Finite Group Databasebeta

← #14916839

Subgroups — #14916839

Order 2816.

2614 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623078C211yesmaximal, characteristic
2#13071781C212yesmaximal, complemented
3#13071769C212yesmaximal, complemented
4#13071598C212yesmaximal, complemented
5#13071596C212yesmaximal, complemented
6#13071552C211yesmaximal, characteristic, complemented
7#13071526C211yesmaximal, characteristic, complemented
8#13071520C211yesmaximal, characteristic, complemented
9#13071477C211yesmaximal, characteristic, complemented
10#13071473C211yesmaximal, characteristic, complemented
11#13071447C211yesmaximal, characteristic, complemented
12#13071440C211yesmaximal, characteristic, complemented
13#13071344C212yesmaximal, complemented
14#13071317C212yesmaximal, complemented
15#13071289C212yesmaximal, complemented
16#13071286C212yesmaximal, complemented
17#13071260C211yesmaximal, characteristic, complemented
18#13071256C211yesmaximal, characteristic, complemented
19#13071247C211yesmaximal, characteristic, complemented
20#13071243C211yesmaximal, characteristic, complemented
21C2×#10622277C211yesmaximal, characteristic, complemented
22D11×#380C211yesmaximal, characteristic, complemented
23C11×#2353C211yesmaximal, characteristic, complemented
24C22×#4339C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×#66992C2211yescharacteristic
28C2×#66990C2211yescharacteristic
29C2×D4×Dic11C2212yes—
30C2×C4×C22⋊D11C2211yescharacteristic
31C2×C4×C22⋊D11C2211yescharacteristic
32C22×(C2×D11)⋊C4C2212yes—
33#10623078C4116yescomplemented
34C2×#66949C2211yescharacteristic
35C2×#66947C2211yescharacteristic
36C2×C4⋊C4×D11C2212yes—
37C2×#66937C2211yescharacteristic
38C2×#66936C2211yescharacteristic
39C2×#66935C2211yescharacteristic
40C2×(C22⋊D11)⋊C4C2212yes—
41C2×(C22⋊D11)⋊C4C2212yes—
42C2×C22⋊C4×D11C2212yes—
43C2×#66931C2211yescharacteristic
44C2×C4×D44C2212yes—
45C2×C4×D44C2211yescharacteristic
46C2×#66925C2211yescharacteristic
47C11×#388C2212yescomplemented
48C11×#387C2212yescomplemented
49C11×#386C2212yes—
50C11×#383C2211yescharacteristic, complemented
51C11×#381C2211yescharacteristic, complemented
52C11×#380C2211yescharacteristic
53C4×C11×C22⋊C4C2212yes—
54C4×C11×C22⋊C4C2211yescharacteristic, complemented
55C11×#376C2211yescharacteristic, complemented
56C2×C11×#95C2211yescharacteristic
57#10622826C2212yes—
58#10622825C2211yescharacteristic
59#10622825C2211yescharacteristic, complemented
60C4×C22⋊Dic11C2212yes—
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2212yes—
63C2×C11⋊#95C2211yescharacteristic, complemented
64#10622602C2212yescomplemented
65#10622600C2212yes—
66#10622598C2212yescomplemented
67#10622585C2212yescomplemented
68#10622571C2212yes—
69#10622571C2212yescomplemented
70#10622570C2212yes—
71#10622569C2212yes—
72#10622569C2212yescomplemented
73#10622563C2212yes—
74#10622563C2212yescomplemented
75#10622559C2212yes—
76#10622559C2212yescomplemented
77#10622558C2212yescomplemented
78#10622555C2212yes—
79#10622553C2212yes—
80#10622552C2212yes—
81C4×(C2×D11)⋊C4C2212yes—
82#10622549C2211yescharacteristic, complemented
83C4×C4⋊Dic11C2211yescharacteristic, complemented
84#10622546C2212yescomplemented
85#10622546C2212yescomplemented
86#10622542C2212yescomplemented
87#10622541C2212yescomplemented
88#10622283C2212yes—
89#10622283C2212yes—
90#10622283C2212yescomplemented
91#10622282C2212yes—
92#10622282C2212yescomplemented
93#10622281C2212yes—
94#10622281C2212yes—
95#10622281C2212yescomplemented
96#10622280C2211yescharacteristic
97#10622280C2211yescharacteristic
98#10622280C2211yescharacteristic, complemented
99#10622279C2212yes—
100#10622279C2211yescharacteristic, complemented
101#10622278C2212yes—
102#10622278C2212yes—
103#10622277C2211yescharacteristic
104#10622277C2211yescharacteristic
105#10622277C2211yescharacteristic
106#10622277C2211yescharacteristic
107#10622277C2212yes—
108#10622277C2212yes—
109#10622277C2211yescharacteristic, complemented
110D11×#95C2211yescharacteristic
111D11×#95C2211yescharacteristic
112D11×#95C2211yescharacteristic, complemented
113#10622268C2212yescomplemented
114#10622268C2212yescomplemented
115#10622268C2212yescomplemented
116#10622267C2212yescomplemented
117#10622265C2212yescomplemented
118#10622264C2211yescharacteristic, complemented
119#10622263C2211yescharacteristic, complemented
120#10622262C2211yescharacteristic, complemented
121#10622261C2211yescharacteristic, complemented
122#10622260C2212yescomplemented
123#10622259C2212yescomplemented
124C24×D11C2311yescharacteristic
125C22×D4×C11C2311yescharacteristic
126C23×C4×C11C2312yes—
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C22×C22⋊D11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C22×C22⋊D11C2311yescharacteristic
133C23×Dic11C2312yes—
134C23×Dic11C2312yes—
135C23×Dic11C2311yescharacteristic
136C2×#4339—44no—
137C2×#4339C2×C418yescomplemented
138C22×D44C2311yescharacteristic
139C22×D44C2311yescharacteristic
140C22×C4×D11—44no—
141C22×C4×D11C2×C418yescomplemented
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2312yes—
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×Dic22C2311yescharacteristic
151C4×D4×C11C2×C418yescomplemented
152C2×C11×C4⋊C4C2312yes—
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C22⋊C4C2312yes—
155C2×C11×C22⋊C4C2312yes—
156C2×C11×C22⋊C4C2312yes—
157C2×C11×C22⋊C4C2311yescharacteristic
158C2×C11×C22⋊C4C2311yescharacteristic
159C2×C42×C11C2312yes—
160C2×C42×C11C2312yes—
161C2×C42×C11C2311yescharacteristic
162C2×C22⋊Dic11C2312yes—
163C2×C22⋊Dic11C2312yes—
164C2×C22⋊Dic11C2311yescharacteristic
165C2×C22⋊Dic11C2311yescharacteristic
166#66992C2×C418yescomplemented
167#66990C2×C418yescomplemented
168D4×Dic11—44no—
169C4×C22⋊D11C2×C418yescomplemented
170C4×C22⋊D11C2×C418yescomplemented
171C2×(C2×D11)⋊C4—44no—
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2312yes—
174C2×(C2×D11)⋊C4C2312yes—
175C2×(C2×D11)⋊C4C2312yes—
176C2×(C2×D11)⋊C4C2312yes—
177C2×(C2×D11)⋊C4C2312yes—
178C2×(C2×D11)⋊C4C2312yes—
179C2×(C2×D11)⋊C4C2312yes—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2311yescharacteristic
182C2×(C2×D11)⋊C4C2311yescharacteristic
183C2×(C2×D11)⋊C4C2311yescharacteristic
184C2×(C2×D11)⋊C4C2311yescharacteristic
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2311yescharacteristic
187C2×C4⋊Dic11C2312yes—
188C2×C4⋊Dic11C2312yes—
189C2×C4⋊Dic11C2312yes—
190C2×C4⋊Dic11C2312yes—
191C2×C4⋊Dic11C2311yescharacteristic
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2312yes—
194C2×Dic11⋊C4C2312yes—
195C2×Dic11⋊C4C2312yes—
196C2×Dic11⋊C4C2312yes—
197C2×Dic11⋊C4C2311yescharacteristic
198C2×Dic11⋊C4C2311yescharacteristic
199C2×Dic11⋊C4C2311yescharacteristic
200C2×Dic11⋊C4C2311yescharacteristic
201C2×C4×Dic11C2312yes—
202C2×C4×Dic11C2312yes—
203C2×C4×Dic11C2312yes—
204C2×C4×Dic11C2312yes—
205C2×C4×Dic11C2311yescharacteristic
206#66949C2×C418yescomplemented
207#66947C2×C418yescomplemented
208C4⋊C4×D11—44no—
209#66937C2×C418yescomplemented
210#66936C2×C418yescomplemented
211#66935C2×C418yescomplemented
212(C22⋊D11)⋊C4—44no—
213(C22⋊D11)⋊C4—44no—
214C22⋊C4×D11—44no—
215#66931C2×C418yescomplemented
216C4×D44—44no—
217C4×D44C2×C418yescomplemented
218#66925C2×C418yescomplemented
219C11×#95C2312yes—
220C11×#95C2311yescharacteristic
221C11×#95C2311yescharacteristic
222C11×#95C2311yescharacteristic
223C11×#95C2311yescharacteristic
224C11×#95C2312yes—
225C11×#95C2312yes—
226C11×#95C2312yes—
227C11×#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2311yescharacteristic
234C11⋊#95C2311yescharacteristic
235C11⋊#95C2312yes—
236C11⋊#95C2311yescharacteristic
237C11⋊#95C2312yes—
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247#34386—111nomaximal, Sylow
248C24×C11C2411yescharacteristic
249C24×C11C2411yescharacteristic
250C23×D11—22no—
251C23×D11—22no—
252C23×D11—24no—
253C23×D11—42no—
254C23×D11C22×C414yes—
255C23×D11C2411yescharacteristic
256C23×D11C2411yescharacteristic
257C23×D11C2411yescharacteristic
258C2×D4×C11—22no—
259C2×D4×C11—22no—
260C2×D4×C11C22×C414yes—
261C22×C4×C11—24no—
262C22×C4×C11—42no—
263C22×C4×C11—42no—
264C22×C4×C11—42no—
265C22×C4×C11—42no—
266C22×C4×C11C22×C414yes—
267C22×C4×C11C22×C414yes—
268C22×C4×C11C2412yes—
269C22×C4×C11C2412yes—
270C22×C4×C11C2412yes—
271C22×C4×C11C2412yes—
272C22×C4×C11C2411yescharacteristic
273C22×C4×C11C2411yescharacteristic
274C22×C4×C11C2411yescharacteristic
275C22×C4×C11C2411yescharacteristic
276C22×C4×C11C2411yescharacteristic
277C2×C22⋊D11—22no—
278C2×C22⋊D11—22no—
279C2×C22⋊D11—24no—
280C2×C22⋊D11—42no—
281C2×C22⋊D11—42no—
282C2×C22⋊D11C22×C414yes—
283C2×C22⋊D11C22×C414yes—
284C2×C22⋊D11C22×C414yes—
285C2×C22⋊D11C22×C414yes—
286C22×Dic11—24no—
287C22×Dic11—42no—
288C22×Dic11—42no—
289C22×Dic11—42no—
290C22×Dic11—42no—
291C22×Dic11—42no—
292C22×Dic11—42no—
293C22×Dic11C22×C414yes—
294C22×Dic11C2412yes—
295C22×Dic11C2412yes—
296C22×Dic11C2412yes—
297C22×Dic11C2412yes—
298C22×Dic11C2411yescharacteristic
299C22×Dic11C2411yescharacteristic
300C22×Dic11C2411yescharacteristic
301C22×Dic11C2411yescharacteristic
302C22×Dic11C2411yescharacteristic
303#4339—416no—
304C2×D44—24no—
305C2×D44—42no—
306C2×D44C22×C414yes—
307C2×D44C22×C414yes—
308C2×C4×D11—24no—
309C2×C4×D11—24no—
310C2×C4×D11—24no—
311C2×C4×D11—24no—
312C2×C4×D11—42no—
313C2×C4×D11—42no—
314C2×C4×D11—42no—
315C2×C4×D11—42no—
316C2×C4×D11—42no—
317C2×C4×D11—42no—
318C2×C4×D11—42no—
319C2×C4×D11—42no—
320C2×C4×D11—42no—
321C2×C4×D11—42no—
322C2×C4×D11—416no—
323C2×C4×D11C22×C414yes—
324C2×C4×D11C22×C414yes—
325C2×C4×D11C22×C414yes—
326C2×C4×D11C22×C414yes—
327C2×C4×D11C22×C414yes—
328C2×Dic22—42no—
329C2×Dic22C22×C414yes—
330C11×C4⋊C4—42no—
331C11×C4⋊C4C22×C414yes—
332C11×C22⋊C4—24no—
333C11×C22⋊C4—42no—
334C11×C22⋊C4—42no—
335C11×C22⋊C4C22×C414yes—
336C11×C22⋊C4C22×C414yes—
337C42×C11—42no—
338C42×C11—42no—
339C42×C11C22×C414yes—
340C22⋊Dic11—24no—
341C22⋊Dic11—42no—
342C22⋊Dic11C22×C414yes—
343C22⋊Dic11C22×C414yes—
344(C2×D11)⋊C4—24no—
345(C2×D11)⋊C4—24no—
346(C2×D11)⋊C4—42no—
347(C2×D11)⋊C4—42no—
348(C2×D11)⋊C4—42no—
349(C2×D11)⋊C4—42no—
350(C2×D11)⋊C4—42no—
351(C2×D11)⋊C4—42no—
352(C2×D11)⋊C4—42no—
353(C2×D11)⋊C4C22×C414yes—
354(C2×D11)⋊C4C22×C414yes—
355(C2×D11)⋊C4C22×C414yes—
356(C2×D11)⋊C4C22×C414yes—
357(C2×D11)⋊C4C22×C414yes—
358(C2×D11)⋊C4C22×C414yes—
359C4⋊Dic11—42no—
360C4⋊Dic11—42no—
361C4⋊Dic11—42no—
362C4⋊Dic11—42no—
363C4⋊Dic11C22×C414yes—
364Dic11⋊C4—42no—
365Dic11⋊C4—42no—
366Dic11⋊C4—42no—
367Dic11⋊C4—42no—
368Dic11⋊C4—42no—
369Dic11⋊C4C22×C414yes—
370Dic11⋊C4C22×C414yes—
371Dic11⋊C4C22×C414yes—
372Dic11⋊C4C22×C414yes—
373C4×Dic11—42no—
374C4×Dic11—42no—
375C4×Dic11—42no—
376C4×Dic11—42no—
377C4×Dic11C22×C414yes—
378C2×#525—111no—
379#2378—112no—
380#2377—112no—
381#2358—112no—
382#2358—112no—
383#2353—111no—
384#2353D1111yescharacteristic, complemented
385#2349—111no—
386#2349—111no—
387#2343—111no—
388#2343—111no—
389#2339—111no—
390#2339—111no—
391#2329—112no—
392#2325—112no—
393#2322—112no—
394#2322—112no—
395#2319—111no—
396#2319—111no—
397#2318—111no—
398#2318—111no—
399C2×#381—111no—
400C2×#380—111no—
401C23×C11—22no—
402C23×C11—22no—
403C23×C11—21no—
404C23×C11—22no—
405C23×C11—21no—
406C23×C11—22no—
407C23×C11C23×C412yes—
408C23×C11C23×C412yes—
409C23×C11H(5,𝔽2)12yes—
410C23×C112−1+412yes—
411C23×C11C2511yescharacteristic
412C22×D11—21no—
413C22×D11—21no—
414C22×D11—22no—
415C22×D11—28no—
416C22×D11—21no—
417C22×D11—21no—
418C22×D11—22no—
419C22×D11—22no—
420C22×D11—21no—
421C22×D11—21no—
422C22×D11—22no—
423C22×D11—22no—
424C22×D11—28no—
425C22×D11—44no—
426C22×D11—48no—
427C22×D11—48no—
428C22×D11C23×C412yes—
429C22×D11C23×C412yes—
430C22×D11C23×C412yes—
431C22×D11H(5,𝔽2)14yes—
432D4×C11—28no—
433C2×C4×C11—21no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—21no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—44no—
452C2×C4×C11—44no—
453C2×C4×C11—84no—
454C2×C4×C11C23×C412yes—
455C2×C4×C11C23×C412yes—
456C2×C4×C11C23×C412yes—
457C2×C4×C11C23×C412yes—
458C2×C4×C11C23×C412yes—
459C22⋊D11—28no—
460C22⋊D11—28no—
461C22⋊D11—44no—
462C22⋊D11—44no—
463C2×Dic11—21no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—21no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—44no—
482C2×Dic11—84no—
483C2×Dic11—84no—
484C2×Dic11C23×C412yes—
485C2×Dic11C23×C412yes—
486C2×Dic11C23×C412yes—
487C2×Dic11C23×C412yes—
488C2×Dic11C23×C412yes—
489D44—28no—
490D44—44no—
491C4×D11—28no—
492C4×D11—28no—
493C4×D11—44no—
494C4×D11—44no—
495C4×D11—44no—
496C4×D11—84no—
497C4×D11—84no—
498C4×D11—84no—
499Dic22—44no—
500C22×#41—111no—
501C24×C4—111no—
502#525—1116no—
503C2×#123—111no—
504C2×#123—111no—
505C2×C22⋊Q8—111no—
506C2×C22⋊Q8—111no—
507C2×#121—111no—
508C2×#121—111no—
509C2×#120—111no—
510C2×#120—111no—
511C2×C4×D4—111no—
512C2×C4×D4—111no—
513C2×C4×D4—112no—
514C2×C4×D4—112no—
515C2×C4×D4—112no—
516C2×C4×D4—111no—
517C2×C4×D4—112no—
518C2×C4×D4C2×D1111yescharacteristic
519C2×#117—111no—
520C22×C4⋊C4—112no—
521C22×C22⋊C4—112no—
522C22×C22⋊C4—112no—
523#391—112no—
524#391—112no—
525#390—112no—
526#390—112no—
527#389—112no—
528#389—112no—
529#389—112no—
530#389—112no—
531#388—112no—
532#388—112no—
533#388—112no—
534#388—112no—
535#388—112no—
536#388—112no—
537#388—112no—
538#388C2×D1112yescomplemented
539#387—112no—
540#387—112no—
541#387—112no—
542#387—112no—
543#387—112no—
544#387—112no—
545#387—112no—
546#387C2×D1112yescomplemented
547#386—112no—
548#386—112no—
549#386—112no—
550#386—112no—
551#386—112no—
552#386—112no—
553#386—112no—
554#386C2×D1112yes—
555#385—112no—
556#385—112no—
557#385—112no—
558#385—112no—
559#385—112no—
560#385—112no—
561#385—112no—
562#385—112no—
563#383—111no—
564#383C2×D1111yescharacteristic, complemented
565#382—111no—
566#382—111no—
567#381—111no—
568#381—111no—
569#381—111no—
570#381—112no—
571#381—111no—
572#381—111no—
573#381—112no—
574#381C2×D1111yescharacteristic, complemented
575#380—111no—
576#380—111no—
577#380—112no—
578#380—112no—
579#380—111no—
580#380—111no—
581#380—111no—
582#380C2×D1111yescharacteristic
583C4×C4⋊C4—111no—
584C4×C4⋊C4—111no—
585C4×C22⋊C4—112no—
586C4×C22⋊C4—112no—
587C4×C22⋊C4—111no—
588C4×C22⋊C4—112no—
589C4×C22⋊C4C2×D1112yes—
590C4×C22⋊C4C2×D1111yescharacteristic, complemented
591#376—111no—
592#376C2×D1111yescharacteristic, complemented
593C2×#95—111no—
594C2×#95—112no—
595C2×#95—111no—
596C2×#95—111no—
597C2×#95—111no—
598C2×#95—111no—
599C2×#95C2×D1111yescharacteristic
600C22×C11—22no—
601C22×C11—22no—
602C22×C11—24no—
603C22×C11—24no—
604C22×C11—22no—
605C22×C11—22no—
606C22×C11—22no—
607C22×C11—42no—
608C22×C11—42no—
609C22×C11#52014yes—
610C22×C11C24×C411yescharacteristic
611C22×C11C2×H(5,𝔽2)11yescharacteristic
612C22×C11C2×H(5,𝔽2)12yes—
613C22×C11C2×2−1+411yescharacteristic
614C22×C11#58512yes—
615C2×D11—22no—
616C2×D11—22no—
617C2×D11—24no—
618C2×D11—24no—
619C2×D11—22no—
620C2×D11—22no—
621C2×D11—22no—
622C2×D11—22no—
623C2×D11—22no—
624C2×D11—22no—
625C2×D11—416no—
626C2×D11—42no—
627C2×D11—42no—
628C2×D11—42no—
629C2×D11—42no—
630C2×D11#51814yes—
631C4×C11—22no—
632C4×C11—22no—
633C4×C11—22no—
634C4×C11—22no—
635C4×C11—22no—
636C4×C11—42no—
637C4×C11—42no—
638C4×C11—42no—
639C4×C11—42no—
640Dic11—22no—
641Dic11—22no—
642Dic11—22no—
643Dic11—22no—
644Dic11—22no—
645Dic11—42no—
646Dic11—42no—
647Dic11—42no—
648Dic11—42no—
649C25—111no—
650C2×#41—118no—
651C2×#41—444no—
652C22×Q8—111no—
653C22×D4—111no—
654C22×D4—111no—
655C22×D4—111no—
656C22×D4—111no—
657C22×D4—111no—
658C22×D4—111no—
659C22×D4C22×D1111yescharacteristic
660C23×C4—111no—
661C23×C4—111no—
662C23×C4—111no—
663C23×C4—118no—
664C23×C4—111no—
665C23×C4—111no—
666C23×C4—111no—
667C23×C4—112no—
668C23×C4—112no—
669C23×C4—112no—
670C23×C4—112no—
671C23×C4—112no—
672C23×C4—444no—
673C23×C4C22×D1112yes—
674C23×C4C22×D1111yescharacteristic
675C23×C4C22×D1111yescharacteristic
676#123—118no—
677#123—118no—
678C22⋊Q8—118no—
679C22⋊Q8—118no—
680#121—118no—
681#121—118no—
682#120—118no—
683#120—118no—
684C4×D4—118no—
685C4×D4—118no—
686C4×D4—118no—
687C4×D4—444no—
688C4×D4—444no—
689C4×D4—444no—
690C4×D4—444no—
691C4×D4C4×D1118yescomplemented
692#117—118no—
693C2×C4⋊C4—111no—
694C2×C4⋊C4—111no—
695C2×C4⋊C4—111no—
696C2×C4⋊C4—111no—
697C2×C4⋊C4—111no—
698C2×C4⋊C4—112no—
699C2×C4⋊C4—112no—
700C2×C4⋊C4—112no—
701C2×C4⋊C4—112no—
702C2×C4⋊C4—112no—
703C2×C4⋊C4—112no—
704C2×C4⋊C4—112no—
705C2×C4⋊C4—112no—
706C2×C4⋊C4—112no—
707C2×C4⋊C4—444no—
708C2×C4⋊C4C22×D1112yes—
709C2×C4⋊C4C22×D1111yescharacteristic
710C2×C22⋊C4—111no—
711C2×C22⋊C4—111no—
712C2×C22⋊C4—111no—
713C2×C22⋊C4—111no—
714C2×C22⋊C4—111no—
715C2×C22⋊C4—111no—
716C2×C22⋊C4—111no—
717C2×C22⋊C4—111no—
718C2×C22⋊C4—112no—
719C2×C22⋊C4—112no—
720C2×C22⋊C4—112no—
721C2×C22⋊C4—112no—
722C2×C22⋊C4—112no—
723C2×C22⋊C4—112no—
724C2×C22⋊C4—112no—
725C2×C22⋊C4—112no—
726C2×C22⋊C4—112no—
727C2×C22⋊C4—112no—
728C2×C22⋊C4—112no—
729C2×C22⋊C4—444no—
730C2×C22⋊C4—444no—
731C2×C22⋊C4C22×D1112yes—
732C2×C22⋊C4C22×D1112yes—
733C2×C22⋊C4C22×D1112yes—
734C2×C22⋊C4C22×D1111yescharacteristic
735C2×C22⋊C4C22×D1111yescharacteristic
736C2×C42—111no—
737C2×C42—112no—
738C2×C42—112no—
739C2×C42—112no—
740C2×C42—112no—
741C2×C42C22×D1112yes—
742C2×C42C22×D1112yes—
743C2×C42C22×D1111yescharacteristic
744#95—111no—
745#95—111no—
746#95—111no—
747#95—111no—
748#95—112no—
749#95—112no—
750#95—112no—
751#95—112no—
752#95—112no—
753#95—112no—
754#95—112no—
755#95—112no—
756#95—112no—
757#95—112no—
758#95—112no—
759#95—112no—
760#95—112no—
761#95—112no—
762#95—112no—
763#95C22×D1111yescharacteristic
764#95C22×D1111yescharacteristic
765#95C22×D1111yescharacteristic
766#95C22×D1111yescharacteristic
767#95C22×D1112yes—
768#95C22×D1112yes—
769#95C22×D1112yes—
770#95C22×D1112yes—
771#95C22×D1112yes—
772C2×C11—24no—
773C2×C11—42no—
774C2×C11C2×#51811yescharacteristic
775C2×C11C2×#52011yescharacteristic
776C2×C11#342811yescharacteristic
777C2×C11#353412yes—
778C2×C11#353512yes—
779D11—24no—
780D11—42no—
781D11—42no—
782C24—111no—
783C24—111no—
784C24—111no—
785C24—114no—
786C24—224no—
787C24—222no—
788C24—222no—
789C24—442no—
790C24C23×D1111yescharacteristic
791C24C23×D1111yescharacteristic
792#41—4416no—
793C2×Q8—114no—
794C2×Q8—442no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—114no—
798C2×D4—114no—
799C2×D4—114no—
800C2×D4—114no—
801C2×D4—114no—
802C2×D4—114no—
803C2×D4—224no—
804C2×D4—224no—
805C2×D4—222no—
806C2×D4—222no—
807C2×D4—442no—
808C2×D4—442no—
809C2×D4—442no—
810C2×D4C2×C4×D1114yes—
811C22×C4—24no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—111no—
817C22×C4—111no—
818C22×C4—111no—
819C22×C4—111no—
820C22×C4—111no—
821C22×C4—114no—
822C22×C4—114no—
823C22×C4—114no—
824C22×C4—114no—
825C22×C4—114no—
826C22×C4—114no—
827C22×C4—112no—
828C22×C4—112no—
829C22×C4—112no—
830C22×C4—112no—
831C22×C4—224no—
832C22×C4—224no—
833C22×C4—224no—
834C22×C4—224no—
835C22×C4—224no—
836C22×C4—442no—
837C22×C4—442no—
838C22×C4—442no—
839C22×C4—442no—
840C22×C4—442no—
841C22×C4—442no—
842C22×C4—442no—
843C22×C4—442no—
844C22×C4—442no—
845C22×C4—442no—
846C22×C4—4416no—
847C22×C4—442no—
848C22×C4—442no—
849C22×C4—442no—
850C22×C4—442no—
851C22×C4—442no—
852C22×C4—442no—
853C22×C4C2×C4×D1114yes—
854C22×C4C2×C4×D1114yes—
855C22×C4C23×D1112yes—
856C22×C4C23×D1112yes—
857C22×C4C23×D1112yes—
858C22×C4C23×D1112yes—
859C22×C4C23×D1111yescharacteristic
860C22×C4C23×D1111yescharacteristic
861C22×C4C23×D1111yescharacteristic
862C22×C4C23×D1111yescharacteristic
863C22×C4C23×D1111yescharacteristic
864C4⋊C4—42no—
865C4⋊C4—114no—
866C4⋊C4—114no—
867C4⋊C4—114no—
868C4⋊C4—114no—
869C4⋊C4—114no—
870C4⋊C4—442no—
871C4⋊C4—442no—
872C4⋊C4—442no—
873C4⋊C4—442no—
874C4⋊C4—442no—
875C4⋊C4—442no—
876C4⋊C4—442no—
877C4⋊C4—442no—
878C4⋊C4—442no—
879C4⋊C4C2×C4×D1114yes—
880C22⋊C4—24no—
881C22⋊C4—42no—
882C22⋊C4—42no—
883C22⋊C4—114no—
884C22⋊C4—114no—
885C22⋊C4—114no—
886C22⋊C4—114no—
887C22⋊C4—114no—
888C22⋊C4—114no—
889C22⋊C4—114no—
890C22⋊C4—114no—
891C22⋊C4—224no—
892C22⋊C4—224no—
893C22⋊C4—224no—
894C22⋊C4—442no—
895C22⋊C4—442no—
896C22⋊C4—442no—
897C22⋊C4—442no—
898C22⋊C4—442no—
899C22⋊C4—442no—
900C22⋊C4—442no—
901C22⋊C4—442no—
902C22⋊C4C2×C4×D1114yes—
903C22⋊C4C2×C4×D1114yes—
904C42—42no—
905C42—42no—
906C42—114no—
907C42—442no—
908C42—442no—
909C42—442no—
910C42—442no—
911C42C2×C4×D1114yes—
912C11#3438611yescharacteristic, complemented, Sylow
913C23—22no—
914C23—22no—
915C23—21no—
916C23—21no—
917C23—22no—
918C23—22no—
919C23—112no—
920C23—114no—
921C23—112no—
922C23—112no—
923C23—228no—
924C23—221no—
925C23—221no—
926C23—222no—
927C23—228no—
928C23—221no—
929C23—221no—
930C23—221no—
931C23—221no—
932C23—222no—
933C23—222no—
934C23—222no—
935C23—222no—
936C23—444no—
937C23—448no—
938C23—448no—
939C23C22×C4×D1112yes—
940C23C22×C4×D1112yes—
941C23#6704212yes—
942C23#6704312yes—
943C23C24×D1111yescharacteristic
944Q8—444no—
945D4—28no—
946D4—228no—
947D4—228no—
948D4—228no—
949D4—444no—
950D4—444no—
951D4—444no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—44no—
971C2×C4—44no—
972C2×C4—84no—
973C2×C4—112no—
974C2×C4—112no—
975C2×C4—112no—
976C2×C4—112no—
977C2×C4—112no—
978C2×C4—228no—
979C2×C4—228no—
980C2×C4—221no—
981C2×C4—221no—
982C2×C4—222no—
983C2×C4—222no—
984C2×C4—222no—
985C2×C4—222no—
986C2×C4—222no—
987C2×C4—222no—
988C2×C4—222no—
989C2×C4—222no—
990C2×C4—222no—
991C2×C4—222no—
992C2×C4—222no—
993C2×C4—222no—
994C2×C4—222no—
995C2×C4—222no—
996C2×C4—222no—
997C2×C4—222no—
998C2×C4—444no—
999C2×C4—444no—
1000C2×C4—444no—
1001C2×C4—444no—
1002C2×C4—884no—
1003C2×C4—884no—
1004C2×C4—884no—
1005C2×C4—884no—
1006C2×C4—884no—
1007C2×C4C22×C4×D1112yes—
1008C2×C4C22×C4×D1112yes—
1009C2×C4C22×C4×D1112yes—
1010C2×C4C22×C4×D1112yes—
1011C2×C4C22×C4×D1112yes—
1012C22—24no—
1013C22—24no—
1014C22—22no—
1015C22—22no—
1016C22—22no—
1017C22—22no—
1018C22—22no—
1019C22—42no—
1020C22—42no—
1021C22—114no—
1022C22—224no—
1023C22—224no—
1024C22—222no—
1025C22—222no—
1026C22—222no—
1027C22—222no—
1028C22—222no—
1029C22—222no—
1030C22—222no—
1031C22—222no—
1032C22—4416no—
1033C22—442no—
1034C22—442no—
1035C22—442no—
1036C22—442no—
1037C22#1062305414yes—
1038C22C23×C4×D1111yescharacteristic
1039C22C2×#6704211yescharacteristic
1040C22C2×#6704311yescharacteristic
1041C22#1062345312yes—
1042C22D11×H(5,𝔽2)12yes—
1043C4—22no—
1044C4—22no—
1045C4—22no—
1046C4—22no—
1047C4—22no—
1048C4—42no—
1049C4—42no—
1050C4—42no—
1051C4—42no—
1052C4—222no—
1053C4—222no—
1054C4—222no—
1055C4—222no—
1056C4—222no—
1057C4—442no—
1058C4—442no—
1059C4—442no—
1060C4—442no—
1061C2—24no—
1062C2—42no—
1063C2—224no—
1064C2—442no—
1065C2—442no—
1066C2D11×#51811yescharacteristic
1067C2C2×#1062305411yescharacteristic
1068C2#1308181511yescharacteristic
1069C2#1308279312yes—
1070C2#1308281212yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2353C2
socle, cosocleC23×C11C25
prime radicalC2×#10623078C2
hypercenter#2353D11
hypocenterC11#34386
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2353

Complements

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

NH ≅ G/Ntype
2. #13071781C2semidirect
3. #13071769C2semidirect
4. #13071598C2semidirect
5. #13071596C2semidirect
6. #13071552C2semidirect
7. #13071526C2semidirect
8. #13071520C2semidirect
9. #13071477C2semidirect
10. #13071473C2semidirect
11. #13071447C2semidirect
12. #13071440C2semidirect
13. #13071344C2semidirect
14. #13071317C2semidirect
15. #13071289C2semidirect
16. #13071286C2semidirect
17. #13071260C2semidirect
18. #13071256C2semidirect
19. #13071247C2semidirect
20. #13071243C2semidirect
21. C2×#10622277C2semidirect
22. D11×#380C2semidirect
23. C11×#2353C2semidirect
33. #10623078C4semidirect
47. C11×#388C22semidirect
48. C11×#387C22semidirect
50. C11×#383C22semidirect
51. C11×#381C22semidirect
54. C4×C11×C22⋊C4C22semidirect
55. C11×#376C22semidirect
59. #10622825C22semidirect
63. C2×C11⋊#95C22semidirect
64. #10622602C22semidirect
66. #10622598C22semidirect
67. #10622585C22semidirect
69. #10622571C22semidirect
72. #10622569C22semidirect
74. #10622563C22semidirect
76. #10622559C22semidirect
77. #10622558C22semidirect
82. #10622549C22semidirect
83. C4×C4⋊Dic11C22semidirect
84. #10622546C22semidirect
85. #10622546C22semidirect
86. #10622542C22semidirect
87. #10622541C22semidirect
90. #10622283C22semidirect
92. #10622282C22semidirect
95. #10622281C22semidirect
98. #10622280C22semidirect
100. #10622279C22semidirect
109. #10622277C22semidirect
112. D11×#95C22semidirect
113. #10622268C22semidirect
114. #10622268C22semidirect
115. #10622268C22semidirect
116. #10622267C22semidirect
117. #10622265C22semidirect
118. #10622264C22semidirect
119. #10622263C22semidirect
120. #10622262C22semidirect
121. #10622261C22semidirect
122. #10622260C22semidirect
123. #10622259C22semidirect
137. C2×#4339C2×C4semidirect
141. C22×C4×D11C2×C4semidirect
151. C4×D4×C11C2×C4semidirect
166. #66992C2×C4semidirect
167. #66990C2×C4semidirect
169. C4×C22⋊D11C2×C4semidirect
170. C4×C22⋊D11C2×C4semidirect
206. #66949C2×C4semidirect
207. #66947C2×C4semidirect
209. #66937C2×C4semidirect
210. #66936C2×C4semidirect
211. #66935C2×C4semidirect
215. #66931C2×C4semidirect
217. C4×D44C2×C4semidirect
218. #66925C2×C4semidirect
384. #2353D11semidirect
538. #388C2×D11semidirect
546. #387C2×D11semidirect
564. #383C2×D11semidirect
574. #381C2×D11semidirect
590. C4×C22⋊C4C2×D11semidirect
592. #376C2×D11semidirect
691. C4×D4C4×D11semidirect
912. C11#34386semidirect

Maximal subgroups

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

subgroupindex
C2×#106230782
#130717812
#130717692
#130715982
#130715962
#130715522
#130715262
#130715202
#130714772
#130714732
#130714472
#130714402
#130713442
#130713172
#130712892
#130712862
#130712602
#130712562
#130712472
#130712432
C2×#106222772
D11×#3802
C11×#23532
#3438611