Finite Group Databasebeta

← #14780081

Subgroups — #14780081

Order 2816.

770 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#13071856C211yesmaximal, characteristic
2#13069414C211yesmaximal, characteristic, complemented
3#13069409C211yesmaximal, characteristic, complemented
4#13069229C211yesmaximal, characteristic, complemented
5#13069220C211yesmaximal, characteristic, complemented
6#13069175C211yesmaximal, characteristic, complemented
7#13068912C211yesmaximal, characteristic, complemented
8#13068912C211yesmaximal, characteristic, complemented
9#13068912C211yesmaximal, characteristic, complemented
10#13068912C211yesmaximal, characteristic, complemented
11#13068800C211yesmaximal, characteristic, complemented
12#13068797C211yesmaximal, characteristic, complemented
13#13068686C211yesmaximal, characteristic, complemented
14#13068599C211yesmaximal, characteristic, complemented
15C11×#1917C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C22×#4313C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×#66925C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#97C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
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×Dic11⋊C8C2211yescharacteristic
37#10622607C411yescharacteristic
38#10622607C411yescharacteristic
39#10622604C411yescharacteristic
40#10622604C411yescharacteristic
41C4×(C2×D11)⋊C4C2211yescharacteristic
42C4×(C2×D11)⋊C4C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622287C411yescharacteristic
46#10622285C411yescharacteristic
47#10622284C411yescharacteristic
48#10622274C411yescharacteristic
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D44C2×C411yescharacteristic
60C22×D44C2×C411yescharacteristic
61C22×D44C2×C411yescharacteristic
62C22×C4×D11C2311yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×C4×D11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C11×C4⋊C4C2×C411yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×(C2×D11)⋊C4C2×C411yescharacteristic
75C2×(C2×D11)⋊C4C2×C411yescharacteristic
76C2×(C2×D11)⋊C4C2×C411yescharacteristic
77C2×(C2×D11)⋊C4C2×C411yescharacteristic
78C2×(C2×D11)⋊C4C2×C411yescharacteristic
79C2×(C2×D11)⋊C4C2×C411yescharacteristic
80C2×(C2×D11)⋊C4C2×C411yescharacteristic
81C2×(C2×D11)⋊C4C2×C411yescharacteristic
82C2×(C2×D11)⋊C4C2×C411yescharacteristic
83C2×(C2×D11)⋊C4C2×C411yescharacteristic
84C2×(C2×D11)⋊C4C2×C411yescharacteristic
85C2×(C2×D11)⋊C4C2×C411yescharacteristic
86C2×C4⋊Dic11C2×C411yescharacteristic
87C2×C4⋊Dic11C2×C411yescharacteristic
88C2×C4⋊Dic11C2×C411yescharacteristic
89C2×Dic11⋊C4C2×C411yescharacteristic
90C2×Dic11⋊C4C2×C411yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C2×#4313—41no—
97C2×#4313—41no—
98C2×#4313—41no—
99C2×#4313—41no—
100C2×#4313—41no—
101C2×#4313—41no—
102C4×D44—41no—
103C4×D44—41no—
104C4×D44—41no—
105C4×D44—41no—
106C4×D44—41no—
107C4×D44—41no—
108#66925—41no—
109#66925—41no—
110C11×C4⋊C8—41no—
111C11×#97—41no—
112C11×#95C2×C411yescharacteristic
113C11×#95C2×C411yescharacteristic
114C11⋊#95C2×C411yescharacteristic
115C11⋊#95C2×C411yescharacteristic
116C11⋊#95C2×C411yescharacteristic
117C11⋊#95C2×C411yescharacteristic
118(C2×D11)⋊C8—41no—
119(C2×D11)⋊C8—41no—
120(C2×D11)⋊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—
129Dic11⋊C8—41no—
130C4⋊(C11⋊C8)—41no—
131C4×C11⋊C8—41no—
132#23332—111nomaximal, Sylow
133C23×D11C22×C411yescharacteristic
134C23×D11C22×C411yescharacteristic
135C23×D11C22×C411yescharacteristic
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C22×C411yescharacteristic
141C22×C4×C11C22×C411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C22×Dic11C22×C411yescharacteristic
144C22×Dic11C22×C411yescharacteristic
145C22×Dic11C22×C411yescharacteristic
146C22×Dic11C22×C411yescharacteristic
147C22×Dic11C22×C411yescharacteristic
148C2×D44—22no—
149C2×D44—41no—
150C2×D44—41no—
151C2×D44—41no—
152C2×D44—41no—
153C2×D44—41no—
154C2×D44—41no—
155C2×D44—41no—
156C2×D44—41no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
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—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—41no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195(C2×D11)⋊C4—22no—
196(C2×D11)⋊C4—41no—
197(C2×D11)⋊C4—41no—
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—
204(C2×D11)⋊C4—41no—
205(C2×D11)⋊C4—41no—
206(C2×D11)⋊C4—41no—
207C4⋊Dic11—41no—
208C4⋊Dic11—41no—
209C4⋊Dic11—41no—
210Dic11⋊C4—41no—
211Dic11⋊C4—41no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C2×C11⋊C8—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—
226#4313—44no—
227#4313—44no—
228#2392—111no—
229#1955—111no—
230#1954—111no—
231#1924—111no—
232#1923—111no—
233#1917D1111yescharacteristic, complemented
234#1916—111no—
235#1870—111no—
236#1870—111no—
237#1870—111no—
238#1870—111no—
239#1851—111no—
240#1851—111no—
241#1818—111no—
242#1798—111no—
243C23×C11C23×C411yescharacteristic
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
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—21no—
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—21no—
281C2×C4×C11—21no—
282C2×C4×C11#13112yes—
283C2×C4×C11H(5,𝔽2)11yescharacteristic
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×C112−1+411yescharacteristic
289C2×Dic11—21no—
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—
304D44—44no—
305D44—44no—
306D44—44no—
307C4×D11—41no—
308C4×D11—41no—
309C4×D11—41no—
310C4×D11—41no—
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—
327C22×M16—111no—
328C22×M16—111no—
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⋊C8—111no—
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⋊C8—111no—
347C2×#97C2×D1111yescharacteristic
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⋊C4C2×D1111yescharacteristic
358C4×C22⋊C4—111no—
359C4×C22⋊C4—111no—
360#336—111no—
361#336—111no—
362#336—111no—
363#336—111no—
364#336—111no—
365#336—111no—
366#336C2×D1111yescharacteristic
367#336C2×D1111yescharacteristic
368#336C2×D1111yescharacteristic
369#336C2×D1111yescharacteristic
370C22×C11#51811yescharacteristic
371C22×C11#51811yescharacteristic
372C22×C11#52011yescharacteristic
373C22×C11C2×#13111yescharacteristic
374C22×C11#56811yescharacteristic
375C22×C11#56811yescharacteristic
376C22×C11#56811yescharacteristic
377C2×D11—41no—
378C2×D11—41no—
379C2×D11—41no—
380C2×D11—41no—
381C2×D11—41no—
382C2×D11—41no—
383C2×D11—41no—
384C2×D11—41no—
385C2×D11—41no—
386C2×D11—41no—
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—22no—
399C4×C11—41no—
400C4×C11—41no—
401C4×C11—41no—
402C4×C11—41no—
403C4×C11—41no—
404C4×C11#56011yescharacteristic
405C4×C11#56011yescharacteristic
406C4×C11#56211yescharacteristic
407C4×C11#56211yescharacteristic
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×C4—111no—
419C2×M16—441no—
420C2×M16—441no—
421C2×M16—441no—
422C2×M16—441no—
423C2×M16—441no—
424C2×M16—441no—
425C22×C8—111no—
426C22×C8—111no—
427C22×C8—111no—
428C22×C8—111no—
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⋊C4C4×D1111yescharacteristic
447C2×C4⋊C4C4×D1111yescharacteristic
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⋊C4—111no—
459C2×C22⋊C4—111no—
460C2×C42—111no—
461C2×C42C22×D1111yescharacteristic
462C2×C42C22×D1111yescharacteristic
463C2×C42C22×D1111yescharacteristic
464C4⋊C8—41no—
465C4⋊C8—441no—
466C4⋊C8—441no—
467C4⋊C8—441no—
468C22⋊C8—441no—
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—41no—
479C4×C8—441no—
480#95—111no—
481#95—111no—
482#95—111no—
483#95—111no—
484#95C4×D1111yescharacteristic
485#95C4×D1111yescharacteristic
486C2×C11#237711yescharacteristic
487C2×C11#297611yescharacteristic
488C2×C11#297811yescharacteristic
489C2×C11#297811yescharacteristic
490C2×C11#298111yescharacteristic
491C2×C11#299311yescharacteristic
492C2×C11#299511yescharacteristic
493D11—81no—
494D11—81no—
495D11—81no—
496C24—111no—
497C24—111no—
498C24—111no—
499C2×D4—222no—
500C2×D4—441no—
501C2×D4—441no—
502C2×D4—441no—
503C2×D4—441no—
504C2×D4—441no—
505C2×D4—441no—
506C2×D4—441no—
507C2×D4—441no—
508C22×C4—111no—
509C22×C4—111no—
510C22×C4—111no—
511C22×C4—111no—
512C22×C4—111no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
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×C4C2×C4×D1111yescharacteristic
532C22×C4C2×C4×D1111yescharacteristic
533C22×C4C2×C4×D1111yescharacteristic
534C22×C4C2×C4×D1111yescharacteristic
535C22×C4C2×C4×D1111yescharacteristic
536C22×C4C2×C4×D1111yescharacteristic
537C22×C4C23×D1111yescharacteristic
538M16—444no—
539M16—444no—
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—21no—
551C2×C8—21no—
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—221no—
564C4⋊C4—22no—
565C4⋊C4—41no—
566C4⋊C4—441no—
567C4⋊C4—441no—
568C4⋊C4—441no—
569C4⋊C4—441no—
570C4⋊C4—441no—
571C22⋊C4—222no—
572C22⋊C4—441no—
573C22⋊C4—441no—
574C22⋊C4—441no—
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—21no—
588C42—21no—
589C42—221no—
590C42—221no—
591C11#2333211yescharacteristic, complemented, Sylow
592C23—221no—
593C23—221no—
594C23—221no—
595C23—221no—
596C23—221no—
597C23—221no—
598C23—221no—
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—221no—
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—21no—
633C2×C4—21no—
634C2×C4—221no—
635C2×C4—221no—
636C2×C4—221no—
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—441no—
650C2×C4—441no—
651C2×C4—441no—
652C2×C4—441no—
653C2×C4—441no—
654C2×C4—441no—
655C2×C4—441no—
656C2×C4—441no—
657C2×C4—441no—
658C2×C4—441no—
659C2×C4—441no—
660C2×C4—441no—
661C2×C4#6696012yes—
662C2×C4#6703711yescharacteristic
663C2×C4#6704011yescharacteristic
664C2×C4#6704211yescharacteristic
665C2×C4#6704211yescharacteristic
666C2×C4#6704211yescharacteristic
667C2×C4#6704211yescharacteristic
668C8—41no—
669C8—41no—
670C8—41no—
671C8—41no—
672C8—441no—
673C8—441no—
674C8—441no—
675C8—441no—
676C22—441no—
677C22—441no—
678C22—441no—
679C22—441no—
680C22—441no—
681C22—441no—
682C22—441no—
683C22—441no—
684C22—441no—
685C22—441no—
686C22—441no—
687C22—441no—
688C22—441no—
689C22—441no—
690C22—441no—
691C22—441no—
692C22—441no—
693C22—441no—
694C22—441no—
695C22—441no—
696C22—441no—
697C22#1062305211yescharacteristic
698C22#1062307611yescharacteristic
699C22#1062310511yescharacteristic
700C22C2×#6696011yescharacteristic
701C22#1062327611yescharacteristic
702C22#1062328111yescharacteristic
703C22#1062328111yescharacteristic
704C4—22no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—41no—
710C4—441no—
711C4—441no—
712C4—441no—
713C4—441no—
714C4—441no—
715C4#1062317811yescharacteristic
716C4#1062319711yescharacteristic
717C4#1062323111yescharacteristic
718C4#1062324211yescharacteristic
719C2—881no—
720C2—881no—
721C2—881no—
722C2#1307177111yescharacteristic
723C2#1307766511yescharacteristic
724C2#1307767311yescharacteristic
725C2#1307767711yescharacteristic
726C2#1307769411yescharacteristic
727C2#1307776811yescharacteristic
728C2#1307778511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1917C2
prime radical#10622284C4
cosocleC22×C4×C11C24
hypercenter#1917D11
hypocenterC11#23332
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1917

Complements

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

NH ≅ G/Ntype
2. #13069414C2semidirect
3. #13069409C2semidirect
4. #13069229C2semidirect
5. #13069220C2semidirect
6. #13069175C2semidirect
7. #13068912C2semidirect
8. #13068912C2semidirect
9. #13068912C2semidirect
10. #13068912C2semidirect
11. #13068800C2semidirect
12. #13068797C2semidirect
13. #13068686C2semidirect
14. #13068599C2semidirect
15. C11×#1917C2semidirect
233. #1917D11semidirect
591. C11#23332semidirect

Maximal subgroups

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

subgroupindex
#130718562
#130694142
#130694092
#130692292
#130692202
#130691752
#130689122
#130688002
#130687972
#130686862
#130685992
C11×#19172
#2333211