Finite Group Databasebeta

← C11×#23330 #14600523

Subgroups — C11×#23330 #14600523

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2392C211yesmaximal, characteristic
2C11×#1955C211yesmaximal, characteristic, complemented
3C11×#1954C211yesmaximal, characteristic, complemented
4C11×#1924C211yesmaximal, characteristic, complemented
5C11×#1923C211yesmaximal, characteristic, complemented
6C11×#1917C211yesmaximal, characteristic, complemented
7C11×#1916C211yesmaximal, characteristic, complemented
8C11×#1869C211yesmaximal, characteristic, complemented
9C11×#1869C211yesmaximal, characteristic, complemented
10C11×#1869C211yesmaximal, characteristic, complemented
11C11×#1869C211yesmaximal, characteristic, complemented
12C11×#1850C211yesmaximal, characteristic, complemented
13C11×#1850C211yesmaximal, characteristic, complemented
14C11×#1818C211yesmaximal, characteristic, complemented
15C11×#1798C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×C11×C22⋊C8C2211yescharacteristic
30C2×C11×C22⋊C8C2211yescharacteristic
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×#97C2211yescharacteristic
37C2×C4×C8×C11C2211yescharacteristic
38C11×#398C411yescharacteristic
39C11×#397C411yescharacteristic
40C11×#396C411yescharacteristic
41C11×#396C411yescharacteristic
42C11×#394C411yescharacteristic
43C11×#394C411yescharacteristic
44C11×#394C411yescharacteristic
45C11×#392C411yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C22⋊C4C2211yescharacteristic
48C4×C11×C22⋊C4C2211yescharacteristic
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C22×D4×C11C2×C411yescharacteristic
60C22×D4×C11C2×C411yescharacteristic
61C22×D4×C11C2×C411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C22×C8×C11—41no—
66C22×C8×C11—41no—
67C22×C8×C11—41no—
68C22×C8×C11—41no—
69C22×C8×C11—41no—
70C22×C8×C11—41no—
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C4×D4×C11—41no—
80C4×D4×C11—41no—
81C4×D4×C11—41no—
82C4×D4×C11—41no—
83C4×D4×C11—41no—
84C4×D4×C11—41no—
85C11×#117—41no—
86C11×#117—41no—
87C2×C11×C4⋊C4C2×C411yescharacteristic
88C2×C11×C4⋊C4C2×C411yescharacteristic
89C2×C11×C4⋊C4C2×C411yescharacteristic
90C2×C11×C4⋊C4C2×C411yescharacteristic
91C2×C11×C4⋊C4C2×C411yescharacteristic
92C2×C11×C4⋊C4C2×C411yescharacteristic
93C2×C11×C4⋊C4C2×C411yescharacteristic
94C2×C11×C22⋊C4C2×C411yescharacteristic
95C2×C11×C22⋊C4C2×C411yescharacteristic
96C2×C11×C22⋊C4C2×C411yescharacteristic
97C2×C11×C22⋊C4C2×C411yescharacteristic
98C2×C11×C22⋊C4C2×C411yescharacteristic
99C2×C11×C22⋊C4C2×C411yescharacteristic
100C2×C11×C22⋊C4C2×C411yescharacteristic
101C2×C11×C22⋊C4C2×C411yescharacteristic
102C2×C11×C22⋊C4C2×C411yescharacteristic
103C2×C11×C22⋊C4C2×C411yescharacteristic
104C2×C11×C22⋊C4C2×C411yescharacteristic
105C2×C11×C22⋊C4C2×C411yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C42×C11C2311yescharacteristic
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C11×C4⋊C8—41no—
111C11×C4⋊C8—41no—
112C11×C4⋊C8—41no—
113C11×C4⋊C8—41no—
114C11×C22⋊C8—41no—
115C11×C22⋊C8—41no—
116C11×C22⋊C8—41no—
117C11×C22⋊C8—41no—
118C11×C22⋊C8—41no—
119C11×C22⋊C8—41no—
120C11×C22⋊C8—41no—
121C11×C22⋊C8—41no—
122C11×C22⋊C8—41no—
123C11×C22⋊C8—41no—
124C11×#97—41no—
125C4×C8×C11—41no—
126C11×#95C2×C411yescharacteristic
127C11×#95C2×C411yescharacteristic
128C11×#95C2×C411yescharacteristic
129C11×#95C2×C411yescharacteristic
130C11×#95C2×C411yescharacteristic
131C11×#95C2×C411yescharacteristic
132#23330C1111yesmaximal, characteristic, direct product factor, Sylow
133C24×C11C22×C411yescharacteristic
134C24×C11C22×C411yescharacteristic
135C24×C11C22×C411yescharacteristic
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—41no—
142C2×D4×C11—41no—
143C2×D4×C11—41no—
144C2×D4×C11—41no—
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×C11C22×C411yescharacteristic
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C22×C411yescharacteristic
166C22×C4×C11C22×C411yescharacteristic
167C22×C4×C11C22×C411yescharacteristic
168C22×C4×C11C22×C411yescharacteristic
169C22×C4×C11C22×C411yescharacteristic
170C22×C4×C11C22×C411yescharacteristic
171C22×C4×C11C22×C411yescharacteristic
172C22×C4×C11C22×C411yescharacteristic
173C22×C4×C11C22×C411yescharacteristic
174C22×C4×C11C2411yescharacteristic
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—44no—
200C2×C8×C11—44no—
201C11×C4⋊C4—22no—
202C11×C4⋊C4—41no—
203C11×C4⋊C4—41no—
204C11×C4⋊C4—41no—
205C11×C4⋊C4—41no—
206C11×C4⋊C4—41no—
207C11×C4⋊C4—41no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—41no—
212C11×C22⋊C4—41no—
213C11×C22⋊C4—41no—
214C11×C22⋊C4—41no—
215C11×C22⋊C4—41no—
216C11×C22⋊C4—41no—
217C11×C22⋊C4—41no—
218C11×C22⋊C4—41no—
219C11×C22⋊C4—41no—
220C42×C11—21no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—21no—
226C42×C11—21no—
227C42×C11—21no—
228#2392C2×C1111yescharacteristic
229#1955C2×C1111yescharacteristic, complemented
230#1954C2×C1111yescharacteristic, complemented
231#1924C2×C1111yescharacteristic, complemented
232#1923C2×C1111yescharacteristic, complemented
233#1917C2×C1111yescharacteristic, complemented
234#1916C2×C1111yescharacteristic, complemented
235#1869C2×C1111yescharacteristic, complemented
236#1869C2×C1111yescharacteristic, complemented
237#1869C2×C1111yescharacteristic, complemented
238#1869C2×C1111yescharacteristic, complemented
239#1850C2×C1111yescharacteristic, complemented
240#1850C2×C1111yescharacteristic, complemented
241#1818C2×C1111yescharacteristic, complemented
242#1798C2×C1111yescharacteristic, complemented
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11#13112yes—
263C23×C11#13112yes—
264C23×C11C23×C411yescharacteristic
265D4×C11—44no—
266D4×C11—44no—
267D4×C11—44no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11#13112yes—
313C2×C4×C11H(5,𝔽2)11yescharacteristic
314C2×C4×C11H(5,𝔽2)11yescharacteristic
315C2×C4×C11H(5,𝔽2)11yescharacteristic
316C2×C4×C11H(5,𝔽2)11yescharacteristic
317C2×C4×C11H(5,𝔽2)11yescharacteristic
318C2×C4×C112−1+411yescharacteristic
319C8×C11—41no—
320C8×C11—41no—
321C8×C11—41no—
322C8×C11—41no—
323C8×C11—41no—
324C8×C11—41no—
325C8×C11—41no—
326C8×C11—41no—
327C23×C8C22×C1111yescharacteristic
328C23×C8C22×C1111yescharacteristic
329C2×C4×D4C22×C1111yescharacteristic
330C2×C4×D4C22×C1111yescharacteristic
331C2×C4×D4C22×C1111yescharacteristic
332C2×#117C22×C1111yescharacteristic
333C2×C4⋊C8C22×C1111yescharacteristic
334C2×C4⋊C8C22×C1111yescharacteristic
335C2×C4⋊C8C22×C1111yescharacteristic
336C2×C4⋊C8C22×C1111yescharacteristic
337C2×C22⋊C8C22×C1111yescharacteristic
338C2×C22⋊C8C22×C1111yescharacteristic
339C2×C22⋊C8C22×C1111yescharacteristic
340C2×C22⋊C8C22×C1111yescharacteristic
341C2×C22⋊C8C22×C1111yescharacteristic
342C2×C22⋊C8C22×C1111yescharacteristic
343C2×C22⋊C8C22×C1111yescharacteristic
344C2×C22⋊C8C22×C1111yescharacteristic
345C2×C22⋊C8C22×C1111yescharacteristic
346C2×C22⋊C8C22×C1111yescharacteristic
347C2×#97C22×C1111yescharacteristic
348C2×C4×C8C22×C1111yescharacteristic
349#398C4×C1111yescharacteristic
350#397C4×C1111yescharacteristic
351#396C4×C1111yescharacteristic
352#396C4×C1111yescharacteristic
353#394C4×C1111yescharacteristic
354#394C4×C1111yescharacteristic
355#394C4×C1111yescharacteristic
356#392C4×C1111yescharacteristic
357C4×C4⋊C4C22×C1111yescharacteristic
358C4×C22⋊C4C22×C1111yescharacteristic
359C4×C22⋊C4C22×C1111yescharacteristic
360#336C22×C1111yescharacteristic
361#336C22×C1111yescharacteristic
362#336C22×C1111yescharacteristic
363#336C22×C1111yescharacteristic
364#336C22×C1111yescharacteristic
365#336C22×C1111yescharacteristic
366#336C22×C1111yescharacteristic
367#336C22×C1111yescharacteristic
368#336C22×C1111yescharacteristic
369#336C22×C1111yescharacteristic
370C22×C11—22no—
371C22×C11—22no—
372C22×C11—22no—
373C22×C11—22no—
374C22×C11—22no—
375C22×C11—22no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11—41no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11—41no—
385C22×C11—41no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11#51811yescharacteristic
392C22×C11#51811yescharacteristic
393C22×C11#52011yescharacteristic
394C22×C11C2×#13111yescharacteristic
395C22×C11C2×#13111yescharacteristic
396C22×C11C2×#13111yescharacteristic
397C22×C11#56811yescharacteristic
398C4×C11—22no—
399C4×C11—41no—
400C4×C11—41no—
401C4×C11—41no—
402C4×C11—41no—
403C4×C11—41no—
404C4×C11—41no—
405C4×C11—41no—
406C4×C11—41no—
407C4×C11—41no—
408C4×C11—41no—
409C4×C11#56011yescharacteristic
410C4×C11#56011yescharacteristic
411C4×C11#56211yescharacteristic
412C4×C11#56211yescharacteristic
413C22×D4C2×C4×C1111yescharacteristic
414C22×D4C2×C4×C1111yescharacteristic
415C22×D4C2×C4×C1111yescharacteristic
416C23×C4C23×C1111yescharacteristic
417C23×C4C23×C1111yescharacteristic
418C23×C4C23×C1111yescharacteristic
419C22×C8—41no—
420C22×C8—41no—
421C22×C8—41no—
422C22×C8—41no—
423C22×C8—41no—
424C22×C8—41no—
425C22×C8C23×C1111yescharacteristic
426C22×C8C23×C1111yescharacteristic
427C22×C8C23×C1111yescharacteristic
428C22×C8C23×C1111yescharacteristic
429C22×C8C23×C1111yescharacteristic
430C22×C8C23×C1111yescharacteristic
431C22×C8C23×C1111yescharacteristic
432C22×C8C23×C1111yescharacteristic
433C4×D4—41no—
434C4×D4—41no—
435C4×D4—41no—
436C4×D4—41no—
437C4×D4—41no—
438C4×D4—41no—
439#117—41no—
440#117—41no—
441C2×C4⋊C4C2×C4×C1111yescharacteristic
442C2×C4⋊C4C2×C4×C1111yescharacteristic
443C2×C4⋊C4C2×C4×C1111yescharacteristic
444C2×C4⋊C4C2×C4×C1111yescharacteristic
445C2×C4⋊C4C2×C4×C1111yescharacteristic
446C2×C4⋊C4C2×C4×C1111yescharacteristic
447C2×C4⋊C4C2×C4×C1111yescharacteristic
448C2×C22⋊C4C2×C4×C1111yescharacteristic
449C2×C22⋊C4C2×C4×C1111yescharacteristic
450C2×C22⋊C4C2×C4×C1111yescharacteristic
451C2×C22⋊C4C2×C4×C1111yescharacteristic
452C2×C22⋊C4C2×C4×C1111yescharacteristic
453C2×C22⋊C4C2×C4×C1111yescharacteristic
454C2×C22⋊C4C2×C4×C1111yescharacteristic
455C2×C22⋊C4C2×C4×C1111yescharacteristic
456C2×C22⋊C4C2×C4×C1111yescharacteristic
457C2×C22⋊C4C2×C4×C1111yescharacteristic
458C2×C22⋊C4C2×C4×C1111yescharacteristic
459C2×C22⋊C4C2×C4×C1111yescharacteristic
460C2×C42C23×C1111yescharacteristic
461C2×C42C23×C1111yescharacteristic
462C2×C42C23×C1111yescharacteristic
463C2×C42C23×C1111yescharacteristic
464C4⋊C8—41no—
465C4⋊C8—41no—
466C4⋊C8—41no—
467C4⋊C8—41no—
468C22⋊C8—41no—
469C22⋊C8—41no—
470C22⋊C8—41no—
471C22⋊C8—41no—
472C22⋊C8—41no—
473C22⋊C8—41no—
474C22⋊C8—41no—
475C22⋊C8—41no—
476C22⋊C8—41no—
477C22⋊C8—41no—
478#97—41no—
479C4×C8—41no—
480#95C2×C4×C1111yescharacteristic
481#95C2×C4×C1111yescharacteristic
482#95C2×C4×C1111yescharacteristic
483#95C2×C4×C1111yescharacteristic
484#95C2×C4×C1111yescharacteristic
485#95C2×C4×C1111yescharacteristic
486C2×C11—42no—
487C2×C11—42no—
488C2×C11—81no—
489C2×C11#237711yescharacteristic
490C2×C11#297611yescharacteristic
491C2×C11#297711yescharacteristic
492C2×C11#297711yescharacteristic
493C2×C11#298111yescharacteristic
494C2×C11#299211yescharacteristic
495C2×C11#299411yescharacteristic
496C24C22×C4×C1111yescharacteristic
497C24C22×C4×C1111yescharacteristic
498C24C22×C4×C1111yescharacteristic
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—41no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4—41no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4C22×C4×C1111yescharacteristic
527C22×C4C22×C4×C1111yescharacteristic
528C22×C4C22×C4×C1111yescharacteristic
529C22×C4C22×C4×C1111yescharacteristic
530C22×C4C22×C4×C1111yescharacteristic
531C22×C4C22×C4×C1111yescharacteristic
532C22×C4C22×C4×C1111yescharacteristic
533C22×C4C22×C4×C1111yescharacteristic
534C22×C4C22×C4×C1111yescharacteristic
535C22×C4C22×C4×C1111yescharacteristic
536C22×C4C22×C4×C1111yescharacteristic
537C22×C4C24×C1111yescharacteristic
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—44no—
563C2×C8—44no—
564C4⋊C4—22no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—41no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C11#2333011yescharacteristic, direct product factor, Sylow
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23C11×#13112yes—
612C23C11×#13112yes—
613C23C23×C4×C1111yescharacteristic
614D4—44no—
615D4—44no—
616D4—44no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4C11×#13112yes—
662C2×C4C11×H(5,𝔽2)11yescharacteristic
663C2×C4C11×H(5,𝔽2)11yescharacteristic
664C2×C4C11×H(5,𝔽2)11yescharacteristic
665C2×C4C11×H(5,𝔽2)11yescharacteristic
666C2×C4C11×H(5,𝔽2)11yescharacteristic
667C2×C4C11×2−1+411yescharacteristic
668C8—41no—
669C8—41no—
670C8—41no—
671C8—41no—
672C8—41no—
673C8—41no—
674C8—41no—
675C8—41no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22C11×#51811yescharacteristic
698C22C11×#51811yescharacteristic
699C22C11×#52011yescharacteristic
700C22C2×C11×#13111yescharacteristic
701C22C2×C11×#13111yescharacteristic
702C22C2×C11×#13111yescharacteristic
703C22C11×#56811yescharacteristic
704C4—22no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4C11×#56011yescharacteristic
716C4C11×#56011yescharacteristic
717C4C11×#56211yescharacteristic
718C4C11×#56211yescharacteristic
719C2—42no—
720C2—42no—
721C2—81no—
722C2C11×#237711yescharacteristic
723C2C11×#297611yescharacteristic
724C2C11×#297711yescharacteristic
725C2C11×#297711yescharacteristic
726C2C11×#298111yescharacteristic
727C2C11×#299211yescharacteristic
728C2C11×#299411yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC11×#392C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1955C2semidirect
3. C11×#1954C2semidirect
4. C11×#1924C2semidirect
5. C11×#1923C2semidirect
6. C11×#1917C2semidirect
7. C11×#1916C2semidirect
8. C11×#1869C2semidirect
9. C11×#1869C2semidirect
10. C11×#1869C2semidirect
11. C11×#1869C2semidirect
12. C11×#1850C2semidirect
13. C11×#1850C2semidirect
14. C11×#1818C2semidirect
15. C11×#1798C2semidirect
132. #23330C11direct (N × H)
229. #1955C2×C11semidirect
230. #1954C2×C11semidirect
231. #1924C2×C11semidirect
232. #1923C2×C11semidirect
233. #1917C2×C11semidirect
234. #1916C2×C11semidirect
235. #1869C2×C11semidirect
236. #1869C2×C11semidirect
237. #1869C2×C11semidirect
238. #1869C2×C11semidirect
239. #1850C2×C11semidirect
240. #1850C2×C11semidirect
241. #1818C2×C11semidirect
242. #1798C2×C11semidirect
591. C11#23330direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23922
C11×#19552
C11×#19542
C11×#19242
C11×#19232
C11×#19172
C11×#19162
C11×#18692
C11×#18502
C11×#18182
C11×#17982
#2333011