Finite Group Databasebeta

← C11×#22470 #14599663

Subgroups — C11×#22470 #14599663

Order 2816.

1202 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×#435C211yesmaximal, characteristic, complemented
3C2×C8×D4×C11C211yesmaximal, characteristic, complemented
4C11×#1985C211yesmaximal, characteristic, complemented
5C11×#1984C211yesmaximal, characteristic, complemented
6C11×#1870C211yesmaximal, characteristic, complemented
7C11×#1869C211yesmaximal, characteristic, complemented
8C11×#1869C211yesmaximal, 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
15C2×C11×#336C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
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×#435—24no—
38C8×D4×C11—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—41no—
75C22×C8×C11—22no—
76C22×C8×C11—22no—
77C22×C8×C11—22no—
78C22×C8×C11—22no—
79C22×C8×C11—22no—
80C22×C8×C11—22no—
81C22×C8×C11—41no—
82C22×C8×C11—41no—
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#22470C1111yesmaximal, 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—22no—
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—22no—
180C22×C4×C11—22no—
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—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—
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—44no—
228C2×C8×C11—44no—
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×#435C2×C1111yescharacteristic, complemented
264C2×C8×D4C2×C1111yescharacteristic, complemented
265#1985C2×C1111yescharacteristic, complemented
266#1984C2×C1111yescharacteristic, complemented
267#1870C2×C1111yescharacteristic, complemented
268#1869C2×C1111yescharacteristic, complemented
269#1869C2×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
276C2×#336C2×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×C11C2×C22⋊C412yes—
295C23×C11C2×C22⋊C412yes—
296C23×C11#13112yes—
297C23×C11#13112yes—
298C23×C11C23×C411yescharacteristic
299Q8×C11—44no—
300D4×C11—28no—
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
365C23×C8C22×C1111yescharacteristic
366C23×C8C22×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#435—24no—
386C8×D4—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—22no—
418C22×C11—22no—
419C22×C11—22no—
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#40814yes—
432C22×C11C22×C22⋊C411yescharacteristic
433C22×C11C4×#4111yescharacteristic
434C22×C11#52011yescharacteristic
435C22×C11C2×#13111yescharacteristic
436C22×C11C2×#13111yescharacteristic
437C22×C11C2×#13111yescharacteristic
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—41no—
466C22×C8—22no—
467C22×C8—22no—
468C22×C8—22no—
469C22×C8—22no—
470C22×C8—22no—
471C22×C8—22no—
472C22×C8—41no—
473C22×C8—41no—
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—24no—
544C2×C11—42no—
545C2×C11—81no—
546C2×C11#233911yescharacteristic
547C2×C11C2×#40811yescharacteristic
548C2×C11#288011yescharacteristic
549C2×C11#296611yescharacteristic
550C2×C11#296811yescharacteristic
551C2×C11#299211yescharacteristic
552C2×C11#299411yescharacteristic
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—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
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—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
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—
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—
628C2×C8—44no—
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#2247011yescharacteristic, 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—
680C23C2×C11×C22⋊C412yes—
681C23C2×C11×C22⋊C412yes—
682C23C11×#13112yes—
683C23C11×#13112yes—
684C23C23×C4×C1111yescharacteristic
685Q8—44no—
686D4—28no—
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—22no—
757C22—22no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22C11×#40814yes—
771C22C22×C11×C22⋊C411yescharacteristic
772C22C4×C11×#4111yescharacteristic
773C22C11×#52011yescharacteristic
774C22C2×C11×#13111yescharacteristic
775C22C2×C11×#13111yescharacteristic
776C22C2×C11×#13111yescharacteristic
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—24no—
794C2—42no—
795C2—81no—
796C2C11×#233911yescharacteristic
797C2C2×C11×#40811yescharacteristic
798C2C11×#288011yescharacteristic
799C2C11×#296611yescharacteristic
800C2C11×#296811yescharacteristic
801C2C11×#299211yescharacteristic
802C2C11×#299411yescharacteristic
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×#435C2semidirect
3. C2×C8×D4×C11C2semidirect
4. C11×#1985C2semidirect
5. C11×#1984C2semidirect
6. C11×#1870C2semidirect
7. C11×#1869C2semidirect
8. C11×#1869C2semidirect
9. C11×#1869C2semidirect
10. C11×#1818C2semidirect
11. C11×#1817C2semidirect
12. C11×#1798C2semidirect
13. C11×#1750C2semidirect
14. C11×#1729C2semidirect
15. C2×C11×#336C2semidirect
152. #22470C11direct (N × H)
263. C2×#435C2×C11semidirect
264. C2×C8×D4C2×C11semidirect
265. #1985C2×C11semidirect
266. #1984C2×C11semidirect
267. #1870C2×C11semidirect
268. #1869C2×C11semidirect
269. #1869C2×C11semidirect
270. #1869C2×C11semidirect
271. #1818C2×C11semidirect
272. #1817C2×C11semidirect
273. #1798C2×C11semidirect
274. #1750C2×C11semidirect
275. #1729C2×C11semidirect
276. C2×#336C2×C11semidirect
662. C11#22470direct (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×#4352
C2×C8×D4×C112
C11×#19852
C11×#19842
C11×#18702
C11×#18692
C11×#18182
C11×#18172
C11×#17982
C11×#17502
C11×#17292
C2×C11×#3362
#2247011