Finite Group Databasebeta

← C2×C11×#2574 #14612026

Subgroups — C2×C11×#2574 #14612026

Order 2816.

2334 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2574C2116yesmaximal, direct product factor
2C2×C11×#398C211yesmaximal, characteristic, complemented
3C2×C11×#396C211yesmaximal, characteristic
4C2×C11×#395C211yesmaximal, characteristic, complemented
5C2×C11×#393C211yesmaximal, characteristic
6C2×C11×#391C211yesmaximal, characteristic, complemented
7C2×C11×#388C211yesmaximal, characteristic
8C2×C11×#388C211yesmaximal, characteristic
9C2×C11×#387C211yesmaximal, characteristic, complemented
10C2×C11×#387C211yesmaximal, characteristic, complemented
11C2×C11×#387C211yesmaximal, characteristic, complemented
12C2×C11×#385C211yesmaximal, characteristic
13C2×C11×#382C211yesmaximal, characteristic, complemented
14C2×C11×#380C211yesmaximal, characteristic
15C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
17C23×Q8×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
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×C42×C11C2211yescharacteristic
35C22×C42×C11C2211yescharacteristic
36C22×C42×C11C2211yescharacteristic
37C22×C42×C11C2211yescharacteristic
38C11×#398C2218yescomplemented
39C11×#396C2218yes—
40C11×#395C2218yescomplemented
41C11×#393C2218yes—
42C11×#391C2218yescomplemented
43C11×#388C2218yes—
44C11×#388C2218yes—
45C11×#387C2218yescomplemented
46C11×#387C2218yescomplemented
47C11×#387C2218yescomplemented
48C11×#385C2218yes—
49C11×#382C2218yescomplemented
50C11×#380C2218yes—
51C4×C11×C4⋊C4C2218yescomplemented
52C4×C11×C22⋊C4C2218yes—
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
68C22×Q8×C11—24no—
69C22×Q8×C11—42no—
70C22×Q8×C11—42no—
71C22×Q8×C11C2314yes—
72C23×C4×C11—24no—
73C23×C4×C11—24no—
74C23×C4×C11—42no—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2314yes—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C2×C11×C4⋊C4—24no—
91C2×C11×C4⋊C4—24no—
92C2×C11×C4⋊C4—24no—
93C2×C11×C4⋊C4—24no—
94C2×C11×C4⋊C4—24no—
95C2×C11×C4⋊C4—42no—
96C2×C11×C4⋊C4—42no—
97C2×C11×C4⋊C4—42no—
98C2×C11×C4⋊C4—42no—
99C2×C11×C4⋊C4C2314yes—
100C2×C11×C4⋊C4C2314yes—
101C2×C11×C4⋊C4C2314yes—
102C2×C11×C4⋊C4C2314yes—
103C2×C11×C4⋊C4C2314yes—
104C2×C11×C4⋊C4C2314yes—
105C2×C11×C4⋊C4C2314yes—
106C2×C11×C4⋊C4C2314yes—
107C2×C11×C4⋊C4C2314yes—
108C2×C11×C22⋊C4—24no—
109C2×C11×C22⋊C4—24no—
110C2×C11×C22⋊C4—42no—
111C2×C11×C22⋊C4—42no—
112C2×C11×C22⋊C4—42no—
113C2×C11×C22⋊C4Q818yescomplemented
114C2×C11×C22⋊C4C2314yes—
115C2×C11×C22⋊C4C2314yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C11×C22⋊C4C2314yes—
118C2×C11×C22⋊C4C2314yes—
119C2×C11×C22⋊C4C2314yes—
120C2×C42×C11—24no—
121C2×C42×C11—24no—
122C2×C42×C11—42no—
123C2×C42×C11—42no—
124C2×C42×C11C2314yes—
125C2×C42×C11C2314yes—
126C2×C42×C11C2314yes—
127C2×C42×C11C2314yes—
128C11×#95C2314yes—
129C11×#95C2314yes—
130C11×#95C2314yes—
131C11×#95C2314yes—
132C11×#95C2314yes—
133C11×#95C2314yes—
134C11×#95C2314yes—
135C11×#95C2314yes—
136C11×#95C2314yes—
137C11×#95C2314yes—
138C11×#95C2314yes—
139C11×#95C2314yes—
140C11×#95C2314yes—
141C11×#95C2314yes—
142C2×#2574C1111yesmaximal, characteristic, direct product factor, Sylow
143C24×C11—22no—
144C24×C11—22no—
145C24×C11—22no—
146C24×C11—22no—
147C24×C11—22no—
148C24×C11—22no—
149C24×C11C2×Q814yes—
150C24×C11C2412yes—
151C24×C11C2411yescharacteristic
152C2×Q8×C11—28no—
153C2×Q8×C11—44no—
154C2×Q8×C11—44no—
155C2×Q8×C11—416no—
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—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—28no—
193C22×C4×C11—28no—
194C22×C4×C11—44no—
195C22×C4×C11—416no—
196C22×C4×C11C2×Q814yes—
197C22×C4×C11C2×Q814yes—
198C22×C4×C11#4114yes—
199C22×C4×C11#4114yes—
200C22×C4×C11#4114yes—
201C22×C4×C11#4114yes—
202C22×C4×C11C2412yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C11×C4⋊C4—28no—
217C11×C4⋊C4—28no—
218C11×C4⋊C4—28no—
219C11×C4⋊C4—28no—
220C11×C4⋊C4—28no—
221C11×C4⋊C4—44no—
222C11×C4⋊C4—44no—
223C11×C4⋊C4—44no—
224C11×C4⋊C4—44no—
225C11×C22⋊C4—28no—
226C11×C22⋊C4—28no—
227C11×C22⋊C4—44no—
228C11×C22⋊C4—44no—
229C11×C22⋊C4—44no—
230C11×C22⋊C4C2×Q8116yescomplemented
231C42×C11—28no—
232C42×C11—28no—
233C42×C11—44no—
234C42×C11—44no—
235#2574C2×C11116yesdirect product factor
236C2×#398C2×C1111yescharacteristic, complemented
237C2×#396C2×C1111yescharacteristic
238C2×#395C2×C1111yescharacteristic, complemented
239C2×#393C2×C1111yescharacteristic
240C2×#391C2×C1111yescharacteristic, complemented
241C2×#388C2×C1111yescharacteristic
242C2×#388C2×C1111yescharacteristic
243C2×#387C2×C1111yescharacteristic, complemented
244C2×#387C2×C1111yescharacteristic, complemented
245C2×#387C2×C1111yescharacteristic, complemented
246C2×#385C2×C1111yescharacteristic
247C2×#382C2×C1111yescharacteristic, complemented
248C2×#380C2×C1111yescharacteristic
249C2×C4×C4⋊C4C2×C1111yescharacteristic, complemented
250C2×C4×C22⋊C4C2×C1111yescharacteristic
251C23×C11—28no—
252C23×C11—28no—
253C23×C11—28no—
254C23×C11—22no—
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—44no—
261C23×C11—44no—
262C23×C11—44no—
263C23×C11—44no—
264C23×C11C22×Q814yes—
265C23×C11C22×Q812yes—
266C23×C11C2×#4112yes—
267C23×C11C2×#4112yes—
268C23×C11C2×#4112yes—
269C23×C11C2×#4112yes—
270C23×C11H(5,𝔽2)12yes—
271C23×C11H(5,𝔽2)12yes—
272C23×C11C2511yescharacteristic
273Q8×C11—416no—
274C2×C4×C11—28no—
275C2×C4×C11—28no—
276C2×C4×C11—28no—
277C2×C4×C11—28no—
278C2×C4×C11—28no—
279C2×C4×C11—28no—
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—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—416no—
317C2×C4×C11—44no—
318C2×C4×C11—44no—
319C2×C4×C11—44no—
320C2×C4×C11—44no—
321C2×C4×C11—44no—
322C2×C4×C11—44no—
323C2×C4×C11—44no—
324C2×C4×C11—44no—
325C2×C4×C11C22×Q814yes—
326C2×C4×C11C22×Q814yes—
327C2×C4×C11C2×#4114yes—
328C2×C4×C11C2×#4114yes—
329C2×C4×C11C2×#4114yes—
330C2×C4×C11C2×#4114yes—
331C23×Q8C22×C1111yescharacteristic
332C24×C4C22×C1111yescharacteristic
333C22×C4⋊C4C22×C1111yescharacteristic
334C22×C4⋊C4C22×C1111yescharacteristic
335C22×C4⋊C4C22×C1111yescharacteristic
336C22×C4⋊C4C22×C1111yescharacteristic
337C22×C4⋊C4C22×C1111yescharacteristic
338C22×C4⋊C4C22×C1111yescharacteristic
339C22×C4⋊C4C22×C1111yescharacteristic
340C22×C4⋊C4C22×C1111yescharacteristic
341C22×C4⋊C4C22×C1111yescharacteristic
342C22×C22⋊C4C22×C1111yescharacteristic
343C22×C22⋊C4C22×C1111yescharacteristic
344C22×C22⋊C4C22×C1111yescharacteristic
345C22×C22⋊C4C22×C1111yescharacteristic
346C22×C22⋊C4C22×C1111yescharacteristic
347C22×C22⋊C4C22×C1111yescharacteristic
348C22×C42C22×C1111yescharacteristic
349C22×C42C22×C1111yescharacteristic
350C22×C42C22×C1111yescharacteristic
351C22×C42C22×C1111yescharacteristic
352#398C22×C1118yescomplemented
353#396C22×C1118yes—
354#395C22×C1118yescomplemented
355#393C22×C1118yes—
356#391C22×C1118yescomplemented
357#388C22×C1118yes—
358#388C22×C1118yes—
359#387C22×C1118yescomplemented
360#387C22×C1118yescomplemented
361#387C22×C1118yescomplemented
362#385C22×C1118yes—
363#382C22×C1118yescomplemented
364#380C22×C1118yes—
365C4×C4⋊C4C22×C1118yescomplemented
366C4×C22⋊C4C22×C1118yes—
367C2×#95C22×C1111yescharacteristic
368C2×#95C22×C1111yescharacteristic
369C2×#95C22×C1111yescharacteristic
370C2×#95C22×C1111yescharacteristic
371C2×#95C22×C1111yescharacteristic
372C2×#95C22×C1111yescharacteristic
373C2×#95C22×C1111yescharacteristic
374C2×#95C22×C1111yescharacteristic
375C2×#95C22×C1111yescharacteristic
376C2×#95C22×C1111yescharacteristic
377C2×#95C22×C1111yescharacteristic
378C2×#95C22×C1111yescharacteristic
379C2×#95C22×C1111yescharacteristic
380C2×#95C22×C1111yescharacteristic
381C22×C11—24no—
382C22×C11—24no—
383C22×C11—24no—
384C22×C11—416no—
385C22×C11—42no—
386C22×C11—42no—
387C22×C11—42no—
388C22×C11—42no—
389C22×C11#52914yes—
390C22×C11#53314yes—
391C22×C11#53814yes—
392C22×C11#55114yes—
393C22×C11#55414yes—
394C22×C11#55414yes—
395C22×C11#55514yes—
396C22×C11C23×Q811yescharacteristic
397C22×C11C22×#4111yescharacteristic
398C22×C11C22×#4111yescharacteristic
399C22×C11C22×#4111yescharacteristic
400C22×C11C22×#4111yescharacteristic
401C22×C11C2×H(5,𝔽2)11yescharacteristic
402C22×C11C2×H(5,𝔽2)11yescharacteristic
403C4×C11—24no—
404C4×C11—24no—
405C4×C11—24no—
406C4×C11—24no—
407C4×C11—24no—
408C4×C11—24no—
409C4×C11—42no—
410C4×C11—42no—
411C4×C11—42no—
412C4×C11—42no—
413C4×C11—42no—
414C4×C11—42no—
415C4×C11—42no—
416C4×C11—42no—
417C25C23×C1111yescharacteristic
418C22×Q8—24no—
419C22×Q8—42no—
420C22×Q8—42no—
421C22×Q8C23×C1114yes—
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—42no—
425C23×C4C23×C1111yescharacteristic
426C23×C4C23×C1111yescharacteristic
427C23×C4C23×C1111yescharacteristic
428C23×C4C23×C1111yescharacteristic
429C23×C4C23×C1111yescharacteristic
430C23×C4C23×C1111yescharacteristic
431C23×C4C23×C1111yescharacteristic
432C23×C4C23×C1111yescharacteristic
433C23×C4C23×C1114yes—
434C23×C4C23×C1111yescharacteristic
435C23×C4C23×C1111yescharacteristic
436C23×C4C23×C1111yescharacteristic
437C23×C4C23×C1111yescharacteristic
438C23×C4C23×C1111yescharacteristic
439C23×C4C23×C1111yescharacteristic
440C2×C4⋊C4—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4C23×C1114yes—
450C2×C4⋊C4C23×C1114yes—
451C2×C4⋊C4C23×C1114yes—
452C2×C4⋊C4C23×C1114yes—
453C2×C4⋊C4C23×C1114yes—
454C2×C4⋊C4C23×C1114yes—
455C2×C4⋊C4C23×C1114yes—
456C2×C4⋊C4C23×C1114yes—
457C2×C4⋊C4C23×C1114yes—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—42no—
461C2×C22⋊C4—42no—
462C2×C22⋊C4—42no—
463C2×C22⋊C4Q8×C1118yescomplemented
464C2×C22⋊C4C23×C1114yes—
465C2×C22⋊C4C23×C1114yes—
466C2×C22⋊C4C23×C1114yes—
467C2×C22⋊C4C23×C1114yes—
468C2×C22⋊C4C23×C1114yes—
469C2×C22⋊C4C23×C1114yes—
470C2×C42—24no—
471C2×C42—24no—
472C2×C42—42no—
473C2×C42—42no—
474C2×C42C23×C1114yes—
475C2×C42C23×C1114yes—
476C2×C42C23×C1114yes—
477C2×C42C23×C1114yes—
478#95C23×C1114yes—
479#95C23×C1114yes—
480#95C23×C1114yes—
481#95C23×C1114yes—
482#95C23×C1114yes—
483#95C23×C1114yes—
484#95C23×C1114yes—
485#95C23×C1114yes—
486#95C23×C1114yes—
487#95C23×C1114yes—
488#95C23×C1114yes—
489#95C23×C1114yes—
490#95C23×C1114yes—
491#95C23×C1114yes—
492C2×C11—44no—
493C2×C11#257418yesdirect product factor
494C2×C11C2×#52911yescharacteristic
495C2×C11C2×#53311yescharacteristic
496C2×C11C2×#53811yescharacteristic
497C2×C11C2×#55111yescharacteristic
498C2×C11C2×#55411yescharacteristic
499C2×C11C2×#55411yescharacteristic
500C2×C11C2×#55511yescharacteristic
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24C2×Q8×C1114yes—
508C24C24×C1112yes—
509C24C24×C1111yescharacteristic
510C2×Q8—28no—
511C2×Q8—44no—
512C2×Q8—44no—
513C2×Q8—416no—
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×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—28no—
551C22×C4—28no—
552C22×C4—44no—
553C22×C4—416no—
554C22×C4C2×Q8×C1114yes—
555C22×C4C2×Q8×C1114yes—
556C22×C4C11×#4114yes—
557C22×C4C11×#4114yes—
558C22×C4C11×#4114yes—
559C22×C4C11×#4114yes—
560C22×C4C24×C1112yes—
561C22×C4C24×C1112yes—
562C22×C4C24×C1112yes—
563C22×C4C24×C1112yes—
564C22×C4C24×C1112yes—
565C22×C4C24×C1112yes—
566C22×C4C24×C1112yes—
567C22×C4C24×C1112yes—
568C22×C4C24×C1112yes—
569C22×C4C24×C1112yes—
570C22×C4C24×C1112yes—
571C22×C4C24×C1112yes—
572C22×C4C24×C1112yes—
573C22×C4C24×C1112yes—
574C4⋊C4—28no—
575C4⋊C4—28no—
576C4⋊C4—28no—
577C4⋊C4—28no—
578C4⋊C4—28no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C22⋊C4—28no—
584C22⋊C4—28no—
585C22⋊C4—44no—
586C22⋊C4—44no—
587C22⋊C4—44no—
588C22⋊C4C2×Q8×C11116yescomplemented
589C42—28no—
590C42—28no—
591C42—44no—
592C42—44no—
593C11C2×#257411yescharacteristic, direct product factor, Sylow
594C23—28no—
595C23—28no—
596C23—28no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—44no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23C22×Q8×C1114yes—
608C23C22×Q8×C1112yes—
609C23C2×C11×#4112yes—
610C23C2×C11×#4112yes—
611C23C2×C11×#4112yes—
612C23C2×C11×#4112yes—
613C23C11×H(5,𝔽2)12yes—
614C23C11×H(5,𝔽2)12yes—
615C23C25×C1111yescharacteristic
616Q8—416no—
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—28no—
621C2×C4—28no—
622C2×C4—28no—
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—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—416no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4C22×Q8×C1114yes—
669C2×C4C22×Q8×C1114yes—
670C2×C4C2×C11×#4114yes—
671C2×C4C2×C11×#4114yes—
672C2×C4C2×C11×#4114yes—
673C2×C4C2×C11×#4114yes—
674C22—24no—
675C22—24no—
676C22—24no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—416no—
682C22C11×#52914yes—
683C22C11×#53314yes—
684C22C11×#53814yes—
685C22C11×#55114yes—
686C22C11×#55414yes—
687C22C11×#55414yes—
688C22C11×#55514yes—
689C22C23×Q8×C1111yescharacteristic
690C22C22×C11×#4111yescharacteristic
691C22C22×C11×#4111yescharacteristic
692C22C22×C11×#4111yescharacteristic
693C22C22×C11×#4111yescharacteristic
694C22C2×C11×H(5,𝔽2)11yescharacteristic
695C22C2×C11×H(5,𝔽2)11yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—24no—
701C4—24no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—42no—
708C4—42no—
709C4—42no—
710C2—44no—
711C2C11×#257418yesdirect product factor
712C2C2×C11×#52911yescharacteristic
713C2C2×C11×#53311yescharacteristic
714C2C2×C11×#53811yescharacteristic
715C2C2×C11×#55111yescharacteristic
716C2C2×C11×#55411yescharacteristic
717C2C2×C11×#55411yescharacteristic
718C2C2×C11×#55511yescharacteristic
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×#2574C2direct (N × H)
2. C2×C11×#398C2semidirect
4. C2×C11×#395C2semidirect
6. C2×C11×#391C2semidirect
9. C2×C11×#387C2semidirect
10. C2×C11×#387C2semidirect
11. C2×C11×#387C2semidirect
13. C2×C11×#382C2semidirect
15. C2×C4×C11×C4⋊C4C2semidirect
38. C11×#398C22semidirect
40. C11×#395C22semidirect
42. C11×#391C22semidirect
45. C11×#387C22semidirect
46. C11×#387C22semidirect
47. C11×#387C22semidirect
49. C11×#382C22semidirect
51. C4×C11×C4⋊C4C22semidirect
113. C2×C11×C22⋊C4Q8semidirect
142. C2×#2574C11direct (N × H)
230. C11×C22⋊C4C2×Q8semidirect
235. #2574C2×C11direct (N × H)
236. C2×#398C2×C11semidirect
238. C2×#395C2×C11semidirect
240. C2×#391C2×C11semidirect
243. C2×#387C2×C11semidirect
244. C2×#387C2×C11semidirect
245. C2×#387C2×C11semidirect
247. C2×#382C2×C11semidirect
249. C2×C4×C4⋊C4C2×C11semidirect
352. #398C22×C11semidirect
354. #395C22×C11semidirect
356. #391C22×C11semidirect
359. #387C22×C11semidirect
360. #387C22×C11semidirect
361. #387C22×C11semidirect
363. #382C22×C11semidirect
365. C4×C4⋊C4C22×C11semidirect
463. C2×C22⋊C4Q8×C11semidirect
493. C2×C11#2574direct (N × H)
588. C22⋊C4C2×Q8×C11semidirect
593. C11C2×#2574direct (N × H)
711. C2C11×#2574direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25742
C2×C11×#3982
C2×C11×#3962
C2×C11×#3952
C2×C11×#3932
C2×C11×#3912
C2×C11×#3882
C2×C11×#3872
C2×C11×#3852
C2×C11×#3822
C2×C11×#3802
C2×C4×C11×C4⋊C42
C2×C4×C11×C22⋊C42
C2×#257411