Finite Group Databasebeta

← C11×#14524 #14591717

Subgroups — C11×#14524 #14591717

Order 2816.

1402 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#395C211yesmaximal, characteristic
2C2×C11×#391C211yesmaximal, characteristic
3C2×C11×#391C211yesmaximal, characteristic
4C2×C11×#389C211yesmaximal, characteristic
5C2×C11×#387C211yesmaximal, characteristic
6C11×#1445C211yesmaximal, characteristic
7C11×#1442C211yesmaximal, characteristic
8C11×#1442C211yesmaximal, characteristic
9C11×#1441C211yesmaximal, characteristic
10C11×#1441C211yesmaximal, characteristic
11C11×#1436C211yesmaximal, characteristic
12C11×#1436C211yesmaximal, characteristic
13C11×#1436C211yesmaximal, characteristic
14C11×#1434C211yesmaximal, characteristic
15C11×#1434C211yesmaximal, 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×C42×C11C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C22×C42×C11C2211yescharacteristic
27C11×#395C418yescomplemented
28C11×#391—24no—
29C11×#391—24no—
30C11×#389—24no—
31C11×#387—24no—
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
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
56C22×Q8×C11—22no—
57C22×Q8×C11—22no—
58C22×Q8×C11—22no—
59C22×Q8×C11—22no—
60C22×Q8×C11—41no—
61C22×Q8×C11—41no—
62C22×Q8×C11C2×C414yes—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
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
78C2×C11×C4⋊C4—22no—
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—41no—
91C2×C11×C4⋊C4—41no—
92C2×C11×C4⋊C4—41no—
93C2×C11×C4⋊C4—41no—
94C2×C11×C4⋊C4—41no—
95C2×C11×C4⋊C4—41no—
96C2×C11×C4⋊C4C2×C414yes—
97C2×C11×C4⋊C4C2×C414yes—
98C2×C11×C4⋊C4C2×C414yes—
99C2×C42×C11—22no—
100C2×C42×C11—22no—
101C2×C42×C11—22no—
102C2×C42×C11—22no—
103C2×C42×C11—22no—
104C2×C42×C11—22no—
105C2×C42×C11—41no—
106C2×C42×C11—41no—
107C2×C42×C11—41no—
108C11×#95—22no—
109C11×#95—22no—
110C11×#95—22no—
111C11×#95—22no—
112C11×#95—22no—
113C11×#95—22no—
114C11×#95—22no—
115C11×#95—22no—
116C11×#95—22no—
117C11×#95—22no—
118C11×#95—22no—
119C11×#95—41no—
120C11×#95—41no—
121C11×#95—41no—
122C11×#95—41no—
123C11×#95—41no—
124C11×#95—41no—
125C11×#95—41no—
126C11×#95C2×C414yes—
127C11×#95C2×C414yes—
128C11×#95C2×C414yes—
129C11×#95D414yes—
130C11×#95D414yes—
131C11×#95Q814yescomplemented
132#14524C1111yesmaximal, characteristic, direct product factor, Sylow
133C24×C11C2411yescharacteristic
134C2×Q8×C11—28no—
135C2×Q8×C11—28no—
136C2×Q8×C11—44no—
137C2×Q8×C11—44no—
138C2×Q8×C11—44no—
139C2×Q8×C11—44no—
140C2×Q8×C11—44no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
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×C11C22×C412yes—
228C22×C4×C11C22×C412yes—
229C22×C4×C11C22×C412yes—
230C22×C4×C11C22×C412yes—
231C22×C4×C11C22×C412yes—
232C22×C4×C11C22×C412yes—
233C22×C4×C11C22×C412yes—
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2×D412yes—
236C22×C4×C11C2×D412yes—
237C22×C4×C11C2×D412yes—
238C22×C4×C11C2×D412yes—
239C22×C4×C11C2×D412yes—
240C22×C4×C11C2×Q812yes—
241C22×C4×C11C2×Q812yes—
242C22×C4×C11C2×Q812yes—
243C22×C4×C11#4112yes—
244C22×C4×C11#4112yes—
245C22×C4×C11#4112yes—
246C11×C4⋊C4—28no—
247C11×C4⋊C4—28no—
248C11×C4⋊C4—44no—
249C11×C4⋊C4—44no—
250C11×C4⋊C4—44no—
251C11×C4⋊C4—44no—
252C11×C4⋊C4—44no—
253C42×C11—44no—
254C42×C11—44no—
255C42×C11—44no—
256C2×#395C2×C1111yescharacteristic
257C2×#391C2×C1111yescharacteristic
258C2×#391C2×C1111yescharacteristic
259C2×#389C2×C1111yescharacteristic
260C2×#387C2×C1111yescharacteristic
261#1445C2×C1111yescharacteristic
262#1442C2×C1111yescharacteristic
263#1442C2×C1111yescharacteristic
264#1441C2×C1111yescharacteristic
265#1441C2×C1111yescharacteristic
266#1436C2×C1111yescharacteristic
267#1436C2×C1111yescharacteristic
268#1436C2×C1111yescharacteristic
269#1434C2×C1111yescharacteristic
270#1434C2×C1111yescharacteristic
271C23×C11C23×C411yescharacteristic
272C23×C11C22×D411yescharacteristic
273C23×C11C22×D411yescharacteristic
274C23×C11C22×Q811yescharacteristic
275C23×C11C2×#4111yescharacteristic
276C23×C11C2×#4111yescharacteristic
277C23×C11C2×#4111yescharacteristic
278C23×C11H(5,𝔽2)11yescharacteristic
279C23×C11H(5,𝔽2)11yescharacteristic
280C23×C11H(5,𝔽2)11yescharacteristic
281C23×C112−1+411yescharacteristic
282C23×C112−1+411yescharacteristic
283C23×C112−1+411yescharacteristic
284C23×C112−1+411yescharacteristic
285C23×C112−1+411yescharacteristic
286Q8×C11—416no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11C4×D414yes—
390C2×C4×C11C4×D414yes—
391C2×C4×C11C4×Q814yes—
392C23×Q8C22×C1111yescharacteristic
393C22×C4⋊C4C22×C1111yescharacteristic
394C22×C4⋊C4C22×C1111yescharacteristic
395C22×C4⋊C4C22×C1111yescharacteristic
396C22×C4⋊C4C22×C1111yescharacteristic
397C22×C4⋊C4C22×C1111yescharacteristic
398C22×C4⋊C4C22×C1111yescharacteristic
399C22×C4⋊C4C22×C1111yescharacteristic
400C22×C42C22×C1111yescharacteristic
401C22×C42C22×C1111yescharacteristic
402C22×C42C22×C1111yescharacteristic
403#395C4×C1118yescomplemented
404#391—24no—
405#391—24no—
406#389—24no—
407#387—24no—
408C2×#95C22×C1111yescharacteristic
409C2×#95C22×C1111yescharacteristic
410C2×#95C22×C1111yescharacteristic
411C2×#95C22×C1111yescharacteristic
412C2×#95C22×C1111yescharacteristic
413C2×#95C22×C1111yescharacteristic
414C2×#95C22×C1111yescharacteristic
415C2×#95C22×C1111yescharacteristic
416C2×#95C22×C1111yescharacteristic
417C2×#95C22×C1111yescharacteristic
418C2×#95C22×C1111yescharacteristic
419C2×#95C22×C1111yescharacteristic
420C2×#95C22×C1111yescharacteristic
421C2×#95C22×C1111yescharacteristic
422C2×#95C22×C1111yescharacteristic
423C2×#95C22×C1111yescharacteristic
424C2×#95C22×C1111yescharacteristic
425C2×#95C22×C1111yescharacteristic
426C2×#95C22×C1111yescharacteristic
427C2×#95C22×C1111yescharacteristic
428C2×#95C22×C1111yescharacteristic
429C2×#95C22×C1111yescharacteristic
430C2×#95C22×C1111yescharacteristic
431C2×#95C22×C1111yescharacteristic
432C22×C11C2×C4×D411yescharacteristic
433C22×C11C2×C4×D411yescharacteristic
434C22×C11C2×C4×Q811yescharacteristic
435C22×C11#51811yescharacteristic
436C22×C11#51911yescharacteristic
437C22×C11#51911yescharacteristic
438C22×C11#52011yescharacteristic
439C22×C11#53611yescharacteristic
440C22×C11#53611yescharacteristic
441C22×C11#53611yescharacteristic
442C22×C11#53711yescharacteristic
443C22×C11#54111yescharacteristic
444C22×C11#54111yescharacteristic
445C22×C11#54111yescharacteristic
446C22×C11#54211yescharacteristic
447C22×C11#54211yescharacteristic
448C22×C11#54211yescharacteristic
449C22×C11#54411yescharacteristic
450C22×C11#54411yescharacteristic
451C22×C11D4211yescharacteristic
452C22×C11#54611yescharacteristic
453C22×C11#54611yescharacteristic
454C22×C11#54611yescharacteristic
455C22×C11#54711yescharacteristic
456C22×C11D4×Q811yescharacteristic
457C22×C11D4×Q811yescharacteristic
458C22×C11#55111yescharacteristic
459C22×C11#55211yescharacteristic
460C22×C11#55411yescharacteristic
461C22×C11#55611yescharacteristic
462C22×C11#55711yescharacteristic
463C22×C11#56211yescharacteristic
464C22×C11#56211yescharacteristic
465C22×C11#56311yescharacteristic
466C22×C11#56311yescharacteristic
467C4×C11—24no—
468C4×C11—24no—
469C4×C11—24no—
470C4×C11—42no—
471C4×C11—42no—
472C4×C11—42no—
473C4×C11—42no—
474C4×C11—42no—
475C4×C11—42no—
476C4×C11—42no—
477C4×C11—42no—
478C4×C11—42no—
479C4×C11—42no—
480C4×C11—81no—
481C4×C11—81no—
482C22×Q8—22no—
483C22×Q8—22no—
484C22×Q8—22no—
485C22×Q8—22no—
486C22×Q8—41no—
487C22×Q8—41no—
488C22×Q8C2×C4×C1114yes—
489C23×C4C23×C1111yescharacteristic
490C23×C4C23×C1111yescharacteristic
491C23×C4C23×C1111yescharacteristic
492C23×C4C23×C1111yescharacteristic
493C23×C4C23×C1111yescharacteristic
494C23×C4C23×C1111yescharacteristic
495C23×C4C23×C1111yescharacteristic
496C23×C4C23×C1111yescharacteristic
497C23×C4C23×C1111yescharacteristic
498C23×C4C23×C1111yescharacteristic
499C23×C4C23×C1111yescharacteristic
500C23×C4C23×C1111yescharacteristic
501C23×C4C23×C1111yescharacteristic
502C23×C4C23×C1111yescharacteristic
503C23×C4C23×C1111yescharacteristic
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—41no—
517C2×C4⋊C4—41no—
518C2×C4⋊C4—41no—
519C2×C4⋊C4—41no—
520C2×C4⋊C4—41no—
521C2×C4⋊C4—41no—
522C2×C4⋊C4C2×C4×C1114yes—
523C2×C4⋊C4C2×C4×C1114yes—
524C2×C4⋊C4C2×C4×C1114yes—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—22no—
529C2×C42—22no—
530C2×C42—22no—
531C2×C42—41no—
532C2×C42—41no—
533C2×C42—41no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—41no—
546#95—41no—
547#95—41no—
548#95—41no—
549#95—41no—
550#95—41no—
551#95—41no—
552#95C2×C4×C1114yes—
553#95C2×C4×C1114yes—
554#95C2×C4×C1114yes—
555#95D4×C1114yes—
556#95D4×C1114yes—
557#95Q8×C1114yescomplemented
558C2×C11#232311yescharacteristic
559C2×C11#232711yescharacteristic
560C2×C11#233111yescharacteristic
561C2×C11#235811yescharacteristic
562C2×C11#236011yescharacteristic
563C2×C11#236511yescharacteristic
564C2×C11#237811yescharacteristic
565C2×C11#267211yescharacteristic
566C2×C11#267711yescharacteristic
567C2×C11#269811yescharacteristic
568C2×C11#270011yescharacteristic
569C2×C11#270411yescharacteristic
570C2×C11#271311yescharacteristic
571C2×C11#275511yescharacteristic
572C2×C11#275811yescharacteristic
573C24C24×C1111yescharacteristic
574C2×Q8—28no—
575C2×Q8—28no—
576C2×Q8—44no—
577C2×Q8—44no—
578C2×Q8—44no—
579C2×Q8—44no—
580C2×Q8—44no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4C22×C4×C1112yes—
668C22×C4C22×C4×C1112yes—
669C22×C4C22×C4×C1112yes—
670C22×C4C22×C4×C1112yes—
671C22×C4C22×C4×C1112yes—
672C22×C4C22×C4×C1112yes—
673C22×C4C22×C4×C1112yes—
674C22×C4C2×D4×C1112yes—
675C22×C4C2×D4×C1112yes—
676C22×C4C2×D4×C1112yes—
677C22×C4C2×D4×C1112yes—
678C22×C4C2×D4×C1112yes—
679C22×C4C2×D4×C1112yes—
680C22×C4C2×Q8×C1112yes—
681C22×C4C2×Q8×C1112yes—
682C22×C4C2×Q8×C1112yes—
683C22×C4C11×#4112yes—
684C22×C4C11×#4112yes—
685C22×C4C11×#4112yes—
686C4⋊C4—28no—
687C4⋊C4—28no—
688C4⋊C4—44no—
689C4⋊C4—44no—
690C4⋊C4—44no—
691C4⋊C4—44no—
692C4⋊C4—44no—
693C42—44no—
694C42—44no—
695C42—44no—
696C11#1452411yescharacteristic, direct product factor, Sylow
697C23C23×C4×C1111yescharacteristic
698C23C22×D4×C1111yescharacteristic
699C23C22×D4×C1111yescharacteristic
700C23C22×Q8×C1111yescharacteristic
701C23C2×C11×#4111yescharacteristic
702C23C2×C11×#4111yescharacteristic
703C23C2×C11×#4111yescharacteristic
704C23C11×H(5,𝔽2)11yescharacteristic
705C23C11×H(5,𝔽2)11yescharacteristic
706C23C11×H(5,𝔽2)11yescharacteristic
707C23C11×2−1+411yescharacteristic
708C23C11×2−1+411yescharacteristic
709C23C11×2−1+411yescharacteristic
710C23C11×2−1+411yescharacteristic
711C23C11×2−1+411yescharacteristic
712Q8—416no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4C4×D4×C1114yes—
816C2×C4C4×D4×C1114yes—
817C2×C4C4×Q8×C1114yes—
818C22C2×C4×D4×C1111yescharacteristic
819C22C2×C4×D4×C1111yescharacteristic
820C22C2×C4×Q8×C1111yescharacteristic
821C22C11×#51811yescharacteristic
822C22C11×#51911yescharacteristic
823C22C11×#51911yescharacteristic
824C22C11×#52011yescharacteristic
825C22C11×#53611yescharacteristic
826C22C11×#53611yescharacteristic
827C22C11×#53611yescharacteristic
828C22C11×#53711yescharacteristic
829C22C11×#54111yescharacteristic
830C22C11×#54111yescharacteristic
831C22C11×#54111yescharacteristic
832C22C11×#54211yescharacteristic
833C22C11×#54211yescharacteristic
834C22C11×#54211yescharacteristic
835C22C11×#54411yescharacteristic
836C22C11×#54411yescharacteristic
837C22D42×C1111yescharacteristic
838C22C11×#54611yescharacteristic
839C22C11×#54611yescharacteristic
840C22C11×#54611yescharacteristic
841C22C11×#54711yescharacteristic
842C22D4×Q8×C1111yescharacteristic
843C22D4×Q8×C1111yescharacteristic
844C22C11×#55111yescharacteristic
845C22C11×#55211yescharacteristic
846C22C11×#55411yescharacteristic
847C22C11×#55611yescharacteristic
848C22C11×#55711yescharacteristic
849C22C11×#56211yescharacteristic
850C22C11×#56211yescharacteristic
851C22C11×#56311yescharacteristic
852C22C11×#56311yescharacteristic
853C4—24no—
854C4—24no—
855C4—24no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—81no—
867C4—81no—
868C2C11×#232311yescharacteristic
869C2C11×#232711yescharacteristic
870C2C11×#233111yescharacteristic
871C2C11×#235811yescharacteristic
872C2C11×#236011yescharacteristic
873C2C11×#236511yescharacteristic
874C2C11×#237811yescharacteristic
875C2C11×#267211yescharacteristic
876C2C11×#267711yescharacteristic
877C2C11×#269811yescharacteristic
878C2C11×#270011yescharacteristic
879C2C11×#270411yescharacteristic
880C2C11×#271311yescharacteristic
881C2C11×#275511yescharacteristic
882C2C11×#275811yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
27. C11×#395C4semidirect
131. C11×#95Q8semidirect
132. #14524C11direct (N × H)
403. #395C4×C11semidirect
557. #95Q8×C11semidirect
696. C11#14524direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3952
C2×C11×#3912
C2×C11×#3892
C2×C11×#3872
C11×#14452
C11×#14422
C11×#14412
C11×#14362
C11×#14342
#1452411