Finite Group Databasebeta

← #14677236

Subgroups — #14677236

Order 2816.

2054 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66941C211yesmaximal, characteristic
2C22×C4×Dic22C211yesmaximal, characteristic
3C2×#10622259C211yesmaximal, characteristic
4C2×#10622259C211yesmaximal, characteristic
5C2×#10622259C211yesmaximal, characteristic
6#13066870C211yesmaximal, characteristic
7#13066869C211yesmaximal, characteristic
8#13066868C211yesmaximal, characteristic
9#13066867C211yesmaximal, characteristic
10#13066850C211yesmaximal, characteristic
11#13066849C211yesmaximal, characteristic
12#13066847C211yesmaximal, characteristic
13Dic11⋊#95C211yesmaximal, characteristic
14#95×Dic11C211yesmaximal, characteristic
15C11×#1436C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×Dic11⋊C4C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×#66941—24no—
32C2×#66941—24no—
33C2×#66941C418yescomplemented
34C2×C4×Dic22—24no—
35C2×C4×Dic22—24no—
36C2×C4×Dic22—24no—
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
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622259—24no—
58#10622259—24no—
59#10622259—24no—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C22×Dic22—22no—
76C22×Dic22—22no—
77C22×Dic22—22no—
78C22×Dic22—22no—
79C22×Dic22—22no—
80C22×Dic22—22no—
81C22×Dic22—22no—
82C22×Dic22—22no—
83C22×Dic22—22no—
84C22×Dic22—22no—
85C22×Dic22C2×C414yes—
86C22×Dic22C2×C414yes—
87C22×Dic22D414yes—
88C22×Dic22D414yes—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4C2×C414yes—
92C2×C42×C11—22no—
93C2×C42×C11—22no—
94C2×C42×C11—22no—
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11—22no—
99C2×C4⋊Dic11—22no—
100C2×C4⋊Dic11C2×C414yes—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—22no—
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⋊C4C2×C414yes—
114C2×Dic11⋊C4C2×C414yes—
115C2×Dic11⋊C4D414yes—
116C2×C4×Dic11—22no—
117C2×C4×Dic11—22no—
118C2×C4×Dic11—22no—
119C2×C4×Dic11—22no—
120C2×C4×Dic11—22no—
121C2×C4×Dic11—22no—
122C2×C4×Dic11—22no—
123C2×C4×Dic11—22no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11—22no—
126C2×C4×Dic11C2×C414yes—
127C2×C4×Dic11D414yes—
128#66941—232no—
129C4×Dic22—232no—
130C11×#95—22no—
131C11×#95—22no—
132C11×#95—22no—
133C11×#95—22no—
134C11×#95Q814yescomplemented
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—22no—
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—22no—
147C11⋊#95—22no—
148C11⋊#95—22no—
149C11⋊#95Q814yescomplemented
150#14024—111nomaximal, Sylow
151C24×C11C2411yescharacteristic
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
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×C11C22×C412yes—
190C22×C4×C11C22×C412yes—
191C22×C4×C11C22×C412yes—
192C22×C4×C11C2×D412yes—
193C22×C4×C11C2×D412yes—
194C22×C4×C11C2×D412yes—
195C22×C4×C11C2×D412yes—
196C22×C4×C11C2×Q812yes—
197C22×C4×C11C2×Q812yes—
198C22×C4×C11C2×Q812yes—
199C22×C4×C11C2×Q812yes—
200C22×C4×C11#4112yes—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
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×Dic11C22×C412yes—
241C22×Dic11C22×C412yes—
242C22×Dic11C22×C412yes—
243C22×Dic11C22×C412yes—
244C22×Dic11C2×D412yes—
245C22×Dic11C2×D412yes—
246C22×Dic11C2×D412yes—
247C22×Dic11C2×D412yes—
248C22×Dic11C2×D412yes—
249C22×Dic11C2×D412yes—
250C22×Dic11C2×D412yes—
251C22×Dic11C2×D412yes—
252C22×Dic11C2×Q812yes—
253C22×Dic11C2×Q812yes—
254C22×Dic11#4112yes—
255C22×Dic11#4112yes—
256C22×Dic11#4112yes—
257C2×Dic22—28no—
258C2×Dic22—28no—
259C2×Dic22—28no—
260C2×Dic22—28no—
261C2×Dic22—28no—
262C2×Dic22—28no—
263C2×Dic22—28no—
264C2×Dic22—28no—
265C2×Dic22—28no—
266C2×Dic22—44no—
267C2×Dic22—44no—
268C2×Dic22—44no—
269C2×Dic22—44no—
270C2×Dic22C22⋊C4116yes—
271C11×C4⋊C4—28no—
272C42×C11—28no—
273C4⋊Dic11—28no—
274C4⋊Dic11—28no—
275Dic11⋊C4—28no—
276Dic11⋊C4—28no—
277Dic11⋊C4—28no—
278Dic11⋊C4—28no—
279Dic11⋊C4—44no—
280C4×Dic11—28no—
281C4×Dic11—28no—
282C4×Dic11—28no—
283C4×Dic11—44no—
284C22×C4⋊Q8—111no—
285C22×C4×Q8—111no—
286C2×#391—111no—
287C2×#391—111no—
288C2×#391—111no—
289#1441—111no—
290#1441—111no—
291#1441—111no—
292#1441—111no—
293#1436—111no—
294#1436—111no—
295#1436—111no—
296#1436D1111yescharacteristic
297C4⋊#95—111no—
298C4×#95—111no—
299C23×C11C23×C411yescharacteristic
300C23×C11C22×D411yescharacteristic
301C23×C11C22×D411yescharacteristic
302C23×C11C22×D411yescharacteristic
303C23×C11C22×D411yescharacteristic
304C23×C11C22×Q811yescharacteristic
305C23×C11C22×Q811yescharacteristic
306C23×C11C2×#4111yescharacteristic
307C23×C11C2×#4111yescharacteristic
308C23×C11C2×#4111yescharacteristic
309C23×C11C2×#4111yescharacteristic
310C23×C112−1+411yescharacteristic
311C23×C112−1+411yescharacteristic
312C23×C112−1+411yescharacteristic
313C23×C112−1+411yescharacteristic
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11C2×C22⋊C414yes—
361C2×C4×C11C4×Q814yescomplemented
362C2×C4×C11C4⋊Q814yescomplemented
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—41no—
388C2×Dic11—41no—
389C2×Dic11—41no—
390C2×Dic11—41no—
391C2×Dic11—41no—
392C2×Dic11—41no—
393C2×Dic11—41no—
394C2×Dic11—41no—
395C2×Dic11—41no—
396C2×Dic11—41no—
397C2×Dic11—41no—
398C2×Dic11—41no—
399C2×Dic11—41no—
400C2×Dic11—41no—
401C2×Dic11—41no—
402C2×Dic11—41no—
403C2×Dic11—41no—
404C2×Dic11—41no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—41no—
409C2×Dic11—41no—
410C2×Dic11C2×C22⋊C414yes—
411C2×Dic11C2×C22⋊C414yes—
412C2×Dic11C4×D414yes—
413C2×Dic11C4×D414yes—
414C2×Dic11C4×Q814yescomplemented
415C2×Dic11#12014yes—
416C2×Dic11#12114yes—
417C2×Dic11#12114yes—
418C2×Dic11#12314yes—
419Dic22—232no—
420Dic22—416no—
421C23×Q8—111no—
422C23×Q8—111no—
423C2×C4⋊Q8—118no—
424C2×C4⋊Q8—224no—
425C2×C4⋊Q8—224no—
426C2×C4×Q8—224no—
427C2×C4×Q8—224no—
428C2×C4×Q8—224no—
429C22×C4⋊C4—111no—
430C22×C4⋊C4—111no—
431C22×C4⋊C4—111no—
432C22×C4⋊C4—111no—
433C22×C4⋊C4—111no—
434C22×C4⋊C4—111no—
435C22×C4⋊C4—111no—
436C22×C4⋊C4C2×D1111yescharacteristic
437C22×C42—111no—
438C22×C42—111no—
439C22×C42—111no—
440C22×C42—111no—
441C22×C42C2×D1111yescharacteristic
442#391—224no—
443#391—224no—
444#391—224no—
445C2×#95—111no—
446C2×#95—111no—
447C2×#95—111no—
448C2×#95—111no—
449C2×#95—111no—
450C2×#95—111no—
451C2×#95—111no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95—111no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95C2×D1111yescharacteristic
461C2×#95C2×D1111yescharacteristic
462C2×#95C2×D1111yescharacteristic
463C2×#95C2×D1111yescharacteristic
464C2×#95C2×D1111yescharacteristic
465C22×C11C22×C22⋊C411yescharacteristic
466C22×C11C2×C4×D411yescharacteristic
467C22×C11C2×C4×D411yescharacteristic
468C22×C11C2×C4×Q811yescharacteristic
469C22×C11C2×C4×Q811yescharacteristic
470C22×C11#51911yescharacteristic
471C22×C11#51911yescharacteristic
472C22×C11C2×#12011yescharacteristic
473C22×C11C2×#12111yescharacteristic
474C22×C11C2×#12111yescharacteristic
475C22×C11C2×#12311yescharacteristic
476C22×C11C2×C4⋊Q811yescharacteristic
477C22×C11#53211yescharacteristic
478C22×C11#53311yescharacteristic
479C22×C11#53311yescharacteristic
480C22×C11#53611yescharacteristic
481C22×C11#53611yescharacteristic
482C22×C11#54111yescharacteristic
483C22×C11#54111yescharacteristic
484C22×C11#54711yescharacteristic
485C22×C11#54711yescharacteristic
486C22×C11#54811yescharacteristic
487C22×C11#54811yescharacteristic
488C22×C11#54811yescharacteristic
489C22×C11#54811yescharacteristic
490C22×C11D4×Q811yescharacteristic
491C22×C11D4×Q811yescharacteristic
492C22×C11D4×Q811yescharacteristic
493C22×C11D4×Q811yescharacteristic
494C22×C11D4×Q811yescharacteristic
495C22×C11D4×Q811yescharacteristic
496C22×C11#55611yescharacteristic
497C22×C11#55611yescharacteristic
498C22×C11#55711yescharacteristic
499C22×C11#55711yescharacteristic
500C4×C11—24no—
501C4×C11—24no—
502C4×C11—24no—
503C4×C11—42no—
504C4×C11—42no—
505C4×C11—42no—
506C4×C11—81no—
507Dic11—24no—
508Dic11—24no—
509Dic11—42no—
510Dic11—42no—
511Dic11—42no—
512Dic11—42no—
513Dic11—81no—
514Dic11#38618yes—
515C22×Q8—114no—
516C22×Q8—114no—
517C22×Q8—114no—
518C22×Q8—114no—
519C22×Q8—222no—
520C22×Q8—222no—
521C22×Q8—222no—
522C22×Q8—222no—
523C22×Q8—222no—
524C22×Q8—222no—
525C22×Q8—222no—
526C22×Q8—222no—
527C22×Q8—222no—
528C22×Q8—222no—
529C23×C4—111no—
530C23×C4—111no—
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4C22×D1111yescharacteristic
538C23×C4C22×D1111yescharacteristic
539C23×C4C22×D1111yescharacteristic
540C23×C4C22×D1111yescharacteristic
541C23×C4C22×D1111yescharacteristic
542C23×C4C22×D1111yescharacteristic
543C23×C4C22×D1111yescharacteristic
544C4⋊Q8—2232no—
545C4×Q8—2232no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—114no—
549C2×C4⋊C4—114no—
550C2×C4⋊C4—114no—
551C2×C4⋊C4—114no—
552C2×C4⋊C4—222no—
553C2×C4⋊C4—222no—
554C2×C4⋊C4—222no—
555C2×C4⋊C4—222no—
556C2×C4⋊C4—222no—
557C2×C4⋊C4—222no—
558C2×C4⋊C4—222no—
559C2×C4⋊C4—222no—
560C2×C4⋊C4—222no—
561C2×C4⋊C4—222no—
562C2×C4⋊C4—222no—
563C2×C4⋊C4—222no—
564C2×C4⋊C4—222no—
565C2×C4⋊C4—222no—
566C2×C4⋊C4—222no—
567C2×C4⋊C4—222no—
568C2×C4⋊C4—222no—
569C2×C4⋊C4C4×D1114yes—
570C2×C42—22no—
571C2×C42—22no—
572C2×C42—22no—
573C2×C42—114no—
574C2×C42—114no—
575C2×C42—222no—
576C2×C42—222no—
577C2×C42—222no—
578C2×C42—222no—
579C2×C42—222no—
580C2×C42—222no—
581C2×C42—222no—
582C2×C42—222no—
583C2×C42—222no—
584C2×C42—222no—
585#95—22no—
586#95—22no—
587#95—22no—
588#95—22no—
589#95—114no—
590#95—222no—
591#95—222no—
592#95—222no—
593#95—222no—
594#95—222no—
595#95—222no—
596#95—222no—
597#95—222no—
598#95—222no—
599#95—222no—
600#95—222no—
601#95—222no—
602#95—222no—
603#95—222no—
604#95Dic2214yescomplemented
605C2×C11C2×#38611yescharacteristic
606C2×C11C4×C4⋊Q811yescharacteristic
607C2×C11#232711yescharacteristic
608C2×C11Q8×C22⋊C411yescharacteristic
609C2×C11Q8×C22⋊C411yescharacteristic
610C2×C11#236511yescharacteristic
611C2×C11#236511yescharacteristic
612C2×C11#242911yescharacteristic
613C2×C11#242911yescharacteristic
614C2×C11#243211yescharacteristic
615C2×C11#243411yescharacteristic
616C2×C11#244611yescharacteristic
617C2×C11#244611yescharacteristic
618C2×C11#254511yescharacteristic
619C2×C11#254611yescharacteristic
620C24C23×D1111yescharacteristic
621C2×Q8—1116no—
622C2×Q8—228no—
623C2×Q8—228no—
624C2×Q8—228no—
625C2×Q8—228no—
626C2×Q8—228no—
627C2×Q8—228no—
628C2×Q8—228no—
629C2×Q8—228no—
630C2×Q8—228no—
631C2×Q8—444no—
632C2×Q8—444no—
633C2×Q8—444no—
634C2×Q8—444no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—112no—
673C22×C4—112no—
674C22×C4—112no—
675C22×C4—112no—
676C22×C4—112no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—112no—
683C22×C4—112no—
684C22×C4—112no—
685C22×C4—112no—
686C22×C4—112no—
687C22×C4—112no—
688C22×C4—112no—
689C22×C4—221no—
690C22×C4—221no—
691C22×C4—221no—
692C22×C4—221no—
693C22×C4—221no—
694C22×C4—221no—
695C22×C4—221no—
696C22×C4—221no—
697C22×C4—221no—
698C22×C4—221no—
699C22×C4—221no—
700C22×C4—221no—
701C22×C4—221no—
702C22×C4—221no—
703C22×C4—221no—
704C22×C4—221no—
705C22×C4—221no—
706C22×C4—221no—
707C22×C4—221no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—221no—
712C22×C4—221no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4C2×Dic2212yes—
729C22×C4C2×Dic2212yes—
730C22×C4C2×Dic2212yes—
731C22×C4C2×C4×D1112yes—
732C22×C4C2×C4×D1112yes—
733C22×C4C2×C4×D1112yes—
734C22×C4#433912yes—
735C22×C4D4×D1112yes—
736C22×C4D4×D1112yes—
737C22×C4D4×D1112yes—
738C22×C4D4×D1112yes—
739C22×C4Q8×D1112yes—
740C4⋊C4—28no—
741C4⋊C4—228no—
742C4⋊C4—228no—
743C4⋊C4—228no—
744C4⋊C4—228no—
745C4⋊C4—228no—
746C4⋊C4—228no—
747C4⋊C4—444no—
748C42—28no—
749C42—228no—
750C42—228no—
751C42—228no—
752C42—444no—
753C11#1402411yescharacteristic, complemented, Sylow
754C23C22×Dic2211yescharacteristic
755C23C22×C4×D1111yescharacteristic
756C23C2×#433911yescharacteristic
757C23C2×D4×D1111yescharacteristic
758C23C2×D4×D1111yescharacteristic
759C23C2×D4×D1111yescharacteristic
760C23C2×D4×D1111yescharacteristic
761C23C2×Q8×D1111yescharacteristic
762C23#6704011yescharacteristic
763C23#41×D1111yescharacteristic
764C23#41×D1111yescharacteristic
765C23#41×D1111yescharacteristic
766C23#6704311yescharacteristic
767C23#6704311yescharacteristic
768C23#6704311yescharacteristic
769Q8—2232no—
770Q8—4416no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—114no—
818C2×C4—114no—
819C2×C4—114no—
820C2×C4—114no—
821C2×C4—114no—
822C2×C4—114no—
823C2×C4—114no—
824C2×C4—114no—
825C2×C4—114no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—222no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—222no—
835C2×C4—222no—
836C2×C4—222no—
837C2×C4—222no—
838C2×C4—222no—
839C2×C4—222no—
840C2×C4—222no—
841C2×C4—222no—
842C2×C4—222no—
843C2×C4—222no—
844C2×C4—222no—
845C2×C4—222no—
846C2×C4—222no—
847C2×C4—222no—
848C2×C4—222no—
849C2×C4—222no—
850C2×C4—441no—
851C2×C4—441no—
852C2×C4—441no—
853C2×C4—441no—
854C2×C4—441no—
855C2×C4—441no—
856C2×C4—441no—
857C2×C4—441no—
858C2×C4—441no—
859C2×C4—441no—
860C2×C4—441no—
861C2×C4—441no—
862C2×C4—441no—
863C2×C4—441no—
864C2×C4—441no—
865C2×C4—441no—
866C2×C4—441no—
867C2×C4—441no—
868C2×C4—441no—
869C2×C4—441no—
870C2×C4—441no—
871C2×C4—441no—
872C2×C4—441no—
873C2×C4C4×Dic2214yescomplemented
874C2×C4C22⋊C4×D1114yes—
875C2×C4#6694114yescomplemented
876C22C2×C4×Dic2211yescharacteristic
877C22C2×C22⋊C4×D1111yescharacteristic
878C22C2×#6694111yescharacteristic
879C22#1062303811yescharacteristic
880C22#1062304711yescharacteristic
881C22#1062304811yescharacteristic
882C22#1062306411yescharacteristic
883C22D4×Dic2211yescharacteristic
884C22D4×Dic2211yescharacteristic
885C22D4×Dic2211yescharacteristic
886C22C4×D4×D1111yescharacteristic
887C22C4×D4×D1111yescharacteristic
888C22#1062307911yescharacteristic
889C22#1062308311yescharacteristic
890C22#1062308311yescharacteristic
891C22#1062310011yescharacteristic
892C22C4×Q8×D1111yescharacteristic
893C22#1062310311yescharacteristic
894C22#1062310911yescharacteristic
895C22D11×#12011yescharacteristic
896C22D11×#12111yescharacteristic
897C22D11×#12111yescharacteristic
898C22#1062315911yescharacteristic
899C22#1062316311yescharacteristic
900C22#1062316311yescharacteristic
901C22#1062316411yescharacteristic
902C22#1062317911yescharacteristic
903C22D11×#12311yescharacteristic
904C22#1062318611yescharacteristic
905C22#1062320811yescharacteristic
906C22#1062321611yescharacteristic
907C22#1062322711yescharacteristic
908C22#1062323211yescharacteristic
909C22#1062323311yescharacteristic
910C22#1062325811yescharacteristic
911C4—24no—
912C4—24no—
913C4—24no—
914C4—42no—
915C4—42no—
916C4—42no—
917C4—81no—
918C4—118no—
919C4—224no—
920C4—224no—
921C4—442no—
922C4—442no—
923C4—442no—
924C4—442no—
925C4—881no—
926C2D11×#38611yescharacteristic
927C2C4×#6694111yescharacteristic
928C2#1307133111yescharacteristic
929C2#1307145011yescharacteristic
930C2C22⋊C4×Dic2211yescharacteristic
931C2#1307167111yescharacteristic
932C2#1307167511yescharacteristic
933C2#1307221211yescharacteristic
934C2#1307221411yescharacteristic
935C2#1307224211yescharacteristic
936C2#1307225811yescharacteristic
937C2#1307238911yescharacteristic
938C2#1307239111yescharacteristic
939C2#1307359411yescharacteristic
940C2#1307360311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1436D11
hypocenterC11#14024
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
33. C2×#66941C4semidirect
134. C11×#95Q8semidirect
149. C11⋊#95Q8semidirect
361. C2×C4×C11C4×Q8semidirect
362. C2×C4×C11C4⋊Q8semidirect
414. C2×Dic11C4×Q8semidirect
604. #95Dic22semidirect
753. C11#14024semidirect
873. C2×C4C4×Dic22semidirect
875. C2×C4#66941semidirect

Maximal subgroups

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

subgroupindex
C22×#669412
C22×C4×Dic222
C2×#106222592
#130668702
#130668692
#130668682
#130668672
#130668502
#130668492
#130668472
Dic11⋊#952
#95×Dic112
C11×#14362
#1402411