Finite Group Databasebeta

← #14677581

Subgroups — #14677581

Order 2816.

1838 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66941C211yesmaximal, characteristic
2C2×#10622542C212yesmaximal
3C2×#10622598C211yesmaximal, characteristic
4#13066886C212yesmaximal
5#13066870C212yesmaximal
6#13066849C212yesmaximal
7#13066846C211yesmaximal, characteristic
8#13066845C211yesmaximal, characteristic
9#13066845C211yesmaximal, characteristic
10C4×C11⋊#95C211yesmaximal, characteristic
11C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
12C23×Dic22C2212yes—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2212yes—
16C22×C42×C11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C2×#66941—24no—
24C2×#66941—24no—
25C2×#66941C418yescomplemented
26C4×C11×C4⋊C4—24no—
27C2×C11×#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39#10622598—24no—
40#10622542—28no—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2311yescharacteristic
52C22×Dic22—24no—
53C22×Dic22—24no—
54C22×Dic22—24no—
55C22×Dic22—24no—
56C22×Dic22—42no—
57C22×Dic22—42no—
58C22×Dic22C2×C418yes—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4C2×C414yes—
62C2×C11×C4⋊C4D414yes—
63C2×C11×C4⋊C4D414yes—
64C2×C11×C4⋊C4Q814yescomplemented
65C2×C42×C11—22no—
66C2×C42×C11—22no—
67C2×C42×C11—24no—
68C2×C42×C11—24no—
69C2×C42×C11—42no—
70C2×C42×C11Q814yescomplemented
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—24no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—24no—
78C2×C4⋊Dic11—42no—
79C2×C4⋊Dic11C2×C414yes—
80C2×Dic11⋊C4—24no—
81C2×Dic11⋊C4—24no—
82C2×Dic11⋊C4C2×C418yes—
83C2×C4×Dic11—22no—
84C2×C4×Dic11—22no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—22no—
88C2×C4×Dic11C2×C414yes—
89#66941—232no—
90C11×#95—24no—
91C11⋊#95—24no—
92C11⋊#95—24no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—22no—
96C11⋊#95—22no—
97C11⋊#95—24no—
98C11⋊#95—42no—
99C11⋊#95—42no—
100C11⋊#95D414yes—
101C11⋊#95Q814yescomplemented
102#14053—111nomaximal, Sylow
103C24×C11C2411yescharacteristic
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11C22×C414yes—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C2×D414yes—
127C22×C4×C11C2×D414yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×Q812yes—
132C22×C4×C11C2×Q814yes—
133C22×C4×C11C2×Q812yes—
134C22×C4×C11C2×Q812yes—
135C22×C4×C11C2×Q812yes—
136C22×C4×C11C2×Q812yes—
137C22×C4×C11#4112yes—
138C22×C4×C11#4112yes—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—22no—
145C22×Dic11—21no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—21no—
166C22×Dic11—22no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—22no—
172C22×Dic11C22×C414yes—
173C22×Dic11C22×C412yes—
174C22×Dic11C22×C412yes—
175C22×Dic11C2×D412yes—
176C22×Dic11C2×D412yes—
177C22×Dic11C2×Q812yes—
178C22×Dic11C2×Q812yes—
179C22×Dic11#4112yes—
180C22×Dic11#4112yes—
181C2×Dic22—216no—
182C2×Dic22—216no—
183C2×Dic22—48no—
184C2×Dic22—48no—
185C2×Dic22—48no—
186C2×Dic22—48no—
187C2×Dic22—48no—
188C11×C4⋊C4—28no—
189C11×C4⋊C4C22⋊C4116yes—
190C42×C11—28no—
191C42×C11—48no—
192C4⋊Dic11—28no—
193C4⋊Dic11—48no—
194C4⋊Dic11—44no—
195Dic11⋊C4—216no—
196C4×Dic11—28no—
197C4×Dic11—44no—
198C22×C4⋊Q8—111no—
199C2×#391—112no—
200C2×#389—111no—
201C2×C4×C4⋊C4D1111yescharacteristic
202#1446—112no—
203#1441—112no—
204#1436—112no—
205C4⋊#95—111no—
206C4⋊#95—111no—
207C4⋊#95—111no—
208C4×#95—111no—
209C23×C11C23×C411yescharacteristic
210C23×C11C22×D411yescharacteristic
211C23×C11C22×D411yescharacteristic
212C23×C11C22×D411yescharacteristic
213C23×C11C22×Q811yescharacteristic
214C23×C11C22×Q811yescharacteristic
215C23×C11C22×Q811yescharacteristic
216C23×C11C2×#4111yescharacteristic
217C23×C11C2×#4111yescharacteristic
218C23×C11C2×#4111yescharacteristic
219C23×C11C2×#4111yescharacteristic
220C23×C11H(5,𝔽2)11yescharacteristic
221C23×C11H(5,𝔽2)11yescharacteristic
222C23×C112−1+411yescharacteristic
223C23×C112−1+411yescharacteristic
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11C2×C22⋊C418yes—
251C2×C4×C11C2×C22⋊C414yes—
252C2×C4×C11C4×Q814yes—
253C2×C4×C11C4×Q814yes—
254C2×C4×C11C22⋊Q814yes—
255C2×C4×C11C22⋊Q814yes—
256C2×C4×C11#12414yes—
257C2×C4×C11C4⋊Q814yes—
258C2×C4×C11C4⋊Q814yescomplemented
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—42no—
293C2×Dic11—42no—
294C2×Dic11—42no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297C2×Dic11—42no—
298C2×Dic11—42no—
299C2×Dic11C4×D414yes—
300C2×Dic11C4×Q814yes—
301Dic22—432no—
302C23×Q8—112no—
303C2×C4⋊Q8—118no—
304C2×C4⋊Q8—224no—
305C2×C4⋊Q8—224no—
306C22×C4⋊C4—112no—
307C22×C4⋊C4—111no—
308C22×C4⋊C4—111no—
309C22×C4⋊C4—112no—
310C22×C4⋊C4C2×D1111yescharacteristic
311C22×C4⋊C4C2×D1111yescharacteristic
312C22×C42—111no—
313C22×C42—111no—
314C22×C42C2×D1112yes—
315C22×C42C2×D1111yescharacteristic
316#391—228no—
317#389—224no—
318C4×C4⋊C4—24no—
319C2×#95—111no—
320C2×#95—111no—
321C2×#95—111no—
322C2×#95—111no—
323C2×#95—112no—
324C2×#95—112no—
325C2×#95—112no—
326C2×#95—112no—
327C2×#95—112no—
328C2×#95—112no—
329C2×#95—112no—
330C2×#95C2×D1112yes—
331C22×C11C22×C22⋊C411yescharacteristic
332C22×C11C2×C4×D411yescharacteristic
333C22×C11C2×C4×Q811yescharacteristic
334C22×C11C2×C4×Q811yescharacteristic
335C22×C11C2×C4×Q811yescharacteristic
336C22×C11#51811yescharacteristic
337C22×C11#51911yescharacteristic
338C22×C11C2×C22⋊Q811yescharacteristic
339C22×C11C2×C22⋊Q811yescharacteristic
340C22×C11C2×#12411yescharacteristic
341C22×C11C2×C4⋊Q811yescharacteristic
342C22×C11C2×C4⋊Q811yescharacteristic
343C22×C11#53211yescharacteristic
344C22×C11#53311yescharacteristic
345C22×C11#53311yescharacteristic
346C22×C11#54211yescharacteristic
347C22×C11#54211yescharacteristic
348C22×C11#54411yescharacteristic
349C22×C11#54411yescharacteristic
350C22×C11D4211yescharacteristic
351C22×C11D4211yescharacteristic
352C22×C11#54611yescharacteristic
353C22×C11#54611yescharacteristic
354C22×C11#54711yescharacteristic
355C22×C11#54811yescharacteristic
356C22×C11#54811yescharacteristic
357C22×C11D4×Q811yescharacteristic
358C22×C11D4×Q811yescharacteristic
359C22×C11D4×Q811yescharacteristic
360C22×C11#55411yescharacteristic
361C22×C11#55411yescharacteristic
362C22×C11#55511yescharacteristic
363C22×C11#55611yescharacteristic
364C22×C11#55711yescharacteristic
365C22×C11Q8211yescharacteristic
366C4×C11—28no—
367C4×C11—24no—
368C4×C11—42no—
369C4×C11—44no—
370C4×C11#39118yescomplemented
371Dic11—24no—
372Dic11—24no—
373Dic11—44no—
374Dic11—42no—
375Dic11—42no—
376Dic11—82no—
377C22×Q8—118no—
378C22×Q8—224no—
379C22×Q8—224no—
380C22×Q8—224no—
381C22×Q8—224no—
382C22×Q8—442no—
383C22×Q8—442no—
384C23×C4—111no—
385C23×C4—111no—
386C23×C4—112no—
387C23×C4—111no—
388C23×C4—111no—
389C23×C4—112no—
390C23×C4C22×D1112yes—
391C23×C4C22×D1111yescharacteristic
392C23×C4C22×D1111yescharacteristic
393C23×C4C22×D1112yes—
394C23×C4C22×D1111yescharacteristic
395C4⋊Q8—2232no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—118no—
399C2×C4⋊C4—114no—
400C2×C4⋊C4—224no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4—224no—
403C2×C4⋊C4—222no—
404C2×C4⋊C4—224no—
405C2×C4⋊C4—224no—
406C2×C4⋊C4—222no—
407C2×C4⋊C4—222no—
408C2×C4⋊C4—222no—
409C2×C4⋊C4—442no—
410C2×C4⋊C4Dic2214yescomplemented
411C2×C4⋊C4C4×D1114yes—
412C2×C4⋊C4D4414yes—
413C2×C4⋊C4C22⋊D1114yes—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—24no—
417C2×C42—24no—
418C2×C42—42no—
419C2×C42—114no—
420C2×C42—222no—
421C2×C42—222no—
422C2×C42—222no—
423C2×C42—222no—
424C2×C42—222no—
425C2×C42Dic2214yescomplemented
426#95—24no—
427#95—114no—
428#95—114no—
429#95—222no—
430#95—224no—
431#95—222no—
432#95—224no—
433#95—224no—
434#95—224no—
435#95—224no—
436#95—442no—
437#95—442no—
438C2×C11C2×#39111yescharacteristic
439C2×C11C4×C4⋊Q811yescharacteristic
440C2×C11#233111yescharacteristic
441C2×C11D4×C22⋊C411yescharacteristic
442C2×C11Q8×C22⋊C411yescharacteristic
443C2×C11#236511yescharacteristic
444C2×C11#236911yescharacteristic
445C2×C11#243911yescharacteristic
446C2×C11#244011yescharacteristic
447C2×C11#245111yescharacteristic
448C2×C11#245211yescharacteristic
449C2×C11#249111yescharacteristic
450C2×C11#249211yescharacteristic
451C2×C11#255011yescharacteristic
452C2×C11#255111yescharacteristic
453C24C23×D1111yescharacteristic
454C2×Q8—2216no—
455C2×Q8—2216no—
456C2×Q8—448no—
457C2×Q8—448no—
458C2×Q8—448no—
459C2×Q8—448no—
460C2×Q8—448no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—112no—
482C22×C4—112no—
483C22×C4—112no—
484C22×C4—112no—
485C22×C4—112no—
486C22×C4—112no—
487C22×C4—114no—
488C22×C4—112no—
489C22×C4—112no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—222no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—222no—
506C22×C4—221no—
507C22×C4—222no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—222no—
518C22×C4—222no—
519C22×C4—222no—
520C22×C4—222no—
521C22×C4—222no—
522C22×C4—222no—
523C22×C4C2×Dic2212yes—
524C22×C4C2×Dic2214yes—
525C22×C4C2×Dic2212yes—
526C22×C4C2×Dic2212yes—
527C22×C4C2×Dic2212yes—
528C22×C4C2×C4×D1114yes—
529C22×C4C2×C4×D1112yes—
530C22×C4C2×D4414yes—
531C22×C4C2×D4412yes—
532C22×C4#433912yes—
533C22×C4#433912yes—
534C22×C4D4×D1112yes—
535C22×C4Q8×D1112yes—
536C22×C4C2×C22⋊D1114yes—
537C22×C4C2×C22⋊D1112yes—
538C4⋊C4—28no—
539C4⋊C4—2216no—
540C4⋊C4—228no—
541C4⋊C4—448no—
542C4⋊C4—444no—
543C4⋊C4(C2×D11)⋊C4116yes—
544C42—28no—
545C42—48no—
546C42—228no—
547C42—444no—
548C11#1405311yescharacteristic, complemented, Sylow
549C23C22×Dic2211yescharacteristic
550C23C22×Dic2211yescharacteristic
551C23C22×C4×D1111yescharacteristic
552C23C22×D4411yescharacteristic
553C23C2×#433911yescharacteristic
554C23C2×#433911yescharacteristic
555C23C2×D4×D1111yescharacteristic
556C23#6703711yescharacteristic
557C23C2×Q8×D1111yescharacteristic
558C23#6704011yescharacteristic
559C23#41×D1111yescharacteristic
560C23#41×D1111yescharacteristic
561C23#6704211yescharacteristic
562C23#6704311yescharacteristic
563C23C22×C22⋊D1111yescharacteristic
564Q8—4432no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—114no—
592C2×C4—114no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—224no—
608C2×C4—224no—
609C2×C4—224no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—442no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—442no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—442no—
627C2×C4—442no—
628C2×C4—442no—
629C2×C4—442no—
630C2×C4—442no—
631C2×C4—442no—
632C2×C4—442no—
633C2×C4C4×Dic2214yes—
634C2×C4C4×Dic2214yes—
635C2×C4#6692214yes—
636C2×C4#6692814yes—
637C2×C4#6694114yescomplemented
638C2×C4#6697714yes—
639C2×C4#6697714yes—
640C2×C4C2×(C2×D11)⋊C418yes—
641C2×C4C2×(C2×D11)⋊C414yes—
642C22C2×C4×Dic2211yescharacteristic
643C22C2×C4×Dic2211yescharacteristic
644C22C2×#6692211yescharacteristic
645C22C2×#6692811yescharacteristic
646C22C2×#6694111yescharacteristic
647C22#1062303111yescharacteristic
648C22#1062303811yescharacteristic
649C22#1062304211yescharacteristic
650C22#1062304811yescharacteristic
651C22#1062305011yescharacteristic
652C22#1062306311yescharacteristic
653C22#1062306411yescharacteristic
654C22D4×Dic2211yescharacteristic
655C22#1062307011yescharacteristic
656C22C4×D4×D1111yescharacteristic
657C22#1062307611yescharacteristic
658C22#1062307911yescharacteristic
659C22D4×D4411yescharacteristic
660C22#1062308511yescharacteristic
661C22#1062309211yescharacteristic
662C22Q8×Dic2211yescharacteristic
663C22#1062310011yescharacteristic
664C22C4×Q8×D1111yescharacteristic
665C22#1062310311yescharacteristic
666C22Q8×D4411yescharacteristic
667C22#1062310711yescharacteristic
668C22#1062310911yescharacteristic
669C22#1062311311yescharacteristic
670C22C2×#6697711yescharacteristic
671C22C2×#6697711yescharacteristic
672C22C22×(C2×D11)⋊C411yescharacteristic
673C22D4×C22⋊D1111yescharacteristic
674C22Q8×C22⋊D1111yescharacteristic
675C22#1062336011yescharacteristic
676C22#1062336211yescharacteristic
677C4—28no—
678C4—24no—
679C4—44no—
680C4—42no—
681C4—224no—
682C4—224no—
683C4—444no—
684C4—442no—
685C4—442no—
686C4—882no—
687C4#1062254218yescomplemented
688C2C2×#1062254211yescharacteristic
689C2C4×#6694111yescharacteristic
690C2#1307136011yescharacteristic
691C2D4×(C2×D11)⋊C411yescharacteristic
692C2Q8×(C2×D11)⋊C411yescharacteristic
693C2#1307167511yescharacteristic
694C2#1307170311yescharacteristic
695C2#1307230111yescharacteristic
696C2#1307231211yescharacteristic
697C2#1307244911yescharacteristic
698C2#1307246011yescharacteristic
699C2#1307297311yescharacteristic
700C2#1307298411yescharacteristic
701C2#1307363111yescharacteristic
702C2#1307364211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C4⋊C4C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#14053
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
25. C2×#66941C4semidirect
64. C2×C11×C4⋊C4Q8semidirect
70. C2×C42×C11Q8semidirect
101. C11⋊#95Q8semidirect
258. C2×C4×C11C4⋊Q8semidirect
370. C4×C11#391semidirect
410. C2×C4⋊C4Dic22semidirect
425. C2×C42Dic22semidirect
548. C11#14053semidirect
637. C2×C4#66941semidirect
687. C4#10622542semidirect

Maximal subgroups

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

subgroupindex
C22×#669412
C2×#106225422
C2×#106225982
#130668862
#130668702
#130668492
#130668462
#130668452
C4×C11⋊#952
C2×C4×C11×C4⋊C42
#1405311