Finite Group Databasebeta

← C11×#23329 #14600522

Subgroups — C11×#23329 #14600522

Order 2816.

854 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×#121C211yesmaximal, characteristic
2C11×#1955C211yesmaximal, characteristic, complemented
3C11×#1954C211yesmaximal, characteristic, complemented
4C11×#1924C211yesmaximal, characteristic, complemented
5C11×#1923C211yesmaximal, characteristic, complemented
6C11×#1917C211yesmaximal, characteristic, complemented
7C11×#1916C211yesmaximal, characteristic, complemented
8C11×#1870C211yesmaximal, characteristic, complemented
9C11×#1870C211yesmaximal, characteristic, complemented
10C11×#1869C211yesmaximal, characteristic, complemented
11C11×#1869C211yesmaximal, characteristic, complemented
12C11×#1851C211yesmaximal, characteristic, complemented
13C11×#1850C211yesmaximal, characteristic, complemented
14C11×#1817C211yesmaximal, characteristic, complemented
15C11×#1797C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×#121C411yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
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×#97C2211yescharacteristic
38C2×C4×C8×C11C2211yescharacteristic
39C11×#390C411yescharacteristic
40C11×#389C411yescharacteristic
41C11×#388C411yescharacteristic
42C11×#388C411yescharacteristic
43C11×#386C411yescharacteristic
44C11×#386C411yescharacteristic
45C11×#380C411yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C22⋊C4C2211yescharacteristic
48C4×C11×C22⋊C4C2211yescharacteristic
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C22×D4×C11C2×C411yescharacteristic
60C22×D4×C11C2×C411yescharacteristic
61C22×D4×C11C2×C411yescharacteristic
62C23×C4×C11C2×C411yescharacteristic
63C23×C4×C11C2×C411yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C2×C11×M16—41no—
68C2×C11×M16—41no—
69C2×C11×M16—41no—
70C22×C8×C11—41no—
71C22×C8×C11—41no—
72C22×C8×C11—41no—
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C11×#121—24no—
82C4×D4×C11—41no—
83C4×D4×C11—41no—
84C4×D4×C11—41no—
85C4×D4×C11—41no—
86C4×D4×C11—41no—
87C4×D4×C11—41no—
88C2×C11×C4⋊C4C2×C411yescharacteristic
89C2×C11×C4⋊C4C2×C411yescharacteristic
90C2×C11×C4⋊C4C2×C411yescharacteristic
91C2×C11×C4⋊C4C2×C411yescharacteristic
92C2×C11×C4⋊C4C2×C411yescharacteristic
93C2×C11×C22⋊C4C2×C411yescharacteristic
94C2×C11×C22⋊C4C2×C411yescharacteristic
95C2×C11×C22⋊C4C2×C411yescharacteristic
96C2×C11×C22⋊C4C2×C411yescharacteristic
97C2×C11×C22⋊C4C2×C411yescharacteristic
98C2×C11×C22⋊C4C2×C411yescharacteristic
99C2×C11×C22⋊C4C2×C411yescharacteristic
100C2×C11×C22⋊C4C2×C411yescharacteristic
101C2×C11×C22⋊C4C2×C411yescharacteristic
102C2×C11×C22⋊C4C2×C411yescharacteristic
103C2×C42×C11—41no—
104C2×C42×C11—41no—
105C2×C42×C11C2×C411yescharacteristic
106C2×C42×C11C2×C411yescharacteristic
107C2×C42×C11C2311yescharacteristic
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C11×C4⋊C8—41no—
112C11×C4⋊C8—41no—
113C11×C4⋊C8—41no—
114C11×C4⋊C8—41no—
115C11×C22⋊C8—41no—
116C11×C22⋊C8—41no—
117C11×C22⋊C8—41no—
118C11×C22⋊C8—41no—
119C11×C22⋊C8—41no—
120C11×C22⋊C8—41no—
121C11×C22⋊C8—41no—
122C11×C22⋊C8—41no—
123C11×C22⋊C8—41no—
124C11×C22⋊C8—41no—
125C11×#97—41no—
126C4×C8×C11—41no—
127C11×#95C2×C411yescharacteristic
128C11×#95C2×C411yescharacteristic
129C11×#95C2×C411yescharacteristic
130C11×#95C2×C411yescharacteristic
131C11×#95C2×C411yescharacteristic
132C11×#95C2×C411yescharacteristic
133#23329C1111yesmaximal, characteristic, direct product factor, Sylow
134C24×C11C22×C411yescharacteristic
135C24×C11C22×C411yescharacteristic
136C24×C11C22×C411yescharacteristic
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—41no—
144C2×D4×C11—41no—
145C2×D4×C11—41no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—41no—
168C22×C4×C11—41no—
169C22×C4×C11—41no—
170C22×C4×C11C22×C411yescharacteristic
171C22×C4×C11C22×C411yescharacteristic
172C22×C4×C11C22×C411yescharacteristic
173C22×C4×C11C22×C411yescharacteristic
174C22×C4×C11C22×C411yescharacteristic
175C22×C4×C11C22×C411yescharacteristic
176C22×C4×C11C22×C411yescharacteristic
177C22×C4×C11C22×C411yescharacteristic
178C22×C4×C11C22×C411yescharacteristic
179C22×C4×C11C22×C411yescharacteristic
180C22×C4×C11C22×C411yescharacteristic
181C22×C4×C11C2411yescharacteristic
182C11×M16—44no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—44no—
208C11×C4⋊C4—22no—
209C11×C4⋊C4—22no—
210C11×C4⋊C4—41no—
211C11×C4⋊C4—41no—
212C11×C4⋊C4—41no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—41no—
215C11×C22⋊C4—41no—
216C11×C22⋊C4—41no—
217C11×C22⋊C4—41no—
218C11×C22⋊C4—41no—
219C11×C22⋊C4—41no—
220C11×C22⋊C4—41no—
221C11×C22⋊C4—41no—
222C11×C22⋊C4M1614yescomplemented
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—21no—
226C42×C11—21no—
227C42×C11—21no—
228C42×C11—21no—
229C42×C11—21no—
230C42×C11—21no—
231C42×C11—41no—
232C42×C11—41no—
233C4×#121C2×C1111yescharacteristic
234#1955C2×C1111yescharacteristic, complemented
235#1954C2×C1111yescharacteristic, complemented
236#1924C2×C1111yescharacteristic, complemented
237#1923C2×C1111yescharacteristic, complemented
238#1917C2×C1111yescharacteristic, complemented
239#1916C2×C1111yescharacteristic, complemented
240#1870C2×C1111yescharacteristic, complemented
241#1870C2×C1111yescharacteristic, complemented
242#1869C2×C1111yescharacteristic, complemented
243#1869C2×C1111yescharacteristic, complemented
244#1851C2×C1111yescharacteristic, complemented
245#1850C2×C1111yescharacteristic, complemented
246#1817C2×C1111yescharacteristic, complemented
247#1797C2×C1111yescharacteristic, complemented
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11C2×M1612yes—
268C23×C11#13112yes—
269C23×C11C23×C411yescharacteristic
270D4×C11—44no—
271D4×C11—44no—
272D4×C11—44no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—44no—
304C2×C4×C11—44no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11C2×M1612yes—
318C2×C4×C11C2×M1612yes—
319C2×C4×C11#13112yes—
320C2×C4×C11H(5,𝔽2)11yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C2×C4×C11H(5,𝔽2)11yescharacteristic
323C2×C4×C11H(5,𝔽2)11yescharacteristic
324C2×C4×C11H(5,𝔽2)11yescharacteristic
325C2×C4×C112−1+411yescharacteristic
326C8×C11—41no—
327C8×C11—41no—
328C8×C11—41no—
329C8×C11—41no—
330C8×C11—41no—
331C8×C11—41no—
332C8×C11—41no—
333C8×C11—41no—
334C22×M16C22×C1111yescharacteristic
335C23×C8C22×C1111yescharacteristic
336C2×#121C4×C1111yescharacteristic
337C2×C4×D4C22×C1111yescharacteristic
338C2×C4×D4C22×C1111yescharacteristic
339C2×C4×D4C22×C1111yescharacteristic
340C22×C42C22×C1111yescharacteristic
341C2×C4⋊C8C22×C1111yescharacteristic
342C2×C4⋊C8C22×C1111yescharacteristic
343C2×C4⋊C8C22×C1111yescharacteristic
344C2×C4⋊C8C22×C1111yescharacteristic
345C2×C22⋊C8C22×C1111yescharacteristic
346C2×C22⋊C8C22×C1111yescharacteristic
347C2×C22⋊C8C22×C1111yescharacteristic
348C2×C22⋊C8C22×C1111yescharacteristic
349C2×C22⋊C8C22×C1111yescharacteristic
350C2×C22⋊C8C22×C1111yescharacteristic
351C2×C22⋊C8C22×C1111yescharacteristic
352C2×C22⋊C8C22×C1111yescharacteristic
353C2×C22⋊C8C22×C1111yescharacteristic
354C2×C22⋊C8C22×C1111yescharacteristic
355C2×#97C22×C1111yescharacteristic
356C2×C4×C8C22×C1111yescharacteristic
357#390C4×C1111yescharacteristic
358#389C4×C1111yescharacteristic
359#388C4×C1111yescharacteristic
360#388C4×C1111yescharacteristic
361#386C4×C1111yescharacteristic
362#386C4×C1111yescharacteristic
363#380C4×C1111yescharacteristic
364C4×C4⋊C4C22×C1111yescharacteristic
365C4×C22⋊C4C22×C1111yescharacteristic
366C4×C22⋊C4C22×C1111yescharacteristic
367#336C22×C1111yescharacteristic
368#336C22×C1111yescharacteristic
369#336C22×C1111yescharacteristic
370#336C22×C1111yescharacteristic
371#336C22×C1111yescharacteristic
372#336C22×C1111yescharacteristic
373#336C22×C1111yescharacteristic
374#336C22×C1111yescharacteristic
375#336C22×C1111yescharacteristic
376#336C22×C1111yescharacteristic
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—22no—
380C22×C11—22no—
381C22×C11—22no—
382C22×C11—22no—
383C22×C11—41no—
384C22×C11—41no—
385C22×C11—41no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11#51811yescharacteristic
399C22×C11#51811yescharacteristic
400C22×C11#52011yescharacteristic
401C22×C11C22×M1611yescharacteristic
402C22×C11C2×#13111yescharacteristic
403C22×C11C2×#13111yescharacteristic
404C22×C11#56811yescharacteristic
405C4×C11—22no—
406C4×C11—22no—
407C4×C11—22no—
408C4×C11—41no—
409C4×C11—41no—
410C4×C11—41no—
411C4×C11—41no—
412C4×C11—41no—
413C4×C11—41no—
414C4×C11—41no—
415C4×C11—41no—
416C4×C11#56011yescharacteristic
417C4×C11#56011yescharacteristic
418C4×C11#56211yescharacteristic
419C4×C11#56211yescharacteristic
420C22×D4C2×C4×C1111yescharacteristic
421C22×D4C2×C4×C1111yescharacteristic
422C22×D4C2×C4×C1111yescharacteristic
423C23×C4C2×C4×C1111yescharacteristic
424C23×C4C2×C4×C1111yescharacteristic
425C23×C4C23×C1111yescharacteristic
426C23×C4C23×C1111yescharacteristic
427C23×C4C23×C1111yescharacteristic
428C2×M16—41no—
429C2×M16—41no—
430C2×M16—41no—
431C22×C8—41no—
432C22×C8—41no—
433C22×C8—41no—
434C22×C8C23×C1111yescharacteristic
435C22×C8C23×C1111yescharacteristic
436C22×C8C23×C1111yescharacteristic
437C22×C8C23×C1111yescharacteristic
438C22×C8C23×C1111yescharacteristic
439C22×C8C23×C1111yescharacteristic
440C22×C8C23×C1111yescharacteristic
441C22×C8C23×C1111yescharacteristic
442#121—24no—
443C4×D4—41no—
444C4×D4—41no—
445C4×D4—41no—
446C4×D4—41no—
447C4×D4—41no—
448C4×D4—41no—
449C2×C4⋊C4C2×C4×C1111yescharacteristic
450C2×C4⋊C4C2×C4×C1111yescharacteristic
451C2×C4⋊C4C2×C4×C1111yescharacteristic
452C2×C4⋊C4C2×C4×C1111yescharacteristic
453C2×C4⋊C4C2×C4×C1111yescharacteristic
454C2×C22⋊C4C2×C4×C1111yescharacteristic
455C2×C22⋊C4C2×C4×C1111yescharacteristic
456C2×C22⋊C4C2×C4×C1111yescharacteristic
457C2×C22⋊C4C2×C4×C1111yescharacteristic
458C2×C22⋊C4C2×C4×C1111yescharacteristic
459C2×C22⋊C4C2×C4×C1111yescharacteristic
460C2×C22⋊C4C2×C4×C1111yescharacteristic
461C2×C22⋊C4C2×C4×C1111yescharacteristic
462C2×C22⋊C4C2×C4×C1111yescharacteristic
463C2×C22⋊C4C2×C4×C1111yescharacteristic
464C2×C42—41no—
465C2×C42—41no—
466C2×C42C2×C4×C1111yescharacteristic
467C2×C42C2×C4×C1111yescharacteristic
468C2×C42C23×C1111yescharacteristic
469C2×C42C23×C1111yescharacteristic
470C2×C42C23×C1111yescharacteristic
471C2×C42C23×C1111yescharacteristic
472C4⋊C8—41no—
473C4⋊C8—41no—
474C4⋊C8—41no—
475C4⋊C8—41no—
476C22⋊C8—41no—
477C22⋊C8—41no—
478C22⋊C8—41no—
479C22⋊C8—41no—
480C22⋊C8—41no—
481C22⋊C8—41no—
482C22⋊C8—41no—
483C22⋊C8—41no—
484C22⋊C8—41no—
485C22⋊C8—41no—
486#97—41no—
487C4×C8—41no—
488#95C2×C4×C1111yescharacteristic
489#95C2×C4×C1111yescharacteristic
490#95C2×C4×C1111yescharacteristic
491#95C2×C4×C1111yescharacteristic
492#95C2×C4×C1111yescharacteristic
493#95C2×C4×C1111yescharacteristic
494C2×C11—42no—
495C2×C11—42no—
496C2×C11—81no—
497C2×C11#237711yescharacteristic
498C2×C11#297411yescharacteristic
499C2×C11#297411yescharacteristic
500C2×C11#297611yescharacteristic
501C2×C11#298111yescharacteristic
502C2×C11#298911yescharacteristic
503C2×C11#299411yescharacteristic
504C24C22×C4×C1111yescharacteristic
505C24C22×C4×C1111yescharacteristic
506C24C22×C4×C1111yescharacteristic
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—41no—
514C2×D4—41no—
515C2×D4—41no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4C22×C4×C1111yescharacteristic
541C22×C4C22×C4×C1111yescharacteristic
542C22×C4C22×C4×C1111yescharacteristic
543C22×C4C22×C4×C1111yescharacteristic
544C22×C4C22×C4×C1111yescharacteristic
545C22×C4C22×C4×C1111yescharacteristic
546C22×C4C22×C4×C1111yescharacteristic
547C22×C4C22×C4×C1111yescharacteristic
548C22×C4C22×C4×C1111yescharacteristic
549C22×C4C22×C4×C1111yescharacteristic
550C22×C4C22×C4×C1111yescharacteristic
551C22×C4C24×C1111yescharacteristic
552M16—44no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—44no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C22⋊C4—22no—
584C22⋊C4—41no—
585C22⋊C4—41no—
586C22⋊C4—41no—
587C22⋊C4—41no—
588C22⋊C4—41no—
589C22⋊C4—41no—
590C22⋊C4—41no—
591C22⋊C4—41no—
592C22⋊C4C11×M1614yescomplemented
593C42—21no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—41no—
602C42—41no—
603C11#2332911yescharacteristic, direct product factor, Sylow
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23C2×C11×M1612yes—
624C23C11×#13112yes—
625C23C23×C4×C1111yescharacteristic
626D4—44no—
627D4—44no—
628D4—44no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4C2×C11×M1612yes—
674C2×C4C2×C11×M1612yes—
675C2×C4C11×#13112yes—
676C2×C4C11×H(5,𝔽2)11yescharacteristic
677C2×C4C11×H(5,𝔽2)11yescharacteristic
678C2×C4C11×H(5,𝔽2)11yescharacteristic
679C2×C4C11×H(5,𝔽2)11yescharacteristic
680C2×C4C11×H(5,𝔽2)11yescharacteristic
681C2×C4C11×2−1+411yescharacteristic
682C8—41no—
683C8—41no—
684C8—41no—
685C8—41no—
686C8—41no—
687C8—41no—
688C8—41no—
689C8—41no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22C11×#51811yescharacteristic
712C22C11×#51811yescharacteristic
713C22C11×#52011yescharacteristic
714C22C22×C11×M1611yescharacteristic
715C22C2×C11×#13111yescharacteristic
716C22C2×C11×#13111yescharacteristic
717C22C11×#56811yescharacteristic
718C4—22no—
719C4—22no—
720C4—22no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4C11×#56011yescharacteristic
730C4C11×#56011yescharacteristic
731C4C11×#56211yescharacteristic
732C4C11×#56211yescharacteristic
733C2—42no—
734C2—42no—
735C2—81no—
736C2C11×#237711yescharacteristic
737C2C11×#297411yescharacteristic
738C2C11×#297411yescharacteristic
739C2C11×#297611yescharacteristic
740C2C11×#298111yescharacteristic
741C2C11×#298911yescharacteristic
742C2C11×#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. C11×#1955C2semidirect
3. C11×#1954C2semidirect
4. C11×#1924C2semidirect
5. C11×#1923C2semidirect
6. C11×#1917C2semidirect
7. C11×#1916C2semidirect
8. C11×#1870C2semidirect
9. C11×#1870C2semidirect
10. C11×#1869C2semidirect
11. C11×#1869C2semidirect
12. C11×#1851C2semidirect
13. C11×#1850C2semidirect
14. C11×#1817C2semidirect
15. C11×#1797C2semidirect
133. #23329C11direct (N × H)
222. C11×C22⋊C4M16semidirect
234. #1955C2×C11semidirect
235. #1954C2×C11semidirect
236. #1924C2×C11semidirect
237. #1923C2×C11semidirect
238. #1917C2×C11semidirect
239. #1916C2×C11semidirect
240. #1870C2×C11semidirect
241. #1870C2×C11semidirect
242. #1869C2×C11semidirect
243. #1869C2×C11semidirect
244. #1851C2×C11semidirect
245. #1850C2×C11semidirect
246. #1817C2×C11semidirect
247. #1797C2×C11semidirect
592. C22⋊C4C11×M16semidirect
603. C11#23329direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C11×#1212
C11×#19552
C11×#19542
C11×#19242
C11×#19232
C11×#19172
C11×#19162
C11×#18702
C11×#18692
C11×#18512
C11×#18502
C11×#18172
C11×#17972
#2332911