Finite Group Databasebeta

← #14676910

Subgroups — #14676910

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×#66950C211yesmaximal, characteristic
2C2×#10622542C211yesmaximal, characteristic, complemented
3C2×#10622587C211yesmaximal, characteristic, complemented
4C2×#10622600C211yesmaximal, characteristic
5C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
7#13066885C212yesmaximal, complemented
8#13066858C212yesmaximal
9#13066852C212yesmaximal
10#13066845C212yesmaximal, complemented
11C2×C11×#389C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×C4⋊Dic11C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4×Dic11C2212yes—
25C22×C4×Dic11C2211yescharacteristic
26C2×#66950—24no—
27C2×#66950—24no—
28C2×#66950C418yescomplemented
29C11×#389—24no—
30C2×C11×#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39#10622600—24no—
40C4⋊C4×Dic11—24no—
41#10622587—24no—
42C4×(C2×D11)⋊C4—24no—
43#10622542—24no—
44C24×D11C2311yescharacteristic
45C23×C4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2312yes—
49C23×C4×C11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2312yes—
52C23×Dic11C2312yes—
53C23×Dic11C2311yescharacteristic
54C23×Dic11C2311yescharacteristic
55C22×C4×D11—22no—
56C22×C4×D11—22no—
57C22×C4×D11—22no—
58C22×C4×D11—22no—
59C22×C4×D11—22no—
60C22×C4×D11—22no—
61C22×C4×D11C2×C414yes—
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—24no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—42no—
75C2×C11×C4⋊C4C2×C414yes—
76C2×C11×C4⋊C4D414yes—
77C2×C11×C4⋊C4D414yes—
78C2×C42×C11—22no—
79C2×C42×C11—22no—
80C2×C42×C11—22no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—24no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—24no—
90C2×(C2×D11)⋊C4—42no—
91C2×(C2×D11)⋊C4C2×C418yes—
92C2×(C2×D11)⋊C4Q814yescomplemented
93C2×C4⋊Dic11—24no—
94C2×C4⋊Dic11—24no—
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11C2×C418yes—
98C2×C4⋊Dic11D414yes—
99C2×C4×Dic11—22no—
100C2×C4×Dic11—22no—
101C2×C4×Dic11—24no—
102C2×C4×Dic11—24no—
103C2×C4×Dic11—42no—
104C2×C4×Dic11D414yes—
105#66950—232no—
106C11×#95—24no—
107C11⋊#95—24no—
108C11⋊#95—24no—
109C11⋊#95—24no—
110C11⋊#95—22no—
111C11⋊#95—22no—
112C11⋊#95—24no—
113C11⋊#95—24no—
114C11⋊#95—24no—
115#13997—111nomaximal, Sylow
116C24×C11C2411yescharacteristic
117C23×D11—21no—
118C23×D11—21no—
119C23×D11—21no—
120C23×D11—21no—
121C23×D11—21no—
122C23×D11—21no—
123C23×D11—21no—
124C23×D11—21no—
125C23×D11—21no—
126C23×D11—21no—
127C23×D11—21no—
128C23×D11—21no—
129C23×D11C22×C412yes—
130C23×D11C2×Q812yes—
131C23×D11#4112yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
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—22no—
155C22×C4×C11C22×C414yes—
156C22×C4×C11C22×C412yes—
157C22×C4×C11C2×D414yes—
158C22×C4×C11C2×D414yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×Q812yes—
164C22×C4×C11#4112yes—
165C22×C4×C11#4112yes—
166C22×C4×C11#4112yes—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—22no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—22no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—22no—
194C22×Dic11—21no—
195C22×Dic11C22×C412yes—
196C22×Dic11C22×C414yes—
197C22×Dic11C2×D412yes—
198C22×Dic11C2×D414yes—
199C22×Dic11C2×D412yes—
200C22×Dic11C2×Q812yes—
201C22×Dic11#4112yes—
202C2×C4×D11—28no—
203C2×C4×D11—28no—
204C2×C4×D11—28no—
205C2×C4×D11—44no—
206C2×C4×D11—44no—
207C2×C4×D11—44no—
208C2×C4×D11—44no—
209C2×Dic22—28no—
210C2×Dic22—28no—
211C2×Dic22—28no—
212C2×Dic22—44no—
213C2×Dic22—44no—
214C2×Dic22—44no—
215C2×Dic22—44no—
216C11×C4⋊C4—48no—
217C11×C4⋊C4—44no—
218C11×C4⋊C4C22⋊C4116yescomplemented
219C42×C11—44no—
220(C2×D11)⋊C4—28no—
221(C2×D11)⋊C4—28no—
222(C2×D11)⋊C4—216no—
223(C2×D11)⋊C4—48no—
224C4⋊Dic11—216no—
225C4⋊Dic11—28no—
226C4×Dic11—28no—
227C4×Dic11—48no—
228C22×C22⋊Q8—111no—
229C2×#391—111no—
230C2×#391—111no—
231C2×#389D1111yescharacteristic, complemented
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×C11C23×C411yescharacteristic
240C23×C11C22×D411yescharacteristic
241C23×C11C22×D411yescharacteristic
242C23×C11C22×D411yescharacteristic
243C23×C11C22×D411yescharacteristic
244C23×C11C22×Q811yescharacteristic
245C23×C11C2×#4111yescharacteristic
246C23×C11C2×#4111yescharacteristic
247C23×C11C2×#4111yescharacteristic
248C23×C11C2×#4111yescharacteristic
249C23×C11C2×#4111yescharacteristic
250C23×C11H(5,𝔽2)11yescharacteristic
251C23×C112−1+411yescharacteristic
252C23×C112−1+411yescharacteristic
253C23×C112−1+411yescharacteristic
254C22×D11—22no—
255C22×D11—22no—
256C22×D11—22no—
257C22×D11—22no—
258C22×D11—22no—
259C22×D11—22no—
260C22×D11—22no—
261C22×D11—22no—
262C22×D11—22no—
263C22×D11—22no—
264C22×D11—22no—
265C22×D11—22no—
266C22×D11—22no—
267C22×D11—22no—
268C22×D11—22no—
269C22×D11—22no—
270C22×D11—22no—
271C22×D11—22no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11—41no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11—41no—
284C22×D11—41no—
285C22×D11—41no—
286C22×D11—41no—
287C22×D11—41no—
288C22×D11C4×Q814yes—
289C2×C4×C11—24no—
290C2×C4×C11—24no—
291C2×C4×C11—24no—
292C2×C4×C11—24no—
293C2×C4×C11—24no—
294C2×C4×C11—24no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11C2×C22⋊C418yes—
317C2×C4×C11C2×C22⋊C414yes—
318C2×C4×C11C4×D414yes—
319C2×C4×C11C4×D414yes—
320C2×C4×C11#12114yes—
321C2×C4×C11#12114yes—
322C2×C4×C11#12414yes—
323C2×C4×C11#12714yes—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—24no—
332C2×Dic11—24no—
333C2×Dic11—24no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—24no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—24no—
341C2×Dic11—24no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—42no—
347C2×Dic11—41no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11—41no—
351C2×Dic11—42no—
352C2×Dic11—42no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—42no—
356C2×Dic11—41no—
357C2×Dic11—41no—
358C2×Dic11C22⋊Q814yescomplemented
359C4×D11—416no—
360Dic22—416no—
361C23×Q8—111no—
362C24×C4—111no—
363C2×C22⋊Q8—118no—
364C2×C22⋊Q8—224no—
365C2×C22⋊Q8—224no—
366C22×C4⋊C4—112no—
367C22×C4⋊C4—111no—
368C22×C4⋊C4C2×D1111yescharacteristic
369C22×C4⋊C4C2×D1112yes—
370C22×C4⋊C4C2×D1111yescharacteristic
371C22×C22⋊C4—112no—
372C22×C22⋊C4—111no—
373C22×C22⋊C4—111no—
374C22×C22⋊C4—112no—
375C22×C42—111no—
376C22×C42—112no—
377C22×C42C2×D1111yescharacteristic
378#391—224no—
379#391—224no—
380#389—24no—
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—111no—
392C2×#95C2×D1112yes—
393C22×C11C22×C22⋊C411yescharacteristic
394C22×C11C2×C4×D411yescharacteristic
395C22×C11C2×C4×D411yescharacteristic
396C22×C11C2×C4×Q811yescharacteristic
397C22×C11C4×#4111yescharacteristic
398C22×C11#51911yescharacteristic
399C22×C11#52011yescharacteristic
400C22×C11C2×#12111yescharacteristic
401C22×C11C2×#12111yescharacteristic
402C22×C11C2×C22⋊Q811yescharacteristic
403C22×C11#52511yescharacteristic
404C22×C11C2×#12411yescharacteristic
405C22×C11#52911yescharacteristic
406C22×C11C2×#12711yescharacteristic
407C22×C11#53311yescharacteristic
408C22×C11#53611yescharacteristic
409C22×C11#53711yescharacteristic
410C22×C11#54111yescharacteristic
411C22×C11#54211yescharacteristic
412C22×C11#54611yescharacteristic
413C22×C11#54611yescharacteristic
414C22×C11#54611yescharacteristic
415C22×C11#54711yescharacteristic
416C22×C11#54711yescharacteristic
417C22×C11#54711yescharacteristic
418C22×C11#54811yescharacteristic
419C22×C11#54811yescharacteristic
420C22×C11#54811yescharacteristic
421C22×C11D4×Q811yescharacteristic
422C22×C11D4×Q811yescharacteristic
423C22×C11D4×Q811yescharacteristic
424C22×C11#55211yescharacteristic
425C22×C11#55211yescharacteristic
426C22×C11#55411yescharacteristic
427C22×C11#55611yescharacteristic
428C2×D11—24no—
429C2×D11—24no—
430C2×D11—24no—
431C2×D11—42no—
432C2×D11—42no—
433C2×D11—42no—
434C2×D11—42no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—42no—
440C2×D11—42no—
441C2×D11—42no—
442C2×D11—42no—
443C4×C11—28no—
444C4×C11—42no—
445C4×C11—42no—
446C4×C11—82no—
447C4×C11#39018yes—
448Dic11—24no—
449Dic11—42no—
450Dic11—44no—
451Dic11—44no—
452Dic11—42no—
453C25—111no—
454C22×Q8—114no—
455C22×Q8—222no—
456C22×Q8—222no—
457C22×Q8—222no—
458C22×Q8—222no—
459C22×Q8—222no—
460C22×Q8—222no—
461C23×C4—111no—
462C23×C4—112no—
463C23×C4—112no—
464C23×C4—111no—
465C23×C4—111no—
466C23×C4—114no—
467C23×C4—222no—
468C23×C4—222no—
469C23×C4—222no—
470C23×C4—222no—
471C23×C4—222no—
472C23×C4—222no—
473C23×C4C22×D1112yes—
474C23×C4C22×D1111yescharacteristic
475C23×C4C22×D1111yescharacteristic
476C23×C4C22×D1112yes—
477C23×C4C22×D1111yescharacteristic
478C22⋊Q8—2232no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—118no—
486C2×C4⋊C4—114no—
487C2×C4⋊C4—224no—
488C2×C4⋊C4—222no—
489C2×C4⋊C4—222no—
490C2×C4⋊C4—224no—
491C2×C4⋊C4C4×D1114yes—
492C2×C4⋊C4D4414yes—
493C2×C4⋊C4C22⋊D1114yes—
494C2×C22⋊C4—118no—
495C2×C22⋊C4—114no—
496C2×C22⋊C4—222no—
497C2×C22⋊C4—222no—
498C2×C22⋊C4—222no—
499C2×C22⋊C4—222no—
500C2×C22⋊C4—224no—
501C2×C22⋊C4—222no—
502C2×C22⋊C4—224no—
503C2×C22⋊C4—224no—
504C2×C22⋊C4—224no—
505C2×C22⋊C4—442no—
506C2×C42—22no—
507C2×C42—22no—
508C2×C42—22no—
509C2×C42—114no—
510C2×C42—222no—
511C2×C42—222no—
512C2×C42—224no—
513C2×C42—224no—
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×C11C2×#39011yescharacteristic
525C2×C11C4×C22⋊Q811yescharacteristic
526C2×C11#232311yescharacteristic
527C2×C11#233911yescharacteristic
528C2×C11Q8×C22⋊C411yescharacteristic
529C2×C11#236011yescharacteristic
530C2×C11#236211yescharacteristic
531C2×C11#241511yescharacteristic
532C2×C11#241711yescharacteristic
533C2×C11#242711yescharacteristic
534C2×C11#242911yescharacteristic
535C2×C11#248911yescharacteristic
536C2×C11#249211yescharacteristic
537C2×C11#254011yescharacteristic
538C2×C11#254211yescharacteristic
539D11—44no—
540C24—112no—
541C24—112no—
542C24—112no—
543C24—221no—
544C24—221no—
545C24—221no—
546C24—221no—
547C24—221no—
548C24—221no—
549C24—221no—
550C24—221no—
551C24—221no—
552C24—221no—
553C24—221no—
554C24—221no—
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—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—112no—
587C22×C4—112no—
588C22×C4—112no—
589C22×C4—114no—
590C22×C4—112no—
591C22×C4—112no—
592C22×C4—114no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—221no—
606C22×C4—222no—
607C22×C4—221no—
608C22×C4—222no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—221no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—221no—
617C22×C4—222no—
618C22×C4—221no—
619C22×C4—222no—
620C22×C4—221no—
621C22×C4—228no—
622C22×C4—228no—
623C22×C4—228no—
624C22×C4—444no—
625C22×C4—444no—
626C22×C4—444no—
627C22×C4—444no—
628C22×C4C2×C4×D1114yes—
629C22×C4C2×C4×D1112yes—
630C22×C4C2×D4414yes—
631C22×C4C2×D4412yes—
632C22×C4D4×D1112yes—
633C22×C4D4×D1112yes—
634C22×C4#434112yes—
635C22×C4Q8×D1112yes—
636C22×C4#434312yes—
637C22×C4#434312yes—
638C22×C4C2×C22⋊D1114yes—
639C22×C4C2×C22⋊D1112yes—
640C4⋊C4—48no—
641C4⋊C4—44no—
642C4⋊C4—228no—
643C4⋊C4—2216no—
644C4⋊C4(C2×D11)⋊C4116yescomplemented
645C22⋊C4—228no—
646C22⋊C4—228no—
647C22⋊C4—2216no—
648C22⋊C4—448no—
649C42—44no—
650C42—228no—
651C42—448no—
652C11#1399711yescharacteristic, complemented, Sylow
653C23—114no—
654C23—222no—
655C23—222no—
656C23—222no—
657C23—222no—
658C23—222no—
659C23—222no—
660C23—222no—
661C23—222no—
662C23—222no—
663C23—222no—
664C23—222no—
665C23—222no—
666C23—222no—
667C23—222no—
668C23—222no—
669C23—222no—
670C23—222no—
671C23—222no—
672C23—441no—
673C23—441no—
674C23—441no—
675C23—441no—
676C23—441no—
677C23—441no—
678C23—441no—
679C23—441no—
680C23—441no—
681C23—441no—
682C23—441no—
683C23—441no—
684C23—441no—
685C23—441no—
686C23—441no—
687C23—441no—
688C23C22×C4×D1111yescharacteristic
689C23C22×D4411yescharacteristic
690C23C2×D4×D1111yescharacteristic
691C23C2×D4×D1111yescharacteristic
692C23C2×#434111yescharacteristic
693C23#6703711yescharacteristic
694C23C2×Q8×D1111yescharacteristic
695C23C2×#434311yescharacteristic
696C23C2×#434311yescharacteristic
697C23#6704011yescharacteristic
698C23#41×D1111yescharacteristic
699C23#41×D1111yescharacteristic
700C23#6704311yescharacteristic
701C23#6704311yescharacteristic
702C23C22×C22⋊D1111yescharacteristic
703Q8—4416no—
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—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—114no—
732C2×C4—222no—
733C2×C4—222no—
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—224no—
744C2×C4—224no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—224no—
748C2×C4—222no—
749C2×C4—224no—
750C2×C4—441no—
751C2×C4—442no—
752C2×C4—441no—
753C2×C4—441no—
754C2×C4—442no—
755C2×C4—442no—
756C2×C4—441no—
757C2×C4—442no—
758C2×C4—442no—
759C2×C4—441no—
760C2×C4—441no—
761C2×C4—442no—
762C2×C4—442no—
763C2×C4—441no—
764C2×C4—442no—
765C2×C4—441no—
766C2×C4—4416no—
767C2×C4#6694614yes—
768C2×C4#6694614yes—
769C2×C4#6694814yes—
770C2×C4#6694814yes—
771C2×C4C2×(C2×D11)⋊C418yes—
772C2×C4C2×(C2×D11)⋊C414yes—
773C2×C4#6699314yes—
774C2×C4#6700014yes—
775C22—224no—
776C22—224no—
777C22—224no—
778C22—442no—
779C22—442no—
780C22—442no—
781C22—442no—
782C22—442no—
783C22—442no—
784C22—442no—
785C22—442no—
786C22—442no—
787C22—442no—
788C22—442no—
789C22—442no—
790C22C2×#6694611yescharacteristic
791C22C2×#6694611yescharacteristic
792C22C2×#6694811yescharacteristic
793C22C2×#6694811yescharacteristic
794C22C4×#434111yescharacteristic
795C22#1062307711yescharacteristic
796C22#1062308511yescharacteristic
797C22#1062308611yescharacteristic
798C22C4×Q8×D1111yescharacteristic
799C22#1062310311yescharacteristic
800C22Q8×D4411yescharacteristic
801C22#1062310711yescharacteristic
802C22#1062312911yescharacteristic
803C22#1062313711yescharacteristic
804C22#1062313911yescharacteristic
805C22#1062314311yescharacteristic
806C22D11×C22⋊Q811yescharacteristic
807C22#1062315911yescharacteristic
808C22#1062316211yescharacteristic
809C22#1062316311yescharacteristic
810C22#1062322211yescharacteristic
811C22#1062322511yescharacteristic
812C22#1062322511yescharacteristic
813C22#1062322811yescharacteristic
814C22#1062325911yescharacteristic
815C22#1062326111yescharacteristic
816C22#1062326311yescharacteristic
817C22#1062326411yescharacteristic
818C22C22×(C2×D11)⋊C411yescharacteristic
819C22C2×#6699311yescharacteristic
820C22#1062333711yescharacteristic
821C22C2×#6700011yescharacteristic
822C22Q8×C22⋊D1111yescharacteristic
823C22#1062335511yescharacteristic
824C22#1062336211yescharacteristic
825C4—28no—
826C4—42no—
827C4—42no—
828C4—82no—
829C4—224no—
830C4—444no—
831C4—442no—
832C4—442no—
833C4—444no—
834C4#1062260118yes—
835C2—444no—
836C2C2×#1062260111yescharacteristic
837C2#1307114611yescharacteristic
838C2#1307129611yescharacteristic
839C2#1307144111yescharacteristic
840C2Q8×(C2×D11)⋊C411yescharacteristic
841C2#1307162011yescharacteristic
842C2#1307164211yescharacteristic
843C2#1307204311yescharacteristic
844C2#1307206511yescharacteristic
845C2#1307219111yescharacteristic
846C2#1307221311yescharacteristic
847C2#1307296011yescharacteristic
848C2#1307299311yescharacteristic
849C2#1307355211yescharacteristic
850C2#1307356611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#389C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#389D11
hypocenterC11#13997
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#10622542C2semidirect
3. C2×#10622587C2semidirect
5. C2×C4⋊C4×Dic11C2semidirect
7. #13066885C2semidirect
10. #13066845C2semidirect
11. C2×C11×#389C2semidirect
28. C2×#66950C4semidirect
92. C2×(C2×D11)⋊C4Q8semidirect
218. C11×C4⋊C4C22⋊C4semidirect
231. C2×#389D11semidirect
358. C2×Dic11C22⋊Q8semidirect
644. C4⋊C4(C2×D11)⋊C4semidirect
652. C11#13997semidirect

Maximal subgroups

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

subgroupindex
C22×#669502
C2×#106225422
C2×#106225872
C2×#106226002
C2×C4⋊C4×Dic112
C2×C4×(C2×D11)⋊C42
#130668852
#130668582
#130668522
#130668452
C2×C11×#3892
#1399711