Finite Group Databasebeta

← #15618920

Subgroups — #15618920

Order 2816.

1918 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077776C214yesmaximal, complemented
2#13077755C214yesmaximal, complemented
3#13077741C214yesmaximal, complemented
4#13077733C212yesmaximal, complemented
5#13077727C212yesmaximal, complemented
6#13077565C212yesmaximal, complemented
7#13077360C212yesmaximal, complemented
8#13077311C214yesmaximal, complemented
9#13077282C212yesmaximal, complemented
10#13077249C211yesmaximal, characteristic, complemented
11#13077184C212yesmaximal, complemented
12C22×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
13C11×#3444C211yesmaximal, characteristic
14C11×#533C411yescharacteristic
15C11×#533C411yescharacteristic
16C11×#533C2211yescharacteristic
17C11×#532C411yescharacteristic
18C11×#532C411yescharacteristic
19C11×#532C2211yescharacteristic
20C11×#529C412yes—
21C11×#529C412yes—
22C11×#529C412yes—
23C11×#529C412yes—
24C11×#529C2212yes—
25C11×#529C2212yes—
26C11×#525C412yes—
27C11×#525C412yes—
28C11×#525C2212yes—
29C4×C11×#41C2212yes—
30C4×C11×#41C2212yes—
31C4×C11×#41C2212yes—
32C22×C42×C11C2211yescharacteristic
33C2×#67001C2214yes—
34C23×C11⋊C8C2212yes—
35#10622847C2214yes—
36#10622820C2212yes—
37#10622637C2214yescomplemented
38#10622637C2218yescomplemented
39Q8×C11⋊C8C2214yescomplemented
40#10622625C2214yescomplemented
41#10622624C2218yes—
42#10622624C2218yes—
43#10622624C2218yescomplemented
44D4×C11⋊C8C2218yes—
45D4×C11⋊C8C2218yes—
46D4×C11⋊C8C2214yescomplemented
47#10622613C2218yescomplemented
48#10622612C2214yes—
49#10622612C2218yescomplemented
50#10622610C2214yes—
51#10622539C2212yes—
52#10622539C2212yes—
53#10622539C2214yescomplemented
54#10622538C2212yes—
55#10622538C2212yes—
56#10622538C2214yescomplemented
57#10622537C2211yescharacteristic
58#10622537C2211yescharacteristic
59#10622537C2214yescomplemented
60C2×C4⋊(C11⋊C8)C2212yes—
61C2×C4⋊(C11⋊C8)C2212yes—
62C2×C4⋊(C11⋊C8)C2212yes—
63C2×C4⋊(C11⋊C8)C2211yescharacteristic
64C2×C4⋊(C11⋊C8)C2211yescharacteristic
65C2×C4⋊(C11⋊C8)C2212yes—
66C2×C4⋊(C11⋊C8)C2212yes—
67C2×C4⋊(C11⋊C8)C2214yescomplemented
68C4×#4318C2212yes—
69C2×C11×#41C2×C412yes—
70C2×C11×#41C2×C412yes—
71C2×C11×#41C2312yes—
72C23×C4×C11C2×C411yescharacteristic
73C23×C4×C11C2×C411yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C11×C4⋊Q8C2×C411yescharacteristic
76C11×C4⋊Q8C2×C411yescharacteristic
77C11×C4⋊Q8C2×C411yescharacteristic
78C11×#127C2×C411yescharacteristic
79C11×#126C2×C414yes—
80C11×#126C2×C414yes—
81C11×#125C2×C412yes—
82C11×#125C2×C412yes—
83C11×#125C2×C412yes—
84C11×#124C2×C412yes—
85C11×#124C2×C412yes—
86C11×#124C2×C412yes—
87C11×#123C2×C414yes—
88C11×#123C2×C414yes—
89C11×#123C2×C414yes—
90C11×C22⋊Q8C2×C412yes—
91C11×C22⋊Q8C2×C412yes—
92C11×C22⋊Q8C2×C412yes—
93C11×C22⋊Q8C2×C412yes—
94C11×C22⋊Q8C2×C412yes—
95C11×C22⋊Q8C2×C412yes—
96C11×#121C2×C412yes—
97C11×#121C2×C412yes—
98C11×#121C2×C412yes—
99C11×#121C2×C412yes—
100C11×#121C2×C412yes—
101C11×#121C2×C412yes—
102C11×#120C2×C414yes—
103C4×Q8×C11C2×C412yes—
104C4×Q8×C11C2×C412yes—
105C4×Q8×C11C2×C412yes—
106C4×Q8×C11C2×C412yes—
107C4×Q8×C11C2312yes—
108C4×Q8×C11C2312yes—
109C4×D4×C11C2×C414yes—
110C4×D4×C11C2×C414yes—
111C4×D4×C11C2×C414yes—
112C4×D4×C11C2×C414yes—
113C4×D4×C11C2×C412yes—
114C4×D4×C11C2×C412yes—
115C4×D4×C11C2×C412yes—
116C4×D4×C11C2×C412yes—
117C4×D4×C11C2314yes—
118C4×D4×C11C2314yes—
119C4×D4×C11C2312yes—
120C4×D4×C11C2312yes—
121C11×#117C2×C412yes—
122C11×#117C2×C412yes—
123C11×#117C2×C414yes—
124C11×#117C2×C414yes—
125C11×#117C2312yes—
126C11×#117C2314yes—
127C2×C42×C11C2×C411yescharacteristic
128C2×C42×C11C2×C411yescharacteristic
129C2×C42×C11C2×C411yescharacteristic
130C2×C42×C11C2×C411yescharacteristic
131C2×C42×C11C2×C411yescharacteristic
132C2×C42×C11C2×C411yescharacteristic
133C2×C42×C11C2311yescharacteristic
134C2×C42×C11C2311yescharacteristic
135C2×C42×C11C2311yescharacteristic
136C2×C42×C11C2311yescharacteristic
137C2×C42×C11C2311yescharacteristic
138C2×C42×C11C2311yescharacteristic
139C2×C42×C11C2314yes—
140#67001—48no—
141C2×#4318C2312yes—
142C2×#4318C2312yes—
143C2×#4318C2318yes—
144C22×C11⋊C8—44no—
145C22×C11⋊C8C2314yes—
146C22×C11⋊C8C2312yes—
147C22×C11⋊C8C2314yes—
148C22×C11⋊C8C2312yes—
149C22×C11⋊C8C2318yes—
150C22⋊(C11⋊C8)C2314yes—
151C22⋊(C11⋊C8)C2314yes—
152C22⋊(C11⋊C8)C2318yes—
153C22⋊(C11⋊C8)C2318yes—
154C4⋊(C11⋊C8)C2312yes—
155C4⋊(C11⋊C8)C2312yes—
156C4⋊(C11⋊C8)C2314yes—
157C4⋊(C11⋊C8)C2312yes—
158C4⋊(C11⋊C8)C2314yes—
159C4⋊(C11⋊C8)C2312yes—
160C4⋊(C11⋊C8)C2312yes—
161C4⋊(C11⋊C8)C2318yes—
162C4⋊(C11⋊C8)C2312yes—
163C4⋊(C11⋊C8)C2312yes—
164C4⋊(C11⋊C8)C2312yes—
165C4⋊(C11⋊C8)C2318yes—
166#66867C2314yes—
167#66867C2318yes—
168C4×C11⋊C8C2314yes—
169C4×C11⋊C8C2318yes—
170#60265—111nomaximal, Sylow
171C24×C11C22×C411yescharacteristic
172C11×#41—28no—
173C11×#41—24no—
174C11×#41—24no—
175C11×#41—44no—
176C2×Q8×C11C22×C412yes—
177C2×Q8×C11C22×C412yes—
178C2×Q8×C11C22×C412yes—
179C2×D4×C11C22×C414yes—
180C2×D4×C11C22×C412yes—
181C2×D4×C11C22×C414yes—
182C2×D4×C11C22×C414yes—
183C2×D4×C11C22×C412yes—
184C2×D4×C11C22×C412yes—
185C22×C4×C11—24no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—42no—
189C22×C4×C11C22×C411yescharacteristic
190C22×C4×C11C22×C411yescharacteristic
191C22×C4×C11C22×C411yescharacteristic
192C22×C4×C11C22×C411yescharacteristic
193C22×C4×C11C22×C411yescharacteristic
194C22×C4×C11C22×C411yescharacteristic
195C22×C4×C11C22×C411yescharacteristic
196C22×C4×C11C22×C411yescharacteristic
197C22×C4×C11C22×C411yescharacteristic
198C22×C4×C11C22×C411yescharacteristic
199C22×C4×C11C22×C414yes—
200C22×C4×C11C22×C411yescharacteristic
201C22×C4×C11C22×C411yescharacteristic
202C22×C4×C11C22×C411yescharacteristic
203C22×C4×C11C22×C411yescharacteristic
204C22×C4×C11C22×C414yes—
205C22×C4×C11C22×C411yescharacteristic
206C22×C4×C11C2411yescharacteristic
207C22×C4×C11C2411yescharacteristic
208C22×C4×C11C2414yes—
209C22×C4×C11C2411yescharacteristic
210C11×C4⋊C4C22×C412yes—
211C11×C4⋊C4C22×C412yes—
212C11×C4⋊C4C22×C414yes—
213C11×C4⋊C4C22×C414yes—
214C11×C4⋊C4C22×C412yes—
215C11×C4⋊C4C22×C412yes—
216C11×C4⋊C4C22×C414yes—
217C11×C4⋊C4C22×C414yes—
218C11×C4⋊C4C22×C412yes—
219C11×C4⋊C4C22×C412yes—
220C11×C4⋊C4C22×C414yes—
221C11×C4⋊C4C22×C414yes—
222C11×C22⋊C4C22×C414yes—
223C11×C22⋊C4C22×C414yes—
224C11×C22⋊C4C22×C414yes—
225C11×C22⋊C4C22×C414yes—
226C11×C22⋊C4C22×C414yes—
227C11×C22⋊C4C22×C414yes—
228C11×C22⋊C4C22×C414yes—
229C11×C22⋊C4C22×C414yes—
230C11×C22⋊C4C22×C414yes—
231C42×C11C22×C411yescharacteristic
232C42×C11C22×C411yescharacteristic
233C42×C11C22×C411yescharacteristic
234C42×C11C22×C411yescharacteristic
235C42×C11C22×C411yescharacteristic
236C42×C11C22×C411yescharacteristic
237C42×C11C22×C411yescharacteristic
238C42×C11C22×C411yescharacteristic
239C42×C11C22×C411yescharacteristic
240C42×C11C22×C411yescharacteristic
241C42×C11C22×C411yescharacteristic
242C42×C11C22×C411yescharacteristic
243C42×C11C22×C414yes—
244C42×C11C22×C414yes—
245C42×C11C2411yescharacteristic
246C42×C11C2414yes—
247C42×C11C2411yescharacteristic
248C42×C11C2411yescharacteristic
249C42×C11C2411yescharacteristic
250#4318—24no—
251#4318—24no—
252#4318—48no—
253C2×C11⋊C8—28no—
254C2×C11⋊C8—42no—
255C2×C11⋊C8—44no—
256C2×C11⋊C8—42no—
257C2×C11⋊C8—48no—
258C2×C11⋊C8C2414yes—
259C2×C11⋊C8C2414yes—
260C2×C11⋊C8C2414yes—
261C2×C11⋊C8C2414yes—
262#3444D1111yescharacteristic
263#2994—114no—
264#2992—114no—
265#2990—114no—
266#2989—112no—
267#2988—112no—
268#2962—112no—
269#2935—112no—
270#2929—114no—
271#2925—112no—
272#2920—111no—
273#2906—112no—
274C22×C4⋊C8—111no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11C23×C414yes—
279C23×C11C23×C411yescharacteristic
280C23×C11C23×C411yescharacteristic
281C23×C11C23×C411yescharacteristic
282Q8×C11—24no—
283Q8×C11—24no—
284Q8×C11—42no—
285D4×C11—28no—
286D4×C11—28no—
287D4×C11—28no—
288D4×C11—24no—
289D4×C11—24no—
290D4×C11—42no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—28no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—24no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—24no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—44no—
313C2×C4×C11#13114yescomplemented
314C2×C4×C11C23×C411yescharacteristic
315C2×C4×C11C23×C411yescharacteristic
316C2×C4×C11C23×C411yescharacteristic
317C2×C4×C11C23×C411yescharacteristic
318C2×C4×C11C23×C411yescharacteristic
319C2×C4×C11C23×C411yescharacteristic
320C2×C4×C11C23×C411yescharacteristic
321C2×C4×C11C23×C411yescharacteristic
322C2×C4×C11C23×C414yes—
323C2×C4×C11C23×C414yes—
324C2×C4×C11C23×C414yes—
325C2×C4×C11C23×C411yescharacteristic
326C2×C4×C11C23×C411yescharacteristic
327C2×C4×C11C23×C411yescharacteristic
328C2×C4×C11H(5,𝔽2)12yes—
329C2×C4×C112−1+412yes—
330C2×C4×C11C2511yescharacteristic
331C11⋊C8—24no—
332C11⋊C8—24no—
333C11⋊C8—24no—
334C11⋊C8—24no—
335C2×#131—114no—
336C23×C8—112no—
337#533Dic1111yescharacteristic
338#533Dic1111yescharacteristic
339#533C2×D1111yescharacteristic
340#532Dic1111yescharacteristic
341#532Dic1111yescharacteristic
342#532C2×D1111yescharacteristic
343#529Dic1112yes—
344#529Dic1112yes—
345#529Dic1112yes—
346#529Dic1112yes—
347#529C2×D1112yes—
348#529C2×D1112yes—
349#525Dic1112yes—
350#525Dic1112yes—
351#525C2×D1112yes—
352C4×#41C2×D1112yes—
353C4×#41C2×D1112yes—
354C4×#41C2×D1112yes—
355C22×C42C2×D1111yescharacteristic
356#446—114no—
357#446—118no—
358C8×Q8—114no—
359#436—114no—
360#435—118no—
361#435—118no—
362#435—118no—
363C8×D4—118no—
364C8×D4—118no—
365C8×D4—114no—
366#433—118no—
367#432—112no—
368#432—112no—
369#432—114no—
370#431—112no—
371#431—112no—
372#431—114no—
373#424—114no—
374#424—118no—
375#423—111no—
376#423—111no—
377#423—114no—
378C2×C4⋊C8—112no—
379C2×C4⋊C8—112no—
380C2×C4⋊C8—111no—
381C2×C4⋊C8—111no—
382C2×C4⋊C8—112no—
383C2×C4⋊C8—112no—
384C2×C4⋊C8—112no—
385C2×C4⋊C8—114no—
386#408—114no—
387#407—112no—
388#405—114no—
389C4×M16—112no—
390C22×C11—28no—
391C22×C11—21no—
392C22×C11—21no—
393C22×C11—21no—
394C22×C11—21no—
395C22×C11—21no—
396C22×C11—21no—
397C22×C11—24no—
398C22×C11—24no—
399C22×C11—24no—
400C22×C11#52012yes—
401C22×C11C2×#13112yes—
402C22×C11#56812yes—
403C22×C11C24×C411yescharacteristic
404C4×C11—21no—
405C4×C11—21no—
406C4×C11—24no—
407C4×C11—21no—
408C4×C11—21no—
409C4×C11—24no—
410C4×C11—21no—
411C4×C11—21no—
412C4×C11—21no—
413C4×C11—21no—
414C4×C11—24no—
415C4×C11#52012yes—
416C4×C11C2×#13112yes—
417C4×C11C2×#13112yes—
418C4×C11C2×H(5,𝔽2)11yescharacteristic
419C4×C11C2×2−1+411yescharacteristic
420C2×#41C2×Dic1112yes—
421C2×#41C2×Dic1112yes—
422C2×#41C22×D1112yes—
423C23×C4C2×Dic1111yescharacteristic
424C23×C4C2×Dic1111yescharacteristic
425C23×C4C22×D1111yescharacteristic
426#131—448no—
427C2×M16—112no—
428C2×M16—112no—
429C2×M16—118no—
430C22×C8—114no—
431C22×C8—112no—
432C22×C8—114no—
433C22×C8—112no—
434C22×C8—118no—
435C22×C8—444no—
436C4⋊Q8C2×Dic1111yescharacteristic
437C4⋊Q8C2×Dic1111yescharacteristic
438C4⋊Q8C2×Dic1111yescharacteristic
439#127C2×Dic1111yescharacteristic
440#126C2×Dic1114yes—
441#126C2×Dic1114yes—
442#125C2×Dic1112yes—
443#125C2×Dic1112yes—
444#125C2×Dic1112yes—
445#124C2×Dic1112yes—
446#124C2×Dic1112yes—
447#124C2×Dic1112yes—
448#123C2×Dic1114yes—
449#123C2×Dic1114yes—
450#123C2×Dic1114yes—
451C22⋊Q8C2×Dic1112yes—
452C22⋊Q8C2×Dic1112yes—
453C22⋊Q8C2×Dic1112yes—
454C22⋊Q8C2×Dic1112yes—
455C22⋊Q8C2×Dic1112yes—
456C22⋊Q8C2×Dic1112yes—
457#121C2×Dic1112yes—
458#121C2×Dic1112yes—
459#121C2×Dic1112yes—
460#121C2×Dic1112yes—
461#121C2×Dic1112yes—
462#121C2×Dic1112yes—
463#120C2×Dic1114yes—
464C4×Q8C2×Dic1112yes—
465C4×Q8C2×Dic1112yes—
466C4×Q8C2×Dic1112yes—
467C4×Q8C2×Dic1112yes—
468C4×Q8C22×D1112yes—
469C4×Q8C22×D1112yes—
470C4×D4C2×Dic1114yes—
471C4×D4C2×Dic1114yes—
472C4×D4C2×Dic1114yes—
473C4×D4C2×Dic1114yes—
474C4×D4C2×Dic1112yes—
475C4×D4C2×Dic1112yes—
476C4×D4C2×Dic1112yes—
477C4×D4C2×Dic1112yes—
478C4×D4C22×D1114yes—
479C4×D4C22×D1114yes—
480C4×D4C22×D1112yes—
481C4×D4C22×D1112yes—
482#117C2×Dic1112yes—
483#117C2×Dic1112yes—
484#117C2×Dic1114yes—
485#117C2×Dic1114yes—
486#117C22×D1112yes—
487#117C22×D1114yes—
488C2×C42C2×Dic1111yescharacteristic
489C2×C42C2×Dic1111yescharacteristic
490C2×C42C2×Dic1111yescharacteristic
491C2×C42C2×Dic1111yescharacteristic
492C2×C42C2×Dic1111yescharacteristic
493C2×C42C2×Dic1111yescharacteristic
494C2×C42C22×D1114yes—
495C2×C42C22×D1111yescharacteristic
496C2×C42C22×D1111yescharacteristic
497C2×C42C22×D1111yescharacteristic
498C2×C42C22×D1111yescharacteristic
499C2×C42C22×D1111yescharacteristic
500C2×C42C22×D1111yescharacteristic
501C4⋊C8—112no—
502C4⋊C8—112no—
503C4⋊C8—114no—
504C4⋊C8—112no—
505C4⋊C8—114no—
506C4⋊C8—112no—
507C4⋊C8—112no—
508C4⋊C8—118no—
509C4⋊C8—112no—
510C4⋊C8—118no—
511C4⋊C8—112no—
512C4⋊C8—112no—
513C22⋊C8—114no—
514C22⋊C8—114no—
515C22⋊C8—118no—
516C22⋊C8—118no—
517#97—114no—
518#97—118no—
519C4×C8—114no—
520C4×C8—118no—
521C2×C11—22no—
522C2×C11—22no—
523C2×C11—22no—
524C2×C11—44no—
525C2×C11C2×#52011yescharacteristic
526C2×C11C22×#13111yescharacteristic
527C2×C11C2×#56811yescharacteristic
528C24C22×Dic1111yescharacteristic
529#41—28no—
530#41—24no—
531#41—24no—
532#41—44no—
533C2×Q8C22×Dic1112yes—
534C2×Q8C22×Dic1112yes—
535C2×Q8C22×Dic1112yes—
536C2×D4C22×Dic1114yes—
537C2×D4C22×Dic1114yes—
538C2×D4C22×Dic1112yes—
539C2×D4C22×Dic1114yes—
540C2×D4C22×Dic1112yes—
541C2×D4C22×Dic1112yes—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—42no—
546C22×C4C22×Dic1111yescharacteristic
547C22×C4C22×Dic1111yescharacteristic
548C22×C4C22×Dic1111yescharacteristic
549C22×C4C22×Dic1111yescharacteristic
550C22×C4C22×Dic1111yescharacteristic
551C22×C4C22×Dic1111yescharacteristic
552C22×C4C22×Dic1111yescharacteristic
553C22×C4C22×Dic1114yes—
554C22×C4C22×Dic1111yescharacteristic
555C22×C4C22×Dic1111yescharacteristic
556C22×C4C22×Dic1111yescharacteristic
557C22×C4C22×Dic1111yescharacteristic
558C22×C4C22×Dic1111yescharacteristic
559C22×C4C22×Dic1111yescharacteristic
560C22×C4C22×Dic1111yescharacteristic
561C22×C4C22×Dic1114yes—
562C22×C4C22×Dic1111yescharacteristic
563C22×C4C23×D1111yescharacteristic
564C22×C4C23×D1111yescharacteristic
565C22×C4C23×D1114yes—
566C22×C4C23×D1111yescharacteristic
567M16—224no—
568M16—224no—
569M16—448no—
570C2×C8—114no—
571C2×C8—114no—
572C2×C8—114no—
573C2×C8—114no—
574C2×C8—228no—
575C2×C8—442no—
576C2×C8—444no—
577C2×C8—442no—
578C2×C8—448no—
579C4⋊C4C22×Dic1112yes—
580C4⋊C4C22×Dic1112yes—
581C4⋊C4C22×Dic1114yes—
582C4⋊C4C22×Dic1114yes—
583C4⋊C4C22×Dic1112yes—
584C4⋊C4C22×Dic1112yes—
585C4⋊C4C22×Dic1114yes—
586C4⋊C4C22×Dic1114yes—
587C4⋊C4C22×Dic1112yes—
588C4⋊C4C22×Dic1112yes—
589C4⋊C4C22×Dic1114yes—
590C4⋊C4C22×Dic1114yes—
591C22⋊C4C22×Dic1114yes—
592C22⋊C4C22×Dic1114yes—
593C22⋊C4C22×Dic1114yes—
594C22⋊C4C22×Dic1114yes—
595C22⋊C4C22×Dic1114yes—
596C22⋊C4C22×Dic1114yes—
597C22⋊C4C22×Dic1114yes—
598C22⋊C4C22×Dic1114yes—
599C22⋊C4C22×Dic1114yes—
600C42C22×Dic1111yescharacteristic
601C42C22×Dic1111yescharacteristic
602C42C22×Dic1111yescharacteristic
603C42C22×Dic1111yescharacteristic
604C42C22×Dic1111yescharacteristic
605C42C22×Dic1111yescharacteristic
606C42C22×Dic1111yescharacteristic
607C42C22×Dic1111yescharacteristic
608C42C22×Dic1111yescharacteristic
609C42C22×Dic1111yescharacteristic
610C42C22×Dic1111yescharacteristic
611C42C22×Dic1111yescharacteristic
612C42C22×Dic1114yes—
613C42C22×Dic1114yes—
614C42C23×D1111yescharacteristic
615C42C23×D1114yes—
616C42C23×D1111yescharacteristic
617C42C23×D1111yescharacteristic
618C42C23×D1111yescharacteristic
619C11#6026511yescharacteristic, complemented, Sylow
620C23—22no—
621C23—22no—
622C23—22no—
623C23C23×Dic1114yes—
624C23C23×Dic1111yescharacteristic
625C23C23×Dic1111yescharacteristic
626C23C23×Dic1111yescharacteristic
627Q8—24no—
628Q8—24no—
629Q8—42no—
630D4—28no—
631D4—28no—
632D4—28no—
633D4—24no—
634D4—24no—
635D4—42no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—24no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—24no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—44no—
658C2×C4#6700114yescomplemented
659C2×C4#6704212yes—
660C2×C4#6704312yes—
661C2×C4C23×Dic1111yescharacteristic
662C2×C4C23×Dic1111yescharacteristic
663C2×C4C23×Dic1111yescharacteristic
664C2×C4C23×Dic1111yescharacteristic
665C2×C4C23×Dic1111yescharacteristic
666C2×C4C23×Dic1111yescharacteristic
667C2×C4C23×Dic1111yescharacteristic
668C2×C4C23×Dic1111yescharacteristic
669C2×C4C23×Dic1114yes—
670C2×C4C23×Dic1114yes—
671C2×C4C23×Dic1114yes—
672C2×C4C23×Dic1111yescharacteristic
673C2×C4C23×Dic1111yescharacteristic
674C2×C4C23×Dic1111yescharacteristic
675C2×C4C24×D1111yescharacteristic
676C8—224no—
677C8—224no—
678C8—224no—
679C8—224no—
680C22—28no—
681C22—21no—
682C22—21no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—21no—
687C22—24no—
688C22—24no—
689C22—24no—
690C22C2×#6700112yes—
691C22#1062335012yes—
692C22#1062335812yes—
693C22C24×Dic1111yescharacteristic
694C4—21no—
695C4—21no—
696C4—24no—
697C4—21no—
698C4—21no—
699C4—21no—
700C4—21no—
701C4—24no—
702C4—21no—
703C4—21no—
704C4—24no—
705C4C2×#6700112yes—
706C4C2×#6700112yes—
707C4#1062335812yes—
708C4C2×#6704211yescharacteristic
709C4C2×#6704311yescharacteristic
710C2—22no—
711C2—22no—
712C2—22no—
713C2—44no—
714C2C2×#1062335811yescharacteristic
715C2C22×#6700111yescharacteristic
716C2C2×#1062335011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
Fitting, prime radicalC11×#3444C2
cosocleC2×C4×C11C25
hypercenter#3444D11
hypocenterC11#60265
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #13077776C2semidirect
2. #13077755C2semidirect
3. #13077741C2semidirect
4. #13077733C2semidirect
5. #13077727C2semidirect
6. #13077565C2semidirect
7. #13077360C2semidirect
8. #13077311C2semidirect
9. #13077282C2semidirect
10. #13077249C2semidirect
11. #13077184C2semidirect
12. C22×C4⋊(C11⋊C8)C2semidirect
37. #10622637C22semidirect
38. #10622637C22semidirect
39. Q8×C11⋊C8C22semidirect
40. #10622625C22semidirect
43. #10622624C22semidirect
46. D4×C11⋊C8C22semidirect
47. #10622613C22semidirect
49. #10622612C22semidirect
53. #10622539C22semidirect
56. #10622538C22semidirect
59. #10622537C22semidirect
67. C2×C4⋊(C11⋊C8)C22semidirect
313. C2×C4×C11#131semidirect
619. C11#60265semidirect
658. C2×C4#67001semidirect

Maximal subgroups

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

subgroupindex
#130777762
#130777552
#130777412
#130777332
#130777272
#130775652
#130773602
#130773112
#130772822
#130772492
#130771842
C22×C4⋊(C11⋊C8)2
C11×#34442
#6026511