Finite Group Databasebeta

← C11×#16296 #14593489

Subgroups — C11×#16296 #14593489

Order 2816.

1530 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#396C211yesmaximal, characteristic
2C2×C11×#396C211yesmaximal, characteristic
3C2×C11×#395C211yesmaximal, characteristic, complemented
4C2×C11×#393C211yesmaximal, characteristic
5C2×C11×#391C211yesmaximal, characteristic, complemented
6C2×C11×#387C211yesmaximal, characteristic, complemented
7C11×#1444C211yesmaximal, characteristic, complemented
8C11×#1442C211yesmaximal, characteristic, complemented
9C11×#1441C211yesmaximal, characteristic, complemented
10C11×#1441C211yesmaximal, characteristic, complemented
11C11×#1441C211yesmaximal, characteristic, complemented
12C11×#1440C211yesmaximal, characteristic
13C11×#1439C211yesmaximal, characteristic
14C11×#1439C211yesmaximal, characteristic
15C11×#1437C211yesmaximal, characteristic
16C23×Q8×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C22×C42×C11C2211yescharacteristic
33C11×#396—24no—
34C11×#396—24no—
35C11×#395—24no—
36C11×#393—24no—
37C11×#391—24no—
38C11×#387—24no—
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2211yescharacteristic
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51C2×C11×#95C2211yescharacteristic
52C2×C11×#95C2211yescharacteristic
53C2×C11×#95C2211yescharacteristic
54C2×C11×#95C2211yescharacteristic
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57C25×C11C2311yescharacteristic
58C22×Q8×C11—22no—
59C22×Q8×C11—22no—
60C22×Q8×C11—22no—
61C22×Q8×C11—22no—
62C22×Q8×C11—22no—
63C22×Q8×C11—41no—
64C22×Q8×C11—41no—
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—41no—
94C2×C11×C4⋊C4—41no—
95C2×C11×C4⋊C4—41no—
96C2×C11×C4⋊C4—41no—
97C2×C11×C4⋊C4—41no—
98C2×C11×C4⋊C4—41no—
99C2×C11×C4⋊C4—41no—
100C2×C11×C4⋊C4—41no—
101C2×C11×C4⋊C4—41no—
102C2×C11×C4⋊C4D414yes—
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4—22no—
108C2×C11×C22⋊C4—22no—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4—22no—
113C2×C11×C22⋊C4—22no—
114C2×C11×C22⋊C4—22no—
115C2×C11×C22⋊C4—41no—
116C2×C11×C22⋊C4—41no—
117C2×C11×C22⋊C4—41no—
118C2×C11×C22⋊C4—41no—
119C2×C11×C22⋊C4—41no—
120C2×C11×C22⋊C4—41no—
121C2×C11×C22⋊C4—41no—
122C2×C11×C22⋊C4—41no—
123C2×C11×C22⋊C4Q814yescomplemented
124C2×C42×C11—22no—
125C2×C42×C11—22no—
126C2×C42×C11—41no—
127C11×#95—22no—
128C11×#95—22no—
129C11×#95—22no—
130C11×#95—22no—
131C11×#95—22no—
132C11×#95—22no—
133C11×#95—22no—
134C11×#95—22no—
135C11×#95—22no—
136C11×#95—22no—
137C11×#95—22no—
138C11×#95—22no—
139C11×#95—41no—
140C11×#95—41no—
141C11×#95—41no—
142C11×#95—41no—
143C11×#95D414yes—
144C11×#95D414yes—
145#16296C1111yesmaximal, characteristic, direct product factor, Sylow
146C24×C11—21no—
147C24×C11—21no—
148C24×C11—21no—
149C24×C11—21no—
150C24×C11—21no—
151C24×C11—21no—
152C24×C11—21no—
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
159C24×C11—21no—
160C24×C11C2×Q812yes—
161C24×C11C2411yescharacteristic
162C2×Q8×C11—28no—
163C2×Q8×C11—44no—
164C2×Q8×C11—44no—
165C2×Q8×C11—44no—
166C2×Q8×C11—44no—
167C2×Q8×C11—44no—
168C2×Q8×C11—44no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
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×C11C2×D412yes—
254C22×C4×C11C2×D412yes—
255C22×C4×C11C2×D412yes—
256C22×C4×C11C2×D412yes—
257C22×C4×C11C2×D412yes—
258C22×C4×C11C2×D412yes—
259C22×C4×C11C2×D412yes—
260C22×C4×C11C2×D412yes—
261C22×C4×C11C2×D412yes—
262C22×C4×C11C2×Q812yes—
263C22×C4×C11C2×Q812yes—
264C22×C4×C11#4112yes—
265C22×C4×C11#4112yes—
266C22×C4×C11#4112yes—
267C11×C4⋊C4—28no—
268C11×C4⋊C4—44no—
269C11×C4⋊C4—44no—
270C11×C4⋊C4—44no—
271C11×C4⋊C4—44no—
272C11×C4⋊C4—44no—
273C11×C4⋊C4—44no—
274C11×C4⋊C4—44no—
275C11×C22⋊C4—44no—
276C11×C22⋊C4—44no—
277C11×C22⋊C4—44no—
278C11×C22⋊C4—44no—
279C11×C22⋊C4—44no—
280C11×C22⋊C4—44no—
281C11×C22⋊C4—44no—
282C42×C11—44no—
283C2×#396C2×C1111yescharacteristic
284C2×#396C2×C1111yescharacteristic
285C2×#395C2×C1111yescharacteristic, complemented
286C2×#393C2×C1111yescharacteristic
287C2×#391C2×C1111yescharacteristic, complemented
288C2×#387C2×C1111yescharacteristic, complemented
289#1444C2×C1111yescharacteristic, complemented
290#1442C2×C1111yescharacteristic, complemented
291#1441C2×C1111yescharacteristic, complemented
292#1441C2×C1111yescharacteristic, complemented
293#1441C2×C1111yescharacteristic, complemented
294#1440C2×C1111yescharacteristic
295#1439C2×C1111yescharacteristic
296#1439C2×C1111yescharacteristic
297#1437C2×C1111yescharacteristic
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11C22×D411yescharacteristic
334C23×C11C22×D411yescharacteristic
335C23×C11C22×D411yescharacteristic
336C23×C11C22×Q811yescharacteristic
337C23×C11C2×#4111yescharacteristic
338C23×C11C2×#4111yescharacteristic
339C23×C11C2×#4111yescharacteristic
340C23×C11H(5,𝔽2)11yescharacteristic
341C23×C11H(5,𝔽2)11yescharacteristic
342C23×C11H(5,𝔽2)11yescharacteristic
343C23×C11H(5,𝔽2)11yescharacteristic
344C23×C112−1+411yescharacteristic
345C23×C112−1+411yescharacteristic
346C23×C112−1+411yescharacteristic
347C23×C112−1+411yescharacteristic
348Q8×C11—416no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11—41no—
422C2×C4×C11—41no—
423C2×C4×C11—41no—
424C2×C4×C11—41no—
425C2×C4×C11—41no—
426C2×C4×C11—41no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11#12114yes—
447C23×Q8C22×C1111yescharacteristic
448C22×C4⋊C4C22×C1111yescharacteristic
449C22×C4⋊C4C22×C1111yescharacteristic
450C22×C4⋊C4C22×C1111yescharacteristic
451C22×C4⋊C4C22×C1111yescharacteristic
452C22×C4⋊C4C22×C1111yescharacteristic
453C22×C4⋊C4C22×C1111yescharacteristic
454C22×C4⋊C4C22×C1111yescharacteristic
455C22×C4⋊C4C22×C1111yescharacteristic
456C22×C22⋊C4C22×C1111yescharacteristic
457C22×C22⋊C4C22×C1111yescharacteristic
458C22×C22⋊C4C22×C1111yescharacteristic
459C22×C22⋊C4C22×C1111yescharacteristic
460C22×C22⋊C4C22×C1111yescharacteristic
461C22×C22⋊C4C22×C1111yescharacteristic
462C22×C22⋊C4C22×C1111yescharacteristic
463C22×C42C22×C1111yescharacteristic
464#396—24no—
465#396—24no—
466#395—24no—
467#393—24no—
468#391—24no—
469#387—24no—
470C2×#95C22×C1111yescharacteristic
471C2×#95C22×C1111yescharacteristic
472C2×#95C22×C1111yescharacteristic
473C2×#95C22×C1111yescharacteristic
474C2×#95C22×C1111yescharacteristic
475C2×#95C22×C1111yescharacteristic
476C2×#95C22×C1111yescharacteristic
477C2×#95C22×C1111yescharacteristic
478C2×#95C22×C1111yescharacteristic
479C2×#95C22×C1111yescharacteristic
480C2×#95C22×C1111yescharacteristic
481C2×#95C22×C1111yescharacteristic
482C2×#95C22×C1111yescharacteristic
483C2×#95C22×C1111yescharacteristic
484C2×#95C22×C1111yescharacteristic
485C2×#95C22×C1111yescharacteristic
486C2×#95C22×C1111yescharacteristic
487C2×#95C22×C1111yescharacteristic
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11—81no—
496C22×C11—81no—
497C22×C11—81no—
498C22×C11—81no—
499C22×C11—81no—
500C22×C11—81no—
501C22×C11—81no—
502C22×C11—81no—
503C22×C11C2×#12111yescharacteristic
504C22×C11#52511yescharacteristic
505C22×C11#53311yescharacteristic
506C22×C11#53511yescharacteristic
507C22×C11#53611yescharacteristic
508C22×C11#53611yescharacteristic
509C22×C11#53711yescharacteristic
510C22×C11#53711yescharacteristic
511C22×C11#53711yescharacteristic
512C22×C11#53811yescharacteristic
513C22×C11#53811yescharacteristic
514C22×C11#54111yescharacteristic
515C22×C11#54111yescharacteristic
516C22×C11#54211yescharacteristic
517C22×C11#54211yescharacteristic
518C22×C11#54211yescharacteristic
519C22×C11#54211yescharacteristic
520C22×C11#54311yescharacteristic
521C22×C11#54411yescharacteristic
522C22×C11D4211yescharacteristic
523C22×C11D4211yescharacteristic
524C22×C11#54611yescharacteristic
525C22×C11#54611yescharacteristic
526C22×C11#54611yescharacteristic
527C22×C11#54711yescharacteristic
528C22×C11#54811yescharacteristic
529C22×C11D4×Q811yescharacteristic
530C22×C11D4×Q811yescharacteristic
531C22×C11D4×Q811yescharacteristic
532C22×C11#55411yescharacteristic
533C22×C11#55611yescharacteristic
534C22×C11#56211yescharacteristic
535C22×C11#56211yescharacteristic
536C22×C11#56311yescharacteristic
537C22×C11#56311yescharacteristic
538C4×C11—24no—
539C4×C11—42no—
540C4×C11—42no—
541C4×C11—42no—
542C4×C11—42no—
543C4×C11—42no—
544C4×C11—42no—
545C4×C11—42no—
546C4×C11—42no—
547C4×C11—42no—
548C4×C11—42no—
549C4×C11—42no—
550C4×C11—81no—
551C4×C11—81no—
552C25C23×C1111yescharacteristic
553C22×Q8—22no—
554C22×Q8—22no—
555C22×Q8—22no—
556C22×Q8—22no—
557C22×Q8—22no—
558C22×Q8—41no—
559C22×Q8—41no—
560C23×C4C23×C1111yescharacteristic
561C23×C4C23×C1111yescharacteristic
562C23×C4C23×C1111yescharacteristic
563C23×C4C23×C1111yescharacteristic
564C23×C4C23×C1111yescharacteristic
565C23×C4C23×C1111yescharacteristic
566C23×C4C23×C1111yescharacteristic
567C23×C4C23×C1111yescharacteristic
568C23×C4C23×C1111yescharacteristic
569C23×C4C23×C1111yescharacteristic
570C23×C4C23×C1111yescharacteristic
571C23×C4C23×C1111yescharacteristic
572C23×C4C23×C1111yescharacteristic
573C23×C4C23×C1111yescharacteristic
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4D4×C1114yes—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—41no—
611C2×C22⋊C4—41no—
612C2×C22⋊C4—41no—
613C2×C22⋊C4—41no—
614C2×C22⋊C4—41no—
615C2×C22⋊C4—41no—
616C2×C22⋊C4—41no—
617C2×C22⋊C4—41no—
618C2×C22⋊C4Q8×C1114yescomplemented
619C2×C42—22no—
620C2×C42—22no—
621C2×C42—41no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—22no—
631#95—22no—
632#95—22no—
633#95—22no—
634#95—41no—
635#95—41no—
636#95—41no—
637#95—41no—
638#95D4×C1114yes—
639#95D4×C1114yes—
640C2×C11—82no—
641C2×C11#242411yescharacteristic
642C2×C11#242911yescharacteristic
643C2×C11#246511yescharacteristic
644C2×C11#262011yescharacteristic
645C2×C11#263711yescharacteristic
646C2×C11#266511yescharacteristic
647C2×C11#267211yescharacteristic
648C2×C11#267611yescharacteristic
649C2×C11#267711yescharacteristic
650C2×C11#268311yescharacteristic
651C2×C11#269211yescharacteristic
652C2×C11#270411yescharacteristic
653C2×C11#271511yescharacteristic
654C2×C11#271611yescharacteristic
655C2×C11#283111yescharacteristic
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24C2×Q8×C1112yes—
671C24C24×C1111yescharacteristic
672C2×Q8—28no—
673C2×Q8—44no—
674C2×Q8—44no—
675C2×Q8—44no—
676C2×Q8—44no—
677C2×Q8—44no—
678C2×Q8—44no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4C2×D4×C1112yes—
764C22×C4C2×D4×C1112yes—
765C22×C4C2×D4×C1112yes—
766C22×C4C2×D4×C1112yes—
767C22×C4C2×D4×C1112yes—
768C22×C4C2×D4×C1112yes—
769C22×C4C2×D4×C1112yes—
770C22×C4C2×D4×C1112yes—
771C22×C4C2×D4×C1112yes—
772C22×C4C2×Q8×C1112yes—
773C22×C4C2×Q8×C1112yes—
774C22×C4C11×#4112yes—
775C22×C4C11×#4112yes—
776C22×C4C11×#4112yes—
777C4⋊C4—28no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—44no—
783C4⋊C4—44no—
784C4⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4—44no—
790C22⋊C4—44no—
791C22⋊C4—44no—
792C42—44no—
793C11#1629611yescharacteristic, direct product factor, Sylow
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23C22×D4×C1111yescharacteristic
830C23C22×D4×C1111yescharacteristic
831C23C22×D4×C1111yescharacteristic
832C23C22×Q8×C1111yescharacteristic
833C23C2×C11×#4111yescharacteristic
834C23C2×C11×#4111yescharacteristic
835C23C2×C11×#4111yescharacteristic
836C23C11×H(5,𝔽2)11yescharacteristic
837C23C11×H(5,𝔽2)11yescharacteristic
838C23C11×H(5,𝔽2)11yescharacteristic
839C23C11×H(5,𝔽2)11yescharacteristic
840C23C11×2−1+411yescharacteristic
841C23C11×2−1+411yescharacteristic
842C23C11×2−1+411yescharacteristic
843C23C11×2−1+411yescharacteristic
844Q8—416no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4C11×#12114yes—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—81no—
951C22—81no—
952C22—81no—
953C22—81no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22—81no—
958C22C2×C11×#12111yescharacteristic
959C22C11×#52511yescharacteristic
960C22C11×#53311yescharacteristic
961C22C11×#53511yescharacteristic
962C22C11×#53611yescharacteristic
963C22C11×#53611yescharacteristic
964C22C11×#53711yescharacteristic
965C22C11×#53711yescharacteristic
966C22C11×#53711yescharacteristic
967C22C11×#53811yescharacteristic
968C22C11×#53811yescharacteristic
969C22C11×#54111yescharacteristic
970C22C11×#54111yescharacteristic
971C22C11×#54211yescharacteristic
972C22C11×#54211yescharacteristic
973C22C11×#54211yescharacteristic
974C22C11×#54211yescharacteristic
975C22C11×#54311yescharacteristic
976C22C11×#54411yescharacteristic
977C22D42×C1111yescharacteristic
978C22D42×C1111yescharacteristic
979C22C11×#54611yescharacteristic
980C22C11×#54611yescharacteristic
981C22C11×#54611yescharacteristic
982C22C11×#54711yescharacteristic
983C22C11×#54811yescharacteristic
984C22D4×Q8×C1111yescharacteristic
985C22D4×Q8×C1111yescharacteristic
986C22D4×Q8×C1111yescharacteristic
987C22C11×#55411yescharacteristic
988C22C11×#55611yescharacteristic
989C22C11×#56211yescharacteristic
990C22C11×#56211yescharacteristic
991C22C11×#56311yescharacteristic
992C22C11×#56311yescharacteristic
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—81no—
1006C4—81no—
1007C2—82no—
1008C2C11×#242411yescharacteristic
1009C2C11×#242911yescharacteristic
1010C2C11×#246511yescharacteristic
1011C2C11×#262011yescharacteristic
1012C2C11×#263711yescharacteristic
1013C2C11×#266511yescharacteristic
1014C2C11×#267211yescharacteristic
1015C2C11×#267611yescharacteristic
1016C2C11×#267711yescharacteristic
1017C2C11×#268311yescharacteristic
1018C2C11×#269211yescharacteristic
1019C2C11×#270411yescharacteristic
1020C2C11×#271511yescharacteristic
1021C2C11×#271611yescharacteristic
1022C2C11×#283111yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC24C24×C11
prime radicalC25×C11C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C11×#395C2semidirect
5. C2×C11×#391C2semidirect
6. C2×C11×#387C2semidirect
7. C11×#1444C2semidirect
8. C11×#1442C2semidirect
9. C11×#1441C2semidirect
10. C11×#1441C2semidirect
11. C11×#1441C2semidirect
123. C2×C11×C22⋊C4Q8semidirect
145. #16296C11direct (N × H)
285. C2×#395C2×C11semidirect
287. C2×#391C2×C11semidirect
288. C2×#387C2×C11semidirect
289. #1444C2×C11semidirect
290. #1442C2×C11semidirect
291. #1441C2×C11semidirect
292. #1441C2×C11semidirect
293. #1441C2×C11semidirect
618. C2×C22⋊C4Q8×C11semidirect
793. C11#16296direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3962
C2×C11×#3952
C2×C11×#3932
C2×C11×#3912
C2×C11×#3872
C11×#14442
C11×#14422
C11×#14412
C11×#14402
C11×#14392
C11×#14372
#1629611