Finite Group Databasebeta

← C11×#21855 #14599048

Subgroups — C11×#21855 #14599048

Order 2816.

1128 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#529C211yesmaximal, characteristic
2C2×C11×#433C211yesmaximal, characteristic, complemented
3C2×C11×#424C211yesmaximal, characteristic, complemented
4C11×#1985C211yesmaximal, characteristic, complemented
5C11×#1984C211yesmaximal, characteristic, complemented
6C11×#1955C211yesmaximal, characteristic, complemented
7C11×#1954C211yesmaximal, characteristic, complemented
8C11×#1870C211yesmaximal, characteristic, complemented
9C11×#1870C211yesmaximal, characteristic, complemented
10C11×#1869C211yesmaximal, characteristic, complemented
11C11×#1869C211yesmaximal, characteristic, complemented
12C11×#1798C211yesmaximal, characteristic, complemented
13C11×#1798C211yesmaximal, characteristic, complemented
14C11×#1797C211yesmaximal, characteristic, complemented
15C11×#1797C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C11×#529—24no—
19C11×#529—24no—
20C2×C11×#126C411yescharacteristic
21C2×C11×#126C411yescharacteristic
22C2×C11×#125C411yescharacteristic
23C2×C11×#124C411yescharacteristic
24C2×C11×#123C411yescharacteristic
25C2×C11×#123C411yescharacteristic
26C2×C11×C22⋊Q8C411yescharacteristic
27C2×C11×#121C411yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C4×D4×C11C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C2×C11×#117C2211yescharacteristic
33C2×C11×#117C2211yescharacteristic
34C22×C42×C11C2211yescharacteristic
35C11×#433—24no—
36C11×#424—24no—
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×C4⋊C8C2211yescharacteristic
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×C4⋊C8C2211yescharacteristic
43C2×C11×C22⋊C8C2211yescharacteristic
44C2×C11×C22⋊C8C2211yescharacteristic
45C2×C11×C22⋊C8C2211yescharacteristic
46C2×C11×C22⋊C8C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic
49C2×C11×C22⋊C8C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×#97C2211yescharacteristic
54C2×C4×C8×C11C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C22×Q8×C11C2×C411yescharacteristic
64C22×D4×C11C2×C411yescharacteristic
65C22×D4×C11C2×C411yescharacteristic
66C22×D4×C11C2×C411yescharacteristic
67C23×C4×C11C2×C411yescharacteristic
68C23×C4×C11C2×C411yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C2×C11×M16—22no—
73C2×C11×M16—41no—
74C2×C11×M16—41no—
75C22×C8×C11—22no—
76C22×C8×C11—41no—
77C22×C8×C11—41no—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C11×#126—24no—
87C11×#126—24no—
88C11×#125—24no—
89C11×#124—24no—
90C11×#123—24no—
91C11×#123—24no—
92C11×C22⋊Q8—24no—
93C11×#121—24no—
94C4×Q8×C11—22no—
95C4×Q8×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C4×D4×C11—22no—
101C4×D4×C11—22no—
102C11×#117—22no—
103C11×#117—22no—
104C11×#117D414yes—
105C11×#117D414yes—
106C2×C11×C4⋊C4C2×C411yescharacteristic
107C2×C11×C4⋊C4C2×C411yescharacteristic
108C2×C11×C4⋊C4C2×C411yescharacteristic
109C2×C11×C4⋊C4C2×C411yescharacteristic
110C2×C11×C4⋊C4C2×C411yescharacteristic
111C2×C11×C4⋊C4C2×C411yescharacteristic
112C2×C11×C4⋊C4C2×C411yescharacteristic
113C2×C11×C4⋊C4C2×C411yescharacteristic
114C2×C11×C4⋊C4C2×C411yescharacteristic
115C2×C11×C4⋊C4C2×C411yescharacteristic
116C2×C11×C22⋊C4C2×C411yescharacteristic
117C2×C11×C22⋊C4C2×C411yescharacteristic
118C2×C11×C22⋊C4C2×C411yescharacteristic
119C2×C11×C22⋊C4C2×C411yescharacteristic
120C2×C11×C22⋊C4C2×C411yescharacteristic
121C2×C11×C22⋊C4C2×C411yescharacteristic
122C2×C11×C22⋊C4C2×C411yescharacteristic
123C2×C11×C22⋊C4C2×C411yescharacteristic
124C2×C11×C22⋊C4C2×C411yescharacteristic
125C2×C11×C22⋊C4C2×C411yescharacteristic
126C2×C42×C11—22no—
127C2×C42×C11—22no—
128C2×C42×C11C2×C411yescharacteristic
129C2×C42×C11C2×C411yescharacteristic
130C2×C42×C11C2311yescharacteristic
131C2×C42×C11C2311yescharacteristic
132C2×C42×C11C2311yescharacteristic
133C2×C42×C11C2311yescharacteristic
134C11×C4⋊C8—22no—
135C11×C4⋊C8—22no—
136C11×C4⋊C8—22no—
137C11×C4⋊C8—22no—
138C11×C4⋊C8—22no—
139C11×C4⋊C8—22no—
140C11×C22⋊C8—22no—
141C11×C22⋊C8—22no—
142C11×C22⋊C8—41no—
143C11×C22⋊C8—41no—
144C11×C22⋊C8—41no—
145C11×C22⋊C8—41no—
146C11×C22⋊C8—41no—
147C11×C22⋊C8—41no—
148C11×C22⋊C8—41no—
149C11×C22⋊C8—41no—
150C11×#97—22no—
151C4×C8×C11—22no—
152#21855C1111yesmaximal, characteristic, direct product factor, Sylow
153C24×C11C22×C411yescharacteristic
154C24×C11C22×C411yescharacteristic
155C24×C11C22×C411yescharacteristic
156C2×Q8×C11—22no—
157C2×Q8×C11—22no—
158C2×Q8×C11—41no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—22no—
162C2×D4×C11—22no—
163C2×D4×C11—22no—
164C2×D4×C11—22no—
165C2×D4×C11—41no—
166C2×D4×C11—41no—
167C2×D4×C11—41no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
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—41no—
189C22×C4×C11—41no—
190C22×C4×C11C22×C411yescharacteristic
191C22×C4×C11C22×C411yescharacteristic
192C22×C4×C11C22×C411yescharacteristic
193C22×C4×C11C22×C411yescharacteristic
194C22×C4×C11C22×C411yescharacteristic
195C22×C4×C11C22×C411yescharacteristic
196C22×C4×C11C22×C411yescharacteristic
197C22×C4×C11C22×C411yescharacteristic
198C22×C4×C11C22×C411yescharacteristic
199C22×C4×C11C22×C411yescharacteristic
200C22×C4×C11C22×C411yescharacteristic
201C22×C4×C11C2×D412yes—
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2411yescharacteristic
204C11×M16—44no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
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—44no—
230C11×C4⋊C4—22no—
231C11×C4⋊C4—22no—
232C11×C4⋊C4—22no—
233C11×C4⋊C4—22no—
234C11×C4⋊C4—22no—
235C11×C4⋊C4—22no—
236C11×C4⋊C4—22no—
237C11×C4⋊C4—22no—
238C11×C4⋊C4C22⋊C414yes—
239C11×C4⋊C4C22⋊C414yes—
240C11×C22⋊C4—22no—
241C11×C22⋊C4—22no—
242C11×C22⋊C4—22no—
243C11×C22⋊C4—22no—
244C11×C22⋊C4—22no—
245C11×C22⋊C4—22no—
246C11×C22⋊C4—22no—
247C11×C22⋊C4—22no—
248C11×C22⋊C4C22⋊C414yes—
249C11×C22⋊C4C22⋊C414yes—
250C42×C11—22no—
251C42×C11—22no—
252C42×C11—21no—
253C42×C11—21no—
254C42×C11—21no—
255C42×C11—21no—
256C42×C11C2×D412yes—
257C42×C11C2×D412yes—
258C42×C11C2×D412yes—
259C42×C11C2×D412yes—
260C2×#529C2×C1111yescharacteristic
261C2×#433C2×C1111yescharacteristic, complemented
262C2×#424C2×C1111yescharacteristic, complemented
263#1985C2×C1111yescharacteristic, complemented
264#1984C2×C1111yescharacteristic, complemented
265#1955C2×C1111yescharacteristic, complemented
266#1954C2×C1111yescharacteristic, complemented
267#1870C2×C1111yescharacteristic, complemented
268#1870C2×C1111yescharacteristic, complemented
269#1869C2×C1111yescharacteristic, complemented
270#1869C2×C1111yescharacteristic, complemented
271#1798C2×C1111yescharacteristic, complemented
272#1798C2×C1111yescharacteristic, complemented
273#1797C2×C1111yescharacteristic, complemented
274#1797C2×C1111yescharacteristic, complemented
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×C11C2×C22⋊C412yes—
295C23×C11#13112yes—
296C23×C11C23×C411yescharacteristic
297Q8×C11—44no—
298D4×C11—44no—
299D4×C11—44no—
300D4×C11—44no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—21no—
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—44no—
333C2×C4×C11—44no—
334C2×C4×C11—41no—
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×C11C2×C22⋊C412yes—
343C2×C4×C11C2×C22⋊C412yes—
344C2×C4×C11C2×C22⋊C412yes—
345C2×C4×C11C2×C22⋊C412yes—
346C2×C4×C11C2×C22⋊C412yes—
347C2×C4×C11#13112yes—
348C2×C4×C11C22×D411yescharacteristic
349C2×C4×C11C22×D411yescharacteristic
350C2×C4×C11H(5,𝔽2)11yescharacteristic
351C2×C4×C11H(5,𝔽2)11yescharacteristic
352C2×C4×C112−1+411yescharacteristic
353C2×C4×C112−1+411yescharacteristic
354C8×C11—41no—
355C8×C11—41no—
356C8×C11—41no—
357C8×C11—41no—
358C8×C11—41no—
359C8×C11—41no—
360C8×C11—41no—
361C8×C11—41no—
362C22×M16C22×C1111yescharacteristic
363C23×C8C22×C1111yescharacteristic
364#529—24no—
365#529—24no—
366C2×#126C4×C1111yescharacteristic
367C2×#126C4×C1111yescharacteristic
368C2×#125C4×C1111yescharacteristic
369C2×#124C4×C1111yescharacteristic
370C2×#123C4×C1111yescharacteristic
371C2×#123C4×C1111yescharacteristic
372C2×C22⋊Q8C4×C1111yescharacteristic
373C2×#121C4×C1111yescharacteristic
374C2×C4×Q8C22×C1111yescharacteristic
375C2×C4×D4C22×C1111yescharacteristic
376C2×C4×D4C22×C1111yescharacteristic
377C2×C4×D4C22×C1111yescharacteristic
378C2×#117C22×C1111yescharacteristic
379C2×#117C22×C1111yescharacteristic
380C22×C42C22×C1111yescharacteristic
381#433—24no—
382#424—24no—
383C2×C4⋊C8C22×C1111yescharacteristic
384C2×C4⋊C8C22×C1111yescharacteristic
385C2×C4⋊C8C22×C1111yescharacteristic
386C2×C4⋊C8C22×C1111yescharacteristic
387C2×C4⋊C8C22×C1111yescharacteristic
388C2×C4⋊C8C22×C1111yescharacteristic
389C2×C22⋊C8C22×C1111yescharacteristic
390C2×C22⋊C8C22×C1111yescharacteristic
391C2×C22⋊C8C22×C1111yescharacteristic
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×#97C22×C1111yescharacteristic
400C2×C4×C8C22×C1111yescharacteristic
401#336C22×C1111yescharacteristic
402#336C22×C1111yescharacteristic
403#336C22×C1111yescharacteristic
404#336C22×C1111yescharacteristic
405#336C22×C1111yescharacteristic
406#336C22×C1111yescharacteristic
407#336C22×C1111yescharacteristic
408#336C22×C1111yescharacteristic
409C22×C11—22no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—41no—
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×C11C22×C22⋊C411yescharacteristic
431C22×C11#52011yescharacteristic
432C22×C11#52011yescharacteristic
433C22×C11C2×#13111yescharacteristic
434C22×C11C2×#13111yescharacteristic
435C22×C11#56811yescharacteristic
436C22×C11#56811yescharacteristic
437C4×C11—22no—
438C4×C11—22no—
439C4×C11—22no—
440C4×C11—22no—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—41no—
444C4×C11—41no—
445C4×C11—41no—
446C4×C11—41no—
447C4×C11—41no—
448C4×C11#53511yescharacteristic
449C4×C11#53611yescharacteristic
450C4×C11#53711yescharacteristic
451C4×C11#53711yescharacteristic
452C22×Q8C2×C4×C1111yescharacteristic
453C22×D4C2×C4×C1111yescharacteristic
454C22×D4C2×C4×C1111yescharacteristic
455C22×D4C2×C4×C1111yescharacteristic
456C23×C4C2×C4×C1111yescharacteristic
457C23×C4C2×C4×C1111yescharacteristic
458C23×C4C23×C1111yescharacteristic
459C23×C4C23×C1111yescharacteristic
460C23×C4C23×C1111yescharacteristic
461C2×M16—22no—
462C2×M16—41no—
463C2×M16—41no—
464C22×C8—22no—
465C22×C8—41no—
466C22×C8—41no—
467C22×C8C23×C1111yescharacteristic
468C22×C8C23×C1111yescharacteristic
469C22×C8C23×C1111yescharacteristic
470C22×C8C23×C1111yescharacteristic
471C22×C8C23×C1111yescharacteristic
472C22×C8C23×C1111yescharacteristic
473C22×C8C23×C1111yescharacteristic
474C22×C8C23×C1111yescharacteristic
475#126—24no—
476#126—24no—
477#125—24no—
478#124—24no—
479#123—24no—
480#123—24no—
481C22⋊Q8—24no—
482#121—24no—
483C4×Q8—22no—
484C4×Q8—22no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—22no—
491#117—22no—
492#117—22no—
493#117D4×C1114yes—
494#117D4×C1114yes—
495C2×C4⋊C4C2×C4×C1111yescharacteristic
496C2×C4⋊C4C2×C4×C1111yescharacteristic
497C2×C4⋊C4C2×C4×C1111yescharacteristic
498C2×C4⋊C4C2×C4×C1111yescharacteristic
499C2×C4⋊C4C2×C4×C1111yescharacteristic
500C2×C4⋊C4C2×C4×C1111yescharacteristic
501C2×C4⋊C4C2×C4×C1111yescharacteristic
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×C42—22no—
516C2×C42—22no—
517C2×C42C2×C4×C1111yescharacteristic
518C2×C42C2×C4×C1111yescharacteristic
519C2×C42C23×C1111yescharacteristic
520C2×C42C23×C1111yescharacteristic
521C2×C42C23×C1111yescharacteristic
522C2×C42C23×C1111yescharacteristic
523C4⋊C8—22no—
524C4⋊C8—22no—
525C4⋊C8—22no—
526C4⋊C8—22no—
527C4⋊C8—22no—
528C4⋊C8—22no—
529C22⋊C8—22no—
530C22⋊C8—22no—
531C22⋊C8—41no—
532C22⋊C8—41no—
533C22⋊C8—41no—
534C22⋊C8—41no—
535C22⋊C8—41no—
536C22⋊C8—41no—
537C22⋊C8—41no—
538C22⋊C8—41no—
539#97—22no—
540C4×C8—22no—
541C2×C11—42no—
542C2×C11—42no—
543C2×C11—81no—
544C2×C11#231111yescharacteristic
545C2×C11#288011yescharacteristic
546C2×C11#288011yescharacteristic
547C2×C11#299211yescharacteristic
548C2×C11#299311yescharacteristic
549C2×C11#299411yescharacteristic
550C2×C11#299511yescharacteristic
551C24C22×C4×C1111yescharacteristic
552C24C22×C4×C1111yescharacteristic
553C24C22×C4×C1111yescharacteristic
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—41no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—41no—
564C2×D4—41no—
565C2×D4—41no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4C22×C4×C1111yescharacteristic
589C22×C4C22×C4×C1111yescharacteristic
590C22×C4C22×C4×C1111yescharacteristic
591C22×C4C22×C4×C1111yescharacteristic
592C22×C4C22×C4×C1111yescharacteristic
593C22×C4C22×C4×C1111yescharacteristic
594C22×C4C22×C4×C1111yescharacteristic
595C22×C4C22×C4×C1111yescharacteristic
596C22×C4C22×C4×C1111yescharacteristic
597C22×C4C22×C4×C1111yescharacteristic
598C22×C4C22×C4×C1111yescharacteristic
599C22×C4C2×D4×C1112yes—
600C22×C4C2×D4×C1112yes—
601C22×C4C24×C1111yescharacteristic
602M16—44no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—44no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4C11×C22⋊C414yes—
637C4⋊C4C11×C22⋊C414yes—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4C11×C22⋊C414yes—
647C22⋊C4C11×C22⋊C414yes—
648C42—22no—
649C42—22no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42C2×D4×C1112yes—
655C42C2×D4×C1112yes—
656C42C2×D4×C1112yes—
657C42C2×D4×C1112yes—
658C11#2185511yescharacteristic, direct product factor, Sylow
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23C2×C11×C22⋊C412yes—
679C23C11×#13112yes—
680C23C23×C4×C1111yescharacteristic
681Q8—44no—
682D4—44no—
683D4—44no—
684D4—44no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4C2×C11×C22⋊C412yes—
727C2×C4C2×C11×C22⋊C412yes—
728C2×C4C2×C11×C22⋊C412yes—
729C2×C4C2×C11×C22⋊C412yes—
730C2×C4C2×C11×C22⋊C412yes—
731C2×C4C11×#13112yes—
732C2×C4C22×D4×C1111yescharacteristic
733C2×C4C22×D4×C1111yescharacteristic
734C2×C4C11×H(5,𝔽2)11yescharacteristic
735C2×C4C11×H(5,𝔽2)11yescharacteristic
736C2×C4C11×2−1+411yescharacteristic
737C2×C4C11×2−1+411yescharacteristic
738C8—41no—
739C8—41no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22C22×C11×C22⋊C411yescharacteristic
768C22C11×#52011yescharacteristic
769C22C11×#52011yescharacteristic
770C22C2×C11×#13111yescharacteristic
771C22C2×C11×#13111yescharacteristic
772C22C11×#56811yescharacteristic
773C22C11×#56811yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—22no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4C11×#53511yescharacteristic
786C4C11×#53611yescharacteristic
787C4C11×#53711yescharacteristic
788C4C11×#53711yescharacteristic
789C2—42no—
790C2—42no—
791C2—81no—
792C2C11×#231111yescharacteristic
793C2C11×#288011yescharacteristic
794C2C11×#288011yescharacteristic
795C2C11×#299211yescharacteristic
796C2C11×#299311yescharacteristic
797C2C11×#299411yescharacteristic
798C2C11×#299511yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC2×C11×#121C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#433C2semidirect
3. C2×C11×#424C2semidirect
4. C11×#1985C2semidirect
5. C11×#1984C2semidirect
6. C11×#1955C2semidirect
7. C11×#1954C2semidirect
8. C11×#1870C2semidirect
9. C11×#1870C2semidirect
10. C11×#1869C2semidirect
11. C11×#1869C2semidirect
12. C11×#1798C2semidirect
13. C11×#1798C2semidirect
14. C11×#1797C2semidirect
15. C11×#1797C2semidirect
152. #21855C11direct (N × H)
261. C2×#433C2×C11semidirect
262. C2×#424C2×C11semidirect
263. #1985C2×C11semidirect
264. #1984C2×C11semidirect
265. #1955C2×C11semidirect
266. #1954C2×C11semidirect
267. #1870C2×C11semidirect
268. #1870C2×C11semidirect
269. #1869C2×C11semidirect
270. #1869C2×C11semidirect
271. #1798C2×C11semidirect
272. #1798C2×C11semidirect
273. #1797C2×C11semidirect
274. #1797C2×C11semidirect
658. C11#21855direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5292
C2×C11×#4332
C2×C11×#4242
C11×#19852
C11×#19842
C11×#19552
C11×#19542
C11×#18702
C11×#18692
C11×#17982
C11×#17972
#2185511