Finite Group Databasebeta

← #14779931

Subgroups — #14779931

Order 2816.

758 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069411C211yesmaximal, characteristic
2#13069340C211yesmaximal, characteristic, complemented
3#13069335C211yesmaximal, characteristic, complemented
4#13069231C211yesmaximal, characteristic, complemented
5#13069231C211yesmaximal, characteristic, complemented
6#13069224C211yesmaximal, characteristic, complemented
7#13069224C211yesmaximal, characteristic, complemented
8#13069175C211yesmaximal, characteristic, complemented
9#13069175C211yesmaximal, characteristic, complemented
10#13068914C211yesmaximal, characteristic
11#13068801C211yesmaximal, characteristic, complemented
12#13068801C211yesmaximal, characteristic, complemented
13#13068596C211yesmaximal, characteristic, complemented
14#13068596C211yesmaximal, characteristic, complemented
15C4×C11×#123C211yesmaximal, characteristic
16C2×C11×#123C411yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C11×#388C411yescharacteristic
21C11×#388C411yescharacteristic
22C11×#387C411yescharacteristic
23C11×#387C411yescharacteristic
24C11×#386C411yescharacteristic
25C11×#385C411yescharacteristic
26C11×#381C411yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C22⋊C4C2211yescharacteristic
30C4×C11×C22⋊C4C2211yescharacteristic
31C4×C11×C22⋊C4C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
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×C4⋊(C11⋊C8)C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47C2×C4×C11⋊C8C2211yescharacteristic
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
60C23×C4×C11C2×C411yescharacteristic
61C23×C4×C11C2×C411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C11×#123—24no—
65C4×D4×C11—41no—
66C4×D4×C11—41no—
67C2×C11×C4⋊C4C2×C411yescharacteristic
68C2×C11×C4⋊C4C2×C411yescharacteristic
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C11×C4⋊C4C2×C411yescharacteristic
71C2×C11×C4⋊C4C2×C411yescharacteristic
72C2×C11×C22⋊C4C2×C411yescharacteristic
73C2×C11×C22⋊C4C2×C411yescharacteristic
74C2×C11×C22⋊C4C2×C411yescharacteristic
75C2×C11×C22⋊C4C2×C411yescharacteristic
76C2×C11×C22⋊C4C2×C411yescharacteristic
77C2×C11×C22⋊C4C2×C411yescharacteristic
78C2×C11×C22⋊C4C2×C411yescharacteristic
79C2×C11×C22⋊C4C2×C411yescharacteristic
80C2×C42×C11—41no—
81C2×C42×C11—41no—
82C2×C42×C11C2×C411yescharacteristic
83C2×C42×C11C2×C411yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×#4318—41no—
90C2×#4318—41no—
91C2×#4318—41no—
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C11×#95C2×C411yescharacteristic
101C11×#95C2×C411yescharacteristic
102C11×#95C2×C411yescharacteristic
103C11×#95C2×C411yescharacteristic
104C11×#95C2×C411yescharacteristic
105C11×#95C2×C411yescharacteristic
106C11×#95C2×C411yescharacteristic
107C11×#95C2×C411yescharacteristic
108C11×#95C2×C411yescharacteristic
109C11×#95C2×C411yescharacteristic
110C22⋊(C11⋊C8)—41no—
111C22⋊(C11⋊C8)—41no—
112C22⋊(C11⋊C8)—41no—
113C22⋊(C11⋊C8)—41no—
114C22⋊(C11⋊C8)—41no—
115C22⋊(C11⋊C8)—41no—
116C22⋊(C11⋊C8)—41no—
117C4⋊(C11⋊C8)—41no—
118C4⋊(C11⋊C8)—41no—
119C4⋊(C11⋊C8)—41no—
120C4⋊(C11⋊C8)—41no—
121C4⋊(C11⋊C8)—41no—
122C4⋊(C11⋊C8)—41no—
123C4⋊(C11⋊C8)—41no—
124#66867—41no—
125C4×C11⋊C8—41no—
126C4×C11⋊C8—41no—
127#23320—111nomaximal, Sylow
128C24×C11C22×C411yescharacteristic
129C24×C11C22×C411yescharacteristic
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—41no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
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×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C22×C411yescharacteristic
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C22×C411yescharacteristic
160C22×C4×C11C22×C411yescharacteristic
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C22×C411yescharacteristic
163C22×C4×C11C2411yescharacteristic
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—41no—
167C11×C4⋊C4—41no—
168C11×C4⋊C4M1614yescomplemented
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—41no—
175C11×C22⋊C4—41no—
176C11×C22⋊C4—41no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—41no—
188C42×C11—41no—
189#4318—44no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—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—
214C4×#123D1111yescharacteristic
215#1954—111no—
216#1940—111no—
217#1939—111no—
218#1924—111no—
219#1924—111no—
220#1923—111no—
221#1923—111no—
222#1916—111no—
223#1916—111no—
224#1870—111no—
225#1851—111no—
226#1851—111no—
227#1797—111no—
228#1797—111no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11#13112yes—
243C23×C11C23×C411yescharacteristic
244D4×C11—44no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—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—44no—
278C2×C4×C11—44no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11C2×M1612yes—
288C2×C4×C11C2×M1612yes—
289C2×C4×C11C2×M1612yes—
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×C112−1+411yescharacteristic
296C2×C4×C112−1+411yescharacteristic
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C11⋊C8—41no—
305C22×M16—111no—
306C2×#123Dic1111yescharacteristic
307C2×C4×D4C2×D1111yescharacteristic
308C22×C42C2×D1111yescharacteristic
309C2×C4⋊C8—111no—
310C2×C4⋊C8—111no—
311C2×C4⋊C8—111no—
312C2×C4⋊C8—111no—
313C2×C4⋊C8—111no—
314C2×C4⋊C8—111no—
315C2×C4⋊C8—111no—
316C2×C22⋊C8—111no—
317C2×C22⋊C8—111no—
318C2×C22⋊C8—111no—
319C2×C22⋊C8—111no—
320C2×C22⋊C8—111no—
321C2×C22⋊C8—111no—
322C2×C22⋊C8—111no—
323C2×#97—111no—
324C2×C4×C8—111no—
325C2×C4×C8—111no—
326#388Dic1111yescharacteristic
327#388Dic1111yescharacteristic
328#387Dic1111yescharacteristic
329#387Dic1111yescharacteristic
330#386Dic1111yescharacteristic
331#385Dic1111yescharacteristic
332#381Dic1111yescharacteristic
333C4×C4⋊C4C2×D1111yescharacteristic
334C4×C4⋊C4C2×D1111yescharacteristic
335C4×C22⋊C4C2×D1111yescharacteristic
336C4×C22⋊C4C2×D1111yescharacteristic
337C4×C22⋊C4C2×D1111yescharacteristic
338#336—111no—
339#336—111no—
340#336—111no—
341#336—111no—
342#336—111no—
343#336—111no—
344#336—111no—
345#336—111no—
346#336—111no—
347#336—111no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11#51811yescharacteristic
363C22×C11#52011yescharacteristic
364C22×C11#52011yescharacteristic
365C22×C11C22×M1611yescharacteristic
366C22×C11C2×#13111yescharacteristic
367C22×C11C2×#13111yescharacteristic
368C22×C11#56811yescharacteristic
369C4×C11—22no—
370C4×C11—22no—
371C4×C11—22no—
372C4×C11—22no—
373C4×C11—41no—
374C4×C11—41no—
375C4×C11—41no—
376C4×C11—41no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11—41no—
380C4×C11—41no—
381C4×C11#56011yescharacteristic
382C4×C11#56211yescharacteristic
383C4×C11#56211yescharacteristic
384C4×C11#56311yescharacteristic
385C22×D4C2×Dic1111yescharacteristic
386C23×C4C2×Dic1111yescharacteristic
387C23×C4C2×Dic1111yescharacteristic
388C23×C4C22×D1111yescharacteristic
389C23×C4C22×D1111yescharacteristic
390C2×M16—441no—
391C2×M16—441no—
392C2×M16—441no—
393C22×C8—111no—
394C22×C8—111no—
395C22×C8—111no—
396C22×C8—111no—
397C22×C8—111no—
398C22×C8—111no—
399C22×C8—111no—
400C22×C8—111no—
401#123—24no—
402C4×D4—41no—
403C4×D4—41no—
404C2×C4⋊C4C2×Dic1111yescharacteristic
405C2×C4⋊C4C2×Dic1111yescharacteristic
406C2×C4⋊C4C2×Dic1111yescharacteristic
407C2×C4⋊C4C2×Dic1111yescharacteristic
408C2×C4⋊C4C2×Dic1111yescharacteristic
409C2×C22⋊C4C2×Dic1111yescharacteristic
410C2×C22⋊C4C2×Dic1111yescharacteristic
411C2×C22⋊C4C2×Dic1111yescharacteristic
412C2×C22⋊C4C2×Dic1111yescharacteristic
413C2×C22⋊C4C2×Dic1111yescharacteristic
414C2×C22⋊C4C2×Dic1111yescharacteristic
415C2×C22⋊C4C2×Dic1111yescharacteristic
416C2×C22⋊C4C2×Dic1111yescharacteristic
417C2×C42—41no—
418C2×C42—41no—
419C2×C42C2×Dic1111yescharacteristic
420C2×C42C2×Dic1111yescharacteristic
421C2×C42C22×D1111yescharacteristic
422C2×C42C22×D1111yescharacteristic
423C2×C42C22×D1111yescharacteristic
424C2×C42C22×D1111yescharacteristic
425C2×C42C22×D1111yescharacteristic
426C4⋊C8—441no—
427C4⋊C8—441no—
428C4⋊C8—441no—
429C4⋊C8—441no—
430C4⋊C8—441no—
431C4⋊C8—441no—
432C4⋊C8—441no—
433C22⋊C8—441no—
434C22⋊C8—441no—
435C22⋊C8—441no—
436C22⋊C8—441no—
437C22⋊C8—441no—
438C22⋊C8—441no—
439C22⋊C8—441no—
440#97—441no—
441C4×C8—441no—
442C4×C8—441no—
443#95C2×Dic1111yescharacteristic
444#95C2×Dic1111yescharacteristic
445#95C2×Dic1111yescharacteristic
446#95C2×Dic1111yescharacteristic
447#95C2×Dic1111yescharacteristic
448#95C2×Dic1111yescharacteristic
449#95C2×Dic1111yescharacteristic
450#95C2×Dic1111yescharacteristic
451#95C2×Dic1111yescharacteristic
452#95C2×Dic1111yescharacteristic
453C2×C11—42no—
454C2×C11—81no—
455C2×C11#237611yescharacteristic
456C2×C11#297411yescharacteristic
457C2×C11#297611yescharacteristic
458C2×C11#298911yescharacteristic
459C2×C11#299111yescharacteristic
460C2×C11#299211yescharacteristic
461C2×C11#299411yescharacteristic
462C24C22×Dic1111yescharacteristic
463C24C22×Dic1111yescharacteristic
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—41no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4C22×Dic1111yescharacteristic
486C22×C4C22×Dic1111yescharacteristic
487C22×C4C22×Dic1111yescharacteristic
488C22×C4C22×Dic1111yescharacteristic
489C22×C4C22×Dic1111yescharacteristic
490C22×C4C22×Dic1111yescharacteristic
491C22×C4C22×Dic1111yescharacteristic
492C22×C4C22×Dic1111yescharacteristic
493C22×C4C22×Dic1111yescharacteristic
494C22×C4C22×Dic1111yescharacteristic
495C22×C4C22×Dic1111yescharacteristic
496C22×C4C22×Dic1111yescharacteristic
497C22×C4C23×D1111yescharacteristic
498M16—444no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C4⋊C4#431814yescomplemented
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4—41no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—41no—
547C42—41no—
548C11#2332011yescharacteristic, complemented, Sylow
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23#6700112yes—
563C23C23×Dic1111yescharacteristic
564D4—44no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—44no—
598C2×C4—44no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4C2×#431812yes—
608C2×C4C2×#431812yes—
609C2×C4C2×#431812yes—
610C2×C4#6700112yes—
611C2×C4#6703711yescharacteristic
612C2×C4#6703711yescharacteristic
613C2×C4#6704211yescharacteristic
614C2×C4#6704211yescharacteristic
615C2×C4#6704311yescharacteristic
616C2×C4#6704311yescharacteristic
617C8—441no—
618C8—441no—
619C8—441no—
620C8—441no—
621C8—441no—
622C8—441no—
623C8—441no—
624C8—441no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22C22×#431811yescharacteristic
640C22#1062332911yescharacteristic
641C22C2×#6700111yescharacteristic
642C22C2×#6700111yescharacteristic
643C22#1062335011yescharacteristic
644C22#1062335811yescharacteristic
645C22#1062335811yescharacteristic
646C4—22no—
647C4—22no—
648C4—22no—
649C4—22no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4#1062318211yescharacteristic
659C4#1062319711yescharacteristic
660C4#1062319811yescharacteristic
661C4#1062319811yescharacteristic
662C2—42no—
663C2—81no—
664C2#1307176411yescharacteristic
665C2#1307765111yescharacteristic
666C2#1307766411yescharacteristic
667C2#1307773311yescharacteristic
668C2#1307774811yescharacteristic
669C2#1307775511yescharacteristic
670C2#1307777611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC4×C11×#123C2
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenterC4×#123D11
hypocenterC11#23320
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#123

Complements

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

NH ≅ G/Ntype
2. #13069340C2semidirect
3. #13069335C2semidirect
4. #13069231C2semidirect
5. #13069231C2semidirect
6. #13069224C2semidirect
7. #13069224C2semidirect
8. #13069175C2semidirect
9. #13069175C2semidirect
11. #13068801C2semidirect
12. #13068801C2semidirect
13. #13068596C2semidirect
14. #13068596C2semidirect
168. C11×C4⋊C4M16semidirect
527. C4⋊C4#4318semidirect
548. C11#23320semidirect

Maximal subgroups

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

subgroupindex
#130694112
#130693402
#130693352
#130692312
#130692242
#130691752
#130689142
#130688012
#130685962
C4×C11×#1232
#2332011