Finite Group Databasebeta

← #14676909

Subgroups — #14676909

Order 2816.

2106 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622843C211yesmaximal, characteristic, complemented
2C2×#10622843C211yesmaximal, characteristic, complemented
3C2×#10622598C211yesmaximal, characteristic, complemented
4C2×#10622825C211yesmaximal, characteristic
5C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic11C211yesmaximal, characteristic
7#13066884C212yesmaximal, complemented
8#13066861C212yesmaximal
9#13066853C212yesmaximal
10#13066845C212yesmaximal, complemented
11C22×C11×C22⋊Q8C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C2×C11×C22⋊Q8—24no—
15C2×C11×C22⋊Q8—24no—
16C2×C11×C22⋊Q8C418yescomplemented
17C22×C11×C4⋊C4C2212yes—
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2212yes—
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2212yes—
28C22×C4×Dic11C2211yescharacteristic
29#10622843—24no—
30#10622843—24no—
31#10622825—24no—
32C4×C22⋊Dic11—24no—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622598—24no—
43C4⋊C4×Dic11—24no—
44C25×C11C2311yescharacteristic
45C22×Q8×C11—22no—
46C22×Q8×C11—22no—
47C22×Q8×C11—22no—
48C22×Q8×C11—22no—
49C22×Q8×C11—22no—
50C22×Q8×C11—22no—
51C22×Q8×C11C2×C414yes—
52C23×C4×C11—22no—
53C23×C4×C11—22no—
54C23×C4×C11—22no—
55C23×C4×C11—22no—
56C23×C4×C11—22no—
57C23×C4×C11—22no—
58C23×C4×C11C2×C414yes—
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C23×Dic11C2312yes—
64C23×Dic11C2312yes—
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C11×C22⋊Q8—232no—
70C2×C11×C4⋊C4—24no—
71C2×C11×C4⋊C4—24no—
72C2×C11×C4⋊C4C2×C418yes—
73C2×C11×C4⋊C4C2×C414yes—
74C2×C11×C4⋊C4D414yes—
75C2×C11×C4⋊C4D414yes—
76C2×C11×C22⋊C4—24no—
77C2×C11×C22⋊C4—24no—
78C2×C11×C22⋊C4C2×C418yes—
79C2×C22⋊Dic11—22no—
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—24no—
85C2×C22⋊Dic11—24no—
86C2×C22⋊Dic11—42no—
87C2×C22⋊Dic11Q814yescomplemented
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—24no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—24no—
95C2×C4⋊Dic11—42no—
96C2×C4⋊Dic11D414yes—
97C2×C4×Dic11—22no—
98C2×C4×Dic11—22no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11—22no—
101C2×C4×Dic11—24no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11—24no—
104C2×C4×Dic11—42no—
105C2×C4×Dic11D414yes—
106C11⋊#95—24no—
107C11⋊#95—24no—
108C11⋊#95—22no—
109C11⋊#95—22no—
110C11⋊#95—24no—
111C11⋊#95—24no—
112C11⋊#95—24no—
113C11⋊#95—24no—
114C11⋊#95—24no—
115#13997—111nomaximal, Sylow
116C24×C11—21no—
117C24×C11—21no—
118C24×C11—21no—
119C24×C11—21no—
120C24×C11—21no—
121C24×C11—21no—
122C24×C11—21no—
123C24×C11—21no—
124C24×C11—21no—
125C24×C11—21no—
126C24×C11—21no—
127C24×C11—21no—
128C24×C11C22×C412yes—
129C24×C11C2×Q812yes—
130C24×C11#4112yes—
131C24×C11C2411yescharacteristic
132C2×Q8×C11—28no—
133C2×Q8×C11—28no—
134C2×Q8×C11—28no—
135C2×Q8×C11—44no—
136C2×Q8×C11—44no—
137C2×Q8×C11—44no—
138C2×Q8×C11—44no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—28no—
156C22×C4×C11—28no—
157C22×C4×C11—28no—
158C22×C4×C11—44no—
159C22×C4×C11—44no—
160C22×C4×C11—44no—
161C22×C4×C11—44no—
162C22×C4×C11C22×C414yes—
163C22×C4×C11C22×C412yes—
164C22×C4×C11C22×C414yes—
165C22×C4×C11C22×C412yes—
166C22×C4×C11C2×D414yes—
167C22×C4×C11C2×D414yes—
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2×D412yes—
170C22×C4×C11C2×D412yes—
171C22×C4×C11C2×D412yes—
172C22×C4×C11#4112yes—
173C22×C4×C11#4112yes—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—22no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—22no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—21no—
198C22×Dic11—22no—
199C22×Dic11—21no—
200C22×Dic11—22no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—22no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—22no—
209C22×Dic11C2×D412yes—
210C22×Dic11C2×D414yes—
211C22×Dic11C2×D412yes—
212C22×Dic11C2×Q812yes—
213C22×Dic11C2×Q812yes—
214C22×Dic11#4112yes—
215C22×Dic11#4112yes—
216C11×C4⋊C4—216no—
217C11×C4⋊C4C22⋊C4116yescomplemented
218C11×C22⋊C4—216no—
219C22⋊Dic11—28no—
220C22⋊Dic11—28no—
221C22⋊Dic11—48no—
222C4⋊Dic11—28no—
223C4⋊Dic11—48no—
224C4⋊Dic11—44no—
225C4×Dic11—28no—
226C4×Dic11—48no—
227C4×Dic11—44no—
228C22×C22⋊Q8D1111yescharacteristic
229C2×#391—111no—
230C2×#391—111no—
231C2×#389—111no—
232C2×#380—111no—
233C2×C4×C4⋊C4—111no—
234C2×C4×C22⋊C4—111no—
235#1445—112no—
236#1439—112no—
237#1437—112no—
238C4⋊#95—112no—
239C23×C11—22no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—22no—
249C23×C11—22no—
250C23×C11—22no—
251C23×C11—22no—
252C23×C11—22no—
253C23×C11—22no—
254C23×C11—22no—
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11C4×Q814yes—
274C23×C11C23×C411yescharacteristic
275C23×C11C22×D411yescharacteristic
276C23×C11C22×D411yescharacteristic
277C23×C11C22×D411yescharacteristic
278C23×C11C22×D411yescharacteristic
279C23×C11C22×Q811yescharacteristic
280C23×C11C2×#4111yescharacteristic
281C23×C11C2×#4111yescharacteristic
282C23×C11C2×#4111yescharacteristic
283C23×C11C2×#4111yescharacteristic
284C23×C11C2×#4111yescharacteristic
285C23×C11H(5,𝔽2)11yescharacteristic
286C23×C112−1+411yescharacteristic
287C23×C112−1+411yescharacteristic
288C23×C112−1+411yescharacteristic
289Q8×C11—416no—
290C2×C4×C11—24no—
291C2×C4×C11—24no—
292C2×C4×C11—24no—
293C2×C4×C11—24no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
296C2×C4×C11—24no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—24no—
301C2×C4×C11—24no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—42no—
305C2×C4×C11—42no—
306C2×C4×C11—41no—
307C2×C4×C11—42no—
308C2×C4×C11—41no—
309C2×C4×C11—42no—
310C2×C4×C11—416no—
311C2×C4×C11C2×C22⋊C418yes—
312C2×C4×C11C2×C22⋊C414yes—
313C2×C4×C11C4×D414yes—
314C2×C4×C11C4×D414yes—
315C2×C4×C11#12114yes—
316C2×C4×C11#12114yes—
317C2×C4×C11#12414yes—
318C2×C4×C11#12714yes—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—24no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—24no—
333C2×Dic11—24no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—42no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—42no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11—42no—
357C2×Dic11—42no—
358C2×Dic11—42no—
359C2×Dic11—42no—
360C2×Dic11C22⋊Q814yescomplemented
361C23×Q8C2×D1111yescharacteristic
362C24×C4C2×D1111yescharacteristic
363C2×C22⋊Q8—24no—
364C2×C22⋊Q8—24no—
365C2×C22⋊Q8Dic1118yescomplemented
366C22×C4⋊C4—111no—
367C22×C4⋊C4—111no—
368C22×C4⋊C4—112no—
369C22×C4⋊C4C2×D1112yes—
370C22×C4⋊C4C2×D1111yescharacteristic
371C22×C22⋊C4—111no—
372C22×C22⋊C4—111no—
373C22×C22⋊C4—112no—
374C22×C22⋊C4C2×D1112yes—
375C22×C42—111no—
376C22×C42—111no—
377C22×C42—112no—
378#391—224no—
379#391—224no—
380#389—224no—
381#380—224no—
382C4×C4⋊C4—224no—
383C4×C22⋊C4—224no—
384C2×#95—111no—
385C2×#95—112no—
386C2×#95—112no—
387C2×#95—112no—
388C2×#95—112no—
389C2×#95—112no—
390C2×#95—112no—
391C2×#95—112no—
392C2×#95—111no—
393C22×C11—24no—
394C22×C11—24no—
395C22×C11—24no—
396C22×C11—42no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—42no—
401C22×C11—42no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—42no—
405C22×C11—42no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11C22×C22⋊C411yescharacteristic
409C22×C11C2×C4×D411yescharacteristic
410C22×C11C2×C4×D411yescharacteristic
411C22×C11C2×C4×Q811yescharacteristic
412C22×C11C4×#4111yescharacteristic
413C22×C11#51911yescharacteristic
414C22×C11#52011yescharacteristic
415C22×C11C2×#12111yescharacteristic
416C22×C11C2×#12111yescharacteristic
417C22×C11C2×C22⋊Q811yescharacteristic
418C22×C11#52511yescharacteristic
419C22×C11C2×#12411yescharacteristic
420C22×C11#52911yescharacteristic
421C22×C11C2×#12711yescharacteristic
422C22×C11#53311yescharacteristic
423C22×C11#53611yescharacteristic
424C22×C11#53711yescharacteristic
425C22×C11#54111yescharacteristic
426C22×C11#54211yescharacteristic
427C22×C11#54611yescharacteristic
428C22×C11#54611yescharacteristic
429C22×C11#54611yescharacteristic
430C22×C11#54711yescharacteristic
431C22×C11#54711yescharacteristic
432C22×C11#54711yescharacteristic
433C22×C11#54811yescharacteristic
434C22×C11#54811yescharacteristic
435C22×C11#54811yescharacteristic
436C22×C11D4×Q811yescharacteristic
437C22×C11D4×Q811yescharacteristic
438C22×C11D4×Q811yescharacteristic
439C22×C11#55211yescharacteristic
440C22×C11#55211yescharacteristic
441C22×C11#55411yescharacteristic
442C22×C11#55611yescharacteristic
443C4×C11—28no—
444C4×C11—42no—
445C4×C11—44no—
446C4×C11#39018yes—
447Dic11—24no—
448Dic11—42no—
449Dic11—44no—
450Dic11—42no—
451Dic11—42no—
452Dic11—82no—
453C25C22×D1111yescharacteristic
454C22×Q8—22no—
455C22×Q8—22no—
456C22×Q8—22no—
457C22×Q8—22no—
458C22×Q8—22no—
459C22×Q8—22no—
460C22×Q8C2×Dic1114yes—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—111no—
468C23×C4—111no—
469C23×C4—112no—
470C23×C4—111no—
471C23×C4—111no—
472C23×C4—112no—
473C23×C4C2×Dic1114yes—
474C23×C4C22×D1112yes—
475C23×C4C22×D1111yescharacteristic
476C23×C4C22×D1112yes—
477C23×C4C22×D1111yescharacteristic
478C22⋊Q8—232no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—114no—
482C2×C4⋊C4—222no—
483C2×C4⋊C4—222no—
484C2×C4⋊C4—224no—
485C2×C4⋊C4—222no—
486C2×C4⋊C4—222no—
487C2×C4⋊C4—224no—
488C2×C4⋊C4—222no—
489C2×C4⋊C4—442no—
490C2×C4⋊C4C2×Dic1118yes—
491C2×C4⋊C4C2×Dic1114yes—
492C2×C4⋊C4C22⋊D1114yes—
493C2×C4⋊C4C22⋊D1114yes—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—114no—
497C2×C22⋊C4—222no—
498C2×C22⋊C4—222no—
499C2×C22⋊C4—222no—
500C2×C22⋊C4—222no—
501C2×C22⋊C4—222no—
502C2×C22⋊C4—224no—
503C2×C22⋊C4—224no—
504C2×C22⋊C4—442no—
505C2×C22⋊C4C2×Dic1118yes—
506C2×C42—114no—
507C2×C42—222no—
508C2×C42—222no—
509C2×C42—224no—
510C2×C42—222no—
511C2×C42—222no—
512C2×C42—224no—
513C2×C42—222no—
514C2×C42—442no—
515#95—222no—
516#95—222no—
517#95—224no—
518#95—224no—
519#95—224no—
520#95—224no—
521#95—224no—
522#95—224no—
523#95—224no—
524C2×C11—44no—
525C2×C11C2×#39011yescharacteristic
526C2×C11C4×C22⋊Q811yescharacteristic
527C2×C11#232311yescharacteristic
528C2×C11#233911yescharacteristic
529C2×C11Q8×C22⋊C411yescharacteristic
530C2×C11#236011yescharacteristic
531C2×C11#236211yescharacteristic
532C2×C11#241511yescharacteristic
533C2×C11#241711yescharacteristic
534C2×C11#242711yescharacteristic
535C2×C11#242911yescharacteristic
536C2×C11#248911yescharacteristic
537C2×C11#249211yescharacteristic
538C2×C11#254011yescharacteristic
539C2×C11#254211yescharacteristic
540C24—21no—
541C24—21no—
542C24—21no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—21no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—21no—
552C24Q8×D1112yes—
553C24#434312yes—
554C24C22×Dic1112yes—
555C24C23×D1111yescharacteristic
556C2×Q8—28no—
557C2×Q8—28no—
558C2×Q8—28no—
559C2×Q8—44no—
560C2×Q8—44no—
561C2×Q8—44no—
562C2×Q8—44no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—112no—
587C22×C4—112no—
588C22×C4—112no—
589C22×C4—112no—
590C22×C4—114no—
591C22×C4—112no—
592C22×C4—112no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—222no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—222no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—222no—
609C22×C4—221no—
610C22×C4—222no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—222no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—221no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—222no—
620C22×C4—221no—
621C22×C4—222no—
622C22×C4—222no—
623C22×C4—222no—
624C22×C4—222no—
625C22×C4—222no—
626C22×C4—222no—
627C22×C4—222no—
628C22×C4D4×D1112yes—
629C22×C4D4×D1112yes—
630C22×C4#434112yes—
631C22×C4#434112yes—
632C22×C4C22×Dic1114yes—
633C22×C4C22×Dic1112yes—
634C22×C4C22×Dic1114yes—
635C22×C4C22×Dic1112yes—
636C22×C4C2×C22⋊D1114yes—
637C22×C4C2×C22⋊D1114yes—
638C22×C4C2×C22⋊D1112yes—
639C22×C4C2×C22⋊D1112yes—
640C4⋊C4—216no—
641C4⋊C4—228no—
642C4⋊C4—448no—
643C4⋊C4—444no—
644C4⋊C4C22⋊Dic11116yescomplemented
645C22⋊C4—216no—
646C22⋊C4—228no—
647C22⋊C4—228no—
648C22⋊C4—448no—
649C42—228no—
650C42—448no—
651C42—444no—
652C11#1399711yescharacteristic, complemented, Sylow
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23Q8×Dic1114yes—
688C23C2×D4×D1111yescharacteristic
689C23C2×D4×D1111yescharacteristic
690C23C2×#434111yescharacteristic
691C23C2×#434111yescharacteristic
692C23C2×Q8×D1111yescharacteristic
693C23C2×#434311yescharacteristic
694C23#6704011yescharacteristic
695C23#6704011yescharacteristic
696C23#41×D1111yescharacteristic
697C23#41×D1111yescharacteristic
698C23#6704211yescharacteristic
699C23#6704311yescharacteristic
700C23C23×Dic1111yescharacteristic
701C23C22×C22⋊D1111yescharacteristic
702C23C22×C22⋊D1111yescharacteristic
703Q8—416no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—416no—
725C2×C4—114no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—224no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—224no—
741C2×C4—224no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—441no—
745C2×C4—441no—
746C2×C4—442no—
747C2×C4—441no—
748C2×C4—441no—
749C2×C4—441no—
750C2×C4—441no—
751C2×C4—442no—
752C2×C4—442no—
753C2×C4—441no—
754C2×C4—441no—
755C2×C4—441no—
756C2×C4—441no—
757C2×C4—441no—
758C2×C4—441no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4—442no—
762C2×C4—442no—
763C2×C4—442no—
764C2×C4—442no—
765C2×C4—442no—
766C2×C4—442no—
767C2×C4D4×Dic1114yes—
768C2×C4D4×Dic1114yes—
769C2×C4#6698914yes—
770C2×C4#6699114yes—
771C2×C4#6699114yes—
772C2×C4#6699314yes—
773C2×C4C2×C22⋊Dic1118yes—
774C2×C4C2×C22⋊Dic1114yes—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22#1062315311yescharacteristic
791C22#1062315511yescharacteristic
792C22#1062315611yescharacteristic
793C22D11×C22⋊Q811yescharacteristic
794C22#1062315811yescharacteristic
795C22#1062315911yescharacteristic
796C22#1062316011yescharacteristic
797C22#1062316111yescharacteristic
798C22#1062316211yescharacteristic
799C22#1062316311yescharacteristic
800C22#1062316411yescharacteristic
801C22#1062316611yescharacteristic
802C22#1062317011yescharacteristic
803C22#1062317211yescharacteristic
804C22#1062317311yescharacteristic
805C22#1062317411yescharacteristic
806C22C2×D4×Dic1111yescharacteristic
807C22C2×D4×Dic1111yescharacteristic
808C22C2×#6698911yescharacteristic
809C22C2×#6699111yescharacteristic
810C22C2×#6699111yescharacteristic
811C22C2×#6699311yescharacteristic
812C22C2×Q8×Dic1111yescharacteristic
813C22#1062334311yescharacteristic
814C22Q8×C22⋊D1111yescharacteristic
815C22Q8×C22⋊D1111yescharacteristic
816C22#1062334811yescharacteristic
817C22#1062334811yescharacteristic
818C22#1062335511yescharacteristic
819C22#1062335511yescharacteristic
820C22#41×Dic1111yescharacteristic
821C22#1062335811yescharacteristic
822C22#1062336011yescharacteristic
823C22#1062336011yescharacteristic
824C22C22×C22⋊Dic1111yescharacteristic
825C4—28no—
826C4—42no—
827C4—44no—
828C4—224no—
829C4—444no—
830C4—442no—
831C4—442no—
832C4—442no—
833C4—882no—
834C4#1062283418yes—
835C2—44no—
836C2C2×#1062283411yescharacteristic
837C2C22⋊Q8×Dic1111yescharacteristic
838C2#1307130011yescharacteristic
839C2#1307144611yescharacteristic
840C2Q8×C22⋊Dic1111yescharacteristic
841C2#1307162511yescharacteristic
842C2#1307164711yescharacteristic
843C2#1307204111yescharacteristic
844C2#1307206311yescharacteristic
845C2#1307218911yescharacteristic
846C2#1307221111yescharacteristic
847C2#1307295911yescharacteristic
848C2#1307299211yescharacteristic
849C2#1307355411yescharacteristic
850C2#1307356611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×C22⋊Q8C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC22×C22⋊Q8D11
hypocenterC11#13997
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#10622843C2semidirect
2. C2×#10622843C2semidirect
3. C2×#10622598C2semidirect
5. C2×C4⋊C4×Dic11C2semidirect
7. #13066884C2semidirect
10. #13066845C2semidirect
16. C2×C11×C22⋊Q8C4semidirect
87. C2×C22⋊Dic11Q8semidirect
217. C11×C4⋊C4C22⋊C4semidirect
360. C2×Dic11C22⋊Q8semidirect
365. C2×C22⋊Q8Dic11semidirect
644. C4⋊C4C22⋊Dic11semidirect
652. C11#13997semidirect

Maximal subgroups

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

subgroupindex
C2×#106228432
C2×#106225982
C2×#106228252
C2×C4⋊C4×Dic112
C2×C4×C22⋊Dic112
#130668842
#130668612
#130668532
#130668452
C22×C11×C22⋊Q82
#1399711