Finite Group Databasebeta

← C11×#22846 #14600039

Subgroups — C11×#22846 #14600039

Order 2816.

1320 conjugacy classes of subgroups.

The subgroup lattice has 866 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×C11×#407C211yesmaximal, characteristic, complemented
4C22×C11×C22⋊C8C211yesmaximal, characteristic, complemented
5C4×C11×#120C211yesmaximal, characteristic
6C11×#1955C211yesmaximal, characteristic, complemented
7C11×#1924C211yesmaximal, characteristic, complemented
8C11×#1923C211yesmaximal, characteristic, complemented
9C11×#1870C211yesmaximal, characteristic, complemented
10C11×#1869C211yesmaximal, characteristic, complemented
11C11×#1869C211yesmaximal, characteristic, complemented
12C11×#1851C211yesmaximal, characteristic, complemented
13C11×#1850C211yesmaximal, characteristic, complemented
14C11×#1753C211yesmaximal, characteristic, complemented
15C11×#1752C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic
21C23×C8×C11C2211yescharacteristic, complemented
22C2×C11×#120C411yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C11×#435—24no—
27C8×D4×C11—24no—
28C2×C11×C4⋊C8C2211yescharacteristic, complemented
29C2×C11×C4⋊C8C2211yescharacteristic, complemented
30C2×C11×C4⋊C8C2211yescharacteristic, complemented
31C11×#407—24no—
32C2×C11×C22⋊C8—24no—
33C2×C11×C22⋊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, complemented
42C2×C11×C22⋊C8C2211yescharacteristic, complemented
43C2×C11×C22⋊C8C2211yescharacteristic, complemented
44C2×C11×#97C2211yescharacteristic, complemented
45C2×C11×#97C2211yescharacteristic, complemented
46C2×C4×C8×C11C2211yescharacteristic, complemented
47C11×#386C411yescharacteristic
48C11×#386C411yescharacteristic
49C11×#386C411yescharacteristic
50C11×#385C411yescharacteristic
51C11×#385C411yescharacteristic
52C11×#385C411yescharacteristic
53C11×#379C411yescharacteristic
54C4×C11×C22⋊C4C2211yescharacteristic
55C4×C11×C22⋊C4C2211yescharacteristic
56C4×C11×C22⋊C4C2211yescharacteristic
57C11×#336C2211yescharacteristic, complemented
58C11×#336C2211yescharacteristic, complemented
59C11×#336C2211yescharacteristic, complemented
60C11×#336C2211yescharacteristic, complemented
61C11×#336C2211yescharacteristic, complemented
62C11×#336C2211yescharacteristic, complemented
63C25×C11C2×C411yescharacteristic
64C22×D4×C11C2×C411yescharacteristic
65C22×D4×C11C2×C411yescharacteristic
66C22×D4×C11C2×C411yescharacteristic
67C23×C4×C11—22no—
68C23×C4×C11—22no—
69C23×C4×C11—22no—
70C23×C4×C11—22no—
71C23×C4×C11—41no—
72C23×C4×C11—41no—
73C23×C4×C11C2×C411yescharacteristic
74C23×C4×C11C2×C411yescharacteristic
75C23×C4×C11C2×C411yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C2×C11×M16—22no—
81C2×C11×M16—22no—
82C2×C11×M16—22no—
83C2×C11×M16—22no—
84C2×C11×M16—41no—
85C2×C11×M16—41no—
86C22×C8×C11—22no—
87C22×C8×C11—22no—
88C22×C8×C11—22no—
89C22×C8×C11—22no—
90C22×C8×C11—22no—
91C22×C8×C11—22no—
92C22×C8×C11—41no—
93C22×C8×C11—41no—
94C22×C8×C11—41no—
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C11×#120—24no—
104C4×D4×C11—22no—
105C4×D4×C11—22no—
106C4×D4×C11—22no—
107C4×D4×C11—22no—
108C4×D4×C11—41no—
109C4×D4×C11—41no—
110C2×C11×C4⋊C4C2×C411yescharacteristic
111C2×C11×C4⋊C4C2×C411yescharacteristic
112C2×C11×C4⋊C4C2×C411yescharacteristic
113C2×C11×C22⋊C4C2×C411yescharacteristic
114C2×C11×C22⋊C4C2×C411yescharacteristic
115C2×C11×C22⋊C4C2×C411yescharacteristic
116C2×C11×C22⋊C4C2×C411yescharacteristic
117C2×C11×C22⋊C4C2×C411yescharacteristic
118C2×C11×C22⋊C4C2×C411yescharacteristic
119C2×C11×C22⋊C4C2×C411yescharacteristic
120C2×C11×C22⋊C4C2×C411yescharacteristic
121C2×C11×C22⋊C4C2×C411yescharacteristic
122C2×C11×C22⋊C4C2×C411yescharacteristic
123C2×C11×C22⋊C4C2×C411yescharacteristic
124C2×C11×C22⋊C4C2×C411yescharacteristic
125C2×C42×C11C2311yescharacteristic
126C2×C42×C11C2311yescharacteristic
127C2×C42×C11C2311yescharacteristic
128C11×C4⋊C8—22no—
129C11×C4⋊C8—22no—
130C11×C4⋊C8—41no—
131C11×C22⋊C8—22no—
132C11×C22⋊C8—22no—
133C11×C22⋊C8—22no—
134C11×C22⋊C8—22no—
135C11×C22⋊C8—22no—
136C11×C22⋊C8—22no—
137C11×C22⋊C8—22no—
138C11×C22⋊C8—22no—
139C11×C22⋊C8—41no—
140C11×C22⋊C8D414yescomplemented
141C11×C22⋊C8D414yescomplemented
142C11×#97—22no—
143C11×#97—41no—
144C4×C8×C11—22no—
145C11×#95C2×C411yescharacteristic
146C11×#95C2×C411yescharacteristic
147C11×#95C2×C411yescharacteristic
148C11×#95C2×C411yescharacteristic
149C11×#95C2×C411yescharacteristic
150C11×#95C2×C411yescharacteristic
151#22846C1111yesmaximal, characteristic, direct product factor, Sylow
152C24×C11—22no—
153C24×C11—22no—
154C24×C11—22no—
155C24×C11—22no—
156C24×C11—22no—
157C24×C11—41no—
158C24×C11—41no—
159C24×C11C22×C411yescharacteristic
160C24×C11C22×C411yescharacteristic
161C24×C11C22×C411yescharacteristic
162C24×C11C22×C411yescharacteristic
163C2×D4×C11—22no—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C2×D4×C11—22no—
167C2×D4×C11—22no—
168C2×D4×C11—22no—
169C2×D4×C11—41no—
170C2×D4×C11—41no—
171C2×D4×C11M1614yescomplemented
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
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—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—41no—
199C22×C4×C11—41no—
200C22×C4×C11—41no—
201C22×C4×C11—44no—
202C22×C4×C11—44no—
203C22×C4×C11—44no—
204C22×C4×C11—44no—
205C22×C4×C11C22×C411yescharacteristic
206C22×C4×C11C22×C411yescharacteristic
207C22×C4×C11C22×C411yescharacteristic
208C22×C4×C11C22×C411yescharacteristic
209C22×C4×C11C22×C411yescharacteristic
210C22×C4×C11C22×C411yescharacteristic
211C22×C4×C11C22×C411yescharacteristic
212C22×C4×C11C22×C411yescharacteristic
213C22×C4×C11C22×C411yescharacteristic
214C22×C4×C11C22×C411yescharacteristic
215C22×C4×C11C2×D412yes—
216C22×C4×C11C2×D412yes—
217C22×C4×C11#4112yes—
218C22×C4×C11#4112yes—
219C22×C4×C11C2411yescharacteristic
220C11×M16—44no—
221C11×M16—44no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C2×C8×C11—21no—
227C2×C8×C11—21no—
228C2×C8×C11—21no—
229C2×C8×C11—21no—
230C2×C8×C11—21no—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—44no—
243C2×C8×C11—44no—
244C2×C8×C11—44no—
245C2×C8×C11C2×D412yes—
246C2×C8×C11C2×D412yes—
247C2×C8×C11C2×D412yes—
248C2×C8×C11C2×D412yes—
249C11×C4⋊C4—22no—
250C11×C4⋊C4—22no—
251C11×C4⋊C4—41no—
252C11×C22⋊C4—22no—
253C11×C22⋊C4—22no—
254C11×C22⋊C4—22no—
255C11×C22⋊C4—22no—
256C11×C22⋊C4—22no—
257C11×C22⋊C4—22no—
258C11×C22⋊C4—22no—
259C11×C22⋊C4—22no—
260C11×C22⋊C4—22no—
261C11×C22⋊C4—41no—
262C11×C22⋊C4—41no—
263C11×C22⋊C4—41no—
264C42×C11—21no—
265C42×C11—21no—
266C42×C11—21no—
267C42×C11—21no—
268C42×C11—21no—
269C42×C11—21no—
270C2×#435C2×C1111yescharacteristic, complemented
271C2×C8×D4C2×C1111yescharacteristic, complemented
272C2×#407C2×C1111yescharacteristic, complemented
273C22×C22⋊C8C2×C1111yescharacteristic, complemented
274C4×#120C2×C1111yescharacteristic
275#1955C2×C1111yescharacteristic, complemented
276#1924C2×C1111yescharacteristic, complemented
277#1923C2×C1111yescharacteristic, complemented
278#1870C2×C1111yescharacteristic, complemented
279#1869C2×C1111yescharacteristic, complemented
280#1869C2×C1111yescharacteristic, complemented
281#1851C2×C1111yescharacteristic, complemented
282#1850C2×C1111yescharacteristic, complemented
283#1753C2×C1111yescharacteristic, complemented
284#1752C2×C1111yescharacteristic, complemented
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—28no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—44no—
309C23×C11—44no—
310C23×C11—44no—
311C23×C11—44no—
312C23×C11—44no—
313C23×C11—44no—
314C23×C11C4×D412yes—
315C23×C11C4×D412yes—
316C23×C11C2×M1612yes—
317C23×C11C2×M1612yes—
318C23×C11#13112yes—
319C23×C11#13112yes—
320C23×C11C23×C411yescharacteristic
321D4×C11—28no—
322D4×C11—44no—
323D4×C11—44no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
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—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—21no—
348C2×C4×C11—21no—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—21no—
357C2×C4×C11—21no—
358C2×C4×C11—21no—
359C2×C4×C11—44no—
360C2×C4×C11—44no—
361C2×C4×C11—44no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11C4×D412yes—
371C2×C4×C11C4×D412yes—
372C2×C4×C11C2×M1612yes—
373C2×C4×C11C22×D411yescharacteristic
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C2×#4111yescharacteristic
376C2×C4×C11C2×#4111yescharacteristic
377C2×C4×C11H(5,𝔽2)11yescharacteristic
378C2×C4×C11H(5,𝔽2)11yescharacteristic
379C8×C11—22no—
380C8×C11—22no—
381C8×C11—22no—
382C8×C11—22no—
383C8×C11—41no—
384C8×C11—41no—
385C8×C11—41no—
386C8×C11—41no—
387C24×C4C22×C1111yescharacteristic
388C22×M16C22×C1111yescharacteristic
389C22×M16C22×C1111yescharacteristic
390C23×C8C22×C1111yescharacteristic
391C23×C8C22×C1111yescharacteristic
392C23×C8C22×C1111yescharacteristic, complemented
393C2×#120C4×C1111yescharacteristic
394C2×C4×D4C22×C1111yescharacteristic
395C2×C4×D4C22×C1111yescharacteristic
396C2×C4×D4C22×C1111yescharacteristic
397#435—24no—
398C8×D4—24no—
399C2×C4⋊C8C22×C1111yescharacteristic, complemented
400C2×C4⋊C8C22×C1111yescharacteristic, complemented
401C2×C4⋊C8C22×C1111yescharacteristic, complemented
402#407—24no—
403C2×C22⋊C8—24no—
404C2×C22⋊C8C22×C1111yescharacteristic
405C2×C22⋊C8C22×C1111yescharacteristic
406C2×C22⋊C8C22×C1111yescharacteristic
407C2×C22⋊C8C22×C1111yescharacteristic
408C2×C22⋊C8C22×C1111yescharacteristic
409C2×C22⋊C8C22×C1111yescharacteristic
410C2×C22⋊C8C22×C1111yescharacteristic
411C2×C22⋊C8C22×C1111yescharacteristic
412C2×C22⋊C8C22×C1111yescharacteristic, complemented
413C2×C22⋊C8C22×C1111yescharacteristic, complemented
414C2×C22⋊C8C22×C1111yescharacteristic, complemented
415C2×#97C22×C1111yescharacteristic, complemented
416C2×#97C22×C1111yescharacteristic, complemented
417C2×C4×C8C22×C1111yescharacteristic, complemented
418#386C4×C1111yescharacteristic
419#386C4×C1111yescharacteristic
420#386C4×C1111yescharacteristic
421#385C4×C1111yescharacteristic
422#385C4×C1111yescharacteristic
423#385C4×C1111yescharacteristic
424#379C4×C1111yescharacteristic
425C4×C22⋊C4C22×C1111yescharacteristic
426C4×C22⋊C4C22×C1111yescharacteristic
427C4×C22⋊C4C22×C1111yescharacteristic
428#336C22×C1111yescharacteristic, complemented
429#336C22×C1111yescharacteristic, complemented
430#336C22×C1111yescharacteristic, complemented
431#336C22×C1111yescharacteristic, complemented
432#336C22×C1111yescharacteristic, complemented
433#336C22×C1111yescharacteristic, complemented
434C22×C11—22no—
435C22×C11—22no—
436C22×C11—22no—
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—22no—
440C22×C11—22no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—22no—
448C22×C11—22no—
449C22×C11—416no—
450C22×C11—41no—
451C22×C11—41no—
452C22×C11—41no—
453C22×C11—41no—
454C22×C11—41no—
455C22×C11—41no—
456C22×C11—41no—
457C22×C11—41no—
458C22×C11—41no—
459C22×C11—41no—
460C22×C11—41no—
461C22×C11—41no—
462C22×C11#43514yescomplemented
463C22×C11C2×C4×D411yescharacteristic
464C22×C11C2×C4×D411yescharacteristic
465C22×C11#51811yescharacteristic
466C22×C11C22×M1611yescharacteristic
467C22×C11C2×#13111yescharacteristic
468C22×C11C2×#13111yescharacteristic
469C22×C11#56811yescharacteristic
470C4×C11—22no—
471C4×C11—22no—
472C4×C11—22no—
473C4×C11—41no—
474C4×C11—41no—
475C4×C11—41no—
476C4×C11—41no—
477C4×C11—41no—
478C4×C11—41no—
479C4×C11—41no—
480C4×C11D4211yescharacteristic
481C4×C11#54611yescharacteristic
482C4×C11#54611yescharacteristic
483C4×C11#55111yescharacteristic
484C25C2×C4×C1111yescharacteristic
485C22×D4C2×C4×C1111yescharacteristic
486C22×D4C2×C4×C1111yescharacteristic
487C22×D4C2×C4×C1111yescharacteristic
488C23×C4—22no—
489C23×C4—22no—
490C23×C4—22no—
491C23×C4—22no—
492C23×C4—41no—
493C23×C4—41no—
494C23×C4C2×C4×C1111yescharacteristic
495C23×C4C2×C4×C1111yescharacteristic
496C23×C4C2×C4×C1111yescharacteristic
497C23×C4C23×C1111yescharacteristic
498C23×C4C23×C1111yescharacteristic
499C23×C4C23×C1111yescharacteristic
500C23×C4C23×C1111yescharacteristic
501C2×M16—22no—
502C2×M16—22no—
503C2×M16—22no—
504C2×M16—22no—
505C2×M16—41no—
506C2×M16—41no—
507C22×C8—22no—
508C22×C8—22no—
509C22×C8—22no—
510C22×C8—22no—
511C22×C8—22no—
512C22×C8—22no—
513C22×C8—41no—
514C22×C8—41no—
515C22×C8—41no—
516C22×C8C23×C1111yescharacteristic
517C22×C8C23×C1111yescharacteristic
518C22×C8C23×C1111yescharacteristic
519C22×C8C23×C1111yescharacteristic
520C22×C8C23×C1111yescharacteristic
521C22×C8C23×C1111yescharacteristic
522C22×C8C23×C1111yescharacteristic
523C22×C8C23×C1111yescharacteristic
524#120—24no—
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—41no—
530C4×D4—41no—
531C2×C4⋊C4C2×C4×C1111yescharacteristic
532C2×C4⋊C4C2×C4×C1111yescharacteristic
533C2×C4⋊C4C2×C4×C1111yescharacteristic
534C2×C22⋊C4C2×C4×C1111yescharacteristic
535C2×C22⋊C4C2×C4×C1111yescharacteristic
536C2×C22⋊C4C2×C4×C1111yescharacteristic
537C2×C22⋊C4C2×C4×C1111yescharacteristic
538C2×C22⋊C4C2×C4×C1111yescharacteristic
539C2×C22⋊C4C2×C4×C1111yescharacteristic
540C2×C22⋊C4C2×C4×C1111yescharacteristic
541C2×C22⋊C4C2×C4×C1111yescharacteristic
542C2×C22⋊C4C2×C4×C1111yescharacteristic
543C2×C22⋊C4C2×C4×C1111yescharacteristic
544C2×C22⋊C4C2×C4×C1111yescharacteristic
545C2×C22⋊C4C2×C4×C1111yescharacteristic
546C2×C42C23×C1111yescharacteristic
547C2×C42C23×C1111yescharacteristic
548C2×C42C23×C1111yescharacteristic
549C4⋊C8—22no—
550C4⋊C8—22no—
551C4⋊C8—41no—
552C22⋊C8—22no—
553C22⋊C8—22no—
554C22⋊C8—22no—
555C22⋊C8—22no—
556C22⋊C8—22no—
557C22⋊C8—22no—
558C22⋊C8—22no—
559C22⋊C8—22no—
560C22⋊C8—41no—
561C22⋊C8D4×C1114yescomplemented
562C22⋊C8D4×C1114yescomplemented
563#97—22no—
564#97—41no—
565C4×C8—22no—
566#95C2×C4×C1111yescharacteristic
567#95C2×C4×C1111yescharacteristic
568#95C2×C4×C1111yescharacteristic
569#95C2×C4×C1111yescharacteristic
570#95C2×C4×C1111yescharacteristic
571#95C2×C4×C1111yescharacteristic
572C2×C11—24no—
573C2×C11—42no—
574C2×C11—42no—
575C2×C11—42no—
576C2×C11#235811yescharacteristic
577C2×C11C2×#43511yescharacteristic
578C2×C11#292911yescharacteristic
579C2×C11#293311yescharacteristic
580C2×C11D4×M1611yescharacteristic
581C2×C11#297411yescharacteristic
582C2×C11#297611yescharacteristic
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—41no—
589C24—41no—
590C24C22×C4×C1111yescharacteristic
591C24C22×C4×C1111yescharacteristic
592C24C22×C4×C1111yescharacteristic
593C24C22×C4×C1111yescharacteristic
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—41no—
601C2×D4—41no—
602C2×D4C11×M1614yescomplemented
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4C22×C4×C1111yescharacteristic
637C22×C4C22×C4×C1111yescharacteristic
638C22×C4C22×C4×C1111yescharacteristic
639C22×C4C22×C4×C1111yescharacteristic
640C22×C4C22×C4×C1111yescharacteristic
641C22×C4C22×C4×C1111yescharacteristic
642C22×C4C22×C4×C1111yescharacteristic
643C22×C4C22×C4×C1111yescharacteristic
644C22×C4C22×C4×C1111yescharacteristic
645C22×C4C22×C4×C1111yescharacteristic
646C22×C4C2×D4×C1112yes—
647C22×C4C2×D4×C1112yes—
648C22×C4C11×#4112yes—
649C22×C4C11×#4112yes—
650C22×C4C24×C1111yescharacteristic
651M16—44no—
652M16—44no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—44no—
674C2×C8—44no—
675C2×C8—44no—
676C2×C8C2×D4×C1112yes—
677C2×C8C2×D4×C1112yes—
678C2×C8C2×D4×C1112yes—
679C2×C8C2×D4×C1112yes—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—41no—
683C22⋊C4—22no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—22no—
689C22⋊C4—22no—
690C22⋊C4—22no—
691C22⋊C4—22no—
692C22⋊C4—41no—
693C22⋊C4—41no—
694C22⋊C4—41no—
695C42—21no—
696C42—21no—
697C42—21no—
698C42—21no—
699C42—21no—
700C42—21no—
701C11#2284611yescharacteristic, direct product factor, Sylow
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—28no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23C4×D4×C1112yes—
732C23C4×D4×C1112yes—
733C23C2×C11×M1612yes—
734C23C2×C11×M1612yes—
735C23C11×#13112yes—
736C23C11×#13112yes—
737C23C23×C4×C1111yescharacteristic
738D4—28no—
739D4—44no—
740D4—44no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4C4×D4×C1112yes—
788C2×C4C4×D4×C1112yes—
789C2×C4C2×C11×M1612yes—
790C2×C4C22×D4×C1111yescharacteristic
791C2×C4C22×D4×C1111yescharacteristic
792C2×C4C2×C11×#4111yescharacteristic
793C2×C4C2×C11×#4111yescharacteristic
794C2×C4C11×H(5,𝔽2)11yescharacteristic
795C2×C4C11×H(5,𝔽2)11yescharacteristic
796C8—22no—
797C8—22no—
798C8—22no—
799C8—22no—
800C8—41no—
801C8—41no—
802C8—41no—
803C8—41no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—416no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22C11×#43514yescomplemented
833C22C2×C4×D4×C1111yescharacteristic
834C22C2×C4×D4×C1111yescharacteristic
835C22C11×#51811yescharacteristic
836C22C22×C11×M1611yescharacteristic
837C22C2×C11×#13111yescharacteristic
838C22C2×C11×#13111yescharacteristic
839C22C11×#56811yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4D42×C1111yescharacteristic
851C4C11×#54611yescharacteristic
852C4C11×#54611yescharacteristic
853C4C11×#55111yescharacteristic
854C2—24no—
855C2—42no—
856C2—42no—
857C2—42no—
858C2C11×#235811yescharacteristic
859C2C2×C11×#43511yescharacteristic
860C2C11×#292911yescharacteristic
861C2C11×#293311yescharacteristic
862C2D4×C11×M1611yescharacteristic
863C2C11×#297411yescharacteristic
864C2C11×#297611yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC2×C11×#120C4
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×C11×#407C2semidirect
4. C22×C11×C22⋊C8C2semidirect
6. C11×#1955C2semidirect
7. C11×#1924C2semidirect
8. C11×#1923C2semidirect
9. C11×#1870C2semidirect
10. C11×#1869C2semidirect
11. C11×#1869C2semidirect
12. C11×#1851C2semidirect
13. C11×#1850C2semidirect
14. C11×#1753C2semidirect
15. C11×#1752C2semidirect
21. C23×C8×C11C22semidirect
28. C2×C11×C4⋊C8C22semidirect
29. C2×C11×C4⋊C8C22semidirect
30. C2×C11×C4⋊C8C22semidirect
41. C2×C11×C22⋊C8C22semidirect
42. C2×C11×C22⋊C8C22semidirect
43. C2×C11×C22⋊C8C22semidirect
44. C2×C11×#97C22semidirect
45. C2×C11×#97C22semidirect
46. C2×C4×C8×C11C22semidirect
57. C11×#336C22semidirect
58. C11×#336C22semidirect
59. C11×#336C22semidirect
60. C11×#336C22semidirect
61. C11×#336C22semidirect
62. C11×#336C22semidirect
140. C11×C22⋊C8D4semidirect
141. C11×C22⋊C8D4semidirect
151. #22846C11direct (N × H)
171. C2×D4×C11M16semidirect
270. C2×#435C2×C11semidirect
271. C2×C8×D4C2×C11semidirect
272. C2×#407C2×C11semidirect
273. C22×C22⋊C8C2×C11semidirect
275. #1955C2×C11semidirect
276. #1924C2×C11semidirect
277. #1923C2×C11semidirect
278. #1870C2×C11semidirect
279. #1869C2×C11semidirect
280. #1869C2×C11semidirect
281. #1851C2×C11semidirect
282. #1850C2×C11semidirect
283. #1753C2×C11semidirect
284. #1752C2×C11semidirect
392. C23×C8C22×C11semidirect
399. C2×C4⋊C8C22×C11semidirect
400. C2×C4⋊C8C22×C11semidirect
401. C2×C4⋊C8C22×C11semidirect
412. C2×C22⋊C8C22×C11semidirect
413. C2×C22⋊C8C22×C11semidirect
414. C2×C22⋊C8C22×C11semidirect
415. C2×#97C22×C11semidirect
416. C2×#97C22×C11semidirect
417. C2×C4×C8C22×C11semidirect
428. #336C22×C11semidirect
429. #336C22×C11semidirect
430. #336C22×C11semidirect
431. #336C22×C11semidirect
432. #336C22×C11semidirect
433. #336C22×C11semidirect
462. C22×C11#435semidirect
561. C22⋊C8D4×C11semidirect
562. C22⋊C8D4×C11semidirect
602. C2×D4C11×M16semidirect
701. C11#22846direct (N × H)
832. C22C11×#435semidirect

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×#4072
C22×C11×C22⋊C82
C4×C11×#1202
C11×#19552
C11×#19242
C11×#19232
C11×#18702
C11×#18692
C11×#18512
C11×#18502
C11×#17532
C11×#17522
#2284611