Finite Group Databasebeta

← #14675744

Subgroups — #14675744

Order 2816.

2006 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66930C211yesmaximal, characteristic
2C2×#10622589C211yesmaximal, characteristic, complemented
3C2×#10622263C211yesmaximal, characteristic, complemented
4C2×#10622555C211yesmaximal, characteristic
5C2×C22⋊C4×Dic11C211yesmaximal, characteristic
6#13066861C211yesmaximal, characteristic
7#13066859C211yesmaximal, characteristic
8#13066859C211yesmaximal, characteristic
9#13066851C211yesmaximal, characteristic, complemented
10#13066850C211yesmaximal, characteristic, complemented
11#13066848C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13Dic11⋊#95C211yesmaximal, characteristic, complemented
14Dic11⋊#95C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic
16C24×Dic11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×#66930—24no—
36C2×#66930—24no—
37C2×#66930—24no—
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#10622589—24no—
55#10622555—24no—
56C22⋊C4×Dic11C418yescomplemented
57#10622263—24no—
58C25×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—22no—
66C23×Dic11—22no—
67C23×Dic11—22no—
68C23×Dic11—22no—
69C23×Dic11C2×C414yes—
70C23×Dic11D414yes—
71C23×Dic11Q814yes—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—41no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—41no—
90C2×C11×C22⋊C4—41no—
91C2×C11×C22⋊C4C2×C414yes—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—41no—
99C2×C22⋊Dic11—41no—
100C2×C22⋊Dic11C2×C414yes—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—41no—
104C2×Dic11⋊C4—22no—
105C2×Dic11⋊C4—22no—
106C2×Dic11⋊C4—22no—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—22no—
111C2×Dic11⋊C4—22no—
112C2×Dic11⋊C4—22no—
113C2×Dic11⋊C4—22no—
114C2×Dic11⋊C4—22no—
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4—22no—
118C2×Dic11⋊C4—41no—
119C2×Dic11⋊C4—41no—
120C2×Dic11⋊C4D414yes—
121C2×Dic11⋊C4D414yes—
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—22no—
130C2×C4×Dic11—22no—
131C2×C4×Dic11—22no—
132C2×C4×Dic11C2×C414yes—
133C2×C4×Dic11C2×C414yes—
134#66930—232no—
135C11×#95—22no—
136C11×#95—22no—
137C11×#95—41no—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—41no—
147C11⋊#95—41no—
148C11⋊#95—41no—
149C11⋊#95C2×C414yes—
150C11⋊#95C2×C414yes—
151#13879—111nomaximal, Sylow
152C24×C11—21no—
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11C22×C412yes—
165C24×C11C2×D412yes—
166C24×C11C2×Q812yes—
167C24×C11C2411yescharacteristic
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
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×C11C22×C412yes—
205C22×C4×C11C22×C412yes—
206C22×C4×C11C2×D412yes—
207C22×C4×C11C2×D412yes—
208C22×C4×C11#4112yes—
209C22×C4×C11#4112yes—
210C22×Dic11—28no—
211C22×Dic11—28no—
212C22×Dic11—28no—
213C22×Dic11—28no—
214C22×Dic11—28no—
215C22×Dic11—28no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
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×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11C4⋊C4116yescomplemented
257C22×Dic11C22×C412yes—
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×Q812yes—
268C22×Dic11C2×Q812yes—
269C22×Dic11#4112yes—
270C22×Dic11#4112yes—
271C22×Dic11#4112yes—
272C22×Dic11#4112yes—
273C11×C4⋊C4—44no—
274C11×C22⋊C4—28no—
275C11×C22⋊C4—28no—
276C11×C22⋊C4—44no—
277C22⋊Dic11—28no—
278C22⋊Dic11—28no—
279C22⋊Dic11—44no—
280C4⋊Dic11—44no—
281Dic11⋊C4—28no—
282Dic11⋊C4—28no—
283Dic11⋊C4—44no—
284Dic11⋊C4—44no—
285Dic11⋊C4—44no—
286Dic11⋊C4—44no—
287C4×Dic11—28no—
288C4×Dic11—28no—
289C4×Dic11—28no—
290C4×Dic11—28no—
291C22×#117—111no—
292C2×#384—111no—
293C2×#382—111no—
294C2×#380—111no—
295C2×C4×C22⋊C4—111no—
296#1439—111no—
297#1439—111no—
298#1439—111no—
299#1439D1111yescharacteristic
300#1436—111no—
301#1436—111no—
302#1436—111no—
303#1436—111no—
304C4⋊#95—111no—
305C4⋊#95—111no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11—41no—
339C23×C11—41no—
340C23×C11C2×C4⋊C414yes—
341C23×C11C23×C411yescharacteristic
342C23×C11C22×D411yescharacteristic
343C23×C11C22×D411yescharacteristic
344C23×C11C22×D411yescharacteristic
345C23×C11C22×Q811yescharacteristic
346C23×C11C2×#4111yescharacteristic
347C23×C11C2×#4111yescharacteristic
348C23×C11C2×#4111yescharacteristic
349C23×C11C2×#4111yescharacteristic
350C23×C11C2×#4111yescharacteristic
351C23×C11C2×#4111yescharacteristic
352C23×C11H(5,𝔽2)11yescharacteristic
353C23×C11H(5,𝔽2)11yescharacteristic
354C23×C112−1+411yescharacteristic
355C23×C112−1+411yescharacteristic
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11#11714yescomplemented
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—232no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—41no—
421C2×Dic11—41no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11—41no—
426C2×Dic11—41no—
427C2×Dic11—41no—
428C2×Dic11—41no—
429C2×Dic11—41no—
430C2×Dic11—41no—
431C2×Dic11—41no—
432C2×Dic11—41no—
433C2×Dic11—41no—
434C2×Dic11—41no—
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×Dic11C2×C4⋊C414yes—
447C2×Dic11C2×C4⋊C414yes—
448C2×Dic11#11714yescomplemented
449C2×Dic11C4×D414yes—
450C2×Dic11C4×D414yes—
451C2×Dic11#12014yes—
452C2×Dic11C22⋊Q814yes—
453C2×Dic11C22⋊Q814yes—
454C2×Dic11#12314yes—
455C24×C4—111no—
456C2×#117—224no—
457C2×#117—224no—
458C2×#117—224no—
459C22×C4⋊C4—111no—
460C22×C4⋊C4—111no—
461C22×C4⋊C4—111no—
462C22×C4⋊C4—111no—
463C22×C4⋊C4—111no—
464C22×C4⋊C4—111no—
465C22×C4⋊C4—111no—
466C22×C4⋊C4C2×D1111yescharacteristic
467C22×C22⋊C4—111no—
468C22×C22⋊C4—111no—
469C22×C22⋊C4—111no—
470C22×C22⋊C4C2×D1111yescharacteristic
471C22×C22⋊C4C2×D1111yescharacteristic
472C22×C22⋊C4C2×D1111yescharacteristic
473C22×C42—111no—
474C22×C42—111no—
475C22×C42—111no—
476C22×C42—111no—
477#384—224no—
478#382—224no—
479#380—224no—
480C4×C22⋊C4—118no—
481C2×#95—111no—
482C2×#95—111no—
483C2×#95—111no—
484C2×#95—111no—
485C2×#95—111no—
486C2×#95—111no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95—111no—
492C2×#95—111no—
493C2×#95—111no—
494C2×#95C2×D1111yescharacteristic
495C2×#95C2×D1111yescharacteristic
496C2×#95C2×D1111yescharacteristic
497C22×C11—24no—
498C22×C11—24no—
499C22×C11—24no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—42no—
509C22×C11—42no—
510C22×C11—42no—
511C22×C11—42no—
512C22×C11C22×C4⋊C411yescharacteristic
513C22×C11C2×#11711yescharacteristic
514C22×C11C2×#11711yescharacteristic
515C22×C11C2×C4×D411yescharacteristic
516C22×C11C2×C4×D411yescharacteristic
517C22×C11#52011yescharacteristic
518C22×C11#52011yescharacteristic
519C22×C11C2×#12011yescharacteristic
520C22×C11C2×C22⋊Q811yescharacteristic
521C22×C11C2×C22⋊Q811yescharacteristic
522C22×C11C2×#12311yescharacteristic
523C22×C11#53211yescharacteristic
524C22×C11#53211yescharacteristic
525C22×C11#53311yescharacteristic
526C22×C11#53311yescharacteristic
527C22×C11#53511yescharacteristic
528C22×C11#53611yescharacteristic
529C22×C11#54411yescharacteristic
530C22×C11#54411yescharacteristic
531C22×C11#54611yescharacteristic
532C22×C11#54611yescharacteristic
533C22×C11#54711yescharacteristic
534C22×C11#54711yescharacteristic
535C22×C11#54811yescharacteristic
536C22×C11#54811yescharacteristic
537C22×C11#55011yescharacteristic
538C22×C11#55011yescharacteristic
539C22×C11#55211yescharacteristic
540C22×C11#55211yescharacteristic
541C22×C11#55311yescharacteristic
542C22×C11#55311yescharacteristic
543C22×C11#55511yescharacteristic
544C22×C11#55511yescharacteristic
545C22×C11#55611yescharacteristic
546C22×C11#55611yescharacteristic
547C4×C11—24no—
548C4×C11—42no—
549C4×C11—42no—
550C4×C11—42no—
551C4×C11—81no—
552C4×C11—81no—
553Dic11—24no—
554Dic11—24no—
555Dic11—42no—
556Dic11—42no—
557Dic11—42no—
558Dic11—81no—
559Dic11—81no—
560Dic11#38518yes—
561C25C22×D1111yescharacteristic
562C23×C4—111no—
563C23×C4—114no—
564C23×C4—114no—
565C23×C4—114no—
566C23×C4—111no—
567C23×C4—111no—
568C23×C4—111no—
569C23×C4—111no—
570C23×C4—111no—
571C23×C4—111no—
572C23×C4—111no—
573C23×C4—222no—
574C23×C4—222no—
575C23×C4—222no—
576C23×C4—222no—
577C23×C4C22×D1111yescharacteristic
578C23×C4C22×D1111yescharacteristic
579C23×C4C22×D1111yescharacteristic
580C23×C4C22×D1111yescharacteristic
581C23×C4C22×D1111yescharacteristic
582C23×C4C22×D1111yescharacteristic
583#117—2232no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—114no—
588C2×C4⋊C4—114no—
589C2×C4⋊C4—222no—
590C2×C4⋊C4—222no—
591C2×C4⋊C4—222no—
592C2×C4⋊C4—222no—
593C2×C4⋊C4—222no—
594C2×C4⋊C4—222no—
595C2×C4⋊C4—222no—
596C2×C4⋊C4—222no—
597C2×C4⋊C4—222no—
598C2×C4⋊C4—222no—
599C2×C4⋊C4—222no—
600C2×C4⋊C4—222no—
601C2×C4⋊C4—222no—
602C2×C4⋊C4—222no—
603C2×C4⋊C4—222no—
604C2×C4⋊C4—222no—
605C2×C4⋊C4—441no—
606C2×C4⋊C4—441no—
607C2×C4⋊C4—441no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—41no—
615C2×C22⋊C4—41no—
616C2×C22⋊C4—114no—
617C2×C22⋊C4—222no—
618C2×C22⋊C4—222no—
619C2×C22⋊C4—222no—
620C2×C22⋊C4—222no—
621C2×C22⋊C4—222no—
622C2×C22⋊C4—222no—
623C2×C22⋊C4—441no—
624C2×C22⋊C4—441no—
625C2×C22⋊C4C4×D1114yes—
626C2×C42—114no—
627C2×C42—114no—
628C2×C42—222no—
629C2×C42—222no—
630C2×C42—222no—
631C2×C42—222no—
632C2×C42—222no—
633C2×C42—222no—
634C2×C42—222no—
635C2×C42—222no—
636C2×C42—222no—
637C2×C42—222no—
638#95—22no—
639#95—22no—
640#95—41no—
641#95—114no—
642#95—114no—
643#95—222no—
644#95—222no—
645#95—222no—
646#95—222no—
647#95—222no—
648#95—222no—
649#95—222no—
650#95—222no—
651#95—441no—
652#95—441no—
653#95—441no—
654C2×C11—44no—
655C2×C11#228511yescharacteristic
656C2×C11C2×#38511yescharacteristic
657C2×C11#231711yescharacteristic
658C2×C11#235211yescharacteristic
659C2×C11#235211yescharacteristic
660C2×C11#235411yescharacteristic
661C2×C11#235411yescharacteristic
662C2×C11#243111yescharacteristic
663C2×C11#243211yescharacteristic
664C2×C11#243911yescharacteristic
665C2×C11#243911yescharacteristic
666C2×C11#244111yescharacteristic
667C2×C11#244111yescharacteristic
668C2×C11#249911yescharacteristic
669C2×C11#250011yescharacteristic
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24C2×C4×D1112yes—
683C24D4×D1112yes—
684C24Q8×D1112yes—
685C24C23×D1111yescharacteristic
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
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—112no—
723C22×C4—112no—
724C22×C4—112no—
725C22×C4—112no—
726C22×C4—112no—
727C22×C4—112no—
728C22×C4—112no—
729C22×C4—1116no—
730C22×C4—112no—
731C22×C4—112no—
732C22×C4—112no—
733C22×C4—112no—
734C22×C4—112no—
735C22×C4—112no—
736C22×C4—112no—
737C22×C4—112no—
738C22×C4—112no—
739C22×C4—228no—
740C22×C4—228no—
741C22×C4—228no—
742C22×C4—228no—
743C22×C4—228no—
744C22×C4—228no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—221no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4—221no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—221no—
756C22×C4—221no—
757C22×C4—221no—
758C22×C4—221no—
759C22×C4—221no—
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×C4C2×C4×D1112yes—
786C22×C4C2×C4×D1112yes—
787C22×C4D4×D1112yes—
788C22×C4D4×D1112yes—
789C22×C4#434112yes—
790C22×C4#434112yes—
791C4⋊C4—44no—
792C4⋊C4—228no—
793C4⋊C4—228no—
794C4⋊C4—444no—
795C4⋊C4—444no—
796C4⋊C4—444no—
797C4⋊C4—444no—
798C4⋊C4—444no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—44no—
802C22⋊C4—228no—
803C22⋊C4—228no—
804C22⋊C4—444no—
805C42—228no—
806C42—228no—
807C42—228no—
808C42—228no—
809C11#1387911yescharacteristic, complemented, Sylow
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23C4⋊C4×D1114yes—
845C23C22×C4×D1111yescharacteristic
846C23C2×D4×D1111yescharacteristic
847C23C2×D4×D1111yescharacteristic
848C23C2×D4×D1111yescharacteristic
849C23C2×#434111yescharacteristic
850C23C2×#434111yescharacteristic
851C23#6703711yescharacteristic
852C23#6703711yescharacteristic
853C23C2×Q8×D1111yescharacteristic
854C23#41×D1111yescharacteristic
855C23#41×D1111yescharacteristic
856C23#41×D1111yescharacteristic
857C23#41×D1111yescharacteristic
858C23#6704311yescharacteristic
859C23#6704311yescharacteristic
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—114no—
902C2×C4—114no—
903C2×C4—114no—
904C2×C4—114no—
905C2×C4—114no—
906C2×C4—114no—
907C2×C4—114no—
908C2×C4—114no—
909C2×C4—114no—
910C2×C4—2232no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—222no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—222no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—441no—
933C2×C4—441no—
934C2×C4—441no—
935C2×C4—441no—
936C2×C4—441no—
937C2×C4—441no—
938C2×C4—441no—
939C2×C4—441no—
940C2×C4—441no—
941C2×C4—441no—
942C2×C4—441no—
943C2×C4—441no—
944C2×C4—441no—
945C2×C4—441no—
946C2×C4—441no—
947C2×C4—441no—
948C2×C4—441no—
949C2×C4—441no—
950C2×C4—441no—
951C2×C4—441no—
952C2×C4—441no—
953C2×C4—441no—
954C2×C4—441no—
955C2×C4—441no—
956C2×C4—441no—
957C2×C4—441no—
958C2×C4#6693014yescomplemented
959C22—24no—
960C22—24no—
961C22—24no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22C2×#6693011yescharacteristic
975C22C2×C4⋊C4×D1111yescharacteristic
976C22D11×#11711yescharacteristic
977C22C4×D4×D1111yescharacteristic
978C22C4×D4×D1111yescharacteristic
979C22#1062307711yescharacteristic
980C22#1062307711yescharacteristic
981C22D11×#12011yescharacteristic
982C22#1062312211yescharacteristic
983C22#1062312311yescharacteristic
984C22#1062312711yescharacteristic
985C22#1062312711yescharacteristic
986C22#1062312911yescharacteristic
987C22#1062313011yescharacteristic
988C22#1062313211yescharacteristic
989C22#1062314111yescharacteristic
990C22#1062314211yescharacteristic
991C22#1062314711yescharacteristic
992C22#1062315311yescharacteristic
993C22#1062315311yescharacteristic
994C22#1062315411yescharacteristic
995C22#1062315411yescharacteristic
996C22D11×C22⋊Q811yescharacteristic
997C22D11×C22⋊Q811yescharacteristic
998C22#1062317911yescharacteristic
999C22#1062318111yescharacteristic
1000C22D11×#12311yescharacteristic
1001C22#1062318611yescharacteristic
1002C22#1062319211yescharacteristic
1003C22#1062320111yescharacteristic
1004C22#1062320211yescharacteristic
1005C22#1062320811yescharacteristic
1006C22#1062323311yescharacteristic
1007C22#1062323911yescharacteristic
1008C22#1062324911yescharacteristic
1009C4—24no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—81no—
1014C4—81no—
1015C4—118no—
1016C4—224no—
1017C4—224no—
1018C4—442no—
1019C4—442no—
1020C4—442no—
1021C4—881no—
1022C4—881no—
1023C2—44no—
1024C2#1307101811yescharacteristic
1025C2D11×#38511yescharacteristic
1026C2#1307123511yescharacteristic
1027C2#1307154311yescharacteristic
1028C2#1307154411yescharacteristic
1029C2#1307156211yescharacteristic
1030C2#1307156411yescharacteristic
1031C2#1307223011yescharacteristic
1032C2#1307223911yescharacteristic
1033C2#1307230011yescharacteristic
1034C2#1307230211yescharacteristic
1035C2#1307232211yescharacteristic
1036C2#1307232411yescharacteristic
1037C2#1307306411yescharacteristic
1038C2#1307307311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1439D11
hypocenterC11#13879
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#10622589C2semidirect
3. C2×#10622263C2semidirect
9. #13066851C2semidirect
10. #13066850C2semidirect
11. #13066848C2semidirect
12. #13066847C2semidirect
13. Dic11⋊#95C2semidirect
14. Dic11⋊#95C2semidirect
56. C22⋊C4×Dic11C4semidirect
256. C22×Dic11C4⋊C4semidirect
397. C2×C4×C11#117semidirect
448. C2×Dic11#117semidirect
809. C11#13879semidirect
958. C2×C4#66930semidirect

Maximal subgroups

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

subgroupindex
C22×#669302
C2×#106225892
C2×#106222632
C2×#106225552
C2×C22⋊C4×Dic112
#130668612
#130668592
#130668512
#130668502
#130668482
#130668472
Dic11⋊#952
C11×#14392
#1387911