Finite Group Databasebeta

← #14914084

Subgroups — #14914084

Order 2816.

3246 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623137C211yesmaximal, characteristic
2C2×#10623077C211yesmaximal, characteristic, complemented
3C2×D11×#117C211yesmaximal, characteristic, complemented
4#13071611C212yesmaximal, complemented
5#13071607C212yesmaximal, complemented
6#13071599C212yesmaximal, complemented
7#13071597C212yesmaximal, complemented
8#13071564C212yesmaximal, complemented
9#13071544C212yesmaximal, complemented
10#13071543C212yesmaximal, complemented
11#13071514C212yesmaximal, complemented
12#13071311C211yesmaximal, characteristic, complemented
13#13071298C211yesmaximal, characteristic, complemented
14#13071294C211yesmaximal, characteristic, complemented
15#13071238C211yesmaximal, characteristic, complemented
16#13071206C211yesmaximal, characteristic, complemented
17C4×#66950C211yesmaximal, characteristic, complemented
18#13071146C211yesmaximal, characteristic, complemented
19#13071132C211yesmaximal, characteristic, complemented
20C4×#66991C211yesmaximal, characteristic, complemented
21D11×#380C211yesmaximal, characteristic, complemented
22#13070970C211yesmaximal, characteristic, complemented
23C11×#2324C211yesmaximal, characteristic, complemented
24C22×#4341C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic, complemented
28C2×C11×#117C2211yescharacteristic
29C2×#66991C2211yescharacteristic
30C2×#66990C2212yes—
31C2×D4×Dic11C2212yes—
32C2×D4×Dic11C2211yescharacteristic, complemented
33C2×C4×C22⋊D11C2212yes—
34C2×C4×C22⋊D11C2212yes—
35C2×#66979C2211yescharacteristic
36C2×#66977C2211yescharacteristic
37C22×Dic11⋊C4C2212yescomplemented
38#10623137C4116yescomplemented
39#10623077—28no—
40D11×#117—28no—
41C2×#66950C2211yescharacteristic
42C2×#66945C2211yescharacteristic
43C2×#66945C2211yescharacteristic
44C2×#66945C2211yescharacteristic
45C2×C4⋊C4×D11C2211yescharacteristic
46C2×C4⋊C4×D11C2211yescharacteristic
47C2×C4⋊C4×D11C2211yescharacteristic
48C2×C4⋊C4×D11C2211yescharacteristic
49C2×#66940C2211yescharacteristic, complemented
50C2×#66936C2212yes—
51C2×(C22⋊D11)⋊C4C2212yes—
52C2×(C22⋊D11)⋊C4C2212yes—
53C2×(C22⋊D11)⋊C4C2212yes—
54C2×C22⋊C4×D11C2211yescharacteristic
55C2×C22⋊C4×D11C2211yescharacteristic
56C2×C22⋊C4×D11C2212yes—
57C2×#66930C2211yescharacteristic
58C2×#66930C2211yescharacteristic
59C2×#66930C2212yescomplemented
60C2×#66925C2211yescharacteristic
61C2×#66925C2211yescharacteristic
62C2×C42×D11C2211yescharacteristic
63C2×C42×D11C2211yescharacteristic
64C2×C4×Dic22C2211yescharacteristic, complemented
65C11×#390C2212yes—
66C11×#390C2211yescharacteristic, complemented
67C11×#389C2211yescharacteristic, complemented
68C11×#388C2212yescomplemented
69C11×#386C2212yes—
70C11×#385C2212yescomplemented
71C11×#380C2211yescharacteristic
72C4×C11×C4⋊C4C2211yescharacteristic, complemented
73#10622834C2212yes—
74#10622834C2211yescharacteristic, complemented
75#10622833C2212yes—
76#10622825C2211yescharacteristic
77C4×C22⋊Dic11C2212yescomplemented
78#10622602C2212yes—
79#10622602C2212yes—
80#10622600C2211yescharacteristic
81#10622600C2211yescharacteristic
82#10622598C2211yescharacteristic, complemented
83#10622591C2212yescomplemented
84#10622589C2212yescomplemented
85C4⋊C4×Dic11C2211yescharacteristic, complemented
86C4⋊C4×Dic11C2211yescharacteristic, complemented
87C4⋊C4×Dic11C2212yescomplemented
88#10622587C2211yescharacteristic, complemented
89#10622586C2211yescharacteristic, complemented
90#10622585C2212yescomplemented
91#10622569C2212yes—
92#10622569C2212yes—
93#10622569C2212yes—
94#10622569C2212yes—
95#10622564C2212yescomplemented
96#10622563C2212yescomplemented
97#10622558C2212yes—
98#10622558C2212yes—
99#10622558C2212yescomplemented
100#10622557C2212yes—
101#10622557C2212yes—
102#10622557C2212yescomplemented
103#10622555C2212yes—
104#10622555C2212yescomplemented
105#10622555C2212yescomplemented
106C22⋊C4×Dic11C2212yescomplemented
107C4×(C2×D11)⋊C4C2212yes—
108C4×(C2×D11)⋊C4C2212yes—
109C4×C4⋊Dic11C2211yescharacteristic, complemented
110C4×C4⋊Dic11C2212yescomplemented
111C4×Dic11⋊C4C2212yescomplemented
112#10622542C2211yescharacteristic, complemented
113#10622541C2211yescharacteristic, complemented
114#10622281C2212yes—
115#10622281C2212yes—
116#10622280C2212yes—
117#10622279C2212yes—
118#10622279C2212yes—
119D11×#95C2212yes—
120#10622268C2212yescomplemented
121#10622267C2212yescomplemented
122#10622266C2212yescomplemented
123#10622263C2212yescomplemented
124#10622262C2212yescomplemented
125#10622260C2212yescomplemented
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C22×D4×C11C2312yes—
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C23×Dic11C2311yescharacteristic
134C23×Dic11C2312yes—
135C23×Dic11C2312yes—
136C2×#4341—24no—
137C2×#4341—24no—
138C2×#4341C2×C418yescomplemented
139C22×C4×D11—24no—
140C22×C4×D11—24no—
141C22×C4×D11C2×C418yescomplemented
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2312yes—
150C22×C4×D11C2312yes—
151C22×C4×D11C2311yescharacteristic
152C22×Dic22C2311yescharacteristic
153C11×#121C2×C418yescomplemented
154C4×D4×C11—24no—
155C11×#117—24no—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2312yes—
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2311yescharacteristic
163C2×C11×C22⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C42×C11C2311yescharacteristic
170C2×C42×C11C2312yes—
171C2×C42×C11C2311yescharacteristic
172C2×C22⋊Dic11C2311yescharacteristic
173C2×C22⋊Dic11C2311yescharacteristic
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180#66991C2×C418yescomplemented
181#66990C2×C4116yescomplemented
182D4×Dic11—24no—
183D4×Dic11C2×C4116yescomplemented
184C4×C22⋊D11—28no—
185C4×C22⋊D11—44no—
186C2×(C2×D11)⋊C4C2311yescharacteristic
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2311yescharacteristic
193C2×(C2×D11)⋊C4C2311yescharacteristic
194#66979—24no—
195C2×C4⋊Dic11C2311yescharacteristic
196C2×C4⋊Dic11C2311yescharacteristic
197C2×C4⋊Dic11C2311yescharacteristic
198C2×C4⋊Dic11C2311yescharacteristic
199C2×C4⋊Dic11C2312yes—
200C2×C4⋊Dic11C2312yes—
201C2×C4⋊Dic11C2311yescharacteristic
202#66977C2×C418yescomplemented
203C2×Dic11⋊C4—28no—
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2311yescharacteristic
206C2×Dic11⋊C4C2311yescharacteristic
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2311yescharacteristic
214C2×Dic11⋊C4C2311yescharacteristic
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2312yes—
222C2×C4×Dic11C2312yes—
223C2×C4×Dic11C2312yes—
224C2×C4×Dic11C2312yes—
225C2×C4×Dic11C2312yes—
226C2×C4×Dic11C2311yescharacteristic
227#66950C2×C418yescomplemented
228#66945—24no—
229#66945—24no—
230#66945C2×C418yescomplemented
231C4⋊C4×D11—24no—
232C4⋊C4×D11—24no—
233C4⋊C4×D11—24no—
234C4⋊C4×D11—24no—
235#66940—24no—
236#66936C2×C4116yescomplemented
237(C22⋊D11)⋊C4—28no—
238(C22⋊D11)⋊C4—44no—
239(C22⋊D11)⋊C4C2×C4116yescomplemented
240C22⋊C4×D11—24no—
241C22⋊C4×D11—24no—
242C22⋊C4×D11—44no—
243#66930—24no—
244#66930—24no—
245#66930—28no—
246#66925—24no—
247#66925D418yescomplemented
248C42×D11—24no—
249C42×D11—24no—
250C4×Dic22—24no—
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×C11C2412yes—
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
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C2×D4×C11—42no—
282C2×D4×C11—42no—
283C2×D4×C11C22×C414yes—
284C2×D4×C11C22×C418yes—
285C22×C4×C11—22no—
286C22×C4×C11—22no—
287C22×C4×C11—24no—
288C22×C4×C11—42no—
289C22×C4×C11—42no—
290C22×C4×C11C22×C414yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2412yes—
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2412yes—
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C2×C22⋊D11—24no—
301C2×C22⋊D11—24no—
302C2×C22⋊D11—24no—
303C2×C22⋊D11—24no—
304C2×C22⋊D11C22×C418yes—
305C2×C22⋊D11C22×C418yes—
306C22×Dic11—22no—
307C22×Dic11—24no—
308C22×Dic11—22no—
309C22×Dic11—24no—
310C22×Dic11—24no—
311C22×Dic11—42no—
312C22×Dic11—42no—
313C22×Dic11C22×C418yes—
314C22×Dic11C22×C414yes—
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2412yes—
317C22×Dic11C2412yes—
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2412yes—
321C22×Dic11C2412yes—
322C22×Dic11C2411yescharacteristic
323C22×Dic11C2411yescharacteristic
324C22×Dic11C2411yescharacteristic
325#4341—232no—
326C2×C4×D11—22no—
327C2×C4×D11—22no—
328C2×C4×D11—232no—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
331C2×C4×D11—22no—
332C2×C4×D11—24no—
333C2×C4×D11—22no—
334C2×C4×D11—24no—
335C2×C4×D11—22no—
336C2×C4×D11—22no—
337C2×C4×D11—22no—
338C2×C4×D11—22no—
339C2×C4×D11—22no—
340C2×C4×D11—22no—
341C2×C4×D11—22no—
342C2×C4×D11—22no—
343C2×C4×D11—41no—
344C2×C4×D11—41no—
345C2×C4×D11—41no—
346C2×C4×D11—41no—
347C2×C4×D11—42no—
348C2×C4×D11—42no—
349C2×C4×D11—42no—
350C2×C4×D11—42no—
351C2×C4×D11C22×C414yes—
352C2×C4×D11C22×C414yes—
353C2×C4×D11C22×C414yes—
354C2×C4×D11C22×C414yes—
355C2×C4×D11C2×D414yes—
356C2×C4×D11#4114yes—
357C2×Dic22—22no—
358C2×Dic22—22no—
359C2×Dic22C22×C414yes—
360C11×C4⋊C4—22no—
361C11×C4⋊C4—22no—
362C11×C4⋊C4—22no—
363C11×C4⋊C4—22no—
364C11×C4⋊C4—42no—
365C11×C4⋊C4C22×C414yes—
366C11×C22⋊C4—22no—
367C11×C22⋊C4—22no—
368C11×C22⋊C4—24no—
369C11×C22⋊C4—42no—
370C11×C22⋊C4—42no—
371C11×C22⋊C4—42no—
372C11×C22⋊C4C22×C418yes—
373C42×C11—22no—
374C42×C11—42no—
375C42×C11C2×D414yes—
376C22⋊Dic11—22no—
377C22⋊Dic11—22no—
378C22⋊Dic11—24no—
379C22⋊Dic11—42no—
380C22⋊Dic11—42no—
381C22⋊Dic11—42no—
382C22⋊Dic11C22×C418yes—
383C22⋊Dic11C22×C418yes—
384(C2×D11)⋊C4—22no—
385(C2×D11)⋊C4—22no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4C22×C418yes—
389(C2×D11)⋊C4C22×C418yes—
390(C2×D11)⋊C4C2×D414yes—
391(C2×D11)⋊C4C2×D414yes—
392C4⋊Dic11—22no—
393C4⋊Dic11—22no—
394C4⋊Dic11—22no—
395C4⋊Dic11—22no—
396C4⋊Dic11—42no—
397C4⋊Dic11C22×C418yes—
398C4⋊Dic11C22×C414yes—
399Dic11⋊C4—22no—
400Dic11⋊C4—22no—
401Dic11⋊C4—24no—
402Dic11⋊C4—24no—
403Dic11⋊C4—24no—
404Dic11⋊C4—24no—
405Dic11⋊C4—42no—
406Dic11⋊C4—42no—
407Dic11⋊C4C22×C418yes—
408Dic11⋊C4C2×D414yes—
409Dic11⋊C4C2×D414yes—
410C4×Dic11—22no—
411C4×Dic11—22no—
412C4×Dic11—24no—
413C4×Dic11—24no—
414C4×Dic11—22no—
415C4×Dic11—22no—
416C4×Dic11—22no—
417C4×Dic11—42no—
418C4×Dic11—42no—
419C4×Dic11—42no—
420C4×Dic11C22×C418yes—
421C4×Dic11C2×D414yes—
422C2×#525—111no—
423C2×#520—111no—
424C22×#117—111no—
425#2359—112no—
426#2359—112no—
427#2358—112no—
428#2358—112no—
429#2354—112no—
430#2352—112no—
431#2352—112no—
432D4×C4⋊C4—112no—
433#2324—111no—
434#2324D1111yescharacteristic, complemented
435#2323—111no—
436#2323—111no—
437#2317—111no—
438#2311—111no—
439C4×C22⋊Q8—111no—
440C4×C22⋊Q8—111no—
441C4×#121—111no—
442C4×#121—111no—
443C2×#380—111no—
444#2274—111no—
445C23×C11—21no—
446C23×C11—22no—
447C23×C11—22no—
448C23×C11—21no—
449C23×C11—21no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11—21no—
453C23×C11—22no—
454C23×C11—22no—
455C23×C11—21no—
456C23×C11—21no—
457C23×C11C23×C412yes—
458C23×C11C23×C414yes—
459C23×C11C2511yescharacteristic
460C22×D11—21no—
461C22×D11—21no—
462C22×D11—21no—
463C22×D11—21no—
464C22×D11—21no—
465C22×D11—21no—
466C22×D11—21no—
467C22×D11—21no—
468C22×D11—28no—
469C22×D11—28no—
470C22×D11—44no—
471C22×D11—44no—
472C22×D11—44no—
473C22×D11—44no—
474C22×D11—44no—
475C22×D11C23×C412yes—
476C22×D11C23×C412yes—
477C22×D11C22×D412yes—
478C22×D11C2×#4112yes—
479C22×D11H(5,𝔽2)12yes—
480C22×D112−1+412yes—
481D4×C11—28no—
482D4×C11—48no—
483C2×C4×C11—21no—
484C2×C4×C11—21no—
485C2×C4×C11—21no—
486C2×C4×C11—21no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—28no—
492C2×C4×C11—22no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
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—22no—
504C2×C4×C11—84no—
505C2×C4×C11C23×C414yes—
506C2×C4×C11C23×C412yes—
507C2×C4×C11C23×C412yes—
508C2×C4×C11C22×D412yes—
509C2×C4×C11C22×D412yes—
510C2×C4×C11C22×D412yes—
511C2×C4×C11C2×#4112yes—
512C22⋊D11—216no—
513C22⋊D11—216no—
514C2×Dic11—21no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—21no—
518C2×Dic11—22no—
519C2×Dic11—21no—
520C2×Dic11—21no—
521C2×Dic11—22no—
522C2×Dic11—21no—
523C2×Dic11—21no—
524C2×Dic11—28no—
525C2×Dic11—216no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—21no—
532C2×Dic11—22no—
533C2×Dic11—21no—
534C2×Dic11—22no—
535C2×Dic11—21no—
536C2×Dic11—22no—
537C2×Dic11—21no—
538C2×Dic11—84no—
539C2×Dic11C23×C414yes—
540C2×Dic11C23×C414yes—
541C2×Dic11C23×C412yes—
542C2×Dic11C23×C412yes—
543C2×Dic11C22×D412yes—
544C2×Dic11C22×D412yes—
545C2×Dic11C22×D412yes—
546C2×Dic11C2×#4112yes—
547C4×D11—28no—
548C4×D11—28no—
549C4×D11—28no—
550C4×D11—44no—
551C4×D11—44no—
552C4×D11—44no—
553C4×D11—44no—
554C4×D11—84no—
555C4×D11—84no—
556C4×D11C4×D4116yescomplemented
557Dic22—28no—
558C22×#41—111no—
559C24×C4—111no—
560#525—1116no—
561C2×#123—112no—
562C2×C22⋊Q8—111no—
563C2×C22⋊Q8—111no—
564C2×#121—111no—
565C2×#121C2×D1111yescharacteristic
566C2×#120—112no—
567#520—228no—
568C2×C4×Q8—111no—
569C2×C4×Q8—111no—
570C2×C4×D4—112no—
571C2×C4×D4—111no—
572C2×C4×D4—112no—
573C2×C4×D4—112no—
574C2×C4×D4—112no—
575C2×C4×D4—112no—
576C2×C4×D4—112no—
577C2×C4×D4C2×D1111yescharacteristic, complemented
578C2×#117—111no—
579C2×#117—111no—
580C2×#117—111no—
581C2×#117—111no—
582C2×#117—111no—
583C2×#117—111no—
584C2×#117—112no—
585C2×#117—111no—
586C2×#117—111no—
587C2×#117—228no—
588C2×#117C2×D1111yescharacteristic
589C22×C4⋊C4—112no—
590C22×C4⋊C4—111no—
591C22×C4⋊C4—111no—
592C22×C4⋊C4—111no—
593C22×C4⋊C4—111no—
594C22×C22⋊C4—111no—
595C22×C22⋊C4—111no—
596C22×C22⋊C4—112no—
597C22×C42—111no—
598C22×C42—111no—
599#391—111no—
600#391—111no—
601#390—111no—
602#390—112no—
603#390C2×D1112yes—
604#390C2×D1111yescharacteristic, complemented
605#389—111no—
606#389—111no—
607#389—112no—
608#389—111no—
609#389—112no—
610#389C2×D1111yescharacteristic, complemented
611#388—112no—
612#388—112no—
613#388—112no—
614#388—112no—
615#388—112no—
616#388—112no—
617#388—112no—
618#388C2×D1112yescomplemented
619#387—112no—
620#387—112no—
621#387—112no—
622#387—112no—
623#386—112no—
624#386—112no—
625#386—112no—
626#386—112no—
627#386—112no—
628#386C2×D1112yes—
629#385—112no—
630#385—112no—
631#385—112no—
632#385—112no—
633#385—112no—
634#385C2×D1112yescomplemented
635#384—112no—
636#382—112no—
637#380—111no—
638#380—111no—
639#380—111no—
640#380—112no—
641#380—112no—
642#380—112no—
643#380—112no—
644#380C2×D1111yescharacteristic
645C4×C4⋊C4—111no—
646C4×C4⋊C4—111no—
647C4×C4⋊C4—112no—
648C4×C4⋊C4—111no—
649C4×C4⋊C4—112no—
650C4×C4⋊C4—112no—
651C4×C4⋊C4—112no—
652C4×C4⋊C4C2×D1111yescharacteristic, complemented
653C4×C22⋊C4—112no—
654C4×C22⋊C4—112no—
655C4×C22⋊C4—112no—
656C4×C22⋊C4—112no—
657C4×C22⋊C4—112no—
658C4×C22⋊C4—112no—
659C2×#95—112no—
660C22×C11—22no—
661C22×C11—24no—
662C22×C11—22no—
663C22×C11—24no—
664C22×C11—22no—
665C22×C11—24no—
666C22×C11—42no—
667C22×C11—41no—
668C22×C11—41no—
669C22×C11—42no—
670C22×C11—41no—
671C22×C11—42no—
672C22×C11—41no—
673C22×C11—42no—
674C22×C11C24×C411yescharacteristic
675C22×C11C23×D411yescharacteristic
676C22×C11C22×#4111yescharacteristic
677C22×C11C2×H(5,𝔽2)11yescharacteristic
678C22×C11C2×2−1+411yescharacteristic
679C22×C11#58511yescharacteristic
680C22×C11#58511yescharacteristic
681C2×D11—22no—
682C2×D11—22no—
683C2×D11—22no—
684C2×D11—22no—
685C2×D11—22no—
686C2×D11—22no—
687C2×D11—22no—
688C2×D11—22no—
689C2×D11—22no—
690C2×D11—22no—
691C2×D11—22no—
692C2×D11—22no—
693C2×D11—416no—
694C2×D11C2×C4×D414yes—
695C2×D11#52014yescomplemented
696C4×C11—22no—
697C4×C11—24no—
698C4×C11—22no—
699C4×C11—22no—
700C4×C11—42no—
701C4×C11—41no—
702C4×C11—41no—
703C4×C11—42no—
704C4×C11C2×C4×D414yes—
705Dic11—24no—
706Dic11—22no—
707Dic11—24no—
708Dic11—22no—
709Dic11—22no—
710Dic11—41no—
711Dic11—42no—
712Dic11—41no—
713Dic11—42no—
714Dic11C2×C4×D414yes—
715C25—111no—
716C2×#41—118no—
717C2×#41—224no—
718C2×#41—224no—
719C22×Q8—111no—
720C22×D4—112no—
721C22×D4—112no—
722C22×D4C22×D1111yescharacteristic
723C22×D4C22×D1112yes—
724C23×C4—111no—
725C23×C4—112no—
726C23×C4—111no—
727C23×C4—118no—
728C23×C4—111no—
729C23×C4—111no—
730C23×C4—111no—
731C23×C4—112no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—111no—
735C23×C4—111no—
736C23×C4—112no—
737C23×C4—112no—
738C23×C4—224no—
739C23×C4—224no—
740C23×C4C22×D1111yescharacteristic
741C23×C4C22×D1112yes—
742#123—1116no—
743C22⋊Q8—118no—
744C22⋊Q8—118no—
745#121—118no—
746#121C4×D1118yescomplemented
747#120—1116no—
748C4×Q8—224no—
749C4×Q8—224no—
750C4×D4—24no—
751C4×D4—1116no—
752C4×D4—1116no—
753C4×D4—224no—
754C4×D4—228no—
755C4×D4—228no—
756C4×D4—444no—
757C4×D4—444no—
758#117—24no—
759#117—118no—
760#117—118no—
761#117—224no—
762#117—224no—
763#117—224no—
764#117—224no—
765#117—228no—
766#117—224no—
767#117—224no—
768C2×C4⋊C4—111no—
769C2×C4⋊C4—111no—
770C2×C4⋊C4—111no—
771C2×C4⋊C4—112no—
772C2×C4⋊C4—112no—
773C2×C4⋊C4—112no—
774C2×C4⋊C4—111no—
775C2×C4⋊C4—111no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—112no—
780C2×C4⋊C4—112no—
781C2×C4⋊C4—112no—
782C2×C4⋊C4—111no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—112no—
786C2×C4⋊C4—224no—
787C2×C4⋊C4—224no—
788C2×C4⋊C4—224no—
789C2×C4⋊C4—224no—
790C2×C4⋊C4—228no—
791C2×C4⋊C4C22×D1111yescharacteristic
792C2×C4⋊C4C22×D1111yescharacteristic
793C2×C4⋊C4C22×D1111yescharacteristic
794C2×C4⋊C4C22×D1111yescharacteristic
795C2×C4⋊C4C22×D1112yes—
796C2×C4⋊C4C22×D1111yescharacteristic
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—111no—
800C2×C22⋊C4—111no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—111no—
804C2×C22⋊C4—111no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—111no—
807C2×C22⋊C4—111no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—224no—
814C2×C22⋊C4—224no—
815C2×C22⋊C4—444no—
816C2×C22⋊C4C22×D1111yescharacteristic
817C2×C22⋊C4C22×D1111yescharacteristic
818C2×C22⋊C4C22×D1112yes—
819C2×C22⋊C4C22×D1112yes—
820C2×C22⋊C4C22×D1112yes—
821C2×C22⋊C4C22×D1112yes—
822C2×C22⋊C4C22×D1112yes—
823C2×C42—111no—
824C2×C42—112no—
825C2×C42—111no—
826C2×C42—111no—
827C2×C42—111no—
828C2×C42—111no—
829C2×C42—111no—
830C2×C42—112no—
831C2×C42—112no—
832C2×C42—112no—
833C2×C42—112no—
834C2×C42—112no—
835C2×C42—224no—
836C2×C42—224no—
837C2×C42C22×D1111yescharacteristic
838C2×C42C22×D1112yes—
839C2×C42C22×D1111yescharacteristic
840#95—112no—
841#95—112no—
842#95—112no—
843#95—112no—
844#95—112no—
845#95—112no—
846#95—112no—
847#95—112no—
848#95—112no—
849#95—112no—
850#95—112no—
851#95—112no—
852#95—112no—
853#95C22×D1112yes—
854#95C22×D1112yes—
855#95C22×D1112yes—
856C2×C11—42no—
857C2×C11—44no—
858C2×C11C22×C4×D411yescharacteristic
859C2×C11C2×#52011yescharacteristic
860C2×C11#342811yescharacteristic
861C2×C11#348811yescharacteristic
862C2×C11#348911yescharacteristic
863C2×C11#349411yescharacteristic
864C2×C11#349511yescharacteristic
865D11—24no—
866D11—24no—
867C24—111no—
868C24—111no—
869C24—114no—
870C24—222no—
871C24—222no—
872C24—222no—
873C24—222no—
874C24—441no—
875C24—441no—
876C24C23×D1111yescharacteristic
877C24C23×D1112yes—
878#41—2232no—
879C2×Q8—114no—
880C2×Q8—222no—
881C2×Q8—222no—
882C2×D4—22no—
883C2×D4—22no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—118no—
887C2×D4—118no—
888C2×D4—224no—
889C2×D4—224no—
890C2×D4—224no—
891C2×D4—224no—
892C2×D4C2×C4×D1114yes—
893C2×D4C2×C4×D1118yes—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—24no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—111no—
900C22×C4—114no—
901C22×C4—114no—
902C22×C4—114no—
903C22×C4—114no—
904C22×C4—118no—
905C22×C4—111no—
906C22×C4—112no—
907C22×C4—112no—
908C22×C4—111no—
909C22×C4—111no—
910C22×C4—114no—
911C22×C4—114no—
912C22×C4—114no—
913C22×C4—111no—
914C22×C4—112no—
915C22×C4—112no—
916C22×C4—111no—
917C22×C4—222no—
918C22×C4—222no—
919C22×C4—2232no—
920C22×C4—222no—
921C22×C4—222no—
922C22×C4—222no—
923C22×C4—222no—
924C22×C4—222no—
925C22×C4—222no—
926C22×C4—222no—
927C22×C4—222no—
928C22×C4—224no—
929C22×C4—224no—
930C22×C4—224no—
931C22×C4—222no—
932C22×C4—222no—
933C22×C4—224no—
934C22×C4—224no—
935C22×C4—222no—
936C22×C4—222no—
937C22×C4—222no—
938C22×C4—222no—
939C22×C4—441no—
940C22×C4—441no—
941C22×C4—441no—
942C22×C4—441no—
943C22×C4—442no—
944C22×C4—442no—
945C22×C4—442no—
946C22×C4—442no—
947C22×C4—442no—
948C22×C4—442no—
949C22×C4C2×C4×D1114yes—
950C22×C4C23×D1111yescharacteristic
951C22×C4C23×D1112yes—
952C22×C4C23×D1112yes—
953C22×C4C23×D1111yescharacteristic
954C22×C4C23×D1112yes—
955C22×C4C23×D1111yescharacteristic
956C22×C4C23×D1111yescharacteristic
957C22×C4C23×D1111yescharacteristic
958C22×C4C23×D1111yescharacteristic
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—42no—
964C4⋊C4—114no—
965C4⋊C4—118no—
966C4⋊C4—118no—
967C4⋊C4—114no—
968C4⋊C4—114no—
969C4⋊C4—224no—
970C4⋊C4—222no—
971C4⋊C4—222no—
972C4⋊C4—222no—
973C4⋊C4—222no—
974C4⋊C4—224no—
975C4⋊C4—224no—
976C4⋊C4—224no—
977C4⋊C4—222no—
978C4⋊C4—222no—
979C4⋊C4—442no—
980C4⋊C4—442no—
981C4⋊C4—442no—
982C4⋊C4C2×C4×D1114yes—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—24no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—118no—
990C22⋊C4—118no—
991C22⋊C4—118no—
992C22⋊C4—118no—
993C22⋊C4—114no—
994C22⋊C4—114no—
995C22⋊C4—222no—
996C22⋊C4—222no—
997C22⋊C4—224no—
998C22⋊C4—224no—
999C22⋊C4—222no—
1000C22⋊C4—222no—
1001C22⋊C4—224no—
1002C22⋊C4—442no—
1003C22⋊C4—442no—
1004C22⋊C4—442no—
1005C22⋊C4C2×C4×D1118yes—
1006C42—22no—
1007C42—42no—
1008C42—118no—
1009C42—114no—
1010C42—222no—
1011C42—222no—
1012C42—224no—
1013C42—222no—
1014C42—222no—
1015C42—222no—
1016C42—224no—
1017C42—442no—
1018C42—442no—
1019C42—442no—
1020C42D4×D1114yes—
1021C11#3420211yescharacteristic, complemented, Sylow
1022C23—21no—
1023C23—22no—
1024C23—21no—
1025C23—22no—
1026C23—21no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—21no—
1031C23—21no—
1032C23—22no—
1033C23—21no—
1034C23—112no—
1035C23—112no—
1036C23—112no—
1037C23—112no—
1038C23—112no—
1039C23—112no—
1040C23—228no—
1041C23—228no—
1042C23—221no—
1043C23—221no—
1044C23—221no—
1045C23—221no—
1046C23—221no—
1047C23—221no—
1048C23—221no—
1049C23—221no—
1050C23—444no—
1051C23—444no—
1052C23—444no—
1053C23—444no—
1054C23—444no—
1055C23C22×C4×D1112yes—
1056C23C22×C4×D1114yes—
1057C23C24×D1111yescharacteristic
1058Q8—228no—
1059D4—28no—
1060D4—48no—
1061D4—2216no—
1062D4—2216no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—28no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—21no—
1084C2×C4—84no—
1085C2×C4—112no—
1086C2×C4—112no—
1087C2×C4—112no—
1088C2×C4—1116no—
1089C2×C4—114no—
1090C2×C4—112no—
1091C2×C4—114no—
1092C2×C4—112no—
1093C2×C4—112no—
1094C2×C4—228no—
1095C2×C4—228no—
1096C2×C4—228no—
1097C2×C4—2216no—
1098C2×C4—221no—
1099C2×C4—222no—
1100C2×C4—221no—
1101C2×C4—222no—
1102C2×C4—222no—
1103C2×C4—221no—
1104C2×C4—221no—
1105C2×C4—221no—
1106C2×C4—221no—
1107C2×C4—222no—
1108C2×C4—228no—
1109C2×C4—221no—
1110C2×C4—221no—
1111C2×C4—222no—
1112C2×C4—222no—
1113C2×C4—222no—
1114C2×C4—222no—
1115C2×C4—221no—
1116C2×C4—222no—
1117C2×C4—221no—
1118C2×C4—221no—
1119C2×C4—222no—
1120C2×C4—221no—
1121C2×C4—444no—
1122C2×C4—444no—
1123C2×C4—444no—
1124C2×C4—444no—
1125C2×C4—884no—
1126C2×C4—884no—
1127C2×C4—884no—
1128C2×C4C22×C4×D1114yes—
1129C2×C4C22×C4×D1112yes—
1130C2×C4C22×C4×D1112yes—
1131C2×C4C2×D4×D1112yes—
1132C2×C4C2×D4×D1112yes—
1133C2×C4C2×D4×D1112yes—
1134C2×C4#41×D1112yes—
1135C22—22no—
1136C22—24no—
1137C22—24no—
1138C22—22no—
1139C22—22no—
1140C22—24no—
1141C22—42no—
1142C22—41no—
1143C22—41no—
1144C22—42no—
1145C22—41no—
1146C22—42no—
1147C22—41no—
1148C22—42no—
1149C22—114no—
1150C22—114no—
1151C22—222no—
1152C22—222no—
1153C22—222no—
1154C22—222no—
1155C22—222no—
1156C22—222no—
1157C22—222no—
1158C22—222no—
1159C22—222no—
1160C22—222no—
1161C22—222no—
1162C22—222no—
1163C22—4416no—
1164C22C23×C4×D1111yescharacteristic
1165C22C22×D4×D1111yescharacteristic
1166C22C2×#41×D1111yescharacteristic
1167C22D11×H(5,𝔽2)11yescharacteristic
1168C22#1062345511yescharacteristic
1169C22#1062345511yescharacteristic
1170C22D11×2−1+411yescharacteristic
1171C4—22no—
1172C4—22no—
1173C4—22no—
1174C4—24no—
1175C4—42no—
1176C4—41no—
1177C4—41no—
1178C4—42no—
1179C4—114no—
1180C4—222no—
1181C4—222no—
1182C4—222no—
1183C4—224no—
1184C4—224no—
1185C4—441no—
1186C4—442no—
1187C4—441no—
1188C4—442no—
1189C4C4×D4×D1114yes—
1190C2—42no—
1191C2—44no—
1192C2—224no—
1193C2—224no—
1194C2C2×C4×D4×D1111yescharacteristic
1195C2D11×#52011yescharacteristic
1196C2#1308181411yescharacteristic
1197C2#1308228311yescharacteristic
1198C2#1308229111yescharacteristic
1199C2#1308234311yescharacteristic
1200C2#1308236611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2324C2
socle, cosocleC23×C11C25
prime radicalC2×#10623137C2
hypercenter#2324D11
hypocenterC11#34202
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. C2×#10623077C2semidirect
3. C2×D11×#117C2semidirect
4. #13071611C2semidirect
5. #13071607C2semidirect
6. #13071599C2semidirect
7. #13071597C2semidirect
8. #13071564C2semidirect
9. #13071544C2semidirect
10. #13071543C2semidirect
11. #13071514C2semidirect
12. #13071311C2semidirect
13. #13071298C2semidirect
14. #13071294C2semidirect
15. #13071238C2semidirect
16. #13071206C2semidirect
17. C4×#66950C2semidirect
18. #13071146C2semidirect
19. #13071132C2semidirect
20. C4×#66991C2semidirect
21. D11×#380C2semidirect
22. #13070970C2semidirect
23. C11×#2324C2semidirect
27. C2×C4×D4×C11C22semidirect
32. C2×D4×Dic11C22semidirect
37. C22×Dic11⋊C4C22semidirect
38. #10623137C4semidirect
49. C2×#66940C22semidirect
59. C2×#66930C22semidirect
64. C2×C4×Dic22C22semidirect
66. C11×#390C22semidirect
67. C11×#389C22semidirect
68. C11×#388C22semidirect
70. C11×#385C22semidirect
72. C4×C11×C4⋊C4C22semidirect
74. #10622834C22semidirect
77. C4×C22⋊Dic11C22semidirect
82. #10622598C22semidirect
83. #10622591C22semidirect
84. #10622589C22semidirect
85. C4⋊C4×Dic11C22semidirect
86. C4⋊C4×Dic11C22semidirect
87. C4⋊C4×Dic11C22semidirect
88. #10622587C22semidirect
89. #10622586C22semidirect
90. #10622585C22semidirect
95. #10622564C22semidirect
96. #10622563C22semidirect
99. #10622558C22semidirect
102. #10622557C22semidirect
104. #10622555C22semidirect
105. #10622555C22semidirect
106. C22⋊C4×Dic11C22semidirect
109. C4×C4⋊Dic11C22semidirect
110. C4×C4⋊Dic11C22semidirect
111. C4×Dic11⋊C4C22semidirect
112. #10622542C22semidirect
113. #10622541C22semidirect
120. #10622268C22semidirect
121. #10622267C22semidirect
122. #10622266C22semidirect
123. #10622263C22semidirect
124. #10622262C22semidirect
125. #10622260C22semidirect
138. C2×#4341C2×C4semidirect
141. C22×C4×D11C2×C4semidirect
153. C11×#121C2×C4semidirect
180. #66991C2×C4semidirect
181. #66990C2×C4semidirect
183. D4×Dic11C2×C4semidirect
202. #66977C2×C4semidirect
227. #66950C2×C4semidirect
230. #66945C2×C4semidirect
236. #66936C2×C4semidirect
239. (C22⋊D11)⋊C4C2×C4semidirect
247. #66925D4semidirect
434. #2324D11semidirect
556. C4×D11C4×D4semidirect
577. C2×C4×D4C2×D11semidirect
604. #390C2×D11semidirect
610. #389C2×D11semidirect
618. #388C2×D11semidirect
634. #385C2×D11semidirect
652. C4×C4⋊C4C2×D11semidirect
695. C2×D11#520semidirect
746. #121C4×D11semidirect
1021. C11#34202semidirect

Maximal subgroups

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

subgroupindex
C2×#106231372
C2×#106230772
C2×D11×#1172
#130716112
#130716072
#130715992
#130715972
#130715642
#130715442
#130715432
#130715142
#130713112
#130712982
#130712942
#130712382
#130712062
C4×#669502
#130711462
#130711322
C4×#669912
D11×#3802
#130709702
C11×#23242
#3420211