Finite Group Databasebeta

← #14913770

Subgroups — #14913770

Order 2816.

2220 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623216C211yesmaximal, characteristic
2#13071715C212yesmaximal
3#13071713C212yesmaximal
4#13071708C211yesmaximal, characteristic
5#13071675C211yesmaximal, characteristic
6#13071671C212yesmaximal
7#13071574C211yesmaximal, characteristic
8#13071570C212yesmaximal
9#13071536C211yesmaximal, characteristic
10#13071535C211yesmaximal, characteristic
11#13071530C211yesmaximal, characteristic
12#13071187C211yesmaximal, characteristic
13#13071187C212yesmaximal
14#125×Dic11C211yesmaximal, characteristic
15#13071175C211yesmaximal, characteristic
16#13071173C212yesmaximal
17#13071173C212yesmaximal
18C4×#66940C212yesmaximal
19C4×#66940C211yesmaximal, characteristic
20C4×#66940C211yesmaximal, characteristic
21C4×#66940C211yesmaximal, characteristic
22C4×#66940C211yesmaximal, characteristic
23C11×#2370C211yesmaximal, characteristic
24C2×C11×#125C2211yescharacteristic
25#10623216C4116yescomplemented
26C2×#66943C2211yescharacteristic
27C2×#66942C2212yes—
28C2×#66942C2212yes—
29C2×#66941C2212yes—
30C2×#66941C2211yescharacteristic
31C2×#66940C2211yescharacteristic
32C2×#66940C2212yes—
33C2×#66940C2211yescharacteristic
34C2×#66940C2211yescharacteristic
35C2×#66940C2211yescharacteristic
36C2×#66940C2211yescharacteristic
37C2×#66940C2212yes—
38C2×#66940C2211yescharacteristic
39C2×C4×Dic22C2212yes—
40C2×C4×Dic22C2211yescharacteristic
41C2×C4×Dic22C2211yescharacteristic
42C2×C4×Dic22C2211yescharacteristic
43C2×C4×Dic22C2211yescharacteristic
44C11×#389C2211yescharacteristic
45C11×#389C2212yes—
46C11×#389C2211yescharacteristic
47C11×#387C2212yes—
48C11×#387C2212yes—
49C4×C11×C4⋊C4C2211yescharacteristic
50C4×C11×C4⋊C4C2211yescharacteristic
51C4×C11×C4⋊C4C2212yes—
52C4×C11×C4⋊C4C2211yescharacteristic
53C4×C11×C4⋊C4C2211yescharacteristic
54#10622598C2211yescharacteristic
55#10622598C2211yescharacteristic
56#10622594C2212yes—
57#10622594C2212yes—
58#10622591C2212yes—
59#10622590C2211yescharacteristic
60#10622589C2212yes—
61#10622589C2211yescharacteristic
62C4⋊C4×Dic11C2211yescharacteristic
63C4⋊C4×Dic11C2211yescharacteristic
64C4⋊C4×Dic11C2211yescharacteristic
65C4⋊C4×Dic11C2212yes—
66C4⋊C4×Dic11C2212yes—
67C4⋊C4×Dic11C2212yes—
68C4⋊C4×Dic11C2211yescharacteristic
69C4⋊C4×Dic11C2211yescharacteristic
70C4⋊C4×Dic11C2211yescharacteristic
71C4⋊C4×Dic11C2211yescharacteristic
72C4⋊C4×Dic11C2211yescharacteristic
73C4⋊C4×Dic11C2212yes—
74#10622585C2212yes—
75#10622585C2212yes—
76#10622585C2212yes—
77#10622585C2212yes—
78#10622585C2212yes—
79#10622549C2211yescharacteristic
80#10622546C2212yes—
81#10622546C2212yes—
82C4×Dic11⋊C4C2212yes—
83C4×Dic11⋊C4C2211yescharacteristic
84C4×Dic11⋊C4C2212yes—
85C4×Dic11⋊C4C2211yescharacteristic
86C4×Dic11⋊C4C2212yes—
87C4×Dic11⋊C4C2212yes—
88C4×Dic11⋊C4C2212yes—
89C42×Dic11C2212yes—
90C42×Dic11C2212yes—
91C42×Dic11C2211yescharacteristic
92C42×Dic11C2211yescharacteristic
93C42×Dic11C2212yes—
94C42×Dic11C2211yescharacteristic
95#10622541C2211yescharacteristic
96#10622541C2212yes—
97#10622541C2211yescharacteristic
98#10622268C2212yes—
99#10622268C2212yes—
100#10622267C2212yes—
101#10622267C2212yes—
102#10622266C2212yes—
103#10622263C2212yes—
104#10622263C2212yes—
105#10622262C2212yes—
106#10622262C2212yes—
107#10622262C2212yes—
108#10622262C2212yes—
109#10622262C2212yes—
110#10622262C2211yescharacteristic
111#10622262C2212yes—
112#10622262C2212yes—
113#10622262C2212yes—
114#10622262C2211yescharacteristic
115#10622262C2212yes—
116#10622262C2212yes—
117#10622262C2211yescharacteristic
118#10622262C2211yescharacteristic
119#10622260C2212yes—
120#10622260C2212yes—
121#10622259C2212yes—
122#10622259C2212yes—
123#10622259C2212yes—
124C22×Dic22C2312yes—
125C22×Dic22C2311yescharacteristic
126C22×Dic22C2311yescharacteristic
127C11×#125C2×C418yes—
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C11×C4⋊C4C2312yes—
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C4⋊C4C2311yescharacteristic
132C2×C11×C4⋊C4C2312yes—
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C4⋊C4C2312yes—
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2312yes—
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C42×C11C2311yescharacteristic
139C2×C42×C11C2311yescharacteristic
140C2×C42×C11C2312yes—
141C2×C42×C11C2312yes—
142C2×C42×C11C2312yes—
143C2×C42×C11C2311yescharacteristic
144C2×C4⋊Dic11C2312yes—
145C2×C4⋊Dic11C2311yescharacteristic
146C2×C4⋊Dic11C2311yescharacteristic
147C2×C4⋊Dic11C2312yes—
148C2×C4⋊Dic11C2311yescharacteristic
149C2×C4⋊Dic11C2311yescharacteristic
150C2×C4⋊Dic11C2312yes—
151C2×Dic11⋊C4C2312yes—
152C2×Dic11⋊C4C2312yes—
153C2×Dic11⋊C4C2312yes—
154C2×Dic11⋊C4C2312yes—
155C2×Dic11⋊C4C2311yescharacteristic
156C2×Dic11⋊C4C2311yescharacteristic
157C2×Dic11⋊C4C2312yes—
158C2×Dic11⋊C4C2311yescharacteristic
159C2×Dic11⋊C4C2312yes—
160C2×Dic11⋊C4C2312yes—
161C2×Dic11⋊C4C2311yescharacteristic
162C2×Dic11⋊C4C2312yes—
163C2×Dic11⋊C4C2311yescharacteristic
164C2×Dic11⋊C4C2312yes—
165C2×Dic11⋊C4C2312yes—
166C2×Dic11⋊C4C2312yes—
167C2×Dic11⋊C4C2312yes—
168C2×Dic11⋊C4C2312yes—
169C2×Dic11⋊C4C2311yescharacteristic
170C2×C4×Dic11C2312yes—
171C2×C4×Dic11C2312yes—
172C2×C4×Dic11C2312yes—
173C2×C4×Dic11C2312yes—
174C2×C4×Dic11C2311yescharacteristic
175C2×C4×Dic11C2312yes—
176C2×C4×Dic11C2312yes—
177C2×C4×Dic11C2311yescharacteristic
178C2×C4×Dic11C2312yes—
179C2×C4×Dic11C2311yescharacteristic
180C2×C4×Dic11C2311yescharacteristic
181C2×C4×Dic11C2311yescharacteristic
182C2×C4×Dic11C2311yescharacteristic
183C2×C4×Dic11C2311yescharacteristic
184C2×C4×Dic11C2311yescharacteristic
185C2×C4×Dic11C2311yescharacteristic
186C2×C4×Dic11C2312yes—
187C2×C4×Dic11C2311yescharacteristic
188C2×C4×Dic11C2311yescharacteristic
189C2×C4×Dic11C2312yes—
190C2×C4×Dic11C2311yescharacteristic
191C2×C4×Dic11C2311yescharacteristic
192C2×C4×Dic11C2312yes—
193C2×C4×Dic11C2311yescharacteristic
194C2×C4×Dic11C2312yes—
195C2×C4×Dic11C2312yes—
196C2×C4×Dic11C2312yes—
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2311yescharacteristic
199#66943C2×C418yes—
200#66942C2×C4116yes—
201#66942C2×C4116yes—
202#66941C2×C418yes—
203#66941C2×C4116yes—
204#66940—24no—
205#66940—24no—
206#66940—28no—
207#66940—24no—
208#66940C2×C418yes—
209#66940C2×C4116yes—
210#66940C2×C418yes—
211#66940Q818yescomplemented
212C4×Dic22—24no—
213C4×Dic22—24no—
214C4×Dic22—28no—
215C4×Dic22C2×C418yes—
216C4×Dic22C2×C418yes—
217C11×#95C2312yes—
218C11×#95C2312yes—
219C11×#95C2312yes—
220C11×#95C2312yes—
221C11×#95C2311yescharacteristic
222C11×#95C2311yescharacteristic
223C11×#95C2312yes—
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2311yescharacteristic
234C11⋊#95C2311yescharacteristic
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2311yescharacteristic
241C11⋊#95C2311yescharacteristic
242C4×#557—111nomaximal, Sylow
243C22×C4×C11C2411yescharacteristic
244C22×C4×C11C2412yes—
245C22×C4×C11C2411yescharacteristic
246C22×C4×C11C2411yescharacteristic
247C22×C4×C11C2412yes—
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2412yes—
250C22×C4×C11C2412yes—
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C22×Dic11C2412yes—
255C22×Dic11C2411yescharacteristic
256C22×Dic11C2412yes—
257C22×Dic11C2411yescharacteristic
258C22×Dic11C2411yescharacteristic
259C22×Dic11C2411yescharacteristic
260C22×Dic11C2412yes—
261C22×Dic11C2411yescharacteristic
262C22×Dic11C2411yescharacteristic
263C22×Dic11C2412yes—
264C22×Dic11C2411yescharacteristic
265C22×Dic11C2411yescharacteristic
266C2×Dic22—24no—
267C2×Dic22—22no—
268C2×Dic22—24no—
269C2×Dic22—22no—
270C2×Dic22C22×C414yes—
271C2×Dic22C22×C418yes—
272C2×Dic22C22×C414yes—
273C2×Dic22C2×Q814yes—
274C2×Dic22#4114yes—
275C11×C4⋊C4—22no—
276C11×C4⋊C4—24no—
277C11×C4⋊C4—22no—
278C11×C4⋊C4—22no—
279C11×C4⋊C4—42no—
280C11×C4⋊C4C22×C414yes—
281C11×C4⋊C4C22×C418yes—
282C11×C4⋊C4C22×C414yes—
283C11×C4⋊C4C22×C418yes—
284C11×C4⋊C4C2×Q814yes—
285C42×C11—24no—
286C42×C11—22no—
287C42×C11—22no—
288C42×C11—42no—
289C42×C11—42no—
290C42×C11C22×C414yes—
291C4⋊Dic11—24no—
292C4⋊Dic11—22no—
293C4⋊Dic11—22no—
294C4⋊Dic11—42no—
295C4⋊Dic11C22×C414yes—
296C4⋊Dic11C22×C414yes—
297C4⋊Dic11C22×C418yes—
298Dic11⋊C4—24no—
299Dic11⋊C4—24no—
300Dic11⋊C4—22no—
301Dic11⋊C4—24no—
302Dic11⋊C4—24no—
303Dic11⋊C4—22no—
304Dic11⋊C4—24no—
305Dic11⋊C4—22no—
306Dic11⋊C4—24no—
307Dic11⋊C4—42no—
308Dic11⋊C4C22×C414yes—
309Dic11⋊C4C22×C418yes—
310Dic11⋊C4C22×C414yes—
311Dic11⋊C4C22×C418yes—
312Dic11⋊C4C22×C418yes—
313Dic11⋊C4C22×C418yes—
314Dic11⋊C4C22×C418yes—
315Dic11⋊C4C2×Q818yes—
316Dic11⋊C4#4114yes—
317C4×Dic11—24no—
318C4×Dic11—24no—
319C4×Dic11—24no—
320C4×Dic11—24no—
321C4×Dic11—22no—
322C4×Dic11—24no—
323C4×Dic11—22no—
324C4×Dic11—24no—
325C4×Dic11—22no—
326C4×Dic11—24no—
327C4×Dic11—22no—
328C4×Dic11—22no—
329C4×Dic11—22no—
330C4×Dic11—24no—
331C4×Dic11—22no—
332C4×Dic11—22no—
333C4×Dic11—22no—
334C4×Dic11—41no—
335C4×Dic11—42no—
336C4×Dic11—41no—
337C4×Dic11—41no—
338C4×Dic11C22×C414yes—
339C4×Dic11C22×C418yes—
340C4×Dic11C22×C414yes—
341C4×Dic11C22×C418yes—
342C4×Dic11C22×C418yes—
343C4×Dic11C2×Q818yes—
344C4×Dic11C2×Q814yes—
345C4×Dic11#4114yes—
346C2×#557—111no—
347#2370—112no—
348#2370—111no—
349#2370—112no—
350#2370D1111yescharacteristic
351#2365—112no—
352#2365—111no—
353#2355—112no—
354#2355—111no—
355#2351—111no—
356#2351—111no—
357Q8×C4⋊C4—111no—
358C4×C4⋊Q8—112no—
359C4×C4⋊Q8—111no—
360C4×#125—111no—
361C4×#125—112no—
362C4×#125—112no—
363C4×#125—111no—
364C42×Q8—111no—
365C42×Q8—111no—
366C42×Q8—112no—
367C42×Q8—111no—
368C42×Q8—111no—
369C23×C11C2511yescharacteristic
370C2×C4×C11—22no—
371C2×C4×C11—21no—
372C2×C4×C11—21no—
373C2×C4×C11—21no—
374C2×C4×C11—22no—
375C2×C4×C11—21no—
376C2×C4×C11—22no—
377C2×C4×C11—21no—
378C2×C4×C11—22no—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—22no—
382C2×C4×C11—21no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—21no—
387C2×C4×C11—21no—
388C2×C4×C11—21no—
389C2×C4×C11—21no—
390C2×C4×C11—21no—
391C2×C4×C11—21no—
392C2×C4×C11—22no—
393C2×C4×C11C23×C412yes—
394C2×C4×C11C23×C414yes—
395C2×C4×C11C23×C414yes—
396C2×C4×C11C23×C412yes—
397C2×C4×C11C23×C412yes—
398C2×C4×C11C22×Q814yes—
399C2×C4×C11C22×Q812yes—
400C2×C4×C11C2×#4112yes—
401C2×C4×C11C2×#4112yes—
402C2×C4×C11C2×#4112yes—
403C2×Dic11—21no—
404C2×Dic11—21no—
405C2×Dic11—21no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—21no—
409C2×Dic11—21no—
410C2×Dic11—21no—
411C2×Dic11—21no—
412C2×Dic11—21no—
413C2×Dic11—21no—
414C2×Dic11—21no—
415C2×Dic11—21no—
416C2×Dic11—21no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—21no—
424C2×Dic11C23×C412yes—
425C2×Dic11C23×C412yes—
426C2×Dic11C23×C414yes—
427C2×Dic11C23×C412yes—
428C2×Dic11C23×C414yes—
429C2×Dic11C23×C412yes—
430C2×Dic11C22×Q812yes—
431C2×Dic11C22×Q814yes—
432C2×Dic11C22×Q812yes—
433C2×Dic11C2×#4112yes—
434C2×Dic11C2×#4114yes—
435C2×Dic11C2×#4112yes—
436C2×Dic11C2×#4112yes—
437C2×Dic11C2×#4112yes—
438C2×Dic112−1+412yes—
439Dic22—216no—
440Dic22—28no—
441Dic22C4×Q8116yescomplemented
442#557—1116no—
443C2×C4⋊Q8—112no—
444C2×C4⋊Q8—111no—
445C2×#125—112no—
446C2×#125—112no—
447C2×#125—111no—
448C2×#125C2×D1111yescharacteristic
449C2×C4×Q8—111no—
450C2×C4×Q8—111no—
451C2×C4×Q8—112no—
452C2×C4×Q8—111no—
453C2×C4×Q8—111no—
454C2×C4×Q8—112no—
455C2×C4×Q8—111no—
456C2×C4×Q8—111no—
457C2×C4×Q8—111no—
458C2×C4×Q8—111no—
459C2×C4×Q8—111no—
460C2×C4×Q8—111no—
461C2×C4×Q8—112no—
462#391—112no—
463#391—112no—
464#391—112no—
465#389—112no—
466#389—111no—
467#389—112no—
468#389—111no—
469#389—112no—
470#389—112no—
471#389—112no—
472#389—111no—
473#389—111no—
474#389—112no—
475#389—112no—
476#389—112no—
477#389C2×D1111yescharacteristic
478#389C2×D1111yescharacteristic
479#389C2×D1112yes—
480#387—112no—
481#387—112no—
482#387—112no—
483#387—112no—
484#387—112no—
485#387—112no—
486#387—112no—
487#387—112no—
488#387—112no—
489#387—112no—
490#387C2×D1112yes—
491#387C2×D1112yes—
492#384—112no—
493#384—111no—
494#382—111no—
495#382—111no—
496#382—112no—
497#382—112no—
498C4×C4⋊C4—112no—
499C4×C4⋊C4—112no—
500C4×C4⋊C4—111no—
501C4×C4⋊C4—112no—
502C4×C4⋊C4—111no—
503C4×C4⋊C4—111no—
504C4×C4⋊C4—111no—
505C4×C4⋊C4—112no—
506C4×C4⋊C4—111no—
507C4×C4⋊C4—111no—
508C4×C4⋊C4—111no—
509C4×C4⋊C4—111no—
510C4×C4⋊C4—111no—
511C4×C4⋊C4—111no—
512C4×C4⋊C4—112no—
513C4×C4⋊C4—112no—
514C4×C4⋊C4—112no—
515C4×C4⋊C4—112no—
516C4×C4⋊C4—112no—
517C4×C4⋊C4—112no—
518C4×C4⋊C4—112no—
519C4×C4⋊C4—112no—
520C4×C4⋊C4—111no—
521C4×C4⋊C4—112no—
522C4×C4⋊C4—112no—
523C4×C4⋊C4—112no—
524C4×C4⋊C4—112no—
525C4×C4⋊C4—111no—
526C4×C4⋊C4—112no—
527C4×C4⋊C4—112no—
528C4×C4⋊C4—112no—
529C4×C4⋊C4—111no—
530C4×C4⋊C4—111no—
531C4×C4⋊C4C2×D1111yescharacteristic
532C4×C4⋊C4C2×D1111yescharacteristic
533C4×C4⋊C4C2×D1111yescharacteristic
534C4×C4⋊C4C2×D1112yes—
535C4×C4⋊C4C2×D1111yescharacteristic
536C43—112no—
537C43—111no—
538C43—112no—
539C43—111no—
540C43—112no—
541C43—111no—
542C22×C11C24×C411yescharacteristic
543C22×C11C23×Q811yescharacteristic
544C22×C11C22×#4111yescharacteristic
545C22×C11C22×#4111yescharacteristic
546C22×C11C22×#4111yescharacteristic
547C22×C11C2×2−1+411yescharacteristic
548C22×C11#58511yescharacteristic
549C4×C11—22no—
550C4×C11—24no—
551C4×C11—22no—
552C4×C11—24no—
553C4×C11—24no—
554C4×C11—22no—
555C4×C11—22no—
556C4×C11—42no—
557C4×C11—41no—
558C4×C11—41no—
559C4×C11C2×C4×Q814yes—
560Dic11—24no—
561Dic11—22no—
562Dic11—22no—
563Dic11—22no—
564Dic11—22no—
565Dic11—22no—
566Dic11—41no—
567Dic11—42no—
568Dic11—42no—
569Dic11C2×C4×Q818yes—
570Dic11C4×#4114yes—
571Dic11#55714yescomplemented
572C22×Q8—111no—
573C22×Q8—112no—
574C22×Q8—111no—
575C4⋊Q8—1116no—
576C4⋊Q8—118no—
577#125—1116no—
578#125—1116no—
579#125—118no—
580#125C4×D1118yes—
581C4×Q8—118no—
582C4×Q8—1116no—
583C4×Q8—118no—
584C4×Q8—118no—
585C4×Q8—118no—
586C4×Q8—118no—
587C4×Q8—228no—
588C4×Q8—224no—
589C4×Q8—224no—
590C4×Q8—224no—
591C4×Q8—228no—
592C4×Q8—224no—
593C4×Q8—224no—
594C2×C4⋊C4—111no—
595C2×C4⋊C4—111no—
596C2×C4⋊C4—112no—
597C2×C4⋊C4—111no—
598C2×C4⋊C4—111no—
599C2×C4⋊C4—112no—
600C2×C4⋊C4—112no—
601C2×C4⋊C4—112no—
602C2×C4⋊C4—111no—
603C2×C4⋊C4—112no—
604C2×C4⋊C4—112no—
605C2×C4⋊C4—112no—
606C2×C4⋊C4—112no—
607C2×C4⋊C4—111no—
608C2×C4⋊C4—112no—
609C2×C4⋊C4—112no—
610C2×C4⋊C4—111no—
611C2×C4⋊C4—111no—
612C2×C4⋊C4—112no—
613C2×C4⋊C4—111no—
614C2×C4⋊C4—112no—
615C2×C4⋊C4—112no—
616C2×C4⋊C4—111no—
617C2×C4⋊C4—112no—
618C2×C4⋊C4—112no—
619C2×C4⋊C4—112no—
620C2×C4⋊C4C22×D1111yescharacteristic
621C2×C4⋊C4C22×D1111yescharacteristic
622C2×C4⋊C4C22×D1112yes—
623C2×C4⋊C4C22×D1111yescharacteristic
624C2×C4⋊C4C22×D1112yes—
625C2×C4⋊C4C22×D1112yes—
626C2×C4⋊C4C22×D1111yescharacteristic
627C2×C4⋊C4C22×D1111yescharacteristic
628C2×C4⋊C4C22×D1112yes—
629C2×C4⋊C4C22×D1111yescharacteristic
630C2×C42—111no—
631C2×C42—112no—
632C2×C42—112no—
633C2×C42—111no—
634C2×C42—112no—
635C2×C42—111no—
636C2×C42—112no—
637C2×C42—111no—
638C2×C42—111no—
639C2×C42—112no—
640C2×C42—111no—
641C2×C42—112no—
642C2×C42—111no—
643C2×C42—112no—
644C2×C42—111no—
645C2×C42—112no—
646C2×C42—112no—
647C2×C42—112no—
648C2×C42—111no—
649C2×C42—111no—
650C2×C42—112no—
651C2×C42—111no—
652C2×C42—111no—
653C2×C42—111no—
654C2×C42—112no—
655C2×C42—111no—
656C2×C42—111no—
657C2×C42—112no—
658C2×C42—111no—
659C2×C42C22×D1112yes—
660C2×C42C22×D1111yescharacteristic
661C2×C42C22×D1111yescharacteristic
662C2×C42C22×D1112yes—
663C2×C42C22×D1112yes—
664C2×C42C22×D1111yescharacteristic
665#95—111no—
666#95—112no—
667#95—111no—
668#95—112no—
669#95—112no—
670#95—112no—
671#95—111no—
672#95—112no—
673#95—111no—
674#95—112no—
675#95—112no—
676#95—112no—
677#95—112no—
678#95—112no—
679#95—112no—
680#95—112no—
681#95—112no—
682#95—112no—
683#95C22×D1111yescharacteristic
684#95C22×D1111yescharacteristic
685#95C22×D1112yes—
686#95C22×D1112yes—
687#95C22×D1112yes—
688#95C22×D1112yes—
689#95C22×D1112yes—
690C2×C11C22×C4×Q811yescharacteristic
691C2×C11C2×C4×#4111yescharacteristic
692C2×C11C4×2−1+411yescharacteristic
693C2×C11C2×#55711yescharacteristic
694C2×C11Q8×#4111yescharacteristic
695C2×C11#348011yescharacteristic
696C2×C11#348211yescharacteristic
697C2×Q8—114no—
698C2×Q8—118no—
699C2×Q8—114no—
700C2×Q8—114no—
701C2×Q8—114no—
702C2×Q8—224no—
703C2×Q8—224no—
704C2×Q8—222no—
705C2×Q8—222no—
706C22×C4—111no—
707C22×C4—112no—
708C22×C4—111no—
709C22×C4—111no—
710C22×C4—111no—
711C22×C4—111no—
712C22×C4—111no—
713C22×C4—111no—
714C22×C4—112no—
715C22×C4—112no—
716C22×C4—111no—
717C22×C4—112no—
718C22×C4C23×D1111yescharacteristic
719C22×C4C23×D1111yescharacteristic
720C22×C4C23×D1112yes—
721C22×C4C23×D1111yescharacteristic
722C22×C4C23×D1112yes—
723C22×C4C23×D1112yes—
724C22×C4C23×D1111yescharacteristic
725C22×C4C23×D1112yes—
726C22×C4C23×D1111yescharacteristic
727C22×C4C23×D1111yescharacteristic
728C22×C4C23×D1111yescharacteristic
729C4⋊C4—22no—
730C4⋊C4—24no—
731C4⋊C4—22no—
732C4⋊C4—22no—
733C4⋊C4—42no—
734C4⋊C4—114no—
735C4⋊C4—118no—
736C4⋊C4—118no—
737C4⋊C4—114no—
738C4⋊C4—114no—
739C4⋊C4—118no—
740C4⋊C4—118no—
741C4⋊C4—114no—
742C4⋊C4—118no—
743C4⋊C4—118no—
744C4⋊C4—118no—
745C4⋊C4—114no—
746C4⋊C4—224no—
747C4⋊C4—224no—
748C4⋊C4—222no—
749C4⋊C4—224no—
750C4⋊C4—224no—
751C4⋊C4—222no—
752C4⋊C4—224no—
753C4⋊C4—224no—
754C4⋊C4—222no—
755C4⋊C4—224no—
756C4⋊C4—222no—
757C4⋊C4—222no—
758C4⋊C4—442no—
759C4⋊C4—442no—
760C4⋊C4C2×C4×D1118yes—
761C4⋊C4C2×C4×D1114yes—
762C4⋊C4C2×C4×D1114yes—
763C4⋊C4C2×C4×D1118yes—
764C4⋊C4Q8×D1114yes—
765C42—24no—
766C42—22no—
767C42—22no—
768C42—42no—
769C42—42no—
770C42—118no—
771C42—118no—
772C42—114no—
773C42—118no—
774C42—114no—
775C42—118no—
776C42—114no—
777C42—114no—
778C42—224no—
779C42—224no—
780C42—224no—
781C42—224no—
782C42—222no—
783C42—224no—
784C42—222no—
785C42—222no—
786C42—224no—
787C42—222no—
788C42—224no—
789C42—222no—
790C42—222no—
791C42—224no—
792C42—222no—
793C42—222no—
794C42—222no—
795C42—441no—
796C42—442no—
797C42—441no—
798C42—441no—
799C42C2×C4×D1114yes—
800C11C4×#55711yescharacteristic, complemented, Sylow
801C23C24×D1111yescharacteristic
802Q8—1116no—
803Q8—2216no—
804Q8—228no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—114no—
829C2×C4—112no—
830C2×C4—112no—
831C2×C4—114no—
832C2×C4—112no—
833C2×C4—112no—
834C2×C4—112no—
835C2×C4—114no—
836C2×C4—112no—
837C2×C4—112no—
838C2×C4—112no—
839C2×C4—112no—
840C2×C4—114no—
841C2×C4—112no—
842C2×C4—112no—
843C2×C4—221no—
844C2×C4—221no—
845C2×C4—221no—
846C2×C4—222no—
847C2×C4—222no—
848C2×C4—221no—
849C2×C4—221no—
850C2×C4—221no—
851C2×C4—221no—
852C2×C4—221no—
853C2×C4—221no—
854C2×C4—221no—
855C2×C4—221no—
856C2×C4—222no—
857C2×C4—222no—
858C2×C4—221no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—221no—
863C2×C4—222no—
864C2×C4C22×C4×D1112yes—
865C2×C4C22×C4×D1114yes—
866C2×C4C22×C4×D1114yes—
867C2×C4C22×C4×D1112yes—
868C2×C4C22×C4×D1112yes—
869C2×C4C2×Q8×D1114yes—
870C2×C4C2×Q8×D1112yes—
871C2×C4#41×D1112yes—
872C2×C4#41×D1112yes—
873C2×C4#41×D1112yes—
874C22C23×C4×D1111yescharacteristic
875C22C22×Q8×D1111yescharacteristic
876C22C2×#41×D1111yescharacteristic
877C22C2×#41×D1111yescharacteristic
878C22C2×#41×D1111yescharacteristic
879C22#1062345511yescharacteristic
880C22D11×2−1+411yescharacteristic
881C4—24no—
882C4—22no—
883C4—22no—
884C4—24no—
885C4—22no—
886C4—22no—
887C4—24no—
888C4—41no—
889C4—42no—
890C4—41no—
891C4—114no—
892C4—118no—
893C4—114no—
894C4—222no—
895C4—222no—
896C4—222no—
897C4—224no—
898C4—222no—
899C4—222no—
900C4—442no—
901C4—441no—
902C4—442no—
903C4C4×Q8×D1114yes—
904C2C2×C4×Q8×D1111yescharacteristic
905C2C4×#41×D1111yescharacteristic
906C2#1308182711yescharacteristic
907C2D11×#55711yescharacteristic
908C2#1308219511yescharacteristic
909C2#1308221011yescharacteristic
910C2#1308223011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2370C2
socle, prime radical, cosocleC23×C11C25
hypercenter#2370D11
hypocenterC11C4×#557
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2370

Complements

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

NH ≅ G/Ntype
25. #10623216C4semidirect
211. #66940Q8semidirect
441. Dic22C4×Q8semidirect
571. Dic11#557semidirect
800. C11C4×#557semidirect

Maximal subgroups

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

subgroupindex
C2×#106232162
#130717152
#130717132
#130717082
#130716752
#130716712
#130715742
#130715702
#130715362
#130715352
#130715302
#130711872
#125×Dic112
#130711752
#130711732
C4×#669402
C11×#23702
C4×#55711