Finite Group Databasebeta

← C11×#22506 #14599699

Subgroups — C11×#22506 #14599699

Order 2816.

1148 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3475C211yesmaximal, characteristic
2D4×C11×M16C211yesmaximal, characteristic, complemented
3C11×#2290C211yesmaximal, characteristic, complemented
4C11×#1995C211yesmaximal, characteristic, complemented
5C11×#1986C211yesmaximal, characteristic, complemented
6C11×#1897C211yesmaximal, characteristic, complemented
7C11×#1896C211yesmaximal, characteristic, complemented
8C11×#1871C211yesmaximal, characteristic, complemented
9C11×#1871C211yesmaximal, characteristic, complemented
10C11×#1826C211yesmaximal, characteristic, complemented
11C11×#1826C211yesmaximal, characteristic, complemented
12C11×#1806C211yesmaximal, characteristic, complemented
13C11×#1759C211yesmaximal, characteristic, complemented
14C11×#1733C211yesmaximal, characteristic, complemented
15C2×C11×#339C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C11×#556C411yescharacteristic, complemented
19C11×#555C411yescharacteristic, complemented
20C11×#554C411yescharacteristic, complemented
21C11×#553C411yescharacteristic, complemented
22C11×#553C411yescharacteristic, complemented
23C11×#552—21no—
24C11×#552C411yescharacteristic, complemented
25C11×#552C411yescharacteristic, complemented
26C11×#551—21no—
27C11×#551—21no—
28C11×#547C411yescharacteristic, complemented
29C11×#546—21no—
30C11×#533C2211yescharacteristic
31C11×#529—21no—
32C11×#529—21no—
33C11×#529—21no—
34C11×#525C2211yescharacteristic
35C11×#525C2211yescharacteristic
36C4×C11×#41—21no—
37C4×C11×#41C2211yescharacteristic
38C2×C4×D4×C11C2211yescharacteristic
39C2×C11×#117C2211yescharacteristic
40C2×C11×#117C2211yescharacteristic
41C2×C11×#117C2211yescharacteristic
42C22×C42×C11C2211yescharacteristic
43C11×#436—21no—
44C11×#435—21no—
45C11×#435—21no—
46C8×D4×C11—21no—
47C11×#423C2211yescharacteristic
48C2×C11×#104C2211yescharacteristic
49C2×C11×#104C2211yescharacteristic
50C2×C11×#104C2211yescharacteristic
51C2×C11×#104C2211yescharacteristic
52C11×#407C2211yescharacteristic
53C11×#407C2211yescharacteristic
54C4×C11×M16C2211yescharacteristic
55C11×#388—21no—
56C11×#387—21no—
57C11×#386—21no—
58C11×#385—21no—
59C4×C11×C4⋊C4C2211yescharacteristic
60C4×C11×C22⋊C4C2211yescharacteristic
61C4×C11×C22⋊C4C2211yescharacteristic
62C11×#376C2211yescharacteristic
63C11×#339C2211yescharacteristic
64C11×#339C2211yescharacteristic
65C11×#339C2211yescharacteristic
66C11×#339C2211yescharacteristic
67C11×#339C2211yescharacteristic
68C11×#339C2211yescharacteristic
69C11×#339C2211yescharacteristic
70C11×#339C2211yescharacteristic
71C11×#339C2211yescharacteristic
72C11×#339C2211yescharacteristic
73C11×#339C2211yescharacteristic
74C11×#339C2211yescharacteristic
75C2×C11×#41—21no—
76C2×C11×#41C2311yescharacteristic
77C22×D4×C11D411yescharacteristic
78C23×C4×C11—21no—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C2×C11×M16—21no—
82C2×C11×M16—21no—
83C2×C11×M16—22no—
84C2×C11×M16—22no—
85C2×C11×M16—41no—
86C2×C11×M16—41no—
87C2×C11×M16C2311yescharacteristic
88C2×C11×M16C2311yescharacteristic
89C2×C11×M16C2311yescharacteristic
90C2×C11×M16C2311yescharacteristic
91C22×C8×C11—21no—
92C22×C8×C11—21no—
93C11×C4⋊Q8C2×C411yescharacteristic, complemented
94C11×C4⋊Q8C2×C411yescharacteristic, complemented
95C11×#126—21no—
96C11×#126—21no—
97C11×#126—21no—
98C11×#126—21no—
99C11×#126—21no—
100C11×#126—21no—
101C11×#125—21no—
102C11×#125—21no—
103C11×#125—21no—
104C11×#125C2×C411yescharacteristic, complemented
105C11×#125C2×C411yescharacteristic, complemented
106C11×#124—21no—
107C11×#124—21no—
108C11×#124—21no—
109C11×#123—21no—
110C11×#123—21no—
111C11×#123—21no—
112C11×#123—21no—
113C11×#123—21no—
114C11×#123—21no—
115C11×#123—21no—
116C11×#123—21no—
117C11×C22⋊Q8—21no—
118C11×C22⋊Q8—21no—
119C11×C22⋊Q8—21no—
120C11×C22⋊Q8—21no—
121C11×C22⋊Q8—21no—
122C11×C22⋊Q8C2×C411yescharacteristic
123C11×C22⋊Q8C2×C411yescharacteristic
124C11×C22⋊Q8C2×C411yescharacteristic, complemented
125C11×C22⋊Q8C2×C411yescharacteristic, complemented
126C11×#121—21no—
127C11×#121—21no—
128C11×#121—21no—
129C11×#121C2×C411yescharacteristic
130C11×#121C2×C411yescharacteristic
131C11×#121C2×C411yescharacteristic, complemented
132C11×#121C2×C411yescharacteristic, complemented
133C11×#120—21no—
134C11×#120—21no—
135C4×Q8×C11—21no—
136C4×Q8×C11—21no—
137C4×Q8×C11—21no—
138C4×Q8×C11C2×C411yescharacteristic, complemented
139C4×Q8×C11C2×C411yescharacteristic, complemented
140C4×D4×C11—21no—
141C4×D4×C11—21no—
142C4×D4×C11—21no—
143C4×D4×C11—21no—
144C4×D4×C11—21no—
145C4×D4×C11—21no—
146C4×D4×C11—21no—
147C4×D4×C11—21no—
148C4×D4×C11—21no—
149C4×D4×C11C2×C411yescharacteristic
150C4×D4×C11C2×C411yescharacteristic
151C4×D4×C11C2×C411yescharacteristic
152C4×D4×C11C2×C411yescharacteristic
153C4×D4×C11C2×C411yescharacteristic, complemented
154C4×D4×C11C2×C411yescharacteristic, complemented
155C4×D4×C11D411yescharacteristic
156C4×D4×C11D411yescharacteristic
157C4×D4×C11D411yescharacteristic
158C4×D4×C11D411yescharacteristic
159C11×#117—21no—
160C11×#117—21no—
161C11×#117—21no—
162C11×#117—21no—
163C11×#117—21no—
164C11×#117—21no—
165C11×#117—21no—
166C11×#117—21no—
167C11×#117—22no—
168C11×#117—41no—
169C11×#117C2×C411yescharacteristic
170C11×#117C2×C411yescharacteristic
171C11×#117C2×C411yescharacteristic, complemented
172C11×#117C2×C411yescharacteristic, complemented
173C11×#117C2311yescharacteristic
174C11×#117C2311yescharacteristic
175C11×#117C2311yescharacteristic
176C2×C11×C4⋊C4—21no—
177C2×C11×C4⋊C4—21no—
178C2×C11×C4⋊C4C2×C411yescharacteristic
179C2×C11×C4⋊C4C2×C411yescharacteristic
180C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
181C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
182C2×C11×C4⋊C4D411yescharacteristic
183C2×C11×C22⋊C4—21no—
184C2×C11×C22⋊C4—21no—
185C2×C11×C22⋊C4—21no—
186C2×C11×C22⋊C4—21no—
187C2×C11×C22⋊C4—21no—
188C2×C11×C22⋊C4D411yescharacteristic
189C2×C11×C22⋊C4D411yescharacteristic
190C2×C42×C11—21no—
191C2×C42×C11—21no—
192C2×C42×C11—21no—
193C2×C42×C11—22no—
194C2×C42×C11—21no—
195C2×C42×C11—41no—
196C2×C42×C11C2311yescharacteristic
197C2×C42×C11C2311yescharacteristic
198C2×C42×C11C2311yescharacteristic
199C2×C42×C11C2311yescharacteristic
200C2×C42×C11C2311yescharacteristic
201C11×C4⋊C8—21no—
202C11×C4⋊C8—21no—
203C11×#104—22no—
204C11×#104—22no—
205C11×#104—41no—
206C11×#104—41no—
207C11×C22⋊C8—21no—
208C11×C22⋊C8—21no—
209C11×C22⋊C8—21no—
210C11×C22⋊C8—21no—
211C11×#97—21no—
212C4×C8×C11—21no—
213C11×#95—21no—
214C11×#95—21no—
215C11×#95—21no—
216C11×#95—21no—
217C11×#95—21no—
218#22506C1111yesmaximal, characteristic, direct product factor, Sylow
219C24×C11C2×D411yescharacteristic
220C24×C11C2×D411yescharacteristic
221C11×#41—21no—
222C11×#41—21no—
223C11×#41—21no—
224C11×#41—21no—
225C11×#41—44no—
226C2×Q8×C11—21no—
227C2×Q8×C11—21no—
228C2×Q8×C11C22×C411yescharacteristic
229C2×D4×C11—21no—
230C2×D4×C11—21no—
231C2×D4×C11—21no—
232C2×D4×C11—21no—
233C2×D4×C11—21no—
234C2×D4×C11—42no—
235C2×D4×C11C22⋊C411yescharacteristic
236C2×D4×C11C22⋊C411yescharacteristic
237C2×D4×C11C22⋊C411yescharacteristic
238C2×D4×C11C22⋊C411yescharacteristic
239C2×D4×C11C22×C411yescharacteristic
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11—42no—
260C22×C4×C11—42no—
261C22×C4×C11—42no—
262C22×C4×C11C22×C411yescharacteristic
263C22×C4×C11C22×C411yescharacteristic
264C22×C4×C11C22×C411yescharacteristic
265C22×C4×C11C22×C411yescharacteristic
266C22×C4×C11C2×D411yescharacteristic
267C22×C4×C11C2×D411yescharacteristic
268C22×C4×C11C2×D411yescharacteristic
269C22×C4×C11C2×D411yescharacteristic
270C22×C4×C11C2×D411yescharacteristic
271C22×C4×C11C2×D411yescharacteristic
272C22×C4×C11C2×D411yescharacteristic
273C22×C4×C11C2×D411yescharacteristic
274C22×C4×C11C2411yescharacteristic
275C11×M16—21no—
276C11×M16—21no—
277C11×M16—21no—
278C11×M16—21no—
279C11×M16—21no—
280C11×M16—21no—
281C11×M16—21no—
282C11×M16—42no—
283C11×M16—42no—
284C11×M16#4112yescomplemented
285C2×C8×C11—21no—
286C2×C8×C11—21no—
287C2×C8×C11—21no—
288C2×C8×C11—21no—
289C2×C8×C11—42no—
290C2×C8×C11—42no—
291C11×C4⋊C4—21no—
292C11×C4⋊C4—21no—
293C11×C4⋊C4—21no—
294C11×C4⋊C4—21no—
295C11×C4⋊C4—21no—
296C11×C4⋊C4—21no—
297C11×C4⋊C4—21no—
298C11×C4⋊C4—21no—
299C11×C4⋊C4—21no—
300C11×C4⋊C4—21no—
301C11×C4⋊C4—21no—
302C11×C4⋊C4—21no—
303C11×C4⋊C4—21no—
304C11×C4⋊C4—21no—
305C11×C4⋊C4—21no—
306C11×C4⋊C4—21no—
307C11×C4⋊C4—42no—
308C11×C4⋊C4—42no—
309C11×C4⋊C4C22⋊C411yescharacteristic
310C11×C4⋊C4C22⋊C411yescharacteristic
311C11×C4⋊C4C22⋊C411yescharacteristic
312C11×C4⋊C4C22⋊C411yescharacteristic
313C11×C4⋊C4C22×C411yescharacteristic
314C11×C4⋊C4C22×C411yescharacteristic
315C11×C4⋊C4C22×C411yescharacteristic
316C11×C4⋊C4C22×C411yescharacteristic
317C11×C4⋊C4C22×C411yescharacteristic
318C11×C4⋊C4C22×C411yescharacteristic
319C11×C22⋊C4—21no—
320C11×C22⋊C4—21no—
321C11×C22⋊C4—21no—
322C11×C22⋊C4—21no—
323C11×C22⋊C4—21no—
324C11×C22⋊C4—21no—
325C11×C22⋊C4—21no—
326C11×C22⋊C4—21no—
327C11×C22⋊C4—21no—
328C11×C22⋊C4—21no—
329C11×C22⋊C4—21no—
330C11×C22⋊C4—21no—
331C11×C22⋊C4—21no—
332C11×C22⋊C4—21no—
333C11×C22⋊C4—21no—
334C11×C22⋊C4—21no—
335C11×C22⋊C4—21no—
336C11×C22⋊C4—42no—
337C11×C22⋊C4—42no—
338C11×C22⋊C4—42no—
339C11×C22⋊C4C22⋊C411yescharacteristic
340C11×C22⋊C4C22⋊C411yescharacteristic
341C11×C22⋊C4C22⋊C411yescharacteristic
342C11×C22⋊C4C22⋊C411yescharacteristic
343C11×C22⋊C4C22⋊C411yescharacteristic
344C11×C22⋊C4C22⋊C411yescharacteristic
345C11×C22⋊C4C22⋊C411yescharacteristic
346C11×C22⋊C4C22⋊C411yescharacteristic
347C42×C11—21no—
348C42×C11—21no—
349C42×C11—21no—
350C42×C11—21no—
351C42×C11—21no—
352C42×C11—21no—
353C42×C11—21no—
354C42×C11—21no—
355C42×C11—21no—
356C42×C11—21no—
357C42×C11—21no—
358C42×C11—21no—
359C42×C11—21no—
360C42×C11—21no—
361C42×C11—21no—
362C42×C11—21no—
363C42×C11—42no—
364C42×C11C22×C411yescharacteristic
365C42×C11C22×C411yescharacteristic
366C42×C11C2×D411yescharacteristic
367C42×C11C2×D411yescharacteristic
368C42×C11#4112yescomplemented
369#3475C2×C1111yescharacteristic
370D4×M16C2×C1111yescharacteristic, complemented
371#2290C2×C1111yescharacteristic, complemented
372#1995C2×C1111yescharacteristic, complemented
373#1986C2×C1111yescharacteristic, complemented
374#1897C2×C1111yescharacteristic, complemented
375#1896C2×C1111yescharacteristic, complemented
376#1871C2×C1111yescharacteristic, complemented
377#1871C2×C1111yescharacteristic, complemented
378#1826C2×C1111yescharacteristic, complemented
379#1826C2×C1111yescharacteristic, complemented
380#1806C2×C1111yescharacteristic, complemented
381#1759C2×C1111yescharacteristic, complemented
382#1733C2×C1111yescharacteristic, complemented
383C2×#339C2×C1111yescharacteristic, complemented
384C23×C11—21no—
385C23×C11—21no—
386C23×C11—22no—
387C23×C11—21no—
388C23×C11—21no—
389C23×C11—21no—
390C23×C11—41no—
391C23×C11—41no—
392C23×C11—41no—
393C23×C11C2×C22⋊C411yescharacteristic
394C23×C11C2×C22⋊C411yescharacteristic
395C23×C11C2×C22⋊C411yescharacteristic
396C23×C11C2×C22⋊C411yescharacteristic
397C23×C11C22×D411yescharacteristic
398Q8×C11—21no—
399Q8×C11—21no—
400Q8×C11—42no—
401Q8×C11—81no—
402D4×C11—22no—
403D4×C11—22no—
404D4×C11—21no—
405D4×C11—21no—
406D4×C11—41no—
407D4×C11—41no—
408D4×C11—42no—
409D4×C11—41no—
410D4×C11—41no—
411D4×C11—42no—
412D4×C11—81no—
413D4×C11—81no—
414C2×C4×C11—21no—
415C2×C4×C11—21no—
416C2×C4×C11—21no—
417C2×C4×C11—21no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—21no—
421C2×C4×C11—21no—
422C2×C4×C11—21no—
423C2×C4×C11—21no—
424C2×C4×C11—21no—
425C2×C4×C11—21no—
426C2×C4×C11—21no—
427C2×C4×C11—21no—
428C2×C4×C11—21no—
429C2×C4×C11—21no—
430C2×C4×C11—21no—
431C2×C4×C11—21no—
432C2×C4×C11—21no—
433C2×C4×C11—21no—
434C2×C4×C11—22no—
435C2×C4×C11—21no—
436C2×C4×C11—21no—
437C2×C4×C11—21no—
438C2×C4×C11—21no—
439C2×C4×C11—21no—
440C2×C4×C11—21no—
441C2×C4×C11—21no—
442C2×C4×C11—22no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—42no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—42no—
450C2×C4×C11—48no—
451C2×C4×C11—41no—
452C2×C4×C11—42no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11—81no—
462C2×C4×C11—81no—
463C2×C4×C11—81no—
464C2×C4×C11C2×C22⋊C411yescharacteristic
465C2×C4×C11C2×C22⋊C411yescharacteristic
466C2×C4×C11C2×C22⋊C411yescharacteristic
467C2×C4×C11C2×C22⋊C411yescharacteristic
468C2×C4×C11C2×C22⋊C411yescharacteristic
469C2×C4×C11C2×C22⋊C411yescharacteristic
470C2×C4×C11C2×C22⋊C411yescharacteristic
471C2×C4×C11C2×C22⋊C411yescharacteristic
472C2×C4×C11C23×C411yescharacteristic
473C2×C4×C11C22×D411yescharacteristic
474C2×C4×C11C2×#4111yescharacteristic
475C2×C4×C11C2×#4111yescharacteristic
476C2×C4×C11H(5,𝔽2)11yescharacteristic
477C2×C4×C112−1+411yescharacteristic
478C8×C11—22no—
479C8×C11—41no—
480C8×C11—41no—
481C8×C11—41no—
482C22×M16C22×C1111yescharacteristic
483C22×M16C22×C1111yescharacteristic
484#556C4×C1111yescharacteristic, complemented
485#555C4×C1111yescharacteristic, complemented
486#554C4×C1111yescharacteristic, complemented
487#553C4×C1111yescharacteristic, complemented
488#553C4×C1111yescharacteristic, complemented
489#552—21no—
490#552C4×C1111yescharacteristic, complemented
491#552C4×C1111yescharacteristic, complemented
492#551—21no—
493#551—21no—
494#547C4×C1111yescharacteristic, complemented
495#546—21no—
496#533C22×C1111yescharacteristic
497#529—21no—
498#529—21no—
499#529—21no—
500#525C22×C1111yescharacteristic
501#525C22×C1111yescharacteristic
502C4×#41—21no—
503C4×#41C22×C1111yescharacteristic
504C2×C4×D4C22×C1111yescharacteristic
505C2×#117C22×C1111yescharacteristic
506C2×#117C22×C1111yescharacteristic
507C2×#117C22×C1111yescharacteristic
508C22×C42C22×C1111yescharacteristic
509#436—21no—
510#435—21no—
511#435—21no—
512C8×D4—21no—
513#423C22×C1111yescharacteristic
514C2×#104C22×C1111yescharacteristic
515C2×#104C22×C1111yescharacteristic
516C2×#104C22×C1111yescharacteristic
517C2×#104C22×C1111yescharacteristic
518#407C22×C1111yescharacteristic
519#407C22×C1111yescharacteristic
520C4×M16C22×C1111yescharacteristic
521#388—21no—
522#387—21no—
523#386—21no—
524#385—21no—
525C4×C4⋊C4C22×C1111yescharacteristic
526C4×C22⋊C4C22×C1111yescharacteristic
527C4×C22⋊C4C22×C1111yescharacteristic
528#376C22×C1111yescharacteristic
529#339C22×C1111yescharacteristic
530#339C22×C1111yescharacteristic
531#339C22×C1111yescharacteristic
532#339C22×C1111yescharacteristic
533#339C22×C1111yescharacteristic
534#339C22×C1111yescharacteristic
535#339C22×C1111yescharacteristic
536#339C22×C1111yescharacteristic
537#339C22×C1111yescharacteristic
538#339C22×C1111yescharacteristic
539#339C22×C1111yescharacteristic
540#339C22×C1111yescharacteristic
541C22×C11—21no—
542C22×C11—21no—
543C22×C11—21no—
544C22×C11—21no—
545C22×C11—21no—
546C22×C11—21no—
547C22×C11—21no—
548C22×C11—21no—
549C22×C11—21no—
550C22×C11—21no—
551C22×C11—21no—
552C22×C11—21no—
553C22×C11—21no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—41no—
557C22×C11—41no—
558C22×C11—41no—
559C22×C11—81no—
560C22×C11—81no—
561C22×C11#42112yes—
562C22×C11C22×C22⋊C411yescharacteristic
563C22×C11#54611yescharacteristic
564C22×C11#54711yescharacteristic
565C4×C11—21no—
566C4×C11—21no—
567C4×C11—21no—
568C4×C11—21no—
569C4×C11—21no—
570C4×C11—21no—
571C4×C11—21no—
572C4×C11—21no—
573C4×C11—42no—
574C4×C11—42no—
575C4×C11—41no—
576C4×C11—41no—
577C4×C11—41no—
578C4×C11—41no—
579C4×C11—41no—
580C4×C11—41no—
581C4×C11—41no—
582C4×C11—81no—
583C4×C11—81no—
584C4×C11C4×#4111yescharacteristic
585C4×C11#52011yescharacteristic
586C4×C11#54611yescharacteristic
587C4×C11#54711yescharacteristic
588C2×#41—21no—
589C2×#41C23×C1111yescharacteristic
590C22×D4D4×C1111yescharacteristic
591C23×C4—21no—
592C23×C4C23×C1111yescharacteristic
593C23×C4C23×C1111yescharacteristic
594C2×M16—21no—
595C2×M16—21no—
596C2×M16—22no—
597C2×M16—22no—
598C2×M16—41no—
599C2×M16—41no—
600C2×M16C23×C1111yescharacteristic
601C2×M16C23×C1111yescharacteristic
602C2×M16C23×C1111yescharacteristic
603C2×M16C23×C1111yescharacteristic
604C22×C8—21no—
605C22×C8—21no—
606C4⋊Q8C2×C4×C1111yescharacteristic, complemented
607C4⋊Q8C2×C4×C1111yescharacteristic, complemented
608#126—21no—
609#126—21no—
610#126—21no—
611#126—21no—
612#126—21no—
613#126—21no—
614#125—21no—
615#125—21no—
616#125—21no—
617#125C2×C4×C1111yescharacteristic, complemented
618#125C2×C4×C1111yescharacteristic, complemented
619#124—21no—
620#124—21no—
621#124—21no—
622#123—21no—
623#123—21no—
624#123—21no—
625#123—21no—
626#123—21no—
627#123—21no—
628#123—21no—
629#123—21no—
630C22⋊Q8—21no—
631C22⋊Q8—21no—
632C22⋊Q8—21no—
633C22⋊Q8—21no—
634C22⋊Q8—21no—
635C22⋊Q8C2×C4×C1111yescharacteristic
636C22⋊Q8C2×C4×C1111yescharacteristic
637C22⋊Q8C2×C4×C1111yescharacteristic, complemented
638C22⋊Q8C2×C4×C1111yescharacteristic, complemented
639#121—21no—
640#121—21no—
641#121—21no—
642#121C2×C4×C1111yescharacteristic
643#121C2×C4×C1111yescharacteristic
644#121C2×C4×C1111yescharacteristic, complemented
645#121C2×C4×C1111yescharacteristic, complemented
646#120—21no—
647#120—21no—
648C4×Q8—21no—
649C4×Q8—21no—
650C4×Q8—21no—
651C4×Q8C2×C4×C1111yescharacteristic, complemented
652C4×Q8C2×C4×C1111yescharacteristic, complemented
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—21no—
660C4×D4—21no—
661C4×D4—21no—
662C4×D4C2×C4×C1111yescharacteristic
663C4×D4C2×C4×C1111yescharacteristic
664C4×D4C2×C4×C1111yescharacteristic
665C4×D4C2×C4×C1111yescharacteristic
666C4×D4C2×C4×C1111yescharacteristic, complemented
667C4×D4C2×C4×C1111yescharacteristic, complemented
668C4×D4D4×C1111yescharacteristic
669C4×D4D4×C1111yescharacteristic
670C4×D4D4×C1111yescharacteristic
671C4×D4D4×C1111yescharacteristic
672#117—21no—
673#117—21no—
674#117—21no—
675#117—21no—
676#117—21no—
677#117—21no—
678#117—21no—
679#117—21no—
680#117—22no—
681#117—41no—
682#117C2×C4×C1111yescharacteristic
683#117C2×C4×C1111yescharacteristic
684#117C2×C4×C1111yescharacteristic, complemented
685#117C2×C4×C1111yescharacteristic, complemented
686#117C23×C1111yescharacteristic
687#117C23×C1111yescharacteristic
688#117C23×C1111yescharacteristic
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4C2×C4×C1111yescharacteristic
692C2×C4⋊C4C2×C4×C1111yescharacteristic
693C2×C4⋊C4C2×C4×C1111yescharacteristic, complemented
694C2×C4⋊C4C2×C4×C1111yescharacteristic, complemented
695C2×C4⋊C4D4×C1111yescharacteristic
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4D4×C1111yescharacteristic
702C2×C22⋊C4D4×C1111yescharacteristic
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—22no—
707C2×C42—21no—
708C2×C42—41no—
709C2×C42C23×C1111yescharacteristic
710C2×C42C23×C1111yescharacteristic
711C2×C42C23×C1111yescharacteristic
712C2×C42C23×C1111yescharacteristic
713C2×C42C23×C1111yescharacteristic
714C4⋊C8—21no—
715C4⋊C8—21no—
716#104—22no—
717#104—22no—
718#104—41no—
719#104—41no—
720C22⋊C8—21no—
721C22⋊C8—21no—
722C22⋊C8—21no—
723C22⋊C8—21no—
724#97—21no—
725C4×C8—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731C2×C11—21no—
732C2×C11—21no—
733C2×C11—22no—
734C2×C11—41no—
735C2×C11—41no—
736C2×C11—41no—
737C2×C11—81no—
738C2×C11#233911yescharacteristic
739C2×C11C2×#42111yescharacteristic
740C2×C11#290111yescharacteristic
741C24C2×D4×C1111yescharacteristic
742C24C2×D4×C1111yescharacteristic
743#41—21no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—44no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8C22×C4×C1111yescharacteristic
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—42no—
757C2×D4C11×C22⋊C411yescharacteristic
758C2×D4C11×C22⋊C411yescharacteristic
759C2×D4C11×C22⋊C411yescharacteristic
760C2×D4C11×C22⋊C411yescharacteristic
761C2×D4C22×C4×C1111yescharacteristic
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4C22×C4×C1111yescharacteristic
785C22×C4C22×C4×C1111yescharacteristic
786C22×C4C22×C4×C1111yescharacteristic
787C22×C4C22×C4×C1111yescharacteristic
788C22×C4C2×D4×C1111yescharacteristic
789C22×C4C2×D4×C1111yescharacteristic
790C22×C4C2×D4×C1111yescharacteristic
791C22×C4C2×D4×C1111yescharacteristic
792C22×C4C2×D4×C1111yescharacteristic
793C22×C4C2×D4×C1111yescharacteristic
794C22×C4C2×D4×C1111yescharacteristic
795C22×C4C2×D4×C1111yescharacteristic
796C22×C4C24×C1111yescharacteristic
797M16—21no—
798M16—21no—
799M16—21no—
800M16—21no—
801M16—21no—
802M16—21no—
803M16—21no—
804M16—42no—
805M16—42no—
806M16C11×#4112yescomplemented
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—21no—
811C2×C8—42no—
812C2×C8—42no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—42no—
830C4⋊C4—42no—
831C4⋊C4C11×C22⋊C411yescharacteristic
832C4⋊C4C11×C22⋊C411yescharacteristic
833C4⋊C4C11×C22⋊C411yescharacteristic
834C4⋊C4C11×C22⋊C411yescharacteristic
835C4⋊C4C22×C4×C1111yescharacteristic
836C4⋊C4C22×C4×C1111yescharacteristic
837C4⋊C4C22×C4×C1111yescharacteristic
838C4⋊C4C22×C4×C1111yescharacteristic
839C4⋊C4C22×C4×C1111yescharacteristic
840C4⋊C4C22×C4×C1111yescharacteristic
841C22⋊C4—21no—
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—21no—
846C22⋊C4—21no—
847C22⋊C4—21no—
848C22⋊C4—21no—
849C22⋊C4—21no—
850C22⋊C4—21no—
851C22⋊C4—21no—
852C22⋊C4—21no—
853C22⋊C4—21no—
854C22⋊C4—21no—
855C22⋊C4—21no—
856C22⋊C4—21no—
857C22⋊C4—21no—
858C22⋊C4—42no—
859C22⋊C4—42no—
860C22⋊C4—42no—
861C22⋊C4C11×C22⋊C411yescharacteristic
862C22⋊C4C11×C22⋊C411yescharacteristic
863C22⋊C4C11×C22⋊C411yescharacteristic
864C22⋊C4C11×C22⋊C411yescharacteristic
865C22⋊C4C11×C22⋊C411yescharacteristic
866C22⋊C4C11×C22⋊C411yescharacteristic
867C22⋊C4C11×C22⋊C411yescharacteristic
868C22⋊C4C11×C22⋊C411yescharacteristic
869C42—21no—
870C42—21no—
871C42—21no—
872C42—21no—
873C42—21no—
874C42—21no—
875C42—21no—
876C42—21no—
877C42—21no—
878C42—21no—
879C42—21no—
880C42—21no—
881C42—21no—
882C42—21no—
883C42—21no—
884C42—21no—
885C42—42no—
886C42C22×C4×C1111yescharacteristic
887C42C22×C4×C1111yescharacteristic
888C42C2×D4×C1111yescharacteristic
889C42C2×D4×C1111yescharacteristic
890C42C11×#4112yescomplemented
891C11#2250611yescharacteristic, direct product factor, Sylow
892C23—21no—
893C23—21no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23C2×C11×C22⋊C411yescharacteristic
902C23C2×C11×C22⋊C411yescharacteristic
903C23C2×C11×C22⋊C411yescharacteristic
904C23C2×C11×C22⋊C411yescharacteristic
905C23C22×D4×C1111yescharacteristic
906Q8—21no—
907Q8—21no—
908Q8—42no—
909Q8—81no—
910D4—22no—
911D4—22no—
912D4—21no—
913D4—21no—
914D4—41no—
915D4—41no—
916D4—42no—
917D4—41no—
918D4—41no—
919D4—42no—
920D4—81no—
921D4—81no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—22no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—42no—
958C2×C4—48no—
959C2×C4—41no—
960C2×C4—42no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—81no—
970C2×C4—81no—
971C2×C4—81no—
972C2×C4C2×C11×C22⋊C411yescharacteristic
973C2×C4C2×C11×C22⋊C411yescharacteristic
974C2×C4C2×C11×C22⋊C411yescharacteristic
975C2×C4C2×C11×C22⋊C411yescharacteristic
976C2×C4C2×C11×C22⋊C411yescharacteristic
977C2×C4C2×C11×C22⋊C411yescharacteristic
978C2×C4C2×C11×C22⋊C411yescharacteristic
979C2×C4C2×C11×C22⋊C411yescharacteristic
980C2×C4C23×C4×C1111yescharacteristic
981C2×C4C22×D4×C1111yescharacteristic
982C2×C4C2×C11×#4111yescharacteristic
983C2×C4C2×C11×#4111yescharacteristic
984C2×C4C11×H(5,𝔽2)11yescharacteristic
985C2×C4C11×2−1+411yescharacteristic
986C8—22no—
987C8—41no—
988C8—41no—
989C8—41no—
990C22—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—42no—
1004C22—42no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—81no—
1009C22—81no—
1010C22C11×#42112yes—
1011C22C22×C11×C22⋊C411yescharacteristic
1012C22C11×#54611yescharacteristic
1013C22C11×#54711yescharacteristic
1014C4—21no—
1015C4—21no—
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—42no—
1023C4—42no—
1024C4—41no—
1025C4—41no—
1026C4—41no—
1027C4—41no—
1028C4—41no—
1029C4—41no—
1030C4—41no—
1031C4—81no—
1032C4—81no—
1033C4C4×C11×#4111yescharacteristic
1034C4C11×#52011yescharacteristic
1035C4C11×#54611yescharacteristic
1036C4C11×#54711yescharacteristic
1037C2—21no—
1038C2—21no—
1039C2—22no—
1040C2—41no—
1041C2—41no—
1042C2—41no—
1043C2—81no—
1044C2C11×#233911yescharacteristic
1045C2C2×C11×#42111yescharacteristic
1046C2C11×#290111yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC22×C11C22×C22⋊C4
prime radicalC11×#3475C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. D4×C11×M16C2semidirect
3. C11×#2290C2semidirect
4. C11×#1995C2semidirect
5. C11×#1986C2semidirect
6. C11×#1897C2semidirect
7. C11×#1896C2semidirect
8. C11×#1871C2semidirect
9. C11×#1871C2semidirect
10. C11×#1826C2semidirect
11. C11×#1826C2semidirect
12. C11×#1806C2semidirect
13. C11×#1759C2semidirect
14. C11×#1733C2semidirect
15. C2×C11×#339C2semidirect
18. C11×#556C4semidirect
19. C11×#555C4semidirect
20. C11×#554C4semidirect
21. C11×#553C4semidirect
22. C11×#553C4semidirect
24. C11×#552C4semidirect
25. C11×#552C4semidirect
28. C11×#547C4semidirect
93. C11×C4⋊Q8C2×C4semidirect
94. C11×C4⋊Q8C2×C4semidirect
104. C11×#125C2×C4semidirect
105. C11×#125C2×C4semidirect
124. C11×C22⋊Q8C2×C4semidirect
125. C11×C22⋊Q8C2×C4semidirect
131. C11×#121C2×C4semidirect
132. C11×#121C2×C4semidirect
138. C4×Q8×C11C2×C4semidirect
139. C4×Q8×C11C2×C4semidirect
153. C4×D4×C11C2×C4semidirect
154. C4×D4×C11C2×C4semidirect
171. C11×#117C2×C4semidirect
172. C11×#117C2×C4semidirect
180. C2×C11×C4⋊C4C2×C4semidirect
181. C2×C11×C4⋊C4C2×C4semidirect
218. #22506C11direct (N × H)
284. C11×M16#41semidirect
368. C42×C11#41semidirect
370. D4×M16C2×C11semidirect
371. #2290C2×C11semidirect
372. #1995C2×C11semidirect
373. #1986C2×C11semidirect
374. #1897C2×C11semidirect
375. #1896C2×C11semidirect
376. #1871C2×C11semidirect
377. #1871C2×C11semidirect
378. #1826C2×C11semidirect
379. #1826C2×C11semidirect
380. #1806C2×C11semidirect
381. #1759C2×C11semidirect
382. #1733C2×C11semidirect
383. C2×#339C2×C11semidirect
484. #556C4×C11semidirect
485. #555C4×C11semidirect
486. #554C4×C11semidirect
487. #553C4×C11semidirect
488. #553C4×C11semidirect
490. #552C4×C11semidirect
491. #552C4×C11semidirect
494. #547C4×C11semidirect
606. C4⋊Q8C2×C4×C11semidirect
607. C4⋊Q8C2×C4×C11semidirect
617. #125C2×C4×C11semidirect
618. #125C2×C4×C11semidirect
637. C22⋊Q8C2×C4×C11semidirect
638. C22⋊Q8C2×C4×C11semidirect
644. #121C2×C4×C11semidirect
645. #121C2×C4×C11semidirect
651. C4×Q8C2×C4×C11semidirect
652. C4×Q8C2×C4×C11semidirect
666. C4×D4C2×C4×C11semidirect
667. C4×D4C2×C4×C11semidirect
684. #117C2×C4×C11semidirect
685. #117C2×C4×C11semidirect
693. C2×C4⋊C4C2×C4×C11semidirect
694. C2×C4⋊C4C2×C4×C11semidirect
806. M16C11×#41semidirect
890. C42C11×#41semidirect
891. C11#22506direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34752
D4×C11×M162
C11×#22902
C11×#19952
C11×#19862
C11×#18972
C11×#18962
C11×#18712
C11×#18262
C11×#18062
C11×#17592
C11×#17332
C2×C11×#3392
#2250611