Finite Group Databasebeta

← #14679161

Subgroups — #14679161

Order 2816.

1318 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622274C211yesmaximal, characteristic
2C2×#10622591C211yesmaximal, characteristic
3C2×C4⋊C4×Dic11C211yesmaximal, characteristic
4#13066883C211yesmaximal, characteristic
5#13066883C211yesmaximal, characteristic
6#13066872C211yesmaximal, characteristic
7#13066851C211yesmaximal, characteristic
8#13066850C211yesmaximal, characteristic
9#13066850C211yesmaximal, characteristic
10#13066850C211yesmaximal, characteristic
11#13066846C211yesmaximal, characteristic
12#13066840C211yesmaximal, characteristic
13#13066840C211yesmaximal, characteristic
14C4×C11⋊#95C211yesmaximal, characteristic
15C11×#1436C211yesmaximal, characteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×Dic11⋊C4C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
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
51#10622591—24no—
52C4⋊C4×Dic11—24no—
53#10622274C418yescomplemented
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4D414yes—
72C2×C42×C11—22no—
73C2×C42×C11—22no—
74C2×C42×C11—41no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—41no—
80C2×C4⋊Dic11—41no—
81C2×C4⋊Dic11—41no—
82C2×C4⋊Dic11—41no—
83C2×C4⋊Dic11—41no—
84C2×C4⋊Dic11C2×C414yes—
85C2×C4⋊Dic11C2×C414yes—
86C2×C4⋊Dic11C2×C414yes—
87C2×Dic11⋊C4—22no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4C2×C414yes—
90C2×C4×Dic11—22no—
91C2×C4×Dic11—22no—
92C2×C4×Dic11—22no—
93C2×C4×Dic11—22no—
94C2×C4×Dic11—22no—
95C2×C4×Dic11—22no—
96C2×C4×Dic11—22no—
97C2×C4×Dic11—22no—
98C2×C4×Dic11—22no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11—41no—
101C2×C4×Dic11—41no—
102C11×#95—22no—
103C11×#95—22no—
104C11×#95—22no—
105C11×#95—41no—
106C11×#95C2×C414yes—
107C11⋊#95—22no—
108C11⋊#95—22no—
109C11⋊#95—22no—
110C11⋊#95—22no—
111C11⋊#95—22no—
112C11⋊#95—22no—
113C11⋊#95—22no—
114C11⋊#95—22no—
115C11⋊#95—22no—
116C11⋊#95—22no—
117C11⋊#95—22no—
118C11⋊#95—22no—
119C11⋊#95—22no—
120C11⋊#95—41no—
121C11⋊#95—41no—
122C11⋊#95—41no—
123C11⋊#95C2×C414yes—
124C11⋊#95C2×C414yes—
125C11⋊#95Q814yes—
126#14179—111nomaximal, Sylow
127C24×C11C2411yescharacteristic
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
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—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
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×C11C22×C412yes—
166C22×C4×C11C22×C412yes—
167C22×C4×C11C22×C412yes—
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2×D412yes—
170C22×C4×C11C2×D412yes—
171C22×C4×C11C2×Q812yes—
172C22×C4×C11#4112yes—
173C22×C4×C11#4112yes—
174C22×C4×C11#4112yes—
175C22×C4×C11#4112yes—
176C22×C4×C11#4112yes—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
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×Dic11C22×C412yes—
225C22×Dic11C22×C412yes—
226C22×Dic11C22×C412yes—
227C22×Dic11C22×C412yes—
228C22×Dic11C2×Q812yes—
229C22×Dic11C2×Q812yes—
230C22×Dic11#4112yes—
231C22×Dic11#4112yes—
232C22×Dic11#4112yes—
233C11×C4⋊C4—28no—
234C42×C11—44no—
235C4⋊Dic11—28no—
236C4⋊Dic11—44no—
237C4⋊Dic11—44no—
238C4⋊Dic11—44no—
239Dic11⋊C4—28no—
240C4×Dic11—28no—
241C4×Dic11—44no—
242C4×Dic11—44no—
243C4×Dic11—44no—
244C2×#398—111no—
245C2×#387—111no—
246C2×C4×C4⋊C4—111no—
247#1445—111no—
248#1445—111no—
249#1442—111no—
250#1436—111no—
251#1436—111no—
252#1436—111no—
253#1436—111no—
254#1436D1111yescharacteristic
255C4⋊#95—111no—
256#1434—111no—
257#1434—111no—
258C4×#95—111no—
259C23×C11C23×C411yescharacteristic
260C23×C11C22×D411yescharacteristic
261C23×C11C22×Q811yescharacteristic
262C23×C11C2×#4111yescharacteristic
263C23×C11C2×#4111yescharacteristic
264C23×C11C2×#4111yescharacteristic
265C23×C11C2×#4111yescharacteristic
266C23×C11C2×#4111yescharacteristic
267C23×C11C2×#4111yescharacteristic
268C23×C11C2×#4111yescharacteristic
269C23×C11C2×#4111yescharacteristic
270C23×C11H(5,𝔽2)11yescharacteristic
271C23×C11H(5,𝔽2)11yescharacteristic
272C23×C112−1+411yescharacteristic
273C23×C112−1+411yescharacteristic
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
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—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11C4×D414yes—
321C2×C4×C11C4×Q814yes—
322C2×C4×C11#12314yes—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
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—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—41no—
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×Dic11—41no—
359C2×Dic11—41no—
360C2×Dic11—41no—
361C2×Dic11—41no—
362C2×Dic11—41no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368C2×Dic11—41no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11#12514yes—
379C22×C4⋊C4—111no—
380C22×C4⋊C4—111no—
381C22×C4⋊C4—111no—
382C22×C4⋊C4—111no—
383C22×C4⋊C4—111no—
384C22×C4⋊C4C2×D1111yescharacteristic
385C22×C42—111no—
386C22×C42—111no—
387C22×C42—111no—
388C22×C42—111no—
389C22×C42C2×D1111yescharacteristic
390#398—118no—
391#387—224no—
392C4×C4⋊C4—224no—
393C2×#95—111no—
394C2×#95—111no—
395C2×#95—111no—
396C2×#95—111no—
397C2×#95—111no—
398C2×#95—111no—
399C2×#95—111no—
400C2×#95—111no—
401C2×#95—111no—
402C2×#95—111no—
403C2×#95—111no—
404C2×#95—111no—
405C2×#95—111no—
406C2×#95—111no—
407C2×#95—111no—
408C2×#95—111no—
409C2×#95—111no—
410C2×#95—111no—
411C2×#95—111no—
412C2×#95C2×D1111yescharacteristic
413C2×#95C2×D1111yescharacteristic
414C2×#95C2×D1111yescharacteristic
415C2×#95C2×D1111yescharacteristic
416C2×#95C2×D1111yescharacteristic
417C22×C11C2×C4×D411yescharacteristic
418C22×C11C2×C4×Q811yescharacteristic
419C22×C11C4×#4111yescharacteristic
420C22×C11C4×#4111yescharacteristic
421C22×C11C4×#4111yescharacteristic
422C22×C11#51811yescharacteristic
423C22×C11#51911yescharacteristic
424C22×C11C2×#12311yescharacteristic
425C22×C11#52511yescharacteristic
426C22×C11C2×#12511yescharacteristic
427C22×C11#52911yescharacteristic
428C22×C11#52911yescharacteristic
429C22×C11#52911yescharacteristic
430C22×C11#52911yescharacteristic
431C22×C11#53311yescharacteristic
432C22×C11#53911yescharacteristic
433C22×C11#53911yescharacteristic
434C22×C11#54211yescharacteristic
435C22×C11#54211yescharacteristic
436C22×C11#54611yescharacteristic
437C22×C11#54711yescharacteristic
438C22×C11D4×Q811yescharacteristic
439C22×C11#55011yescharacteristic
440C22×C11#55111yescharacteristic
441C22×C11#55111yescharacteristic
442C22×C11#55211yescharacteristic
443C22×C11#55211yescharacteristic
444C22×C11#55211yescharacteristic
445C22×C11#55211yescharacteristic
446C22×C11#55311yescharacteristic
447C22×C11#55411yescharacteristic
448C22×C11#55411yescharacteristic
449C22×C11#55511yescharacteristic
450C22×C11#55611yescharacteristic
451C22×C11#55711yescharacteristic
452C4×C11—24no—
453C4×C11—24no—
454C4×C11—24no—
455C4×C11—42no—
456C4×C11—42no—
457C4×C11—42no—
458C4×C11—81no—
459Dic11—24no—
460Dic11—42no—
461Dic11—42no—
462Dic11—42no—
463Dic11—42no—
464Dic11—42no—
465Dic11—42no—
466Dic11—81no—
467C23×C4—111no—
468C23×C4—111no—
469C23×C4—111no—
470C23×C4—111no—
471C23×C4—111no—
472C23×C4—111no—
473C23×C4—111no—
474C23×C4—111no—
475C23×C4C22×D1111yescharacteristic
476C23×C4C22×D1111yescharacteristic
477C23×C4C22×D1111yescharacteristic
478C23×C4C22×D1111yescharacteristic
479C23×C4C22×D1111yescharacteristic
480C23×C4C22×D1111yescharacteristic
481C23×C4C22×D1111yescharacteristic
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—114no—
485C2×C4⋊C4—114no—
486C2×C4⋊C4—114no—
487C2×C4⋊C4—114no—
488C2×C4⋊C4—222no—
489C2×C4⋊C4—222no—
490C2×C4⋊C4—222no—
491C2×C4⋊C4—222no—
492C2×C4⋊C4—222no—
493C2×C4⋊C4—222no—
494C2×C4⋊C4—441no—
495C2×C4⋊C4—441no—
496C2×C4⋊C4—441no—
497C2×C4⋊C4—441no—
498C2×C4⋊C4—441no—
499C2×C4⋊C4D4414yes—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42—41no—
503C2×C42—222no—
504C2×C42—222no—
505C2×C42—222no—
506C2×C42—222no—
507C2×C42—222no—
508C2×C42—222no—
509C2×C42—222no—
510C2×C42—222no—
511C2×C42—222no—
512C2×C42—222no—
513C2×C42—441no—
514C2×C42—441no—
515#95—22no—
516#95—22no—
517#95—22no—
518#95—41no—
519#95—114no—
520#95—114no—
521#95—114no—
522#95—222no—
523#95—222no—
524#95—222no—
525#95—222no—
526#95—222no—
527#95—222no—
528#95—222no—
529#95—222no—
530#95—222no—
531#95—222no—
532#95—222no—
533#95—222no—
534#95—222no—
535#95—441no—
536#95—441no—
537#95—441no—
538#95C4×D1114yes—
539C2×C11C4×#12311yescharacteristic
540C2×C11C4×#12511yescharacteristic
541C2×C11#233211yescharacteristic
542C2×C11#236311yescharacteristic
543C2×C11#236511yescharacteristic
544C2×C11#236811yescharacteristic
545C2×C11#237111yescharacteristic
546C2×C11#241911yescharacteristic
547C2×C11#242311yescharacteristic
548C2×C11#247311yescharacteristic
549C2×C11#247911yescharacteristic
550C2×C11#250811yescharacteristic
551C2×C11#253211yescharacteristic
552C2×C11#257711yescharacteristic
553C2×C11#259011yescharacteristic
554C24C23×D1111yescharacteristic
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
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—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—112no—
593C22×C4—112no—
594C22×C4—112no—
595C22×C4—112no—
596C22×C4—112no—
597C22×C4—112no—
598C22×C4—112no—
599C22×C4—112no—
600C22×C4—112no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—221no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—221no—
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—221no—
631C22×C4—221no—
632C22×C4—221no—
633C22×C4—221no—
634C22×C4—221no—
635C22×C4—221no—
636C22×C4—221no—
637C22×C4—221no—
638C22×C4—221no—
639C22×C4—221no—
640C22×C4—221no—
641C22×C4—221no—
642C22×C4—221no—
643C22×C4—221no—
644C22×C4—221no—
645C22×C4—221no—
646C22×C4—221no—
647C22×C4—221no—
648C22×C4C2×C4×D1112yes—
649C22×C4C2×C4×D1112yes—
650C22×C4C2×C4×D1112yes—
651C22×C4C2×D4412yes—
652C22×C4C2×D4412yes—
653C22×C4C2×D4412yes—
654C22×C4#433912yes—
655C22×C4#434112yes—
656C22×C4#434112yes—
657C22×C4#434112yes—
658C22×C4Q8×D1112yes—
659C22×C4#434312yes—
660C4⋊C4—28no—
661C4⋊C4—228no—
662C4⋊C4—228no—
663C4⋊C4—444no—
664C4⋊C4—444no—
665C4⋊C4—444no—
666C42—44no—
667C42—228no—
668C42—444no—
669C42—444no—
670C42—444no—
671C11#1417911yescharacteristic, complemented, Sylow
672C23C22×C4×D1111yescharacteristic
673C23C22×D4411yescharacteristic
674C23C2×#433911yescharacteristic
675C23C2×#434111yescharacteristic
676C23C2×#434111yescharacteristic
677C23C2×#434111yescharacteristic
678C23#6703711yescharacteristic
679C23C2×Q8×D1111yescharacteristic
680C23C2×#434311yescharacteristic
681C23#41×D1111yescharacteristic
682C23#41×D1111yescharacteristic
683C23#41×D1111yescharacteristic
684C23#6704211yescharacteristic
685C23#6704311yescharacteristic
686C23#6704311yescharacteristic
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—41no—
715C2×C4—41no—
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—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—114no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—222no—
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—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—441no—
759C2×C4—441no—
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×C4—441no—
769C2×C4—441no—
770C2×C4—441no—
771C2×C4—441no—
772C2×C4—441no—
773C2×C4—441no—
774C2×C4—441no—
775C2×C4—441no—
776C2×C4—441no—
777C2×C4—441no—
778C2×C4—441no—
779C2×C4—441no—
780C2×C4—441no—
781C2×C4—441no—
782C2×C4—441no—
783C2×C4—441no—
784C2×C4—441no—
785C2×C4—441no—
786C2×C4—441no—
787C2×C4—441no—
788C2×C4—441no—
789C2×C4C4×D4414yes—
790C2×C4#6693914yes—
791C2×C4#6694014yes—
792C22C2×C4×D4411yescharacteristic
793C22C2×#6693911yescharacteristic
794C22C2×#6694011yescharacteristic
795C22#1062304511yescharacteristic
796C22#1062304711yescharacteristic
797C22#1062305511yescharacteristic
798C22#1062306311yescharacteristic
799C22C4×#434111yescharacteristic
800C22C4×#434111yescharacteristic
801C22#1062306911yescharacteristic
802C22#1062306911yescharacteristic
803C22#1062307311yescharacteristic
804C22#1062307611yescharacteristic
805C22#1062308511yescharacteristic
806C22#1062308611yescharacteristic
807C22#1062309811yescharacteristic
808C22C4×#434311yescharacteristic
809C22Q8×D4411yescharacteristic
810C22#1062310811yescharacteristic
811C22#1062311811yescharacteristic
812C22#1062313111yescharacteristic
813C22#1062313311yescharacteristic
814C22#1062315511yescharacteristic
815C22#1062316611yescharacteristic
816C22#1062316711yescharacteristic
817C22#1062317311yescharacteristic
818C22#1062318111yescharacteristic
819C22#1062318911yescharacteristic
820C22#1062319111yescharacteristic
821C22#1062321311yescharacteristic
822C22D11×#12511yescharacteristic
823C22#1062322511yescharacteristic
824C22#1062323911yescharacteristic
825C22#1062324111yescharacteristic
826C22#1062325911yescharacteristic
827C4—24no—
828C4—24no—
829C4—24no—
830C4—42no—
831C4—42no—
832C4—42no—
833C4—81no—
834C4—224no—
835C4—442no—
836C4—442no—
837C4—442no—
838C4—442no—
839C4—442no—
840C4—442no—
841C4—881no—
842C2C4×#6693911yescharacteristic
843C2#1307117511yescharacteristic
844C2#1307136611yescharacteristic
845C2#1307165611yescharacteristic
846C2#1307167411yescharacteristic
847C2#1307169711yescharacteristic
848C2#1307172011yescharacteristic
849C2#1307209111yescharacteristic
850C2#1307213911yescharacteristic
851C2#1307275511yescharacteristic
852C2#1307284511yescharacteristic
853C2#1307315111yescharacteristic
854C2#1307348311yescharacteristic
855C2#1307393911yescharacteristic
856C2#1307408711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1436D11
hypocenterC11#14179
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
53. #10622274C4semidirect
671. C11#14179semidirect

Maximal subgroups

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

subgroupindex
C2×#106222742
C2×#106225912
C2×C4⋊C4×Dic112
#130668832
#130668722
#130668512
#130668502
#130668462
#130668402
C4×C11⋊#952
C11×#14362
#1417911