Finite Group Databasebeta

← C11×#22141 #14599334

Subgroups — C11×#22141 #14599334

Order 2816.

940 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#435C211yesmaximal, characteristic, complemented
2C2×C11×#432C211yesmaximal, characteristic, complemented
3C4×C11×#121C211yesmaximal, characteristic
4C11×#1955C211yesmaximal, characteristic, complemented
5C11×#1955C211yesmaximal, characteristic, complemented
6C11×#1954C211yesmaximal, characteristic, complemented
7C11×#1940C211yesmaximal, characteristic, complemented
8C11×#1924C211yesmaximal, characteristic, complemented
9C11×#1923C211yesmaximal, characteristic, complemented
10C11×#1870C211yesmaximal, characteristic, complemented
11C11×#1869C211yesmaximal, characteristic, complemented
12C11×#1851C211yesmaximal, characteristic, complemented
13C11×#1850C211yesmaximal, characteristic, complemented
14C11×#1797C211yesmaximal, characteristic, complemented
15C11×#1771C211yesmaximal, 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
23C11×#435—24no—
24C11×#432—24no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×C4⋊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×C11×#97C2211yescharacteristic
43C2×C11×#97C2211yescharacteristic
44C2×C4×C8×C11C2211yescharacteristic
45C11×#390C411yescharacteristic
46C11×#389C411yescharacteristic
47C11×#388C411yescharacteristic
48C11×#388C411yescharacteristic
49C11×#386C411yescharacteristic
50C11×#386C411yescharacteristic
51C11×#380C411yescharacteristic
52C4×C11×C4⋊C4C2211yescharacteristic
53C4×C11×C22⋊C4C2211yescharacteristic
54C4×C11×C22⋊C4C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C22×D4×C11C2×C411yescharacteristic
62C22×D4×C11C2×C411yescharacteristic
63C22×D4×C11C2×C411yescharacteristic
64C23×C4×C11C2×C411yescharacteristic
65C23×C4×C11C2×C411yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C2×C11×M16—22no—
70C2×C11×M16—41no—
71C2×C11×M16—41no—
72C22×C8×C11—22no—
73C22×C8×C11—41no—
74C22×C8×C11—41no—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C11×#121—24no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—41no—
87C4×D4×C11—41no—
88C4×D4×C11—41no—
89C4×D4×C11—41no—
90C2×C11×C4⋊C4C2×C411yescharacteristic
91C2×C11×C4⋊C4C2×C411yescharacteristic
92C2×C11×C4⋊C4C2×C411yescharacteristic
93C2×C11×C4⋊C4C2×C411yescharacteristic
94C2×C11×C4⋊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×C11×C22⋊C4C2×C411yescharacteristic
104C2×C11×C22⋊C4C2×C411yescharacteristic
105C2×C42×C11—22no—
106C2×C42×C11—22no—
107C2×C42×C11C2×C411yescharacteristic
108C2×C42×C11C2×C411yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C2×C42×C11C2311yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C11×C4⋊C8—22no—
114C11×C4⋊C8—22no—
115C11×C4⋊C8—22no—
116C11×C4⋊C8—22no—
117C11×C4⋊C8—41no—
118C11×C4⋊C8—41no—
119C11×C22⋊C8—22no—
120C11×C22⋊C8—22no—
121C11×C22⋊C8—22no—
122C11×C22⋊C8—22no—
123C11×C22⋊C8—41no—
124C11×C22⋊C8—41no—
125C11×C22⋊C8—41no—
126C11×C22⋊C8—41no—
127C11×C22⋊C8—41no—
128C11×C22⋊C8—41no—
129C11×#97—22no—
130C11×#97—41no—
131C11×#97D414yescomplemented
132C4×C8×C11—41no—
133C11×#95C2×C411yescharacteristic
134C11×#95C2×C411yescharacteristic
135C11×#95C2×C411yescharacteristic
136C11×#95C2×C411yescharacteristic
137C11×#95C2×C411yescharacteristic
138C11×#95C2×C411yescharacteristic
139#22141C1111yesmaximal, characteristic, direct product factor, Sylow
140C24×C11C22×C411yescharacteristic
141C24×C11C22×C411yescharacteristic
142C24×C11C22×C411yescharacteristic
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—22no—
149C2×D4×C11—41no—
150C2×D4×C11—41no—
151C2×D4×C11—41no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
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—21no—
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—41no—
175C22×C4×C11—41no—
176C22×C4×C11C22×C411yescharacteristic
177C22×C4×C11C22×C411yescharacteristic
178C22×C4×C11C22×C411yescharacteristic
179C22×C4×C11C22×C411yescharacteristic
180C22×C4×C11C22×C411yescharacteristic
181C22×C4×C11C22×C411yescharacteristic
182C22×C4×C11C22×C411yescharacteristic
183C22×C4×C11C22×C411yescharacteristic
184C22×C4×C11C22×C411yescharacteristic
185C22×C4×C11C22×C411yescharacteristic
186C22×C4×C11C22×C411yescharacteristic
187C22×C4×C11C2411yescharacteristic
188C11×M16—44no—
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—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—44no—
212C2×C8×C11C2×D412yes—
213C2×C8×C11C2×D412yes—
214C11×C4⋊C4—22no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—41no—
217C11×C4⋊C4—41no—
218C11×C4⋊C4—41no—
219C11×C22⋊C4—22no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—41no—
223C11×C22⋊C4—41no—
224C11×C22⋊C4—41no—
225C11×C22⋊C4—41no—
226C11×C22⋊C4—41no—
227C11×C22⋊C4—41no—
228C11×C22⋊C4M1614yescomplemented
229C42×C11—22no—
230C42×C11—22no—
231C42×C11—21no—
232C42×C11—21no—
233C42×C11—21no—
234C42×C11—21no—
235C42×C11—21no—
236C42×C11—21no—
237C42×C11C2×D412yes—
238C42×C11#4112yes—
239C2×#435C2×C1111yescharacteristic, complemented
240C2×#432C2×C1111yescharacteristic, complemented
241C4×#121C2×C1111yescharacteristic
242#1955C2×C1111yescharacteristic, complemented
243#1955C2×C1111yescharacteristic, complemented
244#1954C2×C1111yescharacteristic, complemented
245#1940C2×C1111yescharacteristic, complemented
246#1924C2×C1111yescharacteristic, complemented
247#1923C2×C1111yescharacteristic, complemented
248#1870C2×C1111yescharacteristic, complemented
249#1869C2×C1111yescharacteristic, complemented
250#1851C2×C1111yescharacteristic, complemented
251#1850C2×C1111yescharacteristic, complemented
252#1797C2×C1111yescharacteristic, complemented
253#1771C2×C1111yescharacteristic, complemented
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×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11C2×M1612yes—
274C23×C11#13112yes—
275C23×C11C23×C411yescharacteristic
276D4×C11—44no—
277D4×C11—44no—
278D4×C11—44no—
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—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—44no—
309C2×C4×C11—44no—
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×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11C4×D412yes—
323C2×C4×C11C4×D412yes—
324C2×C4×C11C2×M1612yes—
325C2×C4×C11C2×M1612yes—
326C2×C4×C11C22×D411yescharacteristic
327C2×C4×C11C2×#4111yescharacteristic
328C2×C4×C11H(5,𝔽2)11yescharacteristic
329C2×C4×C11H(5,𝔽2)11yescharacteristic
330C2×C4×C11H(5,𝔽2)11yescharacteristic
331C2×C4×C112−1+411yescharacteristic
332C8×C11—22no—
333C8×C11—22no—
334C8×C11—41no—
335C8×C11—41no—
336C8×C11—41no—
337C8×C11—41no—
338C8×C11—41no—
339C8×C11—41no—
340C22×M16C22×C1111yescharacteristic
341C23×C8C22×C1111yescharacteristic
342C2×#121C4×C1111yescharacteristic
343C2×C4×D4C22×C1111yescharacteristic
344C2×C4×D4C22×C1111yescharacteristic
345C2×C4×D4C22×C1111yescharacteristic
346C22×C42C22×C1111yescharacteristic
347#435—24no—
348#432—24no—
349C2×C4⋊C8C22×C1111yescharacteristic
350C2×C4⋊C8C22×C1111yescharacteristic
351C2×C4⋊C8C22×C1111yescharacteristic
352C2×C4⋊C8C22×C1111yescharacteristic
353C2×C4⋊C8C22×C1111yescharacteristic
354C2×C4⋊C8C22×C1111yescharacteristic
355C2×C22⋊C8C22×C1111yescharacteristic
356C2×C22⋊C8C22×C1111yescharacteristic
357C2×C22⋊C8C22×C1111yescharacteristic
358C2×C22⋊C8C22×C1111yescharacteristic
359C2×C22⋊C8C22×C1111yescharacteristic
360C2×C22⋊C8C22×C1111yescharacteristic
361C2×C22⋊C8C22×C1111yescharacteristic
362C2×C22⋊C8C22×C1111yescharacteristic
363C2×C22⋊C8C22×C1111yescharacteristic
364C2×C22⋊C8C22×C1111yescharacteristic
365C2×#97C22×C1111yescharacteristic
366C2×#97C22×C1111yescharacteristic
367C2×#97C22×C1111yescharacteristic
368C2×C4×C8C22×C1111yescharacteristic
369#390C4×C1111yescharacteristic
370#389C4×C1111yescharacteristic
371#388C4×C1111yescharacteristic
372#388C4×C1111yescharacteristic
373#386C4×C1111yescharacteristic
374#386C4×C1111yescharacteristic
375#380C4×C1111yescharacteristic
376C4×C4⋊C4C22×C1111yescharacteristic
377C4×C22⋊C4C22×C1111yescharacteristic
378C4×C22⋊C4C22×C1111yescharacteristic
379#336C22×C1111yescharacteristic
380#336C22×C1111yescharacteristic
381#336C22×C1111yescharacteristic
382#336C22×C1111yescharacteristic
383#336C22×C1111yescharacteristic
384#336C22×C1111yescharacteristic
385C22×C11—22no—
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11C2×C4×D411yescharacteristic
407C22×C11#51811yescharacteristic
408C22×C11#52011yescharacteristic
409C22×C11C22×M1611yescharacteristic
410C22×C11C2×#13111yescharacteristic
411C22×C11#56811yescharacteristic
412C22×C11#56811yescharacteristic
413C4×C11—22no—
414C4×C11—22no—
415C4×C11—22no—
416C4×C11—22no—
417C4×C11—41no—
418C4×C11—41no—
419C4×C11—41no—
420C4×C11—41no—
421C4×C11—41no—
422C4×C11—41no—
423C4×C11—41no—
424C4×C11#53511yescharacteristic
425C4×C11#53711yescharacteristic
426C4×C11#54011yescharacteristic
427C4×C11#54211yescharacteristic
428C22×D4C2×C4×C1111yescharacteristic
429C22×D4C2×C4×C1111yescharacteristic
430C22×D4C2×C4×C1111yescharacteristic
431C23×C4C2×C4×C1111yescharacteristic
432C23×C4C2×C4×C1111yescharacteristic
433C23×C4C23×C1111yescharacteristic
434C23×C4C23×C1111yescharacteristic
435C23×C4C23×C1111yescharacteristic
436C2×M16—22no—
437C2×M16—41no—
438C2×M16—41no—
439C22×C8—22no—
440C22×C8—41no—
441C22×C8—41no—
442C22×C8C23×C1111yescharacteristic
443C22×C8C23×C1111yescharacteristic
444C22×C8C23×C1111yescharacteristic
445C22×C8C23×C1111yescharacteristic
446C22×C8C23×C1111yescharacteristic
447C22×C8C23×C1111yescharacteristic
448C22×C8C23×C1111yescharacteristic
449C22×C8C23×C1111yescharacteristic
450#121—24no—
451C4×D4—22no—
452C4×D4—22no—
453C4×D4—41no—
454C4×D4—41no—
455C4×D4—41no—
456C4×D4—41no—
457C2×C4⋊C4C2×C4×C1111yescharacteristic
458C2×C4⋊C4C2×C4×C1111yescharacteristic
459C2×C4⋊C4C2×C4×C1111yescharacteristic
460C2×C4⋊C4C2×C4×C1111yescharacteristic
461C2×C4⋊C4C2×C4×C1111yescharacteristic
462C2×C22⋊C4C2×C4×C1111yescharacteristic
463C2×C22⋊C4C2×C4×C1111yescharacteristic
464C2×C22⋊C4C2×C4×C1111yescharacteristic
465C2×C22⋊C4C2×C4×C1111yescharacteristic
466C2×C22⋊C4C2×C4×C1111yescharacteristic
467C2×C22⋊C4C2×C4×C1111yescharacteristic
468C2×C22⋊C4C2×C4×C1111yescharacteristic
469C2×C22⋊C4C2×C4×C1111yescharacteristic
470C2×C22⋊C4C2×C4×C1111yescharacteristic
471C2×C22⋊C4C2×C4×C1111yescharacteristic
472C2×C42—22no—
473C2×C42—22no—
474C2×C42C2×C4×C1111yescharacteristic
475C2×C42C2×C4×C1111yescharacteristic
476C2×C42C23×C1111yescharacteristic
477C2×C42C23×C1111yescharacteristic
478C2×C42C23×C1111yescharacteristic
479C2×C42C23×C1111yescharacteristic
480C4⋊C8—22no—
481C4⋊C8—22no—
482C4⋊C8—22no—
483C4⋊C8—22no—
484C4⋊C8—41no—
485C4⋊C8—41no—
486C22⋊C8—22no—
487C22⋊C8—22no—
488C22⋊C8—22no—
489C22⋊C8—22no—
490C22⋊C8—41no—
491C22⋊C8—41no—
492C22⋊C8—41no—
493C22⋊C8—41no—
494C22⋊C8—41no—
495C22⋊C8—41no—
496#97—22no—
497#97—41no—
498#97D4×C1114yescomplemented
499C4×C8—41no—
500#95C2×C4×C1111yescharacteristic
501#95C2×C4×C1111yescharacteristic
502#95C2×C4×C1111yescharacteristic
503#95C2×C4×C1111yescharacteristic
504#95C2×C4×C1111yescharacteristic
505#95C2×C4×C1111yescharacteristic
506C2×C11—42no—
507C2×C11—42no—
508C2×C11—81no—
509C2×C11#232411yescharacteristic
510C2×C11#293311yescharacteristic
511C2×C11D4×M1611yescharacteristic
512C2×C11#297411yescharacteristic
513C2×C11#298011yescharacteristic
514C2×C11#298911yescharacteristic
515C2×C11#299211yescharacteristic
516C24C22×C4×C1111yescharacteristic
517C24C22×C4×C1111yescharacteristic
518C24C22×C4×C1111yescharacteristic
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—41no—
526C2×D4—41no—
527C2×D4—41no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4C22×C4×C1111yescharacteristic
553C22×C4C22×C4×C1111yescharacteristic
554C22×C4C22×C4×C1111yescharacteristic
555C22×C4C22×C4×C1111yescharacteristic
556C22×C4C22×C4×C1111yescharacteristic
557C22×C4C22×C4×C1111yescharacteristic
558C22×C4C22×C4×C1111yescharacteristic
559C22×C4C22×C4×C1111yescharacteristic
560C22×C4C22×C4×C1111yescharacteristic
561C22×C4C22×C4×C1111yescharacteristic
562C22×C4C22×C4×C1111yescharacteristic
563C22×C4C24×C1111yescharacteristic
564M16—44no—
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—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—44no—
588C2×C8C2×D4×C1112yes—
589C2×C8C2×D4×C1112yes—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—41no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—41no—
599C22⋊C4—41no—
600C22⋊C4—41no—
601C22⋊C4—41no—
602C22⋊C4—41no—
603C22⋊C4—41no—
604C22⋊C4C11×M1614yescomplemented
605C42—22no—
606C42—22no—
607C42—21no—
608C42—21no—
609C42—21no—
610C42—21no—
611C42—21no—
612C42—21no—
613C42C2×D4×C1112yes—
614C42C11×#4112yes—
615C11#2214111yescharacteristic, direct product factor, Sylow
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23C2×C11×M1612yes—
636C23C11×#13112yes—
637C23C23×C4×C1111yescharacteristic
638D4—44no—
639D4—44no—
640D4—44no—
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—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—44no—
671C2×C4—44no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4C4×D4×C1112yes—
685C2×C4C4×D4×C1112yes—
686C2×C4C2×C11×M1612yes—
687C2×C4C2×C11×M1612yes—
688C2×C4C22×D4×C1111yescharacteristic
689C2×C4C2×C11×#4111yescharacteristic
690C2×C4C11×H(5,𝔽2)11yescharacteristic
691C2×C4C11×H(5,𝔽2)11yescharacteristic
692C2×C4C11×H(5,𝔽2)11yescharacteristic
693C2×C4C11×2−1+411yescharacteristic
694C8—22no—
695C8—22no—
696C8—41no—
697C8—41no—
698C8—41no—
699C8—41no—
700C8—41no—
701C8—41no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22C2×C4×D4×C1111yescharacteristic
724C22C11×#51811yescharacteristic
725C22C11×#52011yescharacteristic
726C22C22×C11×M1611yescharacteristic
727C22C2×C11×#13111yescharacteristic
728C22C11×#56811yescharacteristic
729C22C11×#56811yescharacteristic
730C4—22no—
731C4—22no—
732C4—22no—
733C4—22no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4C11×#53511yescharacteristic
742C4C11×#53711yescharacteristic
743C4C11×#54011yescharacteristic
744C4C11×#54211yescharacteristic
745C2—42no—
746C2—42no—
747C2—81no—
748C2C11×#232411yescharacteristic
749C2C11×#293311yescharacteristic
750C2D4×C11×M1611yescharacteristic
751C2C11×#297411yescharacteristic
752C2C11×#298011yescharacteristic
753C2C11×#298911yescharacteristic
754C2C11×#299211yescharacteristic
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
1. C2×C11×#435C2semidirect
2. C2×C11×#432C2semidirect
4. C11×#1955C2semidirect
5. C11×#1955C2semidirect
6. C11×#1954C2semidirect
7. C11×#1940C2semidirect
8. C11×#1924C2semidirect
9. C11×#1923C2semidirect
10. C11×#1870C2semidirect
11. C11×#1869C2semidirect
12. C11×#1851C2semidirect
13. C11×#1850C2semidirect
14. C11×#1797C2semidirect
15. C11×#1771C2semidirect
131. C11×#97D4semidirect
139. #22141C11direct (N × H)
228. C11×C22⋊C4M16semidirect
239. C2×#435C2×C11semidirect
240. C2×#432C2×C11semidirect
242. #1955C2×C11semidirect
243. #1955C2×C11semidirect
244. #1954C2×C11semidirect
245. #1940C2×C11semidirect
246. #1924C2×C11semidirect
247. #1923C2×C11semidirect
248. #1870C2×C11semidirect
249. #1869C2×C11semidirect
250. #1851C2×C11semidirect
251. #1850C2×C11semidirect
252. #1797C2×C11semidirect
253. #1771C2×C11semidirect
498. #97D4×C11semidirect
604. C22⋊C4C11×M16semidirect
615. C11#22141direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4352
C2×C11×#4322
C4×C11×#1212
C11×#19552
C11×#19542
C11×#19402
C11×#19242
C11×#19232
C11×#18702
C11×#18692
C11×#18512
C11×#18502
C11×#17972
C11×#17712
#2214111