Finite Group Databasebeta

← C11×#22172 #14599365

Subgroups — C11×#22172 #14599365

Order 2816.

1004 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×#435C211yesmaximal, characteristic, complemented
2C2×C8×D4×C11C211yesmaximal, 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×#1869C211yesmaximal, characteristic, complemented
10C11×#1869C211yesmaximal, characteristic, complemented
11C11×#1869C211yesmaximal, characteristic, complemented
12C11×#1851C211yesmaximal, characteristic, complemented
13C11×#1850C211yesmaximal, characteristic, complemented
14C11×#1797C211yesmaximal, characteristic, complemented
15C2×C11×#336C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C11×#121C411yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic
25C11×#435—24no—
26C8×D4×C11—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—41no—
71C2×C11×M16—41no—
72C22×C8×C11—22no—
73C22×C8×C11—22no—
74C22×C8×C11—41no—
75C22×C8×C11—41no—
76C22×C8×C11—41no—
77C22×C8×C11—41no—
78C22×C8×C11—41no—
79C22×C8×C11—41no—
80C22×C8×C11D414yescomplemented
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#22172C1111yesmaximal, 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—22no—
150C2×D4×C11—41no—
151C2×D4×C11M1614yescomplemented
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—22no—
159C22×C4×C11—22no—
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—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—
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×C11—44no—
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—22no—
227C11×C22⋊C4—22no—
228C11×C22⋊C4—22no—
229C11×C22⋊C4—41no—
230C11×C22⋊C4—41no—
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×#435C2×C1111yescharacteristic, complemented
242C2×C8×D4C2×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#1869C2×C1111yescharacteristic, complemented
250#1869C2×C1111yescharacteristic, complemented
251#1869C2×C1111yescharacteristic, complemented
252#1851C2×C1111yescharacteristic, complemented
253#1850C2×C1111yescharacteristic, complemented
254#1797C2×C1111yescharacteristic, complemented
255C2×#336C2×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×C11C4×D412yes—
274C23×C11C2×M1612yes—
275C23×C11C2×M1612yes—
276C23×C11#13112yes—
277C23×C11C23×C411yescharacteristic
278D4×C11—28no—
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×C11#13112yes—
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
343C23×C8C22×C1111yescharacteristic
344C23×C8C22×C1111yescharacteristic
345C23×C8C22×C1111yescharacteristic
346C2×#121C4×C1111yescharacteristic
347C2×C4×D4C22×C1111yescharacteristic
348C2×C4×D4C22×C1111yescharacteristic
349C2×C4×D4C22×C1111yescharacteristic
350C22×C42C22×C1111yescharacteristic
351#435—24no—
352C8×D4—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—22no—
394C22×C11—22no—
395C22×C11—22no—
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#43514yes—
408C22×C11C2×C4×D411yescharacteristic
409C22×C11#51811yescharacteristic
410C22×C11#52011yescharacteristic
411C22×C11C22×M1611yescharacteristic
412C22×C11C2×#13111yescharacteristic
413C22×C11C2×#13111yescharacteristic
414C22×C11C2×#13111yescharacteristic
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—41no—
440C2×M16—41no—
441C22×C8—22no—
442C22×C8—22no—
443C22×C8—41no—
444C22×C8—41no—
445C22×C8—41no—
446C22×C8—41no—
447C22×C8—41no—
448C22×C8—41no—
449C22×C8D4×C1114yescomplemented
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—24no—
509C2×C11—42no—
510C2×C11—81no—
511C2×C11#232511yescharacteristic
512C2×C11C2×#43511yescharacteristic
513C2×C11#293111yescharacteristic
514C2×C11#297411yescharacteristic
515C2×C11#297711yescharacteristic
516C2×C11#299011yescharacteristic
517C2×C11#299411yescharacteristic
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—22no—
528C2×D4—41no—
529C2×D4C11×M1614yescomplemented
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
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×C4C2×D4×C1112yes—
564C22×C4C11×#4112yes—
565C22×C4C24×C1111yescharacteristic
566M16—44no—
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—21no—
588C2×C8—21no—
589C2×C8—44no—
590C2×C8—44no—
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—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—41no—
608C22⋊C4—41no—
609C42—21no—
610C42—21no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—41no—
618C42—41no—
619C11#2217211yescharacteristic, 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—
637C23C4×D4×C1112yes—
638C23C2×C11×M1612yes—
639C23C2×C11×M1612yes—
640C23C11×#13112yes—
641C23C23×C4×C1111yescharacteristic
642D4—28no—
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×C4C11×#13112yes—
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—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22C11×#43514yes—
727C22C2×C4×D4×C1111yescharacteristic
728C22C11×#51811yescharacteristic
729C22C11×#52011yescharacteristic
730C22C22×C11×M1611yescharacteristic
731C22C2×C11×#13111yescharacteristic
732C22C2×C11×#13111yescharacteristic
733C22C2×C11×#13111yescharacteristic
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—24no—
750C2—42no—
751C2—81no—
752C2C11×#232511yescharacteristic
753C2C2×C11×#43511yescharacteristic
754C2C11×#293111yescharacteristic
755C2C11×#297411yescharacteristic
756C2C11×#297711yescharacteristic
757C2C11×#299011yescharacteristic
758C2C11×#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
1. C2×C11×#435C2semidirect
2. C2×C8×D4×C11C2semidirect
4. C11×#1924C2semidirect
5. C11×#1923C2semidirect
6. C11×#1917C2semidirect
7. C11×#1916C2semidirect
8. C11×#1870C2semidirect
9. C11×#1869C2semidirect
10. C11×#1869C2semidirect
11. C11×#1869C2semidirect
12. C11×#1851C2semidirect
13. C11×#1850C2semidirect
14. C11×#1797C2semidirect
15. C2×C11×#336C2semidirect
80. C22×C8×C11D4semidirect
139. #22172C11direct (N × H)
151. C2×D4×C11M16semidirect
241. C2×#435C2×C11semidirect
242. C2×C8×D4C2×C11semidirect
244. #1924C2×C11semidirect
245. #1923C2×C11semidirect
246. #1917C2×C11semidirect
247. #1916C2×C11semidirect
248. #1870C2×C11semidirect
249. #1869C2×C11semidirect
250. #1869C2×C11semidirect
251. #1869C2×C11semidirect
252. #1851C2×C11semidirect
253. #1850C2×C11semidirect
254. #1797C2×C11semidirect
255. C2×#336C2×C11semidirect
449. C22×C8D4×C11semidirect
529. C2×D4C11×M16semidirect
619. C11#22172direct (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×C8×D4×C112
C4×C11×#1212
C11×#19242
C11×#19232
C11×#19172
C11×#19162
C11×#18702
C11×#18692
C11×#18512
C11×#18502
C11×#17972
C2×C11×#3362
#2217211