Finite Group Databasebeta

← C11×#22991 #14600184

Subgroups — C11×#22991 #14600184

Order 2816.

1040 conjugacy classes of subgroups.

The subgroup lattice has 758 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
3C2×C8×D4×C11C211yesmaximal, characteristic, complemented
4C2×C11×#424C211yesmaximal, characteristic, complemented
5C11×#2392C211yesmaximal, characteristic
6C11×#1955C211yesmaximal, characteristic, complemented
7C11×#1939C211yesmaximal, characteristic, complemented
8C11×#1924C211yesmaximal, characteristic, complemented
9C11×#1923C211yesmaximal, characteristic, complemented
10C11×#1870C211yesmaximal, characteristic, complemented
11C11×#1869C211yesmaximal, characteristic, complemented
12C11×#1850C211yesmaximal, characteristic, complemented
13C11×#1850C211yesmaximal, characteristic, complemented
14C11×#1771C211yesmaximal, characteristic, complemented
15C11×#1750C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C11×#435—24no—
25C8×D4×C11—24no—
26C8×D4×C11—24no—
27C11×#424—24no—
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×C4⋊C8C2211yescharacteristic
33C2×C11×C4⋊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×C22⋊C8C2211yescharacteristic
42C2×C11×#97C2211yescharacteristic
43C2×C11×#97C2211yescharacteristic
44C2×C4×C8×C11C2211yescharacteristic
45C2×C4×C8×C11C2211yescharacteristic
46C11×#398C411yescharacteristic
47C11×#397C411yescharacteristic
48C11×#396C411yescharacteristic
49C11×#396C411yescharacteristic
50C11×#394C411yescharacteristic
51C11×#394C411yescharacteristic
52C11×#394C411yescharacteristic
53C11×#392C411yescharacteristic
54C4×C11×C4⋊C4C2211yescharacteristic
55C4×C11×C22⋊C4C2211yescharacteristic
56C4×C11×C22⋊C4C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C22×D4×C11C2×C411yescharacteristic
64C22×D4×C11C2×C411yescharacteristic
65C22×D4×C11C2×C411yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C2×C11×M16—22no—
70C2×C11×M16—22no—
71C2×C11×M16—41no—
72C22×C8×C11—22no—
73C22×C8×C11—22no—
74C22×C8×C11—22no—
75C22×C8×C11—22no—
76C22×C8×C11—22no—
77C22×C8×C11—22no—
78C22×C8×C11—41no—
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
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C11×#117—22no—
96C11×#117—22no—
97C2×C11×C4⋊C4C2×C411yescharacteristic
98C2×C11×C4⋊C4C2×C411yescharacteristic
99C2×C11×C4⋊C4C2×C411yescharacteristic
100C2×C11×C4⋊C4C2×C411yescharacteristic
101C2×C11×C4⋊C4C2×C411yescharacteristic
102C2×C11×C4⋊C4C2×C411yescharacteristic
103C2×C11×C4⋊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×C11×C22⋊C4C2×C411yescharacteristic
112C2×C11×C22⋊C4C2×C411yescharacteristic
113C2×C11×C22⋊C4C2×C411yescharacteristic
114C2×C11×C22⋊C4C2×C411yescharacteristic
115C2×C11×C22⋊C4C2×C411yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C2×C42×C11C2311yescharacteristic
119C2×C42×C11C2311yescharacteristic
120C11×C4⋊C8—22no—
121C11×C4⋊C8—22no—
122C11×C4⋊C8—22no—
123C11×C4⋊C8—22no—
124C11×C4⋊C8—22no—
125C11×C4⋊C8D414yescomplemented
126C11×C22⋊C8—22no—
127C11×C22⋊C8—22no—
128C11×C22⋊C8—22no—
129C11×C22⋊C8—22no—
130C11×C22⋊C8—22no—
131C11×C22⋊C8—41no—
132C11×C22⋊C8—41no—
133C11×C22⋊C8D414yescomplemented
134C11×#97—22no—
135C11×#97—22no—
136C4×C8×C11—22no—
137C4×C8×C11—22no—
138C11×#95C2×C411yescharacteristic
139C11×#95C2×C411yescharacteristic
140C11×#95C2×C411yescharacteristic
141C11×#95C2×C411yescharacteristic
142C11×#95C2×C411yescharacteristic
143C11×#95C2×C411yescharacteristic
144#22991C1111yesmaximal, characteristic, direct product factor, Sylow
145C24×C11C22×C411yescharacteristic
146C24×C11C22×C411yescharacteristic
147C24×C11C22×C411yescharacteristic
148C2×D4×C11—22no—
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—22no—
156C2×D4×C11—41no—
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×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×C11C22×C411yescharacteristic
182C22×C4×C11C22×C411yescharacteristic
183C22×C4×C11C22×C411yescharacteristic
184C22×C4×C11C2×D412yes—
185C22×C4×C11#4112yes—
186C22×C4×C11C2411yescharacteristic
187C11×M16—44no—
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—21no—
208C2×C8×C11—44no—
209C2×C8×C11—44no—
210C2×C8×C11—44no—
211C2×C8×C11C2×D412yes—
212C2×C8×C11C2×D412yes—
213C2×C8×C11C2×D412yes—
214C2×C8×C11C2×D412yes—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—22no—
217C11×C4⋊C4—22no—
218C11×C4⋊C4—22no—
219C11×C4⋊C4—22no—
220C11×C4⋊C4—22no—
221C11×C4⋊C4—41no—
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—22no—
230C11×C22⋊C4—22no—
231C11×C22⋊C4—22no—
232C11×C22⋊C4—22no—
233C11×C22⋊C4—41no—
234C42×C11—21no—
235C42×C11—21no—
236C42×C11—21no—
237C42×C11—21no—
238C42×C11—21no—
239C42×C11—21no—
240C42×C11C2×D412yes—
241C42×C11#4112yes—
242C2×#435C2×C1111yescharacteristic, complemented
243C2×C8×D4C2×C1111yescharacteristic, complemented
244C2×C8×D4C2×C1111yescharacteristic, complemented
245C2×#424C2×C1111yescharacteristic, complemented
246#2392C2×C1111yescharacteristic
247#1955C2×C1111yescharacteristic, complemented
248#1939C2×C1111yescharacteristic, complemented
249#1924C2×C1111yescharacteristic, complemented
250#1923C2×C1111yescharacteristic, complemented
251#1870C2×C1111yescharacteristic, complemented
252#1869C2×C1111yescharacteristic, complemented
253#1850C2×C1111yescharacteristic, complemented
254#1850C2×C1111yescharacteristic, complemented
255#1771C2×C1111yescharacteristic, complemented
256#1750C2×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×C11C4×D412yes—
276C23×C11#13112yes—
277C23×C11#13112yes—
278C23×C11C23×C411yescharacteristic
279D4×C11—28no—
280D4×C11—28no—
281D4×C11—44no—
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—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
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—21no—
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×C11—41no—
323C2×C4×C11C4×D412yes—
324C2×C4×C11C4×D412yes—
325C2×C4×C11C4×D412yes—
326C2×C4×C11#13112yes—
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C2×#4111yescharacteristic
330C2×C4×C11C2×#4111yescharacteristic
331C2×C4×C11H(5,𝔽2)11yescharacteristic
332C2×C4×C112−1+411yescharacteristic
333C8×C11—22no—
334C8×C11—22no—
335C8×C11—22no—
336C8×C11—22no—
337C8×C11—41no—
338C8×C11—41no—
339C8×C11—41no—
340C8×C11—41no—
341C22×M16C22×C1111yescharacteristic
342C23×C8C22×C1111yescharacteristic
343C23×C8C22×C1111yescharacteristic
344C23×C8C22×C1111yescharacteristic
345C2×C4×D4C22×C1111yescharacteristic
346C2×C4×D4C22×C1111yescharacteristic
347C2×C4×D4C22×C1111yescharacteristic
348C2×#117C22×C1111yescharacteristic
349#435—24no—
350C8×D4—24no—
351C8×D4—24no—
352#424—24no—
353C2×C4⋊C8C22×C1111yescharacteristic
354C2×C4⋊C8C22×C1111yescharacteristic
355C2×C4⋊C8C22×C1111yescharacteristic
356C2×C4⋊C8C22×C1111yescharacteristic
357C2×C4⋊C8C22×C1111yescharacteristic
358C2×C4⋊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×C22⋊C8C22×C1111yescharacteristic
366C2×C22⋊C8C22×C1111yescharacteristic
367C2×#97C22×C1111yescharacteristic
368C2×#97C22×C1111yescharacteristic
369C2×C4×C8C22×C1111yescharacteristic
370C2×C4×C8C22×C1111yescharacteristic
371#398C4×C1111yescharacteristic
372#397C4×C1111yescharacteristic
373#396C4×C1111yescharacteristic
374#396C4×C1111yescharacteristic
375#394C4×C1111yescharacteristic
376#394C4×C1111yescharacteristic
377#394C4×C1111yescharacteristic
378#392C4×C1111yescharacteristic
379C4×C4⋊C4C22×C1111yescharacteristic
380C4×C22⋊C4C22×C1111yescharacteristic
381C4×C22⋊C4C22×C1111yescharacteristic
382#336C22×C1111yescharacteristic
383#336C22×C1111yescharacteristic
384#336C22×C1111yescharacteristic
385#336C22×C1111yescharacteristic
386#336C22×C1111yescharacteristic
387#336C22×C1111yescharacteristic
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—22no—
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×C11C2×C4×D411yescharacteristic
410C22×C11C2×C4×D411yescharacteristic
411C22×C11#52011yescharacteristic
412C22×C11C2×#13111yescharacteristic
413C22×C11C2×#13111yescharacteristic
414C22×C11C2×#13111yescharacteristic
415C22×C11#56811yescharacteristic
416C4×C11—22no—
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×C11D4211yescharacteristic
428C4×C11#54711yescharacteristic
429C4×C11#54811yescharacteristic
430C4×C11#55311yescharacteristic
431C22×D4C2×C4×C1111yescharacteristic
432C22×D4C2×C4×C1111yescharacteristic
433C22×D4C2×C4×C1111yescharacteristic
434C23×C4C23×C1111yescharacteristic
435C23×C4C23×C1111yescharacteristic
436C23×C4C23×C1111yescharacteristic
437C2×M16—22no—
438C2×M16—22no—
439C2×M16—41no—
440C22×C8—22no—
441C22×C8—22no—
442C22×C8—22no—
443C22×C8—22no—
444C22×C8—22no—
445C22×C8—22no—
446C22×C8—41no—
447C22×C8—41no—
448C22×C8—41no—
449C22×C8C23×C1111yescharacteristic
450C22×C8C23×C1111yescharacteristic
451C22×C8C23×C1111yescharacteristic
452C22×C8C23×C1111yescharacteristic
453C22×C8C23×C1111yescharacteristic
454C22×C8C23×C1111yescharacteristic
455C22×C8C23×C1111yescharacteristic
456C22×C8C23×C1111yescharacteristic
457C4×D4—22no—
458C4×D4—22no—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4—22no—
463#117—22no—
464#117—22no—
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×C4⋊C4C2×C4×C1111yescharacteristic
471C2×C4⋊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×C22⋊C4C2×C4×C1111yescharacteristic
481C2×C22⋊C4C2×C4×C1111yescharacteristic
482C2×C22⋊C4C2×C4×C1111yescharacteristic
483C2×C22⋊C4C2×C4×C1111yescharacteristic
484C2×C42C23×C1111yescharacteristic
485C2×C42C23×C1111yescharacteristic
486C2×C42C23×C1111yescharacteristic
487C2×C42C23×C1111yescharacteristic
488C4⋊C8—22no—
489C4⋊C8—22no—
490C4⋊C8—22no—
491C4⋊C8—22no—
492C4⋊C8—22no—
493C4⋊C8D4×C1114yescomplemented
494C22⋊C8—22no—
495C22⋊C8—22no—
496C22⋊C8—22no—
497C22⋊C8—22no—
498C22⋊C8—22no—
499C22⋊C8—41no—
500C22⋊C8—41no—
501C22⋊C8D4×C1114yescomplemented
502#97—22no—
503#97—22no—
504C4×C8—22no—
505C4×C8—22no—
506#95C2×C4×C1111yescharacteristic
507#95C2×C4×C1111yescharacteristic
508#95C2×C4×C1111yescharacteristic
509#95C2×C4×C1111yescharacteristic
510#95C2×C4×C1111yescharacteristic
511#95C2×C4×C1111yescharacteristic
512C2×C11—42no—
513C2×C11—42no—
514C2×C11—42no—
515C2×C11#236111yescharacteristic
516C2×C11#292911yescharacteristic
517C2×C11#292911yescharacteristic
518C2×C11#293311yescharacteristic
519C2×C11#293511yescharacteristic
520C2×C11#299211yescharacteristic
521C2×C11#299411yescharacteristic
522C24C22×C4×C1111yescharacteristic
523C24C22×C4×C1111yescharacteristic
524C24C22×C4×C1111yescharacteristic
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—41no—
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×C4C22×C4×C1111yescharacteristic
551C22×C4C22×C4×C1111yescharacteristic
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×C4C2×D4×C1112yes—
562C22×C4C11×#4112yes—
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—44no—
586C2×C8—44no—
587C2×C8—44no—
588C2×C8C2×D4×C1112yes—
589C2×C8C2×D4×C1112yes—
590C2×C8C2×D4×C1112yes—
591C2×C8C2×D4×C1112yes—
592C4⋊C4—22no—
593C4⋊C4—22no—
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—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—41no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42C2×D4×C1112yes—
618C42C11×#4112yes—
619C11#2299111yescharacteristic, 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—
638C23C4×D4×C1112yes—
639C23C11×#13112yes—
640C23C11×#13112yes—
641C23C23×C4×C1111yescharacteristic
642D4—28no—
643D4—28no—
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—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4C4×D4×C1112yes—
687C2×C4C4×D4×C1112yes—
688C2×C4C4×D4×C1112yes—
689C2×C4C11×#13112yes—
690C2×C4C22×D4×C1111yescharacteristic
691C2×C4C22×D4×C1111yescharacteristic
692C2×C4C2×C11×#4111yescharacteristic
693C2×C4C2×C11×#4111yescharacteristic
694C2×C4C11×H(5,𝔽2)11yescharacteristic
695C2×C4C11×2−1+411yescharacteristic
696C8—22no—
697C8—22no—
698C8—22no—
699C8—22no—
700C8—41no—
701C8—41no—
702C8—41no—
703C8—41no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22C2×C4×D4×C1111yescharacteristic
726C22C2×C4×D4×C1111yescharacteristic
727C22C11×#52011yescharacteristic
728C22C2×C11×#13111yescharacteristic
729C22C2×C11×#13111yescharacteristic
730C22C2×C11×#13111yescharacteristic
731C22C11×#56811yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—22no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4D42×C1111yescharacteristic
744C4C11×#54711yescharacteristic
745C4C11×#54811yescharacteristic
746C4C11×#55311yescharacteristic
747C2—42no—
748C2—42no—
749C2—42no—
750C2C11×#236111yescharacteristic
751C2C11×#292911yescharacteristic
752C2C11×#292911yescharacteristic
753C2C11×#293311yescharacteristic
754C2C11×#293511yescharacteristic
755C2C11×#299211yescharacteristic
756C2C11×#299411yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC11×#392C4
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
3. C2×C8×D4×C11C2semidirect
4. C2×C11×#424C2semidirect
6. C11×#1955C2semidirect
7. C11×#1939C2semidirect
8. C11×#1924C2semidirect
9. C11×#1923C2semidirect
10. C11×#1870C2semidirect
11. C11×#1869C2semidirect
12. C11×#1850C2semidirect
13. C11×#1850C2semidirect
14. C11×#1771C2semidirect
15. C11×#1750C2semidirect
125. C11×C4⋊C8D4semidirect
133. C11×C22⋊C8D4semidirect
144. #22991C11direct (N × H)
242. C2×#435C2×C11semidirect
243. C2×C8×D4C2×C11semidirect
244. C2×C8×D4C2×C11semidirect
245. C2×#424C2×C11semidirect
247. #1955C2×C11semidirect
248. #1939C2×C11semidirect
249. #1924C2×C11semidirect
250. #1923C2×C11semidirect
251. #1870C2×C11semidirect
252. #1869C2×C11semidirect
253. #1850C2×C11semidirect
254. #1850C2×C11semidirect
255. #1771C2×C11semidirect
256. #1750C2×C11semidirect
493. C4⋊C8D4×C11semidirect
501. C22⋊C8D4×C11semidirect
619. C11#22991direct (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
C2×C11×#4242
C11×#23922
C11×#19552
C11×#19392
C11×#19242
C11×#19232
C11×#18702
C11×#18692
C11×#18502
C11×#17712
C11×#17502
#2299111