Finite Group Databasebeta

← C11×#15507 #14592700

Subgroups — C11×#15507 #14592700

Order 2816.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#398C211yesmaximal, characteristic, complemented
2C2×C11×#396C211yesmaximal, characteristic, complemented
3C2×C11×#396C211yesmaximal, characteristic, complemented
4C2×C11×#390C211yesmaximal, characteristic
5C2×C11×#386C211yesmaximal, characteristic
6C2×C11×#385C211yesmaximal, characteristic, complemented
7C11×#1442C211yesmaximal, characteristic, complemented
8C11×#1439C211yesmaximal, characteristic, complemented
9C11×#1439C211yesmaximal, characteristic, complemented
10C11×#1439C211yesmaximal, characteristic, complemented
11C11×#1439C211yesmaximal, characteristic, complemented
12C11×#1438C211yesmaximal, characteristic
13C11×#1436C211yesmaximal, characteristic, complemented
14C11×C4⋊#95C211yesmaximal, characteristic, complemented
15C11×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
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×C11×C22⋊C4C2211yescharacteristic
33C22×C11×C22⋊C4C2211yescharacteristic
34C22×C11×C22⋊C4C2211yescharacteristic
35C22×C11×C22⋊C4C2211yescharacteristic
36C22×C42×C11C2211yescharacteristic
37C11×#398—24no—
38C11×#396—24no—
39C11×#396—24no—
40C11×#390—24no—
41C11×#386—24no—
42C11×#385—24no—
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
58C25×C11C2311yescharacteristic
59C22×D4×C11—22no—
60C22×D4×C11—22no—
61C22×D4×C11—22no—
62C22×D4×C11—22no—
63C22×D4×C11—41no—
64C22×D4×C11—41no—
65C22×D4×C11Q814yes—
66C23×C4×C11—22no—
67C23×C4×C11—22no—
68C23×C4×C11—22no—
69C23×C4×C11—41no—
70C23×C4×C11—41no—
71C23×C4×C11—41no—
72C23×C4×C11—41no—
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
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—22no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4—22no—
99C2×C11×C4⋊C4—41no—
100C2×C11×C4⋊C4—41no—
101C2×C11×C4⋊C4—41no—
102C2×C11×C4⋊C4—41no—
103C2×C11×C4⋊C4—41no—
104C2×C11×C4⋊C4—41no—
105C2×C11×C4⋊C4—41no—
106C2×C11×C4⋊C4D414yescomplemented
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—22no—
116C2×C11×C22⋊C4—22no—
117C2×C11×C22⋊C4—22no—
118C2×C11×C22⋊C4—22no—
119C2×C11×C22⋊C4—22no—
120C2×C11×C22⋊C4—22no—
121C2×C11×C22⋊C4—22no—
122C2×C11×C22⋊C4—22no—
123C2×C11×C22⋊C4—22no—
124C2×C11×C22⋊C4—22no—
125C2×C11×C22⋊C4—22no—
126C2×C11×C22⋊C4—22no—
127C2×C11×C22⋊C4—41no—
128C2×C11×C22⋊C4—41no—
129C2×C11×C22⋊C4—41no—
130C2×C11×C22⋊C4—41no—
131C2×C11×C22⋊C4—41no—
132C2×C11×C22⋊C4—41no—
133C2×C11×C22⋊C4—41no—
134C2×C11×C22⋊C4—41no—
135C2×C11×C22⋊C4—41no—
136C2×C11×C22⋊C4—41no—
137C2×C11×C22⋊C4—41no—
138C2×C11×C22⋊C4—41no—
139C2×C11×C22⋊C4D414yes—
140C2×C42×C11—22no—
141C2×C42×C11—22no—
142C2×C42×C11—41no—
143C11×#95—22no—
144C11×#95—22no—
145C11×#95—22no—
146C11×#95—22no—
147C11×#95—22no—
148C11×#95—22no—
149C11×#95—22no—
150C11×#95—22no—
151C11×#95—22no—
152C11×#95—41no—
153C11×#95—41no—
154C11×#95—41no—
155C11×#95—41no—
156C11×#95D414yes—
157#15507C1111yesmaximal, characteristic, direct product factor, Sylow
158C24×C11—21no—
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11—21no—
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11—21no—
182C24×C11—21no—
183C24×C11—21no—
184C24×C11C2×D412yes—
185C24×C11C2×Q812yes—
186C24×C11C2×Q812yes—
187C24×C11#4112yes—
188C24×C11C2411yescharacteristic
189C2×D4×C11—28no—
190C2×D4×C11—28no—
191C2×D4×C11—44no—
192C2×D4×C11—44no—
193C2×D4×C11—44no—
194C2×D4×C11—44no—
195C2×D4×C11—44no—
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×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—21no—
260C22×C4×C11—21no—
261C22×C4×C11—21no—
262C22×C4×C11—21no—
263C22×C4×C11—21no—
264C22×C4×C11—21no—
265C22×C4×C11—21no—
266C22×C4×C11—21no—
267C22×C4×C11—21no—
268C22×C4×C11—21no—
269C22×C4×C11—21no—
270C22×C4×C11—21no—
271C22×C4×C11—21no—
272C22×C4×C11—21no—
273C22×C4×C11—21no—
274C22×C4×C11—44no—
275C22×C4×C11—44no—
276C22×C4×C11—44no—
277C22×C4×C11—44no—
278C22×C4×C11—44no—
279C22×C4×C11—44no—
280C22×C4×C11—44no—
281C22×C4×C11C2×D412yes—
282C22×C4×C11C2×D412yes—
283C22×C4×C11C2×D412yes—
284C22×C4×C11C2×D412yes—
285C22×C4×C11C2×D412yes—
286C22×C4×C11C2×D412yes—
287C22×C4×C11C2×D412yes—
288C22×C4×C11C2×D412yes—
289C22×C4×C11C2×Q812yes—
290C22×C4×C11#4112yes—
291C22×C4×C11#4112yes—
292C22×C4×C11#4112yes—
293C22×C4×C11#4112yes—
294C11×C4⋊C4—44no—
295C11×C4⋊C4—44no—
296C11×C4⋊C4—44no—
297C11×C4⋊C4—44no—
298C11×C4⋊C4—44no—
299C11×C4⋊C4—44no—
300C11×C4⋊C4—44no—
301C11×C22⋊C4—28no—
302C11×C22⋊C4—44no—
303C11×C22⋊C4—44no—
304C11×C22⋊C4—44no—
305C11×C22⋊C4—44no—
306C11×C22⋊C4—44no—
307C11×C22⋊C4—44no—
308C11×C22⋊C4—44no—
309C11×C22⋊C4—44no—
310C11×C22⋊C4—44no—
311C11×C22⋊C4—44no—
312C42×C11—44no—
313C2×#398C2×C1111yescharacteristic, complemented
314C2×#396C2×C1111yescharacteristic, complemented
315C2×#396C2×C1111yescharacteristic, complemented
316C2×#390C2×C1111yescharacteristic
317C2×#386C2×C1111yescharacteristic
318C2×#385C2×C1111yescharacteristic, complemented
319#1442C2×C1111yescharacteristic, complemented
320#1439C2×C1111yescharacteristic, complemented
321#1439C2×C1111yescharacteristic, complemented
322#1439C2×C1111yescharacteristic, complemented
323#1439C2×C1111yescharacteristic, complemented
324#1438C2×C1111yescharacteristic
325#1436C2×C1111yescharacteristic, complemented
326C4⋊#95C2×C1111yescharacteristic, complemented
327C22⋊#95C2×C1111yescharacteristic, complemented
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—41no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11—41no—
381C23×C11—41no—
382C23×C11—41no—
383C23×C11—41no—
384C23×C11—41no—
385C23×C11—41no—
386C23×C11—41no—
387C23×C11—41no—
388C23×C11—41no—
389C23×C11—41no—
390C23×C11—41no—
391C23×C11—41no—
392C23×C11—41no—
393C23×C11—41no—
394C23×C11—41no—
395C23×C11—41no—
396C23×C11—41no—
397C23×C11C22⋊Q814yes—
398C23×C11C22×D411yescharacteristic
399C23×C11C22×D411yescharacteristic
400C23×C11C22×D411yescharacteristic
401C23×C11C22×Q811yescharacteristic
402C23×C11C2×#4111yescharacteristic
403C23×C11C2×#4111yescharacteristic
404C23×C11C2×#4111yescharacteristic
405C23×C11C2×#4111yescharacteristic
406C23×C11C2×#4111yescharacteristic
407C23×C11H(5,𝔽2)11yescharacteristic
408C23×C11H(5,𝔽2)11yescharacteristic
409C23×C11H(5,𝔽2)11yescharacteristic
410C23×C11H(5,𝔽2)11yescharacteristic
411C23×C11H(5,𝔽2)11yescharacteristic
412C23×C112−1+411yescharacteristic
413D4×C11—416no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—416no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
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—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—41no—
466C2×C4×C11—41no—
467C2×C4×C11—41no—
468C2×C4×C11—41no—
469C2×C4×C11—41no—
470C2×C4×C11—41no—
471C2×C4×C11—41no—
472C2×C4×C11—41no—
473C2×C4×C11—41no—
474C2×C4×C11—41no—
475C2×C4×C11—41no—
476C2×C4×C11—41no—
477C2×C4×C11—41no—
478C2×C4×C11—41no—
479C2×C4×C11—41no—
480C2×C4×C11—41no—
481C2×C4×C11—41no—
482C2×C4×C11—41no—
483C2×C4×C11—41no—
484C2×C4×C11—41no—
485C2×C4×C11—41no—
486C2×C4×C11—41no—
487C2×C4×C11—41no—
488C2×C4×C11—41no—
489C2×C4×C11—41no—
490C2×C4×C11—41no—
491C2×C4×C11—41no—
492C2×C4×C11—41no—
493C2×C4×C11—41no—
494C2×C4×C11—41no—
495C2×C4×C11—41no—
496C2×C4×C11—41no—
497C2×C4×C11—41no—
498C2×C4×C11—41no—
499C2×C4×C11—41no—
500C2×C4×C11—41no—
501C2×C4×C11—41no—
502C2×C4×C11—41no—
503C2×C4×C11—41no—
504C2×C4×C11#12114yes—
505C2×C4×C11C22⋊Q814yes—
506C23×D4C22×C1111yescharacteristic
507C24×C4C22×C1111yescharacteristic
508C22×C4⋊C4C22×C1111yescharacteristic
509C22×C4⋊C4C22×C1111yescharacteristic
510C22×C4⋊C4C22×C1111yescharacteristic
511C22×C4⋊C4C22×C1111yescharacteristic
512C22×C4⋊C4C22×C1111yescharacteristic
513C22×C4⋊C4C22×C1111yescharacteristic
514C22×C4⋊C4C22×C1111yescharacteristic
515C22×C22⋊C4C22×C1111yescharacteristic
516C22×C22⋊C4C22×C1111yescharacteristic
517C22×C22⋊C4C22×C1111yescharacteristic
518C22×C22⋊C4C22×C1111yescharacteristic
519C22×C22⋊C4C22×C1111yescharacteristic
520C22×C22⋊C4C22×C1111yescharacteristic
521C22×C22⋊C4C22×C1111yescharacteristic
522C22×C22⋊C4C22×C1111yescharacteristic
523C22×C22⋊C4C22×C1111yescharacteristic
524C22×C22⋊C4C22×C1111yescharacteristic
525C22×C22⋊C4C22×C1111yescharacteristic
526C22×C42C22×C1111yescharacteristic
527#398—24no—
528#396—24no—
529#396—24no—
530#390—24no—
531#386—24no—
532#385—24no—
533C2×#95C22×C1111yescharacteristic
534C2×#95C22×C1111yescharacteristic
535C2×#95C22×C1111yescharacteristic
536C2×#95C22×C1111yescharacteristic
537C2×#95C22×C1111yescharacteristic
538C2×#95C22×C1111yescharacteristic
539C2×#95C22×C1111yescharacteristic
540C2×#95C22×C1111yescharacteristic
541C2×#95C22×C1111yescharacteristic
542C2×#95C22×C1111yescharacteristic
543C2×#95C22×C1111yescharacteristic
544C2×#95C22×C1111yescharacteristic
545C2×#95C22×C1111yescharacteristic
546C2×#95C22×C1111yescharacteristic
547C22×C11—24no—
548C22×C11—24no—
549C22×C11—24no—
550C22×C11—42no—
551C22×C11—42no—
552C22×C11—42no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—42no—
561C22×C11—42no—
562C22×C11—42no—
563C22×C11—42no—
564C22×C11—42no—
565C22×C11—42no—
566C22×C11—42no—
567C22×C11—42no—
568C22×C11—42no—
569C22×C11—81no—
570C22×C11—81no—
571C22×C11—81no—
572C22×C11—81no—
573C22×C11—81no—
574C22×C11—81no—
575C22×C11—81no—
576C22×C11—81no—
577C22×C11C2×#12111yescharacteristic
578C22×C11C2×C22⋊Q811yescharacteristic
579C22×C11C2×C22⋊Q811yescharacteristic
580C22×C11#52911yescharacteristic
581C22×C11#53211yescharacteristic
582C22×C11#53211yescharacteristic
583C22×C11#53411yescharacteristic
584C22×C11#53511yescharacteristic
585C22×C11#53711yescharacteristic
586C22×C11#53811yescharacteristic
587C22×C11#53811yescharacteristic
588C22×C11#53911yescharacteristic
589C22×C11#54011yescharacteristic
590C22×C11#54211yescharacteristic
591C22×C11#54311yescharacteristic
592C22×C11D4211yescharacteristic
593C22×C11D4211yescharacteristic
594C22×C11#54611yescharacteristic
595C22×C11#54611yescharacteristic
596C22×C11#54611yescharacteristic
597C22×C11#54611yescharacteristic
598C22×C11#54611yescharacteristic
599C22×C11#54811yescharacteristic
600C22×C11D4×Q811yescharacteristic
601C22×C11#55011yescharacteristic
602C22×C11#55111yescharacteristic
603C22×C11#55211yescharacteristic
604C22×C11#55311yescharacteristic
605C22×C11#55311yescharacteristic
606C22×C11#55311yescharacteristic
607C22×C11#55411yescharacteristic
608C22×C11#55411yescharacteristic
609C22×C11#55411yescharacteristic
610C22×C11#56011yescharacteristic
611C22×C11#56211yescharacteristic
612C4×C11—24no—
613C4×C11—24no—
614C4×C11—42no—
615C4×C11—42no—
616C4×C11—42no—
617C4×C11—42no—
618C4×C11—42no—
619C4×C11—42no—
620C4×C11—42no—
621C4×C11—81no—
622C4×C11—81no—
623C4×C11—81no—
624C4×C11—81no—
625C25C23×C1111yescharacteristic
626C25C23×C1111yescharacteristic
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—22no—
630C22×D4—22no—
631C22×D4—41no—
632C22×D4—41no—
633C22×D4Q8×C1114yes—
634C23×C4—22no—
635C23×C4—22no—
636C23×C4—22no—
637C23×C4—41no—
638C23×C4—41no—
639C23×C4—41no—
640C23×C4—41no—
641C23×C4C23×C1111yescharacteristic
642C23×C4C23×C1111yescharacteristic
643C23×C4C23×C1111yescharacteristic
644C23×C4C23×C1111yescharacteristic
645C23×C4C23×C1111yescharacteristic
646C23×C4C23×C1111yescharacteristic
647C23×C4C23×C1111yescharacteristic
648C23×C4C23×C1111yescharacteristic
649C23×C4C23×C1111yescharacteristic
650C23×C4C23×C1111yescharacteristic
651C23×C4C23×C1111yescharacteristic
652C23×C4C23×C1111yescharacteristic
653C23×C4C23×C1111yescharacteristic
654C2×C4⋊C4—22no—
655C2×C4⋊C4—22no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—41no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4—41no—
673C2×C4⋊C4—41no—
674C2×C4⋊C4D4×C1114yescomplemented
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—41no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—41no—
707C2×C22⋊C4D4×C1114yes—
708C2×C42—22no—
709C2×C42—22no—
710C2×C42—41no—
711#95—22no—
712#95—22no—
713#95—22no—
714#95—22no—
715#95—22no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—41no—
721#95—41no—
722#95—41no—
723#95—41no—
724#95D4×C1114yes—
725C2×C11—44no—
726C2×C11—82no—
727C2×C11#241711yescharacteristic
728C2×C11#242811yescharacteristic
729C2×C11#243711yescharacteristic
730C2×C11#245011yescharacteristic
731C2×C11#245211yescharacteristic
732C2×C11#254311yescharacteristic
733C2×C11#255411yescharacteristic
734C2×C11#255811yescharacteristic
735C2×C11#256611yescharacteristic
736C2×C11#267611yescharacteristic
737C2×C11#267811yescharacteristic
738C2×C11#269111yescharacteristic
739C2×C11#273211yescharacteristic
740C2×C11#276111yescharacteristic
741C2×C11#278011yescharacteristic
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24C2×D4×C1112yes—
769C24C2×Q8×C1112yes—
770C24C2×Q8×C1112yes—
771C24C11×#4112yes—
772C24C24×C1111yescharacteristic
773C2×D4—28no—
774C2×D4—28no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
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—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4C2×D4×C1112yes—
866C22×C4C2×D4×C1112yes—
867C22×C4C2×D4×C1112yes—
868C22×C4C2×D4×C1112yes—
869C22×C4C2×D4×C1112yes—
870C22×C4C2×D4×C1112yes—
871C22×C4C2×D4×C1112yes—
872C22×C4C2×D4×C1112yes—
873C22×C4C2×Q8×C1112yes—
874C22×C4C11×#4112yes—
875C22×C4C11×#4112yes—
876C22×C4C11×#4112yes—
877C22×C4C11×#4112yes—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C22⋊C4—28no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C42—44no—
897C11#1550711yescharacteristic, direct product factor, Sylow
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23C11×C22⋊Q814yes—
968C23C22×D4×C1111yescharacteristic
969C23C22×D4×C1111yescharacteristic
970C23C22×D4×C1111yescharacteristic
971C23C22×Q8×C1111yescharacteristic
972C23C2×C11×#4111yescharacteristic
973C23C2×C11×#4111yescharacteristic
974C23C2×C11×#4111yescharacteristic
975C23C2×C11×#4111yescharacteristic
976C23C2×C11×#4111yescharacteristic
977C23C11×H(5,𝔽2)11yescharacteristic
978C23C11×H(5,𝔽2)11yescharacteristic
979C23C11×H(5,𝔽2)11yescharacteristic
980C23C11×H(5,𝔽2)11yescharacteristic
981C23C11×H(5,𝔽2)11yescharacteristic
982C23C11×2−1+411yescharacteristic
983D4—416no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—416no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4C11×#12114yes—
1075C2×C4C11×C22⋊Q814yes—
1076C22—24no—
1077C22—24no—
1078C22—24no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—81no—
1099C22—81no—
1100C22—81no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22C2×C11×#12111yescharacteristic
1107C22C2×C11×C22⋊Q811yescharacteristic
1108C22C2×C11×C22⋊Q811yescharacteristic
1109C22C11×#52911yescharacteristic
1110C22C11×#53211yescharacteristic
1111C22C11×#53211yescharacteristic
1112C22C11×#53411yescharacteristic
1113C22C11×#53511yescharacteristic
1114C22C11×#53711yescharacteristic
1115C22C11×#53811yescharacteristic
1116C22C11×#53811yescharacteristic
1117C22C11×#53911yescharacteristic
1118C22C11×#54011yescharacteristic
1119C22C11×#54211yescharacteristic
1120C22C11×#54311yescharacteristic
1121C22D42×C1111yescharacteristic
1122C22D42×C1111yescharacteristic
1123C22C11×#54611yescharacteristic
1124C22C11×#54611yescharacteristic
1125C22C11×#54611yescharacteristic
1126C22C11×#54611yescharacteristic
1127C22C11×#54611yescharacteristic
1128C22C11×#54811yescharacteristic
1129C22D4×Q8×C1111yescharacteristic
1130C22C11×#55011yescharacteristic
1131C22C11×#55111yescharacteristic
1132C22C11×#55211yescharacteristic
1133C22C11×#55311yescharacteristic
1134C22C11×#55311yescharacteristic
1135C22C11×#55311yescharacteristic
1136C22C11×#55411yescharacteristic
1137C22C11×#55411yescharacteristic
1138C22C11×#55411yescharacteristic
1139C22C11×#56011yescharacteristic
1140C22C11×#56211yescharacteristic
1141C4—24no—
1142C4—24no—
1143C4—42no—
1144C4—42no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C2—44no—
1155C2—82no—
1156C2C11×#241711yescharacteristic
1157C2C11×#242811yescharacteristic
1158C2C11×#243711yescharacteristic
1159C2C11×#245011yescharacteristic
1160C2C11×#245211yescharacteristic
1161C2C11×#254311yescharacteristic
1162C2C11×#255411yescharacteristic
1163C2C11×#255811yescharacteristic
1164C2C11×#256611yescharacteristic
1165C2C11×#267611yescharacteristic
1166C2C11×#267811yescharacteristic
1167C2C11×#269111yescharacteristic
1168C2C11×#273211yescharacteristic
1169C2C11×#276111yescharacteristic
1170C2C11×#278011yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC24C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#398C2semidirect
2. C2×C11×#396C2semidirect
3. C2×C11×#396C2semidirect
6. C2×C11×#385C2semidirect
7. C11×#1442C2semidirect
8. C11×#1439C2semidirect
9. C11×#1439C2semidirect
10. C11×#1439C2semidirect
11. C11×#1439C2semidirect
13. C11×#1436C2semidirect
14. C11×C4⋊#95C2semidirect
15. C11×C22⋊#95C2semidirect
106. C2×C11×C4⋊C4D4semidirect
157. #15507C11direct (N × H)
313. C2×#398C2×C11semidirect
314. C2×#396C2×C11semidirect
315. C2×#396C2×C11semidirect
318. C2×#385C2×C11semidirect
319. #1442C2×C11semidirect
320. #1439C2×C11semidirect
321. #1439C2×C11semidirect
322. #1439C2×C11semidirect
323. #1439C2×C11semidirect
325. #1436C2×C11semidirect
326. C4⋊#95C2×C11semidirect
327. C22⋊#95C2×C11semidirect
674. C2×C4⋊C4D4×C11semidirect
897. C11#15507direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3982
C2×C11×#3962
C2×C11×#3902
C2×C11×#3862
C2×C11×#3852
C11×#14422
C11×#14392
C11×#14382
C11×#14362
C11×C4⋊#952
C11×C22⋊#952
#1550711