Finite Group Databasebeta

← C11×#34727 #14611920

Subgroups — C11×#34727 #14611920

Order 2816.

2736 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#529C211yesmaximal, characteristic, complemented
2C2×C4×C11×#41C211yesmaximal, characteristic, complemented
3C11×#2479C212yesmaximal, complemented
4C11×#2471C212yesmaximal, complemented
5C11×#2467C212yesmaximal, complemented
6C11×#2456C212yesmaximal, complemented
7C11×#2454C211yesmaximal, characteristic, complemented
8C11×#2448C211yesmaximal, characteristic, complemented
9C11×#2441C211yesmaximal, characteristic, complemented
10C11×#2431C211yesmaximal, characteristic, complemented
11C11×#2428C211yesmaximal, characteristic, complemented
12C11×#2423C211yesmaximal, characteristic, complemented
13C11×#2414C211yesmaximal, characteristic, complemented
14C11×#2407C211yesmaximal, characteristic, complemented
15C11×#2397C212yesmaximal, complemented
16C11×#2392C212yesmaximal, complemented
17C4×C11×#127C211yesmaximal, characteristic, complemented
18C4×C11×#121C211yesmaximal, characteristic, complemented
19C4×C11×#121C212yesmaximal, complemented
20C4×C11×#121C211yesmaximal, characteristic, complemented
21C11×#2295C211yesmaximal, characteristic, complemented
22C11×#2290C212yesmaximal, complemented
23C42×D4×C11C211yesmaximal, characteristic, complemented
24C22×C11×#41C2211yescharacteristic
25C2×C11×#127C2211yescharacteristic
26C11×#529—28no—
27C2×C11×#126C2212yes—
28C2×C11×#125C2211yescharacteristic
29C2×C11×#124C2211yescharacteristic
30C2×C11×#123C2212yes—
31C2×C11×C22⋊Q8C2211yescharacteristic
32C2×C11×#121C2211yescharacteristic
33C2×C11×#121C2211yescharacteristic
34C2×C11×#121C2211yescharacteristic
35C2×C11×#121C2212yes—
36C4×C11×#41—28no—
37C2×C4×Q8×C11C2211yescharacteristic
38C2×C4×Q8×C11C2211yescharacteristic
39C2×C4×D4×C11C2212yes—
40C2×C4×D4×C11C2211yescharacteristic
41C2×C4×D4×C11C2212yes—
42C2×C4×D4×C11C2212yes—
43C2×C4×D4×C11C2211yescharacteristic
44C2×C4×D4×C11C2212yes—
45C2×C4×D4×C11C2211yescharacteristic
46C2×C4×D4×C11C2211yescharacteristic
47C2×C4×D4×C11C2211yescharacteristic
48C2×C4×D4×C11C2211yescharacteristic
49C2×C4×D4×C11C2212yes—
50C2×C4×D4×C11C2212yes—
51C2×C4×D4×C11C2212yes—
52C2×C11×#117C2212yes—
53C2×C11×#117C2211yescharacteristic
54C2×C11×#117C2212yes—
55C22×C42×C11C2211yescharacteristic
56C22×C42×C11C2212yes—
57C22×C42×C11C2211yescharacteristic
58C11×#399C2212yes—
59C11×#399C2212yes—
60C11×#399C2212yes—
61C11×#399C2212yes—
62C11×#398C2212yes—
63C11×#397C2212yes—
64C11×#396C2212yes—
65C11×#396C2212yes—
66C11×#394C2212yes—
67C11×#394C2212yes—
68C11×#394C2212yes—
69C11×#392C2212yes—
70C11×#392C2212yes—
71C11×#392C2212yes—
72C11×#392C2212yes—
73C11×#392C2212yes—
74C11×#391C2211yescharacteristic
75C11×#391C2211yescharacteristic
76C11×#390C2211yescharacteristic
77C11×#390C2211yescharacteristic
78C11×#390C2212yes—
79C11×#390C2211yescharacteristic
80C11×#390C2211yescharacteristic
81C11×#390C2212yes—
82C11×#390C2212yes—
83C11×#389C2211yescharacteristic
84C11×#389C2211yescharacteristic
85C11×#389C2211yescharacteristic
86C11×#389C2211yescharacteristic
87C11×#389C2212yes—
88C11×#388C2212yes—
89C11×#388C2212yes—
90C11×#388C2212yes—
91C11×#388C2212yes—
92C11×#388C2212yes—
93C11×#388C2212yes—
94C11×#387C2212yes—
95C11×#387C2212yes—
96C11×#387C2212yes—
97C11×#387C2212yes—
98C11×#386C2212yes—
99C11×#386C2212yes—
100C11×#386C2212yes—
101C11×#386C2212yes—
102C11×#386C2212yes—
103C11×#386C2212yes—
104C11×#385C2212yes—
105C11×#385C2212yes—
106C11×#384C2211yescharacteristic
107C11×#380C2211yescharacteristic
108C11×#380C2211yescharacteristic
109C11×#380C2212yes—
110C4×C11×C4⋊C4C2212yes—
111C4×C11×C4⋊C4C2211yescharacteristic
112C4×C11×C4⋊C4C2211yescharacteristic
113C4×C11×C4⋊C4C2211yescharacteristic
114C4×C11×C4⋊C4C2211yescharacteristic
115C4×C11×C22⋊C4C2211yescharacteristic
116C4×C11×C22⋊C4C2212yes—
117C4×C11×C22⋊C4C2211yescharacteristic
118C4×C11×C22⋊C4C2211yescharacteristic
119C4×C11×C22⋊C4C2211yescharacteristic
120C4×C11×C22⋊C4C2211yescharacteristic
121C4×C11×C22⋊C4C2211yescharacteristic
122C4×C11×C22⋊C4C2212yes—
123C11×#376C2212yes—
124C43×C11C2211yescharacteristic
125C2×C11×#41—24no—
126C2×C11×#41—24no—
127C2×C11×#41—24no—
128C22×Q8×C11C2311yescharacteristic
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2312yes—
131C22×D4×C11C2311yescharacteristic
132C22×D4×C11C2312yes—
133C22×D4×C11C2312yes—
134C22×D4×C11C2312yes—
135C22×D4×C11C2312yes—
136C22×D4×C11C2311yescharacteristic
137C22×D4×C11C2312yes—
138C23×C4×C11C2312yes—
139C23×C4×C11C2311yescharacteristic
140C23×C4×C11C2311yescharacteristic
141C23×C4×C11C2312yes—
142C23×C4×C11C2311yescharacteristic
143C23×C4×C11C2312yes—
144C23×C4×C11C2311yescharacteristic
145C23×C4×C11C2311yescharacteristic
146C23×C4×C11C2312yes—
147C23×C4×C11C2311yescharacteristic
148C11×#127—24no—
149C11×#126—28no—
150C11×#125—24no—
151C11×#124—24no—
152C11×#123—28no—
153C11×C22⋊Q8—24no—
154C11×#121—24no—
155C11×#121—24no—
156C11×#121—24no—
157C11×#121—28no—
158C4×Q8×C11—24no—
159C4×Q8×C11D418yescomplemented
160C4×D4×C11—24no—
161C4×D4×C11—24no—
162C4×D4×C11—28no—
163C4×D4×C11—24no—
164C4×D4×C11—24no—
165C4×D4×C11—28no—
166C4×D4×C11—24no—
167C4×D4×C11—28no—
168C4×D4×C11—24no—
169C4×D4×C11—28no—
170C4×D4×C11—44no—
171C4×D4×C11—44no—
172C4×D4×C11—44no—
173C11×#117—24no—
174C11×#117—28no—
175C11×#117—28no—
176C2×C11×C4⋊C4C2311yescharacteristic
177C2×C11×C4⋊C4C2312yes—
178C2×C11×C4⋊C4C2312yes—
179C2×C11×C4⋊C4C2312yes—
180C2×C11×C4⋊C4C2311yescharacteristic
181C2×C11×C4⋊C4C2311yescharacteristic
182C2×C11×C4⋊C4C2311yescharacteristic
183C2×C11×C4⋊C4C2311yescharacteristic
184C2×C11×C4⋊C4C2312yes—
185C2×C11×C4⋊C4C2312yes—
186C2×C11×C4⋊C4C2311yescharacteristic
187C2×C11×C4⋊C4C2311yescharacteristic
188C2×C11×C4⋊C4C2312yes—
189C2×C11×C4⋊C4C2312yes—
190C2×C11×C4⋊C4C2312yes—
191C2×C11×C4⋊C4C2312yes—
192C2×C11×C4⋊C4C2312yes—
193C2×C11×C4⋊C4C2311yescharacteristic
194C2×C11×C4⋊C4C2312yes—
195C2×C11×C22⋊C4C2312yes—
196C2×C11×C22⋊C4C2312yes—
197C2×C11×C22⋊C4C2312yes—
198C2×C11×C22⋊C4C2312yes—
199C2×C11×C22⋊C4C2312yes—
200C2×C11×C22⋊C4C2311yescharacteristic
201C2×C11×C22⋊C4C2311yescharacteristic
202C2×C11×C22⋊C4C2311yescharacteristic
203C2×C11×C22⋊C4C2311yescharacteristic
204C2×C11×C22⋊C4C2311yescharacteristic
205C2×C11×C22⋊C4C2312yes—
206C2×C11×C22⋊C4C2312yes—
207C2×C11×C22⋊C4C2312yes—
208C2×C11×C22⋊C4C2312yes—
209C2×C11×C22⋊C4C2312yes—
210C2×C11×C22⋊C4C2312yes—
211C2×C11×C22⋊C4C2312yes—
212C2×C11×C22⋊C4C2312yes—
213C2×C11×C22⋊C4C2312yes—
214C2×C11×C22⋊C4C2312yes—
215C2×C11×C22⋊C4C2312yes—
216C2×C11×C22⋊C4C2312yes—
217C2×C11×C22⋊C4C2312yes—
218C2×C11×C22⋊C4C2312yes—
219C2×C11×C22⋊C4C2312yes—
220C2×C11×C22⋊C4C2311yescharacteristic
221C2×C42×C11—24no—
222C2×C42×C11—28no—
223C2×C42×C11—24no—
224C2×C42×C11C2311yescharacteristic
225C2×C42×C11C2312yes—
226C2×C42×C11C2311yescharacteristic
227C2×C42×C11C2311yescharacteristic
228C2×C42×C11C2311yescharacteristic
229C2×C42×C11C2312yes—
230C2×C42×C11C2311yescharacteristic
231C2×C42×C11C2311yescharacteristic
232C2×C42×C11C2311yescharacteristic
233C2×C42×C11C2311yescharacteristic
234C2×C42×C11C2311yescharacteristic
235C2×C42×C11C2311yescharacteristic
236C2×C42×C11C2312yes—
237C2×C42×C11C2311yescharacteristic
238C2×C42×C11C2311yescharacteristic
239C2×C42×C11C2312yes—
240C2×C42×C11C2311yescharacteristic
241C11×#95C2312yes—
242C11×#95C2312yes—
243C11×#95C2312yes—
244C11×#95C2312yes—
245C11×#95C2311yescharacteristic
246C11×#95C2311yescharacteristic
247C11×#95C2311yescharacteristic
248C11×#95C2311yescharacteristic
249C11×#95C2311yescharacteristic
250C11×#95C2311yescharacteristic
251C11×#95C2312yes—
252C11×#95C2312yes—
253C11×#95C2312yes—
254C11×#95C2312yes—
255C11×#95C2312yes—
256C11×#95C2312yes—
257C11×#95C2312yes—
258#34727C1111yesmaximal, characteristic, direct product factor, Sylow
259C24×C11C2412yes—
260C24×C11C2411yescharacteristic
261C24×C11C2411yescharacteristic
262C24×C11C2412yes—
263C11×#41—232no—
264C2×Q8×C11—22no—
265C2×Q8×C11—22no—
266C2×Q8×C11C2×D414yes—
267C2×D4×C11—22no—
268C2×D4×C11—22no—
269C2×D4×C11—24no—
270C2×D4×C11—24no—
271C2×D4×C11—24no—
272C2×D4×C11—24no—
273C2×D4×C11—24no—
274C2×D4×C11—24no—
275C2×D4×C11—24no—
276C2×D4×C11—24no—
277C2×D4×C11—24no—
278C2×D4×C11—22no—
279C2×D4×C11—24no—
280C2×D4×C11—22no—
281C2×D4×C11—22no—
282C2×D4×C11—22no—
283C2×D4×C11—24no—
284C2×D4×C11—24no—
285C2×D4×C11—22no—
286C2×D4×C11—22no—
287C2×D4×C11—42no—
288C2×D4×C11—42no—
289C2×D4×C11—42no—
290C2×D4×C11—42no—
291C2×D4×C11—42no—
292C2×D4×C11—42no—
293C2×D4×C11#4114yes—
294C22×C4×C11—24no—
295C22×C4×C11—24no—
296C22×C4×C11—22no—
297C22×C4×C11—24no—
298C22×C4×C11—22no—
299C22×C4×C11—22no—
300C22×C4×C11—22no—
301C22×C4×C11—24no—
302C22×C4×C11—22no—
303C22×C4×C11—24no—
304C22×C4×C11—22no—
305C22×C4×C11—22no—
306C22×C4×C11—22no—
307C22×C4×C11—24no—
308C22×C4×C11—22no—
309C22×C4×C11—22no—
310C22×C4×C11—22no—
311C22×C4×C11—22no—
312C22×C4×C11—24no—
313C22×C4×C11—24no—
314C22×C4×C11—24no—
315C22×C4×C11—22no—
316C22×C4×C11—22no—
317C22×C4×C11—24no—
318C22×C4×C11—22no—
319C22×C4×C11—24no—
320C22×C4×C11—41no—
321C22×C4×C11—41no—
322C22×C4×C11—42no—
323C22×C4×C11#4114yes—
324C22×C4×C11C2412yes—
325C22×C4×C11C2412yes—
326C22×C4×C11C2411yescharacteristic
327C22×C4×C11C2411yescharacteristic
328C22×C4×C11C2411yescharacteristic
329C22×C4×C11C2411yescharacteristic
330C22×C4×C11C2411yescharacteristic
331C22×C4×C11C2412yes—
332C22×C4×C11C2412yes—
333C22×C4×C11C2412yes—
334C22×C4×C11C2411yescharacteristic
335C22×C4×C11C2412yes—
336C22×C4×C11C2411yescharacteristic
337C22×C4×C11C2411yescharacteristic
338C22×C4×C11C2411yescharacteristic
339C22×C4×C11C2411yescharacteristic
340C22×C4×C11C2411yescharacteristic
341C22×C4×C11C2411yescharacteristic
342C22×C4×C11C2411yescharacteristic
343C11×C4⋊C4—24no—
344C11×C4⋊C4—22no—
345C11×C4⋊C4—24no—
346C11×C4⋊C4—24no—
347C11×C4⋊C4—22no—
348C11×C4⋊C4—24no—
349C11×C4⋊C4—22no—
350C11×C4⋊C4—22no—
351C11×C4⋊C4—22no—
352C11×C4⋊C4—24no—
353C11×C4⋊C4—24no—
354C11×C4⋊C4—22no—
355C11×C4⋊C4—22no—
356C11×C4⋊C4—42no—
357C11×C4⋊C4—42no—
358C11×C4⋊C4—42no—
359C11×C4⋊C4—42no—
360C11×C4⋊C4C2×D414yes—
361C11×C4⋊C4C2×D418yes—
362C11×C22⋊C4—22no—
363C11×C22⋊C4—24no—
364C11×C22⋊C4—24no—
365C11×C22⋊C4—24no—
366C11×C22⋊C4—24no—
367C11×C22⋊C4—24no—
368C11×C22⋊C4—24no—
369C11×C22⋊C4—24no—
370C11×C22⋊C4—24no—
371C11×C22⋊C4—24no—
372C11×C22⋊C4—22no—
373C11×C22⋊C4—22no—
374C11×C22⋊C4—24no—
375C11×C22⋊C4—24no—
376C11×C22⋊C4—22no—
377C11×C22⋊C4—22no—
378C11×C22⋊C4—24no—
379C11×C22⋊C4—24no—
380C11×C22⋊C4—42no—
381C11×C22⋊C4—42no—
382C11×C22⋊C4—42no—
383C11×C22⋊C4—42no—
384C11×C22⋊C4—42no—
385C11×C22⋊C4—42no—
386C11×C22⋊C4—42no—
387C11×C22⋊C4#4114yescomplemented
388C42×C11—22no—
389C42×C11—22no—
390C42×C11—24no—
391C42×C11—22no—
392C42×C11—24no—
393C42×C11—22no—
394C42×C11—22no—
395C42×C11—22no—
396C42×C11—22no—
397C42×C11—22no—
398C42×C11—22no—
399C42×C11—22no—
400C42×C11—24no—
401C42×C11—41no—
402C42×C11C2×D414yes—
403C42×C11C2×D418yes—
404C42×C11#4114yescomplemented
405C2×#529C2×C1111yescharacteristic, complemented
406C2×C4×#41C2×C1111yescharacteristic, complemented
407#2479C2×C1112yescomplemented
408#2471C2×C1112yescomplemented
409#2467C2×C1112yescomplemented
410#2456C2×C1112yescomplemented
411#2454C2×C1111yescharacteristic, complemented
412#2448C2×C1111yescharacteristic, complemented
413#2441C2×C1111yescharacteristic, complemented
414#2431C2×C1111yescharacteristic, complemented
415#2428C2×C1111yescharacteristic, complemented
416#2423C2×C1111yescharacteristic, complemented
417#2414C2×C1111yescharacteristic, complemented
418#2407C2×C1111yescharacteristic, complemented
419#2397C2×C1112yescomplemented
420#2392C2×C1112yescomplemented
421C4×#127C2×C1111yescharacteristic, complemented
422C4×#121C2×C1111yescharacteristic, complemented
423C4×#121C2×C1111yescharacteristic, complemented
424C4×#121C2×C1112yescomplemented
425#2295C2×C1111yescharacteristic, complemented
426#2290C2×C1112yescomplemented
427C42×D4C2×C1111yescharacteristic, complemented
428C23×C11—22no—
429C23×C11—21no—
430C23×C11—21no—
431C23×C11—21no—
432C23×C11—21no—
433C23×C11—21no—
434C23×C11—21no—
435C23×C11—22no—
436C23×C11—22no—
437C23×C11—21no—
438C23×C11—21no—
439C23×C11—22no—
440C23×C11—21no—
441C23×C11—22no—
442C23×C11—21no—
443C23×C11—22no—
444C23×C11—21no—
445C23×C11—21no—
446C23×C11—22no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11—22no—
453C23×C11C2×#4114yes—
454C23×C11C2×#4112yes—
455C23×C11C2×#4112yes—
456C23×C11C2511yescharacteristic
457Q8×C11—28no—
458D4×C11—28no—
459D4×C11—216no—
460D4×C11—28no—
461D4×C11—48no—
462D4×C11—48no—
463D4×C11—48no—
464D4×C11—48no—
465D4×C11—48no—
466D4×C11—44no—
467C2×C4×C11—216no—
468C2×C4×C11—21no—
469C2×C4×C11—21no—
470C2×C4×C11—21no—
471C2×C4×C11—21no—
472C2×C4×C11—21no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—22no—
476C2×C4×C11—21no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—21no—
480C2×C4×C11—21no—
481C2×C4×C11—21no—
482C2×C4×C11—22no—
483C2×C4×C11—21no—
484C2×C4×C11—28no—
485C2×C4×C11—21no—
486C2×C4×C11—21no—
487C2×C4×C11—22no—
488C2×C4×C11—21no—
489C2×C4×C11—21no—
490C2×C4×C11—22no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—22no—
495C2×C4×C11—21no—
496C2×C4×C11—21no—
497C2×C4×C11—22no—
498C2×C4×C11—21no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—21no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
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—22no—
512C2×C4×C11—44no—
513C2×C4×C11—48no—
514C2×C4×C11—44no—
515C2×C4×C11—44no—
516C2×C4×C11—44no—
517C2×C4×C11—48no—
518C2×C4×C11—44no—
519C2×C4×C11—48no—
520C2×C4×C11C22×D412yes—
521C2×C4×C11C22×D414yes—
522C2×C4×C11C22×D414yes—
523C2×C4×C11C22×D412yes—
524C2×C4×C11C22×D412yes—
525C2×C4×C11C2×#4112yes—
526C2×C4×C11C2×#4112yes—
527C2×C4×C11C2×#4112yes—
528C2×C4×C11C2×#4112yes—
529C2×C4×C11C2×#4112yes—
530C2×C4×C11C2×#4112yes—
531C2×C4×C11C2×#4112yes—
532C2×C4×C11C2×#4112yes—
533C2×C4×C11H(5,𝔽2)12yes—
534C22×#41C22×C1111yescharacteristic
535C2×#127C22×C1111yescharacteristic
536#529—28no—
537C2×#126C22×C1112yes—
538C2×#125C22×C1111yescharacteristic
539C2×#124C22×C1111yescharacteristic
540C2×#123C22×C1112yes—
541C2×C22⋊Q8C22×C1111yescharacteristic
542C2×#121C22×C1111yescharacteristic
543C2×#121C22×C1111yescharacteristic
544C2×#121C22×C1111yescharacteristic
545C2×#121C22×C1112yes—
546C4×#41—28no—
547C2×C4×Q8C22×C1111yescharacteristic
548C2×C4×Q8C22×C1111yescharacteristic
549C2×C4×D4C22×C1112yes—
550C2×C4×D4C22×C1111yescharacteristic
551C2×C4×D4C22×C1111yescharacteristic
552C2×C4×D4C22×C1112yes—
553C2×C4×D4C22×C1111yescharacteristic
554C2×C4×D4C22×C1112yes—
555C2×C4×D4C22×C1111yescharacteristic
556C2×C4×D4C22×C1112yes—
557C2×C4×D4C22×C1111yescharacteristic
558C2×C4×D4C22×C1111yescharacteristic
559C2×C4×D4C22×C1112yes—
560C2×C4×D4C22×C1112yes—
561C2×C4×D4C22×C1112yes—
562C2×#117C22×C1112yes—
563C2×#117C22×C1111yescharacteristic
564C2×#117C22×C1112yes—
565C22×C42C22×C1111yescharacteristic
566C22×C42C22×C1112yes—
567C22×C42C22×C1111yescharacteristic
568#399C22×C1112yes—
569#399C22×C1112yes—
570#399C22×C1112yes—
571#399C22×C1112yes—
572#398C22×C1112yes—
573#397C22×C1112yes—
574#396C22×C1112yes—
575#396C22×C1112yes—
576#394C22×C1112yes—
577#394C22×C1112yes—
578#394C22×C1112yes—
579#392C22×C1112yes—
580#392C22×C1112yes—
581#392C22×C1112yes—
582#392C22×C1112yes—
583#392C22×C1112yes—
584#391C22×C1111yescharacteristic
585#391C22×C1111yescharacteristic
586#390C22×C1111yescharacteristic
587#390C22×C1111yescharacteristic
588#390C22×C1112yes—
589#390C22×C1112yes—
590#390C22×C1112yes—
591#390C22×C1111yescharacteristic
592#390C22×C1111yescharacteristic
593#389C22×C1111yescharacteristic
594#389C22×C1111yescharacteristic
595#389C22×C1111yescharacteristic
596#389C22×C1111yescharacteristic
597#389C22×C1112yes—
598#388C22×C1112yes—
599#388C22×C1112yes—
600#388C22×C1112yes—
601#388C22×C1112yes—
602#388C22×C1112yes—
603#388C22×C1112yes—
604#387C22×C1112yes—
605#387C22×C1112yes—
606#387C22×C1112yes—
607#387C22×C1112yes—
608#386C22×C1112yes—
609#386C22×C1112yes—
610#386C22×C1112yes—
611#386C22×C1112yes—
612#386C22×C1112yes—
613#386C22×C1112yes—
614#385C22×C1112yes—
615#385C22×C1112yes—
616#384C22×C1111yescharacteristic
617#380C22×C1111yescharacteristic
618#380C22×C1111yescharacteristic
619#380C22×C1112yes—
620C4×C4⋊C4C22×C1112yes—
621C4×C4⋊C4C22×C1111yescharacteristic
622C4×C4⋊C4C22×C1111yescharacteristic
623C4×C4⋊C4C22×C1111yescharacteristic
624C4×C4⋊C4C22×C1111yescharacteristic
625C4×C22⋊C4C22×C1111yescharacteristic
626C4×C22⋊C4C22×C1112yes—
627C4×C22⋊C4C22×C1111yescharacteristic
628C4×C22⋊C4C22×C1111yescharacteristic
629C4×C22⋊C4C22×C1111yescharacteristic
630C4×C22⋊C4C22×C1111yescharacteristic
631C4×C22⋊C4C22×C1111yescharacteristic
632C4×C22⋊C4C22×C1112yes—
633#376C22×C1112yes—
634C43C22×C1111yescharacteristic
635C22×C11—24no—
636C22×C11—22no—
637C22×C11—22no—
638C22×C11—22no—
639C22×C11—22no—
640C22×C11—22no—
641C22×C11—24no—
642C22×C11—24no—
643C22×C11—22no—
644C22×C11—41no—
645C22×C11—42no—
646C22×C11—41no—
647C22×C11—42no—
648C22×C11—41no—
649C22×C11—42no—
650C22×C11—41no—
651C22×C11—41no—
652C22×C11—42no—
653C22×C11—41no—
654C22×C11—41no—
655C22×C11—41no—
656C22×C11—42no—
657C22×C11—42no—
658C22×C11—42no—
659C22×C11—42no—
660C22×C11—42no—
661C22×C11—42no—
662C22×C11—42no—
663C22×C11C23×D411yescharacteristic
664C22×C11C22×#4111yescharacteristic
665C22×C11C22×#4111yescharacteristic
666C22×C11C22×#4111yescharacteristic
667C22×C11C22×#4111yescharacteristic
668C22×C11C2×H(5,𝔽2)11yescharacteristic
669C22×C11#58511yescharacteristic
670C4×C11—22no—
671C4×C11—24no—
672C4×C11—22no—
673C4×C11—22no—
674C4×C11—22no—
675C4×C11—24no—
676C4×C11—22no—
677C4×C11—22no—
678C4×C11—41no—
679C4×C11—41no—
680C4×C11—42no—
681C4×C11—41no—
682C4×C11—42no—
683C4×C11—41no—
684C4×C11—42no—
685C4×C11—41no—
686C4×C11—42no—
687C4×C11#52514yes—
688C4×C11#55014yes—
689C2×#41—24no—
690C2×#41—24no—
691C2×#41—24no—
692C22×Q8C23×C1111yescharacteristic
693C22×D4C23×C1111yescharacteristic
694C22×D4C23×C1112yes—
695C22×D4C23×C1111yescharacteristic
696C22×D4C23×C1112yes—
697C22×D4C23×C1112yes—
698C22×D4C23×C1112yes—
699C22×D4C23×C1112yes—
700C22×D4C23×C1111yescharacteristic
701C22×D4C23×C1112yes—
702C23×C4C23×C1112yes—
703C23×C4C23×C1112yes—
704C23×C4C23×C1112yes—
705C23×C4C23×C1111yescharacteristic
706C23×C4C23×C1111yescharacteristic
707C23×C4C23×C1111yescharacteristic
708C23×C4C23×C1111yescharacteristic
709C23×C4C23×C1112yes—
710C23×C4C23×C1111yescharacteristic
711C23×C4C23×C1111yescharacteristic
712#127—24no—
713#126—28no—
714#125—24no—
715#124—24no—
716#123—28no—
717C22⋊Q8—24no—
718#121—24no—
719#121—24no—
720#121—24no—
721#121—28no—
722C4×Q8—24no—
723C4×Q8D4×C1118yescomplemented
724C4×D4—24no—
725C4×D4—24no—
726C4×D4—28no—
727C4×D4—24no—
728C4×D4—24no—
729C4×D4—28no—
730C4×D4—24no—
731C4×D4—28no—
732C4×D4—24no—
733C4×D4—28no—
734C4×D4—44no—
735C4×D4—44no—
736C4×D4—44no—
737#117—24no—
738#117—28no—
739#117—28no—
740C2×C4⋊C4C23×C1111yescharacteristic
741C2×C4⋊C4C23×C1112yes—
742C2×C4⋊C4C23×C1112yes—
743C2×C4⋊C4C23×C1112yes—
744C2×C4⋊C4C23×C1111yescharacteristic
745C2×C4⋊C4C23×C1112yes—
746C2×C4⋊C4C23×C1111yescharacteristic
747C2×C4⋊C4C23×C1111yescharacteristic
748C2×C4⋊C4C23×C1111yescharacteristic
749C2×C4⋊C4C23×C1112yes—
750C2×C4⋊C4C23×C1111yescharacteristic
751C2×C4⋊C4C23×C1111yescharacteristic
752C2×C4⋊C4C23×C1112yes—
753C2×C4⋊C4C23×C1112yes—
754C2×C4⋊C4C23×C1112yes—
755C2×C4⋊C4C23×C1112yes—
756C2×C4⋊C4C23×C1112yes—
757C2×C4⋊C4C23×C1111yescharacteristic
758C2×C4⋊C4C23×C1112yes—
759C2×C22⋊C4C23×C1112yes—
760C2×C22⋊C4C23×C1112yes—
761C2×C22⋊C4C23×C1112yes—
762C2×C22⋊C4C23×C1112yes—
763C2×C22⋊C4C23×C1112yes—
764C2×C22⋊C4C23×C1112yes—
765C2×C22⋊C4C23×C1112yes—
766C2×C22⋊C4C23×C1112yes—
767C2×C22⋊C4C23×C1111yescharacteristic
768C2×C22⋊C4C23×C1111yescharacteristic
769C2×C22⋊C4C23×C1111yescharacteristic
770C2×C22⋊C4C23×C1111yescharacteristic
771C2×C22⋊C4C23×C1111yescharacteristic
772C2×C22⋊C4C23×C1112yes—
773C2×C22⋊C4C23×C1112yes—
774C2×C22⋊C4C23×C1112yes—
775C2×C22⋊C4C23×C1112yes—
776C2×C22⋊C4C23×C1112yes—
777C2×C22⋊C4C23×C1112yes—
778C2×C22⋊C4C23×C1112yes—
779C2×C22⋊C4C23×C1112yes—
780C2×C22⋊C4C23×C1112yes—
781C2×C22⋊C4C23×C1112yes—
782C2×C22⋊C4C23×C1112yes—
783C2×C22⋊C4C23×C1112yes—
784C2×C22⋊C4C23×C1111yescharacteristic
785C2×C42—24no—
786C2×C42—28no—
787C2×C42—24no—
788C2×C42C23×C1111yescharacteristic
789C2×C42C23×C1111yescharacteristic
790C2×C42C23×C1112yes—
791C2×C42C23×C1111yescharacteristic
792C2×C42C23×C1112yes—
793C2×C42C23×C1111yescharacteristic
794C2×C42C23×C1112yes—
795C2×C42C23×C1111yescharacteristic
796C2×C42C23×C1111yescharacteristic
797C2×C42C23×C1111yescharacteristic
798C2×C42C23×C1111yescharacteristic
799C2×C42C23×C1111yescharacteristic
800C2×C42C23×C1111yescharacteristic
801C2×C42C23×C1111yescharacteristic
802C2×C42C23×C1112yes—
803C2×C42C23×C1111yescharacteristic
804C2×C42C23×C1111yescharacteristic
805#95C23×C1112yes—
806#95C23×C1112yes—
807#95C23×C1112yes—
808#95C23×C1112yes—
809#95C23×C1111yescharacteristic
810#95C23×C1111yescharacteristic
811#95C23×C1111yescharacteristic
812#95C23×C1111yescharacteristic
813#95C23×C1111yescharacteristic
814#95C23×C1111yescharacteristic
815#95C23×C1112yes—
816#95C23×C1112yes—
817#95C23×C1112yes—
818#95C23×C1112yes—
819#95C23×C1112yes—
820#95C23×C1112yes—
821#95C23×C1112yes—
822C2×C11—42no—
823C2×C11—44no—
824C2×C11—42no—
825C2×C11—82no—
826C2×C11C2×#52511yescharacteristic
827C2×C11#344411yescharacteristic
828C2×C11#346011yescharacteristic
829C2×C11C2×#55011yescharacteristic
830C2×C11D4×#4111yescharacteristic
831C2×C11#347511yescharacteristic
832C2×C11#348111yescharacteristic
833C24C24×C1112yes—
834C24C24×C1111yescharacteristic
835C24C24×C1111yescharacteristic
836C24C24×C1112yes—
837#41—232no—
838C2×Q8—22no—
839C2×Q8—22no—
840C2×Q8C2×D4×C1114yes—
841C2×D4—22no—
842C2×D4—22no—
843C2×D4—24no—
844C2×D4—24no—
845C2×D4—24no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—24no—
850C2×D4—24no—
851C2×D4—24no—
852C2×D4—22no—
853C2×D4—24no—
854C2×D4—22no—
855C2×D4—22no—
856C2×D4—22no—
857C2×D4—24no—
858C2×D4—24no—
859C2×D4—22no—
860C2×D4—22no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4C11×#4114yes—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—22no—
871C22×C4—24no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—24no—
876C22×C4—22no—
877C22×C4—24no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—24no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—24no—
887C22×C4—24no—
888C22×C4—24no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—24no—
892C22×C4—22no—
893C22×C4—24no—
894C22×C4—41no—
895C22×C4—41no—
896C22×C4—42no—
897C22×C4C11×#4114yes—
898C22×C4C24×C1112yes—
899C22×C4C24×C1112yes—
900C22×C4C24×C1111yescharacteristic
901C22×C4C24×C1111yescharacteristic
902C22×C4C24×C1111yescharacteristic
903C22×C4C24×C1111yescharacteristic
904C22×C4C24×C1111yescharacteristic
905C22×C4C24×C1112yes—
906C22×C4C24×C1112yes—
907C22×C4C24×C1112yes—
908C22×C4C24×C1111yescharacteristic
909C22×C4C24×C1112yes—
910C22×C4C24×C1111yescharacteristic
911C22×C4C24×C1111yescharacteristic
912C22×C4C24×C1111yescharacteristic
913C22×C4C24×C1111yescharacteristic
914C22×C4C24×C1111yescharacteristic
915C22×C4C24×C1111yescharacteristic
916C22×C4C24×C1111yescharacteristic
917C4⋊C4—24no—
918C4⋊C4—22no—
919C4⋊C4—24no—
920C4⋊C4—24no—
921C4⋊C4—22no—
922C4⋊C4—24no—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—24no—
927C4⋊C4—24no—
928C4⋊C4—22no—
929C4⋊C4—22no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4C2×D4×C1114yes—
935C4⋊C4C2×D4×C1118yes—
936C22⋊C4—22no—
937C22⋊C4—24no—
938C22⋊C4—24no—
939C22⋊C4—24no—
940C22⋊C4—24no—
941C22⋊C4—24no—
942C22⋊C4—24no—
943C22⋊C4—24no—
944C22⋊C4—24no—
945C22⋊C4—24no—
946C22⋊C4—22no—
947C22⋊C4—22no—
948C22⋊C4—24no—
949C22⋊C4—24no—
950C22⋊C4—22no—
951C22⋊C4—22no—
952C22⋊C4—24no—
953C22⋊C4—24no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4C11×#4114yescomplemented
962C42—22no—
963C42—22no—
964C42—24no—
965C42—22no—
966C42—24no—
967C42—22no—
968C42—22no—
969C42—22no—
970C42—22no—
971C42—22no—
972C42—22no—
973C42—22no—
974C42—24no—
975C42—41no—
976C42C2×D4×C1114yes—
977C42C2×D4×C1118yes—
978C42C11×#4114yescomplemented
979C11#3472711yescharacteristic, direct product factor, Sylow
980C23—22no—
981C23—21no—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23—21no—
987C23—22no—
988C23—22no—
989C23—21no—
990C23—21no—
991C23—22no—
992C23—21no—
993C23—22no—
994C23—21no—
995C23—22no—
996C23—21no—
997C23—21no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23C2×C11×#4114yes—
1006C23C2×C11×#4112yes—
1007C23C2×C11×#4112yes—
1008C23C25×C1111yescharacteristic
1009Q8—28no—
1010D4—28no—
1011D4—216no—
1012D4—28no—
1013D4—48no—
1014D4—48no—
1015D4—48no—
1016D4—48no—
1017D4—48no—
1018D4—44no—
1019C2×C4—216no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—22no—
1028C2×C4—21no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—21no—
1036C2×C4—28no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—22no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—21no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—22no—
1064C2×C4—44no—
1065C2×C4—48no—
1066C2×C4—44no—
1067C2×C4—44no—
1068C2×C4—44no—
1069C2×C4—48no—
1070C2×C4—44no—
1071C2×C4—48no—
1072C2×C4C22×D4×C1112yes—
1073C2×C4C22×D4×C1114yes—
1074C2×C4C22×D4×C1114yes—
1075C2×C4C22×D4×C1112yes—
1076C2×C4C22×D4×C1112yes—
1077C2×C4C2×C11×#4112yes—
1078C2×C4C2×C11×#4112yes—
1079C2×C4C2×C11×#4112yes—
1080C2×C4C2×C11×#4112yes—
1081C2×C4C2×C11×#4112yes—
1082C2×C4C2×C11×#4112yes—
1083C2×C4C2×C11×#4112yes—
1084C2×C4C2×C11×#4112yes—
1085C2×C4C11×H(5,𝔽2)12yes—
1086C22—24no—
1087C22—22no—
1088C22—22no—
1089C22—22no—
1090C22—22no—
1091C22—22no—
1092C22—24no—
1093C22—24no—
1094C22—22no—
1095C22—41no—
1096C22—42no—
1097C22—41no—
1098C22—42no—
1099C22—41no—
1100C22—42no—
1101C22—41no—
1102C22—41no—
1103C22—42no—
1104C22—41no—
1105C22—41no—
1106C22—41no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22C23×D4×C1111yescharacteristic
1115C22C22×C11×#4111yescharacteristic
1116C22C22×C11×#4111yescharacteristic
1117C22C22×C11×#4111yescharacteristic
1118C22C22×C11×#4111yescharacteristic
1119C22C2×C11×H(5,𝔽2)11yescharacteristic
1120C22C11×#58511yescharacteristic
1121C4—22no—
1122C4—24no—
1123C4—22no—
1124C4—22no—
1125C4—22no—
1126C4—24no—
1127C4—22no—
1128C4—22no—
1129C4—41no—
1130C4—42no—
1131C4—41no—
1132C4—41no—
1133C4—42no—
1134C4—41no—
1135C4—42no—
1136C4—41no—
1137C4—42no—
1138C4C11×#52514yes—
1139C4C11×#55014yes—
1140C2—42no—
1141C2—44no—
1142C2—42no—
1143C2—82no—
1144C2C2×C11×#52511yescharacteristic
1145C2C11×#344411yescharacteristic
1146C2C11×#346011yescharacteristic
1147C2C2×C11×#55011yescharacteristic
1148C2D4×C11×#4111yescharacteristic
1149C2C11×#347511yescharacteristic
1150C2C11×#348111yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC23C25×C11
socleC23×C11C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#529C2semidirect
2. C2×C4×C11×#41C2semidirect
3. C11×#2479C2semidirect
4. C11×#2471C2semidirect
5. C11×#2467C2semidirect
6. C11×#2456C2semidirect
7. C11×#2454C2semidirect
8. C11×#2448C2semidirect
9. C11×#2441C2semidirect
10. C11×#2431C2semidirect
11. C11×#2428C2semidirect
12. C11×#2423C2semidirect
13. C11×#2414C2semidirect
14. C11×#2407C2semidirect
15. C11×#2397C2semidirect
16. C11×#2392C2semidirect
17. C4×C11×#127C2semidirect
18. C4×C11×#121C2semidirect
19. C4×C11×#121C2semidirect
20. C4×C11×#121C2semidirect
21. C11×#2295C2semidirect
22. C11×#2290C2semidirect
23. C42×D4×C11C2semidirect
159. C4×Q8×C11D4semidirect
258. #34727C11direct (N × H)
387. C11×C22⋊C4#41semidirect
404. C42×C11#41semidirect
405. C2×#529C2×C11semidirect
406. C2×C4×#41C2×C11semidirect
407. #2479C2×C11semidirect
408. #2471C2×C11semidirect
409. #2467C2×C11semidirect
410. #2456C2×C11semidirect
411. #2454C2×C11semidirect
412. #2448C2×C11semidirect
413. #2441C2×C11semidirect
414. #2431C2×C11semidirect
415. #2428C2×C11semidirect
416. #2423C2×C11semidirect
417. #2414C2×C11semidirect
418. #2407C2×C11semidirect
419. #2397C2×C11semidirect
420. #2392C2×C11semidirect
421. C4×#127C2×C11semidirect
422. C4×#121C2×C11semidirect
423. C4×#121C2×C11semidirect
424. C4×#121C2×C11semidirect
425. #2295C2×C11semidirect
426. #2290C2×C11semidirect
427. C42×D4C2×C11semidirect
723. C4×Q8D4×C11semidirect
961. C22⋊C4C11×#41semidirect
978. C42C11×#41semidirect
979. C11#34727direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5292
C2×C4×C11×#412
C11×#24792
C11×#24712
C11×#24672
C11×#24562
C11×#24542
C11×#24482
C11×#24412
C11×#24312
C11×#24282
C11×#24232
C11×#24142
C11×#24072
C11×#23972
C11×#23922
C4×C11×#1272
C4×C11×#1212
C11×#22952
C11×#22902
C42×D4×C112
#3472711