Finite Group Databasebeta

← #14780067

Subgroups — #14780067

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×#66937C211yesmaximal, characteristic
2#13069414C211yesmaximal, characteristic, complemented
3#13069408C211yesmaximal, characteristic, complemented
4#13069223C211yesmaximal, characteristic, complemented
5#13069180C211yesmaximal, characteristic, complemented
6#13069176C211yesmaximal, characteristic, complemented
7#13068912C211yesmaximal, characteristic, complemented
8#13068910C211yesmaximal, characteristic, complemented
9#13068906C211yesmaximal, characteristic, complemented
10#13068906C211yesmaximal, characteristic, complemented
11#13068797C211yesmaximal, characteristic, complemented
12#13068796C211yesmaximal, characteristic, complemented
13#13068683C211yesmaximal, characteristic, complemented
14#13068593C211yesmaximal, characteristic, complemented
15C11×#1924C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊D11C2211yescharacteristic
17C2×C4×C22⋊D11C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C2×#66937C411yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×#97C2211yescharacteristic
27C4×C11×C22⋊C4C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
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×(C2×D11)⋊C8C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38#10622570C411yescharacteristic
39#10622569C411yescharacteristic
40#10622564C411yescharacteristic
41C4×(C2×D11)⋊C4C2211yescharacteristic
42C4×Dic11⋊C4C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45#10622282C411yescharacteristic
46#10622280C411yescharacteristic
47#10622278C411yescharacteristic
48#10622260C411yescharacteristic
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×D11C2×C411yescharacteristic
64C22×C4×D11C2×C411yescharacteristic
65C22×C4×D11C2311yescharacteristic
66C22×C4×D11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C2×C11×C22⋊C4C2×C411yescharacteristic
72C2×C11×C22⋊C4C2×C411yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C22⋊Dic11C2×C411yescharacteristic
76C2×C22⋊Dic11C2×C411yescharacteristic
77C4×C22⋊D11—41no—
78C4×C22⋊D11—41no—
79C4×C22⋊D11—41no—
80C4×C22⋊D11—41no—
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×(C2×D11)⋊C4C2×C411yescharacteristic
87C2×C4⋊Dic11C2×C411yescharacteristic
88C2×Dic11⋊C4C2×C411yescharacteristic
89C2×Dic11⋊C4C2×C411yescharacteristic
90C2×Dic11⋊C4C2×C411yescharacteristic
91C2×Dic11⋊C4C2×C411yescharacteristic
92C2×C4×Dic11C2×C411yescharacteristic
93C2×C4×Dic11C2×C411yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C22×C11⋊C8—41no—
97C22×C11⋊C8—41no—
98C22×C11⋊C8—41no—
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C2×#4313—41no—
104C2×#4313—41no—
105C2×#4313—41no—
106#66937—24no—
107C4×D44—41no—
108C4×D44—41no—
109C42×D11—41no—
110C42×D11—41no—
111C11×C4⋊C8—41no—
112C11×C22⋊C8—41no—
113C11×C22⋊C8—41no—
114C11×#97—41no—
115C11×#95C2×C411yescharacteristic
116C11×#95C2×C411yescharacteristic
117C11⋊#95C2×C411yescharacteristic
118C11⋊#95C2×C411yescharacteristic
119C11⋊#95C2×C411yescharacteristic
120C11⋊#95C2×C411yescharacteristic
121C22⋊(C11⋊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—
128(C2×D11)⋊C8—41no—
129Dic11⋊C8—41no—
130C8×Dic11—41no—
131C4⋊(C11⋊C8)—41no—
132C4⋊(C11⋊C8)—41no—
133#23331—111nomaximal, Sylow
134C24×C11C22×C411yescharacteristic
135C23×D11C22×C411yescharacteristic
136C23×D11C22×C411yescharacteristic
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C2×C22⋊D11—22no—
150C2×C22⋊D11—22no—
151C2×C22⋊D11—41no—
152C2×C22⋊D11—41no—
153C2×C22⋊D11—41no—
154C2×C22⋊D11M1614yescomplemented
155C22×Dic11C22×C411yescharacteristic
156C22×Dic11C22×C411yescharacteristic
157C22×Dic11C22×C411yescharacteristic
158C22×Dic11C22×C411yescharacteristic
159C22×Dic11C22×C411yescharacteristic
160C22×Dic11C22×C411yescharacteristic
161C2×D44—22no—
162C2×D44—41no—
163C2×D44—41no—
164C2×C4×D11—22no—
165C2×C4×D11—22no—
166C2×C4×D11—22no—
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×C4×D11—21no—
176C2×C4×D11—21no—
177C2×C4×D11—21no—
178C2×C4×D11—21no—
179C2×C4×D11—41no—
180C2×C4×D11—41no—
181C2×C4×D11—41no—
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—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11—21no—
199C42×C11—21no—
200C22⋊Dic11—41no—
201C22⋊Dic11—41no—
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4—22no—
204(C2×D11)⋊C4—41no—
205(C2×D11)⋊C4—41no—
206(C2×D11)⋊C4—41no—
207(C2×D11)⋊C4—41no—
208C4⋊Dic11—41no—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—41no—
212Dic11⋊C4—41no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—41no—
218C4×Dic11—41no—
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—
231C2×C11⋊C8—44no—
232#4313—44no—
233C4×#121—111no—
234#1955—111no—
235#1954—111no—
236#1924D1111yescharacteristic, complemented
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#1797—111no—
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—21no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11#13112yes—
289C2×C4×C11H(5,𝔽2)11yescharacteristic
290C2×C4×C11H(5,𝔽2)11yescharacteristic
291C2×C4×C11H(5,𝔽2)11yescharacteristic
292C2×C4×C11H(5,𝔽2)11yescharacteristic
293C2×C4×C11H(5,𝔽2)11yescharacteristic
294C2×C4×C112−1+411yescharacteristic
295C22⋊D11—44no—
296C22⋊D11—44no—
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—21no—
310C2×Dic11—21no—
311C2×Dic11—21no—
312C2×Dic11—21no—
313C2×Dic11C2×M1612yes—
314C2×Dic11#13112yes—
315D44—44no—
316C4×D11—44no—
317C4×D11—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×C42—111no—
341C2×C4⋊C8—111no—
342C2×C4⋊C8—111no—
343C2×C4⋊C8—111no—
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×#97C2×D1111yescharacteristic
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⋊C4C2×D1111yescharacteristic
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—41no—
407C4×C11—41no—
408C4×C11—41no—
409C4×C11—41no—
410C4×C11#56011yescharacteristic
411C4×C11#56011yescharacteristic
412C4×C11#56211yescharacteristic
413C4×C11#56211yescharacteristic
414Dic11—22no—
415Dic11—22no—
416Dic11—41no—
417Dic11—41no—
418Dic11—41no—
419Dic11—41no—
420C22×D4—111no—
421C22×D4—111no—
422C22×D4—111no—
423C23×C4—111no—
424C23×C4—111no—
425C23×C4—111no—
426C23×C4—111no—
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⋊C4C4×D1111yescharacteristic
463C2×C22⋊C4C4×D1111yescharacteristic
464C2×C42—111no—
465C2×C42—111no—
466C2×C42—111no—
467C2×C42—111no—
468C2×C42—441no—
469C2×C42—441no—
470C2×C42C22×D1111yescharacteristic
471C2×C42C22×D1111yescharacteristic
472C4⋊C8—41no—
473C4⋊C8—441no—
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—41no—
487C4×C8—441no—
488#95—111no—
489#95—111no—
490#95—111no—
491#95—111no—
492#95C4×D1111yescharacteristic
493#95C4×D1111yescharacteristic
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—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—111no—
523C22×C4—111no—
524C22×C4—111no—
525C22×C4—111no—
526C22×C4—111no—
527C22×C4—111no—
528C22×C4—222no—
529C22×C4—222no—
530C22×C4—222no—
531C22×C4—221no—
532C22×C4—221no—
533C22×C4—221no—
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—441no—
544C22×C4—441no—
545C22×C4—441no—
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—22no—
584C22⋊C4—22no—
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—221no—
598C42—221no—
599C42—221no—
600C42—221no—
601C42—441no—
602C42—441no—
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—21no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—112no—
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—444no—
666C2×C4—444no—
667C2×C4—441no—
668C2×C4—441no—
669C2×C4—441no—
670C2×C4—441no—
671C2×C4—441no—
672C2×C4—441no—
673C2×C4—441no—
674C2×C4—441no—
675C2×C4#6696012yes—
676C2×C4#6703711yescharacteristic
677C2×C4#6703711yescharacteristic
678C2×C4#6704211yescharacteristic
679C2×C4#6704211yescharacteristic
680C2×C4#6704211yescharacteristic
681C2×C4#6704311yescharacteristic
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#1062305411yescharacteristic
712C22#1062307611yescharacteristic
713C22#1062307611yescharacteristic
714C22C2×M16×D1111yescharacteristic
715C22C2×#6696011yescharacteristic
716C22D11×#13111yescharacteristic
717C22#1062328111yescharacteristic
718C4—22no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—222no—
724C4—222no—
725C4—441no—
726C4—441no—
727C4—441no—
728C4—441no—
729C4#1062315111yescharacteristic
730C4#1062319811yescharacteristic
731C4#1062321511yescharacteristic
732C4#1062324211yescharacteristic
733C2—42no—
734C2—442no—
735C2—881no—
736C2#1307176911yescharacteristic
737C2#1307764111yescharacteristic
738C2#1307764611yescharacteristic
739C2#1307766511yescharacteristic
740C2#1307768111yescharacteristic
741C2#1307774311yescharacteristic
742C2#1307775911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1924C2
prime radicalC2×#66937C4
cosocleC22×C4×C11C24
hypercenter#1924D11
hypocenterC11#23331
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
2. #13069414C2semidirect
3. #13069408C2semidirect
4. #13069223C2semidirect
5. #13069180C2semidirect
6. #13069176C2semidirect
7. #13068912C2semidirect
8. #13068910C2semidirect
9. #13068906C2semidirect
10. #13068906C2semidirect
11. #13068797C2semidirect
12. #13068796C2semidirect
13. #13068683C2semidirect
14. #13068593C2semidirect
15. C11×#1924C2semidirect
154. C2×C22⋊D11M16semidirect
236. #1924D11semidirect
603. C11#23331semidirect

Maximal subgroups

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

subgroupindex
C4×#669372
#130694142
#130694082
#130692232
#130691802
#130691762
#130689122
#130689102
#130689062
#130687972
#130687962
#130686832
#130685932
C11×#19242
#2333111