Finite Group Databasebeta

← C11×#22039 #14599232

Subgroups — C11×#22039 #14599232

Order 2816.

1028 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#436C211yesmaximal, characteristic, complemented
2C2×C11×#408C211yesmaximal, characteristic, complemented
3C11×#2388C211yesmaximal, characteristic
4C11×#1955C211yesmaximal, characteristic, complemented
5C11×#1954C211yesmaximal, characteristic, complemented
6C11×#1924C211yesmaximal, characteristic, complemented
7C11×#1923C211yesmaximal, characteristic, complemented
8C11×#1923C211yesmaximal, characteristic, complemented
9C11×#1923C211yesmaximal, characteristic, complemented
10C11×#1870C211yesmaximal, characteristic, complemented
11C11×#1870C211yesmaximal, characteristic, complemented
12C11×#1869C211yesmaximal, characteristic, complemented
13C11×#1850C211yesmaximal, characteristic, complemented
14C11×#1780C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C11×#436—24no—
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C11×#408—24no—
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×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×C22⋊C8C2211yescharacteristic
41C2×C11×#97C2211yescharacteristic
42C2×C4×C8×C11C2211yescharacteristic
43C2×C4×C8×C11C2211yescharacteristic
44C11×#395C411yescharacteristic
45C11×#394C411yescharacteristic
46C11×#394C411yescharacteristic
47C11×#394C411yescharacteristic
48C11×#393C411yescharacteristic
49C11×#392C411yescharacteristic
50C11×#392C411yescharacteristic
51C11×#392C411yescharacteristic
52C4×C11×C22⋊C4C2211yescharacteristic
53C4×C11×C22⋊C4C2211yescharacteristic
54C4×C11×C22⋊C4C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—41no—
64C2×C11×#41—41no—
65C2×C11×#41—41no—
66C2×C11×#41—41no—
67C22×Q8×C11C2×C411yescharacteristic
68C22×D4×C11C2×C411yescharacteristic
69C22×D4×C11C2×C411yescharacteristic
70C22×D4×C11C2×C411yescharacteristic
71C22×D4×C11C2×C411yescharacteristic
72C22×D4×C11C2×C411yescharacteristic
73C22×D4×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
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11—41no—
98C4×D4×C11—41no—
99C4×D4×C11—41no—
100C4×D4×C11—41no—
101C2×C11×C4⋊C4C2×C411yescharacteristic
102C2×C11×C4⋊C4C2×C411yescharacteristic
103C2×C11×C4⋊C4C2×C411yescharacteristic
104C2×C11×C22⋊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×C42×C11C2311yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C2×C42×C11C2311yescharacteristic
119C11×C4⋊C8—22no—
120C11×C4⋊C8—41no—
121C11×C4⋊C8—41no—
122C11×C22⋊C8—22no—
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—41no—
130C11×C22⋊C8—41no—
131C11×C22⋊C8—41no—
132C11×C22⋊C8—41no—
133C11×C22⋊C8—41no—
134C11×C22⋊C8—41no—
135C11×#97—41no—
136C4×C8×C11—22no—
137C4×C8×C11—41no—
138C11×#95C2×C411yescharacteristic
139C11×#95C2×C411yescharacteristic
140C11×#95C2×C411yescharacteristic
141C11×#95C2×C411yescharacteristic
142C11×#95C2×C411yescharacteristic
143C11×#95C2×C411yescharacteristic
144#22039C1111yesmaximal, characteristic, direct product factor, Sylow
145C24×C11C22×C411yescharacteristic
146C24×C11C22×C411yescharacteristic
147C24×C11C22×C411yescharacteristic
148C24×C11C22×C411yescharacteristic
149C11×#41—44no—
150C11×#41—44no—
151C11×#41—44no—
152C11×#41—44no—
153C2×Q8×C11—22no—
154C2×Q8×C11—41no—
155C2×Q8×C11—41no—
156C2×D4×C11—22no—
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—22no—
162C2×D4×C11—41no—
163C2×D4×C11—41no—
164C2×D4×C11—41no—
165C2×D4×C11—41no—
166C2×D4×C11—41no—
167C2×D4×C11—41no—
168C2×D4×C11—41no—
169C2×D4×C11—41no—
170C2×D4×C11—41no—
171C2×D4×C11—41no—
172C2×D4×C11—41no—
173C2×D4×C11—41no—
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×C11C22×C411yescharacteristic
197C22×C4×C11C22×C411yescharacteristic
198C22×C4×C11C22×C411yescharacteristic
199C22×C4×C11C22×C411yescharacteristic
200C22×C4×C11C22×C411yescharacteristic
201C22×C4×C11C22×C411yescharacteristic
202C22×C4×C11C22×C411yescharacteristic
203C22×C4×C11C22×C411yescharacteristic
204C22×C4×C11C22×C411yescharacteristic
205C22×C4×C11C22×C411yescharacteristic
206C22×C4×C11C2×D412yes—
207C22×C4×C11#4112yes—
208C22×C4×C11C2411yescharacteristic
209C11×M16—44no—
210C11×M16—44no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11—21no—
214C2×C8×C11—21no—
215C2×C8×C11—21no—
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—44no—
234C2×C8×C11C2×D412yes—
235C2×C8×C11C2×D412yes—
236C11×C4⋊C4—22no—
237C11×C4⋊C4—41no—
238C11×C4⋊C4—41no—
239C11×C22⋊C4—22no—
240C11×C22⋊C4—22no—
241C11×C22⋊C4—22no—
242C11×C22⋊C4—22no—
243C11×C22⋊C4—22no—
244C11×C22⋊C4—22no—
245C11×C22⋊C4—41no—
246C11×C22⋊C4—41no—
247C11×C22⋊C4—41no—
248C11×C22⋊C4—41no—
249C11×C22⋊C4—41no—
250C11×C22⋊C4—41no—
251C42×C11—21no—
252C42×C11—21no—
253C42×C11—21no—
254C42×C11—21no—
255C42×C11—21no—
256C42×C11—21no—
257C2×#436C2×C1111yescharacteristic, complemented
258C2×#408C2×C1111yescharacteristic, complemented
259#2388C2×C1111yescharacteristic
260#1955C2×C1111yescharacteristic, complemented
261#1954C2×C1111yescharacteristic, complemented
262#1924C2×C1111yescharacteristic, complemented
263#1923C2×C1111yescharacteristic, complemented
264#1923C2×C1111yescharacteristic, complemented
265#1923C2×C1111yescharacteristic, complemented
266#1870C2×C1111yescharacteristic, complemented
267#1870C2×C1111yescharacteristic, complemented
268#1869C2×C1111yescharacteristic, complemented
269#1850C2×C1111yescharacteristic, complemented
270#1780C2×C1111yescharacteristic, complemented
271#1753C2×C1111yescharacteristic, complemented
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
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×C11C4×D412yes—
300C23×C11C23×C411yescharacteristic
301Q8×C11—44no—
302D4×C11—44no—
303D4×C11—44no—
304D4×C11—44no—
305D4×C11—44no—
306D4×C11—44no—
307D4×C11—44no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
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—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×C11C4×D412yes—
352C2×C4×C11#13112yes—
353C2×C4×C11#13112yes—
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C2×#4111yescharacteristic
356C2×C4×C11H(5,𝔽2)11yescharacteristic
357C2×C4×C11H(5,𝔽2)11yescharacteristic
358C2×C4×C11H(5,𝔽2)11yescharacteristic
359C2×C4×C11H(5,𝔽2)11yescharacteristic
360C8×C11—22no—
361C8×C11—22no—
362C8×C11—41no—
363C8×C11—41no—
364C8×C11—41no—
365C8×C11—41no—
366C8×C11—41no—
367C8×C11—41no—
368C22×#41C22×C1111yescharacteristic
369C22×M16C22×C1111yescharacteristic
370C22×M16C22×C1111yescharacteristic
371C23×C8C22×C1111yescharacteristic
372C2×C4×D4C22×C1111yescharacteristic
373C2×C4×D4C22×C1111yescharacteristic
374C2×C4×D4C22×C1111yescharacteristic
375#436—24no—
376C2×C4⋊C8C22×C1111yescharacteristic
377C2×C4⋊C8C22×C1111yescharacteristic
378C2×C4⋊C8C22×C1111yescharacteristic
379#408—24no—
380C2×C22⋊C8C22×C1111yescharacteristic
381C2×C22⋊C8C22×C1111yescharacteristic
382C2×C22⋊C8C22×C1111yescharacteristic
383C2×C22⋊C8C22×C1111yescharacteristic
384C2×C22⋊C8C22×C1111yescharacteristic
385C2×C22⋊C8C22×C1111yescharacteristic
386C2×C22⋊C8C22×C1111yescharacteristic
387C2×C22⋊C8C22×C1111yescharacteristic
388C2×C22⋊C8C22×C1111yescharacteristic
389C2×C22⋊C8C22×C1111yescharacteristic
390C2×C22⋊C8C22×C1111yescharacteristic
391C2×C22⋊C8C22×C1111yescharacteristic
392C2×C22⋊C8C22×C1111yescharacteristic
393C2×#97C22×C1111yescharacteristic
394C2×C4×C8C22×C1111yescharacteristic
395C2×C4×C8C22×C1111yescharacteristic
396#395C4×C1111yescharacteristic
397#394C4×C1111yescharacteristic
398#394C4×C1111yescharacteristic
399#394C4×C1111yescharacteristic
400#393C4×C1111yescharacteristic
401#392C4×C1111yescharacteristic
402#392C4×C1111yescharacteristic
403#392C4×C1111yescharacteristic
404C4×C22⋊C4C22×C1111yescharacteristic
405C4×C22⋊C4C22×C1111yescharacteristic
406C4×C22⋊C4C22×C1111yescharacteristic
407#336C22×C1111yescharacteristic
408#336C22×C1111yescharacteristic
409#336C22×C1111yescharacteristic
410#336C22×C1111yescharacteristic
411#336C22×C1111yescharacteristic
412#336C22×C1111yescharacteristic
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—41no—
427C22×C11—41no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—41no—
431C22×C11—41no—
432C22×C11—41no—
433C22×C11—41no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11—41no—
438C22×C11—41no—
439C22×C11—41no—
440C22×C11—41no—
441C22×C11C2×C4×D411yescharacteristic
442C22×C11#51811yescharacteristic
443C22×C11#51811yescharacteristic
444C22×C11C2×#13111yescharacteristic
445C22×C11C2×#13111yescharacteristic
446C22×C11#56811yescharacteristic
447C22×C11#56811yescharacteristic
448C4×C11—22no—
449C4×C11—22no—
450C4×C11—22no—
451C4×C11—41no—
452C4×C11—41no—
453C4×C11—41no—
454C4×C11—41no—
455C4×C11—41no—
456C4×C11—41no—
457C4×C11—41no—
458C4×C11#53411yescharacteristic
459C4×C11#53511yescharacteristic
460C4×C11#53811yescharacteristic
461C4×C11#53811yescharacteristic
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—41no—
465C2×#41—41no—
466C2×#41—41no—
467C2×#41—41no—
468C22×Q8C2×C4×C1111yescharacteristic
469C22×D4C2×C4×C1111yescharacteristic
470C22×D4C2×C4×C1111yescharacteristic
471C22×D4C2×C4×C1111yescharacteristic
472C22×D4C2×C4×C1111yescharacteristic
473C22×D4C2×C4×C1111yescharacteristic
474C22×D4C2×C4×C1111yescharacteristic
475C23×C4C23×C1111yescharacteristic
476C23×C4C23×C1111yescharacteristic
477C23×C4C23×C1111yescharacteristic
478C23×C4C23×C1111yescharacteristic
479C2×M16—22no—
480C2×M16—41no—
481C2×M16—41no—
482C2×M16—41no—
483C2×M16—41no—
484C2×M16D4×C1114yescomplemented
485C22×C8—22no—
486C22×C8—41no—
487C22×C8—41no—
488C22×C8C23×C1111yescharacteristic
489C22×C8C23×C1111yescharacteristic
490C22×C8C23×C1111yescharacteristic
491C22×C8C23×C1111yescharacteristic
492C22×C8C23×C1111yescharacteristic
493C22×C8C23×C1111yescharacteristic
494C22×C8C23×C1111yescharacteristic
495C22×C8C23×C1111yescharacteristic
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—41no—
499C4×D4—41no—
500C4×D4—41no—
501C4×D4—41no—
502C2×C4⋊C4C2×C4×C1111yescharacteristic
503C2×C4⋊C4C2×C4×C1111yescharacteristic
504C2×C4⋊C4C2×C4×C1111yescharacteristic
505C2×C22⋊C4C2×C4×C1111yescharacteristic
506C2×C22⋊C4C2×C4×C1111yescharacteristic
507C2×C22⋊C4C2×C4×C1111yescharacteristic
508C2×C22⋊C4C2×C4×C1111yescharacteristic
509C2×C22⋊C4C2×C4×C1111yescharacteristic
510C2×C22⋊C4C2×C4×C1111yescharacteristic
511C2×C22⋊C4C2×C4×C1111yescharacteristic
512C2×C22⋊C4C2×C4×C1111yescharacteristic
513C2×C22⋊C4C2×C4×C1111yescharacteristic
514C2×C22⋊C4C2×C4×C1111yescharacteristic
515C2×C22⋊C4C2×C4×C1111yescharacteristic
516C2×C22⋊C4C2×C4×C1111yescharacteristic
517C2×C42C23×C1111yescharacteristic
518C2×C42C23×C1111yescharacteristic
519C2×C42C23×C1111yescharacteristic
520C4⋊C8—22no—
521C4⋊C8—41no—
522C4⋊C8—41no—
523C22⋊C8—22no—
524C22⋊C8—22no—
525C22⋊C8—22no—
526C22⋊C8—22no—
527C22⋊C8—22no—
528C22⋊C8—22no—
529C22⋊C8—22no—
530C22⋊C8—41no—
531C22⋊C8—41no—
532C22⋊C8—41no—
533C22⋊C8—41no—
534C22⋊C8—41no—
535C22⋊C8—41no—
536#97—41no—
537C4×C8—22no—
538C4×C8—41no—
539#95C2×C4×C1111yescharacteristic
540#95C2×C4×C1111yescharacteristic
541#95C2×C4×C1111yescharacteristic
542#95C2×C4×C1111yescharacteristic
543#95C2×C4×C1111yescharacteristic
544#95C2×C4×C1111yescharacteristic
545C2×C11—42no—
546C2×C11—81no—
547C2×C11—81no—
548C2×C11—81no—
549C2×C11#232111yescharacteristic
550C2×C11#293311yescharacteristic
551C2×C11#293511yescharacteristic
552C2×C11#297611yescharacteristic
553C2×C11#297811yescharacteristic
554C2×C11#297911yescharacteristic
555C2×C11#298111yescharacteristic
556C24C22×C4×C1111yescharacteristic
557C24C22×C4×C1111yescharacteristic
558C24C22×C4×C1111yescharacteristic
559C24C22×C4×C1111yescharacteristic
560#41—44no—
561#41—44no—
562#41—44no—
563#41—44no—
564C2×Q8—22no—
565C2×Q8—41no—
566C2×Q8—41no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
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×C4C22×C4×C1111yescharacteristic
608C22×C4C22×C4×C1111yescharacteristic
609C22×C4C22×C4×C1111yescharacteristic
610C22×C4C22×C4×C1111yescharacteristic
611C22×C4C22×C4×C1111yescharacteristic
612C22×C4C22×C4×C1111yescharacteristic
613C22×C4C22×C4×C1111yescharacteristic
614C22×C4C22×C4×C1111yescharacteristic
615C22×C4C22×C4×C1111yescharacteristic
616C22×C4C22×C4×C1111yescharacteristic
617C22×C4C2×D4×C1112yes—
618C22×C4C11×#4112yes—
619C22×C4C24×C1111yescharacteristic
620M16—44no—
621M16—44no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—44no—
645C2×C8C2×D4×C1112yes—
646C2×C8C2×D4×C1112yes—
647C4⋊C4—22no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—41no—
657C22⋊C4—41no—
658C22⋊C4—41no—
659C22⋊C4—41no—
660C22⋊C4—41no—
661C22⋊C4—41no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C11#2203911yescharacteristic, direct product factor, Sylow
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23C4×D4×C1112yes—
697C23C23×C4×C1111yescharacteristic
698Q8—44no—
699D4—44no—
700D4—44no—
701D4—44no—
702D4—44no—
703D4—44no—
704D4—44no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4C4×D4×C1112yes—
749C2×C4C11×#13112yes—
750C2×C4C11×#13112yes—
751C2×C4C22×D4×C1111yescharacteristic
752C2×C4C2×C11×#4111yescharacteristic
753C2×C4C11×H(5,𝔽2)11yescharacteristic
754C2×C4C11×H(5,𝔽2)11yescharacteristic
755C2×C4C11×H(5,𝔽2)11yescharacteristic
756C2×C4C11×H(5,𝔽2)11yescharacteristic
757C8—22no—
758C8—22no—
759C8—41no—
760C8—41no—
761C8—41no—
762C8—41no—
763C8—41no—
764C8—41no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22C2×C4×D4×C1111yescharacteristic
794C22C11×#51811yescharacteristic
795C22C11×#51811yescharacteristic
796C22C2×C11×#13111yescharacteristic
797C22C2×C11×#13111yescharacteristic
798C22C11×#56811yescharacteristic
799C22C11×#56811yescharacteristic
800C4—22no—
801C4—22no—
802C4—22no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4C11×#53411yescharacteristic
811C4C11×#53511yescharacteristic
812C4C11×#53811yescharacteristic
813C4C11×#53811yescharacteristic
814C2—42no—
815C2—81no—
816C2—81no—
817C2—81no—
818C2C11×#232111yescharacteristic
819C2C11×#293311yescharacteristic
820C2C11×#293511yescharacteristic
821C2C11×#297611yescharacteristic
822C2C11×#297811yescharacteristic
823C2C11×#297911yescharacteristic
824C2C11×#298111yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC11×#2388C2
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×#436C2semidirect
2. C2×C11×#408C2semidirect
4. C11×#1955C2semidirect
5. C11×#1954C2semidirect
6. C11×#1924C2semidirect
7. C11×#1923C2semidirect
8. C11×#1923C2semidirect
9. C11×#1923C2semidirect
10. C11×#1870C2semidirect
11. C11×#1870C2semidirect
12. C11×#1869C2semidirect
13. C11×#1850C2semidirect
14. C11×#1780C2semidirect
15. C11×#1753C2semidirect
83. C2×C11×M16D4semidirect
144. #22039C11direct (N × H)
257. C2×#436C2×C11semidirect
258. C2×#408C2×C11semidirect
260. #1955C2×C11semidirect
261. #1954C2×C11semidirect
262. #1924C2×C11semidirect
263. #1923C2×C11semidirect
264. #1923C2×C11semidirect
265. #1923C2×C11semidirect
266. #1870C2×C11semidirect
267. #1870C2×C11semidirect
268. #1869C2×C11semidirect
269. #1850C2×C11semidirect
270. #1780C2×C11semidirect
271. #1753C2×C11semidirect
484. C2×M16D4×C11semidirect
668. C11#22039direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4362
C2×C11×#4082
C11×#23882
C11×#19552
C11×#19542
C11×#19242
C11×#19232
C11×#18702
C11×#18692
C11×#18502
C11×#17802
C11×#17532
#2203911