Finite Group Databasebeta

← #14677202

Subgroups — #14677202

Order 2816.

1506 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622259C211yesmaximal, characteristic
2C2×#10622259C211yesmaximal, characteristic
3C2×#10622259C211yesmaximal, characteristic
4C2×C4×Dic11⋊C4C211yesmaximal, characteristic
5C2×#10622262C211yesmaximal, characteristic
6#13066878C211yesmaximal, characteristic
7#13066876C211yesmaximal, characteristic
8#13066874C211yesmaximal, characteristic
9#13066871C211yesmaximal, characteristic
10#13066851C211yesmaximal, characteristic
11#13066849C211yesmaximal, characteristic
12Dic11⋊#95C211yesmaximal, characteristic
13Dic11⋊#95C211yesmaximal, characteristic
14#13066842C211yesmaximal, characteristic
15C11×#1434C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×Dic11⋊C4C2211yescharacteristic
19C22×Dic11⋊C4C2211yescharacteristic
20C22×Dic11⋊C4C2211yescharacteristic
21C22×Dic11⋊C4C2211yescharacteristic
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
51C4×Dic11⋊C4—24no—
52#10622262—24no—
53#10622259—24no—
54#10622259—24no—
55#10622259C418yescomplemented
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C22×Dic22—22no—
72C22×Dic22—22no—
73C22×Dic22—22no—
74C22×Dic22—22no—
75C22×Dic22—22no—
76C22×Dic22—22no—
77C22×Dic22C2×C414yes—
78C2×C42×C11—22no—
79C2×C42×C11—22no—
80C2×C42×C11—41no—
81C2×Dic11⋊C4—22no—
82C2×Dic11⋊C4—22no—
83C2×Dic11⋊C4—22no—
84C2×Dic11⋊C4—22no—
85C2×Dic11⋊C4—22no—
86C2×Dic11⋊C4—22no—
87C2×Dic11⋊C4—22no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—22no—
92C2×Dic11⋊C4—22no—
93C2×Dic11⋊C4C2×C414yes—
94C2×Dic11⋊C4D414yes—
95C2×Dic11⋊C4Q814yescomplemented
96C2×C4×Dic11—22no—
97C2×C4×Dic11—22no—
98C2×C4×Dic11—22no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11—22no—
101C2×C4×Dic11—22no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11—22no—
104C2×C4×Dic11—22no—
105C2×C4×Dic11—41no—
106C2×C4×Dic11C2×C414yes—
107C2×C4×Dic11D414yes—
108C11×#95—22no—
109C11×#95—22no—
110C11×#95—22no—
111C11×#95—22no—
112C11×#95—41no—
113C11×#95C2×C414yes—
114C11⋊#95—22no—
115C11⋊#95—22no—
116C11⋊#95—22no—
117C11⋊#95—22no—
118C11⋊#95—22no—
119C11⋊#95—22no—
120C11⋊#95—22no—
121C11⋊#95—22no—
122C11⋊#95—22no—
123C11⋊#95—22no—
124C11⋊#95—22no—
125C11⋊#95—22no—
126C11⋊#95—41no—
127C11⋊#95—41no—
128C11⋊#95—41no—
129C11⋊#95C2×C414yes—
130C11⋊#95C2×C414yes—
131C11⋊#95C2×C414yes—
132#14021—111nomaximal, Sylow
133C24×C11C2411yescharacteristic
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×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×C11C22×C412yes—
176C22×C4×C11C22×C412yes—
177C22×C4×C11C22×C412yes—
178C22×C4×C11C2×D412yes—
179C22×C4×C11C2×D412yes—
180C22×C4×C11C2×Q812yes—
181C22×C4×C11#4112yes—
182C22×C4×C11#4112yes—
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×D412yes—
229C22×Dic11C2×D412yes—
230C22×Dic11C2×D412yes—
231C22×Dic11C2×D412yes—
232C22×Dic11C2×Q812yes—
233C22×Dic11C2×Q812yes—
234C22×Dic11#4112yes—
235C22×Dic11#4112yes—
236C22×Dic11#4112yes—
237C22×Dic11#4112yes—
238C22×Dic11#4112yes—
239C2×Dic22—28no—
240C2×Dic22—28no—
241C2×Dic22—28no—
242C2×Dic22—44no—
243C2×Dic22—44no—
244C2×Dic22—44no—
245C2×Dic22—44no—
246C42×C11—44no—
247Dic11⋊C4—28no—
248Dic11⋊C4—28no—
249Dic11⋊C4—28no—
250Dic11⋊C4—28no—
251Dic11⋊C4—44no—
252C4×Dic11—28no—
253C4×Dic11—28no—
254C4×Dic11—44no—
255C4×Dic11—44no—
256C2×#391—111no—
257C2×#391—111no—
258C2×#391—111no—
259C2×C4×C4⋊C4—111no—
260C2×C4×C4⋊C4—111no—
261#1443—111no—
262#1443—111no—
263#1442—111no—
264#1442—111no—
265#1436—111no—
266#1436—111no—
267C4⋊#95—111no—
268C4⋊#95—111no—
269#1434—111no—
270#1434D1111yescharacteristic
271C23×C11C23×C411yescharacteristic
272C23×C11C22×D411yescharacteristic
273C23×C11C22×D411yescharacteristic
274C23×C11C22×Q811yescharacteristic
275C23×C11C2×#4111yescharacteristic
276C23×C11C2×#4111yescharacteristic
277C23×C11C2×#4111yescharacteristic
278C23×C11C2×#4111yescharacteristic
279C23×C11C2×#4111yescharacteristic
280C23×C11C2×#4111yescharacteristic
281C23×C11C2×#4111yescharacteristic
282C23×C11H(5,𝔽2)11yescharacteristic
283C23×C112−1+411yescharacteristic
284C23×C112−1+411yescharacteristic
285C23×C112−1+411yescharacteristic
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—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
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×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11C22⋊Q814yes—
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—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
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—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11#11714yes—
384C2×Dic11C4×D414yes—
385C2×Dic11C4×D414yes—
386C2×Dic11C4×Q814yes—
387C2×Dic11#12114yes—
388C2×Dic11#12314yes—
389C2×Dic11#12414yes—
390C2×Dic11#12614yes—
391Dic22—416no—
392C23×Q8—111no—
393C22×C4⋊C4—111no—
394C22×C4⋊C4—111no—
395C22×C4⋊C4—111no—
396C22×C4⋊C4—111no—
397C22×C4⋊C4—111no—
398C22×C42—111no—
399C22×C42—111no—
400C22×C42—111no—
401C22×C42—111no—
402C22×C42C2×D1111yescharacteristic
403#391—118no—
404#391—224no—
405#391—224no—
406C4×C4⋊C4—224no—
407C4×C4⋊C4—224no—
408C2×#95—111no—
409C2×#95—111no—
410C2×#95—111no—
411C2×#95—111no—
412C2×#95—111no—
413C2×#95—111no—
414C2×#95—111no—
415C2×#95—111no—
416C2×#95—111no—
417C2×#95—111no—
418C2×#95—111no—
419C2×#95—111no—
420C2×#95—111no—
421C2×#95—111no—
422C2×#95—111no—
423C2×#95—111no—
424C2×#95—111no—
425C2×#95—111no—
426C2×#95C2×D1111yescharacteristic
427C2×#95C2×D1111yescharacteristic
428C2×#95C2×D1111yescharacteristic
429C2×#95C2×D1111yescharacteristic
430C2×#95C2×D1111yescharacteristic
431C2×#95C2×D1111yescharacteristic
432C22×C11C2×#11711yescharacteristic
433C22×C11C2×C4×D411yescharacteristic
434C22×C11C2×C4×D411yescharacteristic
435C22×C11C2×C4×Q811yescharacteristic
436C22×C11C4×#4111yescharacteristic
437C22×C11#51911yescharacteristic
438C22×C11#52011yescharacteristic
439C22×C11C2×#12111yescharacteristic
440C22×C11C2×C22⋊Q811yescharacteristic
441C22×C11C2×#12311yescharacteristic
442C22×C11#52511yescharacteristic
443C22×C11C2×#12411yescharacteristic
444C22×C11C2×#12611yescharacteristic
445C22×C11#52911yescharacteristic
446C22×C11#53311yescharacteristic
447C22×C11#53611yescharacteristic
448C22×C11#53711yescharacteristic
449C22×C11#54111yescharacteristic
450C22×C11#54211yescharacteristic
451C22×C11#54611yescharacteristic
452C22×C11#54711yescharacteristic
453C22×C11#54811yescharacteristic
454C22×C11D4×Q811yescharacteristic
455C22×C11#55211yescharacteristic
456C22×C11#55211yescharacteristic
457C22×C11#55411yescharacteristic
458C22×C11#55611yescharacteristic
459C22×C11#55611yescharacteristic
460C22×C11#55611yescharacteristic
461C22×C11#55611yescharacteristic
462C22×C11#55611yescharacteristic
463C22×C11#55711yescharacteristic
464C22×C11#55711yescharacteristic
465C22×C11#55911yescharacteristic
466C22×C11#55911yescharacteristic
467C4×C11—24no—
468C4×C11—42no—
469C4×C11—42no—
470C4×C11—42no—
471C4×C11—42no—
472C4×C11—42no—
473C4×C11—81no—
474Dic11—24no—
475Dic11—42no—
476Dic11—42no—
477Dic11—42no—
478Dic11—42no—
479Dic11—42no—
480Dic11—81no—
481Dic11#38818yes—
482C22×Q8—114no—
483C22×Q8—222no—
484C22×Q8—222no—
485C22×Q8—222no—
486C22×Q8—222no—
487C22×Q8—222no—
488C22×Q8—222no—
489C23×C4—111no—
490C23×C4—111no—
491C23×C4—111no—
492C23×C4—111no—
493C23×C4—111no—
494C23×C4—111no—
495C23×C4—111no—
496C23×C4—111no—
497C23×C4C22×D1111yescharacteristic
498C23×C4C22×D1111yescharacteristic
499C23×C4C22×D1111yescharacteristic
500C23×C4C22×D1111yescharacteristic
501C23×C4C22×D1111yescharacteristic
502C23×C4C22×D1111yescharacteristic
503C23×C4C22×D1111yescharacteristic
504C2×C4⋊C4—114no—
505C2×C4⋊C4—114no—
506C2×C4⋊C4—114no—
507C2×C4⋊C4—222no—
508C2×C4⋊C4—222no—
509C2×C4⋊C4—222no—
510C2×C4⋊C4—222no—
511C2×C4⋊C4—222no—
512C2×C4⋊C4—222no—
513C2×C4⋊C4—222no—
514C2×C4⋊C4—222no—
515C2×C4⋊C4—222no—
516C2×C4⋊C4—222no—
517C2×C4⋊C4—222no—
518C2×C4⋊C4—222no—
519C2×C42—22no—
520C2×C42—22no—
521C2×C42—41no—
522C2×C42—114no—
523C2×C42—114no—
524C2×C42—222no—
525C2×C42—222no—
526C2×C42—222no—
527C2×C42—222no—
528C2×C42—222no—
529C2×C42—222no—
530C2×C42—222no—
531C2×C42—222no—
532C2×C42—222no—
533C2×C42—441no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—41no—
539#95—114no—
540#95—114no—
541#95—114no—
542#95—222no—
543#95—222no—
544#95—222no—
545#95—222no—
546#95—222no—
547#95—222no—
548#95—222no—
549#95—222no—
550#95—222no—
551#95—222no—
552#95—222no—
553#95—222no—
554#95—441no—
555#95—441no—
556#95—441no—
557#95C4×D1114yes—
558C2×C11C2×#38811yescharacteristic
559C2×C11C4×C22⋊Q811yescharacteristic
560C2×C11#232311yescharacteristic
561C2×C11#235511yescharacteristic
562C2×C11#235611yescharacteristic
563C2×C11#236511yescharacteristic
564C2×C11#236711yescharacteristic
565C2×C11#241511yescharacteristic
566C2×C11#241711yescharacteristic
567C2×C11#244611yescharacteristic
568C2×C11#244711yescharacteristic
569C2×C11#251111yescharacteristic
570C2×C11#251411yescharacteristic
571C2×C11#256811yescharacteristic
572C2×C11#259211yescharacteristic
573C24C23×D1111yescharacteristic
574C2×Q8—228no—
575C2×Q8—228no—
576C2×Q8—228no—
577C2×Q8—444no—
578C2×Q8—444no—
579C2×Q8—444no—
580C2×Q8—444no—
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—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—112no—
623C22×C4—112no—
624C22×C4—112no—
625C22×C4—112no—
626C22×C4—112no—
627C22×C4—112no—
628C22×C4—112no—
629C22×C4—112no—
630C22×C4—112no—
631C22×C4—112no—
632C22×C4—112no—
633C22×C4—112no—
634C22×C4—112no—
635C22×C4—112no—
636C22×C4—112no—
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×C4—221no—
649C22×C4—221no—
650C22×C4—221no—
651C22×C4—221no—
652C22×C4—221no—
653C22×C4—221no—
654C22×C4—221no—
655C22×C4—221no—
656C22×C4—221no—
657C22×C4—221no—
658C22×C4—221no—
659C22×C4—221no—
660C22×C4—221no—
661C22×C4—221no—
662C22×C4—221no—
663C22×C4—221no—
664C22×C4—221no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—221no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—221no—
677C22×C4—221no—
678C22×C4C2×C4×D1112yes—
679C22×C4C2×C4×D1112yes—
680C22×C4C2×C4×D1112yes—
681C22×C4#433912yes—
682C22×C4#433912yes—
683C22×C4D4×D1112yes—
684C22×C4D4×D1112yes—
685C22×C4Q8×D1112yes—
686C4⋊C4—228no—
687C4⋊C4—228no—
688C4⋊C4—228no—
689C4⋊C4—228no—
690C4⋊C4—444no—
691C42—44no—
692C42—228no—
693C42—228no—
694C42—444no—
695C42—444no—
696C11#1402111yescharacteristic, complemented, Sylow
697C23C22×C4×D1111yescharacteristic
698C23C2×#433911yescharacteristic
699C23C2×#433911yescharacteristic
700C23C2×D4×D1111yescharacteristic
701C23C2×D4×D1111yescharacteristic
702C23#6703711yescharacteristic
703C23C2×Q8×D1111yescharacteristic
704C23#41×D1111yescharacteristic
705C23#41×D1111yescharacteristic
706C23#41×D1111yescharacteristic
707C23#41×D1111yescharacteristic
708C23#41×D1111yescharacteristic
709C23#6704311yescharacteristic
710C23#6704311yescharacteristic
711C23#6704311yescharacteristic
712Q8—4416no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—114no—
762C2×C4—114no—
763C2×C4—114no—
764C2×C4—114no—
765C2×C4—114no—
766C2×C4—114no—
767C2×C4—114no—
768C2×C4—114no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—222no—
783C2×C4—222no—
784C2×C4—222no—
785C2×C4—222no—
786C2×C4—222no—
787C2×C4—222no—
788C2×C4—222no—
789C2×C4—222no—
790C2×C4—441no—
791C2×C4—441no—
792C2×C4—441no—
793C2×C4—441no—
794C2×C4—441no—
795C2×C4—441no—
796C2×C4—441no—
797C2×C4—441no—
798C2×C4—441no—
799C2×C4—441no—
800C2×C4—441no—
801C2×C4—441no—
802C2×C4—441no—
803C2×C4—441no—
804C2×C4—441no—
805C2×C4—441no—
806C2×C4—441no—
807C2×C4—441no—
808C2×C4—441no—
809C2×C4—441no—
810C2×C4—441no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—441no—
814C2×C4—441no—
815C2×C4—441no—
816C2×C4—441no—
817C2×C4#6694914yes—
818C22C4×#433911yescharacteristic
819C22#1062302111yescharacteristic
820C22C2×#6694911yescharacteristic
821C22#1062304711yescharacteristic
822C22D11×#11711yescharacteristic
823C22#1062305911yescharacteristic
824C22#1062306211yescharacteristic
825C22#1062306211yescharacteristic
826C22#1062306411yescharacteristic
827C22#1062306411yescharacteristic
828C22#1062306411yescharacteristic
829C22C4×D4×D1111yescharacteristic
830C22C4×D4×D1111yescharacteristic
831C22#1062307711yescharacteristic
832C22#1062307811yescharacteristic
833C22#1062308311yescharacteristic
834C22#1062309011yescharacteristic
835C22C4×Q8×D1111yescharacteristic
836C22#1062310911yescharacteristic
837C22#1062312811yescharacteristic
838C22D11×#12111yescharacteristic
839C22#1062316311yescharacteristic
840C22#1062316711yescharacteristic
841C22D11×#12311yescharacteristic
842C22#1062318611yescharacteristic
843C22#1062319311yescharacteristic
844C22#1062319511yescharacteristic
845C22D11×#12411yescharacteristic
846C22#1062320611yescharacteristic
847C22#1062321611yescharacteristic
848C22#1062321611yescharacteristic
849C22#1062323211yescharacteristic
850C22#1062323311yescharacteristic
851C22#1062323311yescharacteristic
852C22D11×#12611yescharacteristic
853C4—24no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—81no—
860C4—118no—
861C4—224no—
862C4—442no—
863C4—442no—
864C4—442no—
865C4—442no—
866C4—442no—
867C4—881no—
868C2D11×#38811yescharacteristic
869C2C4×#6694911yescharacteristic
870C2#1307129111yescharacteristic
871C2#1307157011yescharacteristic
872C2#1307158211yescharacteristic
873C2#1307167111yescharacteristic
874C2#1307168811yescharacteristic
875C2#1307204211yescharacteristic
876C2#1307206611yescharacteristic
877C2#1307238911yescharacteristic
878C2#1307240211yescharacteristic
879C2#1307318811yescharacteristic
880C2#1307322311yescharacteristic
881C2#1307382911yescharacteristic
882C2#1307410211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1434D11
hypocenterC11#14021
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
55. #10622259C4semidirect
95. C2×Dic11⋊C4Q8semidirect
696. C11#14021semidirect

Maximal subgroups

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

subgroupindex
C2×#106222592
C2×C4×Dic11⋊C42
C2×#106222622
#130668782
#130668762
#130668742
#130668712
#130668512
#130668492
Dic11⋊#952
#130668422
C11×#14342
#1402111