Finite Group Databasebeta

← #14722671

Subgroups — #14722671

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082527C211yesmaximal, characteristic
2#13077741C211yesmaximal, characteristic, complemented
3#13067344C211yesmaximal, characteristic, complemented
4#13067339C211yesmaximal, characteristic, complemented
5#13067334C211yesmaximal, characteristic, complemented
6#13067327C211yesmaximal, characteristic, complemented
7#13067319C211yesmaximal, characteristic, complemented
8#13067312C211yesmaximal, characteristic, complemented
9#13067309C211yesmaximal, characteristic, complemented
10#13067304C211yesmaximal, characteristic, complemented
11#13067294C211yesmaximal, characteristic, complemented
12#13067271C211yesmaximal, characteristic, complemented
13#13067266C211yesmaximal, characteristic, complemented
14C2×#10622120C211yesmaximal, characteristic, complemented
15C11×#2990C211yesmaximal, characteristic, complemented
16C4×C11×#41C2211yescharacteristic
17#10623364C412yes—
18#10623115—21no—
19#10623110—21no—
20#10623096—21no—
21#10623096—21no—
22#10623094—21no—
23#10623083—21no—
24#10623083—21no—
25#10623082—21no—
26#10623065C412yes—
27#10623065C412yes—
28#10623054C412yes—
29#10623008C2211yescharacteristic
30#10623008C2211yescharacteristic
31#10623008C2211yescharacteristic
32#10623001C2211yescharacteristic
33#10623001C2211yescharacteristic
34C2×#66922C2211yescharacteristic
35C11×#446—21no—
36C11×#435—21no—
37C11×#435—21no—
38C8×D4×C11—21no—
39C11×#432C2211yescharacteristic
40C11×#432C2211yescharacteristic
41C11×#431C2211yescharacteristic
42C11×#423C2211yescharacteristic
43C2×C11×C4⋊C8C2211yescharacteristic
44C2×C11×C4⋊C8C2211yescharacteristic
45#10622637—21no—
46#10622624—21no—
47#10622624—21no—
48D4×C11⋊C8—21no—
49#10622539C2211yescharacteristic
50#10622539C2211yescharacteristic
51#10622538C2211yescharacteristic
52#10622537C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55#10622123C2211yescharacteristic
56#10622123C2211yescharacteristic
57#10622123C2211yescharacteristic
58#10622123C2211yescharacteristic
59#10622120C2211yescharacteristic
60#10622120C2211yescharacteristic
61#10622120C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622120C2211yescharacteristic
64#10622120C2211yescharacteristic
65#10622120C2211yescharacteristic
66#10622120C2211yescharacteristic
67#10622119C2211yescharacteristic
68#10622119C2211yescharacteristic
69#10622119C2211yescharacteristic
70#10622119C2211yescharacteristic
71C2×C11×#41C2×C411yescharacteristic
72C2×#4339—21no—
73C2×#4339—21no—
74C2×#4339C2×C412yes—
75C22×Dic22—21no—
76C2×C11×M16—21no—
77C22×C8×C11—21no—
78C22×C8×C11—21no—
79C4×Q8×C11D411yescharacteristic
80C4×Q8×C11D411yescharacteristic
81C4×D4×C11D411yescharacteristic
82C4×D4×C11D411yescharacteristic
83C4×D4×C11D411yescharacteristic
84C4×D4×C11D411yescharacteristic
85C4×D4×C11D411yescharacteristic
86C4×D4×C11D411yescharacteristic
87C11×#117C2×C411yescharacteristic
88C11×#117C2×C411yescharacteristic
89C11×#117C2×C411yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2311yescharacteristic
93#66999—22no—
94#66992—22no—
95#66992—22no—
96#66991—22no—
97#66983—21no—
98#66983—21no—
99#66983—21no—
100#66983—21no—
101#66983C2×C412yes—
102#66983C2×C412yes—
103#66979—21no—
104#66979—21no—
105C2×C4⋊Dic11—21no—
106C2×C4⋊Dic11C2×C412yes—
107#66977—21no—
108#66977—21no—
109#66977C2×C412yes—
110#66977C2×C412yes—
111C2×#4318—21no—
112C22×C11⋊C8—21no—
113C22×C11⋊C8—21no—
114#66951—22no—
115#66951—22no—
116#66949—22no—
117#66949—22no—
118#66945—22no—
119C4⋊C4×D11—22no—
120#66938—22no—
121#66938—22no—
122#66936—22no—
123#66936—22no—
124(C22⋊D11)⋊C4—22no—
125(C22⋊D11)⋊C4—22no—
126#66928—21no—
127#66928—21no—
128#66928C2×C412yes—
129#66927C2311yescharacteristic
130C4×D44—21no—
131C4×D44—21no—
132C4×D44—21no—
133C4×D44—21no—
134C4×D44C2×C412yes—
135C4×D44C2×C412yes—
136#66923—21no—
137#66923—21no—
138#66922—21no—
139#66922—21no—
140#66922C2×C412yes—
141#66922C2311yescharacteristic
142#66922C2311yescharacteristic
143#66922C2311yescharacteristic
144C4×Dic22—21no—
145C4×Dic22—21no—
146C4×Dic22C2×C412yes—
147C4×Dic22C2×C412yes—
148C11×C4⋊C8—21no—
149C11×C4⋊C8—21no—
150C11×C4⋊C8—21no—
151C11×C4⋊C8C2311yescharacteristic
152C11×C4⋊C8C2311yescharacteristic
153C11×C4⋊C8C2311yescharacteristic
154C11×C4⋊C8C2311yescharacteristic
155C11×C22⋊C8—21no—
156C11×C22⋊C8—21no—
157C11×C22⋊C8—21no—
158C11×#97—21no—
159C11×#97—21no—
160C4×C8×C11—21no—
161C22⋊(C11⋊C8)—21no—
162C22⋊(C11⋊C8)—21no—
163C22⋊(C11⋊C8)—21no—
164C4⋊(C11⋊C8)—21no—
165C4⋊(C11⋊C8)—21no—
166C4⋊(C11⋊C8)—21no—
167C4⋊(C11⋊C8)C2311yescharacteristic
168C4⋊(C11⋊C8)C2311yescharacteristic
169C4⋊(C11⋊C8)C2311yescharacteristic
170C4⋊(C11⋊C8)C2311yescharacteristic
171#66867—21no—
172#66867—21no—
173C4×C11⋊C8—21no—
174#17775—111nomaximal, Sylow
175C11×#41—42no—
176C2×Q8×C11C22⋊C411yescharacteristic
177C2×D4×C11C22⋊C411yescharacteristic
178C2×D4×C11C22⋊C411yescharacteristic
179C2×D4×C11C22⋊C411yescharacteristic
180C22×C4×C11C22×C411yescharacteristic
181C22×C4×C11C22×C411yescharacteristic
182C22×C4×C11C22×C411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C2×C22⋊D11—22no—
190C2×C22⋊D11—22no—
191C2×C22⋊D11—22no—
192C22×Dic11—22no—
193#4339—44no—
194#4339—81no—
195#4339—81no—
196#4339—81no—
197#4339—81no—
198C2×D44—21no—
199C2×D44—21no—
200C2×D44C22×C412yes—
201C2×C4×D11—22no—
202C2×C4×D11—22no—
203C2×C4×D11—22no—
204C2×Dic22—22no—
205C2×Dic22—21no—
206C2×Dic22—21no—
207C2×Dic22—81no—
208C2×Dic22—81no—
209C2×Dic22C22×C412yes—
210C11×M16—81no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11—21no—
214C2×C8×C11—21no—
215C2×C8×C11—81no—
216C2×C8×C11—81no—
217C11×C4⋊C4C22⋊C411yescharacteristic
218C11×C4⋊C4C22⋊C411yescharacteristic
219C11×C4⋊C4C22⋊C411yescharacteristic
220C11×C4⋊C4C22⋊C411yescharacteristic
221C11×C4⋊C4C22⋊C411yescharacteristic
222C11×C4⋊C4C22⋊C411yescharacteristic
223C11×C22⋊C4C22⋊C411yescharacteristic
224C11×C22⋊C4C22⋊C411yescharacteristic
225C11×C22⋊C4C22⋊C411yescharacteristic
226C11×C22⋊C4C22⋊C411yescharacteristic
227C11×C22⋊C4C22⋊C411yescharacteristic
228C11×C22⋊C4C22⋊C411yescharacteristic
229C42×C11C22×C411yescharacteristic
230C42×C11C22×C411yescharacteristic
231C42×C11C22×C411yescharacteristic
232C42×C11C2×D411yescharacteristic
233C42×C11C2×D411yescharacteristic
234C42×C11C2×D411yescharacteristic
235C42×C11C2×D411yescharacteristic
236C42×C11C2×D411yescharacteristic
237C42×C11C2×D411yescharacteristic
238C42×C11C2411yescharacteristic
239C22⋊Dic11—22no—
240C22⋊Dic11—22no—
241(C2×D11)⋊C4—22no—
242(C2×D11)⋊C4—22no—
243(C2×D11)⋊C4—22no—
244(C2×D11)⋊C4—22no—
245(C2×D11)⋊C4—22no—
246(C2×D11)⋊C4—22no—
247C4⋊Dic11—22no—
248C4⋊Dic11—22no—
249C4⋊Dic11—21no—
250C4⋊Dic11—21no—
251C4⋊Dic11—21no—
252C4⋊Dic11—21no—
253C4⋊Dic11C22×C412yes—
254C4⋊Dic11C22×C412yes—
255Dic11⋊C4—22no—
256Dic11⋊C4—22no—
257Dic11⋊C4—22no—
258Dic11⋊C4—22no—
259C4×Dic11—22no—
260C4×Dic11—22no—
261#4318—81no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8—21no—
266C2×C11⋊C8—81no—
267C2×C11⋊C8—81no—
268#3511—111no—
269#2990—111no—
270#2990D1111yescharacteristic, complemented
271#1559—111no—
272#1557—111no—
273#1556—111no—
274#1554—111no—
275#1553—111no—
276#1551—111no—
277#1551—111no—
278#1550—111no—
279#1547—111no—
280#1542—111no—
281#1540—111no—
282C2×#332—111no—
283C23×C11C2×C22⋊C411yescharacteristic
284C23×C11C2×C22⋊C411yescharacteristic
285C23×C11C2×C22⋊C411yescharacteristic
286C22×D11—22no—
287Q8×C11—41no—
288D4×C11—22no—
289D4×C11—22no—
290D4×C11—41no—
291C2×C4×C11—22no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11C2×C22⋊C411yescharacteristic
307C2×C4×C11C2×C22⋊C411yescharacteristic
308C2×C4×C11C2×C22⋊C411yescharacteristic
309C2×C4×C11C2×C22⋊C411yescharacteristic
310C2×C4×C11C2×C22⋊C411yescharacteristic
311C2×C4×C11C2×C22⋊C411yescharacteristic
312C2×C4×C11C2×C22⋊C411yescharacteristic
313C2×C4×C11C2×C22⋊C411yescharacteristic
314C2×C4×C11C2×C22⋊C411yescharacteristic
315C2×C4×C11C23×C411yescharacteristic
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11C22×D411yescharacteristic
318C22⋊D11—44no—
319C22⋊D11—82no—
320C22⋊D11—82no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—82no—
325D44—42no—
326D44—41no—
327D44—41no—
328D44—41no—
329D44—41no—
330C4×D11—44no—
331C4×D11—82no—
332C4×D11—82no—
333Dic22—41no—
334Dic22—41no—
335Dic22—41no—
336Dic22—41no—
337Dic22—42no—
338Dic22—82no—
339C8×C11—41no—
340C8×C11—41no—
341C8×C11—41no—
342C8×C11—41no—
343C11⋊C8—41no—
344C11⋊C8—41no—
345C11⋊C8—41no—
346C11⋊C8—41no—
347#556—221no—
348#555—221no—
349#554—221no—
350#553—221no—
351#553—221no—
352#548—221no—
353#548—221no—
354#547—221no—
355#542—112no—
356#542—112no—
357#537—112no—
358#533—111no—
359#533—111no—
360#532—111no—
361#532—111no—
362#532—111no—
363C2×C4⋊Q8—111no—
364#520—112no—
365C4×#41C2×D1111yescharacteristic
366#446—21no—
367#446—221no—
368#435—21no—
369#435—21no—
370#435—221no—
371#435—221no—
372C8×D4—21no—
373C8×D4—221no—
374#432—111no—
375#432—111no—
376#432C2×D1111yescharacteristic
377#432C2×D1111yescharacteristic
378#431—111no—
379#431C2×D1111yescharacteristic
380#423—111no—
381#423C2×D1111yescharacteristic
382C2×C4⋊C8—111no—
383C2×C4⋊C8—111no—
384C2×C4⋊C8C2×D1111yescharacteristic
385C2×C4⋊C8C2×D1111yescharacteristic
386#333—111no—
387#333—111no—
388#333—111no—
389#333—111no—
390#332—111no—
391#332—111no—
392#332—111no—
393#332—111no—
394#332—111no—
395#332—111no—
396#332—111no—
397#332—111no—
398#331—111no—
399#331—111no—
400#331—111no—
401#331—111no—
402C22×C11—21no—
403C22×C11—21no—
404C22×C11—21no—
405C22×C11—21no—
406C22×C11—21no—
407C22×C11—21no—
408C22×C11—21no—
409C22×C11—21no—
410C22×C11#41312yes—
411C22×C11C22×C22⋊C411yescharacteristic
412C2×D11—42no—
413C2×D11—42no—
414C2×D11—42no—
415C4×C11—21no—
416C4×C11—21no—
417C4×C11—21no—
418C4×C11—21no—
419C4×C11—21no—
420C4×C11—21no—
421C4×C11—21no—
422C4×C11—21no—
423C4×C11—21no—
424C4×C11—21no—
425C4×C11#57611yescharacteristic
426C4×C11#57711yescharacteristic
427C4×C11#57711yescharacteristic
428C4×C11#57811yescharacteristic
429Dic11—42no—
430Dic11—42no—
431Dic11—42no—
432C2×#41—112no—
433C2×#41—221no—
434C2×#41—221no—
435C2×#41C4×D1111yescharacteristic
436C22×Q8—221no—
437C2×M16—21no—
438C2×M16—221no—
439C22×C8—21no—
440C22×C8—21no—
441C22×C8—221no—
442C22×C8—221no—
443C4⋊Q8—112no—
444C4⋊Q8—111no—
445C4⋊Q8—111no—
446C4⋊Q8—111no—
447C4⋊Q8—221no—
448C4⋊Q8—221no—
449#127—111no—
450#126—222no—
451#126—222no—
452#125—221no—
453#125—221no—
454#124—112no—
455#124—222no—
456#124—222no—
457#124—221no—
458#124—221no—
459#123—222no—
460#123—222no—
461C22⋊Q8—112no—
462C22⋊Q8—112no—
463C22⋊Q8—222no—
464C22⋊Q8—221no—
465C22⋊Q8—221no—
466C22⋊Q8—222no—
467C22⋊Q8—222no—
468#121—112no—
469#121—112no—
470#121—222no—
471#121—222no—
472#121—222no—
473#121—221no—
474#121—221no—
475#121—221no—
476#121—221no—
477C4×Q8—112no—
478C4×Q8—112no—
479C4×Q8—221no—
480C4×Q8—221no—
481C4×Q8D4411yescharacteristic
482C4×Q8C22⋊D1111yescharacteristic
483C4×D4—112no—
484C4×D4—112no—
485C4×D4—222no—
486C4×D4—222no—
487C4×D4—221no—
488C4×D4—221no—
489C4×D4—221no—
490C4×D4—221no—
491C4×D4D4411yescharacteristic
492C4×D4D4411yescharacteristic
493C4×D4D4411yescharacteristic
494C4×D4C22⋊D1111yescharacteristic
495C4×D4C22⋊D1111yescharacteristic
496C4×D4C22⋊D1111yescharacteristic
497#117—221no—
498#117—221no—
499#117—222no—
500#117C4×D1111yescharacteristic
501#117C4×D1111yescharacteristic
502#117C4×D1111yescharacteristic
503C2×C4⋊C4—112no—
504C2×C4⋊C4—221no—
505C2×C4⋊C4—222no—
506C2×C42C22×D1111yescharacteristic
507C2×C42C22×D1111yescharacteristic
508C2×C42C22×D1111yescharacteristic
509C4⋊C8—21no—
510C4⋊C8—21no—
511C4⋊C8—21no—
512C4⋊C8—111no—
513C4⋊C8—111no—
514C4⋊C8—111no—
515C4⋊C8—111no—
516C4⋊C8—221no—
517C4⋊C8—221no—
518C4⋊C8—221no—
519C4⋊C8C22×D1111yescharacteristic
520C4⋊C8C22×D1111yescharacteristic
521C4⋊C8C22×D1111yescharacteristic
522C4⋊C8C22×D1111yescharacteristic
523C22⋊C8—21no—
524C22⋊C8—21no—
525C22⋊C8—21no—
526C22⋊C8—221no—
527C22⋊C8—221no—
528C22⋊C8—221no—
529#97—21no—
530#97—21no—
531#97—221no—
532#97—221no—
533C4×C8—21no—
534C4×C8—221no—
535C2×C11—22no—
536C2×C11—41no—
537C2×C11—41no—
538C2×C11C2×#41311yescharacteristic
539C2×C11#289711yescharacteristic
540C2×C11#289811yescharacteristic
541D11—82no—
542#41—42no—
543#41—444no—
544#41—881no—
545#41—881no—
546#41—881no—
547#41—881no—
548C2×Q8—112no—
549C2×Q8—222no—
550C2×Q8—221no—
551C2×Q8—221no—
552C2×Q8—881no—
553C2×Q8—881no—
554C2×Q8(C2×D11)⋊C411yescharacteristic
555C2×D4—112no—
556C2×D4—222no—
557C2×D4—222no—
558C2×D4—222no—
559C2×D4—221no—
560C2×D4—221no—
561C2×D4(C2×D11)⋊C411yescharacteristic
562C2×D4(C2×D11)⋊C411yescharacteristic
563C2×D4(C2×D11)⋊C411yescharacteristic
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4C2×C4×D1111yescharacteristic
569C22×C4C2×C4×D1111yescharacteristic
570C22×C4C2×C4×D1111yescharacteristic
571C22×C4C2×D4411yescharacteristic
572C22×C4C2×D4411yescharacteristic
573C22×C4C2×D4411yescharacteristic
574C22×C4C2×C22⋊D1111yescharacteristic
575C22×C4C2×C22⋊D1111yescharacteristic
576C22×C4C2×C22⋊D1111yescharacteristic
577M16—81no—
578M16—881no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—81no—
584C2×C8—81no—
585C2×C8—221no—
586C2×C8—221no—
587C2×C8—221no—
588C2×C8—221no—
589C2×C8—881no—
590C2×C8—881no—
591C4⋊C4—112no—
592C4⋊C4—112no—
593C4⋊C4—222no—
594C4⋊C4—222no—
595C4⋊C4—222no—
596C4⋊C4—222no—
597C4⋊C4—222no—
598C4⋊C4—222no—
599C4⋊C4—221no—
600C4⋊C4—221no—
601C4⋊C4—221no—
602C4⋊C4—221no—
603C4⋊C4(C2×D11)⋊C411yescharacteristic
604C4⋊C4(C2×D11)⋊C411yescharacteristic
605C4⋊C4(C2×D11)⋊C411yescharacteristic
606C4⋊C4(C2×D11)⋊C411yescharacteristic
607C4⋊C4(C2×D11)⋊C411yescharacteristic
608C4⋊C4(C2×D11)⋊C411yescharacteristic
609C22⋊C4—222no—
610C22⋊C4—222no—
611C22⋊C4—222no—
612C22⋊C4—222no—
613C22⋊C4—222no—
614C22⋊C4—222no—
615C22⋊C4—222no—
616C22⋊C4—222no—
617C22⋊C4(C2×D11)⋊C411yescharacteristic
618C22⋊C4(C2×D11)⋊C411yescharacteristic
619C22⋊C4(C2×D11)⋊C411yescharacteristic
620C22⋊C4(C2×D11)⋊C411yescharacteristic
621C22⋊C4(C2×D11)⋊C411yescharacteristic
622C22⋊C4(C2×D11)⋊C411yescharacteristic
623C42—222no—
624C42—222no—
625C42C2×C4×D1111yescharacteristic
626C42C2×C4×D1111yescharacteristic
627C42C2×C4×D1111yescharacteristic
628C42C2×D4411yescharacteristic
629C42C2×D4411yescharacteristic
630C42C2×D4411yescharacteristic
631C42C2×C22⋊D1111yescharacteristic
632C42C2×C22⋊D1111yescharacteristic
633C42C2×C22⋊D1111yescharacteristic
634C42C23×D1111yescharacteristic
635C11#1777511yescharacteristic, complemented, Sylow
636C23—222no—
637C23C2×(C2×D11)⋊C411yescharacteristic
638C23C2×(C2×D11)⋊C411yescharacteristic
639C23C2×(C2×D11)⋊C411yescharacteristic
640Q8—41no—
641Q8—442no—
642Q8—441no—
643Q8—441no—
644Q8—441no—
645Q8—441no—
646Q8—882no—
647D4—22no—
648D4—22no—
649D4—41no—
650D4—442no—
651D4—444no—
652D4—441no—
653D4—441no—
654D4—441no—
655D4—441no—
656D4—882no—
657D4—882no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—444no—
677C2×C4—882no—
678C2×C4—882no—
679C2×C4—882no—
680C2×C4C2×(C2×D11)⋊C411yescharacteristic
681C2×C4C2×(C2×D11)⋊C411yescharacteristic
682C2×C4C2×(C2×D11)⋊C411yescharacteristic
683C2×C4C2×(C2×D11)⋊C411yescharacteristic
684C2×C4C2×(C2×D11)⋊C411yescharacteristic
685C2×C4C2×(C2×D11)⋊C411yescharacteristic
686C2×C4C2×(C2×D11)⋊C411yescharacteristic
687C2×C4C2×(C2×D11)⋊C411yescharacteristic
688C2×C4C2×(C2×D11)⋊C411yescharacteristic
689C2×C4C22×C4×D1111yescharacteristic
690C2×C4C22×D4411yescharacteristic
691C2×C4C22×C22⋊D1111yescharacteristic
692C8—41no—
693C8—41no—
694C8—41no—
695C8—41no—
696C8—441no—
697C8—441no—
698C8—441no—
699C8—441no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—442no—
709C22—442no—
710C22—442no—
711C22#1062274512yes—
712C22C22×(C2×D11)⋊C411yescharacteristic
713C4—21no—
714C4—21no—
715C4—21no—
716C4—21no—
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—21no—
723C4—442no—
724C4—442no—
725C4—442no—
726C4#1062328211yescharacteristic
727C4#1062328411yescharacteristic
728C4#1062336611yescharacteristic
729C4#1062336811yescharacteristic
730C2—22no—
731C2—41no—
732C2—41no—
733C2—882no—
734C2C2×#1062274511yescharacteristic
735C2#1307713911yescharacteristic
736C2#1307715011yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2990C2
socleC22×C11C22×C22⋊C4
prime radical#13082527C2
cosocleC42×C11C24
hypercenter#2990D11
hypocenterC11#17775
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
2. #13077741C2semidirect
3. #13067344C2semidirect
4. #13067339C2semidirect
5. #13067334C2semidirect
6. #13067327C2semidirect
7. #13067319C2semidirect
8. #13067312C2semidirect
9. #13067309C2semidirect
10. #13067304C2semidirect
11. #13067294C2semidirect
12. #13067271C2semidirect
13. #13067266C2semidirect
14. C2×#10622120C2semidirect
15. C11×#2990C2semidirect
270. #2990D11semidirect
635. C11#17775semidirect

Maximal subgroups

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

subgroupindex
#130825272
#130777412
#130673442
#130673392
#130673342
#130673272
#130673192
#130673122
#130673092
#130673042
#130672942
#130672712
#130672662
C2×#106221202
C11×#29902
#1777511