Finite Group Databasebeta

← C11×#22174 #14599367

Subgroups — C11×#22174 #14599367

Order 2816.

964 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#436C211yesmaximal, characteristic, complemented
2C2×C11×#435C211yesmaximal, characteristic, complemented
3C4×C11×#121C211yesmaximal, characteristic
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×#1870C211yesmaximal, characteristic, complemented
11C11×#1869C211yesmaximal, characteristic, complemented
12C11×#1851C211yesmaximal, characteristic, complemented
13C11×#1850C211yesmaximal, characteristic, complemented
14C11×#1797C211yesmaximal, characteristic, complemented
15C11×#1728C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C11×#121C411yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic
25C11×#436—24no—
26C11×#435—24no—
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×#97C2211yescharacteristic
40C2×C4×C8×C11C2211yescharacteristic
41C11×#390C411yescharacteristic
42C11×#389C411yescharacteristic
43C11×#388C411yescharacteristic
44C11×#388C411yescharacteristic
45C11×#386C411yescharacteristic
46C11×#386C411yescharacteristic
47C11×#380C411yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C4×C11×C22⋊C4C2211yescharacteristic
50C4×C11×C22⋊C4C2211yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
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—22no—
71C2×C11×M16—41no—
72C2×C11×M16—41no—
73C2×C11×M16—41no—
74C2×C11×M16—41no—
75C2×C11×M16—41no—
76C2×C11×M16—41no—
77C2×C11×M16D414yescomplemented
78C22×C8×C11—22no—
79C22×C8×C11—41no—
80C22×C8×C11—41no—
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C11×#121—24no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—41no—
95C4×D4×C11—41no—
96C2×C11×C4⋊C4C2×C411yescharacteristic
97C2×C11×C4⋊C4C2×C411yescharacteristic
98C2×C11×C4⋊C4C2×C411yescharacteristic
99C2×C11×C4⋊C4C2×C411yescharacteristic
100C2×C11×C4⋊C4C2×C411yescharacteristic
101C2×C11×C22⋊C4C2×C411yescharacteristic
102C2×C11×C22⋊C4C2×C411yescharacteristic
103C2×C11×C22⋊C4C2×C411yescharacteristic
104C2×C11×C22⋊C4C2×C411yescharacteristic
105C2×C11×C22⋊C4C2×C411yescharacteristic
106C2×C11×C22⋊C4C2×C411yescharacteristic
107C2×C11×C22⋊C4C2×C411yescharacteristic
108C2×C11×C22⋊C4C2×C411yescharacteristic
109C2×C11×C22⋊C4C2×C411yescharacteristic
110C2×C11×C22⋊C4C2×C411yescharacteristic
111C2×C42×C11—41no—
112C2×C42×C11—41no—
113C2×C42×C11C2×C411yescharacteristic
114C2×C42×C11C2×C411yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C2×C42×C11C2311yescharacteristic
119C11×C4⋊C8—22no—
120C11×C4⋊C8—22no—
121C11×C4⋊C8—41no—
122C11×C4⋊C8—41no—
123C11×C22⋊C8—22no—
124C11×C22⋊C8—22no—
125C11×C22⋊C8—22no—
126C11×C22⋊C8—22no—
127C11×C22⋊C8—41no—
128C11×C22⋊C8—41no—
129C11×C22⋊C8—41no—
130C11×C22⋊C8—41no—
131C11×#97—22no—
132C4×C8×C11—22no—
133C11×#95C2×C411yescharacteristic
134C11×#95C2×C411yescharacteristic
135C11×#95C2×C411yescharacteristic
136C11×#95C2×C411yescharacteristic
137C11×#95C2×C411yescharacteristic
138C11×#95C2×C411yescharacteristic
139#22174C1111yesmaximal, 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—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
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—41no—
171C22×C4×C11—41no—
172C22×C4×C11—41no—
173C22×C4×C11—41no—
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×C11C22×C411yescharacteristic
182C22×C4×C11C22×C411yescharacteristic
183C22×C4×C11C22×C411yescharacteristic
184C22×C4×C11C22×C411yescharacteristic
185C22×C4×C11C2×D412yes—
186C22×C4×C11#4112yes—
187C22×C4×C11C2411yescharacteristic
188C11×M16—44no—
189C11×M16—44no—
190C11×M16—44no—
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—21no—
212C2×C8×C11—21no—
213C2×C8×C11—44no—
214C2×C8×C11C2×D412yes—
215C2×C8×C11C2×D412yes—
216C11×C4⋊C4—22no—
217C11×C4⋊C4—22no—
218C11×C4⋊C4—22no—
219C11×C4⋊C4—22no—
220C11×C4⋊C4—41no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—22no—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—22no—
226C11×C22⋊C4—41no—
227C11×C22⋊C4—41no—
228C11×C22⋊C4—41no—
229C11×C22⋊C4—41no—
230C11×C22⋊C4M1614yescomplemented
231C42×C11—21no—
232C42×C11—21no—
233C42×C11—21no—
234C42×C11—21no—
235C42×C11—21no—
236C42×C11—21no—
237C42×C11—21no—
238C42×C11—21no—
239C42×C11—41no—
240C42×C11—41no—
241C2×#436C2×C1111yescharacteristic, complemented
242C2×#435C2×C1111yescharacteristic, complemented
243C4×#121C2×C1111yescharacteristic
244#1924C2×C1111yescharacteristic, complemented
245#1923C2×C1111yescharacteristic, complemented
246#1917C2×C1111yescharacteristic, complemented
247#1916C2×C1111yescharacteristic, complemented
248#1870C2×C1111yescharacteristic, complemented
249#1870C2×C1111yescharacteristic, complemented
250#1870C2×C1111yescharacteristic, complemented
251#1869C2×C1111yescharacteristic, complemented
252#1851C2×C1111yescharacteristic, complemented
253#1850C2×C1111yescharacteristic, complemented
254#1797C2×C1111yescharacteristic, complemented
255#1728C2×C1111yescharacteristic, complemented
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×C11—21no—
274C23×C11—21no—
275C23×C11C4×D412yes—
276C23×C11C2×M1612yes—
277C23×C11C23×C411yescharacteristic
278D4×C11—44no—
279D4×C11—44no—
280D4×C11—44no—
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—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
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—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—44no—
315C2×C4×C11—44no—
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×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11C4×D412yes—
325C2×C4×C11C2×M1612yes—
326C2×C4×C11C2×M1612yes—
327C2×C4×C11#13112yes—
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C2×#4111yescharacteristic
330C2×C4×C11H(5,𝔽2)11yescharacteristic
331C2×C4×C11H(5,𝔽2)11yescharacteristic
332C2×C4×C11H(5,𝔽2)11yescharacteristic
333C2×C4×C112−1+411yescharacteristic
334C8×C11—22no—
335C8×C11—22no—
336C8×C11—41no—
337C8×C11—41no—
338C8×C11—41no—
339C8×C11—41no—
340C8×C11—41no—
341C8×C11—41no—
342C22×M16C22×C1111yescharacteristic
343C22×M16C22×C1111yescharacteristic
344C22×M16C22×C1111yescharacteristic
345C23×C8C22×C1111yescharacteristic
346C2×#121C4×C1111yescharacteristic
347C2×C4×D4C22×C1111yescharacteristic
348C2×C4×D4C22×C1111yescharacteristic
349C2×C4×D4C22×C1111yescharacteristic
350C22×C42C22×C1111yescharacteristic
351#436—24no—
352#435—24no—
353C2×C4⋊C8C22×C1111yescharacteristic
354C2×C4⋊C8C22×C1111yescharacteristic
355C2×C4⋊C8C22×C1111yescharacteristic
356C2×C4⋊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×C4×C8C22×C1111yescharacteristic
367#390C4×C1111yescharacteristic
368#389C4×C1111yescharacteristic
369#388C4×C1111yescharacteristic
370#388C4×C1111yescharacteristic
371#386C4×C1111yescharacteristic
372#386C4×C1111yescharacteristic
373#380C4×C1111yescharacteristic
374C4×C4⋊C4C22×C1111yescharacteristic
375C4×C22⋊C4C22×C1111yescharacteristic
376C4×C22⋊C4C22×C1111yescharacteristic
377#336C22×C1111yescharacteristic
378#336C22×C1111yescharacteristic
379#336C22×C1111yescharacteristic
380#336C22×C1111yescharacteristic
381#336C22×C1111yescharacteristic
382#336C22×C1111yescharacteristic
383#336C22×C1111yescharacteristic
384#336C22×C1111yescharacteristic
385#336C22×C1111yescharacteristic
386#336C22×C1111yescharacteristic
387C22×C11—22no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
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×C11—41no—
407C22×C11—41no—
408C22×C11C2×C4×D411yescharacteristic
409C22×C11#51811yescharacteristic
410C22×C11#52011yescharacteristic
411C22×C11C22×M1611yescharacteristic
412C22×C11C2×#13111yescharacteristic
413C22×C11#56811yescharacteristic
414C22×C11#56811yescharacteristic
415C4×C11—22no—
416C4×C11—22no—
417C4×C11—22no—
418C4×C11—22no—
419C4×C11—41no—
420C4×C11—41no—
421C4×C11—41no—
422C4×C11—41no—
423C4×C11—41no—
424C4×C11—41no—
425C4×C11—41no—
426C4×C11#53411yescharacteristic
427C4×C11#53711yescharacteristic
428C4×C11#53811yescharacteristic
429C4×C11#53911yescharacteristic
430C22×D4C2×C4×C1111yescharacteristic
431C22×D4C2×C4×C1111yescharacteristic
432C22×D4C2×C4×C1111yescharacteristic
433C23×C4C2×C4×C1111yescharacteristic
434C23×C4C2×C4×C1111yescharacteristic
435C23×C4C23×C1111yescharacteristic
436C23×C4C23×C1111yescharacteristic
437C23×C4C23×C1111yescharacteristic
438C2×M16—22no—
439C2×M16—22no—
440C2×M16—41no—
441C2×M16—41no—
442C2×M16—41no—
443C2×M16—41no—
444C2×M16—41no—
445C2×M16—41no—
446C2×M16D4×C1114yescomplemented
447C22×C8—22no—
448C22×C8—41no—
449C22×C8—41no—
450C22×C8C23×C1111yescharacteristic
451C22×C8C23×C1111yescharacteristic
452C22×C8C23×C1111yescharacteristic
453C22×C8C23×C1111yescharacteristic
454C22×C8C23×C1111yescharacteristic
455C22×C8C23×C1111yescharacteristic
456C22×C8C23×C1111yescharacteristic
457C22×C8C23×C1111yescharacteristic
458#121—24no—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—41no—
464C4×D4—41no—
465C2×C4⋊C4C2×C4×C1111yescharacteristic
466C2×C4⋊C4C2×C4×C1111yescharacteristic
467C2×C4⋊C4C2×C4×C1111yescharacteristic
468C2×C4⋊C4C2×C4×C1111yescharacteristic
469C2×C4⋊C4C2×C4×C1111yescharacteristic
470C2×C22⋊C4C2×C4×C1111yescharacteristic
471C2×C22⋊C4C2×C4×C1111yescharacteristic
472C2×C22⋊C4C2×C4×C1111yescharacteristic
473C2×C22⋊C4C2×C4×C1111yescharacteristic
474C2×C22⋊C4C2×C4×C1111yescharacteristic
475C2×C22⋊C4C2×C4×C1111yescharacteristic
476C2×C22⋊C4C2×C4×C1111yescharacteristic
477C2×C22⋊C4C2×C4×C1111yescharacteristic
478C2×C22⋊C4C2×C4×C1111yescharacteristic
479C2×C22⋊C4C2×C4×C1111yescharacteristic
480C2×C42—41no—
481C2×C42—41no—
482C2×C42C2×C4×C1111yescharacteristic
483C2×C42C2×C4×C1111yescharacteristic
484C2×C42C23×C1111yescharacteristic
485C2×C42C23×C1111yescharacteristic
486C2×C42C23×C1111yescharacteristic
487C2×C42C23×C1111yescharacteristic
488C4⋊C8—22no—
489C4⋊C8—22no—
490C4⋊C8—41no—
491C4⋊C8—41no—
492C22⋊C8—22no—
493C22⋊C8—22no—
494C22⋊C8—22no—
495C22⋊C8—22no—
496C22⋊C8—41no—
497C22⋊C8—41no—
498C22⋊C8—41no—
499C22⋊C8—41no—
500#97—22no—
501C4×C8—22no—
502#95C2×C4×C1111yescharacteristic
503#95C2×C4×C1111yescharacteristic
504#95C2×C4×C1111yescharacteristic
505#95C2×C4×C1111yescharacteristic
506#95C2×C4×C1111yescharacteristic
507#95C2×C4×C1111yescharacteristic
508C2×C11—42no—
509C2×C11—42no—
510C2×C11—81no—
511C2×C11#232511yescharacteristic
512C2×C11D4×M1611yescharacteristic
513C2×C11#293511yescharacteristic
514C2×C11#297411yescharacteristic
515C2×C11#297811yescharacteristic
516C2×C11#298911yescharacteristic
517C2×C11#299311yescharacteristic
518C24C22×C4×C1111yescharacteristic
519C24C22×C4×C1111yescharacteristic
520C24C22×C4×C1111yescharacteristic
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—41no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
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—41no—
549C22×C4—41no—
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×C4C2×D4×C1112yes—
564C22×C4C11×#4112yes—
565C22×C4C24×C1111yescharacteristic
566M16—44no—
567M16—44no—
568M16—44no—
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—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—44no—
592C2×C8C2×D4×C1112yes—
593C2×C8C2×D4×C1112yes—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—41no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—41no—
605C22⋊C4—41no—
606C22⋊C4—41no—
607C22⋊C4—41no—
608C22⋊C4C11×M1614yescomplemented
609C42—21no—
610C42—21no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—41no—
618C42—41no—
619C11#2217411yescharacteristic, direct product factor, Sylow
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—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23C4×D4×C1112yes—
640C23C2×C11×M1612yes—
641C23C23×C4×C1111yescharacteristic
642D4—44no—
643D4—44no—
644D4—44no—
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—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
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—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4C4×D4×C1112yes—
689C2×C4C2×C11×M1612yes—
690C2×C4C2×C11×M1612yes—
691C2×C4C11×#13112yes—
692C2×C4C22×D4×C1111yescharacteristic
693C2×C4C2×C11×#4111yescharacteristic
694C2×C4C11×H(5,𝔽2)11yescharacteristic
695C2×C4C11×H(5,𝔽2)11yescharacteristic
696C2×C4C11×H(5,𝔽2)11yescharacteristic
697C2×C4C11×2−1+411yescharacteristic
698C8—22no—
699C8—22no—
700C8—41no—
701C8—41no—
702C8—41no—
703C8—41no—
704C8—41no—
705C8—41no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22C2×C4×D4×C1111yescharacteristic
728C22C11×#51811yescharacteristic
729C22C11×#52011yescharacteristic
730C22C22×C11×M1611yescharacteristic
731C22C2×C11×#13111yescharacteristic
732C22C11×#56811yescharacteristic
733C22C11×#56811yescharacteristic
734C4—22no—
735C4—22no—
736C4—22no—
737C4—22no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4C11×#53411yescharacteristic
746C4C11×#53711yescharacteristic
747C4C11×#53811yescharacteristic
748C4C11×#53911yescharacteristic
749C2—42no—
750C2—42no—
751C2—81no—
752C2C11×#232511yescharacteristic
753C2D4×C11×M1611yescharacteristic
754C2C11×#293511yescharacteristic
755C2C11×#297411yescharacteristic
756C2C11×#297811yescharacteristic
757C2C11×#298911yescharacteristic
758C2C11×#299311yescharacteristic
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×#436C2semidirect
2. C2×C11×#435C2semidirect
4. C11×#1924C2semidirect
5. C11×#1923C2semidirect
6. C11×#1917C2semidirect
7. C11×#1916C2semidirect
8. C11×#1870C2semidirect
9. C11×#1870C2semidirect
10. C11×#1870C2semidirect
11. C11×#1869C2semidirect
12. C11×#1851C2semidirect
13. C11×#1850C2semidirect
14. C11×#1797C2semidirect
15. C11×#1728C2semidirect
77. C2×C11×M16D4semidirect
139. #22174C11direct (N × H)
230. C11×C22⋊C4M16semidirect
241. C2×#436C2×C11semidirect
242. C2×#435C2×C11semidirect
244. #1924C2×C11semidirect
245. #1923C2×C11semidirect
246. #1917C2×C11semidirect
247. #1916C2×C11semidirect
248. #1870C2×C11semidirect
249. #1870C2×C11semidirect
250. #1870C2×C11semidirect
251. #1869C2×C11semidirect
252. #1851C2×C11semidirect
253. #1850C2×C11semidirect
254. #1797C2×C11semidirect
255. #1728C2×C11semidirect
446. C2×M16D4×C11semidirect
608. C22⋊C4C11×M16semidirect
619. C11#22174direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4362
C2×C11×#4352
C4×C11×#1212
C11×#19242
C11×#19232
C11×#19172
C11×#19162
C11×#18702
C11×#18692
C11×#18512
C11×#18502
C11×#17972
C11×#17282
#2217411