Finite Group Databasebeta

← #14925911

Subgroups — #14925911

Order 2816.

3206 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623158C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic, complemented
3#13074232C212yesmaximal, complemented
4#13074226C212yesmaximal, complemented
5#13074092C211yesmaximal, characteristic, complemented
6#13073992C211yesmaximal, characteristic, complemented
7#13073798C211yesmaximal, characteristic, complemented
8#13073770C211yesmaximal, characteristic, complemented
9#13073576C211yesmaximal, characteristic, complemented
10#13073572C211yesmaximal, characteristic, complemented
11#13073543C211yesmaximal, characteristic, complemented
12#13072009C212yesmaximal, complemented
13#13071989C212yesmaximal, complemented
14#13071882C211yesmaximal, characteristic, complemented
15#13071881C211yesmaximal, characteristic, complemented
16#13071834C211yesmaximal, characteristic, complemented
17#13071833C211yesmaximal, characteristic, complemented
18#13071137C212yesmaximal, complemented
19#13071126C212yesmaximal, complemented
20#13071122C212yesmaximal, complemented
21#13071117C212yesmaximal, complemented
22C2×#10622279C211yesmaximal, characteristic, complemented
23C11×#2564C211yesmaximal, characteristic, complemented
24C22×#4343C2211yescharacteristic, complemented
25C22×D4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C11×C22⋊Q8C2211yescharacteristic, complemented
29C2×C4×D4×C11C2211yescharacteristic
30C2×#66999C2211yescharacteristic
31C2×#66992C2212yes—
32C2×D4×Dic11C2211yescharacteristic
33C2×#66983C2212yes—
34C2×#66983C2211yescharacteristic, complemented
35C2×C4×C22⋊D11C2211yescharacteristic
36C2×C4×C22⋊D11C2211yescharacteristic
37C22×(C2×D11)⋊C4C2212yes—
38C22×C4×Dic11C2212yescomplemented
39#10623158—28no—
40C4×D4×D11—28no—
41C2×#66948C2211yescharacteristic
42C2×#66947C2212yes—
43C2×#66947C2212yescomplemented
44C2×#66946C2212yes—
45C2×#66946C2211yescharacteristic
46C2×#66946C2212yescomplemented
47C2×#66945C2211yescharacteristic, complemented
48C2×C4⋊C4×D11C2211yescharacteristic
49C2×#66935C2212yes—
50C2×#66935C2212yes—
51C2×(C22⋊D11)⋊C4C2211yescharacteristic
52C2×(C22⋊D11)⋊C4C2211yescharacteristic
53C2×(C22⋊D11)⋊C4C2212yescomplemented
54C2×(C22⋊D11)⋊C4C2212yescomplemented
55C2×C22⋊C4×D11C2211yescharacteristic
56C2×C22⋊C4×D11C2211yescharacteristic
57C2×C4×D44C2211yescharacteristic
58C2×C42×D11C2211yescharacteristic
59C11×#400C2211yescharacteristic, complemented
60C11×#399C2211yescharacteristic, complemented
61C11×#395C2211yescharacteristic, complemented
62C11×#393C2211yescharacteristic, complemented
63C11×#387C2212yescomplemented
64C11×#386C2212yes—
65C11×#385C2212yescomplemented
66C11×#380C2212yescomplemented
67C2×C11×#95C2211yescharacteristic, complemented
68#10622844C2211yescharacteristic, complemented
69#10622842C2211yescharacteristic, complemented
70#10622826C2212yescomplemented
71#10622826C2212yescomplemented
72C2×C11⋊#95C2211yescharacteristic, complemented
73#10622606C2212yescomplemented
74#10622605C2211yescharacteristic, complemented
75#10622604C2212yescomplemented
76#10622604C2211yescharacteristic, complemented
77#10622602C2212yes—
78#10622602C2212yescomplemented
79#10622601C2212yescomplemented
80#10622596C2211yescharacteristic, complemented
81#10622595C2211yescharacteristic, complemented
82#10622591C2212yescomplemented
83C4⋊C4×Dic11C2212yescomplemented
84#10622586C2212yescomplemented
85#10622574C2212yes—
86#10622573C2212yes—
87#10622573C2211yescharacteristic, complemented
88#10622571C2212yes—
89#10622571C2212yescomplemented
90#10622570C2212yescomplemented
91#10622568C2212yes—
92#10622566C2211yescharacteristic, complemented
93#10622557C2212yescomplemented
94#10622555C2212yescomplemented
95C22⋊C4×Dic11C2212yescomplemented
96#10622553C2212yescomplemented
97#10622288C2212yescomplemented
98#10622287C2211yescharacteristic, complemented
99#10622285C2212yes—
100#10622285C2212yescomplemented
101#10622285C2211yescharacteristic, complemented
102#10622284C2212yes—
103#10622284C2211yescharacteristic, complemented
104#10622283C2212yescomplemented
105#10622283C2212yescomplemented
106#10622282C2212yescomplemented
107#10622282C2212yescomplemented
108#10622281C2212yes—
109#10622279C2212yes—
110#10622279C2211yescharacteristic
111#10622279C2211yescharacteristic
112#10622279C2211yescharacteristic, complemented
113#10622279C2212yescomplemented
114#10622279C2211yescharacteristic, complemented
115#10622279C2212yescomplemented
116#10622279C2212yescomplemented
117#10622279C2212yescomplemented
118#10622278C2212yes—
119#10622278C2212yes—
120#10622278C2212yescomplemented
121#10622277C2212yes—
122#10622274C2211yescharacteristic, complemented
123#10622262C2212yescomplemented
124#10622260C2212yescomplemented
125C24×D11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×Q8×C11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C22×C22⋊D11C2311yescharacteristic
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2311yescharacteristic
136C23×Dic11C2311yescharacteristic
137C23×Dic11C2312yes—
138C23×Dic11C2311yescharacteristic
139C2×#4343—24no—
140C2×#4343—44no—
141C2×D4×D11—24no—
142C2×D4×D11—24no—
143C2×D4×D11—24no—
144C22×D44C2311yescharacteristic
145C22×D44C2312yes—
146C22×D44C2312yes—
147C22×D44C2312yes—
148C22×D44C2311yescharacteristic
149C22×C4×D11—24no—
150C22×C4×D11—44no—
151C22×C4×D11—44no—
152C22×C4×D11D418yescomplemented
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2311yescharacteristic
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2312yes—
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2311yescharacteristic
161C22×C4×D11C2311yescharacteristic
162C22×C4×D11C2311yescharacteristic
163C11×C22⋊Q8—24no—
164C4×D4×C11—24no—
165C2×C11×C4⋊C4C2311yescharacteristic
166C2×C11×C4⋊C4C2311yescharacteristic
167C2×C11×C4⋊C4C2312yes—
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C4⋊C4C2312yes—
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C11×C22⋊C4C2311yescharacteristic
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2312yes—
175C2×C42×C11C2311yescharacteristic
176C2×C22⋊Dic11C2311yescharacteristic
177C2×C22⋊Dic11C2311yescharacteristic
178C2×C22⋊Dic11C2312yes—
179#66999—24no—
180#66992—28no—
181D4×Dic11—24no—
182#66983—24no—
183#66983—28no—
184C4×C22⋊D11—24no—
185C4×C22⋊D11—24no—
186C2×(C2×D11)⋊C4—28no—
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2311yescharacteristic
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2311yescharacteristic
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×C4⋊Dic11C2311yescharacteristic
209C2×C4⋊Dic11C2311yescharacteristic
210C2×C4⋊Dic11C2312yes—
211C2×Dic11⋊C4C2311yescharacteristic
212C2×Dic11⋊C4C2311yescharacteristic
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×C4×Dic11—44no—
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2312yes—
222C2×C4×Dic11C2312yes—
223C2×C4×Dic11C2312yes—
224C2×C4×Dic11C2312yes—
225C2×C4×Dic11C2312yes—
226#66948—24no—
227#66947—28no—
228#66947—28no—
229#66946—24no—
230#66946—28no—
231#66946—44no—
232#66945—24no—
233C4⋊C4×D11—24no—
234#66935—28no—
235#66935—28no—
236(C22⋊D11)⋊C4—24no—
237(C22⋊D11)⋊C4—28no—
238(C22⋊D11)⋊C4—24no—
239(C22⋊D11)⋊C4—44no—
240C22⋊C4×D11—24no—
241C22⋊C4×D11—24no—
242C4×D44—24no—
243C42×D11—24no—
244C11×#95C2312yes—
245C11×#95C2312yes—
246C11×#95C2311yescharacteristic
247C11×#95C2312yes—
248C11×#95C2312yes—
249C11×#95C2312yes—
250C11×#95C2311yescharacteristic
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2311yescharacteristic
259C11⋊#95C2311yescharacteristic
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262#34957—111nomaximal, Sylow
263C24×C11C2411yescharacteristic
264C24×C11C2411yescharacteristic
265C23×D11—22no—
266C23×D11—22no—
267C23×D11—22no—
268C23×D11—22no—
269C23×D11—24no—
270C23×D11—22no—
271C23×D11—24no—
272C23×D11—42no—
273C23×D11—42no—
274C23×D11C2×D414yes—
275C23×D11C2412yes—
276C23×D11C2411yescharacteristic
277C23×D11C2411yescharacteristic
278C23×D11C2411yescharacteristic
279C2×Q8×C11—22no—
280C2×Q8×C11—42no—
281C2×D4×C11—22no—
282C2×D4×C11—22no—
283C2×D4×C11#4114yescomplemented
284C22×C4×C11—24no—
285C22×C4×C11—22no—
286C22×C4×C11—24no—
287C22×C4×C11—42no—
288C22×C4×C11—42no—
289C22×C4×C11—42no—
290C22×C4×C11C2×D414yes—
291C22×C4×C11C2412yes—
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2412yes—
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2412yes—
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2412yes—
299C22×C4×C11C2411yescharacteristic
300C2×C22⋊D11—22no—
301C2×C22⋊D11—24no—
302C2×C22⋊D11—22no—
303C2×C22⋊D11—24no—
304C2×C22⋊D11—22no—
305C2×C22⋊D11—22no—
306C2×C22⋊D11—24no—
307C2×C22⋊D11—24no—
308C2×C22⋊D11—24no—
309C2×C22⋊D11—22no—
310C2×C22⋊D11—42no—
311C2×C22⋊D11#4114yescomplemented
312C22×Dic11—24no—
313C22×Dic11—22no—
314C22×Dic11—24no—
315C22×Dic11—24no—
316C22×Dic11—24no—
317C22×Dic11—42no—
318C22×Dic11C2×D414yes—
319C22×Dic11C2412yes—
320C22×Dic11C2411yescharacteristic
321C22×Dic11C2412yes—
322C22×Dic11C2411yescharacteristic
323C22×Dic11C2411yescharacteristic
324C22×Dic11C2412yes—
325C22×Dic11C2411yescharacteristic
326C22×Dic11C2411yescharacteristic
327#4343—416no—
328D4×D11—232no—
329C2×D44—22no—
330C2×D44—24no—
331C2×D44—24no—
332C2×D44—22no—
333C2×D44—24no—
334C2×D44—24no—
335C2×D44—24no—
336C2×D44—22no—
337C2×D44—22no—
338C2×D44—24no—
339C2×D44—42no—
340C2×D44—42no—
341C2×D44—42no—
342C2×D44—42no—
343C2×C4×D11—22no—
344C2×C4×D11—24no—
345C2×C4×D11—24no—
346C2×C4×D11—22no—
347C2×C4×D11—24no—
348C2×C4×D11—24no—
349C2×C4×D11—24no—
350C2×C4×D11—24no—
351C2×C4×D11—22no—
352C2×C4×D11—22no—
353C2×C4×D11—22no—
354C2×C4×D11—24no—
355C2×C4×D11—22no—
356C2×C4×D11—22no—
357C2×C4×D11—42no—
358C2×C4×D11—42no—
359C2×C4×D11—42no—
360C2×C4×D11—42no—
361C2×C4×D11—416no—
362C2×C4×D11—416no—
363C2×C4×D11C2×D414yes—
364C2×C4×D11C2×D414yes—
365C2×C4×D11C2×D414yes—
366C2×C4×D11C2×D414yes—
367C11×C4⋊C4—22no—
368C11×C4⋊C4—22no—
369C11×C4⋊C4—24no—
370C11×C4⋊C4—24no—
371C11×C4⋊C4—42no—
372C11×C22⋊C4—22no—
373C11×C22⋊C4—24no—
374C11×C22⋊C4—22no—
375C11×C22⋊C4—24no—
376C11×C22⋊C4—42no—
377C42×C11—22no—
378C22⋊Dic11—22no—
379C22⋊Dic11—22no—
380C22⋊Dic11—24no—
381(C2×D11)⋊C4—22no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—24no—
384(C2×D11)⋊C4—24no—
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—22no—
388(C2×D11)⋊C4—22no—
389(C2×D11)⋊C4—24no—
390(C2×D11)⋊C4—24no—
391(C2×D11)⋊C4—24no—
392(C2×D11)⋊C4—24no—
393(C2×D11)⋊C4—22no—
394(C2×D11)⋊C4—24no—
395(C2×D11)⋊C4—24no—
396(C2×D11)⋊C4—24no—
397(C2×D11)⋊C4—24no—
398(C2×D11)⋊C4—42no—
399(C2×D11)⋊C4—42no—
400(C2×D11)⋊C4—42no—
401(C2×D11)⋊C4#4118yescomplemented
402C4⋊Dic11—22no—
403C4⋊Dic11—24no—
404C4⋊Dic11—22no—
405Dic11⋊C4—22no—
406Dic11⋊C4—24no—
407Dic11⋊C4—24no—
408Dic11⋊C4—22no—
409Dic11⋊C4—24no—
410Dic11⋊C4—42no—
411C4×Dic11—22no—
412C4×Dic11—22no—
413C4×Dic11—24no—
414C4×Dic11—24no—
415C4×Dic11—24no—
416C4×Dic11—22no—
417C4×Dic11—42no—
418C4×Dic11—42no—
419C2×#525—111no—
420C22×C4×D4—111no—
421#2602—112no—
422#2602—112no—
423#2591—111no—
424#2583—111no—
425#2564—111no—
426#2564D1111yescharacteristic, complemented
427#2561—111no—
428#2543—111no—
429#2543—111no—
430#2539—111no—
431#2412—112no—
432#2410—112no—
433#2395—111no—
434#2395—111no—
435#2388—111no—
436#2388—111no—
437C4×#123—112no—
438C4×#121—112no—
439C4×#121—112no—
440C4×#120—112no—
441C2×C4×C22⋊C4—111no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—21no—
445C23×C11—22no—
446C23×C11—21no—
447C23×C11—22no—
448C23×C11C22×D412yes—
449C23×C11C2×#4112yes—
450C23×C11C2×#4112yes—
451C23×C11C2×#4112yes—
452C23×C11C2511yescharacteristic
453C22×D11—21no—
454C22×D11—21no—
455C22×D11—22no—
456C22×D11—28no—
457C22×D11—28no—
458C22×D11—21no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—21no—
462C22×D11—21no—
463C22×D11—21no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—28no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—44no—
475C22×D11—48no—
476C22×D11—48no—
477C22×D11—48no—
478C22×D11—48no—
479C22×D11—44no—
480C22×D11—44no—
481C22×D11C22×D412yes—
482C22×D11C22×D412yes—
483C22×D11C2×#4112yes—
484C22×D11C2×#4114yes—
485Q8×C11—44no—
486D4×C11—28no—
487C2×C4×C11—21no—
488C2×C4×C11—22no—
489C2×C4×C11—21no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—21no—
494C2×C4×C11—22no—
495C2×C4×C11—21no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11—44no—
507C2×C4×C11—48no—
508C2×C4×C11—44no—
509C2×C4×C11C22×D412yes—
510C2×C4×C11C22×D412yes—
511C2×C4×C11C2×#4112yes—
512C2×C4×C11C2×#4114yes—
513C22⋊D11—28no—
514C22⋊D11—28no—
515C22⋊D11—48no—
516C22⋊D11—48no—
517C2×Dic11—21no—
518C2×Dic11—22no—
519C2×Dic11—21no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—28no—
523C2×Dic11—21no—
524C2×Dic11—22no—
525C2×Dic11—21no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11—48no—
534C2×Dic11—44no—
535C2×Dic11C22×D412yes—
536C2×Dic11C22×D412yes—
537C2×Dic11C2×#4114yes—
538C2×Dic11C2×#4112yes—
539C2×Dic11H(5,𝔽2)14yes—
540D44—28no—
541D44—48no—
542D44—44no—
543D44—48no—
544D44—48no—
545C4×D11—28no—
546C4×D11—28no—
547C4×D11—28no—
548C4×D11—44no—
549C4×D11—44no—
550C4×D11—44no—
551C4×D11—44no—
552C4×D11—44no—
553C4×D11—44no—
554C4×D11—48no—
555C22×#41—111no—
556C23×D4—111no—
557C24×C4—111no—
558C24×C4—111no—
559#525—228no—
560C2×#123—112no—
561C2×#123—112no—
562C2×C22⋊Q8—111no—
563C2×C22⋊Q8C2×D1111yescharacteristic, complemented
564C2×#121—112no—
565C2×#121—112no—
566C2×#121—111no—
567C2×#121—111no—
568C2×#120—112no—
569C2×#120—112no—
570C2×C4×D4—111no—
571C2×C4×D4—111no—
572C2×C4×D4—111no—
573C2×C4×D4—111no—
574C2×C4×D4—112no—
575C2×C4×D4—112no—
576C2×C4×D4—111no—
577C2×C4×D4—111no—
578C2×C4×D4—112no—
579C2×C4×D4—112no—
580C2×C4×D4—111no—
581C2×C4×D4—228no—
582C2×C4×D4C2×D1111yescharacteristic
583C2×#117—111no—
584C22×C4⋊C4—111no—
585C22×C22⋊C4—112no—
586C22×C22⋊C4—111no—
587C22×C22⋊C4—111no—
588C22×C42—112no—
589C22×C42—111no—
590#400—111no—
591#400C2×D1111yescharacteristic, complemented
592#399—111no—
593#399C2×D1111yescharacteristic, complemented
594#398—111no—
595#398—111no—
596#397—112no—
597#397—111no—
598#397—111no—
599#397—112no—
600#395—111no—
601#395C2×D1111yescharacteristic, complemented
602#394—111no—
603#394—112no—
604#394—112no—
605#394—111no—
606#394—112no—
607#394—112no—
608#393—111no—
609#393C2×D1111yescharacteristic, complemented
610#392—112no—
611#392—111no—
612#392—112no—
613#392—111no—
614#390—112no—
615#390—112no—
616#389—112no—
617#389—112no—
618#388—112no—
619#388—112no—
620#388—112no—
621#388—112no—
622#388—112no—
623#388—112no—
624#387—112no—
625#387C2×D1112yescomplemented
626#386—112no—
627#386—112no—
628#386—112no—
629#386—112no—
630#386—112no—
631#386—112no—
632#386—112no—
633#386C2×D1112yes—
634#385—112no—
635#385—112no—
636#385—112no—
637#385C2×D1112yescomplemented
638#381—112no—
639#380—112no—
640#380C2×D1112yescomplemented
641#379—112no—
642C4×C4⋊C4—112no—
643C4×C4⋊C4—112no—
644C4×C22⋊C4—112no—
645C4×C22⋊C4—111no—
646C4×C22⋊C4—111no—
647C4×C22⋊C4—112no—
648C4×C22⋊C4—112no—
649C4×C22⋊C4—111no—
650C4×C22⋊C4—111no—
651C4×C22⋊C4—112no—
652C4×C22⋊C4—112no—
653C4×C22⋊C4—112no—
654C2×#95—111no—
655C2×#95C2×D1111yescharacteristic, complemented
656C22×C11—22no—
657C22×C11—22no—
658C22×C11—24no—
659C22×C11—24no—
660C22×C11—22no—
661C22×C11—24no—
662C22×C11—41no—
663C22×C11—41no—
664C22×C11—42no—
665C22×C11#52514yes—
666C22×C11C23×D411yescharacteristic
667C22×C11C22×#4111yescharacteristic
668C22×C11C22×#4111yescharacteristic
669C22×C11C22×#4112yes—
670C22×C11C2×H(5,𝔽2)12yes—
671C2×D11—22no—
672C2×D11—22no—
673C2×D11—24no—
674C2×D11—24no—
675C2×D11—22no—
676C2×D11—22no—
677C2×D11—22no—
678C2×D11—22no—
679C2×D11—24no—
680C2×D11—416no—
681C2×D11—416no—
682C2×D11—41no—
683C2×D11—41no—
684C2×D11—42no—
685C2×D11—42no—
686C2×D11—42no—
687C2×D11—42no—
688C2×D11—42no—
689C2×D11—42no—
690C2×D11—42no—
691C2×D11—42no—
692C2×D11—42no—
693C2×D11—42no—
694C2×D11#53214yes—
695C4×C11—22no—
696C4×C11—22no—
697C4×C11—22no—
698C4×C11—24no—
699C4×C11—41no—
700C4×C11—42no—
701C4×C11—41no—
702C4×C11—42no—
703C4×C11—42no—
704Dic11—22no—
705Dic11—22no—
706Dic11—24no—
707Dic11—42no—
708Dic11—41no—
709Dic11—41no—
710Dic11—42no—
711Dic11#53414yes—
712C25—111no—
713C25—111no—
714C2×#41—224no—
715C2×#41—444no—
716C22×Q8C22×D1111yescharacteristic
717C22×D4—111no—
718C22×D4—111no—
719C22×D4—112no—
720C22×D4—112no—
721C22×D4—111no—
722C22×D4—112no—
723C22×D4—112no—
724C22×D4—112no—
725C22×D4—111no—
726C22×D4—224no—
727C22×D4—224no—
728C22×D4—224no—
729C22×D4C22×D1111yescharacteristic
730C23×C4—111no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—118no—
734C23×C4—111no—
735C23×C4—111no—
736C23×C4—111no—
737C23×C4—112no—
738C23×C4—111no—
739C23×C4—111no—
740C23×C4—111no—
741C23×C4—112no—
742C23×C4—111no—
743C23×C4—111no—
744C23×C4—224no—
745C23×C4—444no—
746C23×C4—444no—
747C23×C4C22×D1112yes—
748C23×C4C22×D1111yescharacteristic
749C23×C4C22×D1111yescharacteristic
750#123—228no—
751#123—228no—
752C22⋊Q8—24no—
753C22⋊Q8—224no—
754#121—224no—
755#121—228no—
756#121—228no—
757#121—224no—
758#120—228no—
759#120—228no—
760C4×D4—24no—
761C4×D4—224no—
762C4×D4—224no—
763C4×D4—224no—
764C4×D4—228no—
765C4×D4—224no—
766C4×D4—228no—
767C4×D4—224no—
768C4×D4—224no—
769C4×D4—224no—
770C4×D4—444no—
771C4×D4—444no—
772#117—224no—
773C2×C4⋊C4—111no—
774C2×C4⋊C4—111no—
775C2×C4⋊C4—111no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—112no—
779C2×C4⋊C4—112no—
780C2×C4⋊C4—112no—
781C2×C4⋊C4—112no—
782C2×C4⋊C4—224no—
783C2×C4⋊C4C22×D1111yescharacteristic
784C2×C4⋊C4C22×D1111yescharacteristic
785C2×C4⋊C4C22×D1112yes—
786C2×C4⋊C4C22×D1112yes—
787C2×C4⋊C4C22×D1112yes—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—111no—
790C2×C22⋊C4—111no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—111no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—111no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—224no—
813C2×C22⋊C4—224no—
814C2×C22⋊C4—228no—
815C2×C22⋊C4C22×D1111yescharacteristic
816C2×C22⋊C4C22×D1111yescharacteristic
817C2×C22⋊C4C22×D1112yes—
818C2×C22⋊C4C22×D1112yes—
819C2×C22⋊C4C22×D1112yes—
820C2×C42—112no—
821C2×C42—111no—
822C2×C42—111no—
823C2×C42—111no—
824C2×C42—112no—
825C2×C42—112no—
826C2×C42—112no—
827C2×C42—112no—
828C2×C42—224no—
829C2×C42—444no—
830C2×C42C22×D1111yescharacteristic
831#95—112no—
832#95—111no—
833#95—111no—
834#95—112no—
835#95—112no—
836#95—112no—
837#95—112no—
838#95—112no—
839#95—112no—
840#95—112no—
841#95—112no—
842#95C22×D1112yes—
843#95C22×D1111yescharacteristic
844#95C22×D1111yescharacteristic
845#95C22×D1112yes—
846#95C22×D1112yes—
847#95C22×D1112yes—
848#95C22×D1112yes—
849C2×C11—24no—
850C2×C11—42no—
851C2×C11C2×#52511yescharacteristic
852C2×C11C2×#53211yescharacteristic
853C2×C11C2×#53411yescharacteristic
854C2×C11#348112yes—
855C2×C11#348112yes—
856D11—24no—
857D11—42no—
858D11—42no—
859D11—82no—
860C24—111no—
861C24—111no—
862C24—111no—
863C24—114no—
864C24—112no—
865C24—222no—
866C24—224no—
867C24—222no—
868C24—224no—
869C24—222no—
870C24—222no—
871C24—222no—
872C24—442no—
873C24—442no—
874C24C23×D1111yescharacteristic
875C24C23×D1111yescharacteristic
876#41—4416no—
877C2×Q8—22no—
878C2×Q8—42no—
879C2×D4—22no—
880C2×D4—22no—
881C2×D4—114no—
882C2×D4—222no—
883C2×D4—222no—
884C2×D4—224no—
885C2×D4—224no—
886C2×D4—224no—
887C2×D4—224no—
888C2×D4—224no—
889C2×D4—222no—
890C2×D4—224no—
891C2×D4—2232no—
892C2×D4—222no—
893C2×D4—222no—
894C2×D4—222no—
895C2×D4—222no—
896C2×D4—224no—
897C2×D4—224no—
898C2×D4—224no—
899C2×D4—224no—
900C2×D4—222no—
901C2×D4—222no—
902C2×D4—224no—
903C2×D4—442no—
904C2×D4—442no—
905C2×D4—442no—
906C2×D4—442no—
907C2×D4—442no—
908C2×D4#434314yescomplemented
909C22×C4—24no—
910C22×C4—22no—
911C22×C4—24no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—111no—
916C22×C4—114no—
917C22×C4—112no—
918C22×C4—111no—
919C22×C4—111no—
920C22×C4—114no—
921C22×C4—114no—
922C22×C4—114no—
923C22×C4—114no—
924C22×C4—112no—
925C22×C4—111no—
926C22×C4—112no—
927C22×C4—111no—
928C22×C4—224no—
929C22×C4—224no—
930C22×C4—222no—
931C22×C4—222no—
932C22×C4—224no—
933C22×C4—224no—
934C22×C4—224no—
935C22×C4—224no—
936C22×C4—222no—
937C22×C4—222no—
938C22×C4—222no—
939C22×C4—224no—
940C22×C4—224no—
941C22×C4—224no—
942C22×C4—222no—
943C22×C4—224no—
944C22×C4—222no—
945C22×C4—224no—
946C22×C4—222no—
947C22×C4—442no—
948C22×C4—442no—
949C22×C4—442no—
950C22×C4—442no—
951C22×C4—4416no—
952C22×C4—4416no—
953C22×C4—442no—
954C22×C4D4×D1114yes—
955C22×C4C23×D1111yescharacteristic
956C22×C4C23×D1112yes—
957C22×C4C23×D1111yescharacteristic
958C22×C4C23×D1112yes—
959C22×C4C23×D1112yes—
960C22×C4C23×D1111yescharacteristic
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1111yescharacteristic
963C22×C4C23×D1112yes—
964C4⋊C4—22no—
965C4⋊C4—22no—
966C4⋊C4—24no—
967C4⋊C4—24no—
968C4⋊C4—42no—
969C4⋊C4—222no—
970C4⋊C4—222no—
971C4⋊C4—224no—
972C4⋊C4—224no—
973C4⋊C4—224no—
974C4⋊C4—222no—
975C4⋊C4—222no—
976C4⋊C4—224no—
977C4⋊C4—442no—
978C22⋊C4—22no—
979C22⋊C4—24no—
980C22⋊C4—22no—
981C22⋊C4—24no—
982C22⋊C4—42no—
983C22⋊C4—118no—
984C22⋊C4—222no—
985C22⋊C4—224no—
986C22⋊C4—224no—
987C22⋊C4—224no—
988C22⋊C4—224no—
989C22⋊C4—224no—
990C22⋊C4—222no—
991C22⋊C4—222no—
992C22⋊C4—224no—
993C22⋊C4—224no—
994C22⋊C4—224no—
995C22⋊C4—224no—
996C22⋊C4—222no—
997C22⋊C4—222no—
998C22⋊C4—224no—
999C22⋊C4—222no—
1000C22⋊C4—224no—
1001C22⋊C4—224no—
1002C22⋊C4—224no—
1003C22⋊C4—224no—
1004C22⋊C4—442no—
1005C22⋊C4—442no—
1006C22⋊C4—442no—
1007C42—22no—
1008C42—222no—
1009C42—222no—
1010C42—224no—
1011C42—224no—
1012C42—224no—
1013C42—222no—
1014C42—442no—
1015C42—442no—
1016C11#3495711yescharacteristic, complemented, Sylow
1017C23—22no—
1018C23—22no—
1019C23—21no—
1020C23—22no—
1021C23—21no—
1022C23—22no—
1023C23—112no—
1024C23—114no—
1025C23—112no—
1026C23—112no—
1027C23—228no—
1028C23—228no—
1029C23—221no—
1030C23—221no—
1031C23—222no—
1032C23—228no—
1033C23—221no—
1034C23—221no—
1035C23—221no—
1036C23—222no—
1037C23—222no—
1038C23—221no—
1039C23—222no—
1040C23—222no—
1041C23—222no—
1042C23—222no—
1043C23—222no—
1044C23—222no—
1045C23—222no—
1046C23—222no—
1047C23—222no—
1048C23—444no—
1049C23—448no—
1050C23—448no—
1051C23—448no—
1052C23—444no—
1053C23—448no—
1054C23—444no—
1055C23C2×D4×D1112yes—
1056C23C2×#434312yes—
1057C23C2×#434312yes—
1058C23#41×D1112yes—
1059C23C24×D1111yescharacteristic
1060Q8—44no—
1061D4—28no—
1062D4—228no—
1063D4—228no—
1064D4—228no—
1065D4—448no—
1066D4—444no—
1067D4—448no—
1068D4—448no—
1069D4—448no—
1070D4—448no—
1071C2×C4—21no—
1072C2×C4—22no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—44no—
1091C2×C4—48no—
1092C2×C4—44no—
1093C2×C4—112no—
1094C2×C4—114no—
1095C2×C4—112no—
1096C2×C4—114no—
1097C2×C4—112no—
1098C2×C4—228no—
1099C2×C4—228no—
1100C2×C4—228no—
1101C2×C4—228no—
1102C2×C4—221no—
1103C2×C4—222no—
1104C2×C4—221no—
1105C2×C4—222no—
1106C2×C4—222no—
1107C2×C4—221no—
1108C2×C4—222no—
1109C2×C4—221no—
1110C2×C4—222no—
1111C2×C4—222no—
1112C2×C4—222no—
1113C2×C4—222no—
1114C2×C4—222no—
1115C2×C4—222no—
1116C2×C4—222no—
1117C2×C4—444no—
1118C2×C4—444no—
1119C2×C4—444no—
1120C2×C4—444no—
1121C2×C4—448no—
1122C2×C4—444no—
1123C2×C4—444no—
1124C2×C4—444no—
1125C2×C4—448no—
1126C2×C4C2×D4×D1112yes—
1127C2×C4C2×D4×D1112yes—
1128C2×C4C2×#434312yes—
1129C2×C4#41×D1114yes—
1130C22—22no—
1131C22—22no—
1132C22—24no—
1133C22—24no—
1134C22—22no—
1135C22—24no—
1136C22—41no—
1137C22—41no—
1138C22—42no—
1139C22—114no—
1140C22—222no—
1141C22—222no—
1142C22—224no—
1143C22—224no—
1144C22—222no—
1145C22—222no—
1146C22—222no—
1147C22—222no—
1148C22—224no—
1149C22—4416no—
1150C22—4416no—
1151C22—441no—
1152C22—441no—
1153C22—442no—
1154C22—442no—
1155C22—442no—
1156C22—442no—
1157C22—442no—
1158C22—442no—
1159C22—442no—
1160C22—442no—
1161C22—442no—
1162C22—442no—
1163C22#1062315814yes—
1164C22C22×D4×D1111yescharacteristic
1165C22C22×#434311yescharacteristic
1166C22C2×#41×D1111yescharacteristic
1167C22C2×#41×D1112yes—
1168C22D11×H(5,𝔽2)12yes—
1169C4—22no—
1170C4—22no—
1171C4—22no—
1172C4—24no—
1173C4—41no—
1174C4—42no—
1175C4—41no—
1176C4—42no—
1177C4—42no—
1178C4—114no—
1179C4—222no—
1180C4—222no—
1181C4—224no—
1182C4—442no—
1183C4—441no—
1184C4—441no—
1185C4—442no—
1186C2—24no—
1187C2—42no—
1188C2—224no—
1189C2—442no—
1190C2—442no—
1191C2—882no—
1192C2C2×#1062315811yescharacteristic
1193C2D11×#53211yescharacteristic
1194C2D11×#53411yescharacteristic
1195C2#1308221912yes—
1196C2#1308222712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2564C2
hypercenter#2564D11
hypocenterC11#34957
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2564

Complements

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

NH ≅ G/Ntype
1. C2×#10623158C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13074232C2semidirect
4. #13074226C2semidirect
5. #13074092C2semidirect
6. #13073992C2semidirect
7. #13073798C2semidirect
8. #13073770C2semidirect
9. #13073576C2semidirect
10. #13073572C2semidirect
11. #13073543C2semidirect
12. #13072009C2semidirect
13. #13071989C2semidirect
14. #13071882C2semidirect
15. #13071881C2semidirect
16. #13071834C2semidirect
17. #13071833C2semidirect
18. #13071137C2semidirect
19. #13071126C2semidirect
20. #13071122C2semidirect
21. #13071117C2semidirect
22. C2×#10622279C2semidirect
23. C11×#2564C2semidirect
24. C22×#4343C22semidirect
28. C2×C11×C22⋊Q8C22semidirect
34. C2×#66983C22semidirect
38. C22×C4×Dic11C22semidirect
43. C2×#66947C22semidirect
46. C2×#66946C22semidirect
47. C2×#66945C22semidirect
53. C2×(C22⋊D11)⋊C4C22semidirect
54. C2×(C22⋊D11)⋊C4C22semidirect
59. C11×#400C22semidirect
60. C11×#399C22semidirect
61. C11×#395C22semidirect
62. C11×#393C22semidirect
63. C11×#387C22semidirect
65. C11×#385C22semidirect
66. C11×#380C22semidirect
67. C2×C11×#95C22semidirect
68. #10622844C22semidirect
69. #10622842C22semidirect
70. #10622826C22semidirect
71. #10622826C22semidirect
72. C2×C11⋊#95C22semidirect
73. #10622606C22semidirect
74. #10622605C22semidirect
75. #10622604C22semidirect
76. #10622604C22semidirect
78. #10622602C22semidirect
79. #10622601C22semidirect
80. #10622596C22semidirect
81. #10622595C22semidirect
82. #10622591C22semidirect
83. C4⋊C4×Dic11C22semidirect
84. #10622586C22semidirect
87. #10622573C22semidirect
89. #10622571C22semidirect
90. #10622570C22semidirect
92. #10622566C22semidirect
93. #10622557C22semidirect
94. #10622555C22semidirect
95. C22⋊C4×Dic11C22semidirect
96. #10622553C22semidirect
97. #10622288C22semidirect
98. #10622287C22semidirect
100. #10622285C22semidirect
101. #10622285C22semidirect
103. #10622284C22semidirect
104. #10622283C22semidirect
105. #10622283C22semidirect
106. #10622282C22semidirect
107. #10622282C22semidirect
112. #10622279C22semidirect
113. #10622279C22semidirect
114. #10622279C22semidirect
115. #10622279C22semidirect
116. #10622279C22semidirect
117. #10622279C22semidirect
120. #10622278C22semidirect
122. #10622274C22semidirect
123. #10622262C22semidirect
124. #10622260C22semidirect
152. C22×C4×D11D4semidirect
283. C2×D4×C11#41semidirect
311. C2×C22⋊D11#41semidirect
401. (C2×D11)⋊C4#41semidirect
426. #2564D11semidirect
563. C2×C22⋊Q8C2×D11semidirect
591. #400C2×D11semidirect
593. #399C2×D11semidirect
601. #395C2×D11semidirect
609. #393C2×D11semidirect
625. #387C2×D11semidirect
637. #385C2×D11semidirect
640. #380C2×D11semidirect
655. C2×#95C2×D11semidirect
908. C2×D4#4343semidirect
1016. C11#34957semidirect

Maximal subgroups

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

subgroupindex
C2×#106231582
C2×C4×D4×D112
#130742322
#130742262
#130740922
#130739922
#130737982
#130737702
#130735762
#130735722
#130735432
#130720092
#130719892
#130718822
#130718812
#130718342
#130718332
#130711372
#130711262
#130711222
#130711172
C2×#106222792
C11×#25642
#3495711