Finite Group Databasebeta

← #14676903

Subgroups — #14676903

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
1C22×#66977C211yesmaximal, characteristic
2C2×#10622587C211yesmaximal, characteristic, complemented
3C2×#10622587C211yesmaximal, characteristic, complemented
4C2×#10622586C211yesmaximal, characteristic, complemented
5C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic11C211yesmaximal, characteristic
7#13066882C212yesmaximal, complemented
8#13066859C212yesmaximal
9#13066853C212yesmaximal
10Dic11⋊#95C212yesmaximal, complemented
11C2×C11×#380C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C2×#66977—24no—
22C2×#66977—24no—
23C2×#66977C418yescomplemented
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2212yes—
28C22×C4×Dic11C2211yescharacteristic
29C11×#380—24no—
30C2×C11×#95C2212yes—
31C4×C22⋊Dic11—24no—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C4⋊C4×Dic11—24no—
41#10622587—24no—
42#10622587—24no—
43#10622586—24no—
44C25×C11C2311yescharacteristic
45C23×C4×C11—22no—
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11—22no—
49C23×C4×C11—22no—
50C23×C4×C11—22no—
51C23×C4×C11C2×C414yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×Dic11C2312yes—
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2312yes—
61C23×Dic11C2311yescharacteristic
62C22×Dic22—22no—
63C22×Dic22—22no—
64C22×Dic22—22no—
65C22×Dic22—22no—
66C22×Dic22—22no—
67C22×Dic22—22no—
68C22×Dic22C2×C414yes—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4D414yes—
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4—24no—
77C2×C11×C22⋊C4—42no—
78C2×C22⋊Dic11—22no—
79C2×C22⋊Dic11—24no—
80C2×C22⋊Dic11—24no—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—22no—
85C2×C22⋊Dic11C2×C418yes—
86C2×C22⋊Dic11Q814yescomplemented
87C2×C4⋊Dic11C2×C414yes—
88C2×C4⋊Dic11D414yes—
89C2×C4⋊Dic11D414yes—
90#66977—232no—
91C2×Dic11⋊C4—24no—
92C2×Dic11⋊C4—24no—
93C2×Dic11⋊C4—24no—
94C2×Dic11⋊C4—24no—
95C2×Dic11⋊C4—42no—
96C2×Dic11⋊C4C2×C418yes—
97C2×C4×Dic11—22no—
98C2×C4×Dic11—22no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11—22no—
101C2×C4×Dic11—22no—
102C2×C4×Dic11—24no—
103C2×C4×Dic11—24no—
104C2×C4×Dic11—42no—
105C2×C4×Dic11D414yes—
106C11×#95—24no—
107C11⋊#95—24no—
108C11⋊#95—24no—
109C11⋊#95—22no—
110C11⋊#95—22no—
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
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—28no—
145C22×C4×C11—28no—
146C22×C4×C11—28no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—44no—
155C22×C4×C11—44no—
156C22×C4×C11—44no—
157C22×C4×C11—44no—
158C22×C4×C11C22×C412yes—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C2×D414yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D412yes—
165C22×C4×C11#4112yes—
166C22×C4×C11#4112yes—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—21no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—21no—
190C22×Dic11—22no—
191C22×Dic11—21no—
192C22×Dic11—22no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11C22×C414yes—
200C22×Dic11C22×C414yes—
201C22×Dic11C2×D412yes—
202C22×Dic11C2×D414yes—
203C22×Dic11C2×D414yes—
204C22×Dic11C2×D412yes—
205C22×Dic11C2×Q812yes—
206C22×Dic11C2×Q812yes—
207C22×Dic11#4112yes—
208C22×Dic11#4112yes—
209C2×Dic22—28no—
210C2×Dic22—28no—
211C2×Dic22—28no—
212C2×Dic22—44no—
213C2×Dic22—44no—
214C2×Dic22—44no—
215C2×Dic22—44no—
216C11×C4⋊C4—28no—
217C11×C4⋊C4—44no—
218C11×C22⋊C4—48no—
219C22⋊Dic11—28no—
220C22⋊Dic11—216no—
221C22⋊Dic11—28no—
222C4⋊Dic11C22⋊C4116yescomplemented
223Dic11⋊C4—216no—
224Dic11⋊C4—48no—
225C4×Dic11—28no—
226C4×Dic11—48no—
227C4×Dic11—44no—
228C22×C22⋊Q8—111no—
229C2×#391—111no—
230C2×#391—111no—
231C2×#389—111no—
232C2×#380D1111yescharacteristic
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
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—24no—
293C2×C4×C11—24no—
294C2×C4×C11—24no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—42no—
299C2×C4×C11—41no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—416no—
304C2×C4×C11—42no—
305C2×C4×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11C2×C22⋊C414yes—
312C2×C4×C11C4×D414yes—
313C2×C4×C11C4×D414yes—
314C2×C4×C11#12114yes—
315C2×C4×C11#12114yes—
316C2×C4×C11#12414yes—
317C2×C4×C11#12714yes—
318C2×Dic11—24no—
319C2×Dic11—24no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—24no—
331C2×Dic11—24no—
332C2×Dic11—24no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—42no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11—41no—
358C2×Dic11C2×C22⋊C418yes—
359C2×Dic11C22⋊Q814yescomplemented
360Dic22—416no—
361C23×Q8—111no—
362C24×C4C2×D1111yescharacteristic
363C2×C22⋊Q8—118no—
364C2×C22⋊Q8—224no—
365C2×C22⋊Q8—224no—
366C22×C4⋊C4—111no—
367C22×C4⋊C4—112no—
368C22×C4⋊C4—112no—
369C22×C4⋊C4C2×D1111yescharacteristic
370C22×C4⋊C4C2×D1111yescharacteristic
371C22×C22⋊C4—112no—
372C22×C22⋊C4—111no—
373C22×C22⋊C4—111no—
374C22×C22⋊C4C2×D1112yes—
375C22×C42—111no—
376C22×C42—111no—
377C22×C42—112no—
378#391—224no—
379#391—224no—
380#389—224no—
381#380—24no—
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—111no—
392C2×#95C2×D1112yes—
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—44no—
444C4×C11—42no—
445C4×C11—82no—
446C4×C11#39018yes—
447Dic11—28no—
448Dic11—24no—
449Dic11—42no—
450Dic11—42no—
451Dic11—42no—
452Dic11—44no—
453C25C22×D1111yescharacteristic
454C22×Q8—114no—
455C22×Q8—222no—
456C22×Q8—222no—
457C22×Q8—222no—
458C22×Q8—222no—
459C22×Q8—222no—
460C22×Q8—222no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—112no—
468C23×C4—111no—
469C23×C4—111no—
470C23×C4—112no—
471C23×C4—111no—
472C23×C4—111no—
473C23×C4C4×D1114yes—
474C23×C4C22×D1112yes—
475C23×C4C22×D1111yescharacteristic
476C23×C4C22×D1112yes—
477C23×C4C22×D1111yescharacteristic
478C22⋊Q8—2232no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—114no—
485C2×C4⋊C4—114no—
486C2×C4⋊C4—114no—
487C2×C4⋊C4—118no—
488C2×C4⋊C4—224no—
489C2×C4⋊C4—224no—
490C2×C4⋊C4—224no—
491C2×C4⋊C4—224no—
492C2×C4⋊C4—442no—
493C2×C4⋊C4C22⋊D1114yes—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—118no—
498C2×C22⋊C4—114no—
499C2×C22⋊C4—224no—
500C2×C22⋊C4—224no—
501C2×C22⋊C4—222no—
502C2×C22⋊C4—222no—
503C2×C22⋊C4—222no—
504C2×C22⋊C4—222no—
505C2×C22⋊C4—222no—
506C2×C42—114no—
507C2×C42—222no—
508C2×C42—222no—
509C2×C42—224no—
510C2×C42—224no—
511C2×C42—222no—
512C2×C42—222no—
513C2×C42—222no—
514C2×C42—442no—
515#95—24no—
516#95—222no—
517#95—222no—
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—
552C24C2×C4×D1112yes—
553C24#434112yes—
554C24Q8×D1112yes—
555C24C23×D1111yescharacteristic
556C2×Q8—228no—
557C2×Q8—228no—
558C2×Q8—228no—
559C2×Q8—444no—
560C2×Q8—444no—
561C2×Q8—444no—
562C2×Q8—444no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—28no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—114no—
590C22×C4—112no—
591C22×C4—114no—
592C22×C4—114no—
593C22×C4—112no—
594C22×C4—112no—
595C22×C4—114no—
596C22×C4—112no—
597C22×C4—112no—
598C22×C4—112no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—222no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—222no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—222no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—221no—
623C22×C4—221no—
624C22×C4—221no—
625C22×C4—221no—
626C22×C4—221no—
627C22×C4—221no—
628C22×C4—221no—
629C22×C4—221no—
630C22×C4—222no—
631C22×C4C2×C4×D1112yes—
632C22×C4C2×C4×D1112yes—
633C22×C4#433912yes—
634C22×C4D4×D1112yes—
635C22×C4D4×D1112yes—
636C22×C4D4×D1112yes—
637C22×C4#434112yes—
638C22×C4C2×C22⋊D1114yes—
639C22×C4C2×C22⋊D1112yes—
640C4⋊C4—28no—
641C4⋊C4—44no—
642C4⋊C4—1116no—
643C4⋊C4—2216no—
644C4⋊C4—448no—
645C22⋊C4—48no—
646C22⋊C4—2216no—
647C22⋊C4—228no—
648C22⋊C4—228no—
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—
687C23#6694014yes—
688C23C22×C4×D1111yescharacteristic
689C23C2×#433911yescharacteristic
690C23C2×D4×D1111yescharacteristic
691C23C2×D4×D1111yescharacteristic
692C23C2×D4×D1111yescharacteristic
693C23C2×#434111yescharacteristic
694C23C2×#434111yescharacteristic
695C23#6703711yescharacteristic
696C23C2×Q8×D1111yescharacteristic
697C23#6704011yescharacteristic
698C23#41×D1111yescharacteristic
699C23#41×D1111yescharacteristic
700C23#6704311yescharacteristic
701C23#6704311yescharacteristic
702C23C22×C22⋊D1111yescharacteristic
703Q8—4416no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—416no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—118no—
727C2×C4—114no—
728C2×C4—222no—
729C2×C4—224no—
730C2×C4—222no—
731C2×C4—224no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—224no—
736C2×C4—224no—
737C2×C4—224no—
738C2×C4—224no—
739C2×C4—222no—
740C2×C4—224no—
741C2×C4—224no—
742C2×C4—222no—
743C2×C4—224no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—442no—
753C2×C4—442no—
754C2×C4—441no—
755C2×C4—441no—
756C2×C4—442no—
757C2×C4—441no—
758C2×C4—441no—
759C2×C4—442no—
760C2×C4—441no—
761C2×C4—441no—
762C2×C4—441no—
763C2×C4—441no—
764C2×C4—441no—
765C2×C4—441no—
766C2×C4—441no—
767C2×C4—441no—
768C2×C4C22⋊C4×D1114yes—
769C2×C4(C22⋊D11)⋊C414yes—
770C2×C4#6693714yes—
771C2×C4#6693814yes—
772C2×C4C4×C22⋊D1114yes—
773C2×C4#6699214yes—
774C2×C4#6699314yes—
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—
790C22C2×C22⋊C4×D1111yescharacteristic
791C22C2×(C22⋊D11)⋊C411yescharacteristic
792C22C2×#6693711yescharacteristic
793C22C2×#6693811yescharacteristic
794C22C2×#6694011yescharacteristic
795C22#1062303511yescharacteristic
796C22#1062304211yescharacteristic
797C22#1062304411yescharacteristic
798C22#1062304711yescharacteristic
799C22#1062305311yescharacteristic
800C22#1062306011yescharacteristic
801C22#1062306411yescharacteristic
802C22#1062312911yescharacteristic
803C22#1062312911yescharacteristic
804C22#1062313111yescharacteristic
805C22#1062313411yescharacteristic
806C22#1062313711yescharacteristic
807C22#1062313911yescharacteristic
808C22#1062314311yescharacteristic
809C22#1062314311yescharacteristic
810C22#1062315311yescharacteristic
811C22#1062315611yescharacteristic
812C22D11×C22⋊Q811yescharacteristic
813C22#1062315911yescharacteristic
814C22#1062316211yescharacteristic
815C22#1062316211yescharacteristic
816C22#1062316311yescharacteristic
817C22#1062316311yescharacteristic
818C22C2×C4×C22⋊D1111yescharacteristic
819C22C2×#6699211yescharacteristic
820C22C2×#6699311yescharacteristic
821C22#1062333711yescharacteristic
822C22Q8×C22⋊D1111yescharacteristic
823C22#1062335511yescharacteristic
824C22#1062336211yescharacteristic
825C4—44no—
826C4—42no—
827C4—82no—
828C4—228no—
829C4—224no—
830C4—442no—
831C4—442no—
832C4—442no—
833C4—444no—
834C4#1062257018yes—
835C2—44no—
836C2C2×#1062257011yescharacteristic
837C2#1307114411yescharacteristic
838C2#1307129411yescharacteristic
839C2#1307144411yescharacteristic
840C2#1307144811yescharacteristic
841C2#1307162111yescharacteristic
842C2#1307164311yescharacteristic
843C2#1307204711yescharacteristic
844C2#1307206911yescharacteristic
845C2#1307219511yescharacteristic
846C2#1307221711yescharacteristic
847C2#1307295311yescharacteristic
848C2#1307298611yescharacteristic
849C2#1307355211yescharacteristic
850C2#1307356611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#380C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#380D11
hypocenterC11#13997
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#10622587C2semidirect
3. C2×#10622587C2semidirect
4. C2×#10622586C2semidirect
5. C2×C4⋊C4×Dic11C2semidirect
7. #13066882C2semidirect
10. Dic11⋊#95C2semidirect
23. C2×#66977C4semidirect
86. C2×C22⋊Dic11Q8semidirect
222. C4⋊Dic11C22⋊C4semidirect
359. C2×Dic11C22⋊Q8semidirect
652. C11#13997semidirect

Maximal subgroups

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

subgroupindex
C22×#669772
C2×#106225872
C2×#106225862
C2×C4⋊C4×Dic112
C2×C4×C22⋊Dic112
#130668822
#130668592
#130668532
Dic11⋊#952
C2×C11×#3802
#1399711