Finite Group Databasebeta

← #14770524

Subgroups — #14770524

Order 2816.

1172 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623045C211yesmaximal, characteristic
2#13071493C211yesmaximal, characteristic, complemented
3#13069452C211yesmaximal, characteristic, complemented
4#13069452C212yesmaximal, complemented
5#13069451C211yesmaximal, characteristic, complemented
6#13069451C212yesmaximal, complemented
7#13068601C211yesmaximal, characteristic, complemented
8#13068601C212yesmaximal, complemented
9C4×#66870C211yesmaximal, characteristic, complemented
10C4×#66870C212yesmaximal, complemented
11C11×#2345C211yesmaximal, characteristic, complemented
12C22×C11×C4⋊C4C2211yescharacteristic
13C2×#66983C2211yescharacteristic
14C2×#66983C2212yes—
15C2×C4×C22⋊D11C2211yescharacteristic
16C2×C4×C22⋊D11C2212yes—
17#10623045—21no—
18#10623045—22no—
19#10623045—21no—
20#10623045—21no—
21#10623045—22no—
22#10623045—21no—
23C2×#66951C412yescomplemented
24C2×#66948C411yescharacteristic, complemented
25C2×#66947C412yescomplemented
26C2×#66946C411yescharacteristic, complemented
27C2×#66945C411yescharacteristic, complemented
28C2×#66943C411yescharacteristic, complemented
29C11×#389—21no—
30C11×#387—22no—
31C11×#380C2212yes—
32C11×#380C2211yescharacteristic
33C4×C11×C4⋊C4—21no—
34C4×C11×C22⋊C4C2211yescharacteristic
35C4×C11×C22⋊C4C2212yes—
36#10622825C2212yes—
37#10622825C2211yescharacteristic
38C4×C22⋊Dic11C2211yescharacteristic
39C4×C22⋊Dic11C2212yes—
40#10622598—21no—
41#10622594—22no—
42C4⋊C4×Dic11—21no—
43C2×#66870C2211yescharacteristic
44C2×#66870C2212yes—
45C2×#66870C2211yescharacteristic
46C2×#66870C2212yes—
47C2×#66870C2212yes—
48C2×#66870C2212yes—
49C2×#66870C2212yes—
50#10622165C2211yescharacteristic
51#10622165C2212yes—
52#10622165C2211yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C22×C22⋊D11C2311yescharacteristic
56C22×C22⋊D11C2312yes—
57C22×D44C2×C411yescharacteristic
58C22×D44C2×C412yes—
59C22×C4×D11C2×C411yescharacteristic
60C22×C4×D11C2×C412yes—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4C2×C411yescharacteristic
64C2×C11×C4⋊C4C2×C411yescharacteristic
65C2×C11×C4⋊C4C2×C412yes—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4D412yes—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4D412yes—
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C22⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4C2312yes—
74C2×C11×C22⋊C4C2311yescharacteristic
75C2×C42×C11—21no—
76C2×C42×C11—22no—
77C2×C22⋊Dic11C2311yescharacteristic
78C2×C22⋊Dic11C2312yes—
79C2×C22⋊Dic11C2311yescharacteristic
80C2×C22⋊Dic11C2311yescharacteristic
81#66983—21no—
82#66983—21no—
83#66983—22no—
84#66983—22no—
85#66983—21no—
86#66983—21no—
87#66983—22no—
88#66983—22no—
89C4×C22⋊D11—21no—
90C4×C22⋊D11—21no—
91C4×C22⋊D11—22no—
92C4×C22⋊D11—22no—
93C4×C22⋊D11—21no—
94C4×C22⋊D11—21no—
95C4×C22⋊D11—22no—
96C4×C22⋊D11—22no—
97C2×(C2×D11)⋊C4C2×C412yes—
98C2×(C2×D11)⋊C4C2×C412yes—
99C2×(C2×D11)⋊C4C2×C411yescharacteristic
100C2×(C2×D11)⋊C4C2×C412yes—
101C2×(C2×D11)⋊C4C2×C412yes—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11C2×C411yescharacteristic
105C2×C4⋊Dic11C2×C412yes—
106C2×Dic11⋊C4C2×C412yes—
107C2×Dic11⋊C4C2×C411yescharacteristic
108C2×C4×Dic11—21no—
109C2×C4×Dic11—22no—
110C2×C4×Dic11C2×C411yescharacteristic
111C2×C4×Dic11C2×C412yes—
112#66951—22no—
113#66951—22no—
114#66951—22no—
115#66951—22no—
116#66948—22no—
117#66948—21no—
118#66948—21no—
119#66947—22no—
120#66947—22no—
121#66947—22no—
122#66947—22no—
123#66946—22no—
124#66946—21no—
125#66946—21no—
126#66945—22no—
127#66945—21no—
128#66945—21no—
129#66943—22no—
130#66943—21no—
131#66943—21no—
132C11×#95—21no—
133C11×#95—22no—
134C11×#95—22no—
135C11×#95—21no—
136C11⋊#95—21no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—21no—
140#66870—22no—
141#66870—24no—
142#66870—22no—
143#66870—24no—
144#66870—42no—
145#66870—42no—
146#66870—42no—
147#22535—111nomaximal, Sylow
148C24×C11C2411yescharacteristic
149C23×D11C22×C411yescharacteristic
150C23×D11C22×C412yes—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—22no—
154C22×C4×C11—42no—
155C22×C4×C11—82no—
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C22×C412yes—
158C22×C4×C11C22×C412yes—
159C22×C4×C11C22×C411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D412yes—
168C2×C22⋊D11—21no—
169C2×C22⋊D11—22no—
170C2×C22⋊D11—21no—
171C2×C22⋊D11—22no—
172C2×C22⋊D11—21no—
173C2×C22⋊D11—22no—
174C2×C22⋊D11—21no—
175C2×C22⋊D11—22no—
176C2×C22⋊D11—21no—
177C2×C22⋊D11—22no—
178C2×C22⋊D11—21no—
179C2×C22⋊D11—22no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—22no—
183C22×Dic11C22×C411yescharacteristic
184C22×Dic11C22×C412yes—
185C22×Dic11C22×C411yescharacteristic
186C22×Dic11C22×C411yescharacteristic
187C2×D44—21no—
188C2×D44—21no—
189C2×D44—22no—
190C2×D44—22no—
191C2×D44—42no—
192C2×D44—82no—
193C2×C4×D11—21no—
194C2×C4×D11—21no—
195C2×C4×D11—22no—
196C2×C4×D11—22no—
197C2×C4×D11—42no—
198C2×C4×D11—82no—
199C11×C4⋊C4—42no—
200C11×C4⋊C4—82no—
201C11×C4⋊C4C22⋊C412yes—
202C11×C4⋊C4C22⋊C411yescharacteristic
203C11×C4⋊C4C22⋊C411yescharacteristic
204C11×C4⋊C4C22⋊C412yes—
205C11×C4⋊C4C22⋊C411yescharacteristic
206C11×C4⋊C4C22⋊C411yescharacteristic
207C11×C4⋊C4C22⋊C412yes—
208C11×C4⋊C4C22⋊C412yes—
209C11×C4⋊C4C22⋊C412yes—
210C11×C4⋊C4C22⋊C412yes—
211C11×C22⋊C4—21no—
212C11×C22⋊C4—21no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4#4112yes—
217C42×C11—42no—
218C42×C11—82no—
219C22⋊Dic11—21no—
220C22⋊Dic11—21no—
221C22⋊Dic11—21no—
222C22⋊Dic11—22no—
223C22⋊Dic11—21no—
224C22⋊Dic11—22no—
225C22⋊Dic11—21no—
226C22⋊Dic11#4112yes—
227(C2×D11)⋊C4—22no—
228(C2×D11)⋊C4—22no—
229(C2×D11)⋊C4—22no—
230(C2×D11)⋊C4—22no—
231(C2×D11)⋊C4—21no—
232(C2×D11)⋊C4—21no—
233(C2×D11)⋊C4—22no—
234(C2×D11)⋊C4—22no—
235(C2×D11)⋊C4—22no—
236(C2×D11)⋊C4—22no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239C4⋊Dic11—22no—
240C4⋊Dic11—22no—
241C4⋊Dic11—42no—
242C4⋊Dic11—82no—
243Dic11⋊C4—22no—
244Dic11⋊C4—22no—
245Dic11⋊C4—21no—
246Dic11⋊C4—21no—
247C4×Dic11—21no—
248C4×Dic11—21no—
249C4×Dic11—22no—
250C4×Dic11—22no—
251C4×Dic11—42no—
252C4×Dic11—82no—
253C2×#553—111no—
254#2345—111no—
255#2345D1111yescharacteristic, complemented
256#1964—112no—
257#1964—111no—
258#1964—112no—
259#1964—111no—
260#1799—112no—
261#1799—111no—
262C4×#99—112no—
263C4×#99—111no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11C23×C411yescharacteristic
267C23×C11C22×D411yescharacteristic
268C23×C11C22×D411yescharacteristic
269C23×C11C2×#4111yescharacteristic
270C23×C11C2×#4111yescharacteristic
271C23×C11H(5,𝔽2)11yescharacteristic
272C23×C112−1+411yescharacteristic
273C22×D11—21no—
274C22×D11—22no—
275C22×D11—21no—
276C22×D11—22no—
277C22×D11—21no—
278C22×D11—22no—
279C22×D11—41no—
280C22×D11—42no—
281C22×D11—42no—
282C22×D11—41no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—42no—
288C2×C4×C11—42no—
289C2×C4×C11—42no—
290C2×C4×C11—42no—
291C2×C4×C11—42no—
292C2×C4×C11—42no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—42no—
304C2×C4×C11C2×C22⋊C411yescharacteristic
305C2×C4×C11C2×C22⋊C412yes—
306C2×C4×C11C2×C22⋊C412yes—
307C2×C4×C11C2×C22⋊C412yes—
308C2×C4×C11C2×C22⋊C412yes—
309C2×C4×C11C2×C22⋊C411yescharacteristic
310C2×C4×C11C2×C22⋊C411yescharacteristic
311C2×C4×C11C2×C22⋊C411yescharacteristic
312C22⋊D11—41no—
313C22⋊D11—42no—
314C22⋊D11—41no—
315C22⋊D11—42no—
316C22⋊D11—41no—
317C22⋊D11—42no—
318C22⋊D11—41no—
319C22⋊D11—42no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—22no—
324C2×Dic11—21no—
325C2×Dic11—22no—
326C2×Dic11—21no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—42no—
339D44—42no—
340D44—42no—
341D44—82no—
342D44—82no—
343C4×D11—42no—
344C4×D11—42no—
345C4×D11—82no—
346C4×D11—82no—
347#553—221no—
348#553—222no—
349#553—221no—
350#553—221no—
351#553—222no—
352#553—221no—
353C2×#126—112no—
354C2×#125—111no—
355C2×#123—112no—
356C2×#121—112no—
357C2×#121—111no—
358C2×#121—111no—
359C2×C4×D4—112no—
360C2×C4×D4—111no—
361C2×C4×D4—111no—
362C2×#117—111no—
363C22×C4⋊C4C2×D1111yescharacteristic
364C2×#99—111no—
365C2×#99—112no—
366C2×#99—111no—
367C2×#99—112no—
368C2×#99—112no—
369C2×#99—112no—
370C2×#99—112no—
371#389—21no—
372#389—221no—
373#387—22no—
374#387—222no—
375#380—112no—
376#380—111no—
377#380C2×D1112yes—
378#380C2×D1111yescharacteristic
379C4×C4⋊C4—21no—
380C4×C4⋊C4—221no—
381C4×C22⋊C4—111no—
382C4×C22⋊C4—112no—
383C4×C22⋊C4C2×D1111yescharacteristic
384C4×C22⋊C4C2×D1112yes—
385#342—111no—
386#342—112no—
387#342—111no—
388C22×C11—21no—
389C22×C11—21no—
390C22×C11—21no—
391C22×C11—21no—
392C22×C11—21no—
393C22×C11—21no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11C22×C22⋊C411yescharacteristic
399C22×C11C4×#4111yescharacteristic
400C22×C11#52011yescharacteristic
401C22×C11#54811yescharacteristic
402C22×C11#54811yescharacteristic
403C22×C11#55011yescharacteristic
404C22×C11#55011yescharacteristic
405C2×D11—41no—
406C2×D11—42no—
407C2×D11—41no—
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—41no—
411C2×D11—81no—
412C2×D11—82no—
413C2×D11—81no—
414C2×D11—82no—
415C4×C11—21no—
416C4×C11—21no—
417C4×C11—21no—
418C4×C11—22no—
419C4×C11—22no—
420C4×C11—22no—
421C4×C11—22no—
422C4×C11—42no—
423C4×C11—81no—
424C4×C11—82no—
425C4×C11#41012yes—
426Dic11—42no—
427Dic11—41no—
428Dic11—42no—
429Dic11—41no—
430Dic11—41no—
431Dic11—81no—
432Dic11—82no—
433C22×D4—112no—
434C22×D4—111no—
435C22×D4—111no—
436C22×D4—112no—
437C23×C4—111no—
438C23×C4—112no—
439C23×C4C22×D1111yescharacteristic
440C23×C4C22×D1112yes—
441#126—222no—
442#126—222no—
443#126—222no—
444#126—222no—
445#125—222no—
446#125—221no—
447#125—221no—
448#123—222no—
449#123—222no—
450#123—222no—
451#123—222no—
452#121—222no—
453#121—222no—
454#121—221no—
455#121—221no—
456#121—222no—
457#121—222no—
458#121—221no—
459#121—221no—
460#121—222no—
461#121—221no—
462#121—221no—
463C4×D4—222no—
464C4×D4—222no—
465C4×D4—221no—
466C4×D4—221no—
467C4×D4—222no—
468C4×D4—222no—
469C4×D4—221no—
470C4×D4—221no—
471C4×D4—222no—
472C4×D4—221no—
473C4×D4—221no—
474#117—222no—
475#117—221no—
476#117—221no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—111no—
480C2×C4⋊C4—112no—
481C2×C4⋊C4—111no—
482C2×C4⋊C4—112no—
483C2×C4⋊C4—221no—
484C2×C4⋊C4—222no—
485C2×C4⋊C4C4×D1111yescharacteristic
486C2×C4⋊C4C4×D1111yescharacteristic
487C2×C4⋊C4C4×D1112yes—
488C2×C4⋊C4D4411yescharacteristic
489C2×C4⋊C4D4412yes—
490C2×C4⋊C4D4411yescharacteristic
491C2×C4⋊C4C22⋊D1111yescharacteristic
492C2×C4⋊C4C22⋊D1112yes—
493C2×C4⋊C4C22⋊D1111yescharacteristic
494C2×C22⋊C4—111no—
495C2×C22⋊C4—111no—
496C2×C22⋊C4—112no—
497C2×C22⋊C4—112no—
498C2×C22⋊C4—112no—
499C2×C22⋊C4—111no—
500C2×C22⋊C4—112no—
501C2×C22⋊C4—111no—
502C2×C22⋊C4—112no—
503C2×C22⋊C4C22×D1111yescharacteristic
504C2×C22⋊C4C22×D1112yes—
505C2×C22⋊C4C22×D1111yescharacteristic
506C2×C42—21no—
507C2×C42—22no—
508C2×C42—112no—
509C2×C42—111no—
510C2×C42—221no—
511C2×C42—222no—
512#99—222no—
513#99—224no—
514#99—222no—
515#99—224no—
516#99—442no—
517#99—442no—
518#99—442no—
519#95—21no—
520#95—22no—
521#95—22no—
522#95—21no—
523#95—221no—
524#95—222no—
525#95—222no—
526#95—221no—
527C2×C11—21no—
528C2×C11—21no—
529C2×C11—21no—
530C2×C11—21no—
531C2×C11—21no—
532C2×C11—21no—
533C2×C11#234111yescharacteristic
534C2×C11C2×#41011yescharacteristic
535C2×C11#288311yescharacteristic
536D11—81no—
537D11—82no—
538C24—111no—
539C24—112no—
540C24C23×D1111yescharacteristic
541C2×D4—222no—
542C2×D4—221no—
543C2×D4—222no—
544C2×D4—221no—
545C2×D4—222no—
546C2×D4—221no—
547C2×D4—222no—
548C2×D4—221no—
549C2×D4—222no—
550C2×D4—221no—
551C2×D4—222no—
552C2×D4—221no—
553C2×D4—221no—
554C2×D4—221no—
555C2×D4—222no—
556C2×D4—222no—
557C2×D4—442no—
558C2×D4—882no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—42no—
563C22×C4—82no—
564C22×C4—112no—
565C22×C4—111no—
566C22×C4—111no—
567C22×C4—111no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—221no—
574C22×C4—222no—
575C22×C4—442no—
576C22×C4—882no—
577C22×C4C2×C4×D1111yescharacteristic
578C22×C4C2×C4×D1112yes—
579C22×C4C2×C4×D1111yescharacteristic
580C22×C4C2×C4×D1112yes—
581C22×C4C2×D4411yescharacteristic
582C22×C4C2×D4411yescharacteristic
583C22×C4C2×D4412yes—
584C22×C4C2×D4412yes—
585C22×C4C2×C22⋊D1111yescharacteristic
586C22×C4C2×C22⋊D1111yescharacteristic
587C22×C4C2×C22⋊D1112yes—
588C22×C4C2×C22⋊D1112yes—
589C4⋊C4—42no—
590C4⋊C4—82no—
591C4⋊C4—221no—
592C4⋊C4—221no—
593C4⋊C4—222no—
594C4⋊C4—222no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—222no—
598C4⋊C4—222no—
599C4⋊C4—442no—
600C4⋊C4—882no—
601C4⋊C4(C2×D11)⋊C412yes—
602C4⋊C4(C2×D11)⋊C411yescharacteristic
603C4⋊C4(C2×D11)⋊C411yescharacteristic
604C4⋊C4(C2×D11)⋊C412yes—
605C4⋊C4(C2×D11)⋊C411yescharacteristic
606C4⋊C4(C2×D11)⋊C411yescharacteristic
607C4⋊C4(C2×D11)⋊C412yes—
608C4⋊C4(C2×D11)⋊C412yes—
609C4⋊C4(C2×D11)⋊C412yes—
610C4⋊C4(C2×D11)⋊C412yes—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—22no—
614C22⋊C4—21no—
615C22⋊C4—22no—
616C22⋊C4—112no—
617C22⋊C4—221no—
618C22⋊C4—221no—
619C22⋊C4—221no—
620C22⋊C4—222no—
621C22⋊C4—222no—
622C22⋊C4—222no—
623C22⋊C4—222no—
624C22⋊C4—222no—
625C22⋊C4—222no—
626C22⋊C4—221no—
627C22⋊C4—221no—
628C22⋊C4—222no—
629C22⋊C4—222no—
630C22⋊C4—221no—
631C22⋊C4—222no—
632C22⋊C4—221no—
633C22⋊C4—222no—
634C22⋊C4#434312yes—
635C42—42no—
636C42—82no—
637C42—222no—
638C42—222no—
639C42—221no—
640C42—221no—
641C42—442no—
642C42—882no—
643C11#2253511yescharacteristic, complemented, Sylow
644C23—41no—
645C23—41no—
646C23—221no—
647C23—222no—
648C23—221no—
649C23—222no—
650C23—221no—
651C23—222no—
652C23—441no—
653C23—442no—
654C23—442no—
655C23—441no—
656C23C22×C4×D1111yescharacteristic
657C23C22×D4411yescharacteristic
658C23C2×#434311yescharacteristic
659C23#6704011yescharacteristic
660C23#41×D1111yescharacteristic
661C23#6704211yescharacteristic
662C23C22×C22⋊D1111yescharacteristic
663D4—442no—
664D4—442no—
665D4—441no—
666D4—442no—
667D4—441no—
668D4—442no—
669D4—441no—
670D4—442no—
671D4—441no—
672D4—442no—
673D4—882no—
674D4—882no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—221no—
697C2×C4—222no—
698C2×C4—221no—
699C2×C4—221no—
700C2×C4—222no—
701C2×C4—221no—
702C2×C4—222no—
703C2×C4—221no—
704C2×C4—222no—
705C2×C4—442no—
706C2×C4—441no—
707C2×C4—441no—
708C2×C4—442no—
709C2×C4—441no—
710C2×C4—441no—
711C2×C4—441no—
712C2×C4—442no—
713C2×C4—442no—
714C2×C4—441no—
715C2×C4—441no—
716C2×C4—442no—
717C2×C4—882no—
718C2×C4—882no—
719C2×C4C2×(C2×D11)⋊C412yes—
720C2×C4C2×(C2×D11)⋊C412yes—
721C2×C4C2×(C2×D11)⋊C411yescharacteristic
722C2×C4C2×(C2×D11)⋊C411yescharacteristic
723C2×C4C2×(C2×D11)⋊C411yescharacteristic
724C2×C4C2×(C2×D11)⋊C412yes—
725C2×C4C2×(C2×D11)⋊C412yes—
726C2×C4C2×(C2×D11)⋊C411yescharacteristic
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—441no—
738C22—442no—
739C22—442no—
740C22—441no—
741C22—441no—
742C22—442no—
743C22—881no—
744C22—882no—
745C22—881no—
746C22—882no—
747C22C4×#434311yescharacteristic
748C22#1062310511yescharacteristic
749C22#1062310711yescharacteristic
750C22#1062310811yescharacteristic
751C22C22×(C2×D11)⋊C411yescharacteristic
752C22#1062334811yescharacteristic
753C22#1062336511yescharacteristic
754C4—21no—
755C4—21no—
756C4—21no—
757C4—22no—
758C4—22no—
759C4—22no—
760C4—22no—
761C4—42no—
762C4—81no—
763C4—82no—
764C4—442no—
765C4—441no—
766C4—441no—
767C4—442no—
768C4—441no—
769C4—881no—
770C4—882no—
771C4#1062261912yes—
772C2—21no—
773C2—21no—
774C2—21no—
775C2—21no—
776C2—21no—
777C2—21no—
778C2—881no—
779C2—882no—
780C2#1307145411yescharacteristic
781C2C2×#1062261911yescharacteristic
782C2#1307707611yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#2345C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623045C2
cosocleC24×C11C24
hypercenter#2345D11
hypocenterC11#22535
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4⋊C4 ◁ #2345

Complements

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

NH ≅ G/Ntype
2. #13071493C2semidirect
3. #13069452C2semidirect
4. #13069452C2semidirect
5. #13069451C2semidirect
6. #13069451C2semidirect
7. #13068601C2semidirect
8. #13068601C2semidirect
9. C4×#66870C2semidirect
10. C4×#66870C2semidirect
11. C11×#2345C2semidirect
23. C2×#66951C4semidirect
24. C2×#66948C4semidirect
25. C2×#66947C4semidirect
26. C2×#66946C4semidirect
27. C2×#66945C4semidirect
28. C2×#66943C4semidirect
255. #2345D11semidirect
643. C11#22535semidirect

Maximal subgroups

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

subgroupindex
C2×#106230452
#130714932
#130694522
#130694512
#130686012
C4×#668702
C11×#23452
#2253511