Finite Group Databasebeta

← #14914074

Subgroups — #14914074

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×#10623158C211yesmaximal, characteristic
2C2×#10623105C211yesmaximal, characteristic, complemented
3C22×#66925C211yesmaximal, characteristic, complemented
4#13071613C212yesmaximal, complemented
5#13071601C212yesmaximal, complemented
6#13071598C212yesmaximal, complemented
7#13071592C212yesmaximal, complemented
8#13071561C212yesmaximal, complemented
9#13071540C212yesmaximal, complemented
10#13071539C212yesmaximal, complemented
11#13071514C212yesmaximal, complemented
12#13071310C211yesmaximal, characteristic, complemented
13#13071307C211yesmaximal, characteristic, complemented
14#13071301C211yesmaximal, characteristic, complemented
15#13071292C211yesmaximal, characteristic, complemented
16#13071238C211yesmaximal, characteristic, complemented
17#13071207C211yesmaximal, characteristic, complemented
18C22⋊Q8×Dic11C211yesmaximal, characteristic, complemented
19C4×#66983C211yesmaximal, characteristic, complemented
20#13071122C211yesmaximal, characteristic, complemented
21D11×#380C211yesmaximal, characteristic, complemented
22#13070970C211yesmaximal, characteristic, complemented
23C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
24C22×#4343C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic, complemented
28C22×C42×C11C2211yescharacteristic
29C2×#66999C2211yescharacteristic
30C2×Q8×Dic11C2211yescharacteristic, complemented
31C2×#66983C2211yescharacteristic
32C2×C4×C22⋊D11C2212yes—
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38#10623158C4116yescomplemented
39#10623105—28no—
40C2×#66948C2211yescharacteristic
41C2×#66947C2212yes—
42C2×#66946C2212yes—
43C2×#66946C2212yes—
44C2×#66946C2211yescharacteristic, complemented
45C2×#66945C2211yescharacteristic
46C2×C4⋊C4×D11C2211yescharacteristic
47C2×C4⋊C4×D11C2211yescharacteristic
48C2×C4⋊C4×D11C2212yescomplemented
49C2×#66935C2212yes—
50C2×(C22⋊D11)⋊C4C2212yes—
51C2×(C22⋊D11)⋊C4C2212yes—
52C2×C22⋊C4×D11C2212yes—
53C2×C4×D44C2212yes—
54C2×C4×D44C2211yescharacteristic, complemented
55C2×#66925—28no—
56C2×#66925C2211yescharacteristic
57C2×#66925C2211yescharacteristic
58C2×#66925C2211yescharacteristic
59C2×#66925C2211yescharacteristic
60C2×#66925C2211yescharacteristic
61C2×#66925C2211yescharacteristic
62C2×#66925C2211yescharacteristic
63C2×#66925C2211yescharacteristic
64C2×#66925C2212yescomplemented
65C11×#391C2211yescharacteristic, complemented
66C11×#389C2211yescharacteristic, complemented
67C11×#387C2212yescomplemented
68C11×#385C2212yes—
69C11×#380C2211yescharacteristic
70C4×C11×C4⋊C4C2211yescharacteristic, complemented
71C4×C11×C4⋊C4C2212yescomplemented
72C4×C11×C22⋊C4C2212yes—
73#10622843C2211yescharacteristic, complemented
74#10622826C2212yes—
75#10622825C2211yescharacteristic
76#10622603C2212yes—
77#10622602C2212yes—
78#10622602C2212yescomplemented
79#10622601C2212yes—
80#10622601C2211yescharacteristic, complemented
81#10622600C2211yescharacteristic
82#10622600C2211yescharacteristic
83#10622598C2211yescharacteristic, complemented
84#10622594C2212yescomplemented
85#10622589C2212yescomplemented
86C4⋊C4×Dic11C2211yescharacteristic, complemented
87C4⋊C4×Dic11C2211yescharacteristic, complemented
88C4⋊C4×Dic11C2212yescomplemented
89#10622586C2211yescharacteristic, complemented
90#10622585C2212yescomplemented
91#10622571C2212yes—
92#10622563C2212yes—
93#10622555C2212yes—
94C22⋊C4×Dic11C2212yes—
95#10622553C2212yes—
96#10622553C2212yescomplemented
97#10622553C2212yescomplemented
98#10622552C2212yes—
99#10622552C2211yescharacteristic, complemented
100C4×(C2×D11)⋊C4C2212yes—
101C4×(C2×D11)⋊C4C2212yescomplemented
102C4×C4⋊Dic11C2211yescharacteristic, complemented
103#10622546C2212yescomplemented
104C4×Dic11⋊C4C2212yescomplemented
105#10622541C2211yescharacteristic, complemented
106#10622283C2212yes—
107#10622282C2212yes—
108#10622282C2212yescomplemented
109#10622282C2212yescomplemented
110#10622281C2212yes—
111#10622281C2212yescomplemented
112#10622280C2212yes—
113#10622280C2212yescomplemented
114#10622280C2212yescomplemented
115#10622279C2212yes—
116#10622279C2212yescomplemented
117#10622278C2212yes—
118#10622278C2212yes—
119#10622278C2212yes—
120#10622278C2212yes—
121D11×#95C2212yes—
122#10622265C2212yescomplemented
123#10622263C2212yescomplemented
124#10622262C2212yescomplemented
125#10622260C2212yescomplemented
126C24×D11C2311yescharacteristic
127C22×Q8×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C22×C22⋊D11C2312yes—
132C23×Dic11C2311yescharacteristic
133C23×Dic11C2311yescharacteristic
134C23×Dic11C2311yescharacteristic
135C2×#4343—24no—
136C2×#4343—24no—
137C2×#4343C2×C418yescomplemented
138C22×D44C2312yes—
139C22×D44C2311yescharacteristic
140C22×D44C2312yes—
141C22×C4×D11—24no—
142C22×C4×D11—24no—
143C22×C4×D11C2×C418yescomplemented
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2312yes—
148C22×C4×D11C2312yes—
149C22×C4×D11C2312yes—
150C22×C4×D11C2312yes—
151C22×C4×D11C2312yes—
152C22×C4×D11C2311yescharacteristic
153C11×C22⋊Q8C2×C418yescomplemented
154C4×Q8×C11—24no—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C42×C11—24no—
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2312yes—
168C2×C42×C11C2312yes—
169C2×C42×C11C2311yescharacteristic
170C2×C22⋊Dic11C2312yes—
171#66999C2×C418yescomplemented
172Q8×Dic11—24no—
173#66983C2×C418yescomplemented
174C4×C22⋊D11—44no—
175C2×(C2×D11)⋊C4—24no—
176C2×(C2×D11)⋊C4—24no—
177C2×(C2×D11)⋊C4C2311yescharacteristic
178C2×(C2×D11)⋊C4C2311yescharacteristic
179C2×(C2×D11)⋊C4C2311yescharacteristic
180C2×(C2×D11)⋊C4C2311yescharacteristic
181C2×(C2×D11)⋊C4C2311yescharacteristic
182C2×(C2×D11)⋊C4C2311yescharacteristic
183C2×(C2×D11)⋊C4C2312yes—
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)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×C4⋊Dic11C2312yes—
198C2×C4⋊Dic11C2311yescharacteristic
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2312yes—
201C2×C4⋊Dic11C2311yescharacteristic
202C2×Dic11⋊C4—24no—
203C2×Dic11⋊C4—24no—
204C2×Dic11⋊C4C2311yescharacteristic
205C2×Dic11⋊C4C2311yescharacteristic
206C2×Dic11⋊C4C2311yescharacteristic
207C2×Dic11⋊C4C2311yescharacteristic
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2311yescharacteristic
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2311yescharacteristic
216C2×Dic11⋊C4C2311yescharacteristic
217C2×C4×Dic11—24no—
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#66948C2×C418yescomplemented
228#66947C2×C4116yescomplemented
229#66946—28no—
230#66946—24no—
231#66946C2×C4116yescomplemented
232#66945C2×C418yescomplemented
233C4⋊C4×D11—24no—
234C4⋊C4×D11—24no—
235C4⋊C4×D11—28no—
236#66935C2×C4116yescomplemented
237(C22⋊D11)⋊C4—44no—
238(C22⋊D11)⋊C4C2×C4116yescomplemented
239C22⋊C4×D11—44no—
240C4×D44—24no—
241C4×D44—28no—
242#66925—24no—
243#66925—24no—
244#66925—24no—
245#66925—24no—
246#66925—24no—
247#66925—24no—
248#66925—28no—
249#66925—24no—
250#66925D418yescomplemented
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
269C23×D11—22no—
270C23×D11—22no—
271C23×D11—22no—
272C23×D11—22no—
273C23×D11—41no—
274C23×D11—41no—
275C23×D11C22×C414yes—
276C23×D11C2411yescharacteristic
277C23×D11C2412yes—
278C23×D11C2411yescharacteristic
279C2×Q8×C11—22no—
280C2×Q8×C11—22no—
281C2×Q8×C11C22×C414yes—
282C22×C4×C11—22no—
283C22×C4×C11—22no—
284C22×C4×C11—22no—
285C22×C4×C11—22no—
286C22×C4×C11—22no—
287C22×C4×C11—22no—
288C22×C4×C11—41no—
289C22×C4×C11—41no—
290C22×C4×C11C22×C414yes—
291C22×C4×C11C2412yes—
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2412yes—
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2412yes—
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2412yes—
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C22×C4×C11C2411yescharacteristic
301C2×C22⋊D11—24no—
302C2×C22⋊D11—24no—
303C2×C22⋊D11C22×C418yes—
304C22×Dic11—22no—
305C22×Dic11—22no—
306C22×Dic11—22no—
307C22×Dic11—22no—
308C22×Dic11—22no—
309C22×Dic11—22no—
310C22×Dic11—41no—
311C22×Dic11—41no—
312C22×Dic11C22×C414yes—
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2412yes—
315C22×Dic11C2412yes—
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2412yes—
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2411yescharacteristic
321C22×Dic11C2411yescharacteristic
322#4343—232no—
323C2×D44—24no—
324C2×D44—24no—
325C2×D44—22no—
326C2×D44—22no—
327C2×D44—42no—
328C2×D44—42no—
329C2×D44C22×C418yes—
330C2×D44C22×C414yes—
331C2×D44C22×C418yes—
332C2×C4×D11—22no—
333C2×C4×D11—24no—
334C2×C4×D11—22no—
335C2×C4×D11—24no—
336C2×C4×D11—232no—
337C2×C4×D11—24no—
338C2×C4×D11—22no—
339C2×C4×D11—24no—
340C2×C4×D11—22no—
341C2×C4×D11—24no—
342C2×C4×D11—22no—
343C2×C4×D11—24no—
344C2×C4×D11—22no—
345C2×C4×D11—42no—
346C2×C4×D11—42no—
347C2×C4×D11—42no—
348C2×C4×D11—42no—
349C2×C4×D11—42no—
350C2×C4×D11—42no—
351C2×C4×D11—42no—
352C2×C4×D11—42no—
353C2×C4×D11C22×C418yes—
354C2×C4×D11C22×C414yes—
355C2×C4×D11C22×C414yes—
356C2×C4×D11C22×C414yes—
357C2×C4×D11C22×C414yes—
358C2×C4×D11C2×D414yes—
359C2×C4×D11#4114yes—
360C11×C4⋊C4—24no—
361C11×C4⋊C4—22no—
362C11×C4⋊C4—22no—
363C11×C4⋊C4—42no—
364C11×C4⋊C4C22×C414yes—
365C11×C4⋊C4C22×C418yes—
366C11×C22⋊C4—24no—
367C11×C22⋊C4C22×C418yes—
368C42×C11—22no—
369C42×C11—22no—
370C42×C11—22no—
371C42×C11—24no—
372C42×C11—42no—
373C42×C11C2×D414yes—
374C22⋊Dic11—24no—
375(C2×D11)⋊C4—22no—
376(C2×D11)⋊C4—22no—
377(C2×D11)⋊C4—24no—
378(C2×D11)⋊C4—22no—
379(C2×D11)⋊C4—22no—
380(C2×D11)⋊C4—22no—
381(C2×D11)⋊C4—22no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—42no—
384(C2×D11)⋊C4—42no—
385(C2×D11)⋊C4—42no—
386(C2×D11)⋊C4—42no—
387(C2×D11)⋊C4—42no—
388(C2×D11)⋊C4—42no—
389(C2×D11)⋊C4C22×C418yes—
390(C2×D11)⋊C4C22×C418yes—
391(C2×D11)⋊C4C22×C418yes—
392(C2×D11)⋊C4C22×C418yes—
393(C2×D11)⋊C4C2×D414yes—
394(C2×D11)⋊C4C2×D414yes—
395C4⋊Dic11—24no—
396C4⋊Dic11—22no—
397C4⋊Dic11—22no—
398C4⋊Dic11—42no—
399C4⋊Dic11C22×C414yes—
400Dic11⋊C4—22no—
401Dic11⋊C4—22no—
402Dic11⋊C4—22no—
403Dic11⋊C4—22no—
404Dic11⋊C4—24no—
405Dic11⋊C4—24no—
406Dic11⋊C4—22no—
407Dic11⋊C4—22no—
408Dic11⋊C4—42no—
409Dic11⋊C4—42no—
410Dic11⋊C4C22×C418yes—
411Dic11⋊C4C2×D414yes—
412Dic11⋊C4C2×D414yes—
413C4×Dic11—22no—
414C4×Dic11—22no—
415C4×Dic11—24no—
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#2324—111no—
435#2323—111no—
436#2323—111no—
437#2317—111no—
438#2311—111no—
439C4×C22⋊Q8—111no—
440C4×C22⋊Q8D1111yescharacteristic, complemented
441C4×#121—111no—
442C4×#121—111no—
443C2×#380—111no—
444#2274—111no—
445C23×C11—21no—
446C23×C11—21no—
447C23×C11—21no—
448C23×C11—21no—
449C23×C11C23×C412yes—
450C23×C11H(5,𝔽2)12yes—
451C23×C112−1+412yes—
452C23×C11C2511yescharacteristic
453C22×D11—21no—
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—28no—
458C22×D11—21no—
459C22×D11—22no—
460C22×D11—21no—
461C22×D11—22no—
462C22×D11—21no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—21no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—21no—
469C22×D11—21no—
470C22×D11—28no—
471C22×D11—44no—
472C22×D11—44no—
473C22×D11—44no—
474C22×D11—44no—
475C22×D11—44no—
476C22×D11C23×C412yes—
477C22×D11C23×C414yes—
478C22×D11C23×C412yes—
479C22×D11C22×D412yes—
480C22×D11C2×#4112yes—
481Q8×C11—28no—
482C2×C4×C11—21no—
483C2×C4×C11—22no—
484C2×C4×C11—21no—
485C2×C4×C11—22no—
486C2×C4×C11—21no—
487C2×C4×C11—21no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—28no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—21no—
499C2×C4×C11—22no—
500C2×C4×C11—21no—
501C2×C4×C11—21no—
502C2×C4×C11—22no—
503C2×C4×C11—21no—
504C2×C4×C11—22no—
505C2×C4×C11—44no—
506C2×C4×C11—44no—
507C2×C4×C11C23×C414yes—
508C2×C4×C11C23×C414yes—
509C2×C4×C11C23×C412yes—
510C2×C4×C11C23×C412yes—
511C2×C4×C11C22×D412yes—
512C2×C4×C11C22×D412yes—
513C2×C4×C11C22×D412yes—
514C2×C4×C11C2×#4112yes—
515C22⋊D11—216no—
516C2×Dic11—21no—
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—21no—
526C2×Dic11—21no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—21no—
531C2×Dic11—22no—
532C2×Dic11—21no—
533C2×Dic11—22no—
534C2×Dic11—21no—
535C2×Dic11—22no—
536C2×Dic11—21no—
537C2×Dic11—44no—
538C2×Dic11—44no—
539C2×Dic11C23×C414yes—
540C2×Dic11C23×C412yes—
541C2×Dic11C23×C412yes—
542C2×Dic11C22×D412yes—
543C2×Dic11C22×D412yes—
544C2×Dic11C22×D412yes—
545C2×Dic11C2×#4112yes—
546D44—216no—
547D44—28no—
548D44—48no—
549C4×D11—28no—
550C4×D11—28no—
551C4×D11—28no—
552C4×D11—216no—
553C4×D11—84no—
554C4×D11—84no—
555C4×D11—84no—
556C4×D11—84no—
557C4×D11C4×D4116yescomplemented
558C22×#41—111no—
559C24×C4—111no—
560#525—1116no—
561C2×#123—112no—
562C2×C22⋊Q8—111no—
563C2×C22⋊Q8C2×D1111yescharacteristic
564C2×#121—111no—
565C2×#121—111no—
566C2×#120—112no—
567#520—228no—
568C2×C4×Q8—111no—
569C2×C4×Q8C2×D1111yescharacteristic, complemented
570C2×C4×D4—112no—
571C2×C4×D4—112no—
572C2×C4×D4—111no—
573C2×C4×D4—112no—
574C2×C4×D4—112no—
575C2×C4×D4—112no—
576C2×C4×D4—111no—
577C2×C4×D4—112no—
578C2×#117—111no—
579C2×#117—111no—
580C2×#117—111no—
581C2×#117—111no—
582C2×#117—111no—
583C2×#117—111no—
584C2×#117—111no—
585C2×#117—111no—
586C2×#117—111no—
587C2×#117—112no—
588C2×#117—228no—
589C22×C4⋊C4—111no—
590C22×C4⋊C4—111no—
591C22×C4⋊C4—111no—
592C22×C4⋊C4—111no—
593C22×C4⋊C4—112no—
594C22×C22⋊C4—111no—
595C22×C22⋊C4—111no—
596C22×C22⋊C4—112no—
597C22×C42—111no—
598C22×C42C2×D1111yescharacteristic
599#391—111no—
600#391C2×D1111yescharacteristic, complemented
601#390—111no—
602#390—112no—
603#390—111no—
604#390—112no—
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#388—112no—
619#387—112no—
620#387—112no—
621#387—112no—
622#387C2×D1112yescomplemented
623#386—112no—
624#386—112no—
625#386—112no—
626#386—112no—
627#386—112no—
628#386—112no—
629#385—112no—
630#385—112no—
631#385—112no—
632#385—112no—
633#385—112no—
634#385C2×D1112yes—
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⋊C4C2×D1111yescharacteristic, complemented
652C4×C4⋊C4C2×D1112yescomplemented
653C4×C22⋊C4—112no—
654C4×C22⋊C4—112no—
655C4×C22⋊C4—112no—
656C4×C22⋊C4—112no—
657C4×C22⋊C4—112no—
658C4×C22⋊C4C2×D1112yes—
659C2×#95—112no—
660C22×C11—22no—
661C22×C11—22no—
662C22×C11—22no—
663C22×C11—22no—
664C22×C11—22no—
665C22×C11—22no—
666C22×C11#52014yescomplemented
667C22×C11C24×C411yescharacteristic
668C22×C11C23×D411yescharacteristic
669C22×C11C22×#4111yescharacteristic
670C22×C11C2×H(5,𝔽2)11yescharacteristic
671C22×C11C2×2−1+411yescharacteristic
672C22×C11#58511yescharacteristic
673C22×C11#58511yescharacteristic
674C2×D11—22no—
675C2×D11—22no—
676C2×D11—22no—
677C2×D11—22no—
678C2×D11—22no—
679C2×D11—22no—
680C2×D11—22no—
681C2×D11—24no—
682C2×D11—22no—
683C2×D11—24no—
684C2×D11—22no—
685C2×D11—24no—
686C2×D11—416no—
687C2×D11—41no—
688C2×D11—42no—
689C2×D11—42no—
690C2×D11—41no—
691C2×D11—42no—
692C2×D11—41no—
693C2×D11—42no—
694C2×D11—41no—
695C2×D11C2×C4×D414yes—
696C4×C11—22no—
697C4×C11—24no—
698C4×C11—24no—
699C4×C11—22no—
700C4×C11—22no—
701C4×C11—41no—
702C4×C11—42no—
703C4×C11—41no—
704C4×C11—42no—
705C4×C11C2×C4×D414yes—
706Dic11—22no—
707Dic11—24no—
708Dic11—22no—
709Dic11—22no—
710Dic11—42no—
711Dic11—41no—
712Dic11—41no—
713Dic11—42no—
714Dic11C2×C4×D414yes—
715C25—111no—
716C2×#41—118no—
717C2×#41—224no—
718C2×#41—224no—
719C22×Q8C22×D1111yescharacteristic
720C22×D4—112no—
721C22×D4—112no—
722C22×D4—111no—
723C22×D4—112no—
724C23×C4—111no—
725C23×C4—111no—
726C23×C4—118no—
727C23×C4—112no—
728C23×C4—111no—
729C23×C4—111no—
730C23×C4—111no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—112no—
734C23×C4—112no—
735C23×C4—112no—
736C23×C4—112no—
737C23×C4—224no—
738C23×C4—224no—
739C23×C4C22×D1111yescharacteristic
740C23×C4C22×D1111yescharacteristic
741C23×C4C22×D1111yescharacteristic
742#123—1116no—
743C22⋊Q8—118no—
744C22⋊Q8C4×D1118yescomplemented
745#121—118no—
746#121—118no—
747#120—1116no—
748C4×Q8—24no—
749C4×Q8—224no—
750C4×D4—1116no—
751C4×D4—1116no—
752C4×D4—228no—
753C4×D4—224no—
754C4×D4—228no—
755C4×D4—224no—
756C4×D4—444no—
757C4×D4—444no—
758#117—118no—
759#117—118no—
760#117—224no—
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—111no—
774C2×C4⋊C4—111no—
775C2×C4⋊C4—111no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—111no—
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—228no—
787C2×C4⋊C4—224no—
788C2×C4⋊C4—224no—
789C2×C4⋊C4—224no—
790C2×C4⋊C4—224no—
791C2×C4⋊C4C22×D1111yescharacteristic
792C2×C4⋊C4C22×D1112yes—
793C2×C4⋊C4C22×D1111yescharacteristic
794C2×C4⋊C4C22×D1112yes—
795C2×C4⋊C4C22×D1111yescharacteristic
796C2×C4⋊C4C22×D1112yes—
797C2×C22⋊C4—111no—
798C2×C22⋊C4—111no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—111no—
805C2×C22⋊C4—111no—
806C2×C22⋊C4—111no—
807C2×C22⋊C4—111no—
808C2×C22⋊C4—111no—
809C2×C22⋊C4—111no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—112no—
816C2×C22⋊C4—112no—
817C2×C22⋊C4—112no—
818C2×C22⋊C4—224no—
819C2×C22⋊C4—224no—
820C2×C22⋊C4—444no—
821C2×C22⋊C4C22×D1112yes—
822C2×C22⋊C4C22×D1112yes—
823C2×C42—24no—
824C2×C42—111no—
825C2×C42—112no—
826C2×C42—111no—
827C2×C42—111no—
828C2×C42—111no—
829C2×C42—112no—
830C2×C42—112no—
831C2×C42—112no—
832C2×C42—112no—
833C2×C42—224no—
834C2×C42C22×D1111yescharacteristic
835C2×C42C22×D1111yescharacteristic
836C2×C42C22×D1111yescharacteristic
837C2×C42C22×D1112yes—
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#95C22×D1112yes—
852#95C22×D1112yes—
853#95C22×D1112yes—
854#95C22×D1112yes—
855#95C22×D1112yes—
856C2×C11—24no—
857C2×C11C22×C4×D411yescharacteristic
858C2×C11C2×#52011yescharacteristic
859C2×C11#342811yescharacteristic
860C2×C11#348811yescharacteristic
861C2×C11#348911yescharacteristic
862C2×C11#349411yescharacteristic
863C2×C11#349511yescharacteristic
864D11—24no—
865D11—44no—
866D11—42no—
867C24—111no—
868C24—111no—
869C24—112no—
870C24—114no—
871C24—222no—
872C24—222no—
873C24—222no—
874C24—222no—
875C24—441no—
876C24—441no—
877C24C23×D1111yescharacteristic
878#41—2232no—
879C2×Q8—22no—
880C2×Q8—22no—
881C2×Q8C2×C4×D1114yes—
882C2×D4—118no—
883C2×D4—118no—
884C2×D4—114no—
885C2×D4—118no—
886C2×D4—224no—
887C2×D4—224no—
888C2×D4—224no—
889C2×D4—224no—
890C2×D4—222no—
891C2×D4—222no—
892C2×D4—442no—
893C2×D4—442no—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—111no—
903C22×C4—114no—
904C22×C4—114no—
905C22×C4—114no—
906C22×C4—114no—
907C22×C4—112no—
908C22×C4—111no—
909C22×C4—111no—
910C22×C4—111no—
911C22×C4—114no—
912C22×C4—118no—
913C22×C4—114no—
914C22×C4—114no—
915C22×C4—111no—
916C22×C4—112no—
917C22×C4—112no—
918C22×C4—111no—
919C22×C4—224no—
920C22×C4—222no—
921C22×C4—222no—
922C22×C4—2232no—
923C22×C4—224no—
924C22×C4—224no—
925C22×C4—222no—
926C22×C4—222no—
927C22×C4—224no—
928C22×C4—224no—
929C22×C4—222no—
930C22×C4—222no—
931C22×C4—222no—
932C22×C4—222no—
933C22×C4—222no—
934C22×C4—222no—
935C22×C4—222no—
936C22×C4—222no—
937C22×C4—224no—
938C22×C4—442no—
939C22×C4—442no—
940C22×C4—442no—
941C22×C4—442no—
942C22×C4—442no—
943C22×C4—442no—
944C22×C4—442no—
945C22×C4—442no—
946C22×C4—441no—
947C22×C4—441no—
948C22×C4C2×C4×D1114yes—
949C22×C4C23×D1112yes—
950C22×C4C23×D1111yescharacteristic
951C22×C4C23×D1112yes—
952C22×C4C23×D1111yescharacteristic
953C22×C4C23×D1111yescharacteristic
954C22×C4C23×D1112yes—
955C22×C4C23×D1112yes—
956C22×C4C23×D1111yescharacteristic
957C22×C4C23×D1111yescharacteristic
958C22×C4C23×D1111yescharacteristic
959C4⋊C4—24no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—42no—
963C4⋊C4—114no—
964C4⋊C4—118no—
965C4⋊C4—114no—
966C4⋊C4—114no—
967C4⋊C4—224no—
968C4⋊C4—222no—
969C4⋊C4—222no—
970C4⋊C4—222no—
971C4⋊C4—222no—
972C4⋊C4—224no—
973C4⋊C4—224no—
974C4⋊C4—222no—
975C4⋊C4—222no—
976C4⋊C4—222no—
977C4⋊C4—222no—
978C4⋊C4—442no—
979C4⋊C4—442no—
980C4⋊C4—442no—
981C4⋊C4C2×C4×D1114yes—
982C4⋊C4C2×C4×D1118yes—
983C22⋊C4—24no—
984C22⋊C4—118no—
985C22⋊C4—118no—
986C22⋊C4—118no—
987C22⋊C4—118no—
988C22⋊C4—114no—
989C22⋊C4—114no—
990C22⋊C4—222no—
991C22⋊C4—222no—
992C22⋊C4—224no—
993C22⋊C4—222no—
994C22⋊C4—222no—
995C22⋊C4—224no—
996C22⋊C4—222no—
997C22⋊C4—222no—
998C22⋊C4—224no—
999C22⋊C4—442no—
1000C22⋊C4—442no—
1001C22⋊C4—442no—
1002C22⋊C4—442no—
1003C22⋊C4—442no—
1004C22⋊C4—442no—
1005C22⋊C4C2×C4×D1118yes—
1006C42—22no—
1007C42—22no—
1008C42—22no—
1009C42—24no—
1010C42—42no—
1011C42—118no—
1012C42—114no—
1013C42—222no—
1014C42—222no—
1015C42—224no—
1016C42—222no—
1017C42—442no—
1018C42—442no—
1019C42—442no—
1020C42D4×D1114yes—
1021C11#3420211yescharacteristic, complemented, Sylow
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—112no—
1027C23—112no—
1028C23—112no—
1029C23—112no—
1030C23—114no—
1031C23—228no—
1032C23—221no—
1033C23—221no—
1034C23—221no—
1035C23—221no—
1036C23—228no—
1037C23—221no—
1038C23—222no—
1039C23—222no—
1040C23—221no—
1041C23—221no—
1042C23—222no—
1043C23—221no—
1044C23—222no—
1045C23—222no—
1046C23—222no—
1047C23—221no—
1048C23—221no—
1049C23—444no—
1050C23—444no—
1051C23—444no—
1052C23—444no—
1053C23—444no—
1054C23C22×C4×D1112yes—
1055C23#6704012yes—
1056C23#6704212yes—
1057C23C24×D1111yescharacteristic
1058Q8—28no—
1059D4—2216no—
1060D4—2216no—
1061D4—228no—
1062D4—448no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—22no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—21no—
1073C2×C4—28no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—22no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—112no—
1089C2×C4—112no—
1090C2×C4—112no—
1091C2×C4—1116no—
1092C2×C4—114no—
1093C2×C4—112no—
1094C2×C4—112no—
1095C2×C4—112no—
1096C2×C4—228no—
1097C2×C4—2216no—
1098C2×C4—228no—
1099C2×C4—228no—
1100C2×C4—221no—
1101C2×C4—221no—
1102C2×C4—222no—
1103C2×C4—221no—
1104C2×C4—222no—
1105C2×C4—221no—
1106C2×C4—221no—
1107C2×C4—221no—
1108C2×C4—228no—
1109C2×C4—221no—
1110C2×C4—221no—
1111C2×C4—222no—
1112C2×C4—221no—
1113C2×C4—222no—
1114C2×C4—222no—
1115C2×C4—222no—
1116C2×C4—221no—
1117C2×C4—222no—
1118C2×C4—221no—
1119C2×C4—221no—
1120C2×C4—222no—
1121C2×C4—444no—
1122C2×C4—444no—
1123C2×C4—884no—
1124C2×C4—884no—
1125C2×C4—884no—
1126C2×C4—884no—
1127C2×C4C22×C4×D1114yes—
1128C2×C4C22×C4×D1112yes—
1129C2×C4C22×C4×D1114yes—
1130C2×C4C22×C4×D1112yes—
1131C2×C4C2×D4×D1112yes—
1132C2×C4C2×D4×D1112yes—
1133C2×C4C2×D4×D1112yes—
1134C2×C4#41×D1112yes—
1135C22—22no—
1136C22—22no—
1137C22—22no—
1138C22—22no—
1139C22—22no—
1140C22—22no—
1141C22—114no—
1142C22—222no—
1143C22—222no—
1144C22—222no—
1145C22—222no—
1146C22—222no—
1147C22—222no—
1148C22—222no—
1149C22—224no—
1150C22—224no—
1151C22—222no—
1152C22—222no—
1153C22—224no—
1154C22—4416no—
1155C22—442no—
1156C22—441no—
1157C22—441no—
1158C22—442no—
1159C22—441no—
1160C22—442no—
1161C22—441no—
1162C22—442no—
1163C22#1062310514yescomplemented
1164C22C23×C4×D1111yescharacteristic
1165C22C22×D4×D1111yescharacteristic
1166C22C2×#6704011yescharacteristic
1167C22C2×#41×D1111yescharacteristic
1168C22C2×#6704211yescharacteristic
1169C22#1062345311yescharacteristic
1170C22#1062345311yescharacteristic
1171C4—22no—
1172C4—22no—
1173C4—22no—
1174C4—24no—
1175C4—24no—
1176C4—41no—
1177C4—42no—
1178C4—41no—
1179C4—42no—
1180C4—114no—
1181C4—222no—
1182C4—222no—
1183C4—222no—
1184C4—224no—
1185C4—441no—
1186C4—442no—
1187C4—441no—
1188C4—442no—
1189C4C4×D4×D1114yes—
1190C2—24no—
1191C2—224no—
1192C2—442no—
1193C2—444no—
1194C2C2×C4×D4×D1111yescharacteristic
1195C2C2×#1062310511yescharacteristic
1196C2#1308181511yescharacteristic
1197C2#1308227711yescharacteristic
1198C2#1308229211yescharacteristic
1199C2#1308233911yescharacteristic
1200C2#1308236311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC4×C11×C22⋊Q8C2
socle, cosocleC23×C11C25
prime radicalC2×#10623158C2
hypercenterC4×C22⋊Q8D11
hypocenterC11#34202
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×#10623105C2semidirect
3. C22×#66925C2semidirect
4. #13071613C2semidirect
5. #13071601C2semidirect
6. #13071598C2semidirect
7. #13071592C2semidirect
8. #13071561C2semidirect
9. #13071540C2semidirect
10. #13071539C2semidirect
11. #13071514C2semidirect
12. #13071310C2semidirect
13. #13071307C2semidirect
14. #13071301C2semidirect
15. #13071292C2semidirect
16. #13071238C2semidirect
17. #13071207C2semidirect
18. C22⋊Q8×Dic11C2semidirect
19. C4×#66983C2semidirect
20. #13071122C2semidirect
21. D11×#380C2semidirect
22. #13070970C2semidirect
23. C4×C11×C22⋊Q8C2semidirect
27. C2×C4×Q8×C11C22semidirect
30. C2×Q8×Dic11C22semidirect
38. #10623158C4semidirect
44. C2×#66946C22semidirect
48. C2×C4⋊C4×D11C22semidirect
54. C2×C4×D44C22semidirect
64. C2×#66925C22semidirect
65. C11×#391C22semidirect
66. C11×#389C22semidirect
67. C11×#387C22semidirect
70. C4×C11×C4⋊C4C22semidirect
71. C4×C11×C4⋊C4C22semidirect
73. #10622843C22semidirect
78. #10622602C22semidirect
80. #10622601C22semidirect
83. #10622598C22semidirect
84. #10622594C22semidirect
85. #10622589C22semidirect
86. C4⋊C4×Dic11C22semidirect
87. C4⋊C4×Dic11C22semidirect
88. C4⋊C4×Dic11C22semidirect
89. #10622586C22semidirect
90. #10622585C22semidirect
96. #10622553C22semidirect
97. #10622553C22semidirect
99. #10622552C22semidirect
101. C4×(C2×D11)⋊C4C22semidirect
102. C4×C4⋊Dic11C22semidirect
103. #10622546C22semidirect
104. C4×Dic11⋊C4C22semidirect
105. #10622541C22semidirect
108. #10622282C22semidirect
109. #10622282C22semidirect
111. #10622281C22semidirect
113. #10622280C22semidirect
114. #10622280C22semidirect
116. #10622279C22semidirect
122. #10622265C22semidirect
123. #10622263C22semidirect
124. #10622262C22semidirect
125. #10622260C22semidirect
137. C2×#4343C2×C4semidirect
143. C22×C4×D11C2×C4semidirect
153. C11×C22⋊Q8C2×C4semidirect
171. #66999C2×C4semidirect
173. #66983C2×C4semidirect
227. #66948C2×C4semidirect
228. #66947C2×C4semidirect
231. #66946C2×C4semidirect
232. #66945C2×C4semidirect
236. #66935C2×C4semidirect
238. (C22⋊D11)⋊C4C2×C4semidirect
250. #66925D4semidirect
440. C4×C22⋊Q8D11semidirect
557. C4×D11C4×D4semidirect
569. C2×C4×Q8C2×D11semidirect
600. #391C2×D11semidirect
610. #389C2×D11semidirect
622. #387C2×D11semidirect
651. C4×C4⋊C4C2×D11semidirect
652. C4×C4⋊C4C2×D11semidirect
666. C22×C11#520semidirect
744. C22⋊Q8C4×D11semidirect
1021. C11#34202semidirect
1163. C22#10623105semidirect

Maximal subgroups

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

subgroupindex
C2×#106231582
C2×#106231052
C22×#669252
#130716132
#130716012
#130715982
#130715922
#130715612
#130715402
#130715392
#130715142
#130713102
#130713072
#130713012
#130712922
#130712382
#130712072
C22⋊Q8×Dic112
C4×#669832
#130711222
D11×#3802
#130709702
C4×C11×C22⋊Q82
#3420211