Finite Group Databasebeta

← #14916731

Subgroups — #14916731

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#13071772C212yesmaximal, complemented
3#13071769C212yesmaximal, complemented
4#13071636C211yesmaximal, characteristic, complemented
5#13071632C211yesmaximal, characteristic, complemented
6#13071630C211yesmaximal, characteristic, complemented
7#13071492C211yesmaximal, characteristic, complemented
8#13071489C211yesmaximal, characteristic, complemented
9#13071437C211yesmaximal, characteristic, complemented
10#13071434C212yesmaximal, complemented
11D4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
12D4×(C2×D11)⋊C4C212yesmaximal, complemented
13#13071317C212yesmaximal, complemented
14#13071314C212yesmaximal, complemented
15#13071312C211yesmaximal, characteristic, complemented
16#13071310C211yesmaximal, characteristic, complemented
17#13071307C211yesmaximal, characteristic, complemented
18#13071303C211yesmaximal, characteristic, complemented
19#13071227C212yesmaximal, complemented
20#13071210C212yesmaximal, complemented
21#13070997C211yesmaximal, characteristic, complemented
22C2×#10622600C211yesmaximal, characteristic, complemented
23C11×#2361C211yesmaximal, characteristic, complemented
24C22×D4×D11C2212yes—
25C22×D4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic, complemented
29C2×C4×D4×C11C2212yescomplemented
30C22×C11×C4⋊C4C2211yescharacteristic, complemented
31C2×#66992C2212yes—
32C2×#66991C2211yescharacteristic
33C2×D4×Dic11C2211yescharacteristic, complemented
34C2×D4×Dic11C2212yescomplemented
35C2×#66983C2211yescharacteristic
36C2×C4×C22⋊D11C2212yescomplemented
37C22×(C2×D11)⋊C4C2212yes—
38C22×(C2×D11)⋊C4C2212yes—
39C22×C4⋊Dic11C2211yescharacteristic, complemented
40D11×#121C4116yescomplemented
41C2×#66948C2211yescharacteristic
42C2×#66946C2211yescharacteristic, complemented
43C2×C4⋊C4×D11C2211yescharacteristic
44C2×#66937C2212yes—
45C2×(C22⋊D11)⋊C4C2212yescomplemented
46C2×C22⋊C4×D11C2212yes—
47C2×C22⋊C4×D11C2212yes—
48C2×C4×D44C2211yescharacteristic, complemented
49C2×#66925C2211yescharacteristic, complemented
50C2×#66925C2211yescharacteristic, complemented
51C11×#390C2211yescharacteristic, complemented
52C11×#389C2211yescharacteristic, complemented
53C11×#388C2212yescomplemented
54C11×#386C2212yescomplemented
55C11×#385C2212yescomplemented
56C4×C11×C4⋊C4C2211yescharacteristic, complemented
57C4×C11×C22⋊C4C2211yescharacteristic, complemented
58#10622834C2211yescharacteristic, complemented
59#10622833C2212yescomplemented
60#10622826C2212yescomplemented
61#10622826C2212yescomplemented
62#10622826C2212yescomplemented
63#10622823C2212yescomplemented
64C4×C22⋊Dic11C2211yescharacteristic, complemented
65C2×C11⋊#95C2212yescomplemented
66#10622603C2212yescomplemented
67#10622602C2212yescomplemented
68#10622602C2212yescomplemented
69#10622601C2211yescharacteristic, complemented
70#10622601C2212yescomplemented
71#10622600C2212yes—
72#10622600C2211yescharacteristic
73#10622600C2211yescharacteristic
74#10622600C2212yes—
75#10622600C2212yescomplemented
76#10622600C2211yescharacteristic, complemented
77#10622600C2211yescharacteristic, complemented
78#10622598C2211yescharacteristic, complemented
79#10622591C2212yescomplemented
80C4⋊C4×Dic11C2211yescharacteristic, complemented
81C4⋊C4×Dic11C2211yescharacteristic, complemented
82#10622586C2211yescharacteristic, complemented
83#10622571C2212yescomplemented
84#10622571C2212yescomplemented
85#10622571C2212yescomplemented
86#10622570C2212yescomplemented
87#10622570C2212yescomplemented
88#10622569C2212yescomplemented
89#10622569C2212yescomplemented
90#10622568C2211yescharacteristic
91#10622568C2212yes—
92#10622568C2212yes—
93#10622568C2211yescharacteristic
94#10622564C2212yescomplemented
95#10622563C2212yescomplemented
96#10622559C2212yescomplemented
97#10622558C2212yescomplemented
98#10622557C2212yescomplemented
99#10622555C2211yescharacteristic, complemented
100#10622555C2211yescharacteristic, complemented
101#10622553C2212yescomplemented
102#10622552C2211yescharacteristic, complemented
103#10622552C2212yescomplemented
104C4×(C2×D11)⋊C4C2212yes—
105C4×(C2×D11)⋊C4C2211yescharacteristic
106C4×(C2×D11)⋊C4C2211yescharacteristic
107C4×C4⋊Dic11C2211yescharacteristic, complemented
108#10622546C2212yescomplemented
109#10622541C2211yescharacteristic, complemented
110#10622283C2212yescomplemented
111#10622282C2212yescomplemented
112#10622281C2212yescomplemented
113#10622281C2212yescomplemented
114#10622280C2212yes—
115#10622280C2211yescharacteristic
116#10622280C2211yescharacteristic
117#10622279C2212yes—
118#10622278C2212yescomplemented
119#10622278C2212yescomplemented
120#10622277C2211yescharacteristic, complemented
121#10622277C2211yescharacteristic, complemented
122#10622268C2212yescomplemented
123#10622265C2212yescomplemented
124C24×D11C2311yescharacteristic
125C24×D11C2312yes—
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C23×C4×C11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C23×Dic11C2312yes—
135C23×Dic11C2312yes—
136C23×Dic11C2311yescharacteristic
137C2×D4×D11—42no—
138C2×D4×D11—42no—
139C2×D4×D11—44no—
140C2×D4×D11—44no—
141C2×D4×D11C2×C418yescomplemented
142C2×D4×D11C2×C4116yescomplemented
143C22×D44C2311yescharacteristic
144C22×D44C2312yes—
145C22×C4×D11—42no—
146C22×C4×D11—42no—
147C22×C4×D11C2×C418yescomplemented
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2312yes—
151C22×C4×D11C2312yes—
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2312yes—
154C22×C4×D11C2311yescharacteristic
155C11×#121C2×C418yescomplemented
156C4×D4×C11—42no—
157C4×D4×C11—44no—
158C2×C11×C4⋊C4—42no—
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2312yes—
162C2×C11×C4⋊C4C2312yes—
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2311yescharacteristic
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2312yes—
170C2×C42×C11C2311yescharacteristic
171C2×C42×C11C2311yescharacteristic
172C2×C42×C11C2312yes—
173C2×C22⋊Dic11C2311yescharacteristic
174C2×C22⋊Dic11C2311yescharacteristic
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179#66992C2×C4116yescomplemented
180#66991C2×C418yescomplemented
181D4×Dic11—42no—
182D4×Dic11—44no—
183#66983C2×C418yescomplemented
184C4×C22⋊D11—44no—
185C2×(C2×D11)⋊C4—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—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×C4⋊Dic11—42no—
208C2×C4⋊Dic11C2311yescharacteristic
209C2×C4⋊Dic11C2311yescharacteristic
210C2×C4⋊Dic11C2312yes—
211C2×C4⋊Dic11C2312yes—
212C2×C4⋊Dic11C2311yescharacteristic
213C2×Dic11⋊C4C2311yescharacteristic
214C2×Dic11⋊C4C2311yescharacteristic
215C2×Dic11⋊C4C2311yescharacteristic
216C2×Dic11⋊C4C2311yescharacteristic
217C2×Dic11⋊C4C2312yes—
218C2×Dic11⋊C4C2312yes—
219C2×Dic11⋊C4C2312yes—
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2312yes—
223C2×C4×Dic11C2312yes—
224C2×C4×Dic11C2312yes—
225#66948C2×C418yescomplemented
226#66946—42no—
227C4⋊C4×D11C2×C418yescomplemented
228#66937C2×C4116yescomplemented
229(C22⋊D11)⋊C4—44no—
230C22⋊C4×D11—44no—
231C22⋊C4×D11C2×C4116yescomplemented
232C4×D44—42no—
233#66925—42no—
234#66925—42no—
235C11×#95C2312yes—
236C11×#95C2312yes—
237C11×#95C2311yescharacteristic
238C11×#95C2311yescharacteristic
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2311yescharacteristic
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2311yescharacteristic
246C11⋊#95C2311yescharacteristic
247C11⋊#95C2311yescharacteristic
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255#34379—111nomaximal, Sylow
256C24×C11C2412yes—
257C24×C11C2411yescharacteristic
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×D11C2411yescharacteristic
273C23×D11C2412yes—
274C23×D11C2411yescharacteristic
275C2×D4×C11—24no—
276C2×D4×C11—24no—
277C2×D4×C11—22no—
278C2×D4×C11—22no—
279C2×D4×C11C22×C414yes—
280C2×D4×C11C22×C418yes—
281C22×C4×C11—22no—
282C22×C4×C11—22no—
283C22×C4×C11—24no—
284C22×C4×C11—42no—
285C22×C4×C11—42no—
286C22×C4×C11—42no—
287C22×C4×C11—42no—
288C22×C4×C11—42no—
289C22×C4×C11C22×C414yes—
290C22×C4×C11C2412yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2412yes—
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2412yes—
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C2×C22⋊D11—24no—
300C2×C22⋊D11—24no—
301C2×C22⋊D11—42no—
302C2×C22⋊D11—42no—
303C2×C22⋊D11—42no—
304C2×C22⋊D11—42no—
305C2×C22⋊D11C22×C418yes—
306C2×C22⋊D11C22×C418yes—
307C2×C22⋊D11C22×C418yes—
308C22×Dic11—24no—
309C22×Dic11—41no—
310C22×Dic11—41no—
311C22×Dic11—42no—
312C22×Dic11—42no—
313C22×Dic11—42no—
314C22×Dic11—42no—
315C22×Dic11—42no—
316C22×Dic11C22×C414yes—
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2411yescharacteristic
321C22×Dic11C2412yes—
322C22×Dic11C2412yes—
323C22×Dic11C2411yescharacteristic
324C22×Dic11C2412yes—
325C22×Dic11C2411yescharacteristic
326D4×D11—432no—
327D4×D11—416no—
328C2×D44—22no—
329C2×D44—22no—
330C2×D44—42no—
331C2×D44—42no—
332C2×D44C22×C414yes—
333C2×D44C22×C418yes—
334C2×C4×D11—22no—
335C2×C4×D11—22no—
336C2×C4×D11—22no—
337C2×C4×D11—22no—
338C2×C4×D11—41no—
339C2×C4×D11—41no—
340C2×C4×D11—41no—
341C2×C4×D11—41no—
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—42no—
360C11×C4⋊C4C22×C414yes—
361C11×C22⋊C4—22no—
362C11×C22⋊C4—22no—
363C11×C22⋊C4—42no—
364C11×C22⋊C4—42no—
365C11×C22⋊C4—42no—
366C11×C22⋊C4C22×C418yes—
367C42×C11—22no—
368C42×C11—22no—
369C42×C11—42no—
370C22⋊Dic11—22no—
371C22⋊Dic11—22no—
372C22⋊Dic11—42no—
373C22⋊Dic11—42no—
374C22⋊Dic11—42no—
375C22⋊Dic11C22×C418yes—
376(C2×D11)⋊C4—22no—
377(C2×D11)⋊C4—24no—
378(C2×D11)⋊C4—24no—
379(C2×D11)⋊C4—22no—
380(C2×D11)⋊C4—22no—
381(C2×D11)⋊C4—22no—
382(C2×D11)⋊C4—41no—
383(C2×D11)⋊C4—41no—
384(C2×D11)⋊C4—41no—
385(C2×D11)⋊C4—41no—
386(C2×D11)⋊C4—42no—
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)⋊C4C22×C418yes—
395(C2×D11)⋊C4C22×C418yes—
396C4⋊Dic11—22no—
397C4⋊Dic11—22no—
398C4⋊Dic11—42no—
399C4⋊Dic11—42no—
400C4⋊Dic11C22×C414yes—
401Dic11⋊C4—41no—
402Dic11⋊C4—41no—
403Dic11⋊C4—41no—
404Dic11⋊C4—41no—
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#2361D1111yescharacteristic, complemented
420#2345—111no—
421#2345—111no—
422D4×C22⋊C4—111no—
423D4×C22⋊C4—112no—
424D4×C22⋊C4—111no—
425D4×C22⋊C4—112no—
426#2325—112no—
427#2325—112no—
428#2324—111no—
429#2324—111no—
430#2324—111no—
431#2324—111no—
432#2315—112no—
433#2312—112no—
434#2280—111no—
435C2×#380—111no—
436C23×C11—21no—
437C23×C11—21no—
438C23×C11—21no—
439C23×C11—21no—
440C23×C11—22no—
441C23×C11—22no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11C23×C414yes—
447C23×C11C23×C412yes—
448C23×C11H(5,𝔽2)12yes—
449C23×C11H(5,𝔽2)12yes—
450C23×C11C2511yescharacteristic
451C22×D11—21no—
452C22×D11—21no—
453C22×D11—21no—
454C22×D11—21no—
455C22×D11—28no—
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—21no—
465C22×D11—21no—
466C22×D11—21no—
467C22×D11—22no—
468C22×D11—28no—
469C22×D11—216no—
470C22×D11—44no—
471C22×D11—48no—
472C22×D11—48no—
473C22×D11—44no—
474C22×D11—44no—
475C22×D11—44no—
476C22×D11—44no—
477C22×D11—84no—
478C22×D11—84no—
479C22×D11—84no—
480C22×D11—84no—
481C22×D11C23×C414yes—
482C22×D11C23×C412yes—
483C22×D11C23×C412yes—
484C22×D11H(5,𝔽2)12yes—
485C22×D112−1+412yes—
486D4×C11—216no—
487D4×C11—28no—
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—21no—
497C2×C4×C11—21no—
498C2×C4×C11—21no—
499C2×C4×C11—21no—
500C2×C4×C11—22no—
501C2×C4×C11—21no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—21no—
505C2×C4×C11—22no—
506C2×C4×C11—21no—
507C2×C4×C11—21no—
508C2×C4×C11—22no—
509C2×C4×C11—21no—
510C2×C4×C11—21no—
511C2×C4×C11—84no—
512C2×C4×C11—84no—
513C2×C4×C11C23×C414yes—
514C2×C4×C11C23×C412yes—
515C2×C4×C11C23×C412yes—
516C2×C4×C11H(5,𝔽2)12yes—
517C2×C4×C11H(5,𝔽2)12yes—
518C22⋊D11—216no—
519C22⋊D11—48no—
520C22⋊D11—48no—
521C2×Dic11—22no—
522C2×Dic11—22no—
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—21no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—21no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—21no—
539C2×Dic11—21no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—21no—
543C2×Dic11—21no—
544C2×Dic11—21no—
545C2×Dic11—44no—
546C2×Dic11—84no—
547C2×Dic11—84no—
548C2×Dic11C23×C412yes—
549C2×Dic11C23×C414yes—
550C2×Dic11C23×C412yes—
551D44—28no—
552D44—48no—
553C4×D11—28no—
554C4×D11—28no—
555C4×D11—44no—
556C4×D11—44no—
557C4×D11—48no—
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—112no—
573C2×C4×D4—111no—
574C2×C4×D4—112no—
575C2×C4×D4—111no—
576C2×C4×D4C2×D1111yescharacteristic, complemented
577C2×C4×D4C2×D1112yescomplemented
578C2×#117—111no—
579C2×#117—111no—
580C22×C4⋊C4—111no—
581C22×C4⋊C4—111no—
582C22×C4⋊C4C2×D1111yescharacteristic, complemented
583C22×C22⋊C4—112no—
584C22×C22⋊C4—112no—
585C22×C22⋊C4—112no—
586C22×C22⋊C4—112no—
587#390—111no—
588#390—111no—
589#390—112no—
590#390—112no—
591#390—112no—
592#390—111no—
593#390—112no—
594#390C2×D1111yescharacteristic, complemented
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—112no—
634#380—112no—
635#380—111no—
636#380—111no—
637#380—111no—
638#380—111no—
639#380—112no—
640#380—111no—
641#380—111no—
642#380—111no—
643#380—111no—
644#380—112no—
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—111no—
654C4×C22⋊C4—112no—
655C4×C22⋊C4—111no—
656C4×C22⋊C4—111no—
657C4×C22⋊C4—112no—
658C4×C22⋊C4C2×D1111yescharacteristic, complemented
659C2×#95—112no—
660C22×C11—22no—
661C22×C11—22no—
662C22×C11—22no—
663C22×C11—22no—
664C22×C11—22no—
665C22×C11—22no—
666C22×C11—24no—
667C22×C11—24no—
668C22×C11—24no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11—42no—
673C22×C11#51814yes—
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—24no—
690C2×D11—24no—
691C2×D11—22no—
692C2×D11—24no—
693C2×D11—416no—
694C2×D11—41no—
695C2×D11—41no—
696C2×D11—42no—
697C2×D11—42no—
698C2×D11—41no—
699C2×D11—41no—
700C2×D11—42no—
701C2×D11—42no—
702C2×D11—816no—
703C2×D11#52014yes—
704C4×C11—22no—
705C4×C11—24no—
706C4×C11—41no—
707C4×C11—41no—
708C4×C11—41no—
709C4×C11—42no—
710C4×C11—42no—
711C4×C11—41no—
712C4×C11#51814yes—
713Dic11—22no—
714Dic11—22no—
715Dic11—24no—
716Dic11—41no—
717Dic11—41no—
718Dic11—41no—
719Dic11—42no—
720Dic11—41no—
721Dic11—42no—
722C25—111no—
723C25—112no—
724C22×D4—112no—
725C22×D4—112no—
726C22×D4—112no—
727C22×D4—118no—
728C22×D4—1116no—
729C22×D4—111no—
730C22×D4—112no—
731C22×D4—442no—
732C22×D4—442no—
733C22×D4—444no—
734C22×D4—444no—
735C22×D4C22×D1112yes—
736C22×D4C22×D1111yescharacteristic
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—442no—
749C23×C4—442no—
750C23×C4C22×D1111yescharacteristic
751C23×C4C22×D1112yes—
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—44no—
761C4×D4—442no—
762C4×D4—442no—
763C4×D4—442no—
764C4×D4—444no—
765C4×D4—444no—
766C4×D4—444no—
767#117—442no—
768#117—442no—
769C2×C4⋊C4—42no—
770C2×C4⋊C4—111no—
771C2×C4⋊C4—112no—
772C2×C4⋊C4—118no—
773C2×C4⋊C4—111no—
774C2×C4⋊C4—111no—
775C2×C4⋊C4—112no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—111no—
780C2×C4⋊C4—112no—
781C2×C4⋊C4—112no—
782C2×C4⋊C4—112no—
783C2×C4⋊C4—442no—
784C2×C4⋊C4C22×D1111yescharacteristic
785C2×C4⋊C4C22×D1111yescharacteristic
786C2×C4⋊C4C22×D1112yes—
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—111no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—111no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—111no—
799C2×C22⋊C4—111no—
800C2×C22⋊C4—111no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—111no—
809C2×C22⋊C4—111no—
810C2×C22⋊C4—111no—
811C2×C22⋊C4—111no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—112no—
816C2×C22⋊C4—444no—
817C2×C22⋊C4—444no—
818C2×C22⋊C4—444no—
819C2×C22⋊C4C22×D1111yescharacteristic
820C2×C22⋊C4C22×D1111yescharacteristic
821C2×C22⋊C4C22×D1112yes—
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—112no—
837#95—111no—
838#95—111no—
839#95—111no—
840#95—111no—
841#95—111no—
842#95—111no—
843#95—112no—
844#95—112no—
845#95—112no—
846#95—112no—
847#95—112no—
848#95—112no—
849#95C22×D1112yes—
850#95C22×D1111yescharacteristic
851#95C22×D1111yescharacteristic
852#95C22×D1112yes—
853C2×C11—24no—
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—42no—
864D11—44no—
865C24—111no—
866C24—112no—
867C24—111no—
868C24—114no—
869C24—118no—
870C24—222no—
871C24—222no—
872C24—224no—
873C24—224no—
874C24—222no—
875C24—222no—
876C24—441no—
877C24—441no—
878C24—442no—
879C24—442no—
880C24—442no—
881C24—442no—
882C24C23×D1112yes—
883C24C23×D1111yescharacteristic
884C2×D4—24no—
885C2×D4—24no—
886C2×D4—22no—
887C2×D4—22no—
888C2×D4—118no—
889C2×D4—118no—
890C2×D4—118no—
891C2×D4—114no—
892C2×D4—118no—
893C2×D4—224no—
894C2×D4—224no—
895C2×D4—222no—
896C2×D4—222no—
897C2×D4—442no—
898C2×D4—442no—
899C2×D4—4416no—
900C2×D4—442no—
901C2×D4—442no—
902C2×D4—442no—
903C2×D4—442no—
904C2×D4—4432no—
905C2×D4C2×C4×D1118yes—
906C2×D4C2×C4×D1114yes—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—24no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—111no—
916C22×C4—112no—
917C22×C4—111no—
918C22×C4—114no—
919C22×C4—114no—
920C22×C4—114no—
921C22×C4—114no—
922C22×C4—118no—
923C22×C4—114no—
924C22×C4—111no—
925C22×C4—111no—
926C22×C4—111no—
927C22×C4—111no—
928C22×C4—112no—
929C22×C4—112no—
930C22×C4—222no—
931C22×C4—222no—
932C22×C4—222no—
933C22×C4—222no—
934C22×C4—224no—
935C22×C4—4416no—
936C22×C4—441no—
937C22×C4—441no—
938C22×C4—441no—
939C22×C4—441no—
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—441no—
949C22×C4—441no—
950C22×C4—442no—
951C22×C4—442no—
952C22×C4—442no—
953C22×C4—442no—
954C22×C4—442no—
955C22×C4C2×C4×D1114yes—
956C22×C4C23×D1112yes—
957C22×C4C23×D1111yescharacteristic
958C22×C4C23×D1111yescharacteristic
959C22×C4C23×D1112yes—
960C22×C4C23×D1111yescharacteristic
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1112yes—
963C22×C4C23×D1111yescharacteristic
964C22×C4C23×D1111yescharacteristic
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—118no—
970C4⋊C4—114no—
971C4⋊C4—222no—
972C4⋊C4—222no—
973C4⋊C4—442no—
974C4⋊C4—441no—
975C4⋊C4—441no—
976C4⋊C4—441no—
977C4⋊C4—441no—
978C4⋊C4—442no—
979C4⋊C4—442no—
980C4⋊C4—442no—
981C4⋊C4C2×C4×D1114yes—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—118no—
988C22⋊C4—118no—
989C22⋊C4—118no—
990C22⋊C4—222no—
991C22⋊C4—224no—
992C22⋊C4—222no—
993C22⋊C4—224no—
994C22⋊C4—222no—
995C22⋊C4—222no—
996C22⋊C4—222no—
997C22⋊C4—222no—
998C22⋊C4—442no—
999C22⋊C4—442no—
1000C22⋊C4—442no—
1001C22⋊C4—442no—
1002C22⋊C4—441no—
1003C22⋊C4—441no—
1004C22⋊C4—441no—
1005C22⋊C4—441no—
1006C22⋊C4—442no—
1007C22⋊C4—442no—
1008C22⋊C4—442no—
1009C22⋊C4—442no—
1010C22⋊C4—442no—
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—21no—
1025C23—21no—
1026C23—21no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—112no—
1034C23—112no—
1035C23—112no—
1036C23—114no—
1037C23—112no—
1038C23—228no—
1039C23—2216no—
1040C23—221no—
1041C23—221no—
1042C23—221no—
1043C23—221no—
1044C23—228no—
1045C23—221no—
1046C23—222no—
1047C23—222no—
1048C23—221no—
1049C23—221no—
1050C23—222no—
1051C23—222no—
1052C23—221no—
1053C23—221no—
1054C23—222no—
1055C23—221no—
1056C23—222no—
1057C23—444no—
1058C23—448no—
1059C23—448no—
1060C23—444no—
1061C23—444no—
1062C23—444no—
1063C23—444no—
1064C23—884no—
1065C23—884no—
1066C23—884no—
1067C23—884no—
1068C23C22×C4×D1114yes—
1069C23C22×C4×D1112yes—
1070C23#6703712yes—
1071C23#6704212yes—
1072C23C24×D1111yescharacteristic
1073D4—216no—
1074D4—28no—
1075D4—2216no—
1076D4—228no—
1077D4—448no—
1078D4—448no—
1079D4—448no—
1080C2×C4—22no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—21no—
1084C2×C4—28no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—21no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—22no—
1099C2×C4—21no—
1100C2×C4—22no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—84no—
1104C2×C4—84no—
1105C2×C4—112no—
1106C2×C4—114no—
1107C2×C4—112no—
1108C2×C4—222no—
1109C2×C4—221no—
1110C2×C4—221no—
1111C2×C4—222no—
1112C2×C4—221no—
1113C2×C4—221no—
1114C2×C4—228no—
1115C2×C4—228no—
1116C2×C4—221no—
1117C2×C4—221no—
1118C2×C4—221no—
1119C2×C4—221no—
1120C2×C4—221no—
1121C2×C4—221no—
1122C2×C4—221no—
1123C2×C4—222no—
1124C2×C4—222no—
1125C2×C4—221no—
1126C2×C4—222no—
1127C2×C4—222no—
1128C2×C4—221no—
1129C2×C4—221no—
1130C2×C4—222no—
1131C2×C4—222no—
1132C2×C4—221no—
1133C2×C4—221no—
1134C2×C4—444no—
1135C2×C4—444no—
1136C2×C4—448no—
1137C2×C4—444no—
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—22no—
1149C22—22no—
1150C22—22no—
1151C22—22no—
1152C22—22no—
1153C22—24no—
1154C22—24no—
1155C22—24no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—114no—
1161C22—222no—
1162C22—222no—
1163C22—222no—
1164C22—222no—
1165C22—222no—
1166C22—222no—
1167C22—222no—
1168C22—224no—
1169C22—224no—
1170C22—222no—
1171C22—222no—
1172C22—224no—
1173C22—4416no—
1174C22—441no—
1175C22—442no—
1176C22—441no—
1177C22—442no—
1178C22—442no—
1179C22—441no—
1180C22—442no—
1181C22—441no—
1182C22—8816no—
1183C22#1062307614yes—
1184C22C23×C4×D1111yescharacteristic
1185C22C2×#6703711yescharacteristic
1186C22C2×#6703711yescharacteristic
1187C22C2×#6704211yescharacteristic
1188C22C2×#6704211yescharacteristic
1189C22D11×H(5,𝔽2)11yescharacteristic
1190C22D11×2−1+411yescharacteristic
1191C4—22no—
1192C4—24no—
1193C4—41no—
1194C4—41no—
1195C4—41no—
1196C4—42no—
1197C4—42no—
1198C4—41no—
1199C4—222no—
1200C4—222no—
1201C4—224no—
1202C4—441no—
1203C4—441no—
1204C4—441no—
1205C4—441no—
1206C4—442no—
1207C4—442no—
1208C4#1062307614yes—
1209C2—24no—
1210C2—44no—
1211C2—224no—
1212C2—442no—
1213C2—444no—
1214C2C2×#1062307611yescharacteristic
1215C2C2×#1062307611yescharacteristic
1216C2D11×#52011yescharacteristic
1217C2#1308283211yescharacteristic
1218C2#1308283911yescharacteristic
1219C2#1308284711yescharacteristic
1220C2#1308285211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2361C2
socle, cosocleC23×C11C25
prime radicalC2×D11×#121C2
hypercenter#2361D11
hypocenterC11#34379
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. #13071772C2semidirect
3. #13071769C2semidirect
4. #13071636C2semidirect
5. #13071632C2semidirect
6. #13071630C2semidirect
7. #13071492C2semidirect
8. #13071489C2semidirect
9. #13071437C2semidirect
10. #13071434C2semidirect
11. D4×(C2×D11)⋊C4C2semidirect
12. D4×(C2×D11)⋊C4C2semidirect
13. #13071317C2semidirect
14. #13071314C2semidirect
15. #13071312C2semidirect
16. #13071310C2semidirect
17. #13071307C2semidirect
18. #13071303C2semidirect
19. #13071227C2semidirect
20. #13071210C2semidirect
21. #13070997C2semidirect
22. C2×#10622600C2semidirect
23. C11×#2361C2semidirect
28. C2×C4×D4×C11C22semidirect
29. C2×C4×D4×C11C22semidirect
30. C22×C11×C4⋊C4C22semidirect
33. C2×D4×Dic11C22semidirect
34. C2×D4×Dic11C22semidirect
36. C2×C4×C22⋊D11C22semidirect
39. C22×C4⋊Dic11C22semidirect
40. D11×#121C4semidirect
42. C2×#66946C22semidirect
45. C2×(C22⋊D11)⋊C4C22semidirect
48. C2×C4×D44C22semidirect
49. C2×#66925C22semidirect
50. C2×#66925C22semidirect
51. C11×#390C22semidirect
52. C11×#389C22semidirect
53. C11×#388C22semidirect
54. C11×#386C22semidirect
55. C11×#385C22semidirect
56. C4×C11×C4⋊C4C22semidirect
57. C4×C11×C22⋊C4C22semidirect
58. #10622834C22semidirect
59. #10622833C22semidirect
60. #10622826C22semidirect
61. #10622826C22semidirect
62. #10622826C22semidirect
63. #10622823C22semidirect
64. C4×C22⋊Dic11C22semidirect
65. C2×C11⋊#95C22semidirect
66. #10622603C22semidirect
67. #10622602C22semidirect
68. #10622602C22semidirect
69. #10622601C22semidirect
70. #10622601C22semidirect
75. #10622600C22semidirect
76. #10622600C22semidirect
77. #10622600C22semidirect
78. #10622598C22semidirect
79. #10622591C22semidirect
80. C4⋊C4×Dic11C22semidirect
81. C4⋊C4×Dic11C22semidirect
82. #10622586C22semidirect
83. #10622571C22semidirect
84. #10622571C22semidirect
85. #10622571C22semidirect
86. #10622570C22semidirect
87. #10622570C22semidirect
88. #10622569C22semidirect
89. #10622569C22semidirect
94. #10622564C22semidirect
95. #10622563C22semidirect
96. #10622559C22semidirect
97. #10622558C22semidirect
98. #10622557C22semidirect
99. #10622555C22semidirect
100. #10622555C22semidirect
101. #10622553C22semidirect
102. #10622552C22semidirect
103. #10622552C22semidirect
107. C4×C4⋊Dic11C22semidirect
108. #10622546C22semidirect
109. #10622541C22semidirect
110. #10622283C22semidirect
111. #10622282C22semidirect
112. #10622281C22semidirect
113. #10622281C22semidirect
118. #10622278C22semidirect
119. #10622278C22semidirect
120. #10622277C22semidirect
121. #10622277C22semidirect
122. #10622268C22semidirect
123. #10622265C22semidirect
141. C2×D4×D11C2×C4semidirect
142. C2×D4×D11C2×C4semidirect
147. C22×C4×D11C2×C4semidirect
155. C11×#121C2×C4semidirect
179. #66992C2×C4semidirect
180. #66991C2×C4semidirect
183. #66983C2×C4semidirect
225. #66948C2×C4semidirect
227. C4⋊C4×D11C2×C4semidirect
228. #66937C2×C4semidirect
231. C22⋊C4×D11C2×C4semidirect
419. #2361D11semidirect
576. C2×C4×D4C2×D11semidirect
577. C2×C4×D4C2×D11semidirect
582. C22×C4⋊C4C2×D11semidirect
594. #390C2×D11semidirect
598. #389C2×D11semidirect
606. #388C2×D11semidirect
622. #386C2×D11semidirect
630. #385C2×D11semidirect
652. C4×C4⋊C4C2×D11semidirect
658. C4×C22⋊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
#130717722
#130717692
#130716362
#130716322
#130716302
#130714922
#130714892
#130714372
#130714342
D4×(C2×D11)⋊C42
#130713172
#130713142
#130713122
#130713102
#130713072
#130713032
#130712272
#130712102
#130709972
C2×#106226002
C11×#23612
#3437911