Finite Group Databasebeta

← C11×#22036 #14599229

Subgroups — C11×#22036 #14599229

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#435C211yesmaximal, characteristic, complemented
2C2×C11×#407C211yesmaximal, characteristic, complemented
3C4×C11×#120C211yesmaximal, characteristic
4C11×#1955C211yesmaximal, characteristic, complemented
5C11×#1954C211yesmaximal, characteristic, complemented
6C11×#1924C211yesmaximal, characteristic, complemented
7C11×#1924C211yesmaximal, characteristic, complemented
8C11×#1924C211yesmaximal, characteristic, complemented
9C11×#1923C211yesmaximal, characteristic, complemented
10C11×#1870C211yesmaximal, characteristic, complemented
11C11×#1869C211yesmaximal, characteristic, complemented
12C11×#1869C211yesmaximal, characteristic, complemented
13C11×#1851C211yesmaximal, characteristic, complemented
14C11×#1779C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic, complemented
20C2×C11×#120C411yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C11×#435—24no—
25C2×C11×C4⋊C8C2211yescharacteristic, complemented
26C2×C11×C4⋊C8C2211yescharacteristic, complemented
27C2×C11×C4⋊C8C2211yescharacteristic, complemented
28C11×#407—24no—
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×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic, complemented
40C2×C11×C22⋊C8C2211yescharacteristic, complemented
41C2×C11×C22⋊C8C2211yescharacteristic, complemented
42C2×C11×#97C2211yescharacteristic, complemented
43C2×C11×#97C2211yescharacteristic, complemented
44C2×C4×C8×C11C2211yescharacteristic, complemented
45C11×#386C411yescharacteristic
46C11×#386C411yescharacteristic
47C11×#386C411yescharacteristic
48C11×#385C411yescharacteristic
49C11×#385C411yescharacteristic
50C11×#385C411yescharacteristic
51C11×#379C411yescharacteristic
52C4×C11×C22⋊C4C2211yescharacteristic
53C4×C11×C22⋊C4C2211yescharacteristic
54C4×C11×C22⋊C4C2211yescharacteristic
55C11×#336C2211yescharacteristic, complemented
56C11×#336C2211yescharacteristic, complemented
57C11×#336C2211yescharacteristic, complemented
58C11×#336C2211yescharacteristic, complemented
59C11×#336C2211yescharacteristic, complemented
60C11×#336C2211yescharacteristic, complemented
61C25×C11C2×C411yescharacteristic
62C22×D4×C11C2×C411yescharacteristic
63C22×D4×C11C2×C411yescharacteristic
64C22×D4×C11C2×C411yescharacteristic
65C23×C4×C11—22no—
66C23×C4×C11—22no—
67C23×C4×C11—41no—
68C23×C4×C11—41no—
69C23×C4×C11—41no—
70C23×C4×C11—41no—
71C23×C4×C11C2×C411yescharacteristic
72C23×C4×C11C2×C411yescharacteristic
73C23×C4×C11C2×C411yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C2×C11×M16—22no—
79C2×C11×M16—41no—
80C2×C11×M16—41no—
81C2×C11×M16—41no—
82C2×C11×M16—41no—
83C2×C11×M16D414yescomplemented
84C22×C8×C11—22no—
85C22×C8×C11—41no—
86C22×C8×C11—41no—
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C11×#120—24no—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11—41no—
99C4×D4×C11—41no—
100C4×D4×C11—41no—
101C4×D4×C11—41no—
102C2×C11×C4⋊C4C2×C411yescharacteristic
103C2×C11×C4⋊C4C2×C411yescharacteristic
104C2×C11×C4⋊C4C2×C411yescharacteristic
105C2×C11×C22⋊C4C2×C411yescharacteristic
106C2×C11×C22⋊C4C2×C411yescharacteristic
107C2×C11×C22⋊C4C2×C411yescharacteristic
108C2×C11×C22⋊C4C2×C411yescharacteristic
109C2×C11×C22⋊C4C2×C411yescharacteristic
110C2×C11×C22⋊C4C2×C411yescharacteristic
111C2×C11×C22⋊C4C2×C411yescharacteristic
112C2×C11×C22⋊C4C2×C411yescharacteristic
113C2×C11×C22⋊C4C2×C411yescharacteristic
114C2×C11×C22⋊C4C2×C411yescharacteristic
115C2×C11×C22⋊C4C2×C411yescharacteristic
116C2×C11×C22⋊C4C2×C411yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C2×C42×C11C2311yescharacteristic
119C2×C42×C11C2311yescharacteristic
120C11×C4⋊C8—22no—
121C11×C4⋊C8—41no—
122C11×C4⋊C8—41no—
123C11×C22⋊C8—22no—
124C11×C22⋊C8—22no—
125C11×C22⋊C8—22no—
126C11×C22⋊C8—22no—
127C11×C22⋊C8—22no—
128C11×C22⋊C8—22no—
129C11×C22⋊C8—22no—
130C11×C22⋊C8—41no—
131C11×C22⋊C8—41no—
132C11×C22⋊C8—41no—
133C11×C22⋊C8—41no—
134C11×C22⋊C8—41no—
135C11×C22⋊C8—41no—
136C11×#97—22no—
137C11×#97—41no—
138C4×C8×C11—41no—
139C11×#95C2×C411yescharacteristic
140C11×#95C2×C411yescharacteristic
141C11×#95C2×C411yescharacteristic
142C11×#95C2×C411yescharacteristic
143C11×#95C2×C411yescharacteristic
144C11×#95C2×C411yescharacteristic
145#22036C1111yesmaximal, characteristic, direct product factor, Sylow
146C24×C11—22no—
147C24×C11—22no—
148C24×C11—22no—
149C24×C11—41no—
150C24×C11—41no—
151C24×C11—41no—
152C24×C11—41no—
153C24×C11C22×C411yescharacteristic
154C24×C11C22×C411yescharacteristic
155C24×C11C22×C411yescharacteristic
156C24×C11C22×C411yescharacteristic
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—41no—
162C2×D4×C11—41no—
163C2×D4×C11—41no—
164C2×D4×C11—41no—
165C2×D4×C11M1614yescomplemented
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
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—41no—
192C22×C4×C11—41no—
193C22×C4×C11—41no—
194C22×C4×C11—41no—
195C22×C4×C11—41no—
196C22×C4×C11—41no—
197C22×C4×C11—44no—
198C22×C4×C11—44no—
199C22×C4×C11—44no—
200C22×C4×C11—44no—
201C22×C4×C11C22×C411yescharacteristic
202C22×C4×C11C22×C411yescharacteristic
203C22×C4×C11C22×C411yescharacteristic
204C22×C4×C11C22×C411yescharacteristic
205C22×C4×C11C22×C411yescharacteristic
206C22×C4×C11C22×C411yescharacteristic
207C22×C4×C11C22×C411yescharacteristic
208C22×C4×C11C22×C411yescharacteristic
209C22×C4×C11C22×C411yescharacteristic
210C22×C4×C11C22×C411yescharacteristic
211C22×C4×C11C2×D412yes—
212C22×C4×C11#4112yes—
213C22×C4×C11C2411yescharacteristic
214C11×M16—44no—
215C11×M16—44no—
216C2×C8×C11—21no—
217C2×C8×C11—21no—
218C2×C8×C11—21no—
219C2×C8×C11—21no—
220C2×C8×C11—21no—
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C2×C8×C11—21no—
227C2×C8×C11—21no—
228C2×C8×C11—21no—
229C2×C8×C11—21no—
230C2×C8×C11—21no—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—44no—
239C2×C8×C11C2×D412yes—
240C2×C8×C11C2×D412yes—
241C11×C4⋊C4—22no—
242C11×C4⋊C4—41no—
243C11×C4⋊C4—41no—
244C11×C22⋊C4—22no—
245C11×C22⋊C4—22no—
246C11×C22⋊C4—22no—
247C11×C22⋊C4—22no—
248C11×C22⋊C4—22no—
249C11×C22⋊C4—22no—
250C11×C22⋊C4—41no—
251C11×C22⋊C4—41no—
252C11×C22⋊C4—41no—
253C11×C22⋊C4—41no—
254C11×C22⋊C4—41no—
255C11×C22⋊C4—41no—
256C42×C11—21no—
257C42×C11—21no—
258C42×C11—21no—
259C42×C11—21no—
260C42×C11—21no—
261C42×C11—21no—
262C2×#435C2×C1111yescharacteristic, complemented
263C2×#407C2×C1111yescharacteristic, complemented
264C4×#120C2×C1111yescharacteristic
265#1955C2×C1111yescharacteristic, complemented
266#1954C2×C1111yescharacteristic, complemented
267#1924C2×C1111yescharacteristic, complemented
268#1924C2×C1111yescharacteristic, complemented
269#1924C2×C1111yescharacteristic, complemented
270#1923C2×C1111yescharacteristic, complemented
271#1870C2×C1111yescharacteristic, complemented
272#1869C2×C1111yescharacteristic, complemented
273#1869C2×C1111yescharacteristic, complemented
274#1851C2×C1111yescharacteristic, complemented
275#1779C2×C1111yescharacteristic, complemented
276#1753C2×C1111yescharacteristic, complemented
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—44no—
302C23×C11—44no—
303C23×C11—44no—
304C23×C11—44no—
305C23×C11—44no—
306C23×C11—44no—
307C23×C11—44no—
308C23×C11C4×D412yes—
309C23×C11C2×M1612yes—
310C23×C11C2×M1612yes—
311C23×C11#13112yes—
312C23×C11C23×C411yescharacteristic
313D4×C11—44no—
314D4×C11—44no—
315D4×C11—44no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—21no—
348C2×C4×C11—44no—
349C2×C4×C11—44no—
350C2×C4×C11—44no—
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×C11C4×D412yes—
364C2×C4×C11C2×M1612yes—
365C2×C4×C11C22×D411yescharacteristic
366C2×C4×C11C2×#4111yescharacteristic
367C2×C4×C11H(5,𝔽2)11yescharacteristic
368C2×C4×C11H(5,𝔽2)11yescharacteristic
369C2×C4×C11H(5,𝔽2)11yescharacteristic
370C2×C4×C11H(5,𝔽2)11yescharacteristic
371C8×C11—22no—
372C8×C11—22no—
373C8×C11—41no—
374C8×C11—41no—
375C8×C11—41no—
376C8×C11—41no—
377C8×C11—41no—
378C8×C11—41no—
379C24×C4C22×C1111yescharacteristic
380C22×M16C22×C1111yescharacteristic
381C22×M16C22×C1111yescharacteristic
382C23×C8C22×C1111yescharacteristic, complemented
383C2×#120C4×C1111yescharacteristic
384C2×C4×D4C22×C1111yescharacteristic
385C2×C4×D4C22×C1111yescharacteristic
386C2×C4×D4C22×C1111yescharacteristic
387#435—24no—
388C2×C4⋊C8C22×C1111yescharacteristic, complemented
389C2×C4⋊C8C22×C1111yescharacteristic, complemented
390C2×C4⋊C8C22×C1111yescharacteristic, complemented
391#407—24no—
392C2×C22⋊C8C22×C1111yescharacteristic
393C2×C22⋊C8C22×C1111yescharacteristic
394C2×C22⋊C8C22×C1111yescharacteristic
395C2×C22⋊C8C22×C1111yescharacteristic
396C2×C22⋊C8C22×C1111yescharacteristic
397C2×C22⋊C8C22×C1111yescharacteristic
398C2×C22⋊C8C22×C1111yescharacteristic
399C2×C22⋊C8C22×C1111yescharacteristic
400C2×C22⋊C8C22×C1111yescharacteristic
401C2×C22⋊C8C22×C1111yescharacteristic
402C2×C22⋊C8C22×C1111yescharacteristic, complemented
403C2×C22⋊C8C22×C1111yescharacteristic, complemented
404C2×C22⋊C8C22×C1111yescharacteristic, complemented
405C2×#97C22×C1111yescharacteristic, complemented
406C2×#97C22×C1111yescharacteristic, complemented
407C2×C4×C8C22×C1111yescharacteristic, complemented
408#386C4×C1111yescharacteristic
409#386C4×C1111yescharacteristic
410#386C4×C1111yescharacteristic
411#385C4×C1111yescharacteristic
412#385C4×C1111yescharacteristic
413#385C4×C1111yescharacteristic
414#379C4×C1111yescharacteristic
415C4×C22⋊C4C22×C1111yescharacteristic
416C4×C22⋊C4C22×C1111yescharacteristic
417C4×C22⋊C4C22×C1111yescharacteristic
418#336C22×C1111yescharacteristic, complemented
419#336C22×C1111yescharacteristic, complemented
420#336C22×C1111yescharacteristic, complemented
421#336C22×C1111yescharacteristic, complemented
422#336C22×C1111yescharacteristic, complemented
423#336C22×C1111yescharacteristic, complemented
424C22×C11—22no—
425C22×C11—22no—
426C22×C11—22no—
427C22×C11—22no—
428C22×C11—22no—
429C22×C11—22no—
430C22×C11—22no—
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—22no—
434C22×C11—22no—
435C22×C11—22no—
436C22×C11—416no—
437C22×C11—41no—
438C22×C11—41no—
439C22×C11—41no—
440C22×C11—41no—
441C22×C11—41no—
442C22×C11—41no—
443C22×C11—41no—
444C22×C11—41no—
445C22×C11—41no—
446C22×C11—41no—
447C22×C11—41no—
448C22×C11—41no—
449C22×C11—41no—
450C22×C11—41no—
451C22×C11—41no—
452C22×C11—41no—
453C22×C11C2×C4×D411yescharacteristic
454C22×C11#51811yescharacteristic
455C22×C11#51811yescharacteristic
456C22×C11C22×M1611yescharacteristic
457C22×C11C2×#13111yescharacteristic
458C22×C11#56811yescharacteristic
459C22×C11#56811yescharacteristic
460C4×C11—22no—
461C4×C11—22no—
462C4×C11—41no—
463C4×C11—41no—
464C4×C11—41no—
465C4×C11—41no—
466C4×C11—41no—
467C4×C11—41no—
468C4×C11—41no—
469C4×C11—41no—
470C4×C11#53411yescharacteristic
471C4×C11#53511yescharacteristic
472C4×C11#53811yescharacteristic
473C4×C11#53811yescharacteristic
474C25C2×C4×C1111yescharacteristic
475C22×D4C2×C4×C1111yescharacteristic
476C22×D4C2×C4×C1111yescharacteristic
477C22×D4C2×C4×C1111yescharacteristic
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—41no—
481C23×C4—41no—
482C23×C4—41no—
483C23×C4—41no—
484C23×C4C2×C4×C1111yescharacteristic
485C23×C4C2×C4×C1111yescharacteristic
486C23×C4C2×C4×C1111yescharacteristic
487C23×C4C23×C1111yescharacteristic
488C23×C4C23×C1111yescharacteristic
489C23×C4C23×C1111yescharacteristic
490C23×C4C23×C1111yescharacteristic
491C2×M16—22no—
492C2×M16—41no—
493C2×M16—41no—
494C2×M16—41no—
495C2×M16—41no—
496C2×M16D4×C1114yescomplemented
497C22×C8—22no—
498C22×C8—41no—
499C22×C8—41no—
500C22×C8C23×C1111yescharacteristic
501C22×C8C23×C1111yescharacteristic
502C22×C8C23×C1111yescharacteristic
503C22×C8C23×C1111yescharacteristic
504C22×C8C23×C1111yescharacteristic
505C22×C8C23×C1111yescharacteristic
506C22×C8C23×C1111yescharacteristic
507C22×C8C23×C1111yescharacteristic
508#120—24no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—41no—
512C4×D4—41no—
513C4×D4—41no—
514C4×D4—41no—
515C2×C4⋊C4C2×C4×C1111yescharacteristic
516C2×C4⋊C4C2×C4×C1111yescharacteristic
517C2×C4⋊C4C2×C4×C1111yescharacteristic
518C2×C22⋊C4C2×C4×C1111yescharacteristic
519C2×C22⋊C4C2×C4×C1111yescharacteristic
520C2×C22⋊C4C2×C4×C1111yescharacteristic
521C2×C22⋊C4C2×C4×C1111yescharacteristic
522C2×C22⋊C4C2×C4×C1111yescharacteristic
523C2×C22⋊C4C2×C4×C1111yescharacteristic
524C2×C22⋊C4C2×C4×C1111yescharacteristic
525C2×C22⋊C4C2×C4×C1111yescharacteristic
526C2×C22⋊C4C2×C4×C1111yescharacteristic
527C2×C22⋊C4C2×C4×C1111yescharacteristic
528C2×C22⋊C4C2×C4×C1111yescharacteristic
529C2×C22⋊C4C2×C4×C1111yescharacteristic
530C2×C42C23×C1111yescharacteristic
531C2×C42C23×C1111yescharacteristic
532C2×C42C23×C1111yescharacteristic
533C4⋊C8—22no—
534C4⋊C8—41no—
535C4⋊C8—41no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—22no—
540C22⋊C8—22no—
541C22⋊C8—22no—
542C22⋊C8—22no—
543C22⋊C8—41no—
544C22⋊C8—41no—
545C22⋊C8—41no—
546C22⋊C8—41no—
547C22⋊C8—41no—
548C22⋊C8—41no—
549#97—22no—
550#97—41no—
551C4×C8—41no—
552#95C2×C4×C1111yescharacteristic
553#95C2×C4×C1111yescharacteristic
554#95C2×C4×C1111yescharacteristic
555#95C2×C4×C1111yescharacteristic
556#95C2×C4×C1111yescharacteristic
557#95C2×C4×C1111yescharacteristic
558C2×C11—42no—
559C2×C11—42no—
560C2×C11—42no—
561C2×C11—42no—
562C2×C11#232111yescharacteristic
563C2×C11#293311yescharacteristic
564C2×C11D4×M1611yescharacteristic
565C2×C11#297311yescharacteristic
566C2×C11#297411yescharacteristic
567C2×C11#297611yescharacteristic
568C2×C11#297811yescharacteristic
569C24—22no—
570C24—22no—
571C24—22no—
572C24—41no—
573C24—41no—
574C24—41no—
575C24—41no—
576C24C22×C4×C1111yescharacteristic
577C24C22×C4×C1111yescharacteristic
578C24C22×C4×C1111yescharacteristic
579C24C22×C4×C1111yescharacteristic
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4C11×M1614yescomplemented
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
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—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4C22×C4×C1111yescharacteristic
625C22×C4C22×C4×C1111yescharacteristic
626C22×C4C22×C4×C1111yescharacteristic
627C22×C4C22×C4×C1111yescharacteristic
628C22×C4C22×C4×C1111yescharacteristic
629C22×C4C22×C4×C1111yescharacteristic
630C22×C4C22×C4×C1111yescharacteristic
631C22×C4C22×C4×C1111yescharacteristic
632C22×C4C22×C4×C1111yescharacteristic
633C22×C4C22×C4×C1111yescharacteristic
634C22×C4C2×D4×C1112yes—
635C22×C4C11×#4112yes—
636C22×C4C24×C1111yescharacteristic
637M16—44no—
638M16—44no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—44no—
662C2×C8C2×D4×C1112yes—
663C2×C8C2×D4×C1112yes—
664C4⋊C4—22no—
665C4⋊C4—41no—
666C4⋊C4—41no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—41no—
674C22⋊C4—41no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—41no—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—21no—
685C11#2203611yescharacteristic, direct product factor, Sylow
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23C4×D4×C1112yes—
718C23C2×C11×M1612yes—
719C23C2×C11×M1612yes—
720C23C11×#13112yes—
721C23C23×C4×C1111yescharacteristic
722D4—44no—
723D4—44no—
724D4—44no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—41no—
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×C4C4×D4×C1112yes—
773C2×C4C2×C11×M1612yes—
774C2×C4C22×D4×C1111yescharacteristic
775C2×C4C2×C11×#4111yescharacteristic
776C2×C4C11×H(5,𝔽2)11yescharacteristic
777C2×C4C11×H(5,𝔽2)11yescharacteristic
778C2×C4C11×H(5,𝔽2)11yescharacteristic
779C2×C4C11×H(5,𝔽2)11yescharacteristic
780C8—22no—
781C8—22no—
782C8—41no—
783C8—41no—
784C8—41no—
785C8—41no—
786C8—41no—
787C8—41no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—416no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22C2×C4×D4×C1111yescharacteristic
818C22C11×#51811yescharacteristic
819C22C11×#51811yescharacteristic
820C22C22×C11×M1611yescharacteristic
821C22C2×C11×#13111yescharacteristic
822C22C11×#56811yescharacteristic
823C22C11×#56811yescharacteristic
824C4—22no—
825C4—22no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4C11×#53411yescharacteristic
835C4C11×#53511yescharacteristic
836C4C11×#53811yescharacteristic
837C4C11×#53811yescharacteristic
838C2—42no—
839C2—42no—
840C2—42no—
841C2—42no—
842C2C11×#232111yescharacteristic
843C2C11×#293311yescharacteristic
844C2D4×C11×M1611yescharacteristic
845C2C11×#297311yescharacteristic
846C2C11×#297411yescharacteristic
847C2C11×#297611yescharacteristic
848C2C11×#297811yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC2×C11×#120C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#435C2semidirect
2. C2×C11×#407C2semidirect
4. C11×#1955C2semidirect
5. C11×#1954C2semidirect
6. C11×#1924C2semidirect
7. C11×#1924C2semidirect
8. C11×#1924C2semidirect
9. C11×#1923C2semidirect
10. C11×#1870C2semidirect
11. C11×#1869C2semidirect
12. C11×#1869C2semidirect
13. C11×#1851C2semidirect
14. C11×#1779C2semidirect
15. C11×#1753C2semidirect
19. C23×C8×C11C22semidirect
25. C2×C11×C4⋊C8C22semidirect
26. C2×C11×C4⋊C8C22semidirect
27. C2×C11×C4⋊C8C22semidirect
39. C2×C11×C22⋊C8C22semidirect
40. C2×C11×C22⋊C8C22semidirect
41. C2×C11×C22⋊C8C22semidirect
42. C2×C11×#97C22semidirect
43. C2×C11×#97C22semidirect
44. C2×C4×C8×C11C22semidirect
55. C11×#336C22semidirect
56. C11×#336C22semidirect
57. C11×#336C22semidirect
58. C11×#336C22semidirect
59. C11×#336C22semidirect
60. C11×#336C22semidirect
83. C2×C11×M16D4semidirect
145. #22036C11direct (N × H)
165. C2×D4×C11M16semidirect
262. C2×#435C2×C11semidirect
263. C2×#407C2×C11semidirect
265. #1955C2×C11semidirect
266. #1954C2×C11semidirect
267. #1924C2×C11semidirect
268. #1924C2×C11semidirect
269. #1924C2×C11semidirect
270. #1923C2×C11semidirect
271. #1870C2×C11semidirect
272. #1869C2×C11semidirect
273. #1869C2×C11semidirect
274. #1851C2×C11semidirect
275. #1779C2×C11semidirect
276. #1753C2×C11semidirect
382. C23×C8C22×C11semidirect
388. C2×C4⋊C8C22×C11semidirect
389. C2×C4⋊C8C22×C11semidirect
390. C2×C4⋊C8C22×C11semidirect
402. C2×C22⋊C8C22×C11semidirect
403. C2×C22⋊C8C22×C11semidirect
404. C2×C22⋊C8C22×C11semidirect
405. C2×#97C22×C11semidirect
406. C2×#97C22×C11semidirect
407. C2×C4×C8C22×C11semidirect
418. #336C22×C11semidirect
419. #336C22×C11semidirect
420. #336C22×C11semidirect
421. #336C22×C11semidirect
422. #336C22×C11semidirect
423. #336C22×C11semidirect
496. C2×M16D4×C11semidirect
588. C2×D4C11×M16semidirect
685. C11#22036direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4352
C2×C11×#4072
C4×C11×#1202
C11×#19552
C11×#19542
C11×#19242
C11×#19232
C11×#18702
C11×#18692
C11×#18512
C11×#17792
C11×#17532
#2203611