Finite Group Databasebeta

← C2×C11×#2474 #14611907

Subgroups — C2×C11×#2474 #14611907

Order 2816.

2962 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#124C211yesmaximal, characteristic
2C22×C11×#117C211yesmaximal, characteristic, complemented
3C11×#2474C2116yesmaximal, direct product factor
4C2×C11×#397C211yesmaximal, characteristic, complemented
5C2×C11×#396C211yesmaximal, characteristic, complemented
6C2×C11×#395C211yesmaximal, characteristic, complemented
7C2×C11×#394C211yesmaximal, characteristic
8C2×C11×#391C211yesmaximal, characteristic, complemented
9C2×C11×#388C211yesmaximal, characteristic, complemented
10C2×C11×#388C211yesmaximal, characteristic, complemented
11C2×C11×#388C211yesmaximal, characteristic, complemented
12C2×C11×#388C211yesmaximal, characteristic, complemented
13C2×C11×#387C211yesmaximal, characteristic, complemented
14C2×C11×#386C211yesmaximal, characteristic
15C2×C11×#385C211yesmaximal, characteristic, complemented
16C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C2×C11×#124—28no—
21C2×C11×#124C2218yes—
22C2×C11×#117—28no—
23C2×C11×#117C2218yescomplemented
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C22×C11×C22⋊C4C2211yescharacteristic
33C22×C11×C22⋊C4C2211yescharacteristic
34C22×C11×C22⋊C4C2211yescharacteristic
35C22×C11×C22⋊C4C2211yescharacteristic
36C22×C11×C22⋊C4C2211yescharacteristic
37C22×C11×C22⋊C4C2211yescharacteristic
38C22×C11×C22⋊C4C2211yescharacteristic
39C22×C11×C22⋊C4C2211yescharacteristic
40C22×C11×C22⋊C4C2211yescharacteristic
41C22×C11×C22⋊C4C2211yescharacteristic
42C22×C42×C11C2211yescharacteristic
43C22×C42×C11C2211yescharacteristic
44C22×C42×C11C2211yescharacteristic
45C22×C42×C11C2211yescharacteristic
46C11×#397C2218yescomplemented
47C11×#396C2218yescomplemented
48C11×#395C2218yescomplemented
49C11×#394C2218yes—
50C11×#391C2218yescomplemented
51C11×#388C2218yescomplemented
52C11×#388C2218yescomplemented
53C11×#388C2218yescomplemented
54C11×#388C2218yescomplemented
55C11×#387C2218yescomplemented
56C11×#386C2218yes—
57C11×#385C2218yescomplemented
58C4×C11×C4⋊C4C2218yescomplemented
59C2×C11×#95C2211yescharacteristic
60C2×C11×#95C2211yescharacteristic
61C2×C11×#95C2211yescharacteristic
62C2×C11×#95C2211yescharacteristic
63C2×C11×#95C2211yescharacteristic
64C2×C11×#95C2211yescharacteristic
65C2×C11×#95C2211yescharacteristic
66C2×C11×#95C2211yescharacteristic
67C2×C11×#95C2211yescharacteristic
68C2×C11×#95C2211yescharacteristic
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C22×Q8×C11—24no—
72C22×Q8×C11—24no—
73C22×Q8×C11—42no—
74C22×Q8×C11C2314yes—
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11—42no—
78C22×D4×C11C2314yes—
79C23×C4×C11—24no—
80C23×C4×C11—24no—
81C23×C4×C11—24no—
82C23×C4×C11C2314yes—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C11×#124—232no—
97C11×#117—232no—
98C2×C11×C4⋊C4—24no—
99C2×C11×C4⋊C4—24no—
100C2×C11×C4⋊C4—24no—
101C2×C11×C4⋊C4—24no—
102C2×C11×C4⋊C4—24no—
103C2×C11×C4⋊C4—42no—
104C2×C11×C4⋊C4—42no—
105C2×C11×C4⋊C4C2314yes—
106C2×C11×C4⋊C4C2314yes—
107C2×C11×C4⋊C4C2314yes—
108C2×C11×C4⋊C4C2314yes—
109C2×C11×C4⋊C4C2314yes—
110C2×C11×C4⋊C4C2314yes—
111C2×C11×C4⋊C4C2314yes—
112C2×C11×C22⋊C4—24no—
113C2×C11×C22⋊C4—24no—
114C2×C11×C22⋊C4—24no—
115C2×C11×C22⋊C4—24no—
116C2×C11×C22⋊C4—24no—
117C2×C11×C22⋊C4—24no—
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4—24no—
120C2×C11×C22⋊C4—42no—
121C2×C11×C22⋊C4—42no—
122C2×C11×C22⋊C4D418yes—
123C2×C11×C22⋊C4C2314yes—
124C2×C11×C22⋊C4C2314yes—
125C2×C11×C22⋊C4C2314yes—
126C2×C11×C22⋊C4C2314yes—
127C2×C11×C22⋊C4C2314yes—
128C2×C11×C22⋊C4C2314yes—
129C2×C11×C22⋊C4C2314yes—
130C2×C11×C22⋊C4C2314yes—
131C2×C11×C22⋊C4C2314yes—
132C2×C11×C22⋊C4C2314yes—
133C2×C11×C22⋊C4C2314yes—
134C2×C42×C11—24no—
135C2×C42×C11—24no—
136C2×C42×C11—24no—
137C2×C42×C11—24no—
138C2×C42×C11C2314yes—
139C2×C42×C11C2314yes—
140C2×C42×C11C2314yes—
141C2×C42×C11C2314yes—
142C11×#95C2314yes—
143C11×#95C2314yes—
144C11×#95C2314yes—
145C11×#95C2314yes—
146C11×#95C2314yes—
147C11×#95C2314yes—
148C11×#95C2314yes—
149C11×#95C2314yes—
150C11×#95C2314yes—
151C11×#95C2314yes—
152C2×#2474C1111yesmaximal, characteristic, direct product factor, Sylow
153C24×C11—22no—
154C24×C11—22no—
155C24×C11—22no—
156C24×C11—22no—
157C24×C11—22no—
158C24×C11—22no—
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11—22no—
166C24×C11C2×D414yes—
167C24×C11C2412yes—
168C24×C11C2412yes—
169C24×C11C2411yescharacteristic
170C2×Q8×C11—28no—
171C2×Q8×C11—28no—
172C2×Q8×C11—44no—
173C2×Q8×C11—416no—
174C2×D4×C11—28no—
175C2×D4×C11—28no—
176C2×D4×C11—44no—
177C2×D4×C11—416no—
178C22×C4×C11—232no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—28no—
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—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11C2×D414yes—
216C22×C4×C11C2×D414yes—
217C22×C4×C11#4114yes—
218C22×C4×C11#4114yes—
219C22×C4×C11#4114yes—
220C22×C4×C11#4114yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2412yes—
226C22×C4×C11C2412yes—
227C22×C4×C11C2412yes—
228C22×C4×C11C2412yes—
229C22×C4×C11C2412yes—
230C22×C4×C11C2412yes—
231C22×C4×C11C2412yes—
232C22×C4×C11C2412yes—
233C22×C4×C11C2412yes—
234C11×C4⋊C4—28no—
235C11×C4⋊C4—28no—
236C11×C4⋊C4—28no—
237C11×C4⋊C4—28no—
238C11×C4⋊C4—28no—
239C11×C4⋊C4—44no—
240C11×C4⋊C4—44no—
241C11×C22⋊C4—28no—
242C11×C22⋊C4—28no—
243C11×C22⋊C4—28no—
244C11×C22⋊C4—28no—
245C11×C22⋊C4—28no—
246C11×C22⋊C4—28no—
247C11×C22⋊C4—28no—
248C11×C22⋊C4—28no—
249C11×C22⋊C4—44no—
250C11×C22⋊C4—44no—
251C11×C22⋊C4C2×D4116yes—
252C42×C11—28no—
253C42×C11—28no—
254C42×C11—28no—
255C42×C11—28no—
256C22×#124C2×C1111yescharacteristic
257C22×#117C2×C1111yescharacteristic, complemented
258#2474C2×C11116yesdirect product factor
259C2×#397C2×C1111yescharacteristic, complemented
260C2×#396C2×C1111yescharacteristic, complemented
261C2×#395C2×C1111yescharacteristic, complemented
262C2×#394C2×C1111yescharacteristic
263C2×#391C2×C1111yescharacteristic, complemented
264C2×#388C2×C1111yescharacteristic, complemented
265C2×#388C2×C1111yescharacteristic, complemented
266C2×#388C2×C1111yescharacteristic, complemented
267C2×#388C2×C1111yescharacteristic, complemented
268C2×#387C2×C1111yescharacteristic, complemented
269C2×#386C2×C1111yescharacteristic
270C2×#385C2×C1111yescharacteristic, complemented
271C2×C4×C4⋊C4C2×C1111yescharacteristic, complemented
272C23×C11—28no—
273C23×C11—28no—
274C23×C11—28no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—44no—
289C23×C11—44no—
290C23×C11—44no—
291C23×C11—44no—
292C23×C11—44no—
293C23×C11—44no—
294C23×C11—44no—
295C23×C11—44no—
296C23×C11—44no—
297C23×C11—44no—
298C23×C11—44no—
299C23×C11C22×D414yes—
300C23×C11C22×D412yes—
301C23×C11C2×#4112yes—
302C23×C11C2×#4112yes—
303C23×C11C2×#4112yes—
304C23×C11C2×#4112yes—
305C23×C11H(5,𝔽2)12yes—
306C23×C112−1+412yes—
307C23×C11C2511yescharacteristic
308Q8×C11—416no—
309D4×C11—416no—
310C2×C4×C11—232no—
311C2×C4×C11—28no—
312C2×C4×C11—28no—
313C2×C4×C11—28no—
314C2×C4×C11—28no—
315C2×C4×C11—28no—
316C2×C4×C11—28no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—44no—
351C2×C4×C11—44no—
352C2×C4×C11—44no—
353C2×C4×C11—44no—
354C2×C4×C11—44no—
355C2×C4×C11—44no—
356C2×C4×C11—44no—
357C2×C4×C11C22×D414yes—
358C2×C4×C11C22×D414yes—
359C2×C4×C11C2×#4114yes—
360C2×C4×C11C2×#4114yes—
361C2×C4×C11C2×#4114yes—
362C2×C4×C11C2×#4114yes—
363C23×Q8C22×C1111yescharacteristic
364C23×D4C22×C1111yescharacteristic
365C24×C4C22×C1111yescharacteristic
366C2×#124—28no—
367C2×#124C22×C1118yes—
368C2×#117—28no—
369C2×#117C22×C1118yescomplemented
370C22×C4⋊C4C22×C1111yescharacteristic
371C22×C4⋊C4C22×C1111yescharacteristic
372C22×C4⋊C4C22×C1111yescharacteristic
373C22×C4⋊C4C22×C1111yescharacteristic
374C22×C4⋊C4C22×C1111yescharacteristic
375C22×C4⋊C4C22×C1111yescharacteristic
376C22×C4⋊C4C22×C1111yescharacteristic
377C22×C22⋊C4C22×C1111yescharacteristic
378C22×C22⋊C4C22×C1111yescharacteristic
379C22×C22⋊C4C22×C1111yescharacteristic
380C22×C22⋊C4C22×C1111yescharacteristic
381C22×C22⋊C4C22×C1111yescharacteristic
382C22×C22⋊C4C22×C1111yescharacteristic
383C22×C22⋊C4C22×C1111yescharacteristic
384C22×C22⋊C4C22×C1111yescharacteristic
385C22×C22⋊C4C22×C1111yescharacteristic
386C22×C22⋊C4C22×C1111yescharacteristic
387C22×C22⋊C4C22×C1111yescharacteristic
388C22×C42C22×C1111yescharacteristic
389C22×C42C22×C1111yescharacteristic
390C22×C42C22×C1111yescharacteristic
391C22×C42C22×C1111yescharacteristic
392#397C22×C1118yescomplemented
393#396C22×C1118yescomplemented
394#395C22×C1118yescomplemented
395#394C22×C1118yes—
396#391C22×C1118yescomplemented
397#388C22×C1118yescomplemented
398#388C22×C1118yescomplemented
399#388C22×C1118yescomplemented
400#388C22×C1118yescomplemented
401#387C22×C1118yescomplemented
402#386C22×C1118yes—
403#385C22×C1118yescomplemented
404C4×C4⋊C4C22×C1118yescomplemented
405C2×#95C22×C1111yescharacteristic
406C2×#95C22×C1111yescharacteristic
407C2×#95C22×C1111yescharacteristic
408C2×#95C22×C1111yescharacteristic
409C2×#95C22×C1111yescharacteristic
410C2×#95C22×C1111yescharacteristic
411C2×#95C22×C1111yescharacteristic
412C2×#95C22×C1111yescharacteristic
413C2×#95C22×C1111yescharacteristic
414C2×#95C22×C1111yescharacteristic
415C22×C11—24no—
416C22×C11—24no—
417C22×C11—24no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—416no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—42no—
426C22×C11—42no—
427C22×C11—42no—
428C22×C11—42no—
429C22×C11—42no—
430C22×C11—88no—
431C22×C11#52514yes—
432C22×C11#52914yes—
433C22×C11#54214yes—
434C22×C11#54614yes—
435C22×C11#54714yes—
436C22×C11#55514yes—
437C22×C11#55614yes—
438C22×C11C23×D411yescharacteristic
439C22×C11C22×#4111yescharacteristic
440C22×C11C22×#4111yescharacteristic
441C22×C11C22×#4111yescharacteristic
442C22×C11C22×#4111yescharacteristic
443C22×C11C2×H(5,𝔽2)11yescharacteristic
444C22×C11C2×2−1+411yescharacteristic
445C4×C11—24no—
446C4×C11—24no—
447C4×C11—24no—
448C4×C11—24no—
449C4×C11—24no—
450C4×C11—24no—
451C4×C11—42no—
452C4×C11—42no—
453C4×C11—42no—
454C4×C11—42no—
455C4×C11—42no—
456C4×C11—42no—
457C4×C11—42no—
458C25C23×C1111yescharacteristic
459C25C23×C1111yescharacteristic
460C22×Q8—24no—
461C22×Q8—24no—
462C22×Q8—42no—
463C22×Q8C23×C1114yes—
464C22×D4—24no—
465C22×D4—24no—
466C22×D4—42no—
467C22×D4C23×C1114yes—
468C23×C4—24no—
469C23×C4—24no—
470C23×C4—24no—
471C23×C4C23×C1111yescharacteristic
472C23×C4C23×C1111yescharacteristic
473C23×C4C23×C1111yescharacteristic
474C23×C4C23×C1111yescharacteristic
475C23×C4C23×C1111yescharacteristic
476C23×C4C23×C1111yescharacteristic
477C23×C4C23×C1111yescharacteristic
478C23×C4C23×C1114yes—
479C23×C4C23×C1111yescharacteristic
480C23×C4C23×C1111yescharacteristic
481C23×C4C23×C1111yescharacteristic
482C23×C4C23×C1111yescharacteristic
483C23×C4C23×C1111yescharacteristic
484C23×C4C23×C1111yescharacteristic
485#124—232no—
486#117—232no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—24no—
491C2×C4⋊C4—24no—
492C2×C4⋊C4—42no—
493C2×C4⋊C4—42no—
494C2×C4⋊C4C23×C1114yes—
495C2×C4⋊C4C23×C1114yes—
496C2×C4⋊C4C23×C1114yes—
497C2×C4⋊C4C23×C1114yes—
498C2×C4⋊C4C23×C1114yes—
499C2×C4⋊C4C23×C1114yes—
500C2×C4⋊C4C23×C1114yes—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4D4×C1118yes—
512C2×C22⋊C4C23×C1114yes—
513C2×C22⋊C4C23×C1114yes—
514C2×C22⋊C4C23×C1114yes—
515C2×C22⋊C4C23×C1114yes—
516C2×C22⋊C4C23×C1114yes—
517C2×C22⋊C4C23×C1114yes—
518C2×C22⋊C4C23×C1114yes—
519C2×C22⋊C4C23×C1114yes—
520C2×C22⋊C4C23×C1114yes—
521C2×C22⋊C4C23×C1114yes—
522C2×C22⋊C4C23×C1114yes—
523C2×C42—24no—
524C2×C42—24no—
525C2×C42—24no—
526C2×C42—24no—
527C2×C42C23×C1114yes—
528C2×C42C23×C1114yes—
529C2×C42C23×C1114yes—
530C2×C42C23×C1114yes—
531#95C23×C1114yes—
532#95C23×C1114yes—
533#95C23×C1114yes—
534#95C23×C1114yes—
535#95C23×C1114yes—
536#95C23×C1114yes—
537#95C23×C1114yes—
538#95C23×C1114yes—
539#95C23×C1114yes—
540#95C23×C1114yes—
541C2×C11—44no—
542C2×C11—82no—
543C2×C11#247418yesdirect product factor
544C2×C11C2×#52511yescharacteristic
545C2×C11C2×#52911yescharacteristic
546C2×C11C2×#54211yescharacteristic
547C2×C11C2×#54611yescharacteristic
548C2×C11C2×#54711yescharacteristic
549C2×C11C2×#55511yescharacteristic
550C2×C11C2×#55611yescharacteristic
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24C2×D4×C1114yes—
565C24C24×C1112yes—
566C24C24×C1112yes—
567C24C24×C1111yescharacteristic
568C2×Q8—28no—
569C2×Q8—28no—
570C2×Q8—44no—
571C2×Q8—416no—
572C2×D4—28no—
573C2×D4—28no—
574C2×D4—44no—
575C2×D4—416no—
576C22×C4—232no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—28no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
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—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4C2×D4×C1114yes—
614C22×C4C2×D4×C1114yes—
615C22×C4C11×#4114yes—
616C22×C4C11×#4114yes—
617C22×C4C11×#4114yes—
618C22×C4C11×#4114yes—
619C22×C4C24×C1112yes—
620C22×C4C24×C1112yes—
621C22×C4C24×C1112yes—
622C22×C4C24×C1112yes—
623C22×C4C24×C1112yes—
624C22×C4C24×C1112yes—
625C22×C4C24×C1112yes—
626C22×C4C24×C1112yes—
627C22×C4C24×C1112yes—
628C22×C4C24×C1112yes—
629C22×C4C24×C1112yes—
630C22×C4C24×C1112yes—
631C22×C4C24×C1112yes—
632C4⋊C4—28no—
633C4⋊C4—28no—
634C4⋊C4—28no—
635C4⋊C4—28no—
636C4⋊C4—28no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C22⋊C4—28no—
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—28no—
643C22⋊C4—28no—
644C22⋊C4—28no—
645C22⋊C4—28no—
646C22⋊C4—28no—
647C22⋊C4—44no—
648C22⋊C4—44no—
649C22⋊C4C2×D4×C11116yes—
650C42—28no—
651C42—28no—
652C42—28no—
653C42—28no—
654C11C2×#247411yescharacteristic, direct product factor, Sylow
655C23—28no—
656C23—28no—
657C23—28no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23C22×D4×C1114yes—
683C23C22×D4×C1112yes—
684C23C2×C11×#4112yes—
685C23C2×C11×#4112yes—
686C23C2×C11×#4112yes—
687C23C2×C11×#4112yes—
688C23C11×H(5,𝔽2)12yes—
689C23C11×2−1+412yes—
690C23C25×C1111yescharacteristic
691Q8—416no—
692D4—416no—
693C2×C4—232no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4C22×D4×C1114yes—
741C2×C4C22×D4×C1114yes—
742C2×C4C2×C11×#4114yes—
743C2×C4C2×C11×#4114yes—
744C2×C4C2×C11×#4114yes—
745C2×C4C2×C11×#4114yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—416no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—88no—
762C22C11×#52514yes—
763C22C11×#52914yes—
764C22C11×#54214yes—
765C22C11×#54614yes—
766C22C11×#54714yes—
767C22C11×#55514yes—
768C22C11×#55614yes—
769C22C23×D4×C1111yescharacteristic
770C22C22×C11×#4111yescharacteristic
771C22C22×C11×#4111yescharacteristic
772C22C22×C11×#4111yescharacteristic
773C22C22×C11×#4111yescharacteristic
774C22C2×C11×H(5,𝔽2)11yescharacteristic
775C22C2×C11×2−1+411yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—24no—
780C4—24no—
781C4—24no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—42no—
788C4—42no—
789C2—44no—
790C2—82no—
791C2C11×#247418yesdirect product factor
792C2C2×C11×#52511yescharacteristic
793C2C2×C11×#52911yescharacteristic
794C2C2×C11×#54211yescharacteristic
795C2C2×C11×#54611yescharacteristic
796C2C2×C11×#54711yescharacteristic
797C2C2×C11×#55511yescharacteristic
798C2C2×C11×#55611yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC23×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×#117C2semidirect
3. C11×#2474C2direct (N × H)
4. C2×C11×#397C2semidirect
5. C2×C11×#396C2semidirect
6. C2×C11×#395C2semidirect
8. C2×C11×#391C2semidirect
9. C2×C11×#388C2semidirect
10. C2×C11×#388C2semidirect
11. C2×C11×#388C2semidirect
12. C2×C11×#388C2semidirect
13. C2×C11×#387C2semidirect
15. C2×C11×#385C2semidirect
16. C2×C4×C11×C4⋊C4C2semidirect
23. C2×C11×#117C22semidirect
46. C11×#397C22semidirect
47. C11×#396C22semidirect
48. C11×#395C22semidirect
50. C11×#391C22semidirect
51. C11×#388C22semidirect
52. C11×#388C22semidirect
53. C11×#388C22semidirect
54. C11×#388C22semidirect
55. C11×#387C22semidirect
57. C11×#385C22semidirect
58. C4×C11×C4⋊C4C22semidirect
152. C2×#2474C11direct (N × H)
257. C22×#117C2×C11semidirect
258. #2474C2×C11direct (N × H)
259. C2×#397C2×C11semidirect
260. C2×#396C2×C11semidirect
261. C2×#395C2×C11semidirect
263. C2×#391C2×C11semidirect
264. C2×#388C2×C11semidirect
265. C2×#388C2×C11semidirect
266. C2×#388C2×C11semidirect
267. C2×#388C2×C11semidirect
268. C2×#387C2×C11semidirect
270. C2×#385C2×C11semidirect
271. C2×C4×C4⋊C4C2×C11semidirect
369. C2×#117C22×C11semidirect
392. #397C22×C11semidirect
393. #396C22×C11semidirect
394. #395C22×C11semidirect
396. #391C22×C11semidirect
397. #388C22×C11semidirect
398. #388C22×C11semidirect
399. #388C22×C11semidirect
400. #388C22×C11semidirect
401. #387C22×C11semidirect
403. #385C22×C11semidirect
404. C4×C4⋊C4C22×C11semidirect
543. C2×C11#2474direct (N × H)
654. C11C2×#2474direct (N × H)
791. C2C11×#2474direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1242
C22×C11×#1172
C11×#24742
C2×C11×#3972
C2×C11×#3962
C2×C11×#3952
C2×C11×#3942
C2×C11×#3912
C2×C11×#3882
C2×C11×#3872
C2×C11×#3862
C2×C11×#3852
C2×C4×C11×C4⋊C42
C2×#247411