Finite Group Databasebeta

← #14769458

Subgroups — #14769458

Order 2816.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#4318C211yesmaximal, characteristic, complemented
2C2×#10622849C211yesmaximal, characteristic, complemented
3C22×#66901C211yesmaximal, characteristic, complemented
4#13071061C211yesmaximal, characteristic, complemented
5#13069536C211yesmaximal, characteristic, complemented
6#13069449C211yesmaximal, characteristic, complemented
7#13069065C211yesmaximal, characteristic, complemented
8#13069060C211yesmaximal, characteristic, complemented
9#13068919C211yesmaximal, characteristic, complemented
10#13068919C211yesmaximal, characteristic, complemented
11#13068636C211yesmaximal, characteristic, complemented
12#13068560C211yesmaximal, characteristic, complemented
13#13068560C211yesmaximal, characteristic, complemented
14#13068426C211yesmaximal, characteristic, complemented
15D4×C11×#41C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C11×#550C411yescharacteristic, complemented
19D4×Q8×C11C411yescharacteristic, complemented
20C11×#548C411yescharacteristic, complemented
21C11×#548C411yescharacteristic, complemented
22C11×#547—21no—
23C11×#547C411yescharacteristic, complemented
24C11×#546—21no—
25C11×#546—21no—
26C11×#546C411yescharacteristic, complemented
27C11×#546C411yescharacteristic, complemented
28D42×C11—21no—
29D42×C11C411yescharacteristic, complemented
30C11×#532—21no—
31C11×#532C2211yescharacteristic
32C11×#525—21no—
33C11×#525—21no—
34C11×#525C2211yescharacteristic
35C11×#525C2211yescharacteristic
36C4×C11×#41C2211yescharacteristic
37C2×C4×D4×C11—21no—
38C2×C4×D4×C11C2211yescharacteristic
39C2×#66979C2211yescharacteristic, complemented
40C22×C4×Dic11C2211yescharacteristic, complemented
41C22×#4318C2211yescharacteristic, complemented
42C22×#4318C2211yescharacteristic, complemented
43#10622849—24no—
44C2×#66901—24no—
45C2×#66901C2211yescharacteristic
46C2×#66901C2211yescharacteristic
47C2×#66901C2211yescharacteristic
48C2×#66901C2211yescharacteristic
49C2×#66901C2211yescharacteristic, complemented
50C2×#66901C2211yescharacteristic, complemented
51C2×#66901C2211yescharacteristic, complemented
52C2×#66901C2211yescharacteristic, complemented
53C2×#66901C2211yescharacteristic, complemented
54C2×#66901C2211yescharacteristic, complemented
55C2×#66901C2211yescharacteristic, complemented
56C2×#66901C2211yescharacteristic, complemented
57#10622833—21no—
58C4×C22⋊Dic11C2211yescharacteristic, complemented
59C4×C22⋊Dic11C2211yescharacteristic, complemented
60#10622820C2211yescharacteristic, complemented
61#10622820C2211yescharacteristic, complemented
62#10622625—21no—
63#10622624—21no—
64#10622624—21no—
65D4×C11⋊C8—21no—
66#10622594—21no—
67#10622564—21no—
68#10622563—21no—
69C4×C4⋊Dic11C2211yescharacteristic, complemented
70#10622545C2211yescharacteristic, complemented
71#10622537C2211yescharacteristic, complemented
72C4×#4318C2211yescharacteristic, complemented
73#10622170C2211yescharacteristic, complemented
74#10622170C2211yescharacteristic, complemented
75#10622170C2211yescharacteristic, complemented
76#10622170C2211yescharacteristic, complemented
77C2×C11×#41—21no—
78C2×C11×#41—21no—
79C2×C11×#41—21no—
80C2×C11×#41—21no—
81C2×C11×#41—22no—
82C2×C11×#41—22no—
83C2×C11×#41—22no—
84C2×C11×#41—22no—
85C2×C11×#41—41no—
86C2×C11×#41—41no—
87C2×C11×#41—41no—
88C2×C11×#41—41no—
89C2×C11×#41C2×C411yescharacteristic
90C2×C11×#41C2×C411yescharacteristic
91C2×C11×#41C2×C411yescharacteristic, complemented
92C2×C11×#41C2×C411yescharacteristic, complemented
93C2×C11×#41C2311yescharacteristic
94C2×C11×#41C2311yescharacteristic
95C2×C11×#41C2311yescharacteristic
96C22×Q8×C11C2×C411yescharacteristic
97C22×Q8×C11C2×C411yescharacteristic, complemented
98C22×D4×C11—21no—
99C22×D4×C11—21no—
100C22×D4×C11—21no—
101C22×D4×C11C2×C411yescharacteristic
102C22×D4×C11C2×C411yescharacteristic, complemented
103C22×D4×C11D411yescharacteristic
104C23×C4×C11—21no—
105C23×C4×C11—21no—
106C23×C4×C11C2311yescharacteristic
107C23×C4×C11C2311yescharacteristic
108C23×Dic11—21no—
109C11×C4⋊Q8—21no—
110C11×C4⋊Q8C2×C411yescharacteristic, complemented
111C11×#127—21no—
112C11×#127C2×C411yescharacteristic, complemented
113C11×#124—21no—
114C11×#124—21no—
115C11×#124C2×C411yescharacteristic, complemented
116C11×#124C2×C411yescharacteristic, complemented
117C11×#123—21no—
118C11×#123—21no—
119C11×#123—21no—
120C11×#123—21no—
121C11×#123—21no—
122C11×#123—21no—
123C11×C22⋊Q8—21no—
124C11×C22⋊Q8—21no—
125C11×C22⋊Q8—21no—
126C11×C22⋊Q8—21no—
127C11×C22⋊Q8C2×C411yescharacteristic
128C11×C22⋊Q8C2×C411yescharacteristic
129C11×C22⋊Q8C2×C411yescharacteristic, complemented
130C11×C22⋊Q8C2×C411yescharacteristic, complemented
131C11×#121—21no—
132C11×#121—21no—
133C11×#121—21no—
134C11×#121—21no—
135C11×#121—21no—
136C11×#121—21no—
137C11×#121—21no—
138C11×#121—21no—
139C11×#121—21no—
140C11×#121—21no—
141C11×#121C2×C411yescharacteristic
142C11×#121C2×C411yescharacteristic
143C11×#121C2×C411yescharacteristic, complemented
144C11×#121C2×C411yescharacteristic, complemented
145C11×#120—21no—
146C11×#120—21no—
147C11×#120—21no—
148C11×#120—21no—
149C11×#120—21no—
150C11×#120—21no—
151C4×Q8×C11C2×C411yescharacteristic, complemented
152C4×Q8×C11C2×C411yescharacteristic, complemented
153C4×D4×C11—21no—
154C4×D4×C11—21no—
155C4×D4×C11—21no—
156C4×D4×C11—21no—
157C4×D4×C11—21no—
158C4×D4×C11—21no—
159C4×D4×C11—21no—
160C4×D4×C11—21no—
161C4×D4×C11—21no—
162C4×D4×C11—21no—
163C4×D4×C11—21no—
164C4×D4×C11—21no—
165C4×D4×C11C2×C411yescharacteristic
166C4×D4×C11C2×C411yescharacteristic
167C4×D4×C11C2×C411yescharacteristic
168C4×D4×C11C2×C411yescharacteristic
169C4×D4×C11C2×C411yescharacteristic, complemented
170C4×D4×C11C2×C411yescharacteristic, complemented
171C4×D4×C11D411yescharacteristic
172C4×D4×C11D411yescharacteristic
173C4×D4×C11D411yescharacteristic
174C4×D4×C11D411yescharacteristic
175C11×#117—21no—
176C11×#117C2311yescharacteristic
177C2×C11×C4⋊C4—21no—
178C2×C11×C4⋊C4D411yescharacteristic
179C2×C11×C22⋊C4—21no—
180C2×C11×C22⋊C4—21no—
181C2×C11×C22⋊C4D411yescharacteristic
182C2×C11×C22⋊C4D411yescharacteristic
183C2×C42×C11—21no—
184C2×C42×C11C2311yescharacteristic
185C2×C22⋊Dic11—21no—
186C2×C22⋊Dic11—21no—
187C2×C22⋊Dic11—21no—
188#66979—22no—
189#66979—41no—
190C2×C4⋊Dic11—21no—
191C2×C4⋊Dic11—21no—
192C2×C4×Dic11—22no—
193C2×C4×Dic11—21no—
194C2×C4×Dic11—41no—
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2311yescharacteristic
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2311yescharacteristic
199C2×#4318—21no—
200C2×#4318—21no—
201C2×#4318—22no—
202C2×#4318—22no—
203C2×#4318—41no—
204C2×#4318—41no—
205C2×#4318C2311yescharacteristic
206C2×#4318C2311yescharacteristic
207C2×#4318C2311yescharacteristic
208C2×#4318C2311yescharacteristic
209C22×C11⋊C8—21no—
210C22×C11⋊C8—21no—
211#66901—22no—
212#66901—22no—
213#66901—22no—
214#66901—22no—
215#66901—22no—
216#66901—22no—
217#66901—22no—
218#66901—41no—
219#66901—41no—
220#66901—41no—
221#66901—41no—
222#66901D414yescomplemented
223C11⋊#95—21no—
224C11⋊#95—21no—
225C11⋊#95—21no—
226C11⋊#95—21no—
227C11⋊#95—21no—
228C22⋊(C11⋊C8)—21no—
229C22⋊(C11⋊C8)—21no—
230C22⋊(C11⋊C8)—21no—
231C22⋊(C11⋊C8)—21no—
232C4⋊(C11⋊C8)—21no—
233C4⋊(C11⋊C8)—21no—
234#66867—21no—
235C4×C11⋊C8—21no—
236#22434—111nomaximal, Sylow
237C24×C11—21no—
238C24×C11—21no—
239C24×C11C2×D411yescharacteristic
240C24×C11C2×D411yescharacteristic
241C11×#41—21no—
242C11×#41—21no—
243C11×#41—22no—
244C11×#41—22no—
245C11×#41—22no—
246C11×#41—22no—
247C11×#41—21no—
248C11×#41—21no—
249C11×#41—21no—
250C11×#41—21no—
251C11×#41—21no—
252C11×#41—21no—
253C11×#41—21no—
254C11×#41—21no—
255C11×#41—42no—
256C11×#41—42no—
257C11×#41—42no—
258C11×#41—42no—
259C11×#41—41no—
260C11×#41—41no—
261C11×#41—41no—
262C11×#41—41no—
263C11×#41—42no—
264C11×#41—42no—
265C11×#41—42no—
266C11×#41—42no—
267C11×#41C2×D412yes—
268C11×#41#4112yes—
269C2×Q8×C11—21no—
270C2×Q8×C11—21no—
271C2×Q8×C11—22no—
272C2×Q8×C11—22no—
273C2×Q8×C11—41no—
274C2×Q8×C11—41no—
275C2×Q8×C11C22×C411yescharacteristic
276C2×Q8×C11C22×C411yescharacteristic
277C2×Q8×C11C22×C411yescharacteristic
278C2×D4×C11—21no—
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C2×D4×C11—21no—
282C2×D4×C11—21no—
283C2×D4×C11—21no—
284C2×D4×C11—21no—
285C2×D4×C11—21no—
286C2×D4×C11—21no—
287C2×D4×C11—21no—
288C2×D4×C11—21no—
289C2×D4×C11—21no—
290C2×D4×C11—21no—
291C2×D4×C11—21no—
292C2×D4×C11—21no—
293C2×D4×C11—21no—
294C2×D4×C11—21no—
295C2×D4×C11—41no—
296C2×D4×C11—41no—
297C2×D4×C11—42no—
298C2×D4×C11—42no—
299C2×D4×C11—42no—
300C2×D4×C11—42no—
301C2×D4×C11—42no—
302C2×D4×C11—44no—
303C2×D4×C11C22⋊C411yescharacteristic
304C2×D4×C11C22⋊C411yescharacteristic
305C2×D4×C11C22⋊C411yescharacteristic
306C2×D4×C11C22⋊C411yescharacteristic
307C2×D4×C11C22×C411yescharacteristic
308C2×D4×C11C22×C411yescharacteristic
309C2×D4×C11C22×C411yescharacteristic
310C22×C4×C11—21no—
311C22×C4×C11—21no—
312C22×C4×C11—21no—
313C22×C4×C11—21no—
314C22×C4×C11—21no—
315C22×C4×C11—21no—
316C22×C4×C11—21no—
317C22×C4×C11—21no—
318C22×C4×C11—21no—
319C22×C4×C11—21no—
320C22×C4×C11—21no—
321C22×C4×C11—21no—
322C22×C4×C11—21no—
323C22×C4×C11—21no—
324C22×C4×C11—21no—
325C22×C4×C11—21no—
326C22×C4×C11—21no—
327C22×C4×C11—21no—
328C22×C4×C11—21no—
329C22×C4×C11—42no—
330C22×C4×C11—42no—
331C22×C4×C11—42no—
332C22×C4×C11—42no—
333C22×C4×C11C22×C411yescharacteristic
334C22×C4×C11C22×C411yescharacteristic
335C22×C4×C11C22×C411yescharacteristic
336C22×C4×C11C22×C411yescharacteristic
337C22×C4×C11C2×D411yescharacteristic
338C22×C4×C11C2×D411yescharacteristic
339C22×C4×C11C2×D411yescharacteristic
340C22×C4×C11C2×D411yescharacteristic
341C22×C4×C11C2×D411yescharacteristic
342C22×C4×C11C2×D411yescharacteristic
343C22×C4×C11C2×D411yescharacteristic
344C22×C4×C11C2×D411yescharacteristic
345C22×C4×C11C2411yescharacteristic
346C22×Dic11—21no—
347C22×Dic11—21no—
348C22×Dic11—21no—
349C22×Dic11—21no—
350C22×Dic11—42no—
351C22×Dic11—42no—
352C22×Dic11—42no—
353C11×C4⋊C4—21no—
354C11×C4⋊C4—21no—
355C11×C4⋊C4—21no—
356C11×C4⋊C4—21no—
357C11×C4⋊C4—21no—
358C11×C4⋊C4—21no—
359C11×C4⋊C4—21no—
360C11×C4⋊C4—21no—
361C11×C4⋊C4C22⋊C411yescharacteristic
362C11×C4⋊C4C22⋊C411yescharacteristic
363C11×C4⋊C4C22⋊C411yescharacteristic
364C11×C4⋊C4C22⋊C411yescharacteristic
365C11×C4⋊C4C22×C411yescharacteristic
366C11×C4⋊C4C22×C411yescharacteristic
367C11×C22⋊C4—21no—
368C11×C22⋊C4—21no—
369C11×C22⋊C4—21no—
370C11×C22⋊C4—21no—
371C11×C22⋊C4—21no—
372C11×C22⋊C4—21no—
373C11×C22⋊C4—21no—
374C11×C22⋊C4—21no—
375C11×C22⋊C4—21no—
376C11×C22⋊C4—21no—
377C11×C22⋊C4—21no—
378C11×C22⋊C4—21no—
379C11×C22⋊C4—21no—
380C11×C22⋊C4—21no—
381C11×C22⋊C4—21no—
382C11×C22⋊C4C22⋊C411yescharacteristic
383C11×C22⋊C4C22⋊C411yescharacteristic
384C11×C22⋊C4C22⋊C411yescharacteristic
385C11×C22⋊C4C22⋊C411yescharacteristic
386C11×C22⋊C4C22⋊C411yescharacteristic
387C11×C22⋊C4C22⋊C411yescharacteristic
388C11×C22⋊C4C22⋊C411yescharacteristic
389C11×C22⋊C4C22⋊C411yescharacteristic
390C42×C11—21no—
391C42×C11—21no—
392C42×C11—21no—
393C42×C11C22×C411yescharacteristic
394C42×C11C22×C411yescharacteristic
395C42×C11C2×D411yescharacteristic
396C42×C11C2×D411yescharacteristic
397C22⋊Dic11—42no—
398C22⋊Dic11—42no—
399C22⋊Dic11—42no—
400C4⋊Dic11—42no—
401C4⋊Dic11—42no—
402C4×Dic11—21no—
403C4×Dic11—21no—
404C4×Dic11—21no—
405C4×Dic11—21no—
406C4×Dic11—21no—
407C4×Dic11—21no—
408C4×Dic11—21no—
409C4×Dic11—42no—
410C4×Dic11C2×D412yescomplemented
411#4318—21no—
412#4318—21no—
413#4318—21no—
414#4318—21no—
415#4318—21no—
416#4318—21no—
417#4318—21no—
418#4318—42no—
419#4318—42no—
420#4318C2×D412yescomplemented
421C2×C11⋊C8—21no—
422C2×C11⋊C8—21no—
423C2×C11⋊C8—21no—
424C2×C11⋊C8—21no—
425C2×C11⋊C8—42no—
426C2×C11⋊C8—42no—
427D4×#41D1111yescharacteristic
428D4×M16—111no—
429C2×#421—111no—
430C22×#104—111no—
431#2290—111no—
432#1980—111no—
433#1963—111no—
434#1897—111no—
435#1896—111no—
436#1871—111no—
437#1871—111no—
438#1806—111no—
439#1789—111no—
440#1789—111no—
441#1759—111no—
442C23×C11—21no—
443C23×C11—21no—
444C23×C11—21no—
445C23×C11—22no—
446C23×C11—21no—
447C23×C11—21no—
448C23×C11—21no—
449C23×C11—21no—
450C23×C11—41no—
451C23×C11—41no—
452C23×C11—41no—
453C23×C11—42no—
454C23×C11—42no—
455C23×C11—42no—
456C23×C11—42no—
457C23×C11—81no—
458C23×C11—81no—
459C23×C11C2×C22⋊C411yescharacteristic
460C23×C11C2×C22⋊C411yescharacteristic
461C23×C11C2×C22⋊C411yescharacteristic
462C23×C11C2×C22⋊C411yescharacteristic
463C23×C11C22×D411yescharacteristic
464Q8×C11—21no—
465Q8×C11—21no—
466Q8×C11—21no—
467Q8×C11—21no—
468Q8×C11—21no—
469Q8×C11—42no—
470Q8×C11—42no—
471Q8×C11C4×D412yes—
472D4×C11—22no—
473D4×C11—22no—
474D4×C11—22no—
475D4×C11—22no—
476D4×C11—21no—
477D4×C11—21no—
478D4×C11—21no—
479D4×C11—21no—
480D4×C11—21no—
481D4×C11—41no—
482D4×C11—41no—
483D4×C11—42no—
484D4×C11—42no—
485D4×C11—42no—
486D4×C11—42no—
487D4×C11—42no—
488D4×C11—42no—
489D4×C11—42no—
490D4×C11—42no—
491D4×C11—41no—
492D4×C11—41no—
493D4×C11—41no—
494D4×C11—41no—
495D4×C11—42no—
496D4×C11—81no—
497D4×C11—81no—
498D4×C11—81no—
499D4×C11C4×D412yes—
500C2×C4×C11—21no—
501C2×C4×C11—21no—
502C2×C4×C11—21no—
503C2×C4×C11—21no—
504C2×C4×C11—21no—
505C2×C4×C11—21no—
506C2×C4×C11—21no—
507C2×C4×C11—21no—
508C2×C4×C11—21no—
509C2×C4×C11—21no—
510C2×C4×C11—21no—
511C2×C4×C11—21no—
512C2×C4×C11—21no—
513C2×C4×C11—21no—
514C2×C4×C11—21no—
515C2×C4×C11—21no—
516C2×C4×C11—21no—
517C2×C4×C11—22no—
518C2×C4×C11—21no—
519C2×C4×C11—21no—
520C2×C4×C11—21no—
521C2×C4×C11—21no—
522C2×C4×C11—22no—
523C2×C4×C11—21no—
524C2×C4×C11—21no—
525C2×C4×C11—21no—
526C2×C4×C11—21no—
527C2×C4×C11—41no—
528C2×C4×C11—41no—
529C2×C4×C11—42no—
530C2×C4×C11—42no—
531C2×C4×C11—42no—
532C2×C4×C11—42no—
533C2×C4×C11—42no—
534C2×C4×C11—42no—
535C2×C4×C11—42no—
536C2×C4×C11—41no—
537C2×C4×C11—41no—
538C2×C4×C11—41no—
539C2×C4×C11—41no—
540C2×C4×C11—81no—
541C2×C4×C11C2×C22⋊C411yescharacteristic
542C2×C4×C11C2×C22⋊C411yescharacteristic
543C2×C4×C11C2×C22⋊C411yescharacteristic
544C2×C4×C11C2×C22⋊C411yescharacteristic
545C2×C4×C11C2×C22⋊C411yescharacteristic
546C2×C4×C11C2×C22⋊C411yescharacteristic
547C2×C4×C11C2×C22⋊C411yescharacteristic
548C2×C4×C11C2×C22⋊C411yescharacteristic
549C2×C4×C11C23×C411yescharacteristic
550C2×C4×C11C22×D411yescharacteristic
551C2×C4×C11C22×D411yescharacteristic
552C2×C4×C11C2×#4111yescharacteristic
553C2×C4×C11H(5,𝔽2)11yescharacteristic
554C2×C4×C11H(5,𝔽2)11yescharacteristic
555C2×Dic11—22no—
556C2×Dic11—22no—
557C2×Dic11—41no—
558C2×Dic11—41no—
559C2×Dic11—41no—
560C2×Dic11—48no—
561C2×Dic11—41no—
562C2×Dic11—41no—
563C2×Dic11—41no—
564C2×Dic11—41no—
565C2×Dic11—41no—
566C2×Dic11—41no—
567C2×Dic11—41no—
568C11⋊C8—22no—
569C11⋊C8—41no—
570C11⋊C8—41no—
571C11⋊C8—41no—
572C22×#41C2×D1111yescharacteristic
573C22×#41C2×D1111yescharacteristic
574C22×M16—111no—
575C22×M16—111no—
576#550Dic1111yescharacteristic, complemented
577D4×Q8Dic1111yescharacteristic, complemented
578#548Dic1111yescharacteristic, complemented
579#548Dic1111yescharacteristic, complemented
580#547—21no—
581#547Dic1111yescharacteristic, complemented
582#546—21no—
583#546—21no—
584#546Dic1111yescharacteristic, complemented
585#546Dic1111yescharacteristic, complemented
586D42—21no—
587D42Dic1111yescharacteristic, complemented
588#532—21no—
589#532C2×D1111yescharacteristic
590#525—21no—
591#525—21no—
592#525C2×D1111yescharacteristic
593#525C2×D1111yescharacteristic
594C4×#41C2×D1111yescharacteristic
595C2×C4×D4—21no—
596C2×C4×D4C2×D1111yescharacteristic
597C2×#117—111no—
598C22×C42—111no—
599#436—221no—
600#435—221no—
601#435—221no—
602C8×D4—221no—
603#423—111no—
604#421—224no—
605C2×#104—111no—
606C2×#104—111no—
607C2×#104—111no—
608C2×#104—111no—
609C2×#104—111no—
610C2×#104—111no—
611C2×#104—111no—
612C2×#104—111no—
613C2×#104—111no—
614C2×#104—111no—
615C2×#104—111no—
616C2×#104—111no—
617C2×#104—224no—
618#407—111no—
619#407—111no—
620C4×M16—111no—
621#388—221no—
622#387—221no—
623#386—221no—
624#385—221no—
625C4×C4⋊C4—111no—
626C4×C22⋊C4—111no—
627C4×C22⋊C4—111no—
628#376—111no—
629#339—111no—
630#339—111no—
631#339—111no—
632#339—111no—
633C22×C11—21no—
634C22×C11—21no—
635C22×C11—21no—
636C22×C11—21no—
637C22×C11—21no—
638C22×C11—21no—
639C22×C11—21no—
640C22×C11—22no—
641C22×C11—21no—
642C22×C11—21no—
643C22×C11—21no—
644C22×C11—21no—
645C22×C11—21no—
646C22×C11—21no—
647C22×C11—42no—
648C22×C11—42no—
649C22×C11—41no—
650C22×C11—41no—
651C22×C11—41no—
652C22×C11—41no—
653C22×C11—41no—
654C22×C11—41no—
655C22×C11—41no—
656C22×C11—41no—
657C22×C11—81no—
658C22×C11—81no—
659C22×C11—84no—
660C22×C11—84no—
661C22×C11#42112yescomplemented
662C22×C11C22×C22⋊C411yescharacteristic
663C22×C11D4211yescharacteristic
664C22×C11#54611yescharacteristic
665C4×C11—21no—
666C4×C11—21no—
667C4×C11—21no—
668C4×C11—21no—
669C4×C11—22no—
670C4×C11—21no—
671C4×C11—21no—
672C4×C11—21no—
673C4×C11—21no—
674C4×C11—41no—
675C4×C11—41no—
676C4×C11—41no—
677C4×C11—41no—
678C4×C11C2×C4×D411yescharacteristic
679C4×C11#51811yescharacteristic
680C4×C11D4211yescharacteristic
681C4×C11#54611yescharacteristic
682Dic11—42no—
683Dic11—42no—
684Dic11—81no—
685Dic11—81no—
686C2×#41—21no—
687C2×#41—21no—
688C2×#41—21no—
689C2×#41—21no—
690C2×#41—22no—
691C2×#41—22no—
692C2×#41—22no—
693C2×#41—22no—
694C2×#41—41no—
695C2×#41—41no—
696C2×#41—41no—
697C2×#41—41no—
698C2×#41C2×Dic1111yescharacteristic
699C2×#41C2×Dic1111yescharacteristic
700C2×#41C2×Dic1111yescharacteristic, complemented
701C2×#41C2×Dic1111yescharacteristic, complemented
702C2×#41C22×D1111yescharacteristic
703C2×#41C22×D1111yescharacteristic
704C2×#41C22×D1111yescharacteristic
705C22×Q8C2×Dic1111yescharacteristic
706C22×Q8C2×Dic1111yescharacteristic, complemented
707C22×D4—21no—
708C22×D4—21no—
709C22×D4—21no—
710C22×D4C2×Dic1111yescharacteristic
711C22×D4C2×Dic1111yescharacteristic, complemented
712C22×D4C22⋊D1111yescharacteristic
713C23×C4—21no—
714C23×C4—21no—
715C23×C4—221no—
716C23×C4C22×D1111yescharacteristic
717C23×C4C22×D1111yescharacteristic
718C2×M16—111no—
719C2×M16—111no—
720C2×M16—111no—
721C2×M16—111no—
722C2×M16—221no—
723C2×M16—221no—
724C2×M16—222no—
725C2×M16—222no—
726C2×M16—441no—
727C2×M16—441no—
728C22×C8—221no—
729C22×C8—221no—
730C4⋊Q8—21no—
731C4⋊Q8C2×Dic1111yescharacteristic, complemented
732#127—21no—
733#127C2×Dic1111yescharacteristic, complemented
734#124—21no—
735#124—21no—
736#124C2×Dic1111yescharacteristic, complemented
737#124C2×Dic1111yescharacteristic, complemented
738#123—21no—
739#123—21no—
740#123—21no—
741#123—21no—
742#123—21no—
743#123—21no—
744C22⋊Q8—21no—
745C22⋊Q8—21no—
746C22⋊Q8—21no—
747C22⋊Q8—21no—
748C22⋊Q8C2×Dic1111yescharacteristic
749C22⋊Q8C2×Dic1111yescharacteristic
750C22⋊Q8C2×Dic1111yescharacteristic, complemented
751C22⋊Q8C2×Dic1111yescharacteristic, complemented
752#121—21no—
753#121—21no—
754#121—21no—
755#121—21no—
756#121—21no—
757#121—21no—
758#121—21no—
759#121—21no—
760#121—21no—
761#121—21no—
762#121C2×Dic1111yescharacteristic
763#121C2×Dic1111yescharacteristic
764#121C2×Dic1111yescharacteristic, complemented
765#121C2×Dic1111yescharacteristic, complemented
766#120—21no—
767#120—21no—
768#120—21no—
769#120—21no—
770#120—21no—
771#120—21no—
772C4×Q8C2×Dic1111yescharacteristic, complemented
773C4×Q8C2×Dic1111yescharacteristic, complemented
774C4×D4—21no—
775C4×D4—21no—
776C4×D4—21no—
777C4×D4—21no—
778C4×D4—21no—
779C4×D4—21no—
780C4×D4—21no—
781C4×D4—21no—
782C4×D4—21no—
783C4×D4—21no—
784C4×D4—21no—
785C4×D4—21no—
786C4×D4C2×Dic1111yescharacteristic
787C4×D4C2×Dic1111yescharacteristic
788C4×D4C2×Dic1111yescharacteristic
789C4×D4C2×Dic1111yescharacteristic
790C4×D4C2×Dic1111yescharacteristic, complemented
791C4×D4C2×Dic1111yescharacteristic, complemented
792C4×D4C22⋊D1111yescharacteristic
793C4×D4C22⋊D1111yescharacteristic
794C4×D4C22⋊D1111yescharacteristic
795C4×D4C22⋊D1111yescharacteristic
796#117—21no—
797#117—222no—
798#117—441no—
799#117C22×D1111yescharacteristic
800C2×C4⋊C4—21no—
801C2×C4⋊C4—221no—
802C2×C4⋊C4—221no—
803C2×C4⋊C4C22⋊D1111yescharacteristic
804C2×C22⋊C4—21no—
805C2×C22⋊C4—21no—
806C2×C22⋊C4—221no—
807C2×C22⋊C4—221no—
808C2×C22⋊C4—221no—
809C2×C22⋊C4C22⋊D1111yescharacteristic
810C2×C22⋊C4C22⋊D1111yescharacteristic
811C2×C42—21no—
812C2×C42—111no—
813C2×C42—111no—
814C2×C42—111no—
815C2×C42—111no—
816C2×C42—222no—
817C2×C42—221no—
818C2×C42—441no—
819C2×C42C22×D1111yescharacteristic
820C4⋊C8—221no—
821C4⋊C8—221no—
822#104—114no—
823#104—222no—
824#104—222no—
825#104—222no—
826#104—222no—
827#104—222no—
828#104—222no—
829#104—222no—
830#104—441no—
831#104—441no—
832#104—441no—
833#104—441no—
834C22⋊C8—221no—
835C22⋊C8—221no—
836C22⋊C8—221no—
837C22⋊C8—221no—
838#97—221no—
839C4×C8—221no—
840#95—221no—
841#95—221no—
842#95—221no—
843#95—221no—
844#95—221no—
845C2×C11—21no—
846C2×C11—21no—
847C2×C11—22no—
848C2×C11—41no—
849C2×C11—41no—
850C2×C11—41no—
851C2×C11—42no—
852C2×C11—81no—
853C2×C11—81no—
854C2×C11D4×C22⋊C411yescharacteristic
855C2×C11C2×#42111yescharacteristic
856C2×C11#290111yescharacteristic
857C24—21no—
858C24—21no—
859C24C2×C22⋊D1111yescharacteristic
860C24C2×C22⋊D1111yescharacteristic
861#41—21no—
862#41—21no—
863#41—22no—
864#41—22no—
865#41—22no—
866#41—22no—
867#41—21no—
868#41—21no—
869#41—21no—
870#41—21no—
871#41—21no—
872#41—21no—
873#41—21no—
874#41—21no—
875#41—42no—
876#41—42no—
877#41—42no—
878#41—42no—
879#41—41no—
880#41—41no—
881#41—41no—
882#41—41no—
883#41—42no—
884#41—42no—
885#41—42no—
886#41—42no—
887#41D4×D1112yes—
888#41#434112yes—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—22no—
892C2×Q8—22no—
893C2×Q8—41no—
894C2×Q8—41no—
895C2×Q8C22×Dic1111yescharacteristic
896C2×Q8C22×Dic1111yescharacteristic
897C2×Q8C22×Dic1111yescharacteristic
898C2×D4—21no—
899C2×D4—22no—
900C2×D4—22no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—41no—
916C2×D4—41no—
917C2×D4—42no—
918C2×D4—42no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—44no—
923C2×D4C22⋊Dic1111yescharacteristic
924C2×D4C22⋊Dic1111yescharacteristic
925C2×D4C22⋊Dic1111yescharacteristic
926C2×D4C22⋊Dic1111yescharacteristic
927C2×D4C22×Dic1111yescharacteristic
928C2×D4C22×Dic1111yescharacteristic
929C2×D4C22×Dic1111yescharacteristic
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—221no—
954C22×C4—221no—
955C22×C4—221no—
956C22×C4—221no—
957C22×C4—442no—
958C22×C4—442no—
959C22×C4—442no—
960C22×C4C22×Dic1111yescharacteristic
961C22×C4C22×Dic1111yescharacteristic
962C22×C4C22×Dic1111yescharacteristic
963C22×C4C22×Dic1111yescharacteristic
964C22×C4C2×C22⋊D1111yescharacteristic
965C22×C4C2×C22⋊D1111yescharacteristic
966C22×C4C2×C22⋊D1111yescharacteristic
967C22×C4C2×C22⋊D1111yescharacteristic
968C22×C4C2×C22⋊D1111yescharacteristic
969C22×C4C2×C22⋊D1111yescharacteristic
970C22×C4C2×C22⋊D1111yescharacteristic
971C22×C4C2×C22⋊D1111yescharacteristic
972C22×C4C23×D1111yescharacteristic
973M16—112no—
974M16—221no—
975M16—221no—
976M16—221no—
977M16—221no—
978M16—221no—
979M16—221no—
980M16—221no—
981M16—442no—
982M16—442no—
983C2×C8—221no—
984C2×C8—221no—
985C2×C8—221no—
986C2×C8—221no—
987C2×C8—442no—
988C2×C8—442no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—442no—
998C4⋊C4—442no—
999C4⋊C4C22⋊Dic1111yescharacteristic
1000C4⋊C4C22⋊Dic1111yescharacteristic
1001C4⋊C4C22⋊Dic1111yescharacteristic
1002C4⋊C4C22⋊Dic1111yescharacteristic
1003C4⋊C4C22×Dic1111yescharacteristic
1004C4⋊C4C22×Dic1111yescharacteristic
1005C22⋊C4—21no—
1006C22⋊C4—21no—
1007C22⋊C4—21no—
1008C22⋊C4—21no—
1009C22⋊C4—21no—
1010C22⋊C4—21no—
1011C22⋊C4—21no—
1012C22⋊C4—21no—
1013C22⋊C4—21no—
1014C22⋊C4—21no—
1015C22⋊C4—21no—
1016C22⋊C4—21no—
1017C22⋊C4—21no—
1018C22⋊C4—21no—
1019C22⋊C4—21no—
1020C22⋊C4—442no—
1021C22⋊C4—442no—
1022C22⋊C4—442no—
1023C22⋊C4C22⋊Dic1111yescharacteristic
1024C22⋊C4C22⋊Dic1111yescharacteristic
1025C22⋊C4C22⋊Dic1111yescharacteristic
1026C22⋊C4C22⋊Dic1111yescharacteristic
1027C22⋊C4C22⋊Dic1111yescharacteristic
1028C22⋊C4C22⋊Dic1111yescharacteristic
1029C22⋊C4C22⋊Dic1111yescharacteristic
1030C22⋊C4C22⋊Dic1111yescharacteristic
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—112no—
1035C42—221no—
1036C42—221no—
1037C42—221no—
1038C42—221no—
1039C42—221no—
1040C42—221no—
1041C42—221no—
1042C42—442no—
1043C42C22×Dic1111yescharacteristic
1044C42C22×Dic1111yescharacteristic
1045C42C2×C22⋊D1111yescharacteristic
1046C42C2×C22⋊D1111yescharacteristic
1047C11#2243411yescharacteristic, complemented, Sylow
1048C23—21no—
1049C23—21no—
1050C23—22no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—81no—
1064C23—81no—
1065C23C2×C22⋊Dic1111yescharacteristic
1066C23C2×C22⋊Dic1111yescharacteristic
1067C23C2×C22⋊Dic1111yescharacteristic
1068C23C2×C22⋊Dic1111yescharacteristic
1069C23C22×C22⋊D1111yescharacteristic
1070Q8—21no—
1071Q8—21no—
1072Q8—21no—
1073Q8—21no—
1074Q8—21no—
1075Q8—42no—
1076Q8—42no—
1077Q8D4×Dic1112yes—
1078D4—22no—
1079D4—22no—
1080D4—22no—
1081D4—22no—
1082D4—21no—
1083D4—21no—
1084D4—21no—
1085D4—21no—
1086D4—21no—
1087D4—41no—
1088D4—41no—
1089D4—42no—
1090D4—42no—
1091D4—42no—
1092D4—42no—
1093D4—42no—
1094D4—42no—
1095D4—42no—
1096D4—42no—
1097D4—41no—
1098D4—41no—
1099D4—41no—
1100D4—41no—
1101D4—42no—
1102D4—81no—
1103D4—81no—
1104D4—81no—
1105D4D4×Dic1112yes—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—22no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—22no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—81no—
1147C2×C4—222no—
1148C2×C4—222no—
1149C2×C4—441no—
1150C2×C4—441no—
1151C2×C4—441no—
1152C2×C4—448no—
1153C2×C4—441no—
1154C2×C4—441no—
1155C2×C4—441no—
1156C2×C4—441no—
1157C2×C4—441no—
1158C2×C4—441no—
1159C2×C4—441no—
1160C2×C4C2×C22⋊Dic1111yescharacteristic
1161C2×C4C2×C22⋊Dic1111yescharacteristic
1162C2×C4C2×C22⋊Dic1111yescharacteristic
1163C2×C4C2×C22⋊Dic1111yescharacteristic
1164C2×C4C2×C22⋊Dic1111yescharacteristic
1165C2×C4C2×C22⋊Dic1111yescharacteristic
1166C2×C4C2×C22⋊Dic1111yescharacteristic
1167C2×C4C2×C22⋊Dic1111yescharacteristic
1168C2×C4C2×D4×D1111yescharacteristic
1169C2×C4C2×#434111yescharacteristic
1170C2×C4#6703711yescharacteristic
1171C2×C4#6703711yescharacteristic
1172C2×C4C23×Dic1111yescharacteristic
1173C2×C4C22×C22⋊D1111yescharacteristic
1174C8—222no—
1175C8—441no—
1176C8—441no—
1177C8—441no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—21no—
1185C22—22no—
1186C22—21no—
1187C22—21no—
1188C22—21no—
1189C22—21no—
1190C22—21no—
1191C22—21no—
1192C22—42no—
1193C22—42no—
1194C22—41no—
1195C22—41no—
1196C22—41no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—81no—
1203C22—81no—
1204C22—84no—
1205C22—84no—
1206C22#1062284912yescomplemented
1207C22D4×C22⋊D1111yescharacteristic
1208C22#1062333711yescharacteristic
1209C22C22×C22⋊Dic1111yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—21no—
1213C4—21no—
1214C4—22no—
1215C4—21no—
1216C4—21no—
1217C4—21no—
1218C4—21no—
1219C4—41no—
1220C4—41no—
1221C4—41no—
1222C4—41no—
1223C4—442no—
1224C4—442no—
1225C4—881no—
1226C4—881no—
1227C4C2×D4×Dic1111yescharacteristic
1228C4#1062332911yescharacteristic
1229C4D4×C22⋊D1111yescharacteristic
1230C4#1062333711yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—22no—
1234C2—41no—
1235C2—41no—
1236C2—41no—
1237C2—42no—
1238C2—81no—
1239C2—81no—
1240C2D4×C22⋊Dic1111yescharacteristic
1241C2C2×#1062284911yescharacteristic
1242C2#1307716311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalD4×C11×#41C2
socleC22×C11C22×C22⋊C4
cosocleC22×C4×C11C24
hypercenterD4×#41D11
hypocenterC11#22434
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
1. D4×#4318C2semidirect
2. C2×#10622849C2semidirect
3. C22×#66901C2semidirect
4. #13071061C2semidirect
5. #13069536C2semidirect
6. #13069449C2semidirect
7. #13069065C2semidirect
8. #13069060C2semidirect
9. #13068919C2semidirect
10. #13068919C2semidirect
11. #13068636C2semidirect
12. #13068560C2semidirect
13. #13068560C2semidirect
14. #13068426C2semidirect
18. C11×#550C4semidirect
19. D4×Q8×C11C4semidirect
20. C11×#548C4semidirect
21. C11×#548C4semidirect
23. C11×#547C4semidirect
26. C11×#546C4semidirect
27. C11×#546C4semidirect
29. D42×C11C4semidirect
39. C2×#66979C22semidirect
40. C22×C4×Dic11C22semidirect
41. C22×#4318C22semidirect
42. C22×#4318C22semidirect
49. C2×#66901C22semidirect
50. C2×#66901C22semidirect
51. C2×#66901C22semidirect
52. C2×#66901C22semidirect
53. C2×#66901C22semidirect
54. C2×#66901C22semidirect
55. C2×#66901C22semidirect
56. C2×#66901C22semidirect
58. C4×C22⋊Dic11C22semidirect
59. C4×C22⋊Dic11C22semidirect
60. #10622820C22semidirect
61. #10622820C22semidirect
69. C4×C4⋊Dic11C22semidirect
70. #10622545C22semidirect
71. #10622537C22semidirect
72. C4×#4318C22semidirect
73. #10622170C22semidirect
74. #10622170C22semidirect
75. #10622170C22semidirect
76. #10622170C22semidirect
91. C2×C11×#41C2×C4semidirect
92. C2×C11×#41C2×C4semidirect
97. C22×Q8×C11C2×C4semidirect
102. C22×D4×C11C2×C4semidirect
110. C11×C4⋊Q8C2×C4semidirect
112. C11×#127C2×C4semidirect
115. C11×#124C2×C4semidirect
116. C11×#124C2×C4semidirect
129. C11×C22⋊Q8C2×C4semidirect
130. C11×C22⋊Q8C2×C4semidirect
143. C11×#121C2×C4semidirect
144. C11×#121C2×C4semidirect
151. C4×Q8×C11C2×C4semidirect
152. C4×Q8×C11C2×C4semidirect
169. C4×D4×C11C2×C4semidirect
170. C4×D4×C11C2×C4semidirect
222. #66901D4semidirect
410. C4×Dic11C2×D4semidirect
420. #4318C2×D4semidirect
576. #550Dic11semidirect
577. D4×Q8Dic11semidirect
578. #548Dic11semidirect
579. #548Dic11semidirect
581. #547Dic11semidirect
584. #546Dic11semidirect
585. #546Dic11semidirect
587. D42Dic11semidirect
661. C22×C11#421semidirect
700. C2×#41C2×Dic11semidirect
701. C2×#41C2×Dic11semidirect
706. C22×Q8C2×Dic11semidirect
711. C22×D4C2×Dic11semidirect
731. C4⋊Q8C2×Dic11semidirect
733. #127C2×Dic11semidirect
736. #124C2×Dic11semidirect
737. #124C2×Dic11semidirect
750. C22⋊Q8C2×Dic11semidirect
751. C22⋊Q8C2×Dic11semidirect
764. #121C2×Dic11semidirect
765. #121C2×Dic11semidirect
772. C4×Q8C2×Dic11semidirect
773. C4×Q8C2×Dic11semidirect
790. C4×D4C2×Dic11semidirect
791. C4×D4C2×Dic11semidirect
1047. C11#22434semidirect
1206. C22#10622849semidirect

Maximal subgroups

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

subgroupindex
D4×#43182
C2×#106228492
C22×#669012
#130710612
#130695362
#130694492
#130690652
#130690602
#130689192
#130686362
#130685602
#130684262
D4×C11×#412
#2243411