Finite Group Databasebeta

← #14914091

Subgroups — #14914091

Order 2816.

3038 conjugacy classes of subgroups.

The subgroup lattice has 1136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C22⋊Q8C211yesmaximal, characteristic
2C2×#10623103C211yesmaximal, characteristic, complemented
3C22×#66925C211yesmaximal, characteristic
4#13071644C212yesmaximal, complemented
5#13071638C212yesmaximal, complemented
6#13071622C212yesmaximal, complemented
7#13071616C212yesmaximal, complemented
8#13071482C212yesmaximal, complemented
9#13071481C212yesmaximal, complemented
10#13071463C212yesmaximal
11#13071459C212yesmaximal
12#13071301C211yesmaximal, characteristic, complemented
13#13071299C211yesmaximal, characteristic, complemented
14#13071296C211yesmaximal, characteristic, complemented
15#13071292C211yesmaximal, characteristic, complemented
16#13071231C211yesmaximal, characteristic, complemented
17#13071199C211yesmaximal, characteristic, complemented
18C22⋊Q8×Dic11C211yesmaximal, characteristic, complemented
19C4×#66977C211yesmaximal, characteristic, complemented
20#13071144C211yesmaximal, characteristic, complemented
21#13070998C211yesmaximal, characteristic
22#13070970C211yesmaximal, characteristic, complemented
23C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
24C22×Q8×D11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic, complemented
28C22×C42×C11C2211yescharacteristic
29C2×#66999C2211yescharacteristic
30C2×Q8×Dic11C2211yescharacteristic, complemented
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C2×#66977C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37D11×C22⋊Q8C4116yescomplemented
38#10623103—28no—
39C2×#66950C2211yescharacteristic
40C2×#66949C2212yes—
41C2×#66945C2211yescharacteristic
42C2×#66945C2212yes—
43C2×#66945C2211yescharacteristic
44C2×C4⋊C4×D11C2212yes—
45C2×C4⋊C4×D11C2211yescharacteristic
46C2×#66940C2212yescomplemented
47C2×#66940C2211yescharacteristic, complemented
48C2×C22⋊C4×D11C2212yes—
49C2×#66931C2212yes—
50C2×#66925—28no—
51C2×#66925C2211yescharacteristic
52C2×#66925C2211yescharacteristic
53C2×#66925C2211yescharacteristic
54C2×#66925C2212yes—
55C2×#66925C2211yescharacteristic
56C2×#66925C2211yescharacteristic
57C2×#66925C2211yescharacteristic
58C2×#66925C2211yescharacteristic
59C2×#66925C2211yescharacteristic
60C2×C4×Dic22C2212yescomplemented
61C2×C4×Dic22C2211yescharacteristic, complemented
62C11×#391C2211yescharacteristic, complemented
63C11×#389C2211yescharacteristic, complemented
64C11×#387C2212yescomplemented
65C11×#385C2212yes—
66C11×#380C2211yescharacteristic
67C4×C11×C4⋊C4C2212yescomplemented
68C4×C11×C4⋊C4C2211yescharacteristic, complemented
69C4×C11×C22⋊C4C2212yes—
70#10622843C2211yescharacteristic, complemented
71#10622825C2211yescharacteristic
72#10622823C2212yes—
73C4×C22⋊Dic11C2212yes—
74#10622603C2212yes—
75#10622603C2212yes—
76#10622600C2212yes—
77#10622600C2211yescharacteristic
78#10622600C2211yescharacteristic
79#10622598C2211yescharacteristic, complemented
80#10622594C2212yescomplemented
81C4⋊C4×Dic11C2212yescomplemented
82C4⋊C4×Dic11C2211yescharacteristic, complemented
83C4⋊C4×Dic11C2211yescharacteristic, complemented
84#10622587C2211yescharacteristic, complemented
85#10622586C2212yescomplemented
86#10622586C2211yescharacteristic, complemented
87#10622585C2212yescomplemented
88#10622585C2212yescomplemented
89#10622568C2212yes—
90#10622563C2212yes—
91#10622559C2212yes—
92C22⋊C4×Dic11C2212yes—
93C22⋊C4×Dic11C2212yes—
94C22⋊C4×Dic11C2212yes—
95#10622553C2212yes—
96#10622553C2212yes—
97C4×(C2×D11)⋊C4C2212yes—
98C4×C4⋊Dic11C2211yescharacteristic, complemented
99#10622546C2212yescomplemented
100#10622546C2212yescomplemented
101C4×Dic11⋊C4C2212yescomplemented
102C4×Dic11⋊C4C2212yescomplemented
103#10622542C2211yescharacteristic, complemented
104#10622541C2212yescomplemented
105#10622541C2211yescharacteristic, complemented
106#10622283C2212yes—
107#10622283C2212yes—
108#10622282C2212yes—
109#10622282C2212yes—
110#10622280C2212yes—
111#10622279C2212yes—
112#10622279C2212yes—
113#10622277C2212yes—
114#10622277C2212yes—
115#10622277C2212yes—
116#10622267C2212yescomplemented
117#10622266C2212yescomplemented
118#10622265C2212yescomplemented
119#10622265C2212yescomplemented
120#10622262C2212yescomplemented
121#10622262C2212yescomplemented
122#10622260C2212yescomplemented
123#10622260C2212yescomplemented
124#10622259C2212yescomplemented
125#10622259C2212yescomplemented
126C24×D11C2311yescharacteristic
127C22×Q8×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×Dic11C2311yescharacteristic
132C23×Dic11C2311yescharacteristic
133C23×Dic11C2311yescharacteristic
134C2×Q8×D11—24no—
135C2×Q8×D11—24no—
136C2×Q8×D11C2×C418yescomplemented
137C22×C4×D11—24no—
138C22×C4×D11—24no—
139C22×C4×D11C2×C418yes—
140C22×C4×D11C2311yescharacteristic
141C22×C4×D11C2311yescharacteristic
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2312yes—
144C22×C4×D11C2312yes—
145C22×C4×D11C2311yescharacteristic
146C22×Dic22C2312yes—
147C22×Dic22C2311yescharacteristic
148C11×C22⋊Q8C2×C418yes—
149C4×Q8×C11—24no—
150C2×C11×C4⋊C4C2312yes—
151C2×C11×C4⋊C4C2311yescharacteristic
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2312yes—
154C2×C11×C4⋊C4C2312yes—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C22⋊C4C2312yes—
157C2×C11×C22⋊C4C2312yes—
158C2×C42×C11—24no—
159C2×C42×C11C2312yes—
160C2×C42×C11C2311yescharacteristic
161C2×C42×C11C2311yescharacteristic
162C2×C42×C11C2311yescharacteristic
163C2×C42×C11C2312yes—
164C2×C42×C11C2311yescharacteristic
165C2×C22⋊Dic11C2312yes—
166C2×C22⋊Dic11C2312yes—
167#66999C2×C418yescomplemented
168Q8×Dic11—24no—
169C2×(C2×D11)⋊C4—24no—
170C2×(C2×D11)⋊C4—24no—
171C2×(C2×D11)⋊C4C2311yescharacteristic
172C2×(C2×D11)⋊C4C2311yescharacteristic
173C2×(C2×D11)⋊C4C2311yescharacteristic
174C2×(C2×D11)⋊C4C2311yescharacteristic
175C2×(C2×D11)⋊C4C2311yescharacteristic
176C2×(C2×D11)⋊C4C2311yescharacteristic
177C2×(C2×D11)⋊C4C2312yes—
178C2×(C2×D11)⋊C4C2312yes—
179C2×(C2×D11)⋊C4C2312yes—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2311yescharacteristic
184C2×(C2×D11)⋊C4C2311yescharacteristic
185C2×C4⋊Dic11C2312yes—
186C2×C4⋊Dic11C2311yescharacteristic
187C2×C4⋊Dic11C2311yescharacteristic
188C2×C4⋊Dic11C2312yes—
189C2×C4⋊Dic11C2312yes—
190C2×C4⋊Dic11C2311yescharacteristic
191#66977C2×C418yes—
192C2×Dic11⋊C4—24no—
193C2×Dic11⋊C4—24no—
194C2×Dic11⋊C4C2312yes—
195C2×Dic11⋊C4C2311yescharacteristic
196C2×Dic11⋊C4C2311yescharacteristic
197C2×Dic11⋊C4C2311yescharacteristic
198C2×Dic11⋊C4C2311yescharacteristic
199C2×Dic11⋊C4C2311yescharacteristic
200C2×Dic11⋊C4C2311yescharacteristic
201C2×Dic11⋊C4C2312yes—
202C2×Dic11⋊C4C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2311yescharacteristic
208C2×Dic11⋊C4C2311yescharacteristic
209C2×C4×Dic11—24no—
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C2312yes—
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2311yescharacteristic
222#66950C2×C418yescomplemented
223#66949C2×C4116yescomplemented
224#66945—24no—
225#66945—24no—
226#66945—28no—
227C4⋊C4×D11C2×C418yescomplemented
228C4⋊C4×D11C2×C4116yescomplemented
229#66940—28no—
230#66940—24no—
231C22⋊C4×D11C2×C4116yes—
232#66931C2×C4116yes—
233#66925—24no—
234#66925—24no—
235#66925—24no—
236#66925—24no—
237#66925—28no—
238#66925—24no—
239#66925—24no—
240#66925—24no—
241#66925D418yes—
242C4×Dic22—24no—
243C4×Dic22—28no—
244C11×#95C2312yes—
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11×#95C2312yes—
248C11×#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264#34203—111nomaximal, Sylow
265C24×C11C2411yescharacteristic
266C23×D11—22no—
267C23×D11—22no—
268C23×D11—22no—
269C23×D11—22no—
270C23×D11—41no—
271C23×D11—41no—
272C23×D11C22×C414yes—
273C23×D11C2411yescharacteristic
274C23×D11C2411yescharacteristic
275C2×Q8×C11—22no—
276C2×Q8×C11—22no—
277C2×Q8×C11C22×C414yes—
278C22×C4×C11—22no—
279C22×C4×C11—22no—
280C22×C4×C11—22no—
281C22×C4×C11—22no—
282C22×C4×C11—22no—
283C22×C4×C11—22no—
284C22×C4×C11—41no—
285C22×C4×C11—41no—
286C22×C4×C11C22×C414yes—
287C22×C4×C11C2412yes—
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2412yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2412yes—
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×Dic11—22no—
298C22×Dic11—22no—
299C22×Dic11—22no—
300C22×Dic11—22no—
301C22×Dic11—22no—
302C22×Dic11—22no—
303C22×Dic11—41no—
304C22×Dic11—41no—
305C22×Dic11C22×C414yes—
306C22×Dic11C2412yes—
307C22×Dic11C2411yescharacteristic
308C22×Dic11C2411yescharacteristic
309C22×Dic11C2412yes—
310C22×Dic11C2412yes—
311C22×Dic11C2412yes—
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316Q8×D11—232no—
317C2×C4×D11—22no—
318C2×C4×D11—22no—
319C2×C4×D11—232no—
320C2×C4×D11—22no—
321C2×C4×D11—24no—
322C2×C4×D11—22no—
323C2×C4×D11—24no—
324C2×C4×D11—22no—
325C2×C4×D11—22no—
326C2×C4×D11—42no—
327C2×C4×D11—42no—
328C2×C4×D11C22×C418yes—
329C2×C4×D11C22×C414yes—
330C2×C4×D11C22×C414yes—
331C2×C4×D11C22×C414yes—
332C2×C4×D11C22×C418yes—
333C2×C4×D11C22×C414yes—
334C2×C4×D11C2×D414yes—
335C2×C4×D11#4114yes—
336C2×Dic22—24no—
337C2×Dic22—24no—
338C2×Dic22—22no—
339C2×Dic22—22no—
340C2×Dic22C22×C418yes—
341C2×Dic22C22×C414yes—
342C11×C4⋊C4—24no—
343C11×C4⋊C4—22no—
344C11×C4⋊C4—22no—
345C11×C4⋊C4—42no—
346C11×C4⋊C4C22×C418yes—
347C11×C4⋊C4C22×C414yes—
348C11×C22⋊C4—24no—
349C11×C22⋊C4C22×C418yes—
350C42×C11—24no—
351C42×C11—22no—
352C42×C11—22no—
353C42×C11—22no—
354C42×C11—42no—
355C42×C11C2×D414yes—
356C22⋊Dic11—24no—
357C22⋊Dic11C22×C418yes—
358(C2×D11)⋊C4—22no—
359(C2×D11)⋊C4—22no—
360(C2×D11)⋊C4—22no—
361(C2×D11)⋊C4—22no—
362(C2×D11)⋊C4—24no—
363(C2×D11)⋊C4—24no—
364(C2×D11)⋊C4—22no—
365(C2×D11)⋊C4—22no—
366(C2×D11)⋊C4—42no—
367(C2×D11)⋊C4—42no—
368(C2×D11)⋊C4C22×C418yes—
369(C2×D11)⋊C4C22×C418yes—
370(C2×D11)⋊C4C2×D414yes—
371(C2×D11)⋊C4C2×D414yes—
372C4⋊Dic11—24no—
373C4⋊Dic11—22no—
374C4⋊Dic11—22no—
375C4⋊Dic11—42no—
376C4⋊Dic11C22×C418yes—
377C4⋊Dic11C22×C414yes—
378Dic11⋊C4—22no—
379Dic11⋊C4—22no—
380Dic11⋊C4—22no—
381Dic11⋊C4—22no—
382Dic11⋊C4—24no—
383Dic11⋊C4—24no—
384Dic11⋊C4—22no—
385Dic11⋊C4—22no—
386Dic11⋊C4—42no—
387Dic11⋊C4—42no—
388Dic11⋊C4C22×C418yes—
389Dic11⋊C4C22×C418yes—
390Dic11⋊C4C22×C418yes—
391Dic11⋊C4C2×D414yes—
392Dic11⋊C4C2×D414yes—
393C4×Dic11—24no—
394C4×Dic11—24no—
395C4×Dic11—22no—
396C4×Dic11—22no—
397C4×Dic11—24no—
398C4×Dic11—24no—
399C4×Dic11—24no—
400C4×Dic11—22no—
401C4×Dic11—42no—
402C4×Dic11—42no—
403C4×Dic11—42no—
404C4×Dic11C2×D414yes—
405C22×C22⋊Q8—111no—
406C2×#519—111no—
407C22×#117—111no—
408#2362—112no—
409#2362—112no—
410#2360—112no—
411#2360—112no—
412#2344—112no—
413#2344—112no—
414#2342—112no—
415#2342—112no—
416#2323—111no—
417#2323—111no—
418#2323—111no—
419#2323—111no—
420#2316—111no—
421#2310—111no—
422C4×C22⋊Q8—111no—
423C4×C22⋊Q8—111no—
424C4×C22⋊Q8—111no—
425C4×C22⋊Q8D1111yescharacteristic, complemented
426#2280—111no—
427#2274—111no—
428C23×C11—21no—
429C23×C11—21no—
430C23×C11—21no—
431C23×C11—21no—
432C23×C11C23×C412yes—
433C23×C112−1+412yes—
434C23×C112−1+412yes—
435C23×C11C2511yescharacteristic
436C22×D11—21no—
437C22×D11—21no—
438C22×D11—21no—
439C22×D11—21no—
440C22×D11—28no—
441C22×D11—21no—
442C22×D11—21no—
443C22×D11—21no—
444C22×D11—21no—
445C22×D11—21no—
446C22×D11—21no—
447C22×D11—28no—
448C22×D11—44no—
449C22×D11—44no—
450C22×D11—44no—
451C22×D11—44no—
452C22×D11—44no—
453C22×D11C23×C412yes—
454C22×D11C23×C412yes—
455C22×D11C22×D412yes—
456C22×D11C2×#4112yes—
457Q8×C11—28no—
458C2×C4×C11—21no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—21no—
462C2×C4×C11—21no—
463C2×C4×C11—21no—
464C2×C4×C11—21no—
465C2×C4×C11—22no—
466C2×C4×C11—22no—
467C2×C4×C11—21no—
468C2×C4×C11—28no—
469C2×C4×C11—22no—
470C2×C4×C11—21no—
471C2×C4×C11—21no—
472C2×C4×C11—22no—
473C2×C4×C11—22no—
474C2×C4×C11—22no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—22no—
478C2×C4×C11—21no—
479C2×C4×C11—22no—
480C2×C4×C11—21no—
481C2×C4×C11—44no—
482C2×C4×C11—44no—
483C2×C4×C11C23×C412yes—
484C2×C4×C11C23×C414yes—
485C2×C4×C11C23×C414yes—
486C2×C4×C11C23×C412yes—
487C2×C4×C11C22×D412yes—
488C2×C4×C11C22×D412yes—
489C2×C4×C11C22×D412yes—
490C2×C4×C11C2×#4112yes—
491C2×Dic11—22no—
492C2×Dic11—21no—
493C2×Dic11—22no—
494C2×Dic11—21no—
495C2×Dic11—21no—
496C2×Dic11—21no—
497C2×Dic11—21no—
498C2×Dic11—21no—
499C2×Dic11—22no—
500C2×Dic11—22no—
501C2×Dic11—28no—
502C2×Dic11—22no—
503C2×Dic11—21no—
504C2×Dic11—21no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—21no—
509C2×Dic11—21no—
510C2×Dic11—22no—
511C2×Dic11—21no—
512C2×Dic11—22no—
513C2×Dic11—21no—
514C2×Dic11—44no—
515C2×Dic11—44no—
516C2×Dic11C23×C414yes—
517C2×Dic11C23×C412yes—
518C2×Dic11C23×C414yes—
519C2×Dic11C23×C412yes—
520C2×Dic11C22×D412yes—
521C2×Dic11C22×D412yes—
522C2×Dic11C22×D412yes—
523C2×Dic11C2×#4112yes—
524C4×D11—28no—
525C4×D11—216no—
526C4×D11—28no—
527C4×D11—28no—
528C4×D11—48no—
529C4×D11C4×D4116yes—
530Dic22—28no—
531Dic22—216no—
532C23×Q8—111no—
533C24×C4—111no—
534C2×C22⋊Q8—111no—
535C2×C22⋊Q8—111no—
536C2×C22⋊Q8—1116no—
537C2×C22⋊Q8—111no—
538C2×C22⋊Q8—112no—
539C2×C22⋊Q8—112no—
540C2×C22⋊Q8C2×D1111yescharacteristic
541#519—228no—
542C2×C4×Q8—111no—
543C2×C4×Q8—111no—
544C2×C4×Q8—112no—
545C2×C4×Q8—111no—
546C2×C4×Q8—112no—
547C2×C4×Q8C2×D1111yescharacteristic, complemented
548C2×#117—111no—
549C2×#117—111no—
550C2×#117—112no—
551C2×#117—111no—
552C2×#117—111no—
553C2×#117—111no—
554C2×#117—111no—
555C2×#117—112no—
556C2×#117—111no—
557C2×#117—111no—
558C2×#117—111no—
559C2×#117—111no—
560C2×#117—228no—
561C22×C4⋊C4—111no—
562C22×C4⋊C4—112no—
563C22×C4⋊C4—111no—
564C22×C4⋊C4—111no—
565C22×C22⋊C4—112no—
566C22×C22⋊C4—111no—
567C22×C22⋊C4—111no—
568C22×C42—111no—
569C22×C42C2×D1111yescharacteristic
570#391—111no—
571#391—111no—
572#391—111no—
573#391—112no—
574#391—112no—
575#391C2×D1111yescharacteristic, complemented
576#389—111no—
577#389—111no—
578#389—112no—
579#389—112no—
580#389—112no—
581#389—111no—
582#389—112no—
583#389—112no—
584#389—112no—
585#389C2×D1111yescharacteristic, complemented
586#388—112no—
587#388—112no—
588#388—112no—
589#388—112no—
590#388—112no—
591#388—112no—
592#388—112no—
593#388—112no—
594#387—112no—
595#387—112no—
596#387—112no—
597#387—112no—
598#387—112no—
599#387—112no—
600#387—112no—
601#387C2×D1112yescomplemented
602#385—112no—
603#385—112no—
604#385—112no—
605#385C2×D1112yes—
606#381—112no—
607#381—112no—
608#381—112no—
609#380—111no—
610#380—112no—
611#380—111no—
612#380—111no—
613#380—112no—
614#380C2×D1111yescharacteristic
615#379—112no—
616C4×C4⋊C4—111no—
617C4×C4⋊C4—111no—
618C4×C4⋊C4—112no—
619C4×C4⋊C4—111no—
620C4×C4⋊C4—112no—
621C4×C4⋊C4—112no—
622C4×C4⋊C4—112no—
623C4×C4⋊C4—112no—
624C4×C4⋊C4C2×D1111yescharacteristic, complemented
625C4×C4⋊C4C2×D1112yescomplemented
626C4×C22⋊C4—112no—
627C4×C22⋊C4—112no—
628C4×C22⋊C4—112no—
629C4×C22⋊C4—112no—
630C4×C22⋊C4—112no—
631C4×C22⋊C4—112no—
632C4×C22⋊C4—112no—
633C4×C22⋊C4C2×D1112yes—
634C22×C11—22no—
635C22×C11—22no—
636C22×C11—22no—
637C22×C11—22no—
638C22×C11—22no—
639C22×C11—22no—
640C22×C11#51914yescomplemented
641C22×C11C24×C411yescharacteristic
642C22×C11C23×D411yescharacteristic
643C22×C11C22×#4111yescharacteristic
644C22×C11C2×2−1+411yescharacteristic
645C22×C11C2×2−1+411yescharacteristic
646C22×C11#58511yescharacteristic
647C22×C11#58511yescharacteristic
648C2×D11—22no—
649C2×D11—22no—
650C2×D11—22no—
651C2×D11—22no—
652C2×D11—22no—
653C2×D11—22no—
654C2×D11—22no—
655C2×D11—22no—
656C2×D11—22no—
657C2×D11—416no—
658C2×D11—41no—
659C2×D11—41no—
660C2×D11—41no—
661C2×D11—41no—
662C2×D11C2×C4×D414yes—
663C4×C11—22no—
664C4×C11—24no—
665C4×C11—24no—
666C4×C11—22no—
667C4×C11—22no—
668C4×C11—42no—
669C4×C11—41no—
670C4×C11—41no—
671C4×C11—42no—
672C4×C11C2×C4×D414yes—
673Dic11—24no—
674Dic11—22no—
675Dic11—24no—
676Dic11—22no—
677Dic11—22no—
678Dic11—42no—
679Dic11—41no—
680Dic11—41no—
681Dic11—42no—
682Dic11C2×C4×D414yes—
683C25—111no—
684C22×Q8—118no—
685C22×Q8—112no—
686C22×Q8—111no—
687C22×Q8—224no—
688C22×Q8—224no—
689C22×Q8C22×D1111yescharacteristic
690C23×C4—111no—
691C23×C4—111no—
692C23×C4—118no—
693C23×C4—112no—
694C23×C4—111no—
695C23×C4—111no—
696C23×C4—111no—
697C23×C4—112no—
698C23×C4—111no—
699C23×C4—111no—
700C23×C4—224no—
701C23×C4—224no—
702C23×C4C22×D1111yescharacteristic
703C23×C4C22×D1111yescharacteristic
704C23×C4C22×D1111yescharacteristic
705C22⋊Q8—118no—
706C22⋊Q8—118no—
707C22⋊Q8—1116no—
708C22⋊Q8—118no—
709C22⋊Q8—1116no—
710C22⋊Q8C4×D1118yes—
711C4×Q8—24no—
712C4×Q8—228no—
713C4×Q8—224no—
714C4×Q8—224no—
715C4×Q8—228no—
716C4×Q8—224no—
717#117—118no—
718#117—224no—
719#117—224no—
720#117—224no—
721#117—228no—
722#117—224no—
723#117—224no—
724#117—224no—
725#117—228no—
726#117—224no—
727#117—224no—
728#117—224no—
729C2×C4⋊C4—111no—
730C2×C4⋊C4—111no—
731C2×C4⋊C4—112no—
732C2×C4⋊C4—112no—
733C2×C4⋊C4—111no—
734C2×C4⋊C4—112no—
735C2×C4⋊C4—112no—
736C2×C4⋊C4—118no—
737C2×C4⋊C4—1116no—
738C2×C4⋊C4—111no—
739C2×C4⋊C4—111no—
740C2×C4⋊C4—111no—
741C2×C4⋊C4—111no—
742C2×C4⋊C4—111no—
743C2×C4⋊C4—111no—
744C2×C4⋊C4—111no—
745C2×C4⋊C4—112no—
746C2×C4⋊C4—112no—
747C2×C4⋊C4—112no—
748C2×C4⋊C4—111no—
749C2×C4⋊C4—112no—
750C2×C4⋊C4—112no—
751C2×C4⋊C4—112no—
752C2×C4⋊C4—224no—
753C2×C4⋊C4—224no—
754C2×C4⋊C4C22×D1111yescharacteristic
755C2×C4⋊C4C22×D1112yes—
756C2×C4⋊C4C22×D1111yescharacteristic
757C2×C4⋊C4C22×D1112yes—
758C2×C4⋊C4C22×D1112yes—
759C2×C4⋊C4C22×D1111yescharacteristic
760C2×C22⋊C4—112no—
761C2×C22⋊C4—111no—
762C2×C22⋊C4—111no—
763C2×C22⋊C4—112no—
764C2×C22⋊C4—112no—
765C2×C22⋊C4—1116no—
766C2×C22⋊C4—112no—
767C2×C22⋊C4—111no—
768C2×C22⋊C4—111no—
769C2×C22⋊C4—111no—
770C2×C22⋊C4—111no—
771C2×C22⋊C4—111no—
772C2×C22⋊C4—111no—
773C2×C22⋊C4—112no—
774C2×C22⋊C4—112no—
775C2×C22⋊C4—112no—
776C2×C22⋊C4—112no—
777C2×C22⋊C4—224no—
778C2×C22⋊C4—224no—
779C2×C22⋊C4C22×D1112yes—
780C2×C22⋊C4C22×D1112yes—
781C2×C42—24no—
782C2×C42—111no—
783C2×C42—111no—
784C2×C42—111no—
785C2×C42—111no—
786C2×C42—112no—
787C2×C42—112no—
788C2×C42—112no—
789C2×C42—112no—
790C2×C42—112no—
791C2×C42—112no—
792C2×C42—112no—
793C2×C42—112no—
794C2×C42—224no—
795C2×C42C22×D1111yescharacteristic
796C2×C42C22×D1111yescharacteristic
797C2×C42C22×D1111yescharacteristic
798C2×C42C22×D1112yes—
799C2×C42C22×D1112yes—
800C2×C42C22×D1111yescharacteristic
801#95—112no—
802#95—112no—
803#95—112no—
804#95—112no—
805#95—112no—
806#95—112no—
807#95—112no—
808#95—112no—
809#95—112no—
810#95—112no—
811#95—112no—
812#95—112no—
813#95—112no—
814#95—112no—
815#95—112no—
816#95C22×D1112yes—
817#95C22×D1112yes—
818#95C22×D1112yes—
819#95C22×D1112yes—
820#95C22×D1112yes—
821C2×C11—24no—
822C2×C11C22×C4×D411yescharacteristic
823C2×C11C2×#51911yescharacteristic
824C2×C11#342811yescharacteristic
825C2×C11#348911yescharacteristic
826C2×C11#348911yescharacteristic
827C2×C11#349511yescharacteristic
828C2×C11#349511yescharacteristic
829D11—24no—
830D11—42no—
831C24—111no—
832C24—111no—
833C24—114no—
834C24—222no—
835C24—222no—
836C24—222no—
837C24—222no—
838C24—441no—
839C24—441no—
840C24C23×D1111yescharacteristic
841C2×Q8—22no—
842C2×Q8—22no—
843C2×Q8—118no—
844C2×Q8—114no—
845C2×Q8—224no—
846C2×Q8—224no—
847C2×Q8—2232no—
848C2×Q8—222no—
849C2×Q8—222no—
850C2×Q8C2×C4×D1114yes—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—41no—
858C22×C4—41no—
859C22×C4—111no—
860C22×C4—114no—
861C22×C4—114no—
862C22×C4—114no—
863C22×C4—114no—
864C22×C4—112no—
865C22×C4—112no—
866C22×C4—111no—
867C22×C4—111no—
868C22×C4—111no—
869C22×C4—118no—
870C22×C4—114no—
871C22×C4—114no—
872C22×C4—114no—
873C22×C4—118no—
874C22×C4—112no—
875C22×C4—111no—
876C22×C4—111no—
877C22×C4—112no—
878C22×C4—222no—
879C22×C4—222no—
880C22×C4—2232no—
881C22×C4—222no—
882C22×C4—224no—
883C22×C4—222no—
884C22×C4—224no—
885C22×C4—222no—
886C22×C4—222no—
887C22×C4—222no—
888C22×C4—222no—
889C22×C4—222no—
890C22×C4—222no—
891C22×C4—222no—
892C22×C4—222no—
893C22×C4—442no—
894C22×C4—442no—
895C22×C4—441no—
896C22×C4—441no—
897C22×C4C2×C4×D1114yes—
898C22×C4C23×D1112yes—
899C22×C4C23×D1111yescharacteristic
900C22×C4C23×D1111yescharacteristic
901C22×C4C23×D1112yes—
902C22×C4C23×D1111yescharacteristic
903C22×C4C23×D1112yes—
904C22×C4C23×D1112yes—
905C22×C4C23×D1111yescharacteristic
906C22×C4C23×D1111yescharacteristic
907C22×C4C23×D1111yescharacteristic
908C4⋊C4—24no—
909C4⋊C4—22no—
910C4⋊C4—22no—
911C4⋊C4—42no—
912C4⋊C4—118no—
913C4⋊C4—118no—
914C4⋊C4—118no—
915C4⋊C4—114no—
916C4⋊C4—118no—
917C4⋊C4—114no—
918C4⋊C4—114no—
919C4⋊C4—222no—
920C4⋊C4—222no—
921C4⋊C4—222no—
922C4⋊C4—222no—
923C4⋊C4—224no—
924C4⋊C4—224no—
925C4⋊C4—222no—
926C4⋊C4—222no—
927C4⋊C4—224no—
928C4⋊C4—222no—
929C4⋊C4—222no—
930C4⋊C4—442no—
931C4⋊C4—442no—
932C4⋊C4—442no—
933C4⋊C4C2×C4×D1114yes—
934C4⋊C4C2×C4×D1118yes—
935C22⋊C4—24no—
936C22⋊C4—118no—
937C22⋊C4—118no—
938C22⋊C4—118no—
939C22⋊C4—114no—
940C22⋊C4—114no—
941C22⋊C4—222no—
942C22⋊C4—222no—
943C22⋊C4—222no—
944C22⋊C4—222no—
945C22⋊C4—224no—
946C22⋊C4—224no—
947C22⋊C4—224no—
948C22⋊C4—222no—
949C22⋊C4—222no—
950C22⋊C4—442no—
951C22⋊C4—442no—
952C22⋊C4C2×C4×D1118yes—
953C42—22no—
954C42—22no—
955C42—22no—
956C42—24no—
957C42—42no—
958C42—114no—
959C42—222no—
960C42—222no—
961C42—224no—
962C42—224no—
963C42—224no—
964C42—224no—
965C42—222no—
966C42—224no—
967C42—442no—
968C42—442no—
969C42—442no—
970C42D4×D1114yes—
971C11#3420311yescharacteristic, complemented, Sylow
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—112no—
977C23—112no—
978C23—112no—
979C23—112no—
980C23—228no—
981C23—221no—
982C23—221no—
983C23—221no—
984C23—221no—
985C23—228no—
986C23—221no—
987C23—221no—
988C23—221no—
989C23—221no—
990C23—221no—
991C23—221no—
992C23—444no—
993C23—444no—
994C23—444no—
995C23—444no—
996C23—444no—
997C23C22×C4×D1112yes—
998C23#6704012yes—
999C23#6704312yes—
1000C23C24×D1111yescharacteristic
1001Q8—28no—
1002Q8—2216no—
1003Q8—228no—
1004C2×C4—21no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—22no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—21no—
1013C2×C4—22no—
1014C2×C4—28no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—44no—
1028C2×C4—44no—
1029C2×C4—112no—
1030C2×C4—112no—
1031C2×C4—112no—
1032C2×C4—1116no—
1033C2×C4—114no—
1034C2×C4—114no—
1035C2×C4—112no—
1036C2×C4—112no—
1037C2×C4—112no—
1038C2×C4—228no—
1039C2×C4—228no—
1040C2×C4—2216no—
1041C2×C4—228no—
1042C2×C4—222no—
1043C2×C4—221no—
1044C2×C4—221no—
1045C2×C4—221no—
1046C2×C4—222no—
1047C2×C4—221no—
1048C2×C4—221no—
1049C2×C4—221no—
1050C2×C4—222no—
1051C2×C4—222no—
1052C2×C4—228no—
1053C2×C4—222no—
1054C2×C4—221no—
1055C2×C4—221no—
1056C2×C4—222no—
1057C2×C4—222no—
1058C2×C4—221no—
1059C2×C4—222no—
1060C2×C4—221no—
1061C2×C4—222no—
1062C2×C4—222no—
1063C2×C4—221no—
1064C2×C4—221no—
1065C2×C4—448no—
1066C2×C4—444no—
1067C2×C4—444no—
1068C2×C4C22×C4×D1114yes—
1069C2×C4C22×C4×D1114yes—
1070C2×C4C22×C4×D1112yes—
1071C2×C4C22×C4×D1112yes—
1072C2×C4C2×D4×D1112yes—
1073C2×C4C2×D4×D1112yes—
1074C2×C4C2×D4×D1112yes—
1075C2×C4#41×D1112yes—
1076C22—22no—
1077C22—22no—
1078C22—22no—
1079C22—22no—
1080C22—22no—
1081C22—22no—
1082C22—114no—
1083C22—222no—
1084C22—222no—
1085C22—222no—
1086C22—222no—
1087C22—222no—
1088C22—222no—
1089C22—222no—
1090C22—222no—
1091C22—222no—
1092C22—4416no—
1093C22—441no—
1094C22—441no—
1095C22—441no—
1096C22—441no—
1097C22#1062310314yescomplemented
1098C22C23×C4×D1111yescharacteristic
1099C22C22×D4×D1111yescharacteristic
1100C22C2×#6704011yescharacteristic
1101C22C2×#41×D1111yescharacteristic
1102C22C2×#6704311yescharacteristic
1103C22#1062345311yescharacteristic
1104C22#1062345311yescharacteristic
1105C4—22no—
1106C4—22no—
1107C4—22no—
1108C4—24no—
1109C4—24no—
1110C4—41no—
1111C4—42no—
1112C4—41no—
1113C4—42no—
1114C4—114no—
1115C4—222no—
1116C4—222no—
1117C4—222no—
1118C4—224no—
1119C4—224no—
1120C4—441no—
1121C4—441no—
1122C4—442no—
1123C4—442no—
1124C4C4×D4×D1114yes—
1125C2—24no—
1126C2—224no—
1127C2—442no—
1128C2C2×C4×D4×D1111yescharacteristic
1129C2C2×#1062310311yescharacteristic
1130C2#1308181511yescharacteristic
1131C2#1308228811yescharacteristic
1132C2#1308229211yescharacteristic
1133C2#1308235611yescharacteristic
1134C2#1308236311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC4×C11×C22⋊Q8C2
socle, cosocleC23×C11C25
prime radicalC24×D11C23
hypercenterC4×C22⋊Q8D11
hypocenterC11#34203
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#10623103C2semidirect
4. #13071644C2semidirect
5. #13071638C2semidirect
6. #13071622C2semidirect
7. #13071616C2semidirect
8. #13071482C2semidirect
9. #13071481C2semidirect
12. #13071301C2semidirect
13. #13071299C2semidirect
14. #13071296C2semidirect
15. #13071292C2semidirect
16. #13071231C2semidirect
17. #13071199C2semidirect
18. C22⋊Q8×Dic11C2semidirect
19. C4×#66977C2semidirect
20. #13071144C2semidirect
22. #13070970C2semidirect
23. C4×C11×C22⋊Q8C2semidirect
27. C2×C4×Q8×C11C22semidirect
30. C2×Q8×Dic11C22semidirect
37. D11×C22⋊Q8C4semidirect
46. C2×#66940C22semidirect
47. C2×#66940C22semidirect
60. C2×C4×Dic22C22semidirect
61. C2×C4×Dic22C22semidirect
62. C11×#391C22semidirect
63. C11×#389C22semidirect
64. C11×#387C22semidirect
67. C4×C11×C4⋊C4C22semidirect
68. C4×C11×C4⋊C4C22semidirect
70. #10622843C22semidirect
79. #10622598C22semidirect
80. #10622594C22semidirect
81. C4⋊C4×Dic11C22semidirect
82. C4⋊C4×Dic11C22semidirect
83. C4⋊C4×Dic11C22semidirect
84. #10622587C22semidirect
85. #10622586C22semidirect
86. #10622586C22semidirect
87. #10622585C22semidirect
88. #10622585C22semidirect
98. C4×C4⋊Dic11C22semidirect
99. #10622546C22semidirect
100. #10622546C22semidirect
101. C4×Dic11⋊C4C22semidirect
102. C4×Dic11⋊C4C22semidirect
103. #10622542C22semidirect
104. #10622541C22semidirect
105. #10622541C22semidirect
116. #10622267C22semidirect
117. #10622266C22semidirect
118. #10622265C22semidirect
119. #10622265C22semidirect
120. #10622262C22semidirect
121. #10622262C22semidirect
122. #10622260C22semidirect
123. #10622260C22semidirect
124. #10622259C22semidirect
125. #10622259C22semidirect
136. C2×Q8×D11C2×C4semidirect
167. #66999C2×C4semidirect
222. #66950C2×C4semidirect
223. #66949C2×C4semidirect
227. C4⋊C4×D11C2×C4semidirect
228. C4⋊C4×D11C2×C4semidirect
425. C4×C22⋊Q8D11semidirect
547. C2×C4×Q8C2×D11semidirect
575. #391C2×D11semidirect
585. #389C2×D11semidirect
601. #387C2×D11semidirect
624. C4×C4⋊C4C2×D11semidirect
625. C4×C4⋊C4C2×D11semidirect
640. C22×C11#519semidirect
971. C11#34203semidirect
1097. C22#10623103semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C22⋊Q82
C2×#106231032
C22×#669252
#130716442
#130716382
#130716222
#130716162
#130714822
#130714812
#130714632
#130714592
#130713012
#130712992
#130712962
#130712922
#130712312
#130711992
C22⋊Q8×Dic112
C4×#669772
#130711442
#130709982
#130709702
C4×C11×C22⋊Q82
#3420311