Finite Group Databasebeta

← #14675276

Subgroups — #14675276

Order 2816.

2298 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622281C211yesmaximal, characteristic
2C2×#10622602C211yesmaximal, characteristic
3C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
4C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
5C2×#10622279C211yesmaximal, characteristic
6C2×#10622279C211yesmaximal, characteristic
7C2×D11×#95C211yesmaximal, characteristic
8#13066851C211yesmaximal, characteristic, complemented
9#13066850C211yesmaximal, characteristic, complemented
10#13066847C211yesmaximal, characteristic, complemented
11#13066845C211yesmaximal, characteristic, complemented
12#13066842C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic
14#95×Dic11C211yesmaximal, characteristic, complemented
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51#10622602C418yescomplemented
52C4×(C2×D11)⋊C4—24no—
53C4×Dic11⋊C4—24no—
54#10622281C418yescomplemented
55#10622279—24no—
56#10622279C418yescomplemented
57D11×#95—24no—
58C24×D11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C22×C4×D11—22no—
74C22×C4×D11—22no—
75C22×C4×D11—22no—
76C22×C4×D11—22no—
77C22×C4×D11—22no—
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11—22no—
81C22×C4×D11—22no—
82C22×C4×D11—22no—
83C22×C4×D11—22no—
84C22×C4×D11—22no—
85C22×C4×D11—41no—
86C22×C4×D11—41no—
87C22×C4×D11—41no—
88C22×C4×D11—41no—
89C22×C4×D11—41no—
90C22×C4×D11—41no—
91C22×C4×D11C2×C414yes—
92C22×C4×D11C2×C414yes—
93C22×C4×D11C2×C414yes—
94C2×C11×C4⋊C4—41no—
95C2×C11×C4⋊C4—41no—
96C2×C11×C4⋊C4C2×C414yescomplemented
97C2×C42×C11—22no—
98C2×C42×C11—22no—
99C2×C42×C11—41no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4C2×C414yes—
105C2×(C2×D11)⋊C4C2×C414yes—
106C2×(C2×D11)⋊C4C2×C414yes—
107C2×(C2×D11)⋊C4C2×C414yes—
108C2×(C2×D11)⋊C4C2×C414yes—
109C2×(C2×D11)⋊C4C2×C414yes—
110C2×(C2×D11)⋊C4D414yes—
111C2×(C2×D11)⋊C4Q814yes—
112C2×C4⋊Dic11—41no—
113C2×C4⋊Dic11—41no—
114C2×C4⋊Dic11C2×C414yescomplemented
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4—22no—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4C2×C414yescomplemented
120C2×Dic11⋊C4C2×C414yescomplemented
121C2×C4×Dic11—22no—
122C2×C4×Dic11—22no—
123C2×C4×Dic11—22no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11—22no—
126C2×C4×Dic11—22no—
127C2×C4×Dic11—22no—
128C2×C4×Dic11—22no—
129C2×C4×Dic11—41no—
130C2×C4×Dic11—41no—
131C2×C4×Dic11—41no—
132C2×C4×Dic11—41no—
133C2×C4×Dic11—41no—
134C2×C4×Dic11C2×C414yescomplemented
135C2×C4×Dic11C2×C414yescomplemented
136C11×#95—22no—
137C11×#95—22no—
138C11×#95—41no—
139C11×#95C2×C414yescomplemented
140C11×#95C2×C414yescomplemented
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—22no—
148C11⋊#95—41no—
149C11⋊#95C2×C414yescomplemented
150C11⋊#95C2×C414yescomplemented
151C11⋊#95C2×C414yescomplemented
152C11⋊#95C2×C414yescomplemented
153C11⋊#95D414yes—
154#13814—111nomaximal, Sylow
155C24×C11C2411yescharacteristic
156C23×D11—21no—
157C23×D11—21no—
158C23×D11—21no—
159C23×D11—21no—
160C23×D11—21no—
161C23×D11—21no—
162C23×D11—21no—
163C23×D11—21no—
164C23×D11C22×C412yes—
165C23×D11C22×C412yes—
166C23×D11C22×C412yes—
167C23×D11C2×D412yes—
168C23×D11C2×Q812yes—
169C23×D11#4112yes—
170C23×D11#4112yes—
171C22×C4×C11—21no—
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—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
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—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11C22×C412yes—
208C22×C4×C11C22×C412yes—
209C22×C4×C11C22×C412yes—
210C22×C4×C11C22×C412yes—
211C22×C4×C11C22×C412yes—
212C22×C4×C11C22×C412yes—
213C22×C4×C11C22×C412yes—
214C22×C4×C11C22×C412yes—
215C22×C4×C11C22×C412yes—
216C22×C4×C11C2×D412yes—
217C22×C4×C11C2×D412yes—
218C22×C4×C11C2×Q812yes—
219C22×C4×C11#4112yes—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11C22×C412yes—
255C22×Dic11C22×C412yes—
256C22×Dic11C22×C412yes—
257C22×Dic11C22×C412yes—
258C22×Dic11C22×C412yes—
259C22×Dic11C22×C412yes—
260C22×Dic11C22×C412yes—
261C22×Dic11C22×C412yes—
262C22×Dic11C22×C412yes—
263C22×Dic11C2×D412yes—
264C22×Dic11C2×D412yes—
265C22×Dic11C2×D412yes—
266C22×Dic11C2×Q812yes—
267C22×Dic11#4112yes—
268C22×Dic11#4112yes—
269C2×C4×D11—28no—
270C2×C4×D11—28no—
271C2×C4×D11—28no—
272C2×C4×D11—28no—
273C2×C4×D11—28no—
274C2×C4×D11—28no—
275C2×C4×D11—44no—
276C2×C4×D11—44no—
277C2×C4×D11—44no—
278C2×C4×D11—44no—
279C2×C4×D11—44no—
280C2×C4×D11—44no—
281C2×C4×D11—44no—
282C2×C4×D11—44no—
283C2×C4×D11—44no—
284C2×C4×D11—44no—
285C2×C4×D11—44no—
286C2×C4×D11—44no—
287C2×C4×D11—44no—
288C2×C4×D11—44no—
289C2×C4×D11—44no—
290C11×C4⋊C4—44no—
291C42×C11—44no—
292(C2×D11)⋊C4—28no—
293(C2×D11)⋊C4—28no—
294(C2×D11)⋊C4C42116yescomplemented
295(C2×D11)⋊C4C4⋊C4116yescomplemented
296C4⋊Dic11—44no—
297Dic11⋊C4—28no—
298Dic11⋊C4—28no—
299C4×Dic11—28no—
300C4×Dic11—44no—
301C4×Dic11—44no—
302C4×Dic11—44no—
303C4×Dic11—44no—
304C2×#385—111no—
305C2×#385—111no—
306C2×C4×C4⋊C4—111no—
307C2×C4×C22⋊C4—111no—
308C2×C4×C22⋊C4—111no—
309C2×C4×C22⋊C4—111no—
310C22×#95—111no—
311#1436—111no—
312#1436—111no—
313#1436—111no—
314#1436D1111yescharacteristic, complemented
315C4⋊#95—111no—
316#1434—111no—
317C22⋊#95—111no—
318C4×#95—111no—
319C23×C11C23×C411yescharacteristic
320C23×C11C23×C411yescharacteristic
321C23×C11C23×C411yescharacteristic
322C23×C11C22×D411yescharacteristic
323C23×C11C22×D411yescharacteristic
324C23×C11C22×Q811yescharacteristic
325C23×C11C2×#4111yescharacteristic
326C23×C11C2×#4111yescharacteristic
327C23×C11C2×#4111yescharacteristic
328C23×C11C2×#4111yescharacteristic
329C23×C11C2×#4111yescharacteristic
330C23×C11H(5,𝔽2)11yescharacteristic
331C23×C11H(5,𝔽2)11yescharacteristic
332C23×C11H(5,𝔽2)11yescharacteristic
333C23×C112−1+411yescharacteristic
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11C2×C4214yes—
363C22×D11C2×C4⋊C414yes—
364C22×D11#11714yes—
365C22×D11C4×D414yes—
366C22×D11C4×D414yes—
367C22×D11C4×Q814yes—
368C22×D11C4×Q814yes—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11C2×C4214yes—
416C2×C4×C11C2×C4⋊C414yes—
417C2×C4×C11C4×D414yes—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—41no—
452C2×Dic11—41no—
453C2×Dic11—41no—
454C2×Dic11—41no—
455C2×Dic11—41no—
456C2×Dic11—41no—
457C2×Dic11—41no—
458C2×Dic11—41no—
459C2×Dic11—41no—
460C2×Dic11—41no—
461C2×Dic11—41no—
462C2×Dic11—41no—
463C2×Dic11C2×C4214yes—
464C2×Dic11C2×C4⋊C414yes—
465C2×Dic11C4×D414yes—
466C2×Dic11C4×D414yes—
467C4×D11—416no—
468C4×D11—416no—
469C4×D11—416no—
470C24×C4—111no—
471C24×C4—111no—
472C24×C4—111no—
473C22×C4⋊C4—111no—
474C22×C4⋊C4—111no—
475C22×C4⋊C4—111no—
476C22×C4⋊C4C2×D1111yescharacteristic
477C22×C22⋊C4—111no—
478C22×C22⋊C4—111no—
479C22×C22⋊C4—111no—
480C22×C22⋊C4—111no—
481C22×C42—111no—
482C22×C42—111no—
483C22×C42—111no—
484C22×C42—111no—
485C22×C42—111no—
486C22×C42C2×D1111yescharacteristic
487#385—118no—
488#385—118no—
489C4×C4⋊C4—224no—
490C4×C22⋊C4—118no—
491C4×C22⋊C4—224no—
492C4×C22⋊C4—224no—
493C2×#95—111no—
494C2×#95—111no—
495C2×#95—111no—
496C2×#95—111no—
497C2×#95—111no—
498C2×#95—111no—
499C2×#95—111no—
500C2×#95—111no—
501C2×#95—111no—
502C2×#95—111no—
503C2×#95—111no—
504C2×#95—111no—
505C2×#95—111no—
506C2×#95—224no—
507C2×#95C2×D1111yescharacteristic
508C2×#95C2×D1111yescharacteristic
509C2×#95C2×D1111yescharacteristic
510C2×#95C2×D1111yescharacteristic
511C2×#95C2×D1111yescharacteristic
512C22×C11C22×C4211yescharacteristic
513C22×C11C22×C4⋊C411yescharacteristic
514C22×C11C2×#11711yescharacteristic
515C22×C11C2×C4×D411yescharacteristic
516C22×C11C2×C4×D411yescharacteristic
517C22×C11C2×C4×D411yescharacteristic
518C22×C11C2×C4×D411yescharacteristic
519C22×C11C2×C4×D411yescharacteristic
520C22×C11C2×C4×Q811yescharacteristic
521C22×C11C2×C4×Q811yescharacteristic
522C22×C11C4×#4111yescharacteristic
523C22×C11C4×#4111yescharacteristic
524C22×C11C4×#4111yescharacteristic
525C22×C11#51811yescharacteristic
526C22×C11#51811yescharacteristic
527C22×C11#51811yescharacteristic
528C22×C11#52011yescharacteristic
529C22×C11#52011yescharacteristic
530C22×C11#52011yescharacteristic
531C22×C11D4211yescharacteristic
532C22×C11#54611yescharacteristic
533C22×C11#54611yescharacteristic
534C22×C11#54611yescharacteristic
535C22×C11#54611yescharacteristic
536C22×C11#54711yescharacteristic
537C22×C11D4×Q811yescharacteristic
538C22×C11#55111yescharacteristic
539C22×C11#55111yescharacteristic
540C22×C11#55111yescharacteristic
541C22×C11#55111yescharacteristic
542C22×C11#55211yescharacteristic
543C22×C11#55211yescharacteristic
544C22×C11#55411yescharacteristic
545C22×C11#55411yescharacteristic
546C22×C11#55411yescharacteristic
547C2×D11—24no—
548C2×D11—24no—
549C2×D11—24no—
550C2×D11—24no—
551C2×D11—24no—
552C2×D11—24no—
553C2×D11—24no—
554C2×D11—24no—
555C2×D11—24no—
556C2×D11—24no—
557C2×D11—24no—
558C2×D11—24no—
559C2×D11—24no—
560C2×D11—24no—
561C2×D11C4×C4⋊C418yescomplemented
562C4×C11—24no—
563C4×C11—24no—
564C4×C11—24no—
565C4×C11—42no—
566C4×C11—42no—
567C4×C11—42no—
568C4×C11—42no—
569Dic11—24no—
570Dic11—24no—
571Dic11—24no—
572Dic11—24no—
573Dic11—42no—
574Dic11—42no—
575Dic11—42no—
576C25—111no—
577C23×C4—111no—
578C23×C4—111no—
579C23×C4—111no—
580C23×C4—111no—
581C23×C4—111no—
582C23×C4—111no—
583C23×C4—111no—
584C23×C4—114no—
585C23×C4—114no—
586C23×C4—114no—
587C23×C4—222no—
588C23×C4—222no—
589C23×C4—222no—
590C23×C4—222no—
591C23×C4—222no—
592C23×C4—222no—
593C23×C4—222no—
594C23×C4—222no—
595C23×C4—222no—
596C23×C4—222no—
597C23×C4—222no—
598C23×C4—222no—
599C23×C4—441no—
600C23×C4—441no—
601C23×C4—441no—
602C23×C4—441no—
603C23×C4—441no—
604C23×C4—441no—
605C23×C4C22×D1111yescharacteristic
606C23×C4C22×D1111yescharacteristic
607C23×C4C22×D1111yescharacteristic
608C23×C4C22×D1111yescharacteristic
609C23×C4C22×D1111yescharacteristic
610C23×C4C22×D1111yescharacteristic
611C23×C4C22×D1111yescharacteristic
612C2×C4⋊C4—41no—
613C2×C4⋊C4—41no—
614C2×C4⋊C4—114no—
615C2×C4⋊C4—114no—
616C2×C4⋊C4—114no—
617C2×C4⋊C4—222no—
618C2×C4⋊C4—222no—
619C2×C4⋊C4—222no—
620C2×C4⋊C4—222no—
621C2×C4⋊C4—441no—
622C2×C4⋊C4—441no—
623C2×C4⋊C4C4×D1114yescomplemented
624C2×C22⋊C4—114no—
625C2×C22⋊C4—114no—
626C2×C22⋊C4—114no—
627C2×C22⋊C4—114no—
628C2×C22⋊C4—114no—
629C2×C22⋊C4—114no—
630C2×C22⋊C4—114no—
631C2×C22⋊C4—114no—
632C2×C22⋊C4—222no—
633C2×C22⋊C4—222no—
634C2×C22⋊C4—222no—
635C2×C22⋊C4—222no—
636C2×C42—22no—
637C2×C42—22no—
638C2×C42—41no—
639C2×C42—114no—
640C2×C42—114no—
641C2×C42—222no—
642C2×C42—222no—
643C2×C42—222no—
644C2×C42—222no—
645C2×C42—222no—
646C2×C42—222no—
647C2×C42—222no—
648C2×C42—222no—
649C2×C42—441no—
650C2×C42—441no—
651C2×C42—441no—
652C2×C42—441no—
653C2×C42—441no—
654#95—22no—
655#95—22no—
656#95—41no—
657#95—114no—
658#95—114no—
659#95—114no—
660#95—114no—
661#95—114no—
662#95—222no—
663#95—222no—
664#95—222no—
665#95—222no—
666#95—222no—
667#95—222no—
668#95—222no—
669#95—441no—
670#95C4×D1114yescomplemented
671#95C4×D1114yescomplemented
672C2×C11C2×C4×C4⋊C411yescharacteristic
673C2×C11C42×D411yescharacteristic
674C2×C11#227511yescharacteristic
675C2×C11#234211yescharacteristic
676C2×C11#234311yescharacteristic
677C2×C11D4×C4⋊C411yescharacteristic
678C2×C11#234911yescharacteristic
679C2×C11#235811yescharacteristic
680C2×C11#235811yescharacteristic
681C2×C11#235911yescharacteristic
682C2×C11#235911yescharacteristic
683C2×C11#236011yescharacteristic
684C2×C11#236011yescharacteristic
685C2×C11#236811yescharacteristic
686C2×C11#236811yescharacteristic
687D11—28no—
688C24—112no—
689C24—112no—
690C24—112no—
691C24—112no—
692C24—112no—
693C24—112no—
694C24—112no—
695C24—221no—
696C24—221no—
697C24—221no—
698C24—221no—
699C24—221no—
700C24—221no—
701C24—221no—
702C24—221no—
703C24C23×D1111yescharacteristic
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—112no—
741C22×C4—112no—
742C22×C4—112no—
743C22×C4—112no—
744C22×C4—112no—
745C22×C4—112no—
746C22×C4—112no—
747C22×C4—112no—
748C22×C4—112no—
749C22×C4—112no—
750C22×C4—112no—
751C22×C4—112no—
752C22×C4—112no—
753C22×C4—112no—
754C22×C4—112no—
755C22×C4—228no—
756C22×C4—228no—
757C22×C4—228no—
758C22×C4—228no—
759C22×C4—228no—
760C22×C4—221no—
761C22×C4—221no—
762C22×C4—221no—
763C22×C4—221no—
764C22×C4—221no—
765C22×C4—221no—
766C22×C4—221no—
767C22×C4—221no—
768C22×C4—221no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—221no—
773C22×C4—221no—
774C22×C4—221no—
775C22×C4—221no—
776C22×C4—221no—
777C22×C4—221no—
778C22×C4—221no—
779C22×C4—221no—
780C22×C4—221no—
781C22×C4—221no—
782C22×C4—221no—
783C22×C4—221no—
784C22×C4—221no—
785C22×C4—221no—
786C22×C4—221no—
787C22×C4—221no—
788C22×C4—221no—
789C22×C4—221no—
790C22×C4—221no—
791C22×C4—221no—
792C22×C4—221no—
793C22×C4—221no—
794C22×C4—228no—
795C22×C4—444no—
796C22×C4—444no—
797C22×C4—444no—
798C22×C4—444no—
799C22×C4—444no—
800C22×C4—444no—
801C22×C4—444no—
802C22×C4—444no—
803C22×C4—444no—
804C22×C4—444no—
805C22×C4—444no—
806C22×C4—444no—
807C22×C4—444no—
808C22×C4—444no—
809C22×C4—444no—
810C22×C4C2×C4×D1112yes—
811C22×C4C2×C4×D1112yes—
812C22×C4C2×C4×D1112yes—
813C22×C4C2×C4×D1112yes—
814C22×C4C2×C4×D1112yes—
815C22×C4C2×C4×D1112yes—
816C22×C4C2×C4×D1112yes—
817C22×C4C2×C4×D1112yes—
818C22×C4C2×C4×D1112yes—
819C22×C4D4×D1112yes—
820C22×C4D4×D1112yes—
821C22×C4Q8×D1112yes—
822C22×C4#434312yes—
823C4⋊C4—44no—
824C4⋊C4—228no—
825C4⋊C4—228no—
826C4⋊C4—444no—
827C22⋊C4—1116no—
828C22⋊C4—1116no—
829C22⋊C4—228no—
830C22⋊C4—228no—
831C42—44no—
832C42—228no—
833C42—444no—
834C42—444no—
835C42—444no—
836C42—444no—
837C11#1381411yescharacteristic, complemented, Sylow
838C23—114no—
839C23—114no—
840C23—114no—
841C23—114no—
842C23—114no—
843C23—114no—
844C23—114no—
845C23—222no—
846C23—222no—
847C23—222no—
848C23—222no—
849C23—222no—
850C23—222no—
851C23—222no—
852C23—222no—
853C23—222no—
854C23—222no—
855C23—222no—
856C23—222no—
857C23—222no—
858C23—222no—
859C23—222no—
860C23—222no—
861C23—222no—
862C23—222no—
863C23—222no—
864C23—222no—
865C23—222no—
866C23—222no—
867C23—222no—
868C23—222no—
869C23—222no—
870C23—222no—
871C23—222no—
872C23—222no—
873C23C22×C4×D1111yescharacteristic
874C23C22×C4×D1111yescharacteristic
875C23C22×C4×D1111yescharacteristic
876C23C2×D4×D1111yescharacteristic
877C23C2×D4×D1111yescharacteristic
878C23#6703711yescharacteristic
879C23#6703711yescharacteristic
880C23C2×Q8×D1111yescharacteristic
881C23C2×#434311yescharacteristic
882C23#41×D1111yescharacteristic
883C23#41×D1111yescharacteristic
884C23#41×D1111yescharacteristic
885C23#41×D1111yescharacteristic
886C23#6704211yescharacteristic
887C23#6704311yescharacteristic
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—114no—
935C2×C4—114no—
936C2×C4—114no—
937C2×C4—114no—
938C2×C4—222no—
939C2×C4—222no—
940C2×C4—222no—
941C2×C4—222no—
942C2×C4—222no—
943C2×C4—222no—
944C2×C4—222no—
945C2×C4—222no—
946C2×C4—222no—
947C2×C4—222no—
948C2×C4—222no—
949C2×C4—222no—
950C2×C4—222no—
951C2×C4—222no—
952C2×C4—222no—
953C2×C4—222no—
954C2×C4—222no—
955C2×C4—222no—
956C2×C4—222no—
957C2×C4—222no—
958C2×C4—222no—
959C2×C4—222no—
960C2×C4—222no—
961C2×C4—222no—
962C2×C4—222no—
963C2×C4—222no—
964C2×C4—222no—
965C2×C4—222no—
966C2×C4—222no—
967C2×C4—222no—
968C2×C4—222no—
969C2×C4—222no—
970C2×C4—222no—
971C2×C4—4416no—
972C2×C4—4416no—
973C2×C4—4416no—
974C2×C4—441no—
975C2×C4—441no—
976C2×C4—441no—
977C2×C4—441no—
978C2×C4—441no—
979C2×C4—441no—
980C2×C4—441no—
981C2×C4—441no—
982C2×C4—441no—
983C2×C4—441no—
984C2×C4—441no—
985C2×C4—441no—
986C2×C4C42×D1114yes—
987C2×C4C4⋊C4×D1114yes—
988C2×C4#6694614yes—
989C22—118no—
990C22—224no—
991C22—224no—
992C22—224no—
993C22—224no—
994C22—224no—
995C22—224no—
996C22—224no—
997C22—224no—
998C22—224no—
999C22—224no—
1000C22—224no—
1001C22—224no—
1002C22—224no—
1003C22—224no—
1004C22C2×C42×D1111yescharacteristic
1005C22#1062301711yescharacteristic
1006C22C2×C4⋊C4×D1111yescharacteristic
1007C22C2×#6694611yescharacteristic
1008C22D11×#11711yescharacteristic
1009C22#1062305311yescharacteristic
1010C22#1062305411yescharacteristic
1011C22C4×D4×D1111yescharacteristic
1012C22C4×D4×D1111yescharacteristic
1013C22C4×D4×D1111yescharacteristic
1014C22C4×D4×D1111yescharacteristic
1015C22#1062307611yescharacteristic
1016C22#1062307611yescharacteristic
1017C22#1062307711yescharacteristic
1018C22#1062307711yescharacteristic
1019C22C4×Q8×D1111yescharacteristic
1020C22C4×Q8×D1111yescharacteristic
1021C22C4×#434311yescharacteristic
1022C22C4×#434311yescharacteristic
1023C22#1062312111yescharacteristic
1024C22#1062314311yescharacteristic
1025C22#1062314311yescharacteristic
1026C22#1062316111yescharacteristic
1027C22#1062316311yescharacteristic
1028C22#1062316711yescharacteristic
1029C22#1062316811yescharacteristic
1030C22#1062318511yescharacteristic
1031C22#1062318611yescharacteristic
1032C22#1062319011yescharacteristic
1033C22#1062321011yescharacteristic
1034C22#1062322111yescharacteristic
1035C22#1062322511yescharacteristic
1036C22#1062323611yescharacteristic
1037C22#1062323911yescharacteristic
1038C22#1062326111yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—224no—
1047C4—224no—
1048C4—224no—
1049C4—224no—
1050C4—442no—
1051C4—442no—
1052C4—442no—
1053C2—228no—
1054C2C4×C4⋊C4×D1111yescharacteristic
1055C2C4×#6694611yescharacteristic
1056C2#1307097511yescharacteristic
1057C2#1307146011yescharacteristic
1058C2#1307147511yescharacteristic
1059C2#1307151411yescharacteristic
1060C2#1307152511yescharacteristic
1061C2#1307159211yescharacteristic
1062C2#1307159911yescharacteristic
1063C2#1307160511yescharacteristic
1064C2#1307161511yescharacteristic
1065C2#1307162011yescharacteristic
1066C2#1307162411yescharacteristic
1067C2#1307169311yescharacteristic
1068C2#1307169511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1436D11
hypocenterC11#13814
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic11⋊C4C2semidirect
8. #13066851C2semidirect
9. #13066850C2semidirect
10. #13066847C2semidirect
11. #13066845C2semidirect
12. #13066842C2semidirect
14. #95×Dic11C2semidirect
15. C11×#1436C2semidirect
51. #10622602C4semidirect
54. #10622281C4semidirect
56. #10622279C4semidirect
96. C2×C11×C4⋊C4C2×C4semidirect
114. C2×C4⋊Dic11C2×C4semidirect
119. C2×Dic11⋊C4C2×C4semidirect
120. C2×Dic11⋊C4C2×C4semidirect
134. C2×C4×Dic11C2×C4semidirect
135. C2×C4×Dic11C2×C4semidirect
139. C11×#95C2×C4semidirect
140. C11×#95C2×C4semidirect
149. C11⋊#95C2×C4semidirect
150. C11⋊#95C2×C4semidirect
151. C11⋊#95C2×C4semidirect
152. C11⋊#95C2×C4semidirect
294. (C2×D11)⋊C4C42semidirect
295. (C2×D11)⋊C4C4⋊C4semidirect
314. #1436D11semidirect
561. C2×D11C4×C4⋊C4semidirect
623. C2×C4⋊C4C4×D11semidirect
670. #95C4×D11semidirect
671. #95C4×D11semidirect
837. C11#13814semidirect

Maximal subgroups

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

subgroupindex
C2×#106222812
C2×#106226022
C2×C4×Dic11⋊C42
C2×C4×(C2×D11)⋊C42
C2×#106222792
C2×D11×#952
#130668512
#130668502
#130668472
#130668452
#130668422
(C2×D11)⋊#952
#95×Dic112
C11×#14362
#1381411