no—
554C2×C8—221no—
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—444no—
564C4⋊C4—222no—
565C4⋊C4—441no—
566C4⋊C4—441no—
567C4⋊C4—441no—
568C4⋊C4—441no—
569C4⋊C4—441no—
570C4⋊C4—441no—
571C22⋊C4—22no—
572C22⋊C4—41no—
573C22⋊C4—222no—
574C22⋊C4—222no—
575C22⋊C4—441no—
576C22⋊C4—441no—
577C22⋊C4—441no—
578C22⋊C4—441no—
579C22⋊C4—441no—
580C22⋊C4—441no—
581C22⋊C4—441no—
582C22⋊C4—441no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—221no—
588C42—221no—
589C42—221no—
590C42—221no—
591C11#2333011yescharacteristic, complemented, Sylow
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—112no—
599C23—221no—
600C23—221no—
601C23—221no—
602C23—221no—
603C23—221no—
604C23—221no—
605C23—221no—
606C23—221no—
607C23—221no—
608C23—221no—
609C23—221no—
610C23—221no—
611C23—221no—
612C23#6695412yes—
613C23C22×C4×D1111yescharacteristic
614D4—444no—
615D4—444no—
616D4—444no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
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—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—112no—
637C2×C4—221no—
638C2×C4—221no—
639C2×C4—221no—
640C2×C4—221no—
641C2×C4—221no—
642C2×C4—221no—
643C2×C4—221no—
644C2×C4—221no—
645C2×C4—221no—
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—441no—
655C2×C4—441no—
656C2×C4—441no—
657C2×C4—441no—
658C2×C4—441no—
659C2×C4—441no—
660C2×C4—441no—
661C2×C4—441no—
662C2×C4#6703711yescharacteristic
663C2×C4#6703711yescharacteristic
664C2×C4#6703711yescharacteristic
665C2×C4#6704011yescharacteristic
666C2×C4#6704211yescharacteristic
667C2×C4#6704211yescharacteristic
668C8—41no—
669C8—41no—
670C8—41no—
671C8—41no—
672C8—441no—
673C8—441no—
674C8—441no—
675C8—441no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—222no—
684C22—222no—
685C22—222no—
686C22—441no—
687C22—441no—
688C22—441no—
689C22—441no—
690C22—441no—
691C22—441no—
692C22—441no—
693C22—441no—
694C22—441no—
695C22—441no—
696C22—441no—
697C22#1062303511yescharacteristic
698C22#1062307611yescharacteristic
699C22#1062307611yescharacteristic
700C22C2×#6695411yescharacteristic
701C22#1062327611yescharacteristic
702C22D11×#13111yescharacteristic
703C22D11×#13111yescharacteristic
704C4—41no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—222no—
710C4—441no—
711C4—441no—
712C4—441no—
713C4—441no—
714C4—441no—
715C4#1062312611yescharacteristic
716C4#1062317811yescharacteristic
717C4#1062317811yescharacteristic
718C4#1062319711yescharacteristic
719C2—42no—
720C2—442no—
721C2—881no—
722C2#1307177211yescharacteristic
723C2#1307766311yescharacteristic
724C2#1307766911yescharacteristic
725C2#1307766911yescharacteristic
726C2#1307768811yescharacteristic
727C2#1307775211yescharacteristic
728C2#1307777411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1850C2
prime radical#10622573C4
cosocleC22×C4×C11C24
hypercenter#1850D11
hypocenterC11#23330
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
2. #13069413C2semidirect
3. #13069408C2semidirect
4. #13069231C2semidirect
5. #13069221C2semidirect
6. #13069178C2semidirect
7. #13069170C2semidirect
8. #13068908C2semidirect
9. #13068908C2semidirect
10. #13068907C2semidirect
11. #13068905C2semidirect
12. #13068795C2semidirect
13. #13068686C2semidirect
14. #13068597C2semidirect
15. C11×#1850C2semidirect
240. #1850D11semidirect
591. C11#23330semidirect

Maximal subgroups

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

subgroupindex
#130718602
#130694132
#130694082
#130692312
#130692212
#130691782
#130691702
#130689082
#130689072
#130689052
#130687952
#130686862
#130685972
C11×#18502
#2333011