Finite Group Databasebeta

← #15618591

Subgroups — #15618591

Order 2816.

2298 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077672C214yesmaximal, complemented
2#13077664C214yesmaximal, complemented
3#13077651C214yesmaximal, complemented
4#13077645C212yesmaximal, complemented
5#13077640C212yesmaximal, complemented
6#13077343C214yesmaximal, complemented
7#13077311C214yesmaximal, complemented
8#13077274C212yesmaximal, complemented
9#13077065C212yesmaximal, complemented
10C2×#10622820C211yesmaximal, characteristic, complemented
11C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
12C2×C11×#525C211yesmaximal, characteristic
13C22×C11×#41C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C11×#525C412yes—
16C11×#525C412yes—
17C11×#525C412yes—
18C11×#525C412yes—
19C11×#525C2212yes—
20C11×#525C2212yes—
21C11×#525C2212yes—
22C11×#525C2212yes—
23C2×C11×#123C412yes—
24C2×C11×C22⋊Q8C411yescharacteristic
25C2×C11×C22⋊Q8C411yescharacteristic
26C2×C11×#121C411yescharacteristic
27C2×C11×#121C411yescharacteristic
28C2×C11×#120C412yes—
29C2×C4×D4×C11C2212yes—
30C2×C4×D4×C11C2212yes—
31C2×C11×#117C2211yescharacteristic
32C2×#67001C2214yescomplemented
33C22×#4318C2212yescomplemented
34C23×C11⋊C8C2212yescomplemented
35#10622847C2218yescomplemented
36#10622847C2214yescomplemented
37#10622820C2212yes—
38#10622820C2212yes—
39#10622820C2212yescomplemented
40#10622820C2212yescomplemented
41#10622820C2214yescomplemented
42C2×C22⋊(C11⋊C8)C2212yes—
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2212yes—
46C2×C22⋊(C11⋊C8)C2212yes—
47C2×C22⋊(C11⋊C8)C2212yescomplemented
48C2×C22⋊(C11⋊C8)C2212yescomplemented
49C2×C22⋊(C11⋊C8)C2212yescomplemented
50C2×C22⋊(C11⋊C8)C2212yescomplemented
51C2×C22⋊(C11⋊C8)C2214yescomplemented
52#10622625C2218yescomplemented
53#10622624C2218yescomplemented
54#10622624C2218yescomplemented
55#10622624C2218yescomplemented
56#10622624C2218yescomplemented
57D4×C11⋊C8C2218yescomplemented
58D4×C11⋊C8C2218yescomplemented
59D4×C11⋊C8C2218yescomplemented
60#10622613C2218yescomplemented
61#10622612C2214yescomplemented
62#10622610C2214yescomplemented
63#10622539C2214yescomplemented
64#10622538C2214yescomplemented
65C25×C11C2×C411yescharacteristic
66C2×C11×#41—44no—
67C2×C11×#41C2×C412yes—
68C2×C11×#41C2×C412yes—
69C2×C11×#41C2312yes—
70C2×C11×#41C2312yes—
71C22×Q8×C11C2×C411yescharacteristic
72C22×D4×C11C2×C412yes—
73C22×D4×C11C2×C412yes—
74C22×D4×C11C2×C412yes—
75C22×D4×C11C2×C411yescharacteristic
76C23×C4×C11—44no—
77C23×C4×C11C2×C411yescharacteristic
78C23×C4×C11C2×C411yescharacteristic
79C23×C4×C11C2×C411yescharacteristic
80C23×C4×C11C2×C411yescharacteristic
81C23×C4×C11C2×C411yescharacteristic
82C23×C4×C11C2×C411yescharacteristic
83C23×C4×C11C2×C411yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2312yes—
91C23×C4×C11C2311yescharacteristic
92C11×#123C2×C414yes—
93C11×#123C2×C414yes—
94C11×#123C2×C414yes—
95C11×#123C2×C414yes—
96C11×C22⋊Q8C2×C412yes—
97C11×C22⋊Q8C2×C412yes—
98C11×C22⋊Q8C2×C412yes—
99C11×C22⋊Q8C2×C412yes—
100C11×C22⋊Q8C2×C412yes—
101C11×C22⋊Q8C2×C412yes—
102C11×C22⋊Q8C2×C412yes—
103C11×C22⋊Q8C2×C412yes—
104C11×#121C2×C412yes—
105C11×#121C2×C412yes—
106C11×#121C2×C412yes—
107C11×#121C2×C412yes—
108C11×#121C2×C412yes—
109C11×#121C2×C412yes—
110C11×#121C2×C412yes—
111C11×#121C2×C412yes—
112C11×#120C2×C414yes—
113C11×#120C2×C414yes—
114C11×#120C2×C414yes—
115C11×#120C2×C414yes—
116C4×D4×C11C2×C414yes—
117C4×D4×C11C2×C414yes—
118C4×D4×C11C2×C414yes—
119C4×D4×C11C2×C414yes—
120C4×D4×C11C2314yes—
121C4×D4×C11C2314yes—
122C4×D4×C11C2314yes—
123C4×D4×C11C2314yes—
124C11×#117C2×C412yes—
125C11×#117C2×C412yes—
126C11×#117C2312yes—
127C11×#117C2312yes—
128C2×C11×C4⋊C4C2×C411yescharacteristic
129C2×C11×C4⋊C4C2×C411yescharacteristic
130C2×C11×C4⋊C4C2×C412yes—
131C2×C11×C4⋊C4C2×C412yes—
132C2×C11×C22⋊C4C2×C412yes—
133C2×C11×C22⋊C4C2×C412yes—
134C2×C11×C22⋊C4C2×C412yes—
135C2×C11×C22⋊C4C2×C412yes—
136C2×C11×C22⋊C4C2×C412yes—
137C2×C42×C11C2312yes—
138#67001—48no—
139C2×#4318—44no—
140C2×#4318C2314yes—
141C2×#4318C2314yes—
142C2×#4318C2318yescomplemented
143C22×C11⋊C8—44no—
144C22×C11⋊C8C2314yes—
145C22×C11⋊C8C2312yes—
146C22×C11⋊C8C2314yes—
147C22×C11⋊C8C2312yes—
148C22×C11⋊C8C2314yes—
149C22×C11⋊C8C2318yescomplemented
150C22⋊(C11⋊C8)C2312yes—
151C22⋊(C11⋊C8)C2314yes—
152C22⋊(C11⋊C8)C2312yes—
153C22⋊(C11⋊C8)C2314yes—
154C22⋊(C11⋊C8)C2312yes—
155C22⋊(C11⋊C8)C2312yes—
156C22⋊(C11⋊C8)C2314yes—
157C22⋊(C11⋊C8)C2314yes—
158C22⋊(C11⋊C8)C2314yes—
159C22⋊(C11⋊C8)C2314yes—
160C22⋊(C11⋊C8)C2318yescomplemented
161C22⋊(C11⋊C8)C2318yescomplemented
162C4⋊(C11⋊C8)C2318yescomplemented
163C4⋊(C11⋊C8)C2318yescomplemented
164#66867C2318yescomplemented
165C4×C11⋊C8C2318yescomplemented
166#60233—111nomaximal, Sylow
167C24×C11—24no—
168C24×C11—42no—
169C24×C11—42no—
170C24×C11C22×C411yescharacteristic
171C24×C11C22×C411yescharacteristic
172C24×C11C22×C411yescharacteristic
173C24×C11C22×C411yescharacteristic
174C24×C11C22×C411yescharacteristic
175C24×C11C22×C412yes—
176C24×C11C22×C411yescharacteristic
177C24×C11C22×C411yescharacteristic
178C11×#41—28no—
179C11×#41—44no—
180C11×#41—44no—
181C11×#41—44no—
182C2×Q8×C11—42no—
183C2×Q8×C11C22×C412yes—
184C2×Q8×C11C22×C412yes—
185C2×D4×C11—28no—
186C2×D4×C11—42no—
187C2×D4×C11—44no—
188C2×D4×C11—44no—
189C2×D4×C11C22×C414yes—
190C2×D4×C11C22×C414yes—
191C2×D4×C11C22×C414yes—
192C2×D4×C11C22×C414yes—
193C2×D4×C11C22×C412yes—
194C2×D4×C11C22×C414yes—
195C2×D4×C11C22×C414yes—
196C2×D4×C11C22×C412yes—
197C22×C4×C11—24no—
198C22×C4×C11—24no—
199C22×C4×C11—24no—
200C22×C4×C11—42no—
201C22×C4×C11—42no—
202C22×C4×C11—42no—
203C22×C4×C11—42no—
204C22×C4×C11—42no—
205C22×C4×C11—42no—
206C22×C4×C11—42no—
207C22×C4×C11—42no—
208C22×C4×C11—44no—
209C22×C4×C11—42no—
210C22×C4×C11—42no—
211C22×C4×C11—42no—
212C22×C4×C11C22×C412yes—
213C22×C4×C11C22×C411yescharacteristic
214C22×C4×C11C22×C411yescharacteristic
215C22×C4×C11C22×C411yescharacteristic
216C22×C4×C11C22×C411yescharacteristic
217C22×C4×C11C22×C411yescharacteristic
218C22×C4×C11C22×C411yescharacteristic
219C22×C4×C11C22×C411yescharacteristic
220C22×C4×C11C22×C411yescharacteristic
221C22×C4×C11C22×C411yescharacteristic
222C22×C4×C11C22×C412yes—
223C22×C4×C11C22×C411yescharacteristic
224C22×C4×C11C22×C411yescharacteristic
225C22×C4×C11C22×C412yes—
226C22×C4×C11C22×C411yescharacteristic
227C22×C4×C11C22×C411yescharacteristic
228C22×C4×C11C22×C411yescharacteristic
229C22×C4×C11C22×C411yescharacteristic
230C22×C4×C11C22×C414yes—
231C22×C4×C11C22×C411yescharacteristic
232C22×C4×C11C22×C411yescharacteristic
233C22×C4×C11C22×C411yescharacteristic
234C22×C4×C11C22×C411yescharacteristic
235C22×C4×C11C22×C411yescharacteristic
236C22×C4×C11C22×C411yescharacteristic
237C22×C4×C11C2411yescharacteristic
238C22×C4×C11C2411yescharacteristic
239C22×C4×C11C2411yescharacteristic
240C22×C4×C11C2411yescharacteristic
241C22×C4×C11C2411yescharacteristic
242C22×C4×C11C2411yescharacteristic
243C22×C4×C11C2414yes—
244C22×C4×C11C2411yescharacteristic
245C11×C4⋊C4C22×C412yes—
246C11×C4⋊C4C22×C412yes—
247C11×C4⋊C4C22×C412yes—
248C11×C4⋊C4C22×C412yes—
249C11×C4⋊C4C22×C414yes—
250C11×C4⋊C4C22×C414yes—
251C11×C4⋊C4C22×C414yes—
252C11×C4⋊C4C22×C414yes—
253C11×C22⋊C4C22×C414yes—
254C11×C22⋊C4C22×C414yes—
255C11×C22⋊C4C22×C414yes—
256C11×C22⋊C4C22×C414yes—
257C11×C22⋊C4C22×C414yes—
258C11×C22⋊C4C22×C414yes—
259C11×C22⋊C4C22×C414yes—
260C11×C22⋊C4C22×C414yes—
261C11×C22⋊C4C22×C414yes—
262C11×C22⋊C4C22×C414yes—
263C42×C11C22×C414yes—
264C42×C11C2414yes—
265#4318—28no—
266#4318—44no—
267#4318—48no—
268C2×C11⋊C8—28no—
269C2×C11⋊C8—42no—
270C2×C11⋊C8—44no—
271C2×C11⋊C8—42no—
272C2×C11⋊C8—44no—
273C2×C11⋊C8—48no—
274C2×C11⋊C8C2414yes—
275C2×C11⋊C8C2418yes—
276C2×C11⋊C8C2414yes—
277C2×#525D1111yescharacteristic
278#2977—114no—
279#2976—114no—
280#2974—114no—
281#2973—112no—
282#2972—112no—
283#2933—114no—
284#2929—114no—
285#2924—112no—
286#2880—112no—
287C2×#407—111no—
288C22×C22⋊C8—111no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—24no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—42no—
311C23×C11—42no—
312C23×C11—416no—
313C23×C11#13114yescomplemented
314C23×C11C23×C411yescharacteristic
315C23×C11C23×C411yescharacteristic
316C23×C11C23×C414yes—
317C23×C11C23×C411yescharacteristic
318C23×C11C23×C411yescharacteristic
319C23×C11C23×C411yescharacteristic
320C23×C11C23×C411yescharacteristic
321C23×C11C23×C411yescharacteristic
322Q8×C11—24no—
323Q8×C11—42no—
324D4×C11—28no—
325D4×C11—28no—
326D4×C11—28no—
327D4×C11—28no—
328D4×C11—24no—
329D4×C11—44no—
330D4×C11—42no—
331D4×C11—44no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—24no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—28no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—42no—
362C2×C4×C11—44no—
363C2×C4×C11—42no—
364C2×C4×C11C23×C411yescharacteristic
365C2×C4×C11C23×C414yes—
366C2×C4×C11C23×C414yes—
367C2×C4×C11C23×C411yescharacteristic
368C2×C4×C11C23×C411yescharacteristic
369C2×C4×C11C23×C411yescharacteristic
370C2×C4×C11C23×C411yescharacteristic
371C2×C4×C11C23×C414yes—
372C2×C4×C11C23×C411yescharacteristic
373C2×C4×C11C23×C411yescharacteristic
374C2×C4×C11H(5,𝔽2)14yes—
375C2×C4×C11C2511yescharacteristic
376C11⋊C8—24no—
377C11⋊C8—24no—
378C11⋊C8—28no—
379C22×#41C2×D1111yescharacteristic
380C24×C4C2×D1111yescharacteristic
381C2×#131—114no—
382C22×M16—112no—
383C23×C8—112no—
384#525Dic1112yes—
385#525Dic1112yes—
386#525Dic1112yes—
387#525Dic1112yes—
388#525C2×D1112yes—
389#525C2×D1112yes—
390#525C2×D1112yes—
391#525C2×D1112yes—
392C2×#123Dic1112yes—
393C2×C22⋊Q8Dic1111yescharacteristic
394C2×C22⋊Q8Dic1111yescharacteristic
395C2×#121Dic1111yescharacteristic
396C2×#121Dic1111yescharacteristic
397C2×#120Dic1112yes—
398C2×C4×D4C2×D1112yes—
399C2×C4×D4C2×D1112yes—
400C2×#117C2×D1111yescharacteristic
401#436—118no—
402#435—118no—
403#435—118no—
404#435—118no—
405#435—118no—
406C8×D4—118no—
407C8×D4—118no—
408C8×D4—118no—
409#433—118no—
410#432—114no—
411#431—114no—
412#424—114no—
413#408—114no—
414#408—118no—
415#407—112no—
416#407—112no—
417#407—112no—
418#407—112no—
419#407—114no—
420C2×C22⋊C8—112no—
421C2×C22⋊C8—111no—
422C2×C22⋊C8—111no—
423C2×C22⋊C8—112no—
424C2×C22⋊C8—112no—
425C2×C22⋊C8—112no—
426C2×C22⋊C8—112no—
427C2×C22⋊C8—112no—
428C2×C22⋊C8—112no—
429C2×C22⋊C8—114no—
430#405—114no—
431C22×C11—28no—
432C22×C11—21no—
433C22×C11—21no—
434C22×C11—21no—
435C22×C11—21no—
436C22×C11—21no—
437C22×C11—21no—
438C22×C11—21no—
439C22×C11—21no—
440C22×C11—21no—
441C22×C11—21no—
442C22×C11—21no—
443C22×C11—21no—
444C22×C11—24no—
445C22×C11—24no—
446C22×C11—21no—
447C22×C11—21no—
448C22×C11—24no—
449C22×C11—21no—
450C22×C11—21no—
451C22×C11—44no—
452C22×C11—44no—
453C22×C11—44no—
454C22×C11—44no—
455C22×C11—44no—
456C22×C11—44no—
457C22×C11—84no—
458C22×C11#51812yes—
459C22×C11C2×#13112yes—
460C22×C11C2×#13112yes—
461C22×C11C2×#13112yes—
462C22×C11#56812yes—
463C22×C11C24×C411yescharacteristic
464C4×C11—21no—
465C4×C11—21no—
466C4×C11—21no—
467C4×C11—21no—
468C4×C11—21no—
469C4×C11—21no—
470C4×C11—24no—
471C4×C11—24no—
472C4×C11—24no—
473C4×C11#51812yes—
474C4×C11C2×H(5,𝔽2)12yes—
475C25C2×Dic1111yescharacteristic
476C2×#41—44no—
477C2×#41C2×Dic1112yes—
478C2×#41C2×Dic1112yes—
479C2×#41C22×D1112yes—
480C2×#41C22×D1112yes—
481C22×Q8C2×Dic1111yescharacteristic
482C22×D4C2×Dic1112yes—
483C22×D4C2×Dic1112yes—
484C22×D4C2×Dic1112yes—
485C22×D4C2×Dic1111yescharacteristic
486C23×C4—44no—
487C23×C4C2×Dic1111yescharacteristic
488C23×C4C2×Dic1111yescharacteristic
489C23×C4C2×Dic1111yescharacteristic
490C23×C4C2×Dic1111yescharacteristic
491C23×C4C2×Dic1111yescharacteristic
492C23×C4C2×Dic1111yescharacteristic
493C23×C4C2×Dic1111yescharacteristic
494C23×C4C22×D1111yescharacteristic
495C23×C4C22×D1111yescharacteristic
496C23×C4C22×D1111yescharacteristic
497C23×C4C22×D1111yescharacteristic
498C23×C4C22×D1111yescharacteristic
499C23×C4C22×D1112yes—
500C23×C4C22×D1111yescharacteristic
501C23×C4C22×D1111yescharacteristic
502#131—448no—
503C2×M16—114no—
504C2×M16—114no—
505C2×M16—118no—
506C2×M16—444no—
507C22×C8—114no—
508C22×C8—112no—
509C22×C8—114no—
510C22×C8—112no—
511C22×C8—114no—
512C22×C8—118no—
513C22×C8—444no—
514#123C2×Dic1114yes—
515#123C2×Dic1114yes—
516#123C2×Dic1114yes—
517#123C2×Dic1114yes—
518C22⋊Q8C2×Dic1112yes—
519C22⋊Q8C2×Dic1112yes—
520C22⋊Q8C2×Dic1112yes—
521C22⋊Q8C2×Dic1112yes—
522C22⋊Q8C2×Dic1112yes—
523C22⋊Q8C2×Dic1112yes—
524C22⋊Q8C2×Dic1112yes—
525C22⋊Q8C2×Dic1112yes—
526#121C2×Dic1112yes—
527#121C2×Dic1112yes—
528#121C2×Dic1112yes—
529#121C2×Dic1112yes—
530#121C2×Dic1112yes—
531#121C2×Dic1112yes—
532#121C2×Dic1112yes—
533#121C2×Dic1112yes—
534#120C2×Dic1114yes—
535#120C2×Dic1114yes—
536#120C2×Dic1114yes—
537#120C2×Dic1114yes—
538C4×D4C2×Dic1114yes—
539C4×D4C2×Dic1114yes—
540C4×D4C2×Dic1114yes—
541C4×D4C2×Dic1114yes—
542C4×D4C22×D1114yes—
543C4×D4C22×D1114yes—
544C4×D4C22×D1114yes—
545C4×D4C22×D1114yes—
546#117C2×Dic1112yes—
547#117C2×Dic1112yes—
548#117C22×D1112yes—
549#117C22×D1112yes—
550C2×C4⋊C4C2×Dic1111yescharacteristic
551C2×C4⋊C4C2×Dic1111yescharacteristic
552C2×C4⋊C4C2×Dic1112yes—
553C2×C4⋊C4C2×Dic1112yes—
554C2×C22⋊C4C2×Dic1112yes—
555C2×C22⋊C4C2×Dic1112yes—
556C2×C22⋊C4C2×Dic1112yes—
557C2×C22⋊C4C2×Dic1112yes—
558C2×C22⋊C4C2×Dic1112yes—
559C2×C42C22×D1112yes—
560C4⋊C8—118no—
561C4⋊C8—118no—
562C22⋊C8—112no—
563C22⋊C8—112no—
564C22⋊C8—114no—
565C22⋊C8—112no—
566C22⋊C8—112no—
567C22⋊C8—114no—
568C22⋊C8—114no—
569C22⋊C8—114no—
570C22⋊C8—114no—
571C22⋊C8—114no—
572C22⋊C8—118no—
573C22⋊C8—118no—
574#97—118no—
575C4×C8—118no—
576C2×C11—22no—
577C2×C11—22no—
578C2×C11—22no—
579C2×C11—22no—
580C2×C11—22no—
581C2×C11—41no—
582C2×C11—41no—
583C2×C11—44no—
584C2×C11C2×#51811yescharacteristic
585C2×C11C22×#13111yescharacteristic
586C2×C11C2×#56811yescharacteristic
587C24—24no—
588C24—42no—
589C24—42no—
590C24C22×Dic1111yescharacteristic
591C24C22×Dic1111yescharacteristic
592C24C22×Dic1111yescharacteristic
593C24C22×Dic1111yescharacteristic
594C24C22×Dic1111yescharacteristic
595C24C22×Dic1112yes—
596C24C22×Dic1111yescharacteristic
597C24C22×Dic1111yescharacteristic
598#41—28no—
599#41—44no—
600#41—44no—
601#41—44no—
602C2×Q8—42no—
603C2×Q8C22×Dic1112yes—
604C2×Q8C22×Dic1112yes—
605C2×D4—28no—
606C2×D4—42no—
607C2×D4—44no—
608C2×D4—44no—
609C2×D4C22×Dic1114yes—
610C2×D4C22×Dic1114yes—
611C2×D4C22×Dic1114yes—
612C2×D4C22×Dic1114yes—
613C2×D4C22×Dic1112yes—
614C2×D4C22×Dic1114yes—
615C2×D4C22×Dic1114yes—
616C2×D4C22×Dic1112yes—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—24no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—44no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4C22×Dic1112yes—
633C22×C4C22×Dic1111yescharacteristic
634C22×C4C22×Dic1111yescharacteristic
635C22×C4C22×Dic1111yescharacteristic
636C22×C4C22×Dic1111yescharacteristic
637C22×C4C22×Dic1111yescharacteristic
638C22×C4C22×Dic1111yescharacteristic
639C22×C4C22×Dic1111yescharacteristic
640C22×C4C22×Dic1111yescharacteristic
641C22×C4C22×Dic1111yescharacteristic
642C22×C4C22×Dic1112yes—
643C22×C4C22×Dic1111yescharacteristic
644C22×C4C22×Dic1111yescharacteristic
645C22×C4C22×Dic1112yes—
646C22×C4C22×Dic1111yescharacteristic
647C22×C4C22×Dic1111yescharacteristic
648C22×C4C22×Dic1111yescharacteristic
649C22×C4C22×Dic1111yescharacteristic
650C22×C4C22×Dic1114yes—
651C22×C4C22×Dic1111yescharacteristic
652C22×C4C22×Dic1111yescharacteristic
653C22×C4C22×Dic1111yescharacteristic
654C22×C4C22×Dic1111yescharacteristic
655C22×C4C22×Dic1111yescharacteristic
656C22×C4C22×Dic1111yescharacteristic
657C22×C4C23×D1111yescharacteristic
658C22×C4C23×D1111yescharacteristic
659C22×C4C23×D1111yescharacteristic
660C22×C4C23×D1111yescharacteristic
661C22×C4C23×D1111yescharacteristic
662C22×C4C23×D1114yes—
663C22×C4C23×D1111yescharacteristic
664C22×C4C23×D1111yescharacteristic
665M16—228no—
666M16—444no—
667M16—448no—
668C2×C8—114no—
669C2×C8—118no—
670C2×C8—114no—
671C2×C8—228no—
672C2×C8—442no—
673C2×C8—444no—
674C2×C8—442no—
675C2×C8—444no—
676C2×C8—448no—
677C4⋊C4C22×Dic1112yes—
678C4⋊C4C22×Dic1112yes—
679C4⋊C4C22×Dic1112yes—
680C4⋊C4C22×Dic1112yes—
681C4⋊C4C22×Dic1114yes—
682C4⋊C4C22×Dic1114yes—
683C4⋊C4C22×Dic1114yes—
684C4⋊C4C22×Dic1114yes—
685C22⋊C4C22×Dic1114yes—
686C22⋊C4C22×Dic1114yes—
687C22⋊C4C22×Dic1114yes—
688C22⋊C4C22×Dic1114yes—
689C22⋊C4C22×Dic1114yes—
690C22⋊C4C22×Dic1114yes—
691C22⋊C4C22×Dic1114yes—
692C22⋊C4C22×Dic1114yes—
693C22⋊C4C22×Dic1114yes—
694C22⋊C4C22×Dic1114yes—
695C42C22×Dic1114yes—
696C42C23×D1114yes—
697C11#6023311yescharacteristic, complemented, Sylow
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—24no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—42no—
720C23—42no—
721C23—416no—
722C23#6700114yescomplemented
723C23C23×Dic1111yescharacteristic
724C23C23×Dic1111yescharacteristic
725C23C23×Dic1114yes—
726C23C23×Dic1111yescharacteristic
727C23C23×Dic1111yescharacteristic
728C23C23×Dic1111yescharacteristic
729C23C23×Dic1111yescharacteristic
730C23C23×Dic1111yescharacteristic
731Q8—24no—
732Q8—42no—
733D4—28no—
734D4—28no—
735D4—28no—
736D4—28no—
737D4—24no—
738D4—44no—
739D4—42no—
740D4—44no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—28no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—44no—
772C2×C4—42no—
773C2×C4#6703714yes—
774C2×C4C23×Dic1111yescharacteristic
775C2×C4C23×Dic1114yes—
776C2×C4C23×Dic1114yes—
777C2×C4C23×Dic1111yescharacteristic
778C2×C4C23×Dic1111yescharacteristic
779C2×C4C23×Dic1111yescharacteristic
780C2×C4C23×Dic1111yescharacteristic
781C2×C4C23×Dic1114yes—
782C2×C4C23×Dic1111yescharacteristic
783C2×C4C23×Dic1111yescharacteristic
784C2×C4C24×D1111yescharacteristic
785C8—224no—
786C8—224no—
787C8—228no—
788C22—28no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—24no—
800C22—21no—
801C22—21no—
802C22—24no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—24no—
808C22—44no—
809C22—44no—
810C22—44no—
811C22—44no—
812C22—44no—
813C22—44no—
814C22—84no—
815C22#1062332912yes—
816C22C2×#6700112yes—
817C22C2×#6700112yes—
818C22C2×#6700112yes—
819C22#1062335012yes—
820C22C24×Dic1111yescharacteristic
821C4—24no—
822C4—24no—
823C4—21no—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—21no—
829C4—24no—
830C4#1062332912yes—
831C4C2×#6703712yes—
832C2—22no—
833C2—22no—
834C2—22no—
835C2—22no—
836C2—22no—
837C2—41no—
838C2—41no—
839C2—44no—
840C2C2×#1062332911yescharacteristic
841C2C22×#6700111yescharacteristic
842C2C2×#1062335011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
Fitting, prime radicalC2×C11×#525C2
cosocleC2×C4×C11C25
hypercenterC2×#525D11
hypocenterC11#60233
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. #13077672C2semidirect
2. #13077664C2semidirect
3. #13077651C2semidirect
4. #13077645C2semidirect
5. #13077640C2semidirect
6. #13077343C2semidirect
7. #13077311C2semidirect
8. #13077274C2semidirect
9. #13077065C2semidirect
10. C2×#10622820C2semidirect
11. C22×C22⋊(C11⋊C8)C2semidirect
32. C2×#67001C22semidirect
33. C22×#4318C22semidirect
34. C23×C11⋊C8C22semidirect
35. #10622847C22semidirect
36. #10622847C22semidirect
39. #10622820C22semidirect
40. #10622820C22semidirect
41. #10622820C22semidirect
47. C2×C22⋊(C11⋊C8)C22semidirect
48. C2×C22⋊(C11⋊C8)C22semidirect
49. C2×C22⋊(C11⋊C8)C22semidirect
50. C2×C22⋊(C11⋊C8)C22semidirect
51. C2×C22⋊(C11⋊C8)C22semidirect
52. #10622625C22semidirect
53. #10622624C22semidirect
54. #10622624C22semidirect
55. #10622624C22semidirect
56. #10622624C22semidirect
57. D4×C11⋊C8C22semidirect
58. D4×C11⋊C8C22semidirect
59. D4×C11⋊C8C22semidirect
60. #10622613C22semidirect
61. #10622612C22semidirect
62. #10622610C22semidirect
63. #10622539C22semidirect
64. #10622538C22semidirect
142. C2×#4318C23semidirect
149. C22×C11⋊C8C23semidirect
160. C22⋊(C11⋊C8)C23semidirect
161. C22⋊(C11⋊C8)C23semidirect
162. C4⋊(C11⋊C8)C23semidirect
163. C4⋊(C11⋊C8)C23semidirect
164. #66867C23semidirect
165. C4×C11⋊C8C23semidirect
313. C23×C11#131semidirect
697. C11#60233semidirect
722. C23#67001semidirect

Maximal subgroups

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

subgroupindex
#130776722
#130776642
#130776512
#130776452
#130776402
#130773432
#130773112
#130772742
#130770652
C2×#106228202
C22×C22⋊(C11⋊C8)2
C2×C11×#5252
#6023311