Finite Group Databasebeta

← #14960709

Subgroups — #14960709

Order 2816.

3034 conjugacy classes of subgroups.

The subgroup lattice has 1310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623184C211yesmaximal, characteristic, complemented
2C22×#66937C211yesmaximal, characteristic, complemented
3#13076911C211yesmaximal, characteristic, complemented
4#13076907C211yesmaximal, characteristic, complemented
5#13075226C212yesmaximal, complemented
6#13075222C212yesmaximal, complemented
7#13075200C212yesmaximal, complemented
8#13075198C212yesmaximal, complemented
9#13074979C212yesmaximal, complemented
10#13074976C212yesmaximal, complemented
11#13074947C212yesmaximal, complemented
12#13074938C212yesmaximal, complemented
13#13074331C211yesmaximal, characteristic, complemented
14#13074330C211yesmaximal, characteristic, complemented
15#13072896C211yesmaximal, characteristic, complemented
16#13072024C211yesmaximal, characteristic, complemented
17#13072017C211yesmaximal, characteristic, complemented
18#13072001C211yesmaximal, characteristic, complemented
19#13071942C211yesmaximal, characteristic, complemented
20#13071941C211yesmaximal, characteristic, complemented
21#13071927C211yesmaximal, characteristic, complemented
22#13071196C211yesmaximal, characteristic, complemented
23C11×#2411C211yesmaximal, characteristic, complemented
24C23×C22⋊D11C2211yescharacteristic
25C23×C22⋊D11C2211yescharacteristic, complemented
26C22×D4×D11C2211yescharacteristic
27C23×D44C2211yescharacteristic
28C23×C4×D11C2211yescharacteristic, complemented
29C2×C11×#123C2211yescharacteristic
30C2×C11×#120C2211yescharacteristic
31C2×C11×#117C2211yescharacteristic, complemented
32C22×C11×C22⋊C4C2211yescharacteristic, complemented
33C2×#67006C2211yescharacteristic
34C2×#66990C2211yescharacteristic
35C2×#66990C2212yescomplemented
36C2×#66988C2211yescharacteristic
37C2×#66982C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C2×#66979C2211yescharacteristic, complemented
40C22×Dic11⋊C4C2211yescharacteristic, complemented
41#10623184—28no—
42C2×#66948C2211yescharacteristic, complemented
43C2×#66948C2211yescharacteristic, complemented
44C2×#66947C2211yescharacteristic, complemented
45C2×#66947C2211yescharacteristic, complemented
46C2×#66947C2212yescomplemented
47C2×#66939C2211yescharacteristic
48C2×#66937—28no—
49C2×#66937C2212yes—
50C2×#66937C2212yes—
51C2×#66937C2212yescomplemented
52C2×#66937C2212yescomplemented
53C2×#66937C2211yescharacteristic, complemented
54C2×#66937C2211yescharacteristic, complemented
55C2×#66936C2212yescomplemented
56C2×#66936C2212yescomplemented
57C2×#66935C2211yescharacteristic
58C2×#66935C2211yescharacteristic, complemented
59C2×#66935C2211yescharacteristic, complemented
60C2×C22⋊C4×D11C2211yescharacteristic
61C11×#396C2212yescomplemented
62C11×#394C2212yescomplemented
63C11×#390C2212yescomplemented
64C11×#388C2212yescomplemented
65C11×#386C2211yescharacteristic
66C11×#385C2211yescharacteristic, complemented
67C11×#379C2211yescharacteristic, complemented
68#10622860C2211yescharacteristic, complemented
69#10622836C2212yescomplemented
70#10622836C2212yescomplemented
71#10622836C2212yescomplemented
72#10622833C2211yescharacteristic
73#10622826C2211yescharacteristic
74#10622823C2211yescharacteristic, complemented
75#10622607C2212yescomplemented
76#10622606C2212yescomplemented
77#10622602C2212yescomplemented
78#10622602C2212yescomplemented
79#10622601C2212yescomplemented
80#10622601C2212yescomplemented
81#10622597C2212yescomplemented
82#10622596C2212yescomplemented
83#10622585C2212yescomplemented
84#10622574C2212yescomplemented
85#10622574C2212yescomplemented
86#10622574C2212yescomplemented
87#10622574C2212yescomplemented
88#10622574C2212yescomplemented
89#10622573C2212yescomplemented
90#10622573C2212yescomplemented
91#10622573C2212yescomplemented
92#10622572C2212yescomplemented
93#10622572C2212yescomplemented
94#10622572C2212yescomplemented
95#10622571C2211yescharacteristic
96#10622570C2212yescomplemented
97#10622569C2212yescomplemented
98#10622569C2212yescomplemented
99#10622569C2212yescomplemented
100#10622568C2211yescharacteristic
101#10622568C2211yescharacteristic
102#10622568C2212yescomplemented
103#10622568C2211yescharacteristic, complemented
104#10622568C2211yescharacteristic, complemented
105#10622563C2211yescharacteristic, complemented
106#10622561C2212yescomplemented
107#10622561C2212yescomplemented
108#10622559C2211yescharacteristic, complemented
109#10622558C2212yescomplemented
110#10622558C2212yescomplemented
111#10622556C2211yescharacteristic, complemented
112#10622556C2211yescharacteristic, complemented
113#10622553C2212yescomplemented
114#10622552C2212yescomplemented
115#10622552C2212yescomplemented
116#10622541C2212yescomplemented
117#10622288C2212yescomplemented
118#10622285C2212yescomplemented
119#10622281C2212yescomplemented
120#10622281C2212yescomplemented
121#10622278C2212yescomplemented
122#10622277C2212yescomplemented
123#10622277C2212yescomplemented
124#10622277C2212yescomplemented
125C25×C11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C24×D11C2311yescharacteristic
128C24×D11C2311yescharacteristic
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2312yes—
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2311yescharacteristic
133C22×C22⋊D11—24no—
134C22×C22⋊D11—24no—
135C22×C22⋊D11—44no—
136C22×C22⋊D11—42no—
137C22×C22⋊D11—42no—
138C22×C22⋊D11C2311yescharacteristic
139C22×C22⋊D11C2312yes—
140C22×C22⋊D11C2312yes—
141C22×C22⋊D11C2311yescharacteristic
142C22×C22⋊D11C2311yescharacteristic
143C22×C22⋊D11C2312yes—
144C22×C22⋊D11C2312yes—
145C22×C22⋊D11C2311yescharacteristic
146C22×C22⋊D11C2312yes—
147C23×Dic11C2311yescharacteristic
148C23×Dic11C2311yescharacteristic
149C2×D4×D11—24no—
150C2×D4×D11—42no—
151C2×D4×D11—42no—
152C22×D44—42no—
153C22×D44—42no—
154C22×D44D418yescomplemented
155C22×D44C2311yescharacteristic
156C22×D44C2311yescharacteristic
157C22×D44C2311yescharacteristic
158C22×D44C2311yescharacteristic
159C22×D44C2311yescharacteristic
160C22×D44C2311yescharacteristic
161C22×D44C2311yescharacteristic
162C22×C4×D11—24no—
163C22×C4×D11—44no—
164C22×C4×D11C2312yes—
165C22×C4×D11C2312yes—
166C22×C4×D11C2311yescharacteristic
167C22×C4×D11C2311yescharacteristic
168C22×C4×D11C2311yescharacteristic
169C11×#123—24no—
170C11×#120—42no—
171C11×#117—42no—
172C2×C11×C4⋊C4C2311yescharacteristic
173C2×C11×C4⋊C4C2311yescharacteristic
174C2×C11×C4⋊C4C2312yes—
175C2×C11×C4⋊C4C2312yes—
176C2×C11×C22⋊C4—24no—
177C2×C11×C22⋊C4C2311yescharacteristic
178C2×C11×C22⋊C4C2311yescharacteristic
179C2×C11×C22⋊C4C2311yescharacteristic
180C2×C11×C22⋊C4C2312yes—
181C2×C11×C22⋊C4C2312yes—
182C2×C11×C22⋊C4C2311yescharacteristic
183C2×C11×C22⋊C4C2311yescharacteristic
184C2×C11×C22⋊C4C2312yes—
185C2×C11×C22⋊C4C2312yes—
186C2×C11×C22⋊C4C2312yes—
187C2×C11×C22⋊C4C2312yes—
188C2×C42×C11C2312yes—
189#67006—42no—
190C2×C22⋊Dic11C2311yescharacteristic
191C2×C22⋊Dic11C2312yes—
192C2×C22⋊Dic11C2311yescharacteristic
193C2×C22⋊Dic11C2311yescharacteristic
194C2×C22⋊Dic11C2312yes—
195C2×C22⋊Dic11C2312yes—
196C2×C22⋊Dic11C2312yes—
197C2×C22⋊Dic11C2312yes—
198#66990—24no—
199#66990—44no—
200#66988—42no—
201#66982—24no—
202C2×(C2×D11)⋊C4—24no—
203C2×(C2×D11)⋊C4C2311yescharacteristic
204C2×(C2×D11)⋊C4C2311yescharacteristic
205C2×(C2×D11)⋊C4C2311yescharacteristic
206C2×(C2×D11)⋊C4C2311yescharacteristic
207C2×(C2×D11)⋊C4C2311yescharacteristic
208C2×(C2×D11)⋊C4C2311yescharacteristic
209C2×(C2×D11)⋊C4C2312yes—
210C2×(C2×D11)⋊C4C2312yes—
211C2×(C2×D11)⋊C4C2311yescharacteristic
212C2×(C2×D11)⋊C4C2311yescharacteristic
213C2×(C2×D11)⋊C4C2312yes—
214C2×(C2×D11)⋊C4C2312yes—
215C2×(C2×D11)⋊C4C2312yes—
216C2×(C2×D11)⋊C4C2312yes—
217C2×(C2×D11)⋊C4C2312yes—
218C2×(C2×D11)⋊C4C2312yes—
219C2×(C2×D11)⋊C4C2312yes—
220C2×(C2×D11)⋊C4C2312yes—
221C2×(C2×D11)⋊C4C2312yes—
222C2×(C2×D11)⋊C4C2312yes—
223C2×(C2×D11)⋊C4C2312yes—
224#66979—42no—
225C2×C4⋊Dic11C2312yes—
226C2×C4⋊Dic11C2312yes—
227C2×C4⋊Dic11C2312yes—
228C2×Dic11⋊C4—24no—
229C2×Dic11⋊C4C2312yes—
230C2×Dic11⋊C4C2312yes—
231C2×Dic11⋊C4C2312yes—
232C2×Dic11⋊C4C2311yescharacteristic
233C2×Dic11⋊C4C2311yescharacteristic
234C2×Dic11⋊C4C2312yes—
235C2×Dic11⋊C4C2312yes—
236C2×C4×Dic11C2312yes—
237#66948—24no—
238#66948—24no—
239#66947—24no—
240#66947—24no—
241#66947—44no—
242#66939—42no—
243#66937—28no—
244#66937—28no—
245#66937—28no—
246#66937—28no—
247#66937—24no—
248#66937—24no—
249#66936—44no—
250#66936—44no—
251#66935—24no—
252#66935—24no—
253#66935—24no—
254C22⋊C4×D11—24no—
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#36715—111nomaximal, Sylow
268C24×C11—22no—
269C24×C11—22no—
270C24×C11—22no—
271C24×C11—42no—
272C24×C11—42no—
273C24×C11C2411yescharacteristic
274C24×C11C2412yes—
275C24×C11C2411yescharacteristic
276C23×D11—22no—
277C23×D11—22no—
278C23×D11—22no—
279C23×D11—22no—
280C23×D11—22no—
281C23×D11—42no—
282C23×D11—42no—
283C23×D11—41no—
284C23×D11—41no—
285C23×D11—42no—
286C23×D11—42no—
287C23×D11—42no—
288C23×D11—42no—
289C23×D11C2×D414yes—
290C23×D11C2×D414yes—
291C23×D11C2411yescharacteristic
292C23×D11C2411yescharacteristic
293C23×D11C2411yescharacteristic
294C23×D11C2411yescharacteristic
295C23×D11C2411yescharacteristic
296C2×D4×C11—22no—
297C2×D4×C11—22no—
298C2×D4×C11—22no—
299C2×D4×C11—42no—
300C2×D4×C11—42no—
301C2×D4×C11—42no—
302C22×C4×C11—22no—
303C22×C4×C11—22no—
304C22×C4×C11—22no—
305C22×C4×C11—42no—
306C22×C4×C11C2×D414yes—
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2412yes—
309C22×C4×C11C2411yescharacteristic
310C22×C4×C11C2412yes—
311C22×C4×C11C2411yescharacteristic
312C22×C4×C11C2412yes—
313C22×C4×C11C2411yescharacteristic
314C22×C4×C11C2411yescharacteristic
315C2×C22⋊D11—24no—
316C2×C22⋊D11—24no—
317C2×C22⋊D11—22no—
318C2×C22⋊D11—22no—
319C2×C22⋊D11—22no—
320C2×C22⋊D11—22no—
321C2×C22⋊D11—24no—
322C2×C22⋊D11—24no—
323C2×C22⋊D11—24no—
324C2×C22⋊D11—24no—
325C2×C22⋊D11—22no—
326C2×C22⋊D11—22no—
327C2×C22⋊D11—41no—
328C2×C22⋊D11—41no—
329C2×C22⋊D11—42no—
330C2×C22⋊D11—42no—
331C2×C22⋊D11—42no—
332C2×C22⋊D11—42no—
333C2×C22⋊D11—42no—
334C2×C22⋊D11—42no—
335C2×C22⋊D11—42no—
336C2×C22⋊D11—42no—
337C2×C22⋊D11—42no—
338C2×C22⋊D11—42no—
339C2×C22⋊D11—42no—
340C2×C22⋊D11—416no—
341C2×C22⋊D11—416no—
342C22×Dic11—24no—
343C22×Dic11—22no—
344C22×Dic11—22no—
345C22×Dic11—22no—
346C22×Dic11—22no—
347C22×Dic11C2411yescharacteristic
348C22×Dic11C2412yes—
349C22×Dic11C2412yes—
350C22×Dic11C2411yescharacteristic
351C22×Dic11C2412yes—
352C22×Dic11C2411yescharacteristic
353C22×Dic11C2412yes—
354D4×D11—416no—
355C2×D44—22no—
356C2×D44—22no—
357C2×D44—22no—
358C2×D44—416no—
359C2×D44—41no—
360C2×D44—41no—
361C2×D44—41no—
362C2×D44—41no—
363C2×D44—41no—
364C2×D44—41no—
365C2×D44—41no—
366C2×D44—41no—
367C2×D44—41no—
368C2×D44—41no—
369C2×D44—42no—
370C2×D44—42no—
371C2×D44C2×D414yes—
372C2×D44C2×D414yes—
373C2×D44C2×D414yes—
374C2×D44C2×D414yes—
375C2×C4×D11—24no—
376C2×C4×D11—24no—
377C2×C4×D11—24no—
378C2×C4×D11—24no—
379C2×C4×D11—22no—
380C2×C4×D11—22no—
381C2×C4×D11—22no—
382C2×C4×D11—42no—
383C2×C4×D11—42no—
384C2×C4×D11—41no—
385C2×C4×D11—41no—
386C2×C4×D11—42no—
387C2×C4×D11—42no—
388C2×C4×D11—416no—
389C11×C4⋊C4—22no—
390C11×C4⋊C4—22no—
391C11×C4⋊C4—42no—
392C11×C4⋊C4—42no—
393C11×C22⋊C4—22no—
394C11×C22⋊C4—22no—
395C11×C22⋊C4—22no—
396C11×C22⋊C4—22no—
397C11×C22⋊C4—22no—
398C11×C22⋊C4—24no—
399C11×C22⋊C4—24no—
400C11×C22⋊C4—42no—
401C11×C22⋊C4—42no—
402C11×C22⋊C4—42no—
403C11×C22⋊C4—42no—
404C42×C11—42no—
405C22⋊Dic11—24no—
406C22⋊Dic11—22no—
407C22⋊Dic11—22no—
408C22⋊Dic11—22no—
409C22⋊Dic11—42no—
410C22⋊Dic11—42no—
411C22⋊Dic11—42no—
412C22⋊Dic11—42no—
413(C2×D11)⋊C4—24no—
414(C2×D11)⋊C4—22no—
415(C2×D11)⋊C4—22no—
416(C2×D11)⋊C4—22no—
417(C2×D11)⋊C4—22no—
418(C2×D11)⋊C4—24no—
419(C2×D11)⋊C4—24no—
420(C2×D11)⋊C4—22no—
421(C2×D11)⋊C4—22no—
422(C2×D11)⋊C4—22no—
423(C2×D11)⋊C4—22no—
424(C2×D11)⋊C4—42no—
425(C2×D11)⋊C4—42no—
426(C2×D11)⋊C4—42no—
427(C2×D11)⋊C4—42no—
428(C2×D11)⋊C4—42no—
429(C2×D11)⋊C4—42no—
430(C2×D11)⋊C4—42no—
431(C2×D11)⋊C4—42no—
432(C2×D11)⋊C4—42no—
433(C2×D11)⋊C4—42no—
434C4⋊Dic11—24no—
435C4⋊Dic11—42no—
436C4⋊Dic11—42no—
437Dic11⋊C4—24no—
438Dic11⋊C4—24no—
439Dic11⋊C4—24no—
440Dic11⋊C4—22no—
441Dic11⋊C4—22no—
442Dic11⋊C4—42no—
443Dic11⋊C4—42no—
444C4×Dic11—42no—
445C2×#534—111no—
446C22×#121—111no—
447#2849—111no—
448#2849—111no—
449#2701—112no—
450#2701—112no—
451#2699—112no—
452#2699—112no—
453#2682—112no—
454#2682—112no—
455#2678—112no—
456#2678—112no—
457#2613—111no—
458#2613—111no—
459#2483—111no—
460#2413—111no—
461#2413—111no—
462#2411—111no—
463#2411D1111yescharacteristic, complemented
464#2405—111no—
465#2405—111no—
466#2403—111no—
467#2309—111no—
468C23×C11—22no—
469C23×C11—22no—
470C23×C11—22no—
471C23×C11—21no—
472C23×C11—22no—
473C23×C11—21no—
474C23×C11—22no—
475C23×C11—22no—
476C23×C11—22no—
477C23×C11—22no—
478C23×C11—21no—
479C23×C11—22no—
480C23×C11—22no—
481C23×C11—22no—
482C23×C11—44no—
483C23×C11—44no—
484C23×C11—44no—
485C23×C11—84no—
486C23×C11—84no—
487C23×C11C22×D412yes—
488C23×C11H(5,𝔽2)12yes—
489C23×C11H(5,𝔽2)12yes—
490C23×C11C2511yescharacteristic
491C22×D11—28no—
492C22×D11—22no—
493C22×D11—22no—
494C22×D11—22no—
495C22×D11—22no—
496C22×D11—21no—
497C22×D11—21no—
498C22×D11—21no—
499C22×D11—21no—
500C22×D11—21no—
501C22×D11—21no—
502C22×D11—21no—
503C22×D11—21no—
504C22×D11—22no—
505C22×D11—22no—
506C22×D11—22no—
507C22×D11—22no—
508C22×D11—28no—
509C22×D11—21no—
510C22×D11—22no—
511C22×D11—21no—
512C22×D11—21no—
513C22×D11—22no—
514C22×D11—44no—
515C22×D11—44no—
516C22×D11—44no—
517C22×D11—44no—
518C22×D11—44no—
519C22×D11—48no—
520C22×D11—48no—
521C22×D11—82no—
522C22×D11—82no—
523C22×D11—84no—
524C22×D11—84no—
525C22×D11—84no—
526C22×D11—84no—
527C22×D11C22×D412yes—
528C22×D11C22×D412yes—
529C22×D11C22×D412yes—
530C22×D11C22×D412yes—
531D4×C11—44no—
532D4×C11—84no—
533C2×C4×C11—28no—
534C2×C4×C11—21no—
535C2×C4×C11—21no—
536C2×C4×C11—21no—
537C2×C4×C11—21no—
538C2×C4×C11—21no—
539C2×C4×C11—21no—
540C2×C4×C11—22no—
541C2×C4×C11—21no—
542C2×C4×C11—22no—
543C2×C4×C11—21no—
544C2×C4×C11—22no—
545C2×C4×C11—22no—
546C2×C4×C11—22no—
547C2×C4×C11—22no—
548C2×C4×C11—22no—
549C2×C4×C11—22no—
550C2×C4×C11—21no—
551C2×C4×C11—22no—
552C2×C4×C11—22no—
553C2×C4×C11—22no—
554C2×C4×C11—44no—
555C2×C4×C11C22×D412yes—
556C2×C4×C11C22×D412yes—
557C22⋊D11—48no—
558C22⋊D11—48no—
559C22⋊D11—44no—
560C22⋊D11—48no—
561C22⋊D11—48no—
562C22⋊D11—44no—
563C22⋊D11—82no—
564C22⋊D11—82no—
565C22⋊D11—84no—
566C2×Dic11—28no—
567C2×Dic11—22no—
568C2×Dic11—22no—
569C2×Dic11—21no—
570C2×Dic11—22no—
571C2×Dic11—21no—
572C2×Dic11—21no—
573C2×Dic11—22no—
574C2×Dic11—22no—
575C2×Dic11—22no—
576C2×Dic11—22no—
577C2×Dic11—22no—
578C2×Dic11—22no—
579C2×Dic11—21no—
580C2×Dic11—22no—
581C2×Dic11—21no—
582C2×Dic11—22no—
583C2×Dic11—22no—
584C2×Dic11—22no—
585C2×Dic11—44no—
586C2×Dic11H(5,𝔽2)14yes—
587D44—44no—
588D44—44no—
589D44—44no—
590D44—44no—
591D44—44no—
592D44—82no—
593D44—82no—
594C4×D11—48no—
595C4×D11—48no—
596C4×D11—44no—
597C4×D11—82no—
598C4×D11—82no—
599C23×D4—111no—
600C23×D4—111no—
601C23×D4—111no—
602C23×D4—111no—
603C24×C4—111no—
604#534—228no—
605C2×#123—111no—
606C2×#123—111no—
607C2×#123—111no—
608C2×#123—111no—
609C2×#123—112no—
610C2×#123—112no—
611C2×#123—112no—
612C2×#123—111no—
613C2×#123C2×D1111yescharacteristic
614C2×#121—111no—
615C2×#121—111no—
616C2×#121—112no—
617C2×#121—112no—
618C2×#121—112no—
619C2×#121—112no—
620C2×#121—111no—
621C2×#121—111no—
622C2×#121—228no—
623C2×#120—111no—
624C2×#120—111no—
625C2×#120—112no—
626C2×#120—111no—
627C2×#120—111no—
628C2×#120—111no—
629C2×#120C2×D1111yescharacteristic
630C2×#117—111no—
631C2×#117C2×D1111yescharacteristic, complemented
632C22×C4⋊C4—111no—
633C22×C22⋊C4—111no—
634C22×C22⋊C4—111no—
635C22×C22⋊C4C2×D1111yescharacteristic, complemented
636#398—112no—
637#398—112no—
638#397—112no—
639#397—112no—
640#396—112no—
641#396—112no—
642#396—112no—
643#396C2×D1112yescomplemented
644#394—112no—
645#394—112no—
646#394—112no—
647#394—112no—
648#394—112no—
649#394—112no—
650#394—112no—
651#394—112no—
652#394—112no—
653#394C2×D1112yescomplemented
654#392—112no—
655#392—112no—
656#392—112no—
657#392—112no—
658#392—112no—
659#392—112no—
660#390—112no—
661#390—112no—
662#390—112no—
663#390—112no—
664#390—112no—
665#390C2×D1112yescomplemented
666#389—112no—
667#389—112no—
668#388—112no—
669#388—112no—
670#388—112no—
671#388C2×D1112yescomplemented
672#386—111no—
673#386—111no—
674#386—111no—
675#386—112no—
676#386—112no—
677#386—112no—
678#386—112no—
679#386C2×D1111yescharacteristic
680#385—111no—
681#385—112no—
682#385—112no—
683#385—111no—
684#385—111no—
685#385—112no—
686#385—112no—
687#385C2×D1111yescharacteristic, complemented
688#381—111no—
689#381—111no—
690#381—112no—
691#381—112no—
692#381—112no—
693#379—111no—
694#379—111no—
695#379—111no—
696#379—111no—
697#379—111no—
698#379—112no—
699#379C2×D1111yescharacteristic, complemented
700C22×C11—22no—
701C22×C11—22no—
702C22×C11—24no—
703C22×C11—24no—
704C22×C11—41no—
705C22×C11—42no—
706C22×C11—41no—
707C22×C11—42no—
708C22×C11—41no—
709C22×C11—42no—
710C22×C11—42no—
711C22×C11—42no—
712C22×C11—42no—
713C22×C11—42no—
714C22×C11—42no—
715C22×C11—42no—
716C22×C11—88no—
717C22×C11#53414yes—
718C22×C11C23×D411yescharacteristic
719C22×C11C2×H(5,𝔽2)11yescharacteristic
720C22×C11C2×H(5,𝔽2)11yescharacteristic
721C22×C11C2×H(5,𝔽2)12yes—
722C22×C11#58512yes—
723C2×D11—22no—
724C2×D11—22no—
725C2×D11—22no—
726C2×D11—22no—
727C2×D11—22no—
728C2×D11—22no—
729C2×D11—22no—
730C2×D11—22no—
731C2×D11—22no—
732C2×D11—22no—
733C2×D11—22no—
734C2×D11—22no—
735C2×D11—416no—
736C2×D11—42no—
737C2×D11—42no—
738C2×D11—42no—
739C2×D11—42no—
740C2×D11—42no—
741C2×D11—42no—
742C2×D11—42no—
743C2×D11—42no—
744C2×D11—41no—
745C2×D11—41no—
746C2×D11—41no—
747C2×D11—42no—
748C2×D11—42no—
749C2×D11—88no—
750C2×D11—88no—
751C4×C11—22no—
752C4×C11—22no—
753C4×C11—41no—
754C4×C11—42no—
755C4×C11—41no—
756C4×C11—41no—
757C4×C11—42no—
758C4×C11—42no—
759Dic11—24no—
760Dic11—41no—
761Dic11—42no—
762Dic11—41no—
763Dic11—41no—
764Dic11—42no—
765Dic11—42no—
766C25—111no—
767C25—111no—
768C25—111no—
769C25C22×D1111yescharacteristic
770C22×D4—111no—
771C22×D4—112no—
772C22×D4—112no—
773C22×D4—111no—
774C22×D4—111no—
775C22×D4—111no—
776C22×D4—112no—
777C22×D4—112no—
778C22×D4—112no—
779C22×D4—118no—
780C22×D4—111no—
781C22×D4—111no—
782C22×D4—111no—
783C22×D4—111no—
784C22×D4—111no—
785C22×D4—111no—
786C22×D4—111no—
787C22×D4—224no—
788C22×D4—224no—
789C22×D4—224no—
790C22×D4—442no—
791C22×D4—442no—
792C22×D4—444no—
793C22×D4—442no—
794C22×D4—442no—
795C22×D4—442no—
796C22×D4—442no—
797C22×D4C22×D1111yescharacteristic
798C22×D4C22×D1112yes—
799C23×C4—111no—
800C23×C4—111no—
801C23×C4—112no—
802C23×C4—112no—
803C23×C4—111no—
804C23×C4—111no—
805C23×C4—111no—
806C23×C4—224no—
807C23×C4—444no—
808C23×C4C22×D1111yescharacteristic
809C23×C4C22×D1111yescharacteristic
810#123—24no—
811#123—224no—
812#123—224no—
813#123—224no—
814#123—442no—
815#123—444no—
816#123—444no—
817#123—444no—
818#123—442no—
819#121—228no—
820#121—228no—
821#121—228no—
822#121—228no—
823#121—224no—
824#121—224no—
825#121—224no—
826#121—224no—
827#120—42no—
828#120—224no—
829#120—224no—
830#120—224no—
831#120—224no—
832#120—444no—
833#120—442no—
834#117—42no—
835#117—442no—
836C2×C4⋊C4—112no—
837C2×C4⋊C4—112no—
838C2×C4⋊C4—111no—
839C2×C4⋊C4—111no—
840C2×C4⋊C4—112no—
841C2×C4⋊C4—112no—
842C2×C4⋊C4—112no—
843C2×C4⋊C4—112no—
844C2×C4⋊C4—112no—
845C2×C4⋊C4—112no—
846C2×C4⋊C4—224no—
847C2×C4⋊C4C22×D1111yescharacteristic
848C2×C4⋊C4C22×D1111yescharacteristic
849C2×C4⋊C4C22×D1112yes—
850C2×C4⋊C4C22×D1112yes—
851C2×C22⋊C4—24no—
852C2×C22⋊C4—111no—
853C2×C22⋊C4—111no—
854C2×C22⋊C4—111no—
855C2×C22⋊C4—112no—
856C2×C22⋊C4—111no—
857C2×C22⋊C4—111no—
858C2×C22⋊C4—112no—
859C2×C22⋊C4—112no—
860C2×C22⋊C4—111no—
861C2×C22⋊C4—111no—
862C2×C22⋊C4—111no—
863C2×C22⋊C4—111no—
864C2×C22⋊C4—111no—
865C2×C22⋊C4—111no—
866C2×C22⋊C4—112no—
867C2×C22⋊C4—112no—
868C2×C22⋊C4—112no—
869C2×C22⋊C4—112no—
870C2×C22⋊C4—112no—
871C2×C22⋊C4—112no—
872C2×C22⋊C4—112no—
873C2×C22⋊C4—112no—
874C2×C22⋊C4—112no—
875C2×C22⋊C4—112no—
876C2×C22⋊C4—112no—
877C2×C22⋊C4—112no—
878C2×C22⋊C4—112no—
879C2×C22⋊C4—112no—
880C2×C22⋊C4—112no—
881C2×C22⋊C4—224no—
882C2×C22⋊C4—224no—
883C2×C22⋊C4C22×D1111yescharacteristic
884C2×C22⋊C4C22×D1112yes—
885C2×C22⋊C4C22×D1112yes—
886C2×C22⋊C4C22×D1111yescharacteristic
887C2×C22⋊C4C22×D1111yescharacteristic
888C2×C22⋊C4C22×D1111yescharacteristic
889C2×C22⋊C4C22×D1111yescharacteristic
890C2×C22⋊C4C22×D1112yes—
891C2×C22⋊C4C22×D1112yes—
892C2×C22⋊C4C22×D1112yes—
893C2×C22⋊C4C22×D1112yes—
894C2×C42—112no—
895C2×C42C22×D1112yes—
896#95—112no—
897#95—112no—
898#95—112no—
899#95—112no—
900#95—112no—
901#95—112no—
902#95—112no—
903#95—112no—
904#95—112no—
905#95—112no—
906#95C22×D1112yes—
907#95C22×D1112yes—
908C2×C11—24no—
909C2×C11—81no—
910C2×C11—82no—
911C2×C11C2×#53411yescharacteristic
912C2×C11#348411yescharacteristic
913C2×C11#348511yescharacteristic
914C2×C11#354212yes—
915C2×C11#354212yes—
916D11—42no—
917D11—42no—
918D11—42no—
919D11—42no—
920D11—81no—
921C24—22no—
922C24—22no—
923C24—22no—
924C24—42no—
925C24—42no—
926C24—111no—
927C24—111no—
928C24—111no—
929C24—111no—
930C24—114no—
931C24—114no—
932C24—111no—
933C24—222no—
934C24—222no—
935C24—222no—
936C24—222no—
937C24—222no—
938C24—442no—
939C24—442no—
940C24—442no—
941C24—441no—
942C24—441no—
943C24—442no—
944C24—442no—
945C24—442no—
946C24C23×D1111yescharacteristic
947C24C23×D1112yes—
948C24C23×D1111yescharacteristic
949C2×D4—22no—
950C2×D4—22no—
951C2×D4—22no—
952C2×D4—42no—
953C2×D4—42no—
954C2×D4—42no—
955C2×D4—114no—
956C2×D4—114no—
957C2×D4—114no—
958C2×D4—114no—
959C2×D4—222no—
960C2×D4—222no—
961C2×D4—222no—
962C2×D4—224no—
963C2×D4—224no—
964C2×D4—224no—
965C2×D4—224no—
966C2×D4—222no—
967C2×D4—224no—
968C2×D4—224no—
969C2×D4—222no—
970C2×D4—222no—
971C2×D4—222no—
972C2×D4—222no—
973C2×D4—222no—
974C2×D4—4416no—
975C2×D4—441no—
976C2×D4—441no—
977C2×D4—441no—
978C2×D4—441no—
979C2×D4—441no—
980C2×D4—441no—
981C2×D4—441no—
982C2×D4—441no—
983C2×D4—441no—
984C2×D4—441no—
985C2×D4—442no—
986C2×D4—442no—
987C2×D4—442no—
988C2×D4—442no—
989C2×D4—442no—
990C2×D4—442no—
991C2×D4—441no—
992C2×D4—441no—
993C2×D4—442no—
994C2×D4—442no—
995C2×D4—4416no—
996C2×D4—442no—
997C2×D4—442no—
998C2×D4—442no—
999C2×D4—442no—
1000C2×D4—442no—
1001C2×D4—4416no—
1002C2×D4—4416no—
1003C22×C4—22no—
1004C22×C4—22no—
1005C22×C4—22no—
1006C22×C4—42no—
1007C22×C4—112no—
1008C22×C4—111no—
1009C22×C4—112no—
1010C22×C4—112no—
1011C22×C4—111no—
1012C22×C4—112no—
1013C22×C4—111no—
1014C22×C4—224no—
1015C22×C4—224no—
1016C22×C4—224no—
1017C22×C4—224no—
1018C22×C4—222no—
1019C22×C4—222no—
1020C22×C4—222no—
1021C22×C4—224no—
1022C22×C4—222no—
1023C22×C4—222no—
1024C22×C4—222no—
1025C22×C4—222no—
1026C22×C4—442no—
1027C22×C4—442no—
1028C22×C4—441no—
1029C22×C4—441no—
1030C22×C4—442no—
1031C22×C4—442no—
1032C22×C4—4416no—
1033C22×C4D4×D1114yes—
1034C22×C4C23×D1111yescharacteristic
1035C22×C4C23×D1112yes—
1036C22×C4C23×D1112yes—
1037C22×C4C23×D1111yescharacteristic
1038C22×C4C23×D1111yescharacteristic
1039C22×C4C23×D1112yes—
1040C22×C4C23×D1111yescharacteristic
1041C22×C4C23×D1111yescharacteristic
1042C4⋊C4—22no—
1043C4⋊C4—22no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—224no—
1047C4⋊C4—224no—
1048C4⋊C4—224no—
1049C4⋊C4—224no—
1050C4⋊C4—222no—
1051C4⋊C4—222no—
1052C4⋊C4—442no—
1053C4⋊C4—442no—
1054C4⋊C4—442no—
1055C4⋊C4—442no—
1056C22⋊C4—22no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—24no—
1060C22⋊C4—24no—
1061C22⋊C4—22no—
1062C22⋊C4—22no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—224no—
1068C22⋊C4—222no—
1069C22⋊C4—222no—
1070C22⋊C4—224no—
1071C22⋊C4—224no—
1072C22⋊C4—222no—
1073C22⋊C4—222no—
1074C22⋊C4—222no—
1075C22⋊C4—222no—
1076C22⋊C4—224no—
1077C22⋊C4—222no—
1078C22⋊C4—222no—
1079C22⋊C4—222no—
1080C22⋊C4—222no—
1081C22⋊C4—222no—
1082C22⋊C4—442no—
1083C22⋊C4—442no—
1084C22⋊C4—442no—
1085C22⋊C4—442no—
1086C22⋊C4—442no—
1087C22⋊C4—442no—
1088C22⋊C4—442no—
1089C22⋊C4—442no—
1090C22⋊C4—442no—
1091C22⋊C4—442no—
1092C22⋊C4—442no—
1093C22⋊C4—442no—
1094C22⋊C4—442no—
1095C22⋊C4—442no—
1096C42—42no—
1097C42—442no—
1098C11#3671511yescharacteristic, complemented, Sylow
1099C23—22no—
1100C23—22no—
1101C23—21no—
1102C23—22no—
1103C23—22no—
1104C23—21no—
1105C23—21no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—22no—
1111C23—22no—
1112C23—22no—
1113C23—44no—
1114C23—44no—
1115C23—44no—
1116C23—84no—
1117C23—84no—
1118C23—112no—
1119C23—112no—
1120C23—112no—
1121C23—112no—
1122C23—228no—
1123C23—221no—
1124C23—221no—
1125C23—221no—
1126C23—221no—
1127C23—221no—
1128C23—221no—
1129C23—221no—
1130C23—221no—
1131C23—222no—
1132C23—222no—
1133C23—222no—
1134C23—222no—
1135C23—222no—
1136C23—222no—
1137C23—222no—
1138C23—222no—
1139C23—228no—
1140C23—221no—
1141C23—221no—
1142C23—221no—
1143C23—222no—
1144C23—222no—
1145C23—444no—
1146C23—444no—
1147C23—444no—
1148C23—444no—
1149C23—448no—
1150C23—448no—
1151C23—444no—
1152C23—884no—
1153C23—884no—
1154C23—882no—
1155C23—882no—
1156C23—884no—
1157C23—884no—
1158C23C2×D4×D1112yes—
1159C23#6703712yes—
1160C23#6704212yes—
1161C23C24×D1111yescharacteristic
1162D4—44no—
1163D4—84no—
1164D4—444no—
1165D4—444no—
1166D4—444no—
1167D4—444no—
1168D4—444no—
1169D4—448no—
1170D4—448no—
1171D4—444no—
1172D4—448no—
1173D4—448no—
1174D4—444no—
1175D4—882no—
1176D4—882no—
1177D4—882no—
1178D4—882no—
1179D4—884no—
1180C2×C4—28no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—22no—
1188C2×C4—21no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—44no—
1202C2×C4—114no—
1203C2×C4—228no—
1204C2×C4—222no—
1205C2×C4—222no—
1206C2×C4—221no—
1207C2×C4—221no—
1208C2×C4—222no—
1209C2×C4—221no—
1210C2×C4—222no—
1211C2×C4—221no—
1212C2×C4—222no—
1213C2×C4—222no—
1214C2×C4—221no—
1215C2×C4—222no—
1216C2×C4—222no—
1217C2×C4—222no—
1218C2×C4—222no—
1219C2×C4—222no—
1220C2×C4—222no—
1221C2×C4—222no—
1222C2×C4—448no—
1223C2×C4—448no—
1224C2×C4—444no—
1225C2×C4—444no—
1226C2×C4—882no—
1227C2×C4—882no—
1228C2×C4C2×D4×D1112yes—
1229C2×C4C2×D4×D1112yes—
1230C22—24no—
1231C22—24no—
1232C22—22no—
1233C22—22no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—41no—
1241C22—42no—
1242C22—42no—
1243C22—41no—
1244C22—41no—
1245C22—42no—
1246C22—88no—
1247C22—222no—
1248C22—222no—
1249C22—222no—
1250C22—222no—
1251C22—222no—
1252C22—222no—
1253C22—222no—
1254C22—222no—
1255C22—222no—
1256C22—222no—
1257C22—222no—
1258C22—222no—
1259C22—4416no—
1260C22—442no—
1261C22—442no—
1262C22—442no—
1263C22—442no—
1264C22—442no—
1265C22—442no—
1266C22—442no—
1267C22—442no—
1268C22—442no—
1269C22—442no—
1270C22—441no—
1271C22—441no—
1272C22—441no—
1273C22—888no—
1274C22—888no—
1275C22#1062313614yes—
1276C22C22×D4×D1111yescharacteristic
1277C22C2×#6703711yescharacteristic
1278C22C2×#6704211yescharacteristic
1279C22#1062345312yes—
1280C22D11×H(5,𝔽2)12yes—
1281C4—22no—
1282C4—22no—
1283C4—42no—
1284C4—42no—
1285C4—41no—
1286C4—42no—
1287C4—41no—
1288C4—41no—
1289C4—224no—
1290C4—442no—
1291C4—442no—
1292C4—442no—
1293C4—441no—
1294C4—441no—
1295C4—441no—
1296C2—24no—
1297C2—82no—
1298C2—81no—
1299C2—442no—
1300C2—442no—
1301C2—442no—
1302C2—442no—
1303C2—881no—
1304C2C2×#1062313611yescharacteristic
1305C2#1308225011yescharacteristic
1306C2#1308225811yescharacteristic
1307C2#1308291712yes—
1308C2#1308292512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2411C2
hypercenter#2411D11
hypocenterC11#36715
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2411

Complements

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

NH ≅ G/Ntype
1. C2×#10623184C2semidirect
2. C22×#66937C2semidirect
3. #13076911C2semidirect
4. #13076907C2semidirect
5. #13075226C2semidirect
6. #13075222C2semidirect
7. #13075200C2semidirect
8. #13075198C2semidirect
9. #13074979C2semidirect
10. #13074976C2semidirect
11. #13074947C2semidirect
12. #13074938C2semidirect
13. #13074331C2semidirect
14. #13074330C2semidirect
15. #13072896C2semidirect
16. #13072024C2semidirect
17. #13072017C2semidirect
18. #13072001C2semidirect
19. #13071942C2semidirect
20. #13071941C2semidirect
21. #13071927C2semidirect
22. #13071196C2semidirect
23. C11×#2411C2semidirect
25. C23×C22⋊D11C22semidirect
28. C23×C4×D11C22semidirect
31. C2×C11×#117C22semidirect
32. C22×C11×C22⋊C4C22semidirect
35. C2×#66990C22semidirect
39. C2×#66979C22semidirect
40. C22×Dic11⋊C4C22semidirect
42. C2×#66948C22semidirect
43. C2×#66948C22semidirect
44. C2×#66947C22semidirect
45. C2×#66947C22semidirect
46. C2×#66947C22semidirect
51. C2×#66937C22semidirect
52. C2×#66937C22semidirect
53. C2×#66937C22semidirect
54. C2×#66937C22semidirect
55. C2×#66936C22semidirect
56. C2×#66936C22semidirect
58. C2×#66935C22semidirect
59. C2×#66935C22semidirect
61. C11×#396C22semidirect
62. C11×#394C22semidirect
63. C11×#390C22semidirect
64. C11×#388C22semidirect
66. C11×#385C22semidirect
67. C11×#379C22semidirect
68. #10622860C22semidirect
69. #10622836C22semidirect
70. #10622836C22semidirect
71. #10622836C22semidirect
74. #10622823C22semidirect
75. #10622607C22semidirect
76. #10622606C22semidirect
77. #10622602C22semidirect
78. #10622602C22semidirect
79. #10622601C22semidirect
80. #10622601C22semidirect
81. #10622597C22semidirect
82. #10622596C22semidirect
83. #10622585C22semidirect
84. #10622574C22semidirect
85. #10622574C22semidirect
86. #10622574C22semidirect
87. #10622574C22semidirect
88. #10622574C22semidirect
89. #10622573C22semidirect
90. #10622573C22semidirect
91. #10622573C22semidirect
92. #10622572C22semidirect
93. #10622572C22semidirect
94. #10622572C22semidirect
96. #10622570C22semidirect
97. #10622569C22semidirect
98. #10622569C22semidirect
99. #10622569C22semidirect
102. #10622568C22semidirect
103. #10622568C22semidirect
104. #10622568C22semidirect
105. #10622563C22semidirect
106. #10622561C22semidirect
107. #10622561C22semidirect
108. #10622559C22semidirect
109. #10622558C22semidirect
110. #10622558C22semidirect
111. #10622556C22semidirect
112. #10622556C22semidirect
113. #10622553C22semidirect
114. #10622552C22semidirect
115. #10622552C22semidirect
116. #10622541C22semidirect
117. #10622288C22semidirect
118. #10622285C22semidirect
119. #10622281C22semidirect
120. #10622281C22semidirect
121. #10622278C22semidirect
122. #10622277C22semidirect
123. #10622277C22semidirect
124. #10622277C22semidirect
154. C22×D44D4semidirect
463. #2411D11semidirect
631. C2×#117C2×D11semidirect
635. C22×C22⋊C4C2×D11semidirect
643. #396C2×D11semidirect
653. #394C2×D11semidirect
665. #390C2×D11semidirect
671. #388C2×D11semidirect
687. #385C2×D11semidirect
699. #379C2×D11semidirect
1098. C11#36715semidirect

Maximal subgroups

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

subgroupindex
C2×#106231842
C22×#669372
#130769112
#130769072
#130752262
#130752222
#130752002
#130751982
#130749792
#130749762
#130749472
#130749382
#130743312
#130743302
#130728962
#130720242
#130720172
#130720012
#130719422
#130719412
#130719272
#130711962
C11×#24112
#3671511