Finite Group Databasebeta

← #14916737

Subgroups — #14916737

Order 2816.

3082 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#121C211yesmaximal, characteristic
2#13071774C212yesmaximal, complemented
3#13071767C212yesmaximal, complemented
4#13071637C211yesmaximal, characteristic, complemented
5#13071634C211yesmaximal, characteristic, complemented
6#13071631C211yesmaximal, characteristic, complemented
7#13071628C211yesmaximal, characteristic, complemented
8#13071492C211yesmaximal, characteristic, complemented
9#13071489C211yesmaximal, characteristic, complemented
10#13071437C211yesmaximal, characteristic, complemented
11#13071437C212yesmaximal, complemented
12#13071434C212yesmaximal, complemented
13D4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
14#13071320C212yesmaximal, complemented
15#13071313C212yesmaximal, complemented
16#13071311C211yesmaximal, characteristic, complemented
17#13071309C211yesmaximal, characteristic, complemented
18#13071305C211yesmaximal, characteristic, complemented
19#13071227C212yesmaximal, complemented
20#13071210C212yesmaximal, complemented
21#13070995C211yesmaximal, characteristic, complemented
22D11×#380C211yesmaximal, characteristic, complemented
23C11×#2324C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C22×D4×D11C2212yes—
26C23×C4×D11C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic, complemented
29C2×C11×#117C2211yescharacteristic, complemented
30C2×#66992C2212yes—
31C2×#66991C2211yescharacteristic
32C2×D4×Dic11C2211yescharacteristic, complemented
33C2×#66983C2211yescharacteristic
34C2×C4×C22⋊D11C2212yescomplemented
35C22×(C2×D11)⋊C4C2212yes—
36C2×#66979C2211yescharacteristic, complemented
37D11×#121C4116yescomplemented
38C2×#66948C2211yescharacteristic
39C2×#66946C2212yescomplemented
40C2×#66946C2211yescharacteristic, complemented
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×C4⋊C4×D11C2211yescharacteristic, complemented
43C2×C4⋊C4×D11C2211yescharacteristic, complemented
44C2×#66937C2212yes—
45C2×(C22⋊D11)⋊C4C2212yescomplemented
46C2×C22⋊C4×D11C2212yes—
47C2×C22⋊C4×D11C2212yes—
48C2×C22⋊C4×D11C2212yes—
49C2×C4×D44C2211yescharacteristic, complemented
50C2×C4×D44C2212yescomplemented
51C11×#390C2211yescharacteristic, complemented
52C11×#390C2212yescomplemented
53C11×#389C2211yescharacteristic, complemented
54C11×#388C2212yescomplemented
55C11×#386C2212yescomplemented
56C11×#385C2212yescomplemented
57C11×#380C2211yescharacteristic, complemented
58C4×C11×C4⋊C4C2211yescharacteristic, complemented
59#10622834C2211yescharacteristic, complemented
60#10622834C2212yescomplemented
61#10622833C2212yescomplemented
62#10622826C2212yescomplemented
63#10622825C2211yescharacteristic, complemented
64#10622823C2212yescomplemented
65#10622603C2212yescomplemented
66#10622602C2212yescomplemented
67#10622602C2212yescomplemented
68#10622601C2211yescharacteristic, complemented
69#10622600C2211yescharacteristic
70#10622600C2212yes—
71#10622600C2211yescharacteristic
72#10622600C2211yescharacteristic
73#10622600C2211yescharacteristic
74#10622600C2211yescharacteristic, complemented
75#10622600C2211yescharacteristic, complemented
76#10622598C2211yescharacteristic, complemented
77#10622591C2212yescomplemented
78C4⋊C4×Dic11C2211yescharacteristic, complemented
79C4⋊C4×Dic11C2211yescharacteristic, complemented
80#10622586C2211yescharacteristic, complemented
81#10622571C2212yescomplemented
82#10622570C2212yescomplemented
83#10622570C2212yescomplemented
84#10622569C2212yescomplemented
85#10622569C2212yescomplemented
86#10622569C2212yescomplemented
87#10622569C2212yescomplemented
88#10622569C2212yescomplemented
89#10622569C2212yescomplemented
90#10622568C2212yes—
91#10622568C2211yescharacteristic
92#10622568C2212yes—
93#10622568C2211yescharacteristic
94#10622564C2212yescomplemented
95#10622563C2212yescomplemented
96#10622559C2212yescomplemented
97#10622558C2212yescomplemented
98#10622557C2212yescomplemented
99#10622556C2211yescharacteristic, complemented
100#10622556C2211yescharacteristic, complemented
101#10622555C2212yescomplemented
102#10622553C2212yescomplemented
103#10622552C2211yescharacteristic, complemented
104C4×(C2×D11)⋊C4C2211yescharacteristic
105C4×(C2×D11)⋊C4C2212yes—
106C4×(C2×D11)⋊C4C2211yescharacteristic
107C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
108C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
109C4×C4⋊Dic11C2211yescharacteristic, complemented
110#10622546C2212yescomplemented
111#10622541C2211yescharacteristic, complemented
112#10622283C2212yescomplemented
113#10622282C2212yescomplemented
114#10622281C2212yescomplemented
115#10622281C2212yescomplemented
116#10622280C2212yes—
117#10622280C2212yes—
118#10622279C2212yes—
119#10622278C2212yescomplemented
120#10622278C2212yescomplemented
121D11×#95C2212yescomplemented
122#10622268C2212yescomplemented
123#10622265C2212yescomplemented
124C24×D11C2311yescharacteristic
125C24×D11C2312yes—
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C22×C22⋊D11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C23×Dic11C2312yes—
134C23×Dic11C2311yescharacteristic
135C2×D4×D11—42no—
136C2×D4×D11—42no—
137C2×D4×D11—44no—
138C2×D4×D11—44no—
139C2×D4×D11C2×C418yescomplemented
140C2×D4×D11C2×C4116yescomplemented
141C22×D44C2312yes—
142C22×D44C2311yescharacteristic
143C22×C4×D11—42no—
144C22×C4×D11—42no—
145C22×C4×D11C2×C418yescomplemented
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2312yes—
149C22×C4×D11C2312yes—
150C22×C4×D11C2312yes—
151C22×C4×D11C2312yes—
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2312yes—
154C22×C4×D11C2311yescharacteristic
155C11×#121C2×C418yescomplemented
156C4×D4×C11—42no—
157C11×#117—42no—
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2312yes—
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2312yes—
171C2×C42×C11C2311yescharacteristic
172C2×C42×C11C2311yescharacteristic
173C2×C42×C11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2311yescharacteristic
177C2×C22⋊Dic11C2311yescharacteristic
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181#66992C2×C4116yescomplemented
182#66991C2×C418yescomplemented
183D4×Dic11—42no—
184#66983C2×C418yescomplemented
185C4×C22⋊D11—44no—
186C2×(C2×D11)⋊C4—44no—
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2311yescharacteristic
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2311yescharacteristic
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—
205#66979—42no—
206C2×C4⋊Dic11C2311yescharacteristic
207C2×C4⋊Dic11C2311yescharacteristic
208C2×C4⋊Dic11C2312yes—
209C2×C4⋊Dic11C2311yescharacteristic
210C2×C4⋊Dic11C2311yescharacteristic
211C2×C4⋊Dic11C2311yescharacteristic
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2312yes—
222#66948C2×C418yescomplemented
223#66946—42no—
224#66946—44no—
225C4⋊C4×D11—42no—
226C4⋊C4×D11—42no—
227C4⋊C4×D11C2×C418yescomplemented
228#66937C2×C4116yescomplemented
229(C22⋊D11)⋊C4—44no—
230C22⋊C4×D11—44no—
231C22⋊C4×D11—44no—
232C22⋊C4×D11C2×C4116yescomplemented
233C4×D44—42no—
234C4×D44—44no—
235C11×#95C2312yes—
236C11×#95C2312yes—
237C11×#95C2312yes—
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2311yescharacteristic
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2311yescharacteristic
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2312yes—
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2312yes—
252C11⋊#95C2311yescharacteristic
253C11⋊#95C2311yescharacteristic
254C11⋊#95C2311yescharacteristic
255#34379—111nomaximal, Sylow
256C24×C11C2411yescharacteristic
257C24×C11C2412yes—
258C23×D11—22no—
259C23×D11—22no—
260C23×D11—22no—
261C23×D11—22no—
262C23×D11—24no—
263C23×D11—24no—
264C23×D11—41no—
265C23×D11—41no—
266C23×D11—42no—
267C23×D11—42no—
268C23×D11—42no—
269C23×D11—42no—
270C23×D11C22×C414yes—
271C23×D11C22×C418yes—
272C23×D11C2412yes—
273C23×D11C2411yescharacteristic
274C23×D11C2411yescharacteristic
275C2×D4×C11—22no—
276C2×D4×C11—22no—
277C2×D4×C11—42no—
278C2×D4×C11—42no—
279C2×D4×C11C22×C414yes—
280C2×D4×C11C22×C418yes—
281C22×C4×C11—22no—
282C22×C4×C11—22no—
283C22×C4×C11—42no—
284C22×C4×C11—42no—
285C22×C4×C11—42no—
286C22×C4×C11C22×C414yes—
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2412yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2412yes—
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C2×C22⋊D11—24no—
297C2×C22⋊D11—24no—
298C2×C22⋊D11—42no—
299C2×C22⋊D11—42no—
300C2×C22⋊D11—42no—
301C2×C22⋊D11—42no—
302C2×C22⋊D11C22×C418yes—
303C2×C22⋊D11C22×C418yes—
304C2×C22⋊D11C22×C418yes—
305C22×Dic11—41no—
306C22×Dic11—41no—
307C22×Dic11—42no—
308C22×Dic11—42no—
309C22×Dic11—42no—
310C22×Dic11C22×C414yes—
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2412yes—
315C22×Dic11C2412yes—
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2412yes—
319C22×Dic11C2411yescharacteristic
320D4×D11—416no—
321D4×D11—432no—
322C2×D44—24no—
323C2×D44—24no—
324C2×D44—22no—
325C2×D44—22no—
326C2×D44C22×C418yes—
327C2×D44C22×C414yes—
328C2×C4×D11—24no—
329C2×C4×D11—24no—
330C2×C4×D11—22no—
331C2×C4×D11—22no—
332C2×C4×D11—22no—
333C2×C4×D11—22no—
334C2×C4×D11—41no—
335C2×C4×D11—41no—
336C2×C4×D11—41no—
337C2×C4×D11—41no—
338C2×C4×D11—42no—
339C2×C4×D11—42no—
340C2×C4×D11—42no—
341C2×C4×D11—42no—
342C2×C4×D11—42no—
343C2×C4×D11—42no—
344C2×C4×D11—42no—
345C2×C4×D11—42no—
346C2×C4×D11—42no—
347C2×C4×D11—42no—
348C2×C4×D11—42no—
349C2×C4×D11—42no—
350C2×C4×D11—416no—
351C2×C4×D11C22×C414yes—
352C2×C4×D11C22×C414yes—
353C2×C4×D11C22×C414yes—
354C2×C4×D11C22×C418yes—
355C2×C4×D11C22×C414yes—
356C11×C4⋊C4—22no—
357C11×C4⋊C4—22no—
358C11×C4⋊C4—42no—
359C11×C4⋊C4—41no—
360C11×C4⋊C4—41no—
361C11×C4⋊C4C22×C414yes—
362C11×C22⋊C4—42no—
363C11×C22⋊C4—42no—
364C11×C22⋊C4—42no—
365C11×C22⋊C4—41no—
366C11×C22⋊C4—41no—
367C11×C22⋊C4—42no—
368C11×C22⋊C4C22×C418yes—
369C42×C11—22no—
370C42×C11—22no—
371C42×C11—42no—
372C22⋊Dic11—42no—
373C22⋊Dic11—42no—
374C22⋊Dic11—41no—
375C22⋊Dic11—41no—
376C22⋊Dic11—42no—
377C22⋊Dic11—42no—
378C22⋊Dic11C22×C418yes—
379(C2×D11)⋊C4—22no—
380(C2×D11)⋊C4—24no—
381(C2×D11)⋊C4—22no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—22no—
384(C2×D11)⋊C4—22no—
385(C2×D11)⋊C4—22no—
386(C2×D11)⋊C4—22no—
387(C2×D11)⋊C4—22no—
388(C2×D11)⋊C4—22no—
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—
395(C2×D11)⋊C4C22×C418yes—
396(C2×D11)⋊C4C22×C418yes—
397C4⋊Dic11—22no—
398C4⋊Dic11—22no—
399C4⋊Dic11—42no—
400C4⋊Dic11—41no—
401C4⋊Dic11—41no—
402C4⋊Dic11C22×C414yes—
403Dic11⋊C4—42no—
404Dic11⋊C4—42no—
405Dic11⋊C4—42no—
406Dic11⋊C4—42no—
407Dic11⋊C4C22×C418yes—
408C4×Dic11—22no—
409C4×Dic11—22no—
410C4×Dic11—42no—
411C4×Dic11—42no—
412C4×Dic11—42no—
413C22×#121—111no—
414#2377—112no—
415#2377—112no—
416#2361—111no—
417#2361—111no—
418#2361—111no—
419#2361—111no—
420#2345—111no—
421#2345—111no—
422D4×C22⋊C4—111no—
423D4×C22⋊C4—112no—
424D4×C22⋊C4—112no—
425D4×C22⋊C4—111no—
426#2325—112no—
427#2325—112no—
428#2324—111no—
429#2324—111no—
430#2324—111no—
431#2324D1111yescharacteristic, complemented
432#2315—112no—
433#2312—112no—
434#2280—111no—
435C2×#380—111no—
436C23×C11—21no—
437C23×C11—21no—
438C23×C11—22no—
439C23×C11—22no—
440C23×C11—22no—
441C23×C11—21no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—21no—
445C23×C11—21no—
446C23×C11—21no—
447C23×C11—22no—
448C23×C11C23×C414yes—
449C23×C11C23×C412yes—
450C23×C11C2511yescharacteristic
451C22×D11—21no—
452C22×D11—21no—
453C22×D11—21no—
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—28no—
466C22×D11—28no—
467C22×D11—216no—
468C22×D11—44no—
469C22×D11—44no—
470C22×D11—44no—
471C22×D11—44no—
472C22×D11—44no—
473C22×D11—48no—
474C22×D11—48no—
475C22×D11—84no—
476C22×D11—84no—
477C22×D11—84no—
478C22×D11—84no—
479C22×D11C23×C414yes—
480C22×D11C23×C412yes—
481C22×D11C23×C412yes—
482C22×D11H(5,𝔽2)12yes—
483C22×D11H(5,𝔽2)12yes—
484C22×D11H(5,𝔽2)12yes—
485C22×D112−1+412yes—
486D4×C11—28no—
487D4×C11—48no—
488C2×C4×C11—22no—
489C2×C4×C11—21no—
490C2×C4×C11—22no—
491C2×C4×C11—21no—
492C2×C4×C11—28no—
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—21no—
500C2×C4×C11—21no—
501C2×C4×C11—22no—
502C2×C4×C11—21no—
503C2×C4×C11—22no—
504C2×C4×C11—21no—
505C2×C4×C11—21no—
506C2×C4×C11—21no—
507C2×C4×C11—21no—
508C2×C4×C11—21no—
509C2×C4×C11—21no—
510C2×C4×C11—21no—
511C2×C4×C11—84no—
512C2×C4×C11C23×C414yes—
513C2×C4×C11C23×C412yes—
514C2×C4×C11C23×C412yes—
515C2×C4×C11H(5,𝔽2)12yes—
516C2×C4×C11H(5,𝔽2)12yes—
517C22⋊D11—216no—
518C22⋊D11—48no—
519C22⋊D11—48no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—21no—
523C2×Dic11—21no—
524C2×Dic11—21no—
525C2×Dic11—21no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—21no—
529C2×Dic11—21no—
530C2×Dic11—21no—
531C2×Dic11—21no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—21no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—21no—
538C2×Dic11—21no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—21no—
542C2×Dic11—21no—
543C2×Dic11—21no—
544C2×Dic11—44no—
545C2×Dic11—84no—
546C2×Dic11C23×C412yes—
547C2×Dic11C23×C414yes—
548C2×Dic11C23×C412yes—
549D44—216no—
550D44—28no—
551C4×D11—28no—
552C4×D11—28no—
553C4×D11—44no—
554C4×D11—44no—
555C4×D11—48no—
556C4×D11—84no—
557C4×D11—84no—
558C4×D11—84no—
559C4×D11—84no—
560C23×D4—111no—
561C23×D4—112no—
562C24×C4—111no—
563C2×#121—111no—
564C2×#121—112no—
565C2×#121—111no—
566C2×#121—1116no—
567C2×#121—111no—
568C2×#121—112no—
569C2×#121C2×D1111yescharacteristic
570C2×C4×D4—111no—
571C2×C4×D4—112no—
572C2×C4×D4—111no—
573C2×C4×D4—112no—
574C2×C4×D4—112no—
575C2×C4×D4—111no—
576C2×C4×D4—112no—
577C2×C4×D4C2×D1111yescharacteristic, complemented
578C2×#117—111no—
579C2×#117C2×D1111yescharacteristic, complemented
580C22×C4⋊C4—111no—
581C22×C4⋊C4—111no—
582C22×C4⋊C4—111no—
583C22×C22⋊C4—112no—
584C22×C22⋊C4—112no—
585C22×C22⋊C4—112no—
586C22×C22⋊C4—112no—
587#390—111no—
588#390—112no—
589#390—111no—
590#390—112no—
591#390—112no—
592#390—111no—
593#390C2×D1111yescharacteristic, complemented
594#390C2×D1112yescomplemented
595#389—111no—
596#389—111no—
597#389—111no—
598#389C2×D1111yescharacteristic, complemented
599#388—112no—
600#388—112no—
601#388—112no—
602#388—112no—
603#388—112no—
604#388—112no—
605#388—112no—
606#388C2×D1112yescomplemented
607#387—112no—
608#387—112no—
609#387—112no—
610#387—112no—
611#386—112no—
612#386—112no—
613#386—112no—
614#386—112no—
615#386—112no—
616#386—112no—
617#386—112no—
618#386—112no—
619#386—112no—
620#386—112no—
621#386—112no—
622#386C2×D1112yescomplemented
623#385—112no—
624#385—112no—
625#385—112no—
626#385—112no—
627#385—112no—
628#385—112no—
629#385—112no—
630#385C2×D1112yescomplemented
631#381—111no—
632#381—111no—
633#380—111no—
634#380—111no—
635#380—111no—
636#380—112no—
637#380—111no—
638#380—111no—
639#380—111no—
640#380—111no—
641#380—112no—
642#380—112no—
643#380—112no—
644#380C2×D1111yescharacteristic, complemented
645#379—112no—
646#379—112no—
647#379—111no—
648#379—111no—
649C4×C4⋊C4—111no—
650C4×C4⋊C4—111no—
651C4×C4⋊C4—111no—
652C4×C4⋊C4C2×D1111yescharacteristic, complemented
653C4×C22⋊C4—112no—
654C4×C22⋊C4—111no—
655C4×C22⋊C4—111no—
656C4×C22⋊C4—111no—
657C4×C22⋊C4—111no—
658C4×C22⋊C4—112no—
659C2×#95—112no—
660C22×C11—22no—
661C22×C11—24no—
662C22×C11—22no—
663C22×C11—24no—
664C22×C11—22no—
665C22×C11—24no—
666C22×C11—41no—
667C22×C11—41no—
668C22×C11—42no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—41no—
672C22×C11—41no—
673C22×C11—42no—
674C22×C11C24×C411yescharacteristic
675C22×C11C2×H(5,𝔽2)11yescharacteristic
676C22×C11C2×H(5,𝔽2)11yescharacteristic
677C22×C11C2×H(5,𝔽2)11yescharacteristic
678C22×C11C2×H(5,𝔽2)11yescharacteristic
679C22×C11C2×H(5,𝔽2)11yescharacteristic
680C22×C11C2×2−1+411yescharacteristic
681C2×D11—22no—
682C2×D11—22no—
683C2×D11—22no—
684C2×D11—22no—
685C2×D11—22no—
686C2×D11—22no—
687C2×D11—22no—
688C2×D11—22no—
689C2×D11—22no—
690C2×D11—22no—
691C2×D11—22no—
692C2×D11—22no—
693C2×D11—24no—
694C2×D11—24no—
695C2×D11—24no—
696C2×D11—416no—
697C2×D11—42no—
698C2×D11—42no—
699C2×D11—42no—
700C2×D11—42no—
701C2×D11—816no—
702C2×D11#51814yes—
703C2×D11#52014yes—
704C4×C11—22no—
705C4×C11—24no—
706C4×C11—41no—
707C4×C11—41no—
708C4×C11—41no—
709C4×C11—42no—
710C4×C11—41no—
711C4×C11—42no—
712C4×C11#51814yes—
713Dic11—22no—
714Dic11—22no—
715Dic11—24no—
716Dic11—41no—
717Dic11—41no—
718Dic11—42no—
719Dic11—41no—
720Dic11—42no—
721Dic11—41no—
722C25—111no—
723C25—112no—
724C22×D4—112no—
725C22×D4—112no—
726C22×D4—112no—
727C22×D4—118no—
728C22×D4—1116no—
729C22×D4—112no—
730C22×D4—111no—
731C22×D4—442no—
732C22×D4—442no—
733C22×D4—444no—
734C22×D4—444no—
735C22×D4C22×D1111yescharacteristic
736C22×D4C22×D1112yes—
737C23×C4—111no—
738C23×C4—111no—
739C23×C4—111no—
740C23×C4—118no—
741C23×C4—111no—
742C23×C4—112no—
743C23×C4—111no—
744C23×C4—112no—
745C23×C4—112no—
746C23×C4—112no—
747C23×C4—112no—
748C23×C4—112no—
749C23×C4—442no—
750C23×C4—442no—
751C23×C4C22×D1111yescharacteristic
752C23×C4C22×D1112yes—
753#121—118no—
754#121—1116no—
755#121—118no—
756#121—118no—
757#121—1116no—
758#121C4×D1118yescomplemented
759C4×D4—42no—
760C4×D4—442no—
761C4×D4—444no—
762C4×D4—442no—
763C4×D4—442no—
764C4×D4—444no—
765C4×D4—444no—
766C4×D4—444no—
767#117—42no—
768#117—442no—
769C2×C4⋊C4—111no—
770C2×C4⋊C4—112no—
771C2×C4⋊C4—118no—
772C2×C4⋊C4—111no—
773C2×C4⋊C4—111no—
774C2×C4⋊C4—112no—
775C2×C4⋊C4—112no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—112no—
779C2×C4⋊C4—112no—
780C2×C4⋊C4—112no—
781C2×C4⋊C4—442no—
782C2×C4⋊C4—442no—
783C2×C4⋊C4C22×D1111yescharacteristic
784C2×C4⋊C4C22×D1111yescharacteristic
785C2×C4⋊C4C22×D1111yescharacteristic
786C2×C4⋊C4C22×D1111yescharacteristic
787C2×C4⋊C4C22×D1112yes—
788C2×C4⋊C4C22×D1111yescharacteristic
789C2×C22⋊C4—112no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—1116no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—111no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—111no—
798C2×C22⋊C4—111no—
799C2×C22⋊C4—111no—
800C2×C22⋊C4—111no—
801C2×C22⋊C4—111no—
802C2×C22⋊C4—111no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—111no—
806C2×C22⋊C4—111no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—444no—
816C2×C22⋊C4—444no—
817C2×C22⋊C4—444no—
818C2×C22⋊C4C22×D1112yes—
819C2×C22⋊C4C22×D1112yes—
820C2×C22⋊C4C22×D1111yescharacteristic
821C2×C22⋊C4C22×D1111yescharacteristic
822C2×C22⋊C4C22×D1112yes—
823C2×C22⋊C4C22×D1112yes—
824C2×C22⋊C4C22×D1112yes—
825C2×C42—111no—
826C2×C42—111no—
827C2×C42—112no—
828C2×C42—112no—
829C2×C42—112no—
830C2×C42C22×D1111yescharacteristic
831C2×C42C22×D1111yescharacteristic
832C2×C42C22×D1112yes—
833#95—112no—
834#95—112no—
835#95—112no—
836#95—111no—
837#95—111no—
838#95—111no—
839#95—111no—
840#95—111no—
841#95—111no—
842#95—111no—
843#95—111no—
844#95—112no—
845#95—112no—
846#95—112no—
847#95—112no—
848#95—112no—
849#95—112no—
850#95C22×D1112yes—
851#95C22×D1112yes—
852#95C22×D1112yes—
853C2×C11—42no—
854C2×C11—44no—
855C2×C11C2×#51811yescharacteristic
856C2×C11C2×#51811yescharacteristic
857C2×C11C2×#52011yescharacteristic
858C2×C11#353611yescharacteristic
859C2×C11#353611yescharacteristic
860C2×C11#353711yescharacteristic
861C2×C11#353711yescharacteristic
862D11—24no—
863D11—24no—
864D11—44no—
865C24—111no—
866C24—111no—
867C24—112no—
868C24—114no—
869C24—118no—
870C24—222no—
871C24—222no—
872C24—222no—
873C24—222no—
874C24—224no—
875C24—224no—
876C24—441no—
877C24—441no—
878C24—442no—
879C24—442no—
880C24—442no—
881C24—442no—
882C24C23×D1111yescharacteristic
883C24C23×D1112yes—
884C2×D4—22no—
885C2×D4—22no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—118no—
889C2×D4—118no—
890C2×D4—118no—
891C2×D4—118no—
892C2×D4—114no—
893C2×D4—224no—
894C2×D4—224no—
895C2×D4—224no—
896C2×D4—224no—
897C2×D4—222no—
898C2×D4—222no—
899C2×D4—4416no—
900C2×D4—442no—
901C2×D4—442no—
902C2×D4—442no—
903C2×D4—442no—
904C2×D4—4432no—
905C2×D4C2×C4×D1114yes—
906C2×D4C2×C4×D1118yes—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—111no—
913C22×C4—112no—
914C22×C4—111no—
915C22×C4—114no—
916C22×C4—114no—
917C22×C4—114no—
918C22×C4—114no—
919C22×C4—118no—
920C22×C4—114no—
921C22×C4—111no—
922C22×C4—111no—
923C22×C4—112no—
924C22×C4—111no—
925C22×C4—111no—
926C22×C4—112no—
927C22×C4—224no—
928C22×C4—224no—
929C22×C4—222no—
930C22×C4—222no—
931C22×C4—222no—
932C22×C4—222no—
933C22×C4—4416no—
934C22×C4—441no—
935C22×C4—441no—
936C22×C4—441no—
937C22×C4—441no—
938C22×C4—442no—
939C22×C4—442no—
940C22×C4—442no—
941C22×C4—442no—
942C22×C4—442no—
943C22×C4—442no—
944C22×C4—442no—
945C22×C4—442no—
946C22×C4—442no—
947C22×C4—442no—
948C22×C4—442no—
949C22×C4—442no—
950C22×C4—441no—
951C22×C4—441no—
952C22×C4—442no—
953C22×C4—442no—
954C22×C4—442no—
955C22×C4C2×C4×D1114yes—
956C22×C4C23×D1111yescharacteristic
957C22×C4C23×D1111yescharacteristic
958C22×C4C23×D1111yescharacteristic
959C22×C4C23×D1112yes—
960C22×C4C23×D1111yescharacteristic
961C22×C4C23×D1112yes—
962C22×C4C23×D1112yes—
963C22×C4C23×D1111yescharacteristic
964C22×C4C23×D1111yescharacteristic
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—41no—
968C4⋊C4—41no—
969C4⋊C4—42no—
970C4⋊C4—118no—
971C4⋊C4—114no—
972C4⋊C4—222no—
973C4⋊C4—222no—
974C4⋊C4—442no—
975C4⋊C4—442no—
976C4⋊C4—441no—
977C4⋊C4—441no—
978C4⋊C4—442no—
979C4⋊C4—442no—
980C4⋊C4—442no—
981C4⋊C4C2×C4×D1114yes—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—41no—
985C22⋊C4—41no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—118no—
989C22⋊C4—118no—
990C22⋊C4—118no—
991C22⋊C4—222no—
992C22⋊C4—224no—
993C22⋊C4—224no—
994C22⋊C4—222no—
995C22⋊C4—222no—
996C22⋊C4—222no—
997C22⋊C4—222no—
998C22⋊C4—222no—
999C22⋊C4—222no—
1000C22⋊C4—222no—
1001C22⋊C4—442no—
1002C22⋊C4—442no—
1003C22⋊C4—442no—
1004C22⋊C4—442no—
1005C22⋊C4—442no—
1006C22⋊C4—442no—
1007C22⋊C4—442no—
1008C22⋊C4—442no—
1009C22⋊C4—441no—
1010C22⋊C4—441no—
1011C22⋊C4—442no—
1012C22⋊C4—442no—
1013C22⋊C4C2×C4×D1118yes—
1014C42—22no—
1015C42—22no—
1016C42—42no—
1017C42—222no—
1018C42—222no—
1019C42—442no—
1020C42—442no—
1021C42—442no—
1022C11#3437911yescharacteristic, complemented, Sylow
1023C23—21no—
1024C23—22no—
1025C23—21no—
1026C23—22no—
1027C23—21no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—22no—
1035C23—112no—
1036C23—112no—
1037C23—112no—
1038C23—112no—
1039C23—112no—
1040C23—112no—
1041C23—114no—
1042C23—228no—
1043C23—228no—
1044C23—2216no—
1045C23—221no—
1046C23—221no—
1047C23—221no—
1048C23—221no—
1049C23—221no—
1050C23—221no—
1051C23—221no—
1052C23—221no—
1053C23—222no—
1054C23—222no—
1055C23—222no—
1056C23—222no—
1057C23—222no—
1058C23—222no—
1059C23—444no—
1060C23—448no—
1061C23—448no—
1062C23—444no—
1063C23—444no—
1064C23—444no—
1065C23—444no—
1066C23—884no—
1067C23—884no—
1068C23—884no—
1069C23—884no—
1070C23C22×C4×D1114yes—
1071C23C22×C4×D1112yes—
1072C23C24×D1111yescharacteristic
1073D4—28no—
1074D4—48no—
1075D4—2216no—
1076D4—2216no—
1077D4—228no—
1078D4—448no—
1079D4—448no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—28no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—21no—
1092C2×C4—22no—
1093C2×C4—21no—
1094C2×C4—22no—
1095C2×C4—21no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—84no—
1104C2×C4—112no—
1105C2×C4—114no—
1106C2×C4—112no—
1107C2×C4—221no—
1108C2×C4—221no—
1109C2×C4—221no—
1110C2×C4—221no—
1111C2×C4—222no—
1112C2×C4—222no—
1113C2×C4—228no—
1114C2×C4—228no—
1115C2×C4—222no—
1116C2×C4—221no—
1117C2×C4—221no—
1118C2×C4—221no—
1119C2×C4—221no—
1120C2×C4—222no—
1121C2×C4—221no—
1122C2×C4—221no—
1123C2×C4—222no—
1124C2×C4—222no—
1125C2×C4—222no—
1126C2×C4—221no—
1127C2×C4—222no—
1128C2×C4—221no—
1129C2×C4—221no—
1130C2×C4—221no—
1131C2×C4—221no—
1132C2×C4—221no—
1133C2×C4—444no—
1134C2×C4—444no—
1135C2×C4—448no—
1136C2×C4—444no—
1137C2×C4—884no—
1138C2×C4—884no—
1139C2×C4—884no—
1140C2×C4—884no—
1141C2×C4—884no—
1142C2×C4C22×C4×D1112yes—
1143C2×C4C22×C4×D1114yes—
1144C2×C4C22×C4×D1112yes—
1145C2×C4#6703712yes—
1146C2×C4#6704212yes—
1147C22—22no—
1148C22—24no—
1149C22—22no—
1150C22—24no—
1151C22—22no—
1152C22—24no—
1153C22—41no—
1154C22—42no—
1155C22—41no—
1156C22—42no—
1157C22—42no—
1158C22—41no—
1159C22—42no—
1160C22—41no—
1161C22—114no—
1162C22—114no—
1163C22—222no—
1164C22—222no—
1165C22—222no—
1166C22—222no—
1167C22—222no—
1168C22—222no—
1169C22—222no—
1170C22—222no—
1171C22—222no—
1172C22—222no—
1173C22—222no—
1174C22—222no—
1175C22—224no—
1176C22—224no—
1177C22—224no—
1178C22—4416no—
1179C22—442no—
1180C22—442no—
1181C22—442no—
1182C22—442no—
1183C22—8816no—
1184C22C23×C4×D1111yescharacteristic
1185C22C2×#6703711yescharacteristic
1186C22C2×#6704211yescharacteristic
1187C22D11×H(5,𝔽2)11yescharacteristic
1188C22D11×H(5,𝔽2)11yescharacteristic
1189C22D11×H(5,𝔽2)11yescharacteristic
1190C22D11×2−1+411yescharacteristic
1191C4—24no—
1192C4—22no—
1193C4—41no—
1194C4—41no—
1195C4—41no—
1196C4—42no—
1197C4—41no—
1198C4—42no—
1199C4—224no—
1200C4—222no—
1201C4—222no—
1202C4—441no—
1203C4—441no—
1204C4—442no—
1205C4—441no—
1206C4—441no—
1207C4—442no—
1208C4#1062307614yes—
1209C2—42no—
1210C2—44no—
1211C2—224no—
1212C2—224no—
1213C2—444no—
1214C2D11×#51811yescharacteristic
1215C2C2×#1062307611yescharacteristic
1216C2D11×#52011yescharacteristic
1217C2#1308283411yescharacteristic
1218C2#1308284111yescharacteristic
1219C2#1308284911yescharacteristic
1220C2#1308285411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2324C2
socle, cosocleC23×C11C25
prime radicalC2×D11×#121C2
hypercenter#2324D11
hypocenterC11#34379
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. #13071774C2semidirect
3. #13071767C2semidirect
4. #13071637C2semidirect
5. #13071634C2semidirect
6. #13071631C2semidirect
7. #13071628C2semidirect
8. #13071492C2semidirect
9. #13071489C2semidirect
10. #13071437C2semidirect
11. #13071437C2semidirect
12. #13071434C2semidirect
13. D4×(C2×D11)⋊C4C2semidirect
14. #13071320C2semidirect
15. #13071313C2semidirect
16. #13071311C2semidirect
17. #13071309C2semidirect
18. #13071305C2semidirect
19. #13071227C2semidirect
20. #13071210C2semidirect
21. #13070995C2semidirect
22. D11×#380C2semidirect
23. C11×#2324C2semidirect
28. C2×C4×D4×C11C22semidirect
29. C2×C11×#117C22semidirect
32. C2×D4×Dic11C22semidirect
34. C2×C4×C22⋊D11C22semidirect
36. C2×#66979C22semidirect
37. D11×#121C4semidirect
39. C2×#66946C22semidirect
40. C2×#66946C22semidirect
42. C2×C4⋊C4×D11C22semidirect
43. C2×C4⋊C4×D11C22semidirect
45. C2×(C22⋊D11)⋊C4C22semidirect
49. C2×C4×D44C22semidirect
50. C2×C4×D44C22semidirect
51. C11×#390C22semidirect
52. C11×#390C22semidirect
53. C11×#389C22semidirect
54. C11×#388C22semidirect
55. C11×#386C22semidirect
56. C11×#385C22semidirect
57. C11×#380C22semidirect
58. C4×C11×C4⋊C4C22semidirect
59. #10622834C22semidirect
60. #10622834C22semidirect
61. #10622833C22semidirect
62. #10622826C22semidirect
63. #10622825C22semidirect
64. #10622823C22semidirect
65. #10622603C22semidirect
66. #10622602C22semidirect
67. #10622602C22semidirect
68. #10622601C22semidirect
74. #10622600C22semidirect
75. #10622600C22semidirect
76. #10622598C22semidirect
77. #10622591C22semidirect
78. C4⋊C4×Dic11C22semidirect
79. C4⋊C4×Dic11C22semidirect
80. #10622586C22semidirect
81. #10622571C22semidirect
82. #10622570C22semidirect
83. #10622570C22semidirect
84. #10622569C22semidirect
85. #10622569C22semidirect
86. #10622569C22semidirect
87. #10622569C22semidirect
88. #10622569C22semidirect
89. #10622569C22semidirect
94. #10622564C22semidirect
95. #10622563C22semidirect
96. #10622559C22semidirect
97. #10622558C22semidirect
98. #10622557C22semidirect
99. #10622556C22semidirect
100. #10622556C22semidirect
101. #10622555C22semidirect
102. #10622553C22semidirect
103. #10622552C22semidirect
107. C4×(C2×D11)⋊C4C22semidirect
108. C4×(C2×D11)⋊C4C22semidirect
109. C4×C4⋊Dic11C22semidirect
110. #10622546C22semidirect
111. #10622541C22semidirect
112. #10622283C22semidirect
113. #10622282C22semidirect
114. #10622281C22semidirect
115. #10622281C22semidirect
119. #10622278C22semidirect
120. #10622278C22semidirect
121. D11×#95C22semidirect
122. #10622268C22semidirect
123. #10622265C22semidirect
139. C2×D4×D11C2×C4semidirect
140. C2×D4×D11C2×C4semidirect
145. C22×C4×D11C2×C4semidirect
155. C11×#121C2×C4semidirect
181. #66992C2×C4semidirect
182. #66991C2×C4semidirect
184. #66983C2×C4semidirect
222. #66948C2×C4semidirect
227. C4⋊C4×D11C2×C4semidirect
228. #66937C2×C4semidirect
232. C22⋊C4×D11C2×C4semidirect
431. #2324D11semidirect
577. C2×C4×D4C2×D11semidirect
579. C2×#117C2×D11semidirect
593. #390C2×D11semidirect
594. #390C2×D11semidirect
598. #389C2×D11semidirect
606. #388C2×D11semidirect
622. #386C2×D11semidirect
630. #385C2×D11semidirect
644. #380C2×D11semidirect
652. C4×C4⋊C4C2×D11semidirect
758. #121C4×D11semidirect
1022. C11#34379semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1212
#130717742
#130717672
#130716372
#130716342
#130716312
#130716282
#130714922
#130714892
#130714372
#130714342
D4×(C2×D11)⋊C42
#130713202
#130713132
#130713112
#130713092
#130713052
#130712272
#130712102
#130709952
D11×#3802
C11×#23242
#3437911