Finite Group Databasebeta

← C2×C11×#2654 #14611775

Subgroups — C2×C11×#2654 #14611775

Order 2816.

1962 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2654C2116yesmaximal, direct product factor
2C2×C11×#400C211yesmaximal, characteristic, complemented
3C2×C11×#400C211yesmaximal, characteristic, complemented
4C2×C11×#399C211yesmaximal, characteristic
5C2×C11×#398C211yesmaximal, characteristic, complemented
6C2×C11×#398C211yesmaximal, characteristic, complemented
7C2×C11×#397C211yesmaximal, characteristic
8C2×C11×#397C211yesmaximal, characteristic
9C2×C11×#396C211yesmaximal, characteristic
10C2×C11×#389C211yesmaximal, characteristic, complemented
11C2×C11×#388C211yesmaximal, characteristic
12C2×C11×#388C211yesmaximal, characteristic
13C2×C11×#388C211yesmaximal, characteristic
14C2×C11×#387C211yesmaximal, characteristic, complemented
15C2×C11×#387C211yesmaximal, characteristic, complemented
16C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C22×C11×C22⋊C4C2211yescharacteristic
33C22×C11×C22⋊C4C2211yescharacteristic
34C22×C11×C22⋊C4C2211yescharacteristic
35C22×C42×C11C2211yescharacteristic
36C22×C42×C11C2211yescharacteristic
37C22×C42×C11C2211yescharacteristic
38C11×#400C2218yescomplemented
39C11×#400C2218yescomplemented
40C11×#399C2218yes—
41C11×#398C2218yescomplemented
42C11×#398C2218yescomplemented
43C11×#397C2218yes—
44C11×#397C2218yes—
45C11×#396C2218yes—
46C11×#389C2218yescomplemented
47C11×#388C2218yes—
48C11×#388C2218yes—
49C11×#388C2218yes—
50C11×#387C2218yescomplemented
51C11×#387C2218yescomplemented
52C4×C11×C4⋊C4C2218yescomplemented
53C2×C11×#95C2211yescharacteristic
54C2×C11×#95C2211yescharacteristic
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57C2×C11×#95C2211yescharacteristic
58C2×C11×#95C2211yescharacteristic
59C2×C11×#95C2211yescharacteristic
60C2×C11×#95C2211yescharacteristic
61C2×C11×#95C2211yescharacteristic
62C2×C11×#95C2211yescharacteristic
63C2×C11×#95C2211yescharacteristic
64C2×C11×#95C2211yescharacteristic
65C2×C11×#95C2211yescharacteristic
66C2×C11×#95C2211yescharacteristic
67C25×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C2×C11×C4⋊C4—24no—
83C2×C11×C4⋊C4—24no—
84C2×C11×C4⋊C4—24no—
85C2×C11×C4⋊C4—24no—
86C2×C11×C4⋊C4—24no—
87C2×C11×C4⋊C4—42no—
88C2×C11×C4⋊C4—42no—
89C2×C11×C4⋊C4—42no—
90C2×C11×C4⋊C4—42no—
91C2×C11×C4⋊C4—42no—
92C2×C11×C4⋊C4—42no—
93C2×C11×C4⋊C4C2314yes—
94C2×C11×C4⋊C4C2314yes—
95C2×C11×C4⋊C4C2314yes—
96C2×C11×C4⋊C4C2314yes—
97C2×C11×C4⋊C4C2314yes—
98C2×C11×C4⋊C4C2314yes—
99C2×C11×C4⋊C4C2314yes—
100C2×C11×C4⋊C4C2314yes—
101C2×C11×C4⋊C4C2314yes—
102C2×C11×C4⋊C4C2314yes—
103C2×C11×C4⋊C4C2314yes—
104C2×C11×C22⋊C4—24no—
105C2×C11×C22⋊C4—24no—
106C2×C11×C22⋊C4—24no—
107C2×C11×C22⋊C4—42no—
108C2×C11×C22⋊C4—42no—
109C2×C11×C22⋊C4—42no—
110C2×C11×C22⋊C4—42no—
111C2×C11×C22⋊C4C2314yes—
112C2×C11×C22⋊C4C2314yes—
113C2×C11×C22⋊C4C2314yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C11×C22⋊C4C2314yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C11×C22⋊C4C2314yes—
118C2×C42×C11—24no—
119C2×C42×C11—42no—
120C2×C42×C11—42no—
121C2×C42×C11C2314yes—
122C2×C42×C11C2314yes—
123C2×C42×C11C2314yes—
124C11×#95C2314yes—
125C11×#95C2314yes—
126C11×#95C2314yes—
127C11×#95C2314yes—
128C11×#95C2314yes—
129C11×#95C2314yes—
130C11×#95C2314yes—
131C11×#95C2314yes—
132C11×#95C2314yes—
133C11×#95C2314yes—
134C11×#95C2314yes—
135C11×#95C2314yes—
136C11×#95C2314yes—
137C11×#95C2314yes—
138C2×#2654C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—22no—
140C24×C11—22no—
141C24×C11—22no—
142C24×C11—22no—
143C24×C11—22no—
144C24×C11—22no—
145C24×C11—22no—
146C24×C11C2412yes—
147C24×C11C2411yescharacteristic
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11#4114yes—
188C22×C4×C11#4114yes—
189C22×C4×C11#4114yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2412yes—
192C22×C4×C11C2412yes—
193C22×C4×C11C2412yes—
194C22×C4×C11C2412yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2412yes—
200C22×C4×C11C2412yes—
201C22×C4×C11C2412yes—
202C22×C4×C11C2412yes—
203C22×C4×C11C2412yes—
204C11×C4⋊C4—28no—
205C11×C4⋊C4—28no—
206C11×C4⋊C4—28no—
207C11×C4⋊C4—28no—
208C11×C4⋊C4—28no—
209C11×C4⋊C4—44no—
210C11×C4⋊C4—44no—
211C11×C4⋊C4—44no—
212C11×C4⋊C4—44no—
213C11×C4⋊C4—44no—
214C11×C4⋊C4—44no—
215C11×C22⋊C4—28no—
216C11×C22⋊C4—28no—
217C11×C22⋊C4—28no—
218C11×C22⋊C4—44no—
219C11×C22⋊C4—44no—
220C11×C22⋊C4—44no—
221C11×C22⋊C4—44no—
222C42×C11—28no—
223C42×C11—44no—
224C42×C11—44no—
225#2654C2×C11116yesdirect product factor
226C2×#400C2×C1111yescharacteristic, complemented
227C2×#400C2×C1111yescharacteristic, complemented
228C2×#399C2×C1111yescharacteristic
229C2×#398C2×C1111yescharacteristic, complemented
230C2×#398C2×C1111yescharacteristic, complemented
231C2×#397C2×C1111yescharacteristic
232C2×#397C2×C1111yescharacteristic
233C2×#396C2×C1111yescharacteristic
234C2×#389C2×C1111yescharacteristic, complemented
235C2×#388C2×C1111yescharacteristic
236C2×#388C2×C1111yescharacteristic
237C2×#388C2×C1111yescharacteristic
238C2×#387C2×C1111yescharacteristic, complemented
239C2×#387C2×C1111yescharacteristic, complemented
240C2×C4×C4⋊C4C2×C1111yescharacteristic, complemented
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—44no—
249C23×C11—44no—
250C23×C11—44no—
251C23×C11—44no—
252C23×C11—44no—
253C23×C11—44no—
254C23×C11—44no—
255C23×C11C2×#4112yes—
256C23×C11C2×#4112yes—
257C23×C11C2×#4112yes—
258C23×C11H(5,𝔽2)12yes—
259C23×C11H(5,𝔽2)12yes—
260C23×C112−1+412yes—
261C23×C112−1+412yes—
262C23×C11C2511yescharacteristic
263C2×C4×C11—28no—
264C2×C4×C11—28no—
265C2×C4×C11—28no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
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—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—44no—
306C2×C4×C11—44no—
307C2×C4×C11—44no—
308C2×C4×C11—44no—
309C2×C4×C11—44no—
310C2×C4×C11—44no—
311C2×C4×C11—44no—
312C2×C4×C11—44no—
313C2×C4×C11—44no—
314C2×C4×C11—44no—
315C2×C4×C11—44no—
316C2×C4×C11C2×#4114yes—
317C2×C4×C11C2×#4114yes—
318C2×C4×C11C2×#4114yes—
319C22×C4⋊C4C22×C1111yescharacteristic
320C22×C4⋊C4C22×C1111yescharacteristic
321C22×C4⋊C4C22×C1111yescharacteristic
322C22×C4⋊C4C22×C1111yescharacteristic
323C22×C4⋊C4C22×C1111yescharacteristic
324C22×C4⋊C4C22×C1111yescharacteristic
325C22×C4⋊C4C22×C1111yescharacteristic
326C22×C4⋊C4C22×C1111yescharacteristic
327C22×C4⋊C4C22×C1111yescharacteristic
328C22×C4⋊C4C22×C1111yescharacteristic
329C22×C4⋊C4C22×C1111yescharacteristic
330C22×C22⋊C4C22×C1111yescharacteristic
331C22×C22⋊C4C22×C1111yescharacteristic
332C22×C22⋊C4C22×C1111yescharacteristic
333C22×C22⋊C4C22×C1111yescharacteristic
334C22×C22⋊C4C22×C1111yescharacteristic
335C22×C22⋊C4C22×C1111yescharacteristic
336C22×C22⋊C4C22×C1111yescharacteristic
337C22×C42C22×C1111yescharacteristic
338C22×C42C22×C1111yescharacteristic
339C22×C42C22×C1111yescharacteristic
340#400C22×C1118yescomplemented
341#400C22×C1118yescomplemented
342#399C22×C1118yes—
343#398C22×C1118yescomplemented
344#398C22×C1118yescomplemented
345#397C22×C1118yes—
346#397C22×C1118yes—
347#396C22×C1118yes—
348#389C22×C1118yescomplemented
349#388C22×C1118yes—
350#388C22×C1118yes—
351#388C22×C1118yes—
352#387C22×C1118yescomplemented
353#387C22×C1118yescomplemented
354C4×C4⋊C4C22×C1118yescomplemented
355C2×#95C22×C1111yescharacteristic
356C2×#95C22×C1111yescharacteristic
357C2×#95C22×C1111yescharacteristic
358C2×#95C22×C1111yescharacteristic
359C2×#95C22×C1111yescharacteristic
360C2×#95C22×C1111yescharacteristic
361C2×#95C22×C1111yescharacteristic
362C2×#95C22×C1111yescharacteristic
363C2×#95C22×C1111yescharacteristic
364C2×#95C22×C1111yescharacteristic
365C2×#95C22×C1111yescharacteristic
366C2×#95C22×C1111yescharacteristic
367C2×#95C22×C1111yescharacteristic
368C2×#95C22×C1111yescharacteristic
369C22×C11—42no—
370C22×C11—42no—
371C22×C11—42no—
372C22×C11—42no—
373C22×C11—42no—
374C22×C11—42no—
375C22×C11—42no—
376C22×C11—88no—
377C22×C11#52914yes—
378C22×C11#53914yes—
379C22×C11#53914yes—
380C22×C11#54014yes—
381C22×C11#54114yes—
382C22×C11#54214yes—
383C22×C11#54214yes—
384C22×C11C22×#4111yescharacteristic
385C22×C11C22×#4111yescharacteristic
386C22×C11C22×#4111yescharacteristic
387C22×C11C2×H(5,𝔽2)11yescharacteristic
388C22×C11C2×H(5,𝔽2)11yescharacteristic
389C22×C11C2×2−1+411yescharacteristic
390C22×C11C2×2−1+411yescharacteristic
391C4×C11—24no—
392C4×C11—24no—
393C4×C11—24no—
394C4×C11—42no—
395C4×C11—42no—
396C4×C11—42no—
397C4×C11—42no—
398C4×C11—42no—
399C4×C11—42no—
400C4×C11—42no—
401C4×C11—42no—
402C4×C11—42no—
403C4×C11—42no—
404C4×C11—42no—
405C25C23×C1111yescharacteristic
406C23×C4C23×C1111yescharacteristic
407C23×C4C23×C1111yescharacteristic
408C23×C4C23×C1111yescharacteristic
409C23×C4C23×C1111yescharacteristic
410C23×C4C23×C1111yescharacteristic
411C23×C4C23×C1111yescharacteristic
412C23×C4C23×C1111yescharacteristic
413C23×C4C23×C1111yescharacteristic
414C23×C4C23×C1111yescharacteristic
415C23×C4C23×C1111yescharacteristic
416C23×C4C23×C1111yescharacteristic
417C23×C4C23×C1111yescharacteristic
418C23×C4C23×C1111yescharacteristic
419C23×C4C23×C1111yescharacteristic
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4—42no—
431C2×C4⋊C4C23×C1114yes—
432C2×C4⋊C4C23×C1114yes—
433C2×C4⋊C4C23×C1114yes—
434C2×C4⋊C4C23×C1114yes—
435C2×C4⋊C4C23×C1114yes—
436C2×C4⋊C4C23×C1114yes—
437C2×C4⋊C4C23×C1114yes—
438C2×C4⋊C4C23×C1114yes—
439C2×C4⋊C4C23×C1114yes—
440C2×C4⋊C4C23×C1114yes—
441C2×C4⋊C4C23×C1114yes—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—42no—
446C2×C22⋊C4—42no—
447C2×C22⋊C4—42no—
448C2×C22⋊C4—42no—
449C2×C22⋊C4C23×C1114yes—
450C2×C22⋊C4C23×C1114yes—
451C2×C22⋊C4C23×C1114yes—
452C2×C22⋊C4C23×C1114yes—
453C2×C22⋊C4C23×C1114yes—
454C2×C22⋊C4C23×C1114yes—
455C2×C22⋊C4C23×C1114yes—
456C2×C42—24no—
457C2×C42—42no—
458C2×C42—42no—
459C2×C42C23×C1114yes—
460C2×C42C23×C1114yes—
461C2×C42C23×C1114yes—
462#95C23×C1114yes—
463#95C23×C1114yes—
464#95C23×C1114yes—
465#95C23×C1114yes—
466#95C23×C1114yes—
467#95C23×C1114yes—
468#95C23×C1114yes—
469#95C23×C1114yes—
470#95C23×C1114yes—
471#95C23×C1114yes—
472#95C23×C1114yes—
473#95C23×C1114yes—
474#95C23×C1114yes—
475#95C23×C1114yes—
476C2×C11—82no—
477C2×C11#265418yesdirect product factor
478C2×C11C2×#52911yescharacteristic
479C2×C11C2×#53911yescharacteristic
480C2×C11C2×#53911yescharacteristic
481C2×C11C2×#54011yescharacteristic
482C2×C11C2×#54111yescharacteristic
483C2×C11C2×#54211yescharacteristic
484C2×C11C2×#54211yescharacteristic
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24C24×C1112yes—
493C24C24×C1111yescharacteristic
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4C11×#4114yes—
534C22×C4C11×#4114yes—
535C22×C4C11×#4114yes—
536C22×C4C24×C1112yes—
537C22×C4C24×C1112yes—
538C22×C4C24×C1112yes—
539C22×C4C24×C1112yes—
540C22×C4C24×C1112yes—
541C22×C4C24×C1112yes—
542C22×C4C24×C1112yes—
543C22×C4C24×C1112yes—
544C22×C4C24×C1112yes—
545C22×C4C24×C1112yes—
546C22×C4C24×C1112yes—
547C22×C4C24×C1112yes—
548C22×C4C24×C1112yes—
549C22×C4C24×C1112yes—
550C4⋊C4—28no—
551C4⋊C4—28no—
552C4⋊C4—28no—
553C4⋊C4—28no—
554C4⋊C4—28no—
555C4⋊C4—44no—
556C4⋊C4—44no—
557C4⋊C4—44no—
558C4⋊C4—44no—
559C4⋊C4—44no—
560C4⋊C4—44no—
561C22⋊C4—28no—
562C22⋊C4—28no—
563C22⋊C4—28no—
564C22⋊C4—44no—
565C22⋊C4—44no—
566C22⋊C4—44no—
567C22⋊C4—44no—
568C42—28no—
569C42—44no—
570C42—44no—
571C11C2×#265411yescharacteristic, direct product factor, Sylow
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—44no—
580C23—44no—
581C23—44no—
582C23—44no—
583C23—44no—
584C23—44no—
585C23—44no—
586C23C2×C11×#4112yes—
587C23C2×C11×#4112yes—
588C23C2×C11×#4112yes—
589C23C11×H(5,𝔽2)12yes—
590C23C11×H(5,𝔽2)12yes—
591C23C11×2−1+412yes—
592C23C11×2−1+412yes—
593C23C25×C1111yescharacteristic
594C2×C4—28no—
595C2×C4—28no—
596C2×C4—28no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4C2×C11×#4114yes—
648C2×C4C2×C11×#4114yes—
649C2×C4C2×C11×#4114yes—
650C22—42no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—88no—
658C22C11×#52914yes—
659C22C11×#53914yes—
660C22C11×#53914yes—
661C22C11×#54014yes—
662C22C11×#54114yes—
663C22C11×#54214yes—
664C22C11×#54214yes—
665C22C22×C11×#4111yescharacteristic
666C22C22×C11×#4111yescharacteristic
667C22C22×C11×#4111yescharacteristic
668C22C2×C11×H(5,𝔽2)11yescharacteristic
669C22C2×C11×H(5,𝔽2)11yescharacteristic
670C22C2×C11×2−1+411yescharacteristic
671C22C2×C11×2−1+411yescharacteristic
672C4—24no—
673C4—24no—
674C4—24no—
675C4—42no—
676C4—42no—
677C4—42no—
678C4—42no—
679C4—42no—
680C4—42no—
681C4—42no—
682C4—42no—
683C4—42no—
684C4—42no—
685C4—42no—
686C2—82no—
687C2C11×#265418yesdirect product factor
688C2C2×C11×#52911yescharacteristic
689C2C2×C11×#53911yescharacteristic
690C2C2×C11×#53911yescharacteristic
691C2C2×C11×#54011yescharacteristic
692C2C2×C11×#54111yescharacteristic
693C2C2×C11×#54211yescharacteristic
694C2C2×C11×#54211yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC25×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C11×#2654C2direct (N × H)
2. C2×C11×#400C2semidirect
3. C2×C11×#400C2semidirect
5. C2×C11×#398C2semidirect
6. C2×C11×#398C2semidirect
10. C2×C11×#389C2semidirect
14. C2×C11×#387C2semidirect
15. C2×C11×#387C2semidirect
16. C2×C4×C11×C4⋊C4C2semidirect
38. C11×#400C22semidirect
39. C11×#400C22semidirect
41. C11×#398C22semidirect
42. C11×#398C22semidirect
46. C11×#389C22semidirect
50. C11×#387C22semidirect
51. C11×#387C22semidirect
52. C4×C11×C4⋊C4C22semidirect
138. C2×#2654C11direct (N × H)
225. #2654C2×C11direct (N × H)
226. C2×#400C2×C11semidirect
227. C2×#400C2×C11semidirect
229. C2×#398C2×C11semidirect
230. C2×#398C2×C11semidirect
234. C2×#389C2×C11semidirect
238. C2×#387C2×C11semidirect
239. C2×#387C2×C11semidirect
240. C2×C4×C4⋊C4C2×C11semidirect
340. #400C22×C11semidirect
341. #400C22×C11semidirect
343. #398C22×C11semidirect
344. #398C22×C11semidirect
348. #389C22×C11semidirect
352. #387C22×C11semidirect
353. #387C22×C11semidirect
354. C4×C4⋊C4C22×C11semidirect
477. C2×C11#2654direct (N × H)
571. C11C2×#2654direct (N × H)
687. C2C11×#2654direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26542
C2×C11×#4002
C2×C11×#3992
C2×C11×#3982
C2×C11×#3972
C2×C11×#3962
C2×C11×#3892
C2×C11×#3882
C2×C11×#3872
C2×C4×C11×C4⋊C42
C2×#265411