Finite Group Databasebeta

← C11×#22472 #14599665

Subgroups — C11×#22472 #14599665

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#529C211yesmaximal, characteristic
2C2×C11×#436C211yesmaximal, characteristic, complemented
3C2×C11×#435C211yesmaximal, characteristic, complemented
4C11×#1985C211yesmaximal, characteristic, complemented
5C11×#1984C211yesmaximal, characteristic, complemented
6C11×#1870C211yesmaximal, characteristic, complemented
7C11×#1870C211yesmaximal, characteristic, complemented
8C11×#1870C211yesmaximal, characteristic, complemented
9C11×#1869C211yesmaximal, characteristic, complemented
10C11×#1818C211yesmaximal, characteristic, complemented
11C11×#1817C211yesmaximal, characteristic, complemented
12C11×#1798C211yesmaximal, characteristic, complemented
13C11×#1750C211yesmaximal, characteristic, complemented
14C11×#1729C211yesmaximal, characteristic, complemented
15C11×#1728C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C11×#529—24no—
21C11×#529—24no—
22C2×C11×#126C411yescharacteristic
23C2×C11×#126C411yescharacteristic
24C2×C11×#125C411yescharacteristic
25C2×C11×#124C411yescharacteristic
26C2×C11×#123C411yescharacteristic
27C2×C11×#123C411yescharacteristic
28C2×C11×C22⋊Q8C411yescharacteristic
29C2×C11×#121C411yescharacteristic
30C2×C4×Q8×C11C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C2×C4×D4×C11C2211yescharacteristic
33C2×C4×D4×C11C2211yescharacteristic
34C2×C11×#117C2211yescharacteristic
35C2×C11×#117C2211yescharacteristic
36C22×C42×C11C2211yescharacteristic
37C11×#436—24no—
38C11×#435—24no—
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×C4⋊C8C2211yescharacteristic
41C2×C11×C22⋊C8C2211yescharacteristic
42C2×C11×C22⋊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×#97C2211yescharacteristic
50C2×C4×C8×C11C2211yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
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—22no—
74C2×C11×M16—22no—
75C2×C11×M16—22no—
76C2×C11×M16—22no—
77C2×C11×M16—22no—
78C2×C11×M16—41no—
79C2×C11×M16—41no—
80C2×C11×M16—41no—
81C22×C8×C11—22no—
82C22×C8×C11—22no—
83C22×C8×C11—41no—
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C11×#126—24no—
93C11×#126—24no—
94C11×#125—24no—
95C11×#124—24no—
96C11×#123—24no—
97C11×#123—24no—
98C11×C22⋊Q8—24no—
99C11×#121—24no—
100C4×Q8×C11—22no—
101C4×Q8×C11—22no—
102C4×D4×C11—22no—
103C4×D4×C11—22no—
104C4×D4×C11—22no—
105C4×D4×C11—22no—
106C4×D4×C11D414yes—
107C4×D4×C11D414yes—
108C11×#117—22no—
109C11×#117—22no—
110C11×#117—22no—
111C11×#117—22no—
112C2×C11×C4⋊C4C2×C411yescharacteristic
113C2×C11×C4⋊C4C2×C411yescharacteristic
114C2×C11×C4⋊C4C2×C411yescharacteristic
115C2×C11×C4⋊C4C2×C411yescharacteristic
116C2×C11×C4⋊C4C2×C411yescharacteristic
117C2×C11×C4⋊C4C2×C411yescharacteristic
118C2×C11×C4⋊C4C2×C411yescharacteristic
119C2×C11×C4⋊C4C2×C411yescharacteristic
120C2×C11×C4⋊C4C2×C411yescharacteristic
121C2×C11×C4⋊C4C2×C411yescharacteristic
122C2×C11×C22⋊C4C2×C411yescharacteristic
123C2×C11×C22⋊C4C2×C411yescharacteristic
124C2×C11×C22⋊C4C2×C411yescharacteristic
125C2×C11×C22⋊C4C2×C411yescharacteristic
126C2×C11×C22⋊C4C2×C411yescharacteristic
127C2×C11×C22⋊C4C2×C411yescharacteristic
128C2×C11×C22⋊C4C2×C411yescharacteristic
129C2×C11×C22⋊C4C2×C411yescharacteristic
130C2×C11×C22⋊C4C2×C411yescharacteristic
131C2×C11×C22⋊C4C2×C411yescharacteristic
132C2×C42×C11—22no—
133C2×C42×C11—22no—
134C2×C42×C11C2×C411yescharacteristic
135C2×C42×C11C2×C411yescharacteristic
136C2×C42×C11C2311yescharacteristic
137C2×C42×C11C2311yescharacteristic
138C2×C42×C11C2311yescharacteristic
139C2×C42×C11C2311yescharacteristic
140C11×C4⋊C8—22no—
141C11×C4⋊C8—22no—
142C11×C22⋊C8—22no—
143C11×C22⋊C8—22no—
144C11×C22⋊C8—22no—
145C11×C22⋊C8—22no—
146C11×C22⋊C8—22no—
147C11×C22⋊C8—22no—
148C11×C22⋊C8—41no—
149C11×C22⋊C8—41no—
150C11×#97—22no—
151C4×C8×C11—22no—
152#22472C1111yesmaximal, 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—41no—
163C2×D4×C11—41no—
164C2×D4×C11—41no—
165C2×D4×C11—41no—
166C2×D4×C11—41no—
167C2×D4×C11C22⋊C414yes—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
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—41no—
186C22×C4×C11—41no—
187C22×C4×C11—41no—
188C22×C4×C11C22×C411yescharacteristic
189C22×C4×C11C22×C411yescharacteristic
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×C11C2×D412yes—
200C22×C4×C11C2×D412yes—
201C22×C4×C11C2×D412yes—
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2411yescharacteristic
204C11×M16—44no—
205C11×M16—44no—
206C11×M16—44no—
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—
230C2×C8×C11#4112yes—
231C2×C8×C11#4112yes—
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⋊C4—22no—
239C11×C4⋊C4—22no—
240C11×C4⋊C4—22no—
241C11×C4⋊C4C22⋊C414yes—
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⋊C4—22no—
249C11×C22⋊C4—22no—
250C11×C22⋊C4C22⋊C414yes—
251C11×C22⋊C4C22⋊C414yes—
252C42×C11—22no—
253C42×C11—22no—
254C42×C11—21no—
255C42×C11—21no—
256C42×C11—21no—
257C42×C11—21no—
258C42×C11—21no—
259C42×C11—21no—
260C42×C11C2×D412yes—
261C42×C11C2×D412yes—
262C2×#529C2×C1111yescharacteristic
263C2×#436C2×C1111yescharacteristic, complemented
264C2×#435C2×C1111yescharacteristic, complemented
265#1985C2×C1111yescharacteristic, complemented
266#1984C2×C1111yescharacteristic, complemented
267#1870C2×C1111yescharacteristic, complemented
268#1870C2×C1111yescharacteristic, complemented
269#1870C2×C1111yescharacteristic, complemented
270#1869C2×C1111yescharacteristic, complemented
271#1818C2×C1111yescharacteristic, complemented
272#1817C2×C1111yescharacteristic, complemented
273#1798C2×C1111yescharacteristic, complemented
274#1750C2×C1111yescharacteristic, complemented
275#1729C2×C1111yescharacteristic, complemented
276#1728C2×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×C11C2×C22⋊C412yes—
297C23×C11C2×C22⋊C412yes—
298C23×C11C23×C411yescharacteristic
299Q8×C11—44no—
300D4×C11—44no—
301D4×C11—44no—
302D4×C11—44no—
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—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
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—44no—
340C2×C4×C11—44no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11C2×C22⋊C412yes—
346C2×C4×C11C2×C22⋊C412yes—
347C2×C4×C11C2×C22⋊C412yes—
348C2×C4×C11C2×C22⋊C412yes—
349C2×C4×C11#13112yes—
350C2×C4×C11C22×D411yescharacteristic
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11C2×#4111yescharacteristic
353C2×C4×C11C2×#4111yescharacteristic
354C2×C4×C11H(5,𝔽2)11yescharacteristic
355C2×C4×C112−1+411yescharacteristic
356C8×C11—22no—
357C8×C11—22no—
358C8×C11—41no—
359C8×C11—41no—
360C8×C11—41no—
361C8×C11—41no—
362C8×C11—41no—
363C8×C11—41no—
364C22×M16C22×C1111yescharacteristic
365C22×M16C22×C1111yescharacteristic
366C22×M16C22×C1111yescharacteristic
367C23×C8C22×C1111yescharacteristic
368#529—24no—
369#529—24no—
370C2×#126C4×C1111yescharacteristic
371C2×#126C4×C1111yescharacteristic
372C2×#125C4×C1111yescharacteristic
373C2×#124C4×C1111yescharacteristic
374C2×#123C4×C1111yescharacteristic
375C2×#123C4×C1111yescharacteristic
376C2×C22⋊Q8C4×C1111yescharacteristic
377C2×#121C4×C1111yescharacteristic
378C2×C4×Q8C22×C1111yescharacteristic
379C2×C4×D4C22×C1111yescharacteristic
380C2×C4×D4C22×C1111yescharacteristic
381C2×C4×D4C22×C1111yescharacteristic
382C2×#117C22×C1111yescharacteristic
383C2×#117C22×C1111yescharacteristic
384C22×C42C22×C1111yescharacteristic
385#436—24no—
386#435—24no—
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×#97C22×C1111yescharacteristic
398C2×C4×C8C22×C1111yescharacteristic
399#336C22×C1111yescharacteristic
400#336C22×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
409#336C22×C1111yescharacteristic
410#336C22×C1111yescharacteristic
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—22no—
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×C11C22×C22⋊C411yescharacteristic
433C22×C11C4×#4111yescharacteristic
434C22×C11#52011yescharacteristic
435C22×C11C2×#13111yescharacteristic
436C22×C11#56811yescharacteristic
437C22×C11#56811yescharacteristic
438C22×C11#56811yescharacteristic
439C4×C11—22no—
440C4×C11—22no—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—22no—
444C4×C11—41no—
445C4×C11—41no—
446C4×C11—41no—
447C4×C11—41no—
448C4×C11—41no—
449C4×C11—41no—
450C4×C11#54611yescharacteristic
451C4×C11#54611yescharacteristic
452C4×C11#54711yescharacteristic
453C4×C11#54711yescharacteristic
454C22×Q8C2×C4×C1111yescharacteristic
455C22×D4C2×C4×C1111yescharacteristic
456C22×D4C2×C4×C1111yescharacteristic
457C22×D4C2×C4×C1111yescharacteristic
458C23×C4C2×C4×C1111yescharacteristic
459C23×C4C2×C4×C1111yescharacteristic
460C23×C4C23×C1111yescharacteristic
461C23×C4C23×C1111yescharacteristic
462C23×C4C23×C1111yescharacteristic
463C2×M16—22no—
464C2×M16—22no—
465C2×M16—22no—
466C2×M16—22no—
467C2×M16—22no—
468C2×M16—22no—
469C2×M16—41no—
470C2×M16—41no—
471C2×M16—41no—
472C22×C8—22no—
473C22×C8—22no—
474C22×C8—41no—
475C22×C8C23×C1111yescharacteristic
476C22×C8C23×C1111yescharacteristic
477C22×C8C23×C1111yescharacteristic
478C22×C8C23×C1111yescharacteristic
479C22×C8C23×C1111yescharacteristic
480C22×C8C23×C1111yescharacteristic
481C22×C8C23×C1111yescharacteristic
482C22×C8C23×C1111yescharacteristic
483#126—24no—
484#126—24no—
485#125—24no—
486#124—24no—
487#123—24no—
488#123—24no—
489C22⋊Q8—24no—
490#121—24no—
491C4×Q8—22no—
492C4×Q8—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4D4×C1114yes—
498C4×D4D4×C1114yes—
499#117—22no—
500#117—22no—
501#117—22no—
502#117—22no—
503C2×C4⋊C4C2×C4×C1111yescharacteristic
504C2×C4⋊C4C2×C4×C1111yescharacteristic
505C2×C4⋊C4C2×C4×C1111yescharacteristic
506C2×C4⋊C4C2×C4×C1111yescharacteristic
507C2×C4⋊C4C2×C4×C1111yescharacteristic
508C2×C4⋊C4C2×C4×C1111yescharacteristic
509C2×C4⋊C4C2×C4×C1111yescharacteristic
510C2×C4⋊C4C2×C4×C1111yescharacteristic
511C2×C4⋊C4C2×C4×C1111yescharacteristic
512C2×C4⋊C4C2×C4×C1111yescharacteristic
513C2×C22⋊C4C2×C4×C1111yescharacteristic
514C2×C22⋊C4C2×C4×C1111yescharacteristic
515C2×C22⋊C4C2×C4×C1111yescharacteristic
516C2×C22⋊C4C2×C4×C1111yescharacteristic
517C2×C22⋊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×C42—22no—
524C2×C42—22no—
525C2×C42C2×C4×C1111yescharacteristic
526C2×C42C2×C4×C1111yescharacteristic
527C2×C42C23×C1111yescharacteristic
528C2×C42C23×C1111yescharacteristic
529C2×C42C23×C1111yescharacteristic
530C2×C42C23×C1111yescharacteristic
531C4⋊C8—22no—
532C4⋊C8—22no—
533C22⋊C8—22no—
534C22⋊C8—22no—
535C22⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—41no—
540C22⋊C8—41no—
541#97—22no—
542C4×C8—22no—
543C2×C11—42no—
544C2×C11—42no—
545C2×C11—81no—
546C2×C11#233911yescharacteristic
547C2×C11#287911yescharacteristic
548C2×C11#288011yescharacteristic
549C2×C11#296711yescharacteristic
550C2×C11#296911yescharacteristic
551C2×C11#299311yescharacteristic
552C2×C11#299511yescharacteristic
553C24C22×C4×C1111yescharacteristic
554C24C22×C4×C1111yescharacteristic
555C24C22×C4×C1111yescharacteristic
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—41no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C2×D4C11×C22⋊C414yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—41no—
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×C4C2×D4×C1112yes—
602C22×C4C2×D4×C1112yes—
603C22×C4C24×C1111yescharacteristic
604M16—44no—
605M16—44no—
606M16—44no—
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—21no—
628C2×C8—21no—
629C2×C8—44no—
630C2×C8C11×#4112yes—
631C2×C8C11×#4112yes—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4C11×C22⋊C414yes—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4C11×C22⋊C414yes—
651C22⋊C4C11×C22⋊C414yes—
652C42—22no—
653C42—22no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42C2×D4×C1112yes—
661C42C2×D4×C1112yes—
662C11#2247211yescharacteristic, direct product factor, Sylow
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—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23C2×C11×C22⋊C412yes—
683C23C2×C11×C22⋊C412yes—
684C23C23×C4×C1111yescharacteristic
685Q8—44no—
686D4—44no—
687D4—44no—
688D4—44no—
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—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
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—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—44no—
726C2×C4—44no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4C2×C11×C22⋊C412yes—
732C2×C4C2×C11×C22⋊C412yes—
733C2×C4C2×C11×C22⋊C412yes—
734C2×C4C2×C11×C22⋊C412yes—
735C2×C4C11×#13112yes—
736C2×C4C22×D4×C1111yescharacteristic
737C2×C4C22×D4×C1111yescharacteristic
738C2×C4C2×C11×#4111yescharacteristic
739C2×C4C2×C11×#4111yescharacteristic
740C2×C4C11×H(5,𝔽2)11yescharacteristic
741C2×C4C11×2−1+411yescharacteristic
742C8—22no—
743C8—22no—
744C8—41no—
745C8—41no—
746C8—41no—
747C8—41no—
748C8—41no—
749C8—41no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22C22×C11×C22⋊C411yescharacteristic
772C22C4×C11×#4111yescharacteristic
773C22C11×#52011yescharacteristic
774C22C2×C11×#13111yescharacteristic
775C22C11×#56811yescharacteristic
776C22C11×#56811yescharacteristic
777C22C11×#56811yescharacteristic
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—22no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4C11×#54611yescharacteristic
790C4C11×#54611yescharacteristic
791C4C11×#54711yescharacteristic
792C4C11×#54711yescharacteristic
793C2—42no—
794C2—42no—
795C2—81no—
796C2C11×#233911yescharacteristic
797C2C11×#287911yescharacteristic
798C2C11×#288011yescharacteristic
799C2C11×#296711yescharacteristic
800C2C11×#296911yescharacteristic
801C2C11×#299311yescharacteristic
802C2C11×#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×#436C2semidirect
3. C2×C11×#435C2semidirect
4. C11×#1985C2semidirect
5. C11×#1984C2semidirect
6. C11×#1870C2semidirect
7. C11×#1870C2semidirect
8. C11×#1870C2semidirect
9. C11×#1869C2semidirect
10. C11×#1818C2semidirect
11. C11×#1817C2semidirect
12. C11×#1798C2semidirect
13. C11×#1750C2semidirect
14. C11×#1729C2semidirect
15. C11×#1728C2semidirect
152. #22472C11direct (N × H)
263. C2×#436C2×C11semidirect
264. C2×#435C2×C11semidirect
265. #1985C2×C11semidirect
266. #1984C2×C11semidirect
267. #1870C2×C11semidirect
268. #1870C2×C11semidirect
269. #1870C2×C11semidirect
270. #1869C2×C11semidirect
271. #1818C2×C11semidirect
272. #1817C2×C11semidirect
273. #1798C2×C11semidirect
274. #1750C2×C11semidirect
275. #1729C2×C11semidirect
276. #1728C2×C11semidirect
662. C11#22472direct (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×#4362
C2×C11×#4352
C11×#19852
C11×#19842
C11×#18702
C11×#18692
C11×#18182
C11×#18172
C11×#17982
C11×#17502
C11×#17292
C11×#17282
#2247211