Finite Group Databasebeta

← #14676906

Subgroups — #14676906

Order 2816.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C211yesmaximal, characteristic
2C2×#10622259C211yesmaximal, characteristic, complemented
3C2×#10622259C211yesmaximal, characteristic, complemented
4C2×#10622585C211yesmaximal, characteristic, complemented
5C2×#10622280C211yesmaximal, characteristic
6C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
7C2×#10622279C211yesmaximal, characteristic
8#13066884C211yesmaximal, characteristic, complemented
9#13066882C211yesmaximal, characteristic, complemented
10#13066860C211yesmaximal, characteristic
11#13066858C211yesmaximal, characteristic
12#13066854C211yesmaximal, characteristic
13#13066852C211yesmaximal, characteristic
14Dic11⋊#95C211yesmaximal, characteristic, complemented
15C11×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×#66949—24no—
36C2×#66949—24no—
37C2×#66949C418yescomplemented
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
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54#10622585—24no—
55C4×Dic11⋊C4—24no—
56#10622280—24no—
57#10622279—24no—
58#10622259—24no—
59#10622259—24no—
60C24×D11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
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×D11C2×C414yes—
82C22×Dic22—22no—
83C22×Dic22—22no—
84C22×Dic22—22no—
85C22×Dic22—22no—
86C22×Dic22—22no—
87C22×Dic22—22no—
88C22×Dic22C2×C414yes—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—41no—
94C2×C11×C4⋊C4C2×C414yes—
95C2×C42×C11—22no—
96C2×C42×C11—22no—
97C2×C42×C11—41no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4—22no—
105C2×(C2×D11)⋊C4—22no—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—41no—
112C2×(C2×D11)⋊C4—41no—
113C2×(C2×D11)⋊C4C2×C414yes—
114C2×(C2×D11)⋊C4C2×C414yes—
115C2×(C2×D11)⋊C4Q814yescomplemented
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4—22no—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4—22no—
120C2×Dic11⋊C4—22no—
121C2×Dic11⋊C4—22no—
122C2×Dic11⋊C4—22no—
123C2×Dic11⋊C4—22no—
124C2×Dic11⋊C4—22no—
125C2×Dic11⋊C4—41no—
126C2×Dic11⋊C4C2×C414yes—
127C2×Dic11⋊C4C2×C414yes—
128C2×Dic11⋊C4D414yes—
129C2×Dic11⋊C4D414yes—
130C2×Dic11⋊C4D414yes—
131C2×C4×Dic11—22no—
132C2×C4×Dic11—22no—
133C2×C4×Dic11—22no—
134C2×C4×Dic11—22no—
135C2×C4×Dic11—22no—
136C2×C4×Dic11—22no—
137C2×C4×Dic11—22no—
138C2×C4×Dic11—41no—
139C2×C4×Dic11D414yes—
140#66949—232no—
141C11×#95—22no—
142C11×#95—22no—
143C11×#95—22no—
144C11×#95—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—22no—
148C11⋊#95—22no—
149C11⋊#95—22no—
150C11⋊#95—22no—
151C11⋊#95—22no—
152C11⋊#95—22no—
153C11⋊#95—22no—
154C11⋊#95—22no—
155C11⋊#95—22no—
156C11⋊#95—22no—
157#13997—111nomaximal, Sylow
158C24×C11C2411yescharacteristic
159C23×D11—21no—
160C23×D11—21no—
161C23×D11—21no—
162C23×D11—21no—
163C23×D11—21no—
164C23×D11—21no—
165C23×D11—21no—
166C23×D11—21no—
167C23×D11—21no—
168C23×D11—21no—
169C23×D11—21no—
170C23×D11—21no—
171C23×D11C22×C412yes—
172C23×D11C2×Q812yes—
173C23×D11#4112yes—
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×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11C22×C412yes—
214C22×C4×C11C22×C412yes—
215C22×C4×C11C22×C412yes—
216C22×C4×C11C2×D412yes—
217C22×C4×C11C2×D412yes—
218C22×C4×C11C2×D412yes—
219C22×C4×C11C2×D412yes—
220C22×C4×C11C2×Q812yes—
221C22×C4×C11#4112yes—
222C22×C4×C11#4112yes—
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×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11C22×C412yes—
259C22×Dic11C22×C412yes—
260C22×Dic11C22×C412yes—
261C22×Dic11C2×D412yes—
262C22×Dic11C2×D412yes—
263C22×Dic11C2×D412yes—
264C22×Dic11C2×D412yes—
265C22×Dic11C2×D412yes—
266C22×Dic11C2×D412yes—
267C22×Dic11C2×D412yes—
268C22×Dic11C2×D412yes—
269C22×Dic11C2×Q812yes—
270C22×Dic11#4112yes—
271C22×Dic11#4112yes—
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×Dic22—28no—
280C2×Dic22—28no—
281C2×Dic22—28no—
282C2×Dic22—44no—
283C2×Dic22—44no—
284C2×Dic22—44no—
285C2×Dic22—44no—
286C11×C4⋊C4—28no—
287C11×C4⋊C4—44no—
288C42×C11—44no—
289(C2×D11)⋊C4—28no—
290(C2×D11)⋊C4—28no—
291(C2×D11)⋊C4—28no—
292(C2×D11)⋊C4—28no—
293(C2×D11)⋊C4—44no—
294(C2×D11)⋊C4—44no—
295Dic11⋊C4—28no—
296Dic11⋊C4—28no—
297Dic11⋊C4—44no—
298Dic11⋊C4—44no—
299Dic11⋊C4C22⋊C4116yescomplemented
300C4×Dic11—28no—
301C4×Dic11—44no—
302C4×Dic11—44no—
303C22×C22⋊Q8—111no—
304C2×#391—111no—
305C2×#391—111no—
306C2×#389—111no—
307C2×#380—111no—
308C2×C4×C4⋊C4—111no—
309C2×C4×C22⋊C4—111no—
310#1445—111no—
311#1445—111no—
312#1439—111no—
313#1439—111no—
314#1437—111no—
315#1437—111no—
316C4⋊#95—111no—
317C4⋊#95D1111yescharacteristic, complemented
318C23×C11C23×C411yescharacteristic
319C23×C11C22×D411yescharacteristic
320C23×C11C22×D411yescharacteristic
321C23×C11C22×D411yescharacteristic
322C23×C11C22×D411yescharacteristic
323C23×C11C22×Q811yescharacteristic
324C23×C11C2×#4111yescharacteristic
325C23×C11C2×#4111yescharacteristic
326C23×C11C2×#4111yescharacteristic
327C23×C11C2×#4111yescharacteristic
328C23×C11C2×#4111yescharacteristic
329C23×C11H(5,𝔽2)11yescharacteristic
330C23×C112−1+411yescharacteristic
331C23×C112−1+411yescharacteristic
332C23×C112−1+411yescharacteristic
333C22×D11—22no—
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—41no—
352C22×D11—41no—
353C22×D11—41no—
354C22×D11—41no—
355C22×D11—41no—
356C22×D11—41no—
357C22×D11—41no—
358C22×D11—41no—
359C22×D11—41no—
360C22×D11—41no—
361C22×D11—41no—
362C22×D11—41no—
363C22×D11—41no—
364C22×D11—41no—
365C22×D11—41no—
366C22×D11—41no—
367C22×D11C4×Q814yes—
368C2×C4×C11—22no—
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—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
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×C22⋊C414yes—
416C2×C4×C11C22⋊Q814yescomplemented
417C2×Dic11—22no—
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—41no—
436C2×Dic11—41no—
437C2×Dic11—41no—
438C2×Dic11—41no—
439C2×Dic11—41no—
440C2×Dic11—41no—
441C2×Dic11—41no—
442C2×Dic11—41no—
443C2×Dic11—41no—
444C2×Dic11—41no—
445C2×Dic11—41no—
446C2×Dic11—41no—
447C2×Dic11—41no—
448C2×Dic11—41no—
449C2×Dic11—41no—
450C2×Dic11—41no—
451C2×Dic11—41no—
452C2×Dic11—41no—
453C2×Dic11—41no—
454C2×Dic11—41no—
455C2×Dic11—41no—
456C2×Dic11—41no—
457C2×Dic11—41no—
458C2×Dic11C2×C22⋊C414yes—
459C2×Dic11C2×C22⋊C414yes—
460C2×Dic11C4×D414yes—
461C2×Dic11C4×D414yes—
462C2×Dic11#12114yes—
463C2×Dic11#12114yes—
464C2×Dic11#12414yes—
465C2×Dic11#12714yes—
466C4×D11—416no—
467Dic22—416no—
468C23×Q8—111no—
469C24×C4—111no—
470C2×C22⋊Q8—118no—
471C2×C22⋊Q8—224no—
472C2×C22⋊Q8—224no—
473C22×C4⋊C4—111no—
474C22×C4⋊C4—111no—
475C22×C4⋊C4—111no—
476C22×C4⋊C4—111no—
477C22×C4⋊C4—111no—
478C22×C4⋊C4C2×D1111yescharacteristic
479C22×C4⋊C4C2×D1111yescharacteristic
480C22×C22⋊C4—111no—
481C22×C22⋊C4—111no—
482C22×C22⋊C4—111no—
483C22×C22⋊C4—111no—
484C22×C22⋊C4—111no—
485C22×C22⋊C4—111no—
486C22×C42—111no—
487C22×C42—111no—
488C22×C42—111no—
489C22×C42C2×D1111yescharacteristic
490#391—224no—
491#391—224no—
492#389—224no—
493#380—224no—
494C4×C4⋊C4—224no—
495C4×C22⋊C4—224no—
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—111no—
507C2×#95—111no—
508C2×#95C2×D1111yescharacteristic
509C2×#95C2×D1111yescharacteristic
510C2×#95C2×D1111yescharacteristic
511C2×#95C2×D1111yescharacteristic
512C22×C11C22×C22⋊C411yescharacteristic
513C22×C11C2×C4×D411yescharacteristic
514C22×C11C2×C4×D411yescharacteristic
515C22×C11C2×C4×Q811yescharacteristic
516C22×C11C4×#4111yescharacteristic
517C22×C11#51911yescharacteristic
518C22×C11#52011yescharacteristic
519C22×C11C2×#12111yescharacteristic
520C22×C11C2×#12111yescharacteristic
521C22×C11C2×C22⋊Q811yescharacteristic
522C22×C11#52511yescharacteristic
523C22×C11C2×#12411yescharacteristic
524C22×C11#52911yescharacteristic
525C22×C11C2×#12711yescharacteristic
526C22×C11#53311yescharacteristic
527C22×C11#53611yescharacteristic
528C22×C11#53711yescharacteristic
529C22×C11#54111yescharacteristic
530C22×C11#54211yescharacteristic
531C22×C11#54611yescharacteristic
532C22×C11#54611yescharacteristic
533C22×C11#54611yescharacteristic
534C22×C11#54711yescharacteristic
535C22×C11#54711yescharacteristic
536C22×C11#54711yescharacteristic
537C22×C11#54811yescharacteristic
538C22×C11#54811yescharacteristic
539C22×C11#54811yescharacteristic
540C22×C11D4×Q811yescharacteristic
541C22×C11D4×Q811yescharacteristic
542C22×C11D4×Q811yescharacteristic
543C22×C11#55211yescharacteristic
544C22×C11#55211yescharacteristic
545C22×C11#55411yescharacteristic
546C22×C11#55611yescharacteristic
547C2×D11—24no—
548C2×D11—24no—
549C2×D11—24no—
550C2×D11—42no—
551C2×D11—42no—
552C2×D11—42no—
553C2×D11—42no—
554C2×D11—42no—
555C2×D11—42no—
556C2×D11—42no—
557C2×D11—42no—
558C2×D11—42no—
559C2×D11—42no—
560C2×D11—42no—
561C2×D11—42no—
562C4×C11—24no—
563C4×C11—24no—
564C4×C11—42no—
565C4×C11—42no—
566C4×C11—42no—
567C4×C11—42no—
568C4×C11—81no—
569Dic11—24no—
570Dic11—42no—
571Dic11—42no—
572Dic11—42no—
573Dic11—42no—
574Dic11—81no—
575Dic11#39018yes—
576C25—111no—
577C22×Q8—114no—
578C22×Q8—222no—
579C22×Q8—222no—
580C22×Q8—222no—
581C22×Q8—222no—
582C22×Q8—222no—
583C22×Q8—222no—
584C23×C4—111no—
585C23×C4—111no—
586C23×C4—111no—
587C23×C4—111no—
588C23×C4—111no—
589C23×C4—111no—
590C23×C4—114no—
591C23×C4—111no—
592C23×C4—222no—
593C23×C4—222no—
594C23×C4—222no—
595C23×C4—222no—
596C23×C4—222no—
597C23×C4—222no—
598C23×C4C22×D1111yescharacteristic
599C23×C4C22×D1111yescharacteristic
600C23×C4C22×D1111yescharacteristic
601C23×C4C22×D1111yescharacteristic
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1111yescharacteristic
604C23×C4C22×D1111yescharacteristic
605C22⋊Q8—2232no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—114no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4—114no—
614C2×C4⋊C4—114no—
615C2×C4⋊C4—114no—
616C2×C4⋊C4—222no—
617C2×C4⋊C4—222no—
618C2×C4⋊C4—222no—
619C2×C4⋊C4—222no—
620C2×C4⋊C4—222no—
621C2×C4⋊C4—222no—
622C2×C4⋊C4—222no—
623C2×C4⋊C4—222no—
624C2×C4⋊C4—222no—
625C2×C4⋊C4—441no—
626C2×C4⋊C4C4×D1114yes—
627C2×C22⋊C4—114no—
628C2×C22⋊C4—114no—
629C2×C22⋊C4—114no—
630C2×C22⋊C4—222no—
631C2×C22⋊C4—222no—
632C2×C22⋊C4—222no—
633C2×C22⋊C4—222no—
634C2×C22⋊C4—222no—
635C2×C22⋊C4—222no—
636C2×C22⋊C4—222no—
637C2×C22⋊C4—222no—
638C2×C22⋊C4—222no—
639C2×C22⋊C4—222no—
640C2×C22⋊C4—222no—
641C2×C22⋊C4—222no—
642C2×C22⋊C4—222no—
643C2×C22⋊C4—441no—
644C2×C22⋊C4—441no—
645C2×C42—22no—
646C2×C42—22no—
647C2×C42—41no—
648C2×C42—114no—
649C2×C42—222no—
650C2×C42—222no—
651C2×C42—222no—
652C2×C42—222no—
653C2×C42—222no—
654C2×C42—222no—
655C2×C42—222no—
656C2×C42—441no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—222no—
662#95—222no—
663#95—222no—
664#95—222no—
665#95—222no—
666#95—222no—
667#95—222no—
668#95—222no—
669#95—222no—
670#95—222no—
671#95—222no—
672#95—222no—
673C2×C11C2×#39011yescharacteristic
674C2×C11C4×C22⋊Q811yescharacteristic
675C2×C11#232311yescharacteristic
676C2×C11#233911yescharacteristic
677C2×C11Q8×C22⋊C411yescharacteristic
678C2×C11#236011yescharacteristic
679C2×C11#236211yescharacteristic
680C2×C11#241511yescharacteristic
681C2×C11#241711yescharacteristic
682C2×C11#242711yescharacteristic
683C2×C11#242911yescharacteristic
684C2×C11#248911yescharacteristic
685C2×C11#249211yescharacteristic
686C2×C11#254011yescharacteristic
687C2×C11#254211yescharacteristic
688D11—44no—
689C24—112no—
690C24—112no—
691C24—112no—
692C24—221no—
693C24—221no—
694C24—221no—
695C24—221no—
696C24—221no—
697C24—221no—
698C24—221no—
699C24—221no—
700C24—221no—
701C24—221no—
702C24—221no—
703C24—221no—
704C24C23×D1111yescharacteristic
705C2×Q8—228no—
706C2×Q8—228no—
707C2×Q8—228no—
708C2×Q8—444no—
709C2×Q8—444no—
710C2×Q8—444no—
711C2×Q8—444no—
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—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—112no—
752C22×C4—112no—
753C22×C4—112no—
754C22×C4—112no—
755C22×C4—112no—
756C22×C4—112no—
757C22×C4—112no—
758C22×C4—112no—
759C22×C4—112no—
760C22×C4—112no—
761C22×C4—112no—
762C22×C4—112no—
763C22×C4—112no—
764C22×C4—112no—
765C22×C4—228no—
766C22×C4—228no—
767C22×C4—228no—
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—221no—
795C22×C4—221no—
796C22×C4—221no—
797C22×C4—221no—
798C22×C4—221no—
799C22×C4—221no—
800C22×C4—221no—
801C22×C4—221no—
802C22×C4—221no—
803C22×C4—444no—
804C22×C4—444no—
805C22×C4—444no—
806C22×C4—444no—
807C22×C4C2×C4×D1112yes—
808C22×C4C2×C4×D1112yes—
809C22×C4C2×C4×D1112yes—
810C22×C4#433912yes—
811C22×C4#433912yes—
812C22×C4D4×D1112yes—
813C22×C4D4×D1112yes—
814C22×C4D4×D1112yes—
815C22×C4D4×D1112yes—
816C22×C4Q8×D1112yes—
817C4⋊C4—28no—
818C4⋊C4—44no—
819C4⋊C4—1116no—
820C4⋊C4—228no—
821C4⋊C4—228no—
822C4⋊C4—444no—
823C4⋊C4—444no—
824C22⋊C4—228no—
825C22⋊C4—228no—
826C22⋊C4—228no—
827C22⋊C4—228no—
828C22⋊C4—444no—
829C22⋊C4—444no—
830C42—44no—
831C42—228no—
832C42—444no—
833C42—444no—
834C11#1399711yescharacteristic, complemented, Sylow
835C23—114no—
836C23—222no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—222no—
841C23—222no—
842C23—222no—
843C23—222no—
844C23—222no—
845C23—222no—
846C23—222no—
847C23—222no—
848C23—222no—
849C23—222no—
850C23—222no—
851C23—222no—
852C23—222no—
853C23—222no—
854C23—441no—
855C23—441no—
856C23—441no—
857C23—441no—
858C23—441no—
859C23—441no—
860C23—441no—
861C23—441no—
862C23—441no—
863C23—441no—
864C23—441no—
865C23—441no—
866C23—441no—
867C23—441no—
868C23—441no—
869C23—441no—
870C23C22×C4×D1111yescharacteristic
871C23C2×#433911yescharacteristic
872C23C2×#433911yescharacteristic
873C23C2×D4×D1111yescharacteristic
874C23C2×D4×D1111yescharacteristic
875C23C2×D4×D1111yescharacteristic
876C23C2×D4×D1111yescharacteristic
877C23#6703711yescharacteristic
878C23C2×Q8×D1111yescharacteristic
879C23#6704011yescharacteristic
880C23#6704011yescharacteristic
881C23#41×D1111yescharacteristic
882C23#41×D1111yescharacteristic
883C23#41×D1111yescharacteristic
884C23#6704311yescharacteristic
885Q8—4416no—
886C2×C4—22no—
887C2×C4—22no—
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—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
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—114no—
934C2×C4—114no—
935C2×C4—114no—
936C2×C4—114no—
937C2×C4—114no—
938C2×C4—114no—
939C2×C4—114no—
940C2×C4—114no—
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—4416no—
960C2×C4—441no—
961C2×C4—441no—
962C2×C4—441no—
963C2×C4—441no—
964C2×C4—441no—
965C2×C4—441no—
966C2×C4—441no—
967C2×C4—441no—
968C2×C4—441no—
969C2×C4—441no—
970C2×C4—441no—
971C2×C4—441no—
972C2×C4—441no—
973C2×C4—441no—
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×C4C22⋊C4×D1114yes—
984C2×C4#6694914yescomplemented
985C22—224no—
986C22—224no—
987C22—224no—
988C22—442no—
989C22—442no—
990C22—442no—
991C22—442no—
992C22—442no—
993C22—442no—
994C22—442no—
995C22—442no—
996C22—442no—
997C22—442no—
998C22—442no—
999C22—442no—
1000C22C4×#433911yescharacteristic
1001C22C2×C22⋊C4×D1111yescharacteristic
1002C22#1062302111yescharacteristic
1003C22#1062302111yescharacteristic
1004C22#1062303511yescharacteristic
1005C22#1062303811yescharacteristic
1006C22#1062303811yescharacteristic
1007C22#1062303811yescharacteristic
1008C22C2×#6694911yescharacteristic
1009C22#1062305911yescharacteristic
1010C22#1062306211yescharacteristic
1011C22C4×D4×D1111yescharacteristic
1012C22C4×D4×D1111yescharacteristic
1013C22#1062307811yescharacteristic
1014C22#1062308311yescharacteristic
1015C22#1062309911yescharacteristic
1016C22C4×Q8×D1111yescharacteristic
1017C22#1062310311yescharacteristic
1018C22#1062310911yescharacteristic
1019C22#1062312811yescharacteristic
1020C22D11×#12111yescharacteristic
1021C22D11×#12111yescharacteristic
1022C22#1062314111yescharacteristic
1023C22#1062316311yescharacteristic
1024C22#1062316411yescharacteristic
1025C22#1062316711yescharacteristic
1026C22#1062317111yescharacteristic
1027C22D11×#12411yescharacteristic
1028C22#1062320811yescharacteristic
1029C22#1062322411yescharacteristic
1030C22#1062322711yescharacteristic
1031C22D11×#12711yescharacteristic
1032C22#1062325511yescharacteristic
1033C22#1062325811yescharacteristic
1034C22#1062325811yescharacteristic
1035C4—24no—
1036C4—24no—
1037C4—42no—
1038C4—42no—
1039C4—42no—
1040C4—42no—
1041C4—81no—
1042C4—118no—
1043C4—224no—
1044C4—442no—
1045C4—442no—
1046C4—442no—
1047C4—442no—
1048C4—881no—
1049C2—444no—
1050C2D11×#39011yescharacteristic
1051C2C4×#6694911yescharacteristic
1052C2#1307129311yescharacteristic
1053C2#1307144311yescharacteristic
1054C2#1307145011yescharacteristic
1055C2#1307161811yescharacteristic
1056C2#1307164411yescharacteristic
1057C2#1307204411yescharacteristic
1058C2#1307206611yescharacteristic
1059C2#1307219211yescharacteristic
1060C2#1307221411yescharacteristic
1061C2#1307295611yescharacteristic
1062C2#1307298911yescharacteristic
1063C2#1307355311yescharacteristic
1064C2#1307356811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC4⋊#95D11
hypocenterC11#13997
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622259C2semidirect
3. C2×#10622259C2semidirect
4. C2×#10622585C2semidirect
6. C2×C4×Dic11⋊C4C2semidirect
8. #13066884C2semidirect
9. #13066882C2semidirect
14. Dic11⋊#95C2semidirect
15. C11×C4⋊#95C2semidirect
37. C2×#66949C4semidirect
115. C2×(C2×D11)⋊C4Q8semidirect
299. Dic11⋊C4C22⋊C4semidirect
317. C4⋊#95D11semidirect
416. C2×C4×C11C22⋊Q8semidirect
834. C11#13997semidirect
984. C2×C4#66949semidirect

Maximal subgroups

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

subgroupindex
C22×#669492
C2×#106222592
C2×#106225852
C2×#106222802
C2×C4×Dic11⋊C42
C2×#106222792
#130668842
#130668822
#130668602
#130668582
#130668542
#130668522
Dic11⋊#952
C11×C4⋊#952
#1399711