Finite Group Databasebeta

← #14780056

Subgroups — #14780056

Order 2816.

854 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66983C211yesmaximal, characteristic
2#13069412C211yesmaximal, characteristic, complemented
3#13069408C211yesmaximal, characteristic, complemented
4#13069228C211yesmaximal, characteristic, complemented
5#13069221C211yesmaximal, characteristic, complemented
6#13069181C211yesmaximal, characteristic, complemented
7#13069174C211yesmaximal, characteristic, complemented
8#13068912C211yesmaximal, characteristic, complemented
9#13068910C211yesmaximal, characteristic, complemented
10#13068907C211yesmaximal, characteristic, complemented
11#13068905C211yesmaximal, characteristic, complemented
12#13068797C211yesmaximal, characteristic, complemented
13#13068792C211yesmaximal, characteristic, complemented
14#13068684C211yesmaximal, characteristic, complemented
15C11×#1797C211yesmaximal, characteristic, complemented
16C22×C42×C11C2211yescharacteristic
17C2×#66983C411yescharacteristic
18C2×C4×C22⋊D11C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622826C411yescharacteristic
28#10622826C411yescharacteristic
29#10622825C411yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×#66879C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41C2×C8×Dic11C2211yescharacteristic
42#10622553C411yescharacteristic
43#10622553C411yescharacteristic
44#10622552C411yescharacteristic
45C4×(C2×D11)⋊C4C2211yescharacteristic
46C4×(C2×D11)⋊C4C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48#10622541C411yescharacteristic
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C23×C4×C11C2×C411yescharacteristic
60C23×C4×C11C2×C411yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11C2×C411yescharacteristic
63C22×C22⋊D11C2×C411yescharacteristic
64C22×D44C2×C411yescharacteristic
65C22×C4×D11C2311yescharacteristic
66C22×C4×D11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C2×C42×C11—41no—
72C2×C42×C11—41no—
73C2×C42×C11C2×C411yescharacteristic
74C2×C42×C11C2×C411yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11C2×C411yescharacteristic
78C2×C22⋊Dic11C2×C411yescharacteristic
79#66983—24no—
80C4×C22⋊D11—41no—
81C4×C22⋊D11—41no—
82C4×C22⋊D11—41no—
83C4×C22⋊D11—41no—
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×(C2×D11)⋊C4C2×C411yescharacteristic
92C2×C4⋊Dic11C2×C411yescharacteristic
93C2×C4⋊Dic11C2×C411yescharacteristic
94C2×C4⋊Dic11C2×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×#4313—41no—
104C2×#4313—41no—
105C2×#4313—41no—
106C2×C8×D11—41no—
107C2×C8×D11—41no—
108C2×C8×D11—41no—
109C4×D44—41no—
110C4×D44—41no—
111C11×C4⋊C8—41no—
112C11×C4⋊C8—41no—
113C11×C22⋊C8—41no—
114C11×C22⋊C8—41no—
115C11⋊#95C2×C411yescharacteristic
116C11⋊#95C2×C411yescharacteristic
117C11⋊#95C2×C411yescharacteristic
118C11⋊#95C2×C411yescharacteristic
119C11⋊#95C2×C411yescharacteristic
120C11⋊#95C2×C411yescharacteristic
121C22⋊(C11⋊C8)—41no—
122C22⋊(C11⋊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—
128(C2×D11)⋊C8—41no—
129#66879—41no—
130Dic11⋊C8—41no—
131Dic11⋊C8—41no—
132C8×Dic11—41no—
133#23331—111nomaximal, Sylow
134C24×C11C22×C411yescharacteristic
135C23×D11C22×C411yescharacteristic
136C23×D11C22×C411yescharacteristic
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—41no—
147C22×C4×C11—41no—
148C22×C4×C11—41no—
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—22no—
156C2×C22⋊D11—41no—
157C2×C22⋊D11—41no—
158C2×C22⋊D11—41no—
159C2×C22⋊D11—41no—
160C2×C22⋊D11M1614yescomplemented
161C22×Dic11C22×C411yescharacteristic
162C22×Dic11C22×C411yescharacteristic
163C22×Dic11C22×C411yescharacteristic
164C22×Dic11C22×C411yescharacteristic
165C22×Dic11C22×C411yescharacteristic
166C22×Dic11C22×C411yescharacteristic
167C2×D44—22no—
168C2×D44—22no—
169C2×D44—41no—
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C4×D11—21no—
174C2×C4×D11—21no—
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×C8×C11—21no—
183C2×C8×C11—21no—
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—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11—41no—
199C42×C11—41no—
200C22⋊Dic11—41no—
201C22⋊Dic11—41no—
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4—22no—
204(C2×D11)⋊C4—22no—
205(C2×D11)⋊C4—22no—
206(C2×D11)⋊C4—41no—
207(C2×D11)⋊C4—41no—
208(C2×D11)⋊C4—41no—
209(C2×D11)⋊C4—41no—
210C4⋊Dic11—22no—
211C4⋊Dic11—22no—
212C4⋊Dic11—41no—
213Dic11⋊C4—41no—
214Dic11⋊C4—41no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—21no—
218C4×Dic11—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—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231#4313—44no—
232C8×D11—44no—
233C4×#121—111no—
234#1955—111no—
235#1954—111no—
236#1924—111no—
237#1923—111no—
238#1917—111no—
239#1916—111no—
240#1870—111no—
241#1870—111no—
242#1869—111no—
243#1869—111no—
244#1851—111no—
245#1850—111no—
246#1817—111no—
247#1797D1111yescharacteristic, complemented
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11C2×M1612yes—
255C23×C11C23×C411yescharacteristic
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—
265C22×D11—21no—
266C22×D11—21no—
267C22×D11—21no—
268C22×D11—21no—
269C22×D11C2×M1612yes—
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—21no—
283C2×C4×C11—44no—
284C2×C4×C11—44no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11#13112yes—
290C2×C4×C11#13112yes—
291C2×C4×C11H(5,𝔽2)11yescharacteristic
292C2×C4×C11H(5,𝔽2)11yescharacteristic
293C2×C4×C11H(5,𝔽2)11yescharacteristic
294C2×C4×C11H(5,𝔽2)11yescharacteristic
295C2×C4×C11H(5,𝔽2)11yescharacteristic
296C2×C4×C112−1+411yescharacteristic
297C22⋊D11—44no—
298C22⋊D11—44no—
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×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11C2×M1612yes—
317D44—44no—
318C4×D11—41no—
319C4×D11—41no—
320C4×D11—41no—
321C4×D11—41no—
322C4×D11—41no—
323C4×D11—41no—
324C4×D11—41no—
325C4×D11—41no—
326C8×C11—41no—
327C8×C11—41no—
328C8×C11—41no—
329C8×C11—41no—
330C11⋊C8—41no—
331C11⋊C8—41no—
332C11⋊C8—41no—
333C11⋊C8—41no—
334C22×M16—111no—
335C23×C8—111no—
336C2×#121—111no—
337C2×C4×D4—111no—
338C2×C4×D4—111no—
339C2×C4×D4—111no—
340C22×C42C2×D1111yescharacteristic
341C2×C4⋊C8—111no—
342C2×C4⋊C8—111no—
343C2×C4⋊C8C2×D1111yescharacteristic
344C2×C4⋊C8C2×D1111yescharacteristic
345C2×C22⋊C8—111no—
346C2×C22⋊C8—111no—
347C2×C22⋊C8—111no—
348C2×C22⋊C8—111no—
349C2×C22⋊C8—111no—
350C2×C22⋊C8—111no—
351C2×C22⋊C8—111no—
352C2×C22⋊C8—111no—
353C2×C22⋊C8C2×D1111yescharacteristic
354C2×C22⋊C8C2×D1111yescharacteristic
355C2×#97—111no—
356C2×C4×C8—111no—
357#390—111no—
358#389—111no—
359#388—111no—
360#388—111no—
361#386—111no—
362#386—111no—
363#380—111no—
364C4×C4⋊C4—111no—
365C4×C22⋊C4—111no—
366C4×C22⋊C4—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#336C2×D1111yescharacteristic
376#336C2×D1111yescharacteristic
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—22no—
380C22×C11—41no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11#51811yescharacteristic
385C22×C11#51811yescharacteristic
386C22×C11#52011yescharacteristic
387C22×C11C22×M1611yescharacteristic
388C22×C11C2×#13111yescharacteristic
389C22×C11C2×#13111yescharacteristic
390C22×C11#56811yescharacteristic
391C2×D11—22no—
392C2×D11—22no—
393C2×D11—22no—
394C2×D11—41no—
395C2×D11—41no—
396C2×D11—41no—
397C2×D11—41no—
398C2×D11—41no—
399C2×D11—41no—
400C2×D11—41no—
401C2×D11—41no—
402C2×D11—41no—
403C2×D11—41no—
404C2×D11—41no—
405C4×C11—22no—
406C4×C11—22no—
407C4×C11—41no—
408C4×C11—41no—
409C4×C11—41no—
410C4×C11#56011yescharacteristic
411C4×C11#56011yescharacteristic
412C4×C11#56211yescharacteristic
413C4×C11#56211yescharacteristic
414Dic11—22no—
415Dic11—41no—
416Dic11—41no—
417Dic11—41no—
418Dic11—41no—
419Dic11—41no—
420C22×D4—111no—
421C22×D4—111no—
422C22×D4—111no—
423C23×C4—111no—
424C23×C4—111no—
425C23×C4C4×D1111yescharacteristic
426C23×C4C4×D1111yescharacteristic
427C23×C4C22×D1111yescharacteristic
428C2×M16—441no—
429C2×M16—441no—
430C2×M16—441no—
431C22×C8—111no—
432C22×C8—111no—
433C22×C8—111no—
434C22×C8—111no—
435C22×C8—441no—
436C22×C8—441no—
437C22×C8—441no—
438C22×C8C22×D1111yescharacteristic
439C22×C8C22×D1111yescharacteristic
440C22×C8C22×D1111yescharacteristic
441C22×C8C22×D1111yescharacteristic
442#121—224no—
443C4×D4—441no—
444C4×D4—441no—
445C4×D4—441no—
446C4×D4—441no—
447C4×D4—441no—
448C4×D4—441no—
449C2×C4⋊C4—111no—
450C2×C4⋊C4—111no—
451C2×C4⋊C4—111no—
452C2×C4⋊C4—111no—
453C2×C4⋊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×C22⋊C4—111no—
461C2×C22⋊C4—111no—
462C2×C22⋊C4—111no—
463C2×C22⋊C4—111no—
464C2×C42—41no—
465C2×C42—41no—
466C2×C42—111no—
467C2×C42—111no—
468C2×C42C4×D1111yescharacteristic
469C2×C42C4×D1111yescharacteristic
470C2×C42C22×D1111yescharacteristic
471C2×C42C22×D1111yescharacteristic
472C4⋊C8—41no—
473C4⋊C8—41no—
474C4⋊C8—441no—
475C4⋊C8—441no—
476C22⋊C8—41no—
477C22⋊C8—41no—
478C22⋊C8—441no—
479C22⋊C8—441no—
480C22⋊C8—441no—
481C22⋊C8—441no—
482C22⋊C8—441no—
483C22⋊C8—441no—
484C22⋊C8—441no—
485C22⋊C8—441no—
486#97—441no—
487C4×C8—441no—
488#95—111no—
489#95—111no—
490#95—111no—
491#95—111no—
492#95—111no—
493#95—111no—
494C2×C11—42no—
495C2×C11#237711yescharacteristic
496C2×C11#297311yescharacteristic
497C2×C11#297411yescharacteristic
498C2×C11#297611yescharacteristic
499C2×C11#297911yescharacteristic
500C2×C11#299011yescharacteristic
501C2×C11#299311yescharacteristic
502D11—42no—
503D11—81no—
504C24—111no—
505C24—111no—
506C24C2×C4×D1111yescharacteristic
507C2×D4—114no—
508C2×D4—222no—
509C2×D4—222no—
510C2×D4—222no—
511C2×D4—441no—
512C2×D4—441no—
513C2×D4—441no—
514C2×D4—441no—
515C2×D4—441no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—111no—
529C22×C4—111no—
530C22×C4—111no—
531C22×C4—111no—
532C22×C4—111no—
533C22×C4—111no—
534C22×C4—221no—
535C22×C4—221no—
536C22×C4—221no—
537C22×C4—221no—
538C22×C4—221no—
539C22×C4—221no—
540C22×C4—221no—
541C22×C4—221no—
542C22×C4—221no—
543C22×C4—221no—
544C22×C4—221no—
545C22×C4—221no—
546C22×C4C2×C4×D1111yescharacteristic
547C22×C4C2×C4×D1111yescharacteristic
548C22×C4C2×C4×D1111yescharacteristic
549C22×C4C2×C4×D1111yescharacteristic
550C22×C4C2×C4×D1111yescharacteristic
551C22×C4C23×D1111yescharacteristic
552M16—444no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—221no—
566C2×C8—221no—
567C2×C8—221no—
568C2×C8—221no—
569C2×C8—221no—
570C2×C8—221no—
571C2×C8—221no—
572C2×C8—221no—
573C2×C8—221no—
574C2×C8—221no—
575C2×C8—221no—
576C2×C8—221no—
577C2×C8—444no—
578C4⋊C4—222no—
579C4⋊C4—222no—
580C4⋊C4—441no—
581C4⋊C4—441no—
582C4⋊C4—441no—
583C22⋊C4—222no—
584C22⋊C4—222no—
585C22⋊C4—222no—
586C22⋊C4—222no—
587C22⋊C4—441no—
588C22⋊C4—441no—
589C22⋊C4—441no—
590C22⋊C4—441no—
591C22⋊C4—441no—
592C22⋊C4—441no—
593C42—21no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—41no—
598C42—41no—
599C42—221no—
600C42—221no—
601C42—221no—
602C42—221no—
603C11#2333111yescharacteristic, complemented, Sylow
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—112no—
611C23—221no—
612C23—221no—
613C23—221no—
614C23—221no—
615C23—221no—
616C23—221no—
617C23—221no—
618C23—221no—
619C23—221no—
620C23—221no—
621C23—221no—
622C23—221no—
623C23—221no—
624C23M16×D1112yes—
625C23C22×C4×D1111yescharacteristic
626D4—444no—
627D4—444no—
628D4—444no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—112no—
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—221no—
662C2×C4—221no—
663C2×C4—221no—
664C2×C4—221no—
665C2×C4—221no—
666C2×C4—441no—
667C2×C4—441no—
668C2×C4—441no—
669C2×C4—441no—
670C2×C4—441no—
671C2×C4—441no—
672C2×C4—441no—
673C2×C4—441no—
674C2×C4#6695412yes—
675C2×C4#6696012yes—
676C2×C4#6703711yescharacteristic
677C2×C4#6703711yescharacteristic
678C2×C4#6703711yescharacteristic
679C2×C4#6704011yescharacteristic
680C2×C4#6704211yescharacteristic
681C2×C4#6704211yescharacteristic
682C8—41no—
683C8—41no—
684C8—41no—
685C8—41no—
686C8—441no—
687C8—441no—
688C8—441no—
689C8—441no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—222no—
698C22—222no—
699C22—222no—
700C22—441no—
701C22—441no—
702C22—441no—
703C22—441no—
704C22—441no—
705C22—441no—
706C22—441no—
707C22—441no—
708C22—441no—
709C22—441no—
710C22—441no—
711C22#1062301711yescharacteristic
712C22#1062303511yescharacteristic
713C22#1062305211yescharacteristic
714C22C2×#6695411yescharacteristic
715C22C2×M16×D1111yescharacteristic
716C22C2×#6696011yescharacteristic
717C22#1062327611yescharacteristic
718C4—22no—
719C4—22no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—222no—
724C4—441no—
725C4—441no—
726C4—441no—
727C4—441no—
728C4—441no—
729C4#1062315111yescharacteristic
730C4#1062315111yescharacteristic
731C4#1062317811yescharacteristic
732C4#1062317811yescharacteristic
733C2—42no—
734C2—442no—
735C2—881no—
736C2#1307177011yescharacteristic
737C2#1307764411yescharacteristic
738C2#1307765211yescharacteristic
739C2#1307766111yescharacteristic
740C2#1307768211yescharacteristic
741C2#1307773811yescharacteristic
742C2#1307776111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1797C2
prime radicalC2×#66983C4
cosocleC22×C4×C11C24
hypercenter#1797D11
hypocenterC11#23331
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. #13069412C2semidirect
3. #13069408C2semidirect
4. #13069228C2semidirect
5. #13069221C2semidirect
6. #13069181C2semidirect
7. #13069174C2semidirect
8. #13068912C2semidirect
9. #13068910C2semidirect
10. #13068907C2semidirect
11. #13068905C2semidirect
12. #13068797C2semidirect
13. #13068792C2semidirect
14. #13068684C2semidirect
15. C11×#1797C2semidirect
160. C2×C22⋊D11M16semidirect
247. #1797D11semidirect
603. C11#23331semidirect

Maximal subgroups

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

subgroupindex
C4×#669832
#130694122
#130694082
#130692282
#130692212
#130691812
#130691742
#130689122
#130689102
#130689072
#130689052
#130687972
#130687922
#130686842
C11×#17972
#2333111