Finite Group Databasebeta

← #14914085

Subgroups — #14914085

Order 2816.

3246 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623078C211yesmaximal, characteristic
2C2×#10623054C211yesmaximal, characteristic, complemented
3C2×D11×#117C211yesmaximal, characteristic, complemented
4#13071613C212yesmaximal, complemented
5#13071605C212yesmaximal, complemented
6#13071597C212yesmaximal, complemented
7#13071594C212yesmaximal, complemented
8#13071566C211yesmaximal, characteristic, complemented
9#13071548C211yesmaximal, characteristic, complemented
10#13071546C211yesmaximal, characteristic, complemented
11#13071545C211yesmaximal, characteristic, complemented
12#13071538C211yesmaximal, characteristic, complemented
13#13071516C211yesmaximal, characteristic, complemented
14#13071512C211yesmaximal, characteristic, complemented
15#13071302C212yesmaximal, complemented
16#13071295C212yesmaximal, complemented
17#13071237C211yesmaximal, characteristic, complemented
18#13071205C211yesmaximal, characteristic, complemented
19C4×#66949C212yesmaximal, complemented
20#13071128C212yesmaximal, complemented
21D11×#380C211yesmaximal, characteristic, complemented
22#13070970C211yesmaximal, characteristic, complemented
23C11×#2354C211yesmaximal, characteristic, complemented
24C22×#4339C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C11×#117C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic, complemented
29C2×#66992C2211yescharacteristic
30C2×#66990C2211yescharacteristic
31C2×C4×C22⋊D11C2211yescharacteristic
32C2×C4×C22⋊D11C2211yescharacteristic
33C2×#66979C2211yescharacteristic
34C22×C4⋊Dic11C2211yescharacteristic, complemented
35#10623078C4116yescomplemented
36#10623054—28no—
37D11×#117—28no—
38C2×#66949C2211yescharacteristic
39C2×#66947C2211yescharacteristic
40C2×#66946C2212yes—
41C2×#66945C2211yescharacteristic
42C2×#66945C2211yescharacteristic
43C2×#66945C2211yescharacteristic, complemented
44C2×C4⋊C4×D11C2211yescharacteristic
45C2×C4⋊C4×D11C2211yescharacteristic
46C2×C4⋊C4×D11C2211yescharacteristic
47C2×C4⋊C4×D11C2211yescharacteristic
48C2×C4⋊C4×D11C2211yescharacteristic, complemented
49C2×#66937C2211yescharacteristic
50C2×#66936C2211yescharacteristic
51C2×#66935C2211yescharacteristic
52C2×(C22⋊D11)⋊C4C2212yes—
53C2×(C22⋊D11)⋊C4C2212yes—
54C2×(C22⋊D11)⋊C4C2212yescomplemented
55C2×C22⋊C4×D11C2212yes—
56C2×C22⋊C4×D11C2212yes—
57C2×#66931C2211yescharacteristic
58C2×#66930C2212yes—
59C2×C4×D44C2212yes—
60C2×C4×D44C2211yescharacteristic
61C2×#66925C2212yes—
62C2×#66925C2211yescharacteristic
63C2×C42×D11C2212yes—
64C2×C4×Dic22C2212yescomplemented
65C11×#390C2212yes—
66C11×#388C2212yes—
67C11×#388C2212yescomplemented
68C11×#384C2211yescharacteristic, complemented
69C11×#380C2211yescharacteristic
70C11×#380C2211yescharacteristic, complemented
71C4×C11×C4⋊C4C2212yescomplemented
72C4×C11×C4⋊C4C2211yescharacteristic, complemented
73#10622833C2212yes—
74#10622825C2211yescharacteristic
75#10622825C2211yescharacteristic, complemented
76#10622602C2212yes—
77#10622602C2212yes—
78#10622602C2212yes—
79#10622602C2212yescomplemented
80#10622600C2211yescharacteristic
81#10622600C2211yescharacteristic
82#10622600C2211yescharacteristic, complemented
83#10622600C2211yescharacteristic, complemented
84#10622594C2212yescomplemented
85#10622590C2211yescharacteristic, complemented
86#10622589C2211yescharacteristic, complemented
87C4⋊C4×Dic11C2211yescharacteristic, complemented
88C4⋊C4×Dic11C2211yescharacteristic, complemented
89#10622586C2212yescomplemented
90#10622585C2212yescomplemented
91#10622585C2212yescomplemented
92#10622570C2212yes—
93#10622570C2212yescomplemented
94#10622569C2212yes—
95#10622569C2212yes—
96#10622569C2212yes—
97#10622564C2212yes—
98#10622559C2212yescomplemented
99#10622558C2212yescomplemented
100#10622557C2212yes—
101#10622557C2212yes—
102#10622555C2212yes—
103C22⋊C4×Dic11C2212yescomplemented
104#10622553C2212yescomplemented
105#10622553C2212yescomplemented
106C4×(C2×D11)⋊C4C2212yes—
107C4×(C2×D11)⋊C4C2212yes—
108C4×(C2×D11)⋊C4C2212yes—
109#10622549C2211yescharacteristic, complemented
110C4×C4⋊Dic11C2211yescharacteristic, complemented
111#10622546C2212yescomplemented
112C4×Dic11⋊C4C2212yescomplemented
113C4×Dic11⋊C4C2212yescomplemented
114#10622281C2212yes—
115#10622280C2212yes—
116#10622279C2212yes—
117#10622279C2212yescomplemented
118#10622278C2212yes—
119#10622278C2212yes—
120D11×#95C2212yes—
121#10622266C2212yescomplemented
122#10622265C2212yescomplemented
123#10622262C2212yescomplemented
124#10622260C2212yescomplemented
125#10622259C2212yescomplemented
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C22×C22⋊D11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
134C23×Dic11C2311yescharacteristic
135C23×Dic11C2312yes—
136C2×#4339—24no—
137C2×#4339—24no—
138C2×#4339C2×C418yescomplemented
139C22×D44C2311yescharacteristic
140C22×D44C2311yescharacteristic
141C22×C4×D11—24no—
142C22×C4×D11—24no—
143C22×C4×D11C2×C418yescomplemented
144C22×C4×D11C2312yes—
145C22×C4×D11C2312yes—
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2312yes—
151C22×C4×D11C2312yes—
152C22×C4×D11C2312yes—
153C22×C4×D11C2311yescharacteristic
154C22×Dic22C2311yescharacteristic
155C4×D4×C11C2×C418yescomplemented
156C11×#117—24no—
157C11×#117—24no—
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2312yes—
162C2×C11×C4⋊C4C2312yes—
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C42×C11C2312yes—
172C2×C42×C11C2312yes—
173C2×C42×C11C2312yes—
174C2×C42×C11C2311yescharacteristic
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2311yescharacteristic
179C2×C22⋊Dic11C2311yescharacteristic
180#66992C2×C418yescomplemented
181#66990C2×C418yescomplemented
182C4×C22⋊D11C2×C418yescomplemented
183C4×C22⋊D11C2×C418yescomplemented
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2311yescharacteristic
191C2×(C2×D11)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2311yescharacteristic
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2312yes—
197#66979—24no—
198C2×C4⋊Dic11—24no—
199C2×C4⋊Dic11C2312yes—
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2311yescharacteristic
203C2×C4⋊Dic11C2311yescharacteristic
204C2×C4⋊Dic11C2311yescharacteristic
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2311yescharacteristic
213C2×Dic11⋊C4C2311yescharacteristic
214C2×Dic11⋊C4C2311yescharacteristic
215C2×Dic11⋊C4C2311yescharacteristic
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2312yes—
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2312yes—
224#66949C2×C418yescomplemented
225#66947C2×C418yescomplemented
226#66946—44no—
227#66945—24no—
228#66945—24no—
229#66945D418yescomplemented
230C4⋊C4×D11—24no—
231C4⋊C4×D11—24no—
232C4⋊C4×D11—24no—
233C4⋊C4×D11—24no—
234C4⋊C4×D11—24no—
235#66937C2×C418yescomplemented
236#66936C2×C418yescomplemented
237#66935C2×C418yescomplemented
238(C22⋊D11)⋊C4—28no—
239(C22⋊D11)⋊C4—28no—
240(C22⋊D11)⋊C4—44no—
241C22⋊C4×D11—28no—
242C22⋊C4×D11—44no—
243#66931C2×C418yescomplemented
244#66930—28no—
245C4×D44—28no—
246C4×D44C2×C418yescomplemented
247#66925—28no—
248#66925C2×C418yescomplemented
249C42×D11—28no—
250C4×Dic22—28no—
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—
264C11⋊#95C2312yes—
265C11⋊#95C2312yes—
266C11⋊#95C2312yes—
267#34202—111nomaximal, Sylow
268C24×C11C2411yescharacteristic
269C24×C11C2411yescharacteristic
270C23×D11—22no—
271C23×D11—22no—
272C23×D11—22no—
273C23×D11—22no—
274C23×D11—41no—
275C23×D11—41no—
276C23×D11C22×C414yes—
277C23×D11C2411yescharacteristic
278C23×D11C2411yescharacteristic
279C23×D11C2411yescharacteristic
280C2×D4×C11—41no—
281C2×D4×C11—41no—
282C2×D4×C11C22×C414yes—
283C22×C4×C11—22no—
284C22×C4×C11—22no—
285C22×C4×C11—22no—
286C22×C4×C11—22no—
287C22×C4×C11C22×C414yes—
288C22×C4×C11C22×C414yes—
289C22×C4×C11C2412yes—
290C22×C4×C11C2412yes—
291C22×C4×C11C2412yes—
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2412yes—
297C22×C4×C11C2411yescharacteristic
298C2×C22⋊D11—22no—
299C2×C22⋊D11—22no—
300C2×C22⋊D11—22no—
301C2×C22⋊D11—22no—
302C2×C22⋊D11—22no—
303C2×C22⋊D11—22no—
304C2×C22⋊D11—41no—
305C2×C22⋊D11—41no—
306C2×C22⋊D11C22×C414yes—
307C2×C22⋊D11C22×C414yes—
308C2×C22⋊D11C22×C414yes—
309C2×C22⋊D11C22×C414yes—
310C22×Dic11—22no—
311C22×Dic11—22no—
312C22×Dic11—24no—
313C22×Dic11—42no—
314C22×Dic11—42no—
315C22×Dic11C22×C414yes—
316C22×Dic11C2412yes—
317C22×Dic11C2412yes—
318C22×Dic11C2412yes—
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2411yescharacteristic
321C22×Dic11C2411yescharacteristic
322C22×Dic11C2411yescharacteristic
323C22×Dic11C2412yes—
324C22×Dic11C2411yescharacteristic
325#4339—232no—
326C2×D44—22no—
327C2×D44—22no—
328C2×D44—22no—
329C2×D44—22no—
330C2×D44C22×C414yes—
331C2×D44C22×C414yes—
332C2×C4×D11—22no—
333C2×C4×D11—22no—
334C2×C4×D11—232no—
335C2×C4×D11—24no—
336C2×C4×D11—24no—
337C2×C4×D11—22no—
338C2×C4×D11—24no—
339C2×C4×D11—22no—
340C2×C4×D11—24no—
341C2×C4×D11—24no—
342C2×C4×D11—24no—
343C2×C4×D11—22no—
344C2×C4×D11—22no—
345C2×C4×D11—24no—
346C2×C4×D11—22no—
347C2×C4×D11—22no—
348C2×C4×D11—42no—
349C2×C4×D11—42no—
350C2×C4×D11—42no—
351C2×C4×D11—42no—
352C2×C4×D11—42no—
353C2×C4×D11—42no—
354C2×C4×D11—42no—
355C2×C4×D11—42no—
356C2×C4×D11C22×C414yes—
357C2×C4×D11C22×C414yes—
358C2×C4×D11C22×C414yes—
359C2×C4×D11C22×C414yes—
360C2×C4×D11C22×C414yes—
361C2×C4×D11C2×D414yes—
362C2×C4×D11#4114yes—
363C2×Dic22—22no—
364C2×Dic22—22no—
365C2×Dic22C22×C414yes—
366C11×C4⋊C4—22no—
367C11×C4⋊C4—22no—
368C11×C4⋊C4—22no—
369C11×C4⋊C4—42no—
370C11×C4⋊C4—42no—
371C11×C4⋊C4C22×C414yes—
372C11×C4⋊C4C2×D414yes—
373C11×C22⋊C4—24no—
374C11×C22⋊C4—24no—
375C11×C22⋊C4—42no—
376C11×C22⋊C4—42no—
377C11×C22⋊C4C22×C414yes—
378C11×C22⋊C4C22×C414yes—
379C42×C11—24no—
380C42×C11—24no—
381C42×C11—42no—
382C42×C11C22×C414yes—
383C22⋊Dic11—24no—
384C22⋊Dic11—42no—
385C22⋊Dic11—42no—
386C22⋊Dic11C22×C414yes—
387C22⋊Dic11C22×C414yes—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—24no—
390(C2×D11)⋊C4—24no—
391(C2×D11)⋊C4—24no—
392(C2×D11)⋊C4—42no—
393(C2×D11)⋊C4—42no—
394(C2×D11)⋊C4C22×C414yes—
395(C2×D11)⋊C4C22×C414yes—
396(C2×D11)⋊C4C22×C414yes—
397(C2×D11)⋊C4C22×C414yes—
398(C2×D11)⋊C4C22×C414yes—
399(C2×D11)⋊C4C22×C414yes—
400(C2×D11)⋊C4C2×D418yes—
401C4⋊Dic11—24no—
402C4⋊Dic11—22no—
403C4⋊Dic11—22no—
404C4⋊Dic11—22no—
405C4⋊Dic11C22×C414yes—
406C4⋊Dic11C2×D414yes—
407Dic11⋊C4—24no—
408Dic11⋊C4—24no—
409Dic11⋊C4—24no—
410Dic11⋊C4—24no—
411Dic11⋊C4—24no—
412Dic11⋊C4—42no—
413Dic11⋊C4—42no—
414Dic11⋊C4C22×C414yes—
415Dic11⋊C4C22×C414yes—
416Dic11⋊C4C22×C414yes—
417Dic11⋊C4C22×C414yes—
418C4×Dic11—24no—
419C4×Dic11—24no—
420C4×Dic11—24no—
421C4×Dic11—42no—
422C4×Dic11—42no—
423C4×Dic11—42no—
424C4×Dic11C22×C414yes—
425C4×Dic11C2×D418yes—
426C2×#525—111no—
427C2×#520—111no—
428C22×#117—111no—
429#2359—112no—
430#2359—112no—
431#2358—112no—
432#2358—112no—
433#2354—111no—
434#2354D1111yescharacteristic, complemented
435#2352—111no—
436#2352—111no—
437#2352—111no—
438#2352—111no—
439D4×C4⋊C4—111no—
440D4×C4⋊C4—111no—
441#2324—112no—
442#2323—112no—
443#2317—111no—
444#2311—111no—
445C4×C22⋊Q8—112no—
446C4×#121—112no—
447C2×#380—111no—
448#2274—111no—
449C23×C11—21no—
450C23×C11—21no—
451C23×C11—21no—
452C23×C11—21no—
453C23×C11—21no—
454C23×C11—21no—
455C23×C11—21no—
456C23×C11—21no—
457C23×C11—21no—
458C23×C11—21no—
459C23×C11—21no—
460C23×C11—21no—
461C23×C11C23×C412yes—
462C23×C11C23×C412yes—
463C23×C11C2511yescharacteristic
464C22×D11—21no—
465C22×D11—21no—
466C22×D11—21no—
467C22×D11—21no—
468C22×D11—21no—
469C22×D11—21no—
470C22×D11—21no—
471C22×D11—21no—
472C22×D11—21no—
473C22×D11—21no—
474C22×D11—21no—
475C22×D11—21no—
476C22×D11—21no—
477C22×D11—21no—
478C22×D11—28no—
479C22×D11—28no—
480C22×D11—44no—
481C22×D11—44no—
482C22×D11—44no—
483C22×D11—44no—
484C22×D11—44no—
485C22×D11C23×C412yes—
486C22×D11C23×C412yes—
487C22×D11C23×C412yes—
488C22×D11C22×D412yes—
489C22×D11C2×#4112yes—
490C22×D11H(5,𝔽2)12yes—
491C22×D112−1+412yes—
492D4×C11—44no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11—21no—
496C2×C4×C11—21no—
497C2×C4×C11—21no—
498C2×C4×C11—22no—
499C2×C4×C11—21no—
500C2×C4×C11—22no—
501C2×C4×C11—21no—
502C2×C4×C11—21no—
503C2×C4×C11—28no—
504C2×C4×C11—28no—
505C2×C4×C11—22no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—22no—
510C2×C4×C11—22no—
511C2×C4×C11—22no—
512C2×C4×C11—22no—
513C2×C4×C11—22no—
514C2×C4×C11C23×C412yes—
515C2×C4×C11C23×C412yes—
516C2×C4×C11C23×C412yes—
517C2×C4×C11C23×C412yes—
518C2×C4×C11C23×C412yes—
519C2×C4×C11C22×D414yes—
520C2×C4×C11C22×D412yes—
521C2×C4×C11C2×#4112yes—
522C22⋊D11—28no—
523C22⋊D11—28no—
524C22⋊D11—28no—
525C22⋊D11—44no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—21no—
529C2×Dic11—21no—
530C2×Dic11—21no—
531C2×Dic11—22no—
532C2×Dic11—21no—
533C2×Dic11—21no—
534C2×Dic11—21no—
535C2×Dic11—22no—
536C2×Dic11—28no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—22no—
545C2×Dic11—22no—
546C2×Dic11—84no—
547C2×Dic11C23×C412yes—
548C2×Dic11C23×C412yes—
549C2×Dic11C23×C412yes—
550C2×Dic11C23×C412yes—
551C2×Dic11C23×C412yes—
552C2×Dic11C22×D414yes—
553C2×Dic11C22×D412yes—
554C2×Dic11C2×#4112yes—
555D44—28no—
556D44—28no—
557C4×D11—28no—
558C4×D11—28no—
559C4×D11—28no—
560C4×D11—28no—
561C4×D11—48no—
562C4×D11—48no—
563C4×D11—84no—
564C4×D11—84no—
565C4×D11—84no—
566C4×D11C4×D4116yescomplemented
567Dic22—28no—
568C22×#41—111no—
569C24×C4—111no—
570#525—1116no—
571C2×#123—111no—
572C2×#123—111no—
573C2×C22⋊Q8—111no—
574C2×C22⋊Q8—111no—
575C2×#121—111no—
576C2×#121—111no—
577C2×#120—111no—
578C2×#120—111no—
579#520—228no—
580C2×C4×Q8—112no—
581C2×C4×D4—111no—
582C2×C4×D4—111no—
583C2×C4×D4—112no—
584C2×C4×D4—112no—
585C2×C4×D4—112no—
586C2×C4×D4—112no—
587C2×C4×D4—111no—
588C2×C4×D4—112no—
589C2×C4×D4C2×D1111yescharacteristic
590C2×#117—111no—
591C2×#117—111no—
592C2×#117—111no—
593C2×#117—111no—
594C2×#117—112no—
595C2×#117—111no—
596C2×#117—112no—
597C2×#117—228no—
598C2×#117C2×D1111yescharacteristic
599C2×#117C2×D1111yescharacteristic, complemented
600C22×C4⋊C4—111no—
601C22×C4⋊C4—111no—
602C22×C4⋊C4—111no—
603C22×C4⋊C4—111no—
604C22×C4⋊C4—111no—
605C22×C4⋊C4—111no—
606C22×C22⋊C4—112no—
607C22×C22⋊C4—112no—
608C22×C42—112no—
609#391—112no—
610#390—112no—
611#390—112no—
612#390C2×D1112yes—
613#389—112no—
614#389—112no—
615#389—112no—
616#389—112no—
617#388—112no—
618#388—112no—
619#388—112no—
620#388—112no—
621#388—112no—
622#388—112no—
623#388C2×D1112yes—
624#388C2×D1112yescomplemented
625#387—112no—
626#387—112no—
627#387—112no—
628#387—112no—
629#386—112no—
630#386—112no—
631#386—112no—
632#386—112no—
633#386—112no—
634#386—112no—
635#385—112no—
636#385—112no—
637#385—112no—
638#385—112no—
639#385—112no—
640#385—112no—
641#384—111no—
642#384C2×D1111yescharacteristic, complemented
643#382—111no—
644#382—111no—
645#380—111no—
646#380—111no—
647#380—111no—
648#380—111no—
649#380—111no—
650#380—111no—
651#380—112no—
652#380—112no—
653#380C2×D1111yescharacteristic
654#380C2×D1111yescharacteristic, complemented
655C4×C4⋊C4—111no—
656C4×C4⋊C4—111no—
657C4×C4⋊C4—112no—
658C4×C4⋊C4—111no—
659C4×C4⋊C4—112no—
660C4×C4⋊C4—112no—
661C4×C4⋊C4C2×D1111yescharacteristic, complemented
662C4×C4⋊C4C2×D1112yescomplemented
663C4×C22⋊C4—112no—
664C4×C22⋊C4—112no—
665C4×C22⋊C4—112no—
666C4×C22⋊C4—112no—
667C4×C22⋊C4—112no—
668C4×C22⋊C4—112no—
669C2×#95—112no—
670C22×C11—22no—
671C22×C11—22no—
672C22×C11—22no—
673C22×C11—22no—
674C22×C11—22no—
675C22×C11—22no—
676C22×C11—41no—
677C22×C11—41no—
678C22×C11—41no—
679C22×C11—41no—
680C22×C11—41no—
681C22×C11—41no—
682C22×C11—41no—
683C22×C11—41no—
684C22×C11C24×C411yescharacteristic
685C22×C11C23×D411yescharacteristic
686C22×C11C22×#4111yescharacteristic
687C22×C11C2×H(5,𝔽2)11yescharacteristic
688C22×C11C2×2−1+411yescharacteristic
689C22×C11#58511yescharacteristic
690C22×C11#58511yescharacteristic
691C2×D11—22no—
692C2×D11—22no—
693C2×D11—22no—
694C2×D11—22no—
695C2×D11—22no—
696C2×D11—22no—
697C2×D11—22no—
698C2×D11—22no—
699C2×D11—22no—
700C2×D11—22no—
701C2×D11—22no—
702C2×D11—22no—
703C2×D11—22no—
704C2×D11—22no—
705C2×D11—22no—
706C2×D11—416no—
707C2×D11—41no—
708C2×D11—41no—
709C2×D11—41no—
710C2×D11—41no—
711C2×D11C2×C4×D414yes—
712C2×D11#52014yescomplemented
713C4×C11—22no—
714C4×C11—22no—
715C4×C11—22no—
716C4×C11—22no—
717C4×C11—24no—
718C4×C11—42no—
719C4×C11—42no—
720C4×C11—42no—
721C4×C11C2×C4×D414yes—
722Dic11—22no—
723Dic11—22no—
724Dic11—22no—
725Dic11—22no—
726Dic11—24no—
727Dic11—42no—
728Dic11—42no—
729Dic11—42no—
730Dic11C2×C4×D414yes—
731C25—111no—
732C2×#41—118no—
733C2×#41—224no—
734C2×#41—224no—
735C22×Q8—111no—
736C22×D4—111no—
737C22×D4—111no—
738C22×D4—111no—
739C22×D4—111no—
740C22×D4—111no—
741C22×D4—111no—
742C22×D4C22×D1111yescharacteristic
743C23×C4—111no—
744C23×C4—111no—
745C23×C4—118no—
746C23×C4—111no—
747C23×C4—111no—
748C23×C4—111no—
749C23×C4—111no—
750C23×C4—112no—
751C23×C4—112no—
752C23×C4—112no—
753C23×C4—112no—
754C23×C4—112no—
755C23×C4—112no—
756C23×C4—224no—
757C23×C4—224no—
758C23×C4C22×D1111yescharacteristic
759C23×C4C22×D1111yescharacteristic
760#123—118no—
761#123—118no—
762C22⋊Q8—118no—
763C22⋊Q8—118no—
764#121—118no—
765#121—118no—
766#120—118no—
767#120—118no—
768C4×Q8—228no—
769C4×D4—118no—
770C4×D4—118no—
771C4×D4—118no—
772C4×D4—228no—
773C4×D4—228no—
774C4×D4—228no—
775C4×D4—444no—
776C4×D4—444no—
777C4×D4C4×D1118yescomplemented
778#117—24no—
779#117—24no—
780#117—118no—
781#117—118no—
782#117—228no—
783#117—228no—
784#117—224no—
785#117—224no—
786#117—224no—
787C2×C4⋊C4—111no—
788C2×C4⋊C4—111no—
789C2×C4⋊C4—111no—
790C2×C4⋊C4—111no—
791C2×C4⋊C4—111no—
792C2×C4⋊C4—111no—
793C2×C4⋊C4—111no—
794C2×C4⋊C4—111no—
795C2×C4⋊C4—112no—
796C2×C4⋊C4—112no—
797C2×C4⋊C4—112no—
798C2×C4⋊C4—112no—
799C2×C4⋊C4—112no—
800C2×C4⋊C4—111no—
801C2×C4⋊C4—112no—
802C2×C4⋊C4—112no—
803C2×C4⋊C4—112no—
804C2×C4⋊C4—224no—
805C2×C4⋊C4—224no—
806C2×C4⋊C4—224no—
807C2×C4⋊C4—224no—
808C2×C4⋊C4—224no—
809C2×C4⋊C4—224no—
810C2×C4⋊C4C22×D1111yescharacteristic
811C2×C4⋊C4C22×D1111yescharacteristic
812C2×C4⋊C4C22×D1111yescharacteristic
813C2×C4⋊C4C22×D1112yes—
814C2×C4⋊C4C22×D1112yes—
815C2×C4⋊C4C22×D1111yescharacteristic
816C2×C4⋊C4C22×D1111yescharacteristic
817C2×C22⋊C4—111no—
818C2×C22⋊C4—111no—
819C2×C22⋊C4—112no—
820C2×C22⋊C4—111no—
821C2×C22⋊C4—111no—
822C2×C22⋊C4—111no—
823C2×C22⋊C4—111no—
824C2×C22⋊C4—111no—
825C2×C22⋊C4—111no—
826C2×C22⋊C4—112no—
827C2×C22⋊C4—112no—
828C2×C22⋊C4—112no—
829C2×C22⋊C4—112no—
830C2×C22⋊C4—112no—
831C2×C22⋊C4—112no—
832C2×C22⋊C4—112no—
833C2×C22⋊C4—112no—
834C2×C22⋊C4—112no—
835C2×C22⋊C4—228no—
836C2×C22⋊C4—444no—
837C2×C22⋊C4C22×D1112yes—
838C2×C22⋊C4C22×D1112yes—
839C2×C22⋊C4C22×D1112yes—
840C2×C22⋊C4C22×D1112yes—
841C2×C22⋊C4C22×D1111yescharacteristic
842C2×C22⋊C4C22×D1111yescharacteristic
843C2×C42—112no—
844C2×C42—111no—
845C2×C42—112no—
846C2×C42—112no—
847C2×C42—112no—
848C2×C42—112no—
849C2×C42—112no—
850C2×C42—112no—
851C2×C42—228no—
852C2×C42C22×D1112yes—
853C2×C42C22×D1112yes—
854C2×C42C22×D1112yes—
855C2×C42C22×D1111yescharacteristic
856#95—112no—
857#95—112no—
858#95—112no—
859#95—112no—
860#95—112no—
861#95—112no—
862#95—112no—
863#95—112no—
864#95—112no—
865#95—112no—
866#95—112no—
867#95—112no—
868#95—112no—
869#95C22×D1112yes—
870#95C22×D1112yes—
871#95C22×D1112yes—
872C2×C11—42no—
873C2×C11—42no—
874C2×C11C22×C4×D411yescharacteristic
875C2×C11C2×#52011yescharacteristic
876C2×C11#342811yescharacteristic
877C2×C11#348811yescharacteristic
878C2×C11#348911yescharacteristic
879C2×C11#349411yescharacteristic
880C2×C11#349511yescharacteristic
881D11—24no—
882D11—24no—
883D11—42no—
884C24—111no—
885C24—111no—
886C24—111no—
887C24—114no—
888C24—222no—
889C24—222no—
890C24—222no—
891C24—222no—
892C24—441no—
893C24—441no—
894C24C23×D1111yescharacteristic
895C24C23×D1111yescharacteristic
896#41—2232no—
897C2×Q8—114no—
898C2×Q8—222no—
899C2×Q8—222no—
900C2×D4—41no—
901C2×D4—41no—
902C2×D4—114no—
903C2×D4—114no—
904C2×D4—114no—
905C2×D4—114no—
906C2×D4—114no—
907C2×D4—114no—
908C2×D4—222no—
909C2×D4—222no—
910C2×D4—222no—
911C2×D4—222no—
912C2×D4—222no—
913C2×D4—222no—
914C2×D4—222no—
915C2×D4—222no—
916C2×D4—222no—
917C2×D4—222no—
918C2×D4—441no—
919C2×D4—441no—
920C2×D4C2×C4×D1114yes—
921C22×C4—22no—
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—111no—
926C22×C4—114no—
927C22×C4—114no—
928C22×C4—114no—
929C22×C4—114no—
930C22×C4—111no—
931C22×C4—111no—
932C22×C4—111no—
933C22×C4—111no—
934C22×C4—112no—
935C22×C4—114no—
936C22×C4—114no—
937C22×C4—114no—
938C22×C4—114no—
939C22×C4—112no—
940C22×C4—112no—
941C22×C4—112no—
942C22×C4—222no—
943C22×C4—222no—
944C22×C4—2232no—
945C22×C4—224no—
946C22×C4—224no—
947C22×C4—222no—
948C22×C4—222no—
949C22×C4—224no—
950C22×C4—224no—
951C22×C4—224no—
952C22×C4—224no—
953C22×C4—222no—
954C22×C4—222no—
955C22×C4—224no—
956C22×C4—222no—
957C22×C4—222no—
958C22×C4—222no—
959C22×C4—222no—
960C22×C4—224no—
961C22×C4—442no—
962C22×C4—442no—
963C22×C4—442no—
964C22×C4—442no—
965C22×C4—442no—
966C22×C4—442no—
967C22×C4—442no—
968C22×C4—442no—
969C22×C4—442no—
970C22×C4—442no—
971C22×C4C2×C4×D1114yes—
972C22×C4C2×C4×D1114yes—
973C22×C4C23×D1112yes—
974C22×C4C23×D1112yes—
975C22×C4C23×D1112yes—
976C22×C4C23×D1111yescharacteristic
977C22×C4C23×D1111yescharacteristic
978C22×C4C23×D1111yescharacteristic
979C22×C4C23×D1111yescharacteristic
980C22×C4C23×D1112yes—
981C22×C4C23×D1111yescharacteristic
982C4⋊C4—22no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—114no—
988C4⋊C4—114no—
989C4⋊C4—114no—
990C4⋊C4—114no—
991C4⋊C4—114no—
992C4⋊C4—114no—
993C4⋊C4—224no—
994C4⋊C4—224no—
995C4⋊C4—224no—
996C4⋊C4—224no—
997C4⋊C4—224no—
998C4⋊C4—222no—
999C4⋊C4—224no—
1000C4⋊C4—222no—
1001C4⋊C4—222no—
1002C4⋊C4—442no—
1003C4⋊C4—442no—
1004C4⋊C4C2×C4×D1114yes—
1005C4⋊C4D4×D1114yes—
1006C22⋊C4—24no—
1007C22⋊C4—24no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—114no—
1011C22⋊C4—114no—
1012C22⋊C4—114no—
1013C22⋊C4—114no—
1014C22⋊C4—114no—
1015C22⋊C4—114no—
1016C22⋊C4—114no—
1017C22⋊C4—114no—
1018C22⋊C4—118no—
1019C22⋊C4—224no—
1020C22⋊C4—224no—
1021C22⋊C4—224no—
1022C22⋊C4—224no—
1023C22⋊C4—224no—
1024C22⋊C4—442no—
1025C22⋊C4—442no—
1026C22⋊C4—442no—
1027C22⋊C4—442no—
1028C22⋊C4C2×C4×D1114yes—
1029C22⋊C4C2×C4×D1114yes—
1030C42—24no—
1031C42—24no—
1032C42—42no—
1033C42—114no—
1034C42—118no—
1035C42—224no—
1036C42—224no—
1037C42—224no—
1038C42—442no—
1039C42—442no—
1040C42—442no—
1041C42C2×C4×D1114yes—
1042C11#3420211yescharacteristic, complemented, Sylow
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—112no—
1056C23—112no—
1057C23—112no—
1058C23—112no—
1059C23—112no—
1060C23—112no—
1061C23—112no—
1062C23—228no—
1063C23—228no—
1064C23—221no—
1065C23—221no—
1066C23—221no—
1067C23—221no—
1068C23—221no—
1069C23—221no—
1070C23—221no—
1071C23—221no—
1072C23—221no—
1073C23—221no—
1074C23—221no—
1075C23—221no—
1076C23—221no—
1077C23—221no—
1078C23—444no—
1079C23—444no—
1080C23—444no—
1081C23—444no—
1082C23—444no—
1083C23C22×C4×D1112yes—
1084C23C22×C4×D1112yes—
1085C23C24×D1111yescharacteristic
1086Q8—228no—
1087D4—44no—
1088D4—228no—
1089D4—228no—
1090D4—228no—
1091D4—228no—
1092D4—228no—
1093D4—444no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—22no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—22no—
1103C2×C4—21no—
1104C2×C4—28no—
1105C2×C4—28no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—112no—
1116C2×C4—112no—
1117C2×C4—112no—
1118C2×C4—1116no—
1119C2×C4—112no—
1120C2×C4—112no—
1121C2×C4—112no—
1122C2×C4—112no—
1123C2×C4—114no—
1124C2×C4—228no—
1125C2×C4—228no—
1126C2×C4—228no—
1127C2×C4—221no—
1128C2×C4—221no—
1129C2×C4—221no—
1130C2×C4—221no—
1131C2×C4—221no—
1132C2×C4—221no—
1133C2×C4—222no—
1134C2×C4—221no—
1135C2×C4—222no—
1136C2×C4—221no—
1137C2×C4—228no—
1138C2×C4—228no—
1139C2×C4—222no—
1140C2×C4—222no—
1141C2×C4—222no—
1142C2×C4—222no—
1143C2×C4—222no—
1144C2×C4—222no—
1145C2×C4—222no—
1146C2×C4—222no—
1147C2×C4—222no—
1148C2×C4—448no—
1149C2×C4—448no—
1150C2×C4—884no—
1151C2×C4—884no—
1152C2×C4—884no—
1153C2×C4—884no—
1154C2×C4C22×C4×D1112yes—
1155C2×C4C22×C4×D1112yes—
1156C2×C4C22×C4×D1112yes—
1157C2×C4C22×C4×D1112yes—
1158C2×C4C22×C4×D1112yes—
1159C2×C4C2×D4×D1114yes—
1160C2×C4C2×D4×D1112yes—
1161C2×C4#41×D1112yes—
1162C22—22no—
1163C22—22no—
1164C22—22no—
1165C22—22no—
1166C22—22no—
1167C22—22no—
1168C22—41no—
1169C22—41no—
1170C22—41no—
1171C22—41no—
1172C22—41no—
1173C22—41no—
1174C22—41no—
1175C22—41no—
1176C22—114no—
1177C22—114no—
1178C22—222no—
1179C22—222no—
1180C22—222no—
1181C22—222no—
1182C22—222no—
1183C22—222no—
1184C22—222no—
1185C22—222no—
1186C22—222no—
1187C22—222no—
1188C22—222no—
1189C22—222no—
1190C22—222no—
1191C22—222no—
1192C22—222no—
1193C22—4416no—
1194C22—441no—
1195C22—441no—
1196C22—441no—
1197C22—441no—
1198C22C23×C4×D1111yescharacteristic
1199C22C22×D4×D1111yescharacteristic
1200C22C2×#41×D1111yescharacteristic
1201C22#1062345311yescharacteristic
1202C22#1062345311yescharacteristic
1203C22D11×H(5,𝔽2)11yescharacteristic
1204C22D11×2−1+411yescharacteristic
1205C4—24no—
1206C4—22no—
1207C4—22no—
1208C4—22no—
1209C4—22no—
1210C4—42no—
1211C4—42no—
1212C4—42no—
1213C4—114no—
1214C4—224no—
1215C4—222no—
1216C4—222no—
1217C4—222no—
1218C4—222no—
1219C4—442no—
1220C4—442no—
1221C4—442no—
1222C4C4×D4×D1114yes—
1223C2—42no—
1224C2—42no—
1225C2—224no—
1226C2—224no—
1227C2—442no—
1228C2C2×C4×D4×D1111yescharacteristic
1229C2D11×#52011yescharacteristic
1230C2#1308181711yescharacteristic
1231C2#1308228411yescharacteristic
1232C2#1308229011yescharacteristic
1233C2#1308235011yescharacteristic
1234C2#1308236111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2354C2
socle, cosocleC23×C11C25
prime radicalC2×#10623078C2
hypercenter#2354D11
hypocenterC11#34202
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. C2×#10623054C2semidirect
3. C2×D11×#117C2semidirect
4. #13071613C2semidirect
5. #13071605C2semidirect
6. #13071597C2semidirect
7. #13071594C2semidirect
8. #13071566C2semidirect
9. #13071548C2semidirect
10. #13071546C2semidirect
11. #13071545C2semidirect
12. #13071538C2semidirect
13. #13071516C2semidirect
14. #13071512C2semidirect
15. #13071302C2semidirect
16. #13071295C2semidirect
17. #13071237C2semidirect
18. #13071205C2semidirect
19. C4×#66949C2semidirect
20. #13071128C2semidirect
21. D11×#380C2semidirect
22. #13070970C2semidirect
23. C11×#2354C2semidirect
28. C2×C11×#117C22semidirect
34. C22×C4⋊Dic11C22semidirect
35. #10623078C4semidirect
43. C2×#66945C22semidirect
48. C2×C4⋊C4×D11C22semidirect
54. C2×(C22⋊D11)⋊C4C22semidirect
64. C2×C4×Dic22C22semidirect
67. C11×#388C22semidirect
68. C11×#384C22semidirect
70. C11×#380C22semidirect
71. C4×C11×C4⋊C4C22semidirect
72. C4×C11×C4⋊C4C22semidirect
75. #10622825C22semidirect
79. #10622602C22semidirect
82. #10622600C22semidirect
83. #10622600C22semidirect
84. #10622594C22semidirect
85. #10622590C22semidirect
86. #10622589C22semidirect
87. C4⋊C4×Dic11C22semidirect
88. C4⋊C4×Dic11C22semidirect
89. #10622586C22semidirect
90. #10622585C22semidirect
91. #10622585C22semidirect
93. #10622570C22semidirect
98. #10622559C22semidirect
99. #10622558C22semidirect
103. C22⋊C4×Dic11C22semidirect
104. #10622553C22semidirect
105. #10622553C22semidirect
109. #10622549C22semidirect
110. C4×C4⋊Dic11C22semidirect
111. #10622546C22semidirect
112. C4×Dic11⋊C4C22semidirect
113. C4×Dic11⋊C4C22semidirect
117. #10622279C22semidirect
121. #10622266C22semidirect
122. #10622265C22semidirect
123. #10622262C22semidirect
124. #10622260C22semidirect
125. #10622259C22semidirect
138. C2×#4339C2×C4semidirect
143. C22×C4×D11C2×C4semidirect
155. C4×D4×C11C2×C4semidirect
180. #66992C2×C4semidirect
181. #66990C2×C4semidirect
182. C4×C22⋊D11C2×C4semidirect
183. C4×C22⋊D11C2×C4semidirect
224. #66949C2×C4semidirect
225. #66947C2×C4semidirect
229. #66945D4semidirect
235. #66937C2×C4semidirect
236. #66936C2×C4semidirect
237. #66935C2×C4semidirect
243. #66931C2×C4semidirect
246. C4×D44C2×C4semidirect
248. #66925C2×C4semidirect
434. #2354D11semidirect
566. C4×D11C4×D4semidirect
599. C2×#117C2×D11semidirect
624. #388C2×D11semidirect
642. #384C2×D11semidirect
654. #380C2×D11semidirect
661. C4×C4⋊C4C2×D11semidirect
662. C4×C4⋊C4C2×D11semidirect
712. C2×D11#520semidirect
777. C4×D4C4×D11semidirect
1042. C11#34202semidirect

Maximal subgroups

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

subgroupindex
C2×#106230782
C2×#106230542
C2×D11×#1172
#130716132
#130716052
#130715972
#130715942
#130715662
#130715482
#130715462
#130715452
#130715382
#130715162
#130715122
#130713022
#130712952
#130712372
#130712052
C4×#669492
#130711282
D11×#3802
#130709702
C11×#23542
#3420211