Finite Group Databasebeta

← #14920203

Subgroups — #14920203

Order 2816.

2982 conjugacy classes of subgroups.

The subgroup lattice has 1180 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#13074534C211yesmaximal, characteristic, complemented
4#13074503C211yesmaximal, characteristic, complemented
5#13074500C211yesmaximal, characteristic, complemented
6#13074465C212yesmaximal, complemented
7#13074461C212yesmaximal, complemented
8#13074428C211yesmaximal, characteristic, complemented
9#13074420C211yesmaximal, characteristic, complemented
10#13074390C212yesmaximal, complemented
11#13074359C211yesmaximal, characteristic, complemented
12#13074351C211yesmaximal, characteristic, complemented
13#13074329C212yesmaximal, complemented
14#13071880C211yesmaximal, characteristic, complemented
15#13071878C211yesmaximal, characteristic, complemented
16#13071859C212yesmaximal, complemented
17#13071853C212yesmaximal, complemented
18#13071834C211yesmaximal, characteristic, complemented
19#13071833C211yesmaximal, characteristic, complemented
20#13071137C212yesmaximal, complemented
21#13071117C212yesmaximal, complemented
22#13070996C211yesmaximal, characteristic, complemented
23C11×#2638C211yesmaximal, 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×D4×Dic11C2211yescharacteristic
32C2×#66983C2211yescharacteristic, complemented
33C2×C4×C22⋊D11C2211yescharacteristic
34C2×C4×C22⋊D11C2211yescharacteristic
35#10623158—28no—
36C4×D4×D11—28no—
37C2×#66948C2211yescharacteristic
38C2×#66947C2212yes—
39C2×#66947C2212yescomplemented
40C2×#66946C2212yes—
41C2×#66946C2211yescharacteristic
42C2×#66946C2212yescomplemented
43C2×#66945C2211yescharacteristic, complemented
44C2×C4⋊C4×D11C2211yescharacteristic
45C2×#66935C2212yes—
46C2×#66935C2212yes—
47C2×(C22⋊D11)⋊C4C2211yescharacteristic
48C2×(C22⋊D11)⋊C4C2211yescharacteristic
49C2×(C22⋊D11)⋊C4C2212yescomplemented
50C2×(C22⋊D11)⋊C4C2212yescomplemented
51C2×C22⋊C4×D11C2211yescharacteristic
52C2×C22⋊C4×D11C2211yescharacteristic
53C2×#66930C2212yescomplemented
54C2×C4×D44C2211yescharacteristic
55C2×C42×D11C2211yescharacteristic
56C11×#398C2211yescharacteristic, complemented
57C11×#397C2211yescharacteristic, complemented
58C11×#397C2212yescomplemented
59C11×#395C2211yescharacteristic, complemented
60C11×#394C2212yes—
61C11×#393C2211yescharacteristic, complemented
62C11×#387C2212yescomplemented
63C11×#385C2212yescomplemented
64C11×#381C2211yescharacteristic, complemented
65#10622844C2211yescharacteristic, complemented
66#10622842C2211yescharacteristic, complemented
67#10622836C2212yes—
68#10622826C2212yescomplemented
69#10622824C2211yescharacteristic, complemented
70#10622607C2212yescomplemented
71#10622606C2211yescharacteristic, complemented
72#10622604C2212yes—
73#10622604C2212yescomplemented
74#10622604C2211yescharacteristic, complemented
75#10622602C2212yes—
76#10622602C2212yescomplemented
77#10622599C2211yescharacteristic, complemented
78#10622593C2211yescharacteristic, complemented
79#10622593C2212yescomplemented
80#10622591C2212yescomplemented
81C4⋊C4×Dic11C2212yescomplemented
82#10622574C2212yescomplemented
83#10622573C2212yes—
84#10622573C2212yes—
85#10622573C2211yescharacteristic, complemented
86#10622572C2212yes—
87#10622572C2212yes—
88#10622572C2212yescomplemented
89#10622572C2212yescomplemented
90#10622568C2212yes—
91#10622568C2212yes—
92#10622565C2212yescomplemented
93#10622562C2211yescharacteristic, complemented
94#10622561C2212yescomplemented
95C22⋊C4×Dic11C2212yescomplemented
96#10622553C2212yescomplemented
97#10622290C2211yescharacteristic, complemented
98#10622289C2212yescomplemented
99#10622289C2212yescomplemented
100#10622288C2212yescomplemented
101#10622287C2212yescomplemented
102#10622285C2212yescomplemented
103#10622285C2212yescomplemented
104#10622285C2211yescharacteristic, complemented
105#10622284C2212yes—
106#10622284C2211yescharacteristic, complemented
107#10622283C2212yescomplemented
108#10622281C2212yes—
109#10622280C2211yescharacteristic
110#10622280C2211yescharacteristic
111#10622280C2212yescomplemented
112#10622279C2212yes—
113#10622279C2211yescharacteristic, complemented
114#10622279C2212yescomplemented
115#10622279C2211yescharacteristic, complemented
116#10622279C2212yescomplemented
117#10622279C2212yescomplemented
118#10622278C2212yes—
119#10622278C2212yes—
120#10622278C2212yescomplemented
121#10622277C2212yes—
122#10622272C2211yescharacteristic, complemented
123#10622270C2212yescomplemented
124#10622262C2212yescomplemented
125C24×D11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×Q8×C11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C22×C22⋊D11C2311yescharacteristic
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2312yes—
135C23×Dic11C2311yescharacteristic
136C23×Dic11C2311yescharacteristic
137C2×#4343—24no—
138C2×#4343—44no—
139C2×D4×D11—24no—
140C2×D4×D11—24no—
141C2×D4×D11—24no—
142C22×D44C2311yescharacteristic
143C22×D44C2312yes—
144C22×D44C2312yes—
145C22×D44C2312yes—
146C22×D44C2311yescharacteristic
147C22×C4×D11—24no—
148C22×C4×D11—44no—
149C22×C4×D11—44no—
150C22×C4×D11D418yescomplemented
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2312yes—
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2311yescharacteristic
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2311yescharacteristic
161C11×C22⋊Q8—24no—
162C4×D4×C11—24no—
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C4⋊C4C2312yes—
166C2×C11×C4⋊C4C2312yes—
167C2×C11×C4⋊C4C2312yes—
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2312yes—
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2312yes—
174C2×C42×C11C2311yescharacteristic
175C2×C22⋊Dic11C2311yescharacteristic
176C2×C22⋊Dic11C2311yescharacteristic
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179#66999—24no—
180D4×Dic11—24no—
181#66983—24no—
182C4×C22⋊D11—24no—
183C4×C22⋊D11—24no—
184C2×(C2×D11)⋊C4C2311yescharacteristic
185C2×(C2×D11)⋊C4C2311yescharacteristic
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)⋊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×C4⋊Dic11C2311yescharacteristic
206C2×C4⋊Dic11C2311yescharacteristic
207C2×C4⋊Dic11C2312yes—
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2311yescharacteristic
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2312yes—
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2312yes—
222#66948—24no—
223#66947—28no—
224#66947—28no—
225#66946—24no—
226#66946—28no—
227#66946—44no—
228#66945—24no—
229C4⋊C4×D11—24no—
230#66935—28no—
231#66935—28no—
232(C22⋊D11)⋊C4—24no—
233(C22⋊D11)⋊C4—28no—
234(C22⋊D11)⋊C4—24no—
235(C22⋊D11)⋊C4—44no—
236C22⋊C4×D11—24no—
237C22⋊C4×D11—24no—
238#66930—44no—
239C4×D44—24no—
240C42×D11—24no—
241C11×#95C2312yes—
242C11×#95C2312yes—
243C11×#95C2311yescharacteristic
244C11×#95C2312yes—
245C11×#95C2312yes—
246C11×#95C2311yescharacteristic
247C11×#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2311yescharacteristic
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259#34562—111nomaximal, Sylow
260C24×C11C2411yescharacteristic
261C24×C11C2411yescharacteristic
262C23×D11—22no—
263C23×D11—22no—
264C23×D11—22no—
265C23×D11—22no—
266C23×D11—42no—
267C23×D11—42no—
268C23×D11—42no—
269C23×D11—42no—
270C23×D11C2×D414yes—
271C23×D11#4114yescomplemented
272C23×D11C2412yes—
273C23×D11C2411yescharacteristic
274C23×D11C2411yescharacteristic
275C23×D11C2411yescharacteristic
276C2×Q8×C11—22no—
277C2×Q8×C11—42no—
278C2×D4×C11—22no—
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C22×C4×C11—22no—
282C22×C4×C11—42no—
283C22×C4×C11—42no—
284C22×C4×C11C2×D414yes—
285C22×C4×C11C2412yes—
286C22×C4×C11C2412yes—
287C22×C4×C11C2412yes—
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2412yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C2×C22⋊D11—22no—
295C2×C22⋊D11—22no—
296C2×C22⋊D11—22no—
297C2×C22⋊D11—24no—
298C2×C22⋊D11—22no—
299C2×C22⋊D11—24no—
300C2×C22⋊D11—22no—
301C2×C22⋊D11—22no—
302C2×C22⋊D11—42no—
303C2×C22⋊D11—42no—
304C2×C22⋊D11—42no—
305C2×C22⋊D11—42no—
306C22×Dic11—24no—
307C22×Dic11—22no—
308C22×Dic11—24no—
309C22×Dic11C2×D414yes—
310C22×Dic11C2412yes—
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2412yes—
313C22×Dic11C2412yes—
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318#4343—416no—
319D4×D11—232no—
320C2×D44—22no—
321C2×D44—24no—
322C2×D44—24no—
323C2×D44—22no—
324C2×D44—24no—
325C2×D44—24no—
326C2×D44—24no—
327C2×D44—22no—
328C2×D44—22no—
329C2×D44—42no—
330C2×D44—42no—
331C2×D44—42no—
332C2×D44—42no—
333C2×D44—42no—
334C2×C4×D11—24no—
335C2×C4×D11—24no—
336C2×C4×D11—22no—
337C2×C4×D11—24no—
338C2×C4×D11—24no—
339C2×C4×D11—24no—
340C2×C4×D11—24no—
341C2×C4×D11—22no—
342C2×C4×D11—22no—
343C2×C4×D11—22no—
344C2×C4×D11—22no—
345C2×C4×D11—22no—
346C2×C4×D11—42no—
347C2×C4×D11—42no—
348C2×C4×D11—42no—
349C2×C4×D11—42no—
350C2×C4×D11—42no—
351C2×C4×D11—416no—
352C2×C4×D11—416no—
353C2×C4×D11C2×D414yes—
354C2×C4×D11C2×D414yes—
355C2×C4×D11C2×D414yes—
356C2×C4×D11C2×D414yes—
357C2×C4×D11#4114yescomplemented
358C11×C4⋊C4—22no—
359C11×C4⋊C4—22no—
360C11×C4⋊C4—24no—
361C11×C4⋊C4—24no—
362C11×C4⋊C4—42no—
363C11×C22⋊C4—22no—
364C11×C22⋊C4—24no—
365C11×C22⋊C4—24no—
366C11×C22⋊C4—22no—
367C11×C22⋊C4—42no—
368C11×C22⋊C4—42no—
369C42×C11—22no—
370C22⋊Dic11—22no—
371C22⋊Dic11—22no—
372C22⋊Dic11—42no—
373C22⋊Dic11—42no—
374(C2×D11)⋊C4—22no—
375(C2×D11)⋊C4—24no—
376(C2×D11)⋊C4—24no—
377(C2×D11)⋊C4—22no—
378(C2×D11)⋊C4—22no—
379(C2×D11)⋊C4—24no—
380(C2×D11)⋊C4—24no—
381(C2×D11)⋊C4—24no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—24no—
384(C2×D11)⋊C4—22no—
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—42no—
388(C2×D11)⋊C4—42no—
389(C2×D11)⋊C4—42no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4—42no—
393(C2×D11)⋊C4—42no—
394(C2×D11)⋊C4—42no—
395C4⋊Dic11—22no—
396C4⋊Dic11—22no—
397C4⋊Dic11—42no—
398Dic11⋊C4—22no—
399Dic11⋊C4—24no—
400Dic11⋊C4—24no—
401Dic11⋊C4—22no—
402Dic11⋊C4—42no—
403Dic11⋊C4—42no—
404Dic11⋊C4—42no—
405Dic11⋊C4—42no—
406C4×Dic11—22no—
407C4×Dic11—22no—
408C4×Dic11—24no—
409C4×Dic11—24no—
410C4×Dic11—24no—
411C4×Dic11—22no—
412C2×#525—111no—
413C22×C4×D4—111no—
414#2638—111no—
415#2638D1111yescharacteristic, complemented
416#2635—111no—
417#2635—111no—
418#2630—112no—
419#2630—112no—
420#2627—111no—
421#2626—111no—
422#2622—112no—
423#2618—111no—
424#2617—111no—
425#2613—112no—
426#2395—111no—
427#2395—111no—
428#2392—112no—
429#2392—112no—
430#2388—111no—
431#2388—111no—
432C4×#123—112no—
433C4×#120—112no—
434#2280—111no—
435C23×C11—21no—
436C23×C11—21no—
437C23×C11—21no—
438C23×C11—21no—
439C23×C11—22no—
440C23×C11—22no—
441C23×C11—22no—
442C23×C11—22no—
443C23×C11C22×D412yes—
444C23×C11C2×#4112yes—
445C23×C11C2511yescharacteristic
446C22×D11—22no—
447C22×D11—22no—
448C22×D11—21no—
449C22×D11—21no—
450C22×D11—21no—
451C22×D11—21no—
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—22no—
456C22×D11—28no—
457C22×D11—28no—
458C22×D11—22no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—44no—
466C22×D11—44no—
467C22×D11—48no—
468C22×D11—44no—
469C22×D11—44no—
470C22×D11—48no—
471C22×D11—48no—
472C22×D11—48no—
473C22×D11C22×D412yes—
474C22×D11C22×D412yes—
475C22×D11C2×#4112yes—
476C22×D11C2×#4112yes—
477C22×D11C2×#4112yes—
478Q8×C11—44no—
479D4×C11—28no—
480C2×C4×C11—21no—
481C2×C4×C11—21no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—21no—
485C2×C4×C11—22no—
486C2×C4×C11—21no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—44no—
501C2×C4×C11—44no—
502C2×C4×C11C22×D412yes—
503C2×C4×C11C22×D412yes—
504C2×C4×C11C2×#4112yes—
505C22⋊D11—28no—
506C22⋊D11—28no—
507C22⋊D11—48no—
508C22⋊D11—48no—
509C2×Dic11—21no—
510C2×Dic11—21no—
511C2×Dic11—22no—
512C2×Dic11—28no—
513C2×Dic11—21no—
514C2×Dic11—22no—
515C2×Dic11—21no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—44no—
527C2×Dic11C22×D412yes—
528C2×Dic11C22×D412yes—
529C2×Dic11C2×#4112yes—
530C2×Dic11H(5,𝔽2)14yes—
531D44—28no—
532D44—44no—
533D44—48no—
534D44—48no—
535D44—48no—
536C4×D11—28no—
537C4×D11—28no—
538C4×D11—28no—
539C4×D11—44no—
540C4×D11—44no—
541C4×D11—44no—
542C4×D11—44no—
543C4×D11—44no—
544C4×D11—44no—
545C4×D11—48no—
546C22×#41—111no—
547C23×D4—111no—
548C24×C4—111no—
549C24×C4—111no—
550#525—228no—
551C2×#123—112no—
552C2×#123—112no—
553C2×C22⋊Q8—111no—
554C2×C22⋊Q8C2×D1111yescharacteristic, complemented
555C2×#121—111no—
556C2×#121—111no—
557C2×#120—112no—
558C2×#120—112no—
559C2×C4×D4—111no—
560C2×C4×D4—111no—
561C2×C4×D4—111no—
562C2×C4×D4—111no—
563C2×C4×D4—112no—
564C2×C4×D4—112no—
565C2×C4×D4—111no—
566C2×C4×D4—111no—
567C2×C4×D4—112no—
568C2×C4×D4—112no—
569C2×C4×D4—111no—
570C2×C4×D4—228no—
571C2×C4×D4C2×D1111yescharacteristic
572C2×#117—111no—
573C2×#117—112no—
574C22×C4⋊C4—111no—
575C22×C22⋊C4—111no—
576C22×C22⋊C4—111no—
577C22×C42—111no—
578#400—111no—
579#400—111no—
580#399—111no—
581#399—111no—
582#398—111no—
583#398—112no—
584#398—112no—
585#398C2×D1111yescharacteristic, complemented
586#397—111no—
587#397—112no—
588#397—112no—
589#397—112no—
590#397C2×D1111yescharacteristic, complemented
591#397C2×D1112yescomplemented
592#396—112no—
593#396—112no—
594#396—112no—
595#396—112no—
596#395—111no—
597#395C2×D1111yescharacteristic, complemented
598#394—112no—
599#394—111no—
600#394—112no—
601#394—112no—
602#394—112no—
603#394—112no—
604#394—112no—
605#394—112no—
606#394—112no—
607#394—111no—
608#394—112no—
609#394C2×D1112yes—
610#393—111no—
611#393C2×D1111yescharacteristic, complemented
612#392—112no—
613#392—112no—
614#392—112no—
615#392—111no—
616#392—112no—
617#392—111no—
618#388—112no—
619#388—112no—
620#387—112no—
621#387C2×D1112yescomplemented
622#386—112no—
623#386—112no—
624#386—112no—
625#386—112no—
626#385—112no—
627#385—112no—
628#385—112no—
629#385C2×D1112yescomplemented
630#381—111no—
631#381—112no—
632#381C2×D1111yescharacteristic, complemented
633#380—111no—
634#380—111no—
635#380—112no—
636#379—112no—
637#379—112no—
638C4×C4⋊C4—112no—
639C4×C4⋊C4—112no—
640C4×C22⋊C4—112no—
641C4×C22⋊C4—112no—
642C4×C22⋊C4—112no—
643C4×C22⋊C4—112no—
644C4×C22⋊C4—111no—
645C4×C22⋊C4—111no—
646C4×C22⋊C4—112no—
647C22×C11—22no—
648C22×C11—22no—
649C22×C11—22no—
650C22×C11—22no—
651C22×C11—24no—
652C22×C11—41no—
653C22×C11—41no—
654C22×C11—42no—
655C22×C11—42no—
656C22×C11—42no—
657C22×C11C23×D411yescharacteristic
658C22×C11C22×#4111yescharacteristic
659C22×C11C22×#4111yescharacteristic
660C22×C11C2×H(5,𝔽2)12yes—
661C22×C11#58512yes—
662C2×D11—22no—
663C2×D11—22no—
664C2×D11—24no—
665C2×D11—24no—
666C2×D11—22no—
667C2×D11—22no—
668C2×D11—22no—
669C2×D11—22no—
670C2×D11—24no—
671C2×D11—416no—
672C2×D11—416no—
673C2×D11—41no—
674C2×D11—41no—
675C2×D11—42no—
676C2×D11—42no—
677C2×D11—42no—
678C2×D11—42no—
679C2×D11—42no—
680C2×D11—42no—
681C2×D11—42no—
682C2×D11—42no—
683C2×D11—42no—
684C2×D11—42no—
685C2×D11#52514yes—
686C4×C11—22no—
687C4×C11—22no—
688C4×C11—22no—
689C4×C11—42no—
690C4×C11—41no—
691C4×C11—42no—
692C4×C11—41no—
693C4×C11—42no—
694C4×C11—42no—
695Dic11—22no—
696Dic11—22no—
697Dic11—41no—
698Dic11—41no—
699Dic11—42no—
700Dic11—42no—
701Dic11—42no—
702Dic11#53414yes—
703C25—111no—
704C25—111no—
705C2×#41—224no—
706C2×#41—444no—
707C22×Q8C22×D1111yescharacteristic
708C22×D4—111no—
709C22×D4—111no—
710C22×D4—112no—
711C22×D4—112no—
712C22×D4—111no—
713C22×D4—112no—
714C22×D4—112no—
715C22×D4—112no—
716C22×D4—111no—
717C22×D4—224no—
718C22×D4—224no—
719C22×D4—224no—
720C22×D4C22×D1111yescharacteristic
721C23×C4—111no—
722C23×C4—111no—
723C23×C4—111no—
724C23×C4—111no—
725C23×C4—118no—
726C23×C4—111no—
727C23×C4—111no—
728C23×C4—111no—
729C23×C4—111no—
730C23×C4—112no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—224no—
735C23×C4—444no—
736C23×C4—444no—
737C23×C4C22×D1111yescharacteristic
738C23×C4C22×D1111yescharacteristic
739#123—228no—
740#123—228no—
741C22⋊Q8—24no—
742C22⋊Q8—224no—
743#121—224no—
744#121—224no—
745#120—228no—
746#120—228no—
747C4×D4—24no—
748C4×D4—224no—
749C4×D4—224no—
750C4×D4—224no—
751C4×D4—228no—
752C4×D4—224no—
753C4×D4—228no—
754C4×D4—224no—
755C4×D4—224no—
756C4×D4—224no—
757C4×D4—444no—
758C4×D4—444no—
759#117—224no—
760#117—444no—
761C2×C4⋊C4—111no—
762C2×C4⋊C4—111no—
763C2×C4⋊C4—111no—
764C2×C4⋊C4—111no—
765C2×C4⋊C4—112no—
766C2×C4⋊C4—112no—
767C2×C4⋊C4—112no—
768C2×C4⋊C4—112no—
769C2×C4⋊C4—112no—
770C2×C4⋊C4—112no—
771C2×C4⋊C4—112no—
772C2×C4⋊C4—224no—
773C2×C4⋊C4C22×D1111yescharacteristic
774C2×C4⋊C4C22×D1111yescharacteristic
775C2×C4⋊C4C22×D1112yes—
776C2×C4⋊C4C22×D1112yes—
777C2×C4⋊C4C22×D1112yes—
778C2×C22⋊C4—111no—
779C2×C22⋊C4—111no—
780C2×C22⋊C4—111no—
781C2×C22⋊C4—111no—
782C2×C22⋊C4—111no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—112no—
786C2×C22⋊C4—112no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
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—224no—
804C2×C22⋊C4—224no—
805C2×C22⋊C4C22×D1111yescharacteristic
806C2×C22⋊C4C22×D1111yescharacteristic
807C2×C22⋊C4C22×D1112yes—
808C2×C22⋊C4C22×D1112yes—
809C2×C22⋊C4C22×D1112yes—
810C2×C22⋊C4C22×D1112yes—
811C2×C42—112no—
812C2×C42—112no—
813C2×C42—112no—
814C2×C42—111no—
815C2×C42—111no—
816C2×C42—111no—
817C2×C42—224no—
818C2×C42C22×D1111yescharacteristic
819#95—112no—
820#95—111no—
821#95—111no—
822#95—112no—
823#95—112no—
824#95—112no—
825#95—112no—
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95C22×D1112yes—
831#95C22×D1111yescharacteristic
832#95C22×D1111yescharacteristic
833#95C22×D1112yes—
834#95C22×D1112yes—
835#95C22×D1112yes—
836#95C22×D1112yes—
837C2×C11—42no—
838C2×C11—42no—
839C2×C11C2×#52511yescharacteristic
840C2×C11C2×#53411yescharacteristic
841C2×C11#344911yescharacteristic
842C2×C11#345912yes—
843C2×C11#346012yes—
844D11—24no—
845D11—42no—
846D11—42no—
847D11—82no—
848C24—111no—
849C24—111no—
850C24—111no—
851C24—114no—
852C24—114no—
853C24—112no—
854C24—222no—
855C24—222no—
856C24—222no—
857C24—222no—
858C24—442no—
859C24—442no—
860C24—442no—
861C24—442no—
862C24C23×D1111yescharacteristic
863C24C23×D1111yescharacteristic
864#41—4416no—
865C2×Q8—22no—
866C2×Q8—42no—
867C2×D4—22no—
868C2×D4—22no—
869C2×D4—22no—
870C2×D4—222no—
871C2×D4—222no—
872C2×D4—224no—
873C2×D4—224no—
874C2×D4—224no—
875C2×D4—224no—
876C2×D4—224no—
877C2×D4—222no—
878C2×D4—222no—
879C2×D4—2232no—
880C2×D4—222no—
881C2×D4—222no—
882C2×D4—222no—
883C2×D4—222no—
884C2×D4—224no—
885C2×D4—224no—
886C2×D4—222no—
887C2×D4—222no—
888C2×D4—442no—
889C2×D4—442no—
890C2×D4—442no—
891C2×D4—442no—
892C2×D4—442no—
893C2×D4—442no—
894C2×D4—442no—
895C2×D4—442no—
896C2×D4—442no—
897C22×C4—22no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—111no—
901C22×C4—114no—
902C22×C4—111no—
903C22×C4—111no—
904C22×C4—114no—
905C22×C4—114no—
906C22×C4—114no—
907C22×C4—114no—
908C22×C4—114no—
909C22×C4—112no—
910C22×C4—111no—
911C22×C4—112no—
912C22×C4—112no—
913C22×C4—111no—
914C22×C4—224no—
915C22×C4—224no—
916C22×C4—222no—
917C22×C4—224no—
918C22×C4—224no—
919C22×C4—224no—
920C22×C4—224no—
921C22×C4—222no—
922C22×C4—222no—
923C22×C4—222no—
924C22×C4—222no—
925C22×C4—224no—
926C22×C4—222no—
927C22×C4—224no—
928C22×C4—222no—
929C22×C4—442no—
930C22×C4—442no—
931C22×C4—442no—
932C22×C4—442no—
933C22×C4—442no—
934C22×C4—4416no—
935C22×C4—4416no—
936C22×C4D4×D1114yes—
937C22×C4C23×D1112yes—
938C22×C4C23×D1112yes—
939C22×C4C23×D1111yescharacteristic
940C22×C4C23×D1112yes—
941C22×C4C23×D1111yescharacteristic
942C22×C4C23×D1112yes—
943C22×C4C23×D1111yescharacteristic
944C22×C4C23×D1111yescharacteristic
945C22×C4C23×D1111yescharacteristic
946C4⋊C4—22no—
947C4⋊C4—22no—
948C4⋊C4—24no—
949C4⋊C4—24no—
950C4⋊C4—42no—
951C4⋊C4—222no—
952C4⋊C4—222no—
953C4⋊C4—224no—
954C4⋊C4—224no—
955C4⋊C4—222no—
956C4⋊C4—222no—
957C4⋊C4—442no—
958C4⋊C4—442no—
959C4⋊C4—442no—
960C4⋊C4—442no—
961C4⋊C4—442no—
962C22⋊C4—22no—
963C22⋊C4—24no—
964C22⋊C4—24no—
965C22⋊C4—22no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—222no—
969C22⋊C4—224no—
970C22⋊C4—224no—
971C22⋊C4—222no—
972C22⋊C4—222no—
973C22⋊C4—224no—
974C22⋊C4—224no—
975C22⋊C4—224no—
976C22⋊C4—224no—
977C22⋊C4—224no—
978C22⋊C4—222no—
979C22⋊C4—222no—
980C22⋊C4—222no—
981C22⋊C4—224no—
982C22⋊C4—224no—
983C22⋊C4—442no—
984C22⋊C4—442no—
985C22⋊C4—442no—
986C22⋊C4—442no—
987C22⋊C4—442no—
988C22⋊C4—442no—
989C22⋊C4—442no—
990C22⋊C4—442no—
991C22⋊C4—442no—
992C22⋊C4—442no—
993C42—22no—
994C42—222no—
995C42—222no—
996C42—224no—
997C42—224no—
998C42—224no—
999C42—222no—
1000C11#3456211yescharacteristic, complemented, Sylow
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—112no—
1010C23—112no—
1011C23—112no—
1012C23—112no—
1013C23—112no—
1014C23—228no—
1015C23—228no—
1016C23—222no—
1017C23—222no—
1018C23—221no—
1019C23—221no—
1020C23—221no—
1021C23—221no—
1022C23—222no—
1023C23—222no—
1024C23—222no—
1025C23—222no—
1026C23—222no—
1027C23—222no—
1028C23—222no—
1029C23—222no—
1030C23—222no—
1031C23—222no—
1032C23—222no—
1033C23—444no—
1034C23—444no—
1035C23—448no—
1036C23—444no—
1037C23—444no—
1038C23—448no—
1039C23—448no—
1040C23—448no—
1041C23C2×D4×D1112yes—
1042C23#41×D1112yes—
1043C23C24×D1111yescharacteristic
1044Q8—44no—
1045D4—28no—
1046D4—228no—
1047D4—228no—
1048D4—228no—
1049D4—444no—
1050D4—448no—
1051D4—448no—
1052D4—448no—
1053D4—448no—
1054D4—448no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—21no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—44no—
1076C2×C4—44no—
1077C2×C4—112no—
1078C2×C4—114no—
1079C2×C4—112no—
1080C2×C4—112no—
1081C2×C4—228no—
1082C2×C4—228no—
1083C2×C4—228no—
1084C2×C4—228no—
1085C2×C4—221no—
1086C2×C4—221no—
1087C2×C4—222no—
1088C2×C4—221no—
1089C2×C4—222no—
1090C2×C4—221no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—222no—
1099C2×C4—222no—
1100C2×C4—222no—
1101C2×C4—444no—
1102C2×C4—444no—
1103C2×C4—444no—
1104C2×C4—444no—
1105C2×C4—448no—
1106C2×C4—444no—
1107C2×C4—444no—
1108C2×C4—444no—
1109C2×C4C2×D4×D1112yes—
1110C2×C4C2×D4×D1112yes—
1111C2×C4#41×D1112yes—
1112C22—22no—
1113C22—22no—
1114C22—24no—
1115C22—22no—
1116C22—22no—
1117C22—41no—
1118C22—41no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—114no—
1123C22—222no—
1124C22—222no—
1125C22—224no—
1126C22—224no—
1127C22—222no—
1128C22—222no—
1129C22—224no—
1130C22—222no—
1131C22—222no—
1132C22—4416no—
1133C22—4416no—
1134C22—441no—
1135C22—441no—
1136C22—442no—
1137C22—442no—
1138C22—442no—
1139C22—442no—
1140C22—442no—
1141C22—442no—
1142C22—442no—
1143C22—442no—
1144C22—442no—
1145C22—442no—
1146C22C22×D4×D1111yescharacteristic
1147C22C2×#41×D1111yescharacteristic
1148C22C2×#41×D1111yescharacteristic
1149C22D11×H(5,𝔽2)12yes—
1150C22#1062345712yes—
1151C4—22no—
1152C4—22no—
1153C4—22no—
1154C4—41no—
1155C4—42no—
1156C4—41no—
1157C4—42no—
1158C4—42no—
1159C4—42no—
1160C4—114no—
1161C4—222no—
1162C4—222no—
1163C4—441no—
1164C4—441no—
1165C4—442no—
1166C4—442no—
1167C4—442no—
1168C2—42no—
1169C2—42no—
1170C2—224no—
1171C2—442no—
1172C2—442no—
1173C2—882no—
1174C2D11×#52511yescharacteristic
1175C2D11×#53411yescharacteristic
1176C2#1308194811yescharacteristic
1177C2#1308202412yes—
1178C2#1308203612yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2638C2
hypercenter#2638D11
hypocenterC11#34562
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2638

Complements

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

NH ≅ G/Ntype
1. C2×#10623158C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13074534C2semidirect
4. #13074503C2semidirect
5. #13074500C2semidirect
6. #13074465C2semidirect
7. #13074461C2semidirect
8. #13074428C2semidirect
9. #13074420C2semidirect
10. #13074390C2semidirect
11. #13074359C2semidirect
12. #13074351C2semidirect
13. #13074329C2semidirect
14. #13071880C2semidirect
15. #13071878C2semidirect
16. #13071859C2semidirect
17. #13071853C2semidirect
18. #13071834C2semidirect
19. #13071833C2semidirect
20. #13071137C2semidirect
21. #13071117C2semidirect
22. #13070996C2semidirect
23. C11×#2638C2semidirect
24. C22×#4343C22semidirect
28. C2×C11×C22⋊Q8C22semidirect
32. C2×#66983C22semidirect
39. C2×#66947C22semidirect
42. C2×#66946C22semidirect
43. C2×#66945C22semidirect
49. C2×(C22⋊D11)⋊C4C22semidirect
50. C2×(C22⋊D11)⋊C4C22semidirect
53. C2×#66930C22semidirect
56. C11×#398C22semidirect
57. C11×#397C22semidirect
58. C11×#397C22semidirect
59. C11×#395C22semidirect
61. C11×#393C22semidirect
62. C11×#387C22semidirect
63. C11×#385C22semidirect
64. C11×#381C22semidirect
65. #10622844C22semidirect
66. #10622842C22semidirect
68. #10622826C22semidirect
69. #10622824C22semidirect
70. #10622607C22semidirect
71. #10622606C22semidirect
73. #10622604C22semidirect
74. #10622604C22semidirect
76. #10622602C22semidirect
77. #10622599C22semidirect
78. #10622593C22semidirect
79. #10622593C22semidirect
80. #10622591C22semidirect
81. C4⋊C4×Dic11C22semidirect
82. #10622574C22semidirect
85. #10622573C22semidirect
88. #10622572C22semidirect
89. #10622572C22semidirect
92. #10622565C22semidirect
93. #10622562C22semidirect
94. #10622561C22semidirect
95. C22⋊C4×Dic11C22semidirect
96. #10622553C22semidirect
97. #10622290C22semidirect
98. #10622289C22semidirect
99. #10622289C22semidirect
100. #10622288C22semidirect
101. #10622287C22semidirect
102. #10622285C22semidirect
103. #10622285C22semidirect
104. #10622285C22semidirect
106. #10622284C22semidirect
107. #10622283C22semidirect
111. #10622280C22semidirect
113. #10622279C22semidirect
114. #10622279C22semidirect
115. #10622279C22semidirect
116. #10622279C22semidirect
117. #10622279C22semidirect
120. #10622278C22semidirect
122. #10622272C22semidirect
123. #10622270C22semidirect
124. #10622262C22semidirect
150. C22×C4×D11D4semidirect
271. C23×D11#41semidirect
357. C2×C4×D11#41semidirect
415. #2638D11semidirect
554. C2×C22⋊Q8C2×D11semidirect
585. #398C2×D11semidirect
590. #397C2×D11semidirect
591. #397C2×D11semidirect
597. #395C2×D11semidirect
611. #393C2×D11semidirect
621. #387C2×D11semidirect
629. #385C2×D11semidirect
632. #381C2×D11semidirect
1000. C11#34562semidirect

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
#130745342
#130745032
#130745002
#130744652
#130744612
#130744282
#130744202
#130743902
#130743592
#130743512
#130743292
#130718802
#130718782
#130718592
#130718532
#130718342
#130718332
#130711372
#130711172
#130709962
C11×#26382
#3456211