Finite Group Databasebeta

← #14780045

Subgroups — #14780045

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#13069415C211yesmaximal, characteristic, complemented
2#13069411C211yesmaximal, characteristic, complemented
3#13069231C211yesmaximal, characteristic, complemented
4#13069224C211yesmaximal, characteristic, complemented
5#13069182C211yesmaximal, characteristic, complemented
6#13069175C211yesmaximal, characteristic, complemented
7#13068909C211yesmaximal, characteristic, complemented
8#13068909C211yesmaximal, characteristic, complemented
9#13068909C211yesmaximal, characteristic, complemented
10#13068909C211yesmaximal, characteristic, complemented
11#13068796C211yesmaximal, characteristic, complemented
12#13068796C211yesmaximal, characteristic, complemented
13#13068687C211yesmaximal, characteristic, complemented
14#13068600C211yesmaximal, characteristic, complemented
15C11×#2392C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C11×#398C411yescharacteristic
23C11×#397C411yescharacteristic
24C11×#396C411yescharacteristic
25C11×#396C411yescharacteristic
26C11×#394C411yescharacteristic
27C11×#394C411yescharacteristic
28C11×#394C411yescharacteristic
29C11×#392C411yescharacteristic
30C4×C11×C4⋊C4C2211yescharacteristic
31C4×C11×C22⋊C4C2211yescharacteristic
32C4×C11×C22⋊C4C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47C2×#66867C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622162C2211yescharacteristic
50#10622162C2211yescharacteristic
51#10622162C2211yescharacteristic
52#10622162C2211yescharacteristic
53#10622162C2211yescharacteristic
54#10622162C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2×C411yescharacteristic
60C22×D4×C11C2×C411yescharacteristic
61C22×D4×C11C2×C411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C4×D4×C11—41no—
66C4×D4×C11—41no—
67C4×D4×C11—41no—
68C4×D4×C11—41no—
69C4×D4×C11—41no—
70C4×D4×C11—41no—
71C11×#117—41no—
72C11×#117—41no—
73C2×C11×C4⋊C4C2×C411yescharacteristic
74C2×C11×C4⋊C4C2×C411yescharacteristic
75C2×C11×C4⋊C4C2×C411yescharacteristic
76C2×C11×C4⋊C4C2×C411yescharacteristic
77C2×C11×C4⋊C4C2×C411yescharacteristic
78C2×C11×C4⋊C4C2×C411yescharacteristic
79C2×C11×C4⋊C4C2×C411yescharacteristic
80C2×C11×C22⋊C4C2×C411yescharacteristic
81C2×C11×C22⋊C4C2×C411yescharacteristic
82C2×C11×C22⋊C4C2×C411yescharacteristic
83C2×C11×C22⋊C4C2×C411yescharacteristic
84C2×C11×C22⋊C4C2×C411yescharacteristic
85C2×C11×C22⋊C4C2×C411yescharacteristic
86C2×C11×C22⋊C4C2×C411yescharacteristic
87C2×C11×C22⋊C4C2×C411yescharacteristic
88C2×C11×C22⋊C4C2×C411yescharacteristic
89C2×C11×C22⋊C4C2×C411yescharacteristic
90C2×C11×C22⋊C4C2×C411yescharacteristic
91C2×C11×C22⋊C4C2×C411yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C22×C11⋊C8—41no—
97C22×C11⋊C8—41no—
98C22×C11⋊C8—41no—
99C22×C11⋊C8—41no—
100C22×C11⋊C8—41no—
101C22×C11⋊C8—41no—
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C11×#95C2×C411yescharacteristic
111C11×#95C2×C411yescharacteristic
112C11×#95C2×C411yescharacteristic
113C11×#95C2×C411yescharacteristic
114C11×#95C2×C411yescharacteristic
115C11×#95C2×C411yescharacteristic
116C22⋊(C11⋊C8)—41no—
117C22⋊(C11⋊C8)—41no—
118C22⋊(C11⋊C8)—41no—
119C22⋊(C11⋊C8)—41no—
120C22⋊(C11⋊C8)—41no—
121C22⋊(C11⋊C8)—41no—
122C22⋊(C11⋊C8)—41no—
123C22⋊(C11⋊C8)—41no—
124C22⋊(C11⋊C8)—41no—
125C22⋊(C11⋊C8)—41no—
126C4⋊(C11⋊C8)—41no—
127C4⋊(C11⋊C8)—41no—
128C4⋊(C11⋊C8)—41no—
129C4⋊(C11⋊C8)—41no—
130#66867—41no—
131C4×C11⋊C8—41no—
132#23330—111nomaximal, Sylow
133C24×C11C22×C411yescharacteristic
134C24×C11C22×C411yescharacteristic
135C24×C11C22×C411yescharacteristic
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—41no—
142C2×D4×C11—41no—
143C2×D4×C11—41no—
144C2×D4×C11—41no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
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×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11C22×C411yescharacteristic
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C22×C411yescharacteristic
166C22×C4×C11C22×C411yescharacteristic
167C22×C4×C11C22×C411yescharacteristic
168C22×C4×C11C22×C411yescharacteristic
169C22×C4×C11C22×C411yescharacteristic
170C22×C4×C11C22×C411yescharacteristic
171C22×C4×C11C22×C411yescharacteristic
172C22×C4×C11C22×C411yescharacteristic
173C22×C4×C11C22×C411yescharacteristic
174C22×C4×C11C2411yescharacteristic
175C11×C4⋊C4—22no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4—41no—
178C11×C4⋊C4—41no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4—41no—
181C11×C4⋊C4—41no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—41no—
186C11×C22⋊C4—41no—
187C11×C22⋊C4—41no—
188C11×C22⋊C4—41no—
189C11×C22⋊C4—41no—
190C11×C22⋊C4—41no—
191C11×C22⋊C4—41no—
192C11×C22⋊C4—41no—
193C11×C22⋊C4—41no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11—21no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—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—
226C2×C11⋊C8—44no—
227C2×C11⋊C8—44no—
228#2392D1111yescharacteristic
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#1850—111no—
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—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11#13112yes—
263C23×C11#13112yes—
264C23×C11C23×C411yescharacteristic
265D4×C11—44no—
266D4×C11—44no—
267D4×C11—44no—
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—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—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11#13112yes—
313C2×C4×C11H(5,𝔽2)11yescharacteristic
314C2×C4×C11H(5,𝔽2)11yescharacteristic
315C2×C4×C11H(5,𝔽2)11yescharacteristic
316C2×C4×C11H(5,𝔽2)11yescharacteristic
317C2×C4×C11H(5,𝔽2)11yescharacteristic
318C2×C4×C112−1+411yescharacteristic
319C11⋊C8—41no—
320C11⋊C8—41no—
321C11⋊C8—41no—
322C11⋊C8—41no—
323C11⋊C8—41no—
324C11⋊C8—41no—
325C11⋊C8—41no—
326C11⋊C8—41no—
327C23×C8—111no—
328C23×C8—111no—
329C2×C4×D4C2×D1111yescharacteristic
330C2×C4×D4C2×D1111yescharacteristic
331C2×C4×D4C2×D1111yescharacteristic
332C2×#117C2×D1111yescharacteristic
333C2×C4⋊C8—111no—
334C2×C4⋊C8—111no—
335C2×C4⋊C8—111no—
336C2×C4⋊C8—111no—
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×#97—111no—
348C2×C4×C8—111no—
349#398Dic1111yescharacteristic
350#397Dic1111yescharacteristic
351#396Dic1111yescharacteristic
352#396Dic1111yescharacteristic
353#394Dic1111yescharacteristic
354#394Dic1111yescharacteristic
355#394Dic1111yescharacteristic
356#392Dic1111yescharacteristic
357C4×C4⋊C4C2×D1111yescharacteristic
358C4×C22⋊C4C2×D1111yescharacteristic
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#336—111no—
369#336—111no—
370C22×C11—22no—
371C22×C11—22no—
372C22×C11—22no—
373C22×C11—22no—
374C22×C11—22no—
375C22×C11—22no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11—41no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11—41no—
385C22×C11—41no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11#51811yescharacteristic
392C22×C11#51811yescharacteristic
393C22×C11#52011yescharacteristic
394C22×C11C2×#13111yescharacteristic
395C22×C11C2×#13111yescharacteristic
396C22×C11C2×#13111yescharacteristic
397C22×C11#56811yescharacteristic
398C4×C11—22no—
399C4×C11—41no—
400C4×C11—41no—
401C4×C11—41no—
402C4×C11—41no—
403C4×C11—41no—
404C4×C11—41no—
405C4×C11—41no—
406C4×C11—41no—
407C4×C11—41no—
408C4×C11—41no—
409C4×C11#56011yescharacteristic
410C4×C11#56011yescharacteristic
411C4×C11#56211yescharacteristic
412C4×C11#56211yescharacteristic
413C22×D4C2×Dic1111yescharacteristic
414C22×D4C2×Dic1111yescharacteristic
415C22×D4C2×Dic1111yescharacteristic
416C23×C4C22×D1111yescharacteristic
417C23×C4C22×D1111yescharacteristic
418C23×C4C22×D1111yescharacteristic
419C22×C8—111no—
420C22×C8—111no—
421C22×C8—111no—
422C22×C8—111no—
423C22×C8—111no—
424C22×C8—111no—
425C22×C8—111no—
426C22×C8—111no—
427C22×C8—441no—
428C22×C8—441no—
429C22×C8—441no—
430C22×C8—441no—
431C22×C8—441no—
432C22×C8—441no—
433C4×D4—41no—
434C4×D4—41no—
435C4×D4—41no—
436C4×D4—41no—
437C4×D4—41no—
438C4×D4—41no—
439#117—41no—
440#117—41no—
441C2×C4⋊C4C2×Dic1111yescharacteristic
442C2×C4⋊C4C2×Dic1111yescharacteristic
443C2×C4⋊C4C2×Dic1111yescharacteristic
444C2×C4⋊C4C2×Dic1111yescharacteristic
445C2×C4⋊C4C2×Dic1111yescharacteristic
446C2×C4⋊C4C2×Dic1111yescharacteristic
447C2×C4⋊C4C2×Dic1111yescharacteristic
448C2×C22⋊C4C2×Dic1111yescharacteristic
449C2×C22⋊C4C2×Dic1111yescharacteristic
450C2×C22⋊C4C2×Dic1111yescharacteristic
451C2×C22⋊C4C2×Dic1111yescharacteristic
452C2×C22⋊C4C2×Dic1111yescharacteristic
453C2×C22⋊C4C2×Dic1111yescharacteristic
454C2×C22⋊C4C2×Dic1111yescharacteristic
455C2×C22⋊C4C2×Dic1111yescharacteristic
456C2×C22⋊C4C2×Dic1111yescharacteristic
457C2×C22⋊C4C2×Dic1111yescharacteristic
458C2×C22⋊C4C2×Dic1111yescharacteristic
459C2×C22⋊C4C2×Dic1111yescharacteristic
460C2×C42C22×D1111yescharacteristic
461C2×C42C22×D1111yescharacteristic
462C2×C42C22×D1111yescharacteristic
463C2×C42C22×D1111yescharacteristic
464C4⋊C8—441no—
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—441no—
479C4×C8—441no—
480#95C2×Dic1111yescharacteristic
481#95C2×Dic1111yescharacteristic
482#95C2×Dic1111yescharacteristic
483#95C2×Dic1111yescharacteristic
484#95C2×Dic1111yescharacteristic
485#95C2×Dic1111yescharacteristic
486C2×C11—42no—
487C2×C11—42no—
488C2×C11—81no—
489C2×C11#237711yescharacteristic
490C2×C11#297611yescharacteristic
491C2×C11#297711yescharacteristic
492C2×C11#297711yescharacteristic
493C2×C11#298111yescharacteristic
494C2×C11#299211yescharacteristic
495C2×C11#299411yescharacteristic
496C24C22×Dic1111yescharacteristic
497C24C22×Dic1111yescharacteristic
498C24C22×Dic1111yescharacteristic
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—41no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4—41no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4C22×Dic1111yescharacteristic
527C22×C4C22×Dic1111yescharacteristic
528C22×C4C22×Dic1111yescharacteristic
529C22×C4C22×Dic1111yescharacteristic
530C22×C4C22×Dic1111yescharacteristic
531C22×C4C22×Dic1111yescharacteristic
532C22×C4C22×Dic1111yescharacteristic
533C22×C4C22×Dic1111yescharacteristic
534C22×C4C22×Dic1111yescharacteristic
535C22×C4C22×Dic1111yescharacteristic
536C22×C4C22×Dic1111yescharacteristic
537C22×C4C23×D1111yescharacteristic
538C2×C8—221no—
539C2×C8—221no—
540C2×C8—221no—
541C2×C8—221no—
542C2×C8—221no—
543C2×C8—221no—
544C2×C8—221no—
545C2×C8—221no—
546C2×C8—221no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
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—444no—
563C2×C8—444no—
564C4⋊C4—22no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—41no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C11#2333011yescharacteristic, complemented, Sylow
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23#6700112yes—
612C23#6700112yes—
613C23C23×Dic1111yescharacteristic
614D4—44no—
615D4—44no—
616D4—44no—
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—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—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4#6700112yes—
662C2×C4#6703711yescharacteristic
663C2×C4#6703711yescharacteristic
664C2×C4#6703711yescharacteristic
665C2×C4#6703711yescharacteristic
666C2×C4#6704211yescharacteristic
667C2×C4#6704311yescharacteristic
668C8—441no—
669C8—441no—
670C8—441no—
671C8—441no—
672C8—441no—
673C8—441no—
674C8—441no—
675C8—441no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22#1062332911yescharacteristic
698C22#1062332911yescharacteristic
699C22C2×#6700111yescharacteristic
700C22C2×#6700111yescharacteristic
701C22C2×#6700111yescharacteristic
702C22#1062335011yescharacteristic
703C22#1062335811yescharacteristic
704C4—22no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4#1062315111yescharacteristic
716C4#1062315111yescharacteristic
717C4#1062315211yescharacteristic
718C4#1062315211yescharacteristic
719C2—42no—
720C2—42no—
721C2—81no—
722C2#1307177311yescharacteristic
723C2#1307766411yescharacteristic
724C2#1307767211yescharacteristic
725C2#1307767211yescharacteristic
726C2#1307769211yescharacteristic
727C2#1307775511yescharacteristic
728C2#1307777611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#2392C2
prime radicalC11×#392C4
cosocleC22×C4×C11C24
hypercenter#2392D11
hypocenterC11#23330
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2392

Complements

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

NH ≅ G/Ntype
1. #13069415C2semidirect
2. #13069411C2semidirect
3. #13069231C2semidirect
4. #13069224C2semidirect
5. #13069182C2semidirect
6. #13069175C2semidirect
7. #13068909C2semidirect
8. #13068909C2semidirect
9. #13068909C2semidirect
10. #13068909C2semidirect
11. #13068796C2semidirect
12. #13068796C2semidirect
13. #13068687C2semidirect
14. #13068600C2semidirect
591. C11#23330semidirect

Maximal subgroups

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

subgroupindex
#130694152
#130694112
#130692312
#130692242
#130691822
#130691752
#130689092
#130687962
#130686872
#130686002
C11×#23922
#2333011