Finite Group Databasebeta

← #14761710

Subgroups — #14761710

Order 2816.

848 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622637C211yesmaximal, characteristic, complemented
2C2×#10622624C211yesmaximal, characteristic
3#13069553C211yesmaximal, characteristic, complemented
4#13069411C211yesmaximal, characteristic
5#13069231C211yesmaximal, characteristic, complemented
6#13069231C211yesmaximal, characteristic, complemented
7#13069224C211yesmaximal, characteristic, complemented
8#13069224C211yesmaximal, characteristic, complemented
9#13068736C211yesmaximal, characteristic, complemented
10#13068400C211yesmaximal, characteristic, complemented
11#13068400C211yesmaximal, characteristic, complemented
12#13068394C211yesmaximal, characteristic, complemented
13C22⋊C4×C11⋊C8C211yesmaximal, characteristic, complemented
14#13068303C211yesmaximal, characteristic, complemented
15C11×#2398C211yesmaximal, characteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19C23×C11⋊C8C2211yescharacteristic
20C11×#400C411yescharacteristic
21C11×#400C411yescharacteristic
22C11×#397C411yescharacteristic
23C11×#397C411yescharacteristic
24C11×#394C411yescharacteristic
25C11×#394C411yescharacteristic
26C11×#393C411yescharacteristic
27C11×#393C411yescharacteristic
28C4×C11×C22⋊C4C2211yescharacteristic
29C4×C11×C22⋊C4C2211yescharacteristic
30C4×C11×C22⋊C4C2211yescharacteristic
31C4×C11×C22⋊C4C2211yescharacteristic
32C11×#376C2211yescharacteristic
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
39#10622637—24no—
40#10622624—24no—
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45C2×#66867C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47C2×#66867C2211yescharacteristic
48C2×#66867C2211yescharacteristic
49C2×C4×C11⋊C8C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51C2×C4×C11⋊C8C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622162C2211yescharacteristic
54#10622162C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2×C411yescharacteristic
62C22×D4×C11C2×C411yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C11×C4⋊C4C2×C411yescharacteristic
71C2×C11×C4⋊C4C2×C411yescharacteristic
72C2×C11×C4⋊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×C11×C22⋊C4C2×C411yescharacteristic
81C2×C11×C22⋊C4C2×C411yescharacteristic
82C2×C11×C22⋊C4C2×C411yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×#4318—22no—
89C2×#4318—22no—
90C2×#4318—22no—
91C22×C11⋊C8—22no—
92C22×C11⋊C8—22no—
93C22×C11⋊C8—22no—
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C11×#95C2×C411yescharacteristic
103C11×#95C2×C411yescharacteristic
104C11×#95C2×C411yescharacteristic
105C11×#95C2×C411yescharacteristic
106C11×#95C2×C411yescharacteristic
107C11×#95C2×C411yescharacteristic
108C11×#95C2×C411yescharacteristic
109C11×#95C2×C411yescharacteristic
110C11×#95C2×C411yescharacteristic
111C11×#95C2×C411yescharacteristic
112C11×#95C2×C411yescharacteristic
113C11×#95C2×C411yescharacteristic
114C22⋊(C11⋊C8)—22no—
115C22⋊(C11⋊C8)—22no—
116C22⋊(C11⋊C8)—22no—
117C22⋊(C11⋊C8)—22no—
118C22⋊(C11⋊C8)—22no—
119C22⋊(C11⋊C8)—22no—
120C4⋊(C11⋊C8)—22no—
121C4⋊(C11⋊C8)—22no—
122C4⋊(C11⋊C8)—22no—
123C4⋊(C11⋊C8)—22no—
124#66867—22no—
125#66867—22no—
126#66867—22no—
127#66867D414yes—
128C4×C11⋊C8—22no—
129C4×C11⋊C8—22no—
130C4×C11⋊C8—22no—
131C4×C11⋊C8—22no—
132#21637—111nomaximal, Sylow
133C24×C11C22×C411yescharacteristic
134C24×C11C22×C411yescharacteristic
135C2×Q8×C11—22no—
136C2×Q8×C11—22no—
137C2×Q8×C11—41no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—41no—
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—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
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×C11C22×C411yescharacteristic
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C2411yescharacteristic
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—41no—
177C11×C22⋊C4—41no—
178C11×C22⋊C4—41no—
179C11×C22⋊C4—41no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11C2×D412yes—
189C42×C11#4112yes—
190#4318—44no—
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—44no—
210C2×C11⋊C8C2×D412yes—
211C2×C11⋊C8C2×D412yes—
212C2×C11⋊C8#4112yes—
213C2×C11⋊C8#4112yes—
214C2×C11⋊C8#4112yes—
215C2×C11⋊C8#4112yes—
216C2×#446—111no—
217C2×#435—111no—
218#2398D1111yescharacteristic
219#1984—111no—
220#1954—111no—
221#1924—111no—
222#1924—111no—
223#1923—111no—
224#1923—111no—
225#1832—111no—
226#1753—111no—
227#1753—111no—
228#1752—111no—
229C8×C22⋊C4—111no—
230#1726—111no—
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—21no—
243C23×C11—21no—
244C23×C11#13112yes—
245C23×C11C23×C411yescharacteristic
246Q8×C11—44no—
247D4×C11—44no—
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—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
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×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11C4×D412yes—
290C2×C4×C11C4×D412yes—
291C2×C4×C11#13112yes—
292C2×C4×C11C22×D411yescharacteristic
293C2×C4×C11C2×#4111yescharacteristic
294C2×C4×C11C2×#4111yescharacteristic
295C2×C4×C11C2×#4111yescharacteristic
296C2×C4×C11C2×#4111yescharacteristic
297C2×C4×C11C2×#4111yescharacteristic
298C11⋊C8—22no—
299C11⋊C8—22no—
300C11⋊C8—22no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C11⋊C8—41no—
305C11⋊C8#12414yes—
306C22×M16—111no—
307C23×C8—111no—
308C2×C4×Q8C2×D1111yescharacteristic
309C2×C4×D4C2×D1111yescharacteristic
310#446—224no—
311#435—224no—
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×#97—111no—
323C2×#97—111no—
324C2×#97—111no—
325C2×#97—111no—
326C2×C4×C8—111no—
327C2×C4×C8—111no—
328C2×C4×C8—111no—
329C2×C4×C8—111no—
330#400Dic1111yescharacteristic
331#400Dic1111yescharacteristic
332#397Dic1111yescharacteristic
333#397Dic1111yescharacteristic
334#394Dic1111yescharacteristic
335#394Dic1111yescharacteristic
336#393Dic1111yescharacteristic
337#393Dic1111yescharacteristic
338C4×C22⋊C4C2×D1111yescharacteristic
339C4×C22⋊C4C2×D1111yescharacteristic
340C4×C22⋊C4C2×D1111yescharacteristic
341C4×C22⋊C4C2×D1111yescharacteristic
342#376C2×D1111yescharacteristic
343#336—111no—
344#336—111no—
345#336—111no—
346#336—111no—
347#336—111no—
348#336—111no—
349#336—111no—
350#336—111no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
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—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11C2×C4×D411yescharacteristic
366C22×C11C4×#4111yescharacteristic
367C22×C11C4×#4111yescharacteristic
368C22×C11C2×#13111yescharacteristic
369C22×C11C2×#13111yescharacteristic
370C22×C11#56811yescharacteristic
371C22×C11#56811yescharacteristic
372C4×C11—22no—
373C4×C11—22no—
374C4×C11—22no—
375C4×C11—41no—
376C4×C11—41no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11—41no—
380C4×C11—41no—
381C4×C11—41no—
382C4×C11—41no—
383C4×C11—41no—
384C4×C11C2×#12411yescharacteristic
385C4×C11#52911yescharacteristic
386C4×C11#52911yescharacteristic
387C4×C11#53211yescharacteristic
388C22×Q8C2×Dic1111yescharacteristic
389C22×D4C2×Dic1111yescharacteristic
390C23×C4C22×D1111yescharacteristic
391C23×C4C22×D1111yescharacteristic
392C2×M16—222no—
393C2×M16—222no—
394C2×M16—222no—
395C22×C8—111no—
396C22×C8—111no—
397C22×C8—111no—
398C22×C8—111no—
399C22×C8—111no—
400C22×C8—111no—
401C22×C8—111no—
402C22×C8—111no—
403C22×C8—222no—
404C22×C8—222no—
405C22×C8—222no—
406C4×Q8—22no—
407C4×Q8—22no—
408C4×D4—22no—
409C4×D4—22no—
410C2×C4⋊C4C2×Dic1111yescharacteristic
411C2×C4⋊C4C2×Dic1111yescharacteristic
412C2×C4⋊C4C2×Dic1111yescharacteristic
413C2×C4⋊C4C2×Dic1111yescharacteristic
414C2×C22⋊C4C2×Dic1111yescharacteristic
415C2×C22⋊C4C2×Dic1111yescharacteristic
416C2×C22⋊C4C2×Dic1111yescharacteristic
417C2×C22⋊C4C2×Dic1111yescharacteristic
418C2×C22⋊C4C2×Dic1111yescharacteristic
419C2×C22⋊C4C2×Dic1111yescharacteristic
420C2×C22⋊C4C2×Dic1111yescharacteristic
421C2×C22⋊C4C2×Dic1111yescharacteristic
422C2×C22⋊C4C2×Dic1111yescharacteristic
423C2×C22⋊C4C2×Dic1111yescharacteristic
424C2×C42C22×D1111yescharacteristic
425C2×C42C22×D1111yescharacteristic
426C2×C42C22×D1111yescharacteristic
427C2×C42C22×D1111yescharacteristic
428C2×C42C22×D1111yescharacteristic
429C4⋊C8—222no—
430C4⋊C8—222no—
431C4⋊C8—222no—
432C4⋊C8—222no—
433C22⋊C8—222no—
434C22⋊C8—222no—
435C22⋊C8—222no—
436C22⋊C8—222no—
437C22⋊C8—222no—
438C22⋊C8—222no—
439#97—114no—
440#97—222no—
441#97—222no—
442#97—222no—
443C4×C8—222no—
444C4×C8—222no—
445C4×C8—222no—
446C4×C8—222no—
447#95C2×Dic1111yescharacteristic
448#95C2×Dic1111yescharacteristic
449#95C2×Dic1111yescharacteristic
450#95C2×Dic1111yescharacteristic
451#95C2×Dic1111yescharacteristic
452#95C2×Dic1111yescharacteristic
453#95C2×Dic1111yescharacteristic
454#95C2×Dic1111yescharacteristic
455#95C2×Dic1111yescharacteristic
456#95C2×Dic1111yescharacteristic
457#95C2×Dic1111yescharacteristic
458#95C2×Dic1111yescharacteristic
459C2×C11—42no—
460C2×C11—81no—
461C2×C11C4×#12411yescharacteristic
462C2×C11#293311yescharacteristic
463C2×C11#293311yescharacteristic
464C2×C11#296611yescharacteristic
465C2×C11#296711yescharacteristic
466C2×C11#296811yescharacteristic
467C2×C11#296911yescharacteristic
468C24C22×Dic1111yescharacteristic
469C24C22×Dic1111yescharacteristic
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—41no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—41no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
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×C4C22×Dic1111yescharacteristic
498C22×C4C22×Dic1111yescharacteristic
499C22×C4C22×Dic1111yescharacteristic
500C22×C4C23×D1111yescharacteristic
501M16—444no—
502C2×C8—112no—
503C2×C8—112no—
504C2×C8—112no—
505C2×C8—112no—
506C2×C8—112no—
507C2×C8—112no—
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—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—444no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42D4×D1112yes—
550C42#434112yes—
551C11#2163711yescharacteristic, complemented, Sylow
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23#6700112yes—
566C23C23×Dic1111yescharacteristic
567Q8—44no—
568D4—44no—
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—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4D4×Dic1112yes—
611C2×C4D4×Dic1112yes—
612C2×C4#6700112yes—
613C2×C4C2×D4×D1111yescharacteristic
614C2×C4C2×#434111yescharacteristic
615C2×C4#41×D1111yescharacteristic
616C2×C4#41×D1111yescharacteristic
617C2×C4#41×D1111yescharacteristic
618C2×C4#41×D1111yescharacteristic
619C8—114no—
620C8—222no—
621C8—222no—
622C8—222no—
623C8—441no—
624C8—441no—
625C8—441no—
626C8—441no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22C2×D4×Dic1111yescharacteristic
642C22C2×#6700111yescharacteristic
643C22C2×#6700111yescharacteristic
644C22#1062335011yescharacteristic
645C22#1062335011yescharacteristic
646C22#41×Dic1111yescharacteristic
647C22#41×Dic1111yescharacteristic
648C4—22no—
649C4—22no—
650C4—22no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—41no—
660C4#1062319911yescharacteristic
661C4D11×#12411yescharacteristic
662C4#1062321111yescharacteristic
663C4#1062321111yescharacteristic
664C2—42no—
665C2—81no—
666C2#124×Dic1111yescharacteristic
667C2#1307734311yescharacteristic
668C2#1307734311yescharacteristic
669C2#1307759211yescharacteristic
670C2#1307760311yescharacteristic
671C2#1307761211yescharacteristic
672C2#1307762111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#2398C2
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenter#2398D11
hypocenterC11#21637
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2398

Complements

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

NH ≅ G/Ntype
1. C2×#10622637C2semidirect
3. #13069553C2semidirect
5. #13069231C2semidirect
6. #13069231C2semidirect
7. #13069224C2semidirect
8. #13069224C2semidirect
9. #13068736C2semidirect
10. #13068400C2semidirect
11. #13068400C2semidirect
12. #13068394C2semidirect
13. C22⋊C4×C11⋊C8C2semidirect
14. #13068303C2semidirect
551. C11#21637semidirect

Maximal subgroups

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

subgroupindex
C2×#106226372
C2×#106226242
#130695532
#130694112
#130692312
#130692242
#130687362
#130684002
#130683942
C22⋊C4×C11⋊C82
#130683032
C11×#23982
#2163711