Finite Group Databasebeta

← C11×#22561 #14599754

Subgroups — C11×#22561 #14599754

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#433C211yesmaximal, characteristic, complemented
2C2×C11×#408C211yesmaximal, characteristic
3C11×#2297C211yesmaximal, characteristic
4C11×#1924C211yesmaximal, characteristic, complemented
5C11×#1924C211yesmaximal, characteristic, complemented
6C11×#1924C211yesmaximal, characteristic, complemented
7C11×#1923C211yesmaximal, characteristic, complemented
8C11×#1851C211yesmaximal, characteristic, complemented
9C11×#1850C211yesmaximal, characteristic, complemented
10C11×#1818C211yesmaximal, characteristic, complemented
11C11×#1797C211yesmaximal, characteristic, complemented
12C11×#1780C211yesmaximal, characteristic
13C11×#1753C211yesmaximal, characteristic, complemented
14C11×#1752C211yesmaximal, characteristic, complemented
15C11×#1749C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C11×#433—24no—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C11×#408—24no—
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×C11×#97C2211yescharacteristic
39C2×C11×#97C2211yescharacteristic
40C2×C4×C8×C11C2211yescharacteristic
41C11×#391C411yescharacteristic
42C11×#391C411yescharacteristic
43C11×#390C411yescharacteristic
44C11×#390C411yescharacteristic
45C11×#386C411yescharacteristic
46C11×#386C411yescharacteristic
47C11×#386C411yescharacteristic
48C11×#386C411yescharacteristic
49C4×C11×C22⋊C4C2211yescharacteristic
50C4×C11×C22⋊C4C2211yescharacteristic
51C4×C11×C22⋊C4C2211yescharacteristic
52C4×C11×C22⋊C4C2211yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—41no—
66C2×C11×#41—41no—
67C22×Q8×C11C2×C411yescharacteristic
68C22×D4×C11C2×C411yescharacteristic
69C22×D4×C11C2×C411yescharacteristic
70C22×D4×C11C2×C411yescharacteristic
71C23×C4×C11C2×C411yescharacteristic
72C23×C4×C11C2×C411yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C2×C11×M16—22no—
77C2×C11×M16—22no—
78C2×C11×M16—41no—
79C22×C8×C11—22no—
80C22×C8×C11—22no—
81C22×C8×C11—41no—
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C11×#117—22no—
91C11×#117—22no—
92C2×C11×C4⋊C4C2×C411yescharacteristic
93C2×C11×C4⋊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×C11×C22⋊C4C2×C411yescharacteristic
104C2×C42×C11—41no—
105C2×C42×C11—41no—
106C2×C42×C11C2×C411yescharacteristic
107C2×C42×C11C2×C411yescharacteristic
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C2×C42×C11C2311yescharacteristic
112C11×C4⋊C8—22no—
113C11×C4⋊C8—22no—
114C11×C4⋊C8—41no—
115C11×C4⋊C8—41no—
116C11×C22⋊C8—22no—
117C11×C22⋊C8—22no—
118C11×C22⋊C8—22no—
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⋊C8D414yes—
126C11×#97—22no—
127C11×#97—41no—
128C11×#97—41no—
129C4×C8×C11—22no—
130C11×#95C2×C411yescharacteristic
131C11×#95C2×C411yescharacteristic
132C11×#95C2×C411yescharacteristic
133C11×#95C2×C411yescharacteristic
134C11×#95C2×C411yescharacteristic
135C11×#95C2×C411yescharacteristic
136C11×#95C2×C411yescharacteristic
137C11×#95C2×C411yescharacteristic
138#22561C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11C22×C411yescharacteristic
140C24×C11C22×C411yescharacteristic
141C24×C11C22×C411yescharacteristic
142C11×#41—44no—
143C11×#41—44no—
144C11×#41—44no—
145C11×#41—44no—
146C2×Q8×C11—22no—
147C2×Q8×C11—22no—
148C2×Q8×C11—41no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—41no—
156C2×D4×C11—41no—
157C2×D4×C11—41no—
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—22no—
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—41no—
174C22×C4×C11—41no—
175C22×C4×C11—41no—
176C22×C4×C11—41no—
177C22×C4×C11—41no—
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×C11C22×C411yescharacteristic
188C22×C4×C11C22×C411yescharacteristic
189C22×C4×C11C2×D412yes—
190C22×C4×C11#4112yes—
191C22×C4×C11#4112yes—
192C22×C4×C11#4112yes—
193C22×C4×C11C2411yescharacteristic
194C11×M16—44no—
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—21no—
214C2×C8×C11—21no—
215C2×C8×C11—21no—
216C2×C8×C11—21no—
217C2×C8×C11—44no—
218C2×C8×C11C2×D412yes—
219C2×C8×C11C2×D412yes—
220C11×C4⋊C4—22no—
221C11×C4⋊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⋊C4—41no—
231C11×C22⋊C4—41no—
232C42×C11—21no—
233C42×C11—21no—
234C42×C11—21no—
235C42×C11—21no—
236C42×C11—21no—
237C42×C11—21no—
238C42×C11—21no—
239C42×C11—21no—
240C42×C11—41no—
241C42×C11—41no—
242C2×#433C2×C1111yescharacteristic, complemented
243C2×#408C2×C1111yescharacteristic
244#2297C2×C1111yescharacteristic
245#1924C2×C1111yescharacteristic, complemented
246#1924C2×C1111yescharacteristic, complemented
247#1924C2×C1111yescharacteristic, complemented
248#1923C2×C1111yescharacteristic, complemented
249#1851C2×C1111yescharacteristic, complemented
250#1850C2×C1111yescharacteristic, complemented
251#1818C2×C1111yescharacteristic, complemented
252#1797C2×C1111yescharacteristic, complemented
253#1780C2×C1111yescharacteristic
254#1753C2×C1111yescharacteristic, complemented
255#1752C2×C1111yescharacteristic, complemented
256#1749C2×C1111yescharacteristic, complemented
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×C11—21no—
276C23×C11#11712yes—
277C23×C11C4×D412yes—
278C23×C11C23×C411yescharacteristic
279Q8×C11—44no—
280D4×C11—44no—
281D4×C11—44no—
282D4×C11—44no—
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—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
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—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—44no—
322C2×C4×C11—44no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11#11712yes—
328C2×C4×C11C4×D412yes—
329C2×C4×C11#13112yes—
330C2×C4×C11C22×D411yescharacteristic
331C2×C4×C11C2×#4111yescharacteristic
332C2×C4×C11C2×#4111yescharacteristic
333C2×C4×C11C2×#4111yescharacteristic
334C2×C4×C11H(5,𝔽2)11yescharacteristic
335C2×C4×C11H(5,𝔽2)11yescharacteristic
336C8×C11—22no—
337C8×C11—22no—
338C8×C11—41no—
339C8×C11—41no—
340C8×C11—41no—
341C8×C11—41no—
342C8×C11—41no—
343C8×C11—41no—
344C22×#41C22×C1111yescharacteristic
345C22×M16C22×C1111yescharacteristic
346C23×C8C22×C1111yescharacteristic
347C2×#117C22×C1111yescharacteristic
348C22×C42C22×C1111yescharacteristic
349#433—24no—
350C2×C4⋊C8C22×C1111yescharacteristic
351C2×C4⋊C8C22×C1111yescharacteristic
352C2×C4⋊C8C22×C1111yescharacteristic
353C2×C4⋊C8C22×C1111yescharacteristic
354#408—24no—
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#391C4×C1111yescharacteristic
370#391C4×C1111yescharacteristic
371#390C4×C1111yescharacteristic
372#390C4×C1111yescharacteristic
373#386C4×C1111yescharacteristic
374#386C4×C1111yescharacteristic
375#386C4×C1111yescharacteristic
376#386C4×C1111yescharacteristic
377C4×C22⋊C4C22×C1111yescharacteristic
378C4×C22⋊C4C22×C1111yescharacteristic
379C4×C22⋊C4C22×C1111yescharacteristic
380C4×C22⋊C4C22×C1111yescharacteristic
381#336C22×C1111yescharacteristic
382#336C22×C1111yescharacteristic
383#336C22×C1111yescharacteristic
384#336C22×C1111yescharacteristic
385#336C22×C1111yescharacteristic
386#336C22×C1111yescharacteristic
387#336C22×C1111yescharacteristic
388#336C22×C1111yescharacteristic
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—22no—
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×C11—41no—
409C22×C11—41no—
410C22×C11C2×#11711yescharacteristic
411C22×C11C2×C4×D411yescharacteristic
412C22×C11#51811yescharacteristic
413C22×C11C2×#13111yescharacteristic
414C22×C11#56811yescharacteristic
415C22×C11#56811yescharacteristic
416C22×C11#56811yescharacteristic
417C4×C11—22no—
418C4×C11—22no—
419C4×C11—22no—
420C4×C11—41no—
421C4×C11—41no—
422C4×C11—41no—
423C4×C11—41no—
424C4×C11—41no—
425C4×C11—41no—
426C4×C11—41no—
427C4×C11—41no—
428C4×C11#54611yescharacteristic
429C4×C11#54611yescharacteristic
430C4×C11#55111yescharacteristic
431C4×C11#55111yescharacteristic
432C2×#41—22no—
433C2×#41—22no—
434C2×#41—22no—
435C2×#41—22no—
436C2×#41—41no—
437C2×#41—41no—
438C22×Q8C2×C4×C1111yescharacteristic
439C22×D4C2×C4×C1111yescharacteristic
440C22×D4C2×C4×C1111yescharacteristic
441C22×D4C2×C4×C1111yescharacteristic
442C23×C4C2×C4×C1111yescharacteristic
443C23×C4C2×C4×C1111yescharacteristic
444C23×C4C23×C1111yescharacteristic
445C23×C4C23×C1111yescharacteristic
446C23×C4C23×C1111yescharacteristic
447C2×M16—22no—
448C2×M16—22no—
449C2×M16—41no—
450C22×C8—22no—
451C22×C8—22no—
452C22×C8—41no—
453C22×C8C23×C1111yescharacteristic
454C22×C8C23×C1111yescharacteristic
455C22×C8C23×C1111yescharacteristic
456C22×C8C23×C1111yescharacteristic
457C22×C8C23×C1111yescharacteristic
458C22×C8C23×C1111yescharacteristic
459C22×C8C23×C1111yescharacteristic
460C22×C8C23×C1111yescharacteristic
461#117—22no—
462#117—22no—
463C2×C4⋊C4C2×C4×C1111yescharacteristic
464C2×C4⋊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×C22⋊C4C2×C4×C1111yescharacteristic
473C2×C22⋊C4C2×C4×C1111yescharacteristic
474C2×C22⋊C4C2×C4×C1111yescharacteristic
475C2×C42—41no—
476C2×C42—41no—
477C2×C42C2×C4×C1111yescharacteristic
478C2×C42C2×C4×C1111yescharacteristic
479C2×C42C23×C1111yescharacteristic
480C2×C42C23×C1111yescharacteristic
481C2×C42C23×C1111yescharacteristic
482C2×C42C23×C1111yescharacteristic
483C4⋊C8—22no—
484C4⋊C8—22no—
485C4⋊C8—41no—
486C4⋊C8—41no—
487C22⋊C8—22no—
488C22⋊C8—22no—
489C22⋊C8—22no—
490C22⋊C8—22no—
491C22⋊C8—22no—
492C22⋊C8—22no—
493C22⋊C8—22no—
494C22⋊C8—41no—
495C22⋊C8—41no—
496C22⋊C8D4×C1114yes—
497#97—22no—
498#97—41no—
499#97—41no—
500C4×C8—22no—
501#95C2×C4×C1111yescharacteristic
502#95C2×C4×C1111yescharacteristic
503#95C2×C4×C1111yescharacteristic
504#95C2×C4×C1111yescharacteristic
505#95C2×C4×C1111yescharacteristic
506#95C2×C4×C1111yescharacteristic
507#95C2×C4×C1111yescharacteristic
508#95C2×C4×C1111yescharacteristic
509C2×C11—42no—
510C2×C11—42no—
511C2×C11—81no—
512C2×C11#234211yescharacteristic
513C2×C11#292311yescharacteristic
514C2×C11#292511yescharacteristic
515C2×C11#293211yescharacteristic
516C2×C11#293511yescharacteristic
517C2×C11#297611yescharacteristic
518C2×C11#297811yescharacteristic
519C24C22×C4×C1111yescharacteristic
520C24C22×C4×C1111yescharacteristic
521C24C22×C4×C1111yescharacteristic
522#41—44no—
523#41—44no—
524#41—44no—
525#41—44no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—41no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—41no—
536C2×D4—41no—
537C2×D4—41no—
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—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4C22×C4×C1111yescharacteristic
559C22×C4C22×C4×C1111yescharacteristic
560C22×C4C22×C4×C1111yescharacteristic
561C22×C4C22×C4×C1111yescharacteristic
562C22×C4C22×C4×C1111yescharacteristic
563C22×C4C22×C4×C1111yescharacteristic
564C22×C4C22×C4×C1111yescharacteristic
565C22×C4C22×C4×C1111yescharacteristic
566C22×C4C22×C4×C1111yescharacteristic
567C22×C4C22×C4×C1111yescharacteristic
568C22×C4C22×C4×C1111yescharacteristic
569C22×C4C2×D4×C1112yes—
570C22×C4C11×#4112yes—
571C22×C4C11×#4112yes—
572C22×C4C11×#4112yes—
573C22×C4C24×C1111yescharacteristic
574M16—44no—
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—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—44no—
598C2×C8C2×D4×C1112yes—
599C2×C8C2×D4×C1112yes—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—41no—
607C22⋊C4—41no—
608C22⋊C4—41no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C22⋊C4—41no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—41no—
621C42—41no—
622C11#2256111yescharacteristic, direct product factor, Sylow
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—
639C23—21no—
640C23—21no—
641C23—21no—
642C23C11×#11712yes—
643C23C4×D4×C1112yes—
644C23C23×C4×C1111yescharacteristic
645Q8—44no—
646D4—44no—
647D4—44no—
648D4—44no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
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—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4C11×#11712yes—
694C2×C4C4×D4×C1112yes—
695C2×C4C11×#13112yes—
696C2×C4C22×D4×C1111yescharacteristic
697C2×C4C2×C11×#4111yescharacteristic
698C2×C4C2×C11×#4111yescharacteristic
699C2×C4C2×C11×#4111yescharacteristic
700C2×C4C11×H(5,𝔽2)11yescharacteristic
701C2×C4C11×H(5,𝔽2)11yescharacteristic
702C8—22no—
703C8—22no—
704C8—41no—
705C8—41no—
706C8—41no—
707C8—41no—
708C8—41no—
709C8—41no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22C2×C11×#11711yescharacteristic
732C22C2×C4×D4×C1111yescharacteristic
733C22C11×#51811yescharacteristic
734C22C2×C11×#13111yescharacteristic
735C22C11×#56811yescharacteristic
736C22C11×#56811yescharacteristic
737C22C11×#56811yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4C11×#54611yescharacteristic
750C4C11×#54611yescharacteristic
751C4C11×#55111yescharacteristic
752C4C11×#55111yescharacteristic
753C2—42no—
754C2—42no—
755C2—81no—
756C2C11×#234211yescharacteristic
757C2C11×#292311yescharacteristic
758C2C11×#292511yescharacteristic
759C2C11×#293211yescharacteristic
760C2C11×#293511yescharacteristic
761C2C11×#297611yescharacteristic
762C2C11×#297811yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC22×C11×#41C22
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×#433C2semidirect
4. C11×#1924C2semidirect
5. C11×#1924C2semidirect
6. C11×#1924C2semidirect
7. C11×#1923C2semidirect
8. C11×#1851C2semidirect
9. C11×#1850C2semidirect
10. C11×#1818C2semidirect
11. C11×#1797C2semidirect
13. C11×#1753C2semidirect
14. C11×#1752C2semidirect
15. C11×#1749C2semidirect
138. #22561C11direct (N × H)
242. C2×#433C2×C11semidirect
245. #1924C2×C11semidirect
246. #1924C2×C11semidirect
247. #1924C2×C11semidirect
248. #1923C2×C11semidirect
249. #1851C2×C11semidirect
250. #1850C2×C11semidirect
251. #1818C2×C11semidirect
252. #1797C2×C11semidirect
254. #1753C2×C11semidirect
255. #1752C2×C11semidirect
256. #1749C2×C11semidirect
622. C11#22561direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4332
C2×C11×#4082
C11×#22972
C11×#19242
C11×#19232
C11×#18512
C11×#18502
C11×#18182
C11×#17972
C11×#17802
C11×#17532
C11×#17522
C11×#17492
#2256111