Finite Group Databasebeta

← #14677589

Subgroups — #14677589

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
1C2×#10622843C212yesmaximal
2C2×#10622598C211yesmaximal, characteristic
3C2×C4⋊C4×Dic11C211yesmaximal, characteristic
4#13066887C212yesmaximal
5#13066869C212yesmaximal
6#13066848C212yesmaximal
7#13066846C211yesmaximal, characteristic
8#13066845C211yesmaximal, characteristic
9#13066845C211yesmaximal, characteristic
10C4×C11⋊#95C211yesmaximal, characteristic
11C22×C11×C4⋊Q8C211yesmaximal, characteristic
12C23×Q8×C11C2212yes—
13C2×C11×C4⋊Q8—24no—
14C2×C11×C4⋊Q8—24no—
15C2×C11×C4⋊Q8C418yescomplemented
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2212yes—
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2212yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2212yes—
25C22×C4×Dic11C2211yescharacteristic
26#10622843—28no—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
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—
40C4⋊C4×Dic11—24no—
41C22×Q8×C11—24no—
42C22×Q8×C11—24no—
43C22×Q8×C11—24no—
44C22×Q8×C11—24no—
45C22×Q8×C11—42no—
46C22×Q8×C11—42no—
47C22×Q8×C11C2×C418yes—
48C23×C4×C11C2312yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×Dic11C2312yes—
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2312yes—
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2311yescharacteristic
59C11×C4⋊Q8—232no—
60C2×C11×C4⋊C4—24no—
61C2×C11×C4⋊C4—24no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4C2×C414yes—
65C2×C11×C4⋊C4C2×C418yes—
66C2×C11×C4⋊C4C2×C414yes—
67C2×C11×C4⋊C4D414yes—
68C2×C11×C4⋊C4D414yes—
69C2×C42×C11—22no—
70C2×C42×C11—22no—
71C2×C42×C11C2×C414yes—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—24no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—24no—
79C2×C4⋊Dic11—42no—
80C2×C4⋊Dic11Q814yescomplemented
81C2×C4×Dic11—22no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—24no—
84C2×C4×Dic11—22no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—24no—
88C2×C4×Dic11—42no—
89C2×C4×Dic11Q814yescomplemented
90C11⋊#95—24no—
91C11⋊#95—24no—
92C11⋊#95—24no—
93C11⋊#95—22no—
94C11⋊#95—22no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95—42no—
99C11⋊#95—42no—
100C11⋊#95D414yes—
101C11⋊#95Q814yescomplemented
102#14053—111nomaximal, Sylow
103C24×C11C2411yescharacteristic
104C2×Q8×C11—216no—
105C2×Q8×C11—216no—
106C2×Q8×C11—48no—
107C2×Q8×C11—48no—
108C2×Q8×C11—48no—
109C2×Q8×C11—48no—
110C2×Q8×C11—48no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11C22×C414yes—
130C22×C4×C11C22×C414yes—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C2×D414yes—
135C22×C4×C11C2×D414yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×Q812yes—
140C22×C4×C11C2×Q812yes—
141C22×C4×C11C2×Q812yes—
142C22×C4×C11#4112yes—
143C22×C4×C11#4112yes—
144C22×C4×C11#4112yes—
145C22×C4×C11#4112yes—
146C22×Dic11—21no—
147C22×Dic11—22no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—22no—
151C22×Dic11—21no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—22no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—22no—
173C22×Dic11—21no—
174C22×Dic11—22no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—22no—
179C22×Dic11—21no—
180C22×Dic11—22no—
181C22×Dic11C2×D412yes—
182C22×Dic11C2×D412yes—
183C22×Dic11C2×Q812yes—
184C22×Dic11C2×Q812yes—
185C22×Dic11C2×Q814yes—
186C22×Dic11C2×Q812yes—
187C22×Dic11C2×Q812yes—
188C11×C4⋊C4—216no—
189C11×C4⋊C4—28no—
190C11×C4⋊C4C22⋊C4116yes—
191C42×C11—28no—
192C4⋊Dic11—28no—
193C4⋊Dic11—48no—
194C4⋊Dic11—44no—
195C4×Dic11—28no—
196C4×Dic11—48no—
197C4×Dic11—44no—
198C22×C4⋊Q8D1111yescharacteristic
199C2×#391—112no—
200C2×#389—111no—
201C2×C4×C4⋊C4—111no—
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
224Q8×C11—432no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11C2×C22⋊C418yes—
251C2×C4×C11C2×C22⋊C414yes—
252C2×C4×C11C4×D414yes—
253C2×C4×C11C4×Q814yes—
254C2×C4×C11C4×Q814yes—
255C2×C4×C11C4×Q814yes—
256C2×C4×C11C22⋊Q814yes—
257C2×C4×C11C22⋊Q814yes—
258C2×C4×C11#12414yes—
259C2×C4×C11C4⋊Q814yes—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—24no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—24no—
275C2×Dic11—22no—
276C2×Dic11—24no—
277C2×Dic11—22no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—42no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—42no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—42no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297C2×Dic11—42no—
298C2×Dic11—42no—
299C2×Dic11—42no—
300C2×Dic11—42no—
301C2×Dic11C4⋊Q814yescomplemented
302C23×Q8C2×D1112yes—
303C2×C4⋊Q8—24no—
304C2×C4⋊Q8—24no—
305C2×C4⋊Q8Dic1118yescomplemented
306C22×C4⋊C4—111no—
307C22×C4⋊C4—111no—
308C22×C4⋊C4—112no—
309C22×C4⋊C4C2×D1111yescharacteristic
310C22×C4⋊C4C2×D1112yes—
311C22×C4⋊C4C2×D1111yescharacteristic
312C22×C42—111no—
313C22×C42—111no—
314C22×C42—112no—
315C22×C42C2×D1111yescharacteristic
316#391—228no—
317#389—224no—
318C4×C4⋊C4—224no—
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×#95—112no—
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—24no—
369C4×C11—44no—
370C4×C11#39118yescomplemented
371Dic11—24no—
372Dic11—42no—
373Dic11—44no—
374Dic11—42no—
375Dic11—42no—
376Dic11—82no—
377C22×Q8—24no—
378C22×Q8—24no—
379C22×Q8—24no—
380C22×Q8—24no—
381C22×Q8—42no—
382C22×Q8—42no—
383C22×Q8C2×Dic1118yes—
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—232no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—114no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4—222no—
403C2×C4⋊C4—224no—
404C2×C4⋊C4—222no—
405C2×C4⋊C4—222no—
406C2×C4⋊C4—224no—
407C2×C4⋊C4—222no—
408C2×C4⋊C4—442no—
409C2×C4⋊C4C2×Dic1114yes—
410C2×C4⋊C4C2×Dic1118yes—
411C2×C4⋊C4C2×Dic1114yes—
412C2×C4⋊C4C22⋊D1114yes—
413C2×C4⋊C4C22⋊D1114yes—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—114no—
417C2×C42—222no—
418C2×C42—222no—
419C2×C42—224no—
420C2×C42—222no—
421C2×C42—222no—
422C2×C42—224no—
423C2×C42—222no—
424C2×C42—442no—
425C2×C42C2×Dic1114yes—
426#95—114no—
427#95—114no—
428#95—224no—
429#95—224no—
430#95—224no—
431#95—222no—
432#95—222no—
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—216no—
455C2×Q8—216no—
456C2×Q8—48no—
457C2×Q8—48no—
458C2×Q8—48no—
459C2×Q8—48no—
460C2×Q8—48no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—112no—
480C22×C4—112no—
481C22×C4—112no—
482C22×C4—112no—
483C22×C4—112no—
484C22×C4—112no—
485C22×C4—114no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—222no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—222no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—222no—
500C22×C4—221no—
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—221no—
512C22×C4—222no—
513C22×C4—221no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—222no—
518C22×C4—222no—
519C22×C4—222no—
520C22×C4—222no—
521C22×C4D4×D1112yes—
522C22×C4#434112yes—
523C22×C4Q8×D1112yes—
524C22×C4Q8×D1112yes—
525C22×C4Q8×D1112yes—
526C22×C4#434312yes—
527C22×C4#434312yes—
528C22×C4#434312yes—
529C22×C4C22×Dic1114yes—
530C22×C4C22×Dic1112yes—
531C22×C4C22×Dic1112yes—
532C22×C4C22×Dic1114yes—
533C22×C4C22×Dic1112yes—
534C22×C4C2×C22⋊D1114yes—
535C22×C4C2×C22⋊D1114yes—
536C22×C4C2×C22⋊D1112yes—
537C22×C4C2×C22⋊D1112yes—
538C4⋊C4—216no—
539C4⋊C4—28no—
540C4⋊C4—228no—
541C4⋊C4—448no—
542C4⋊C4—444no—
543C4⋊C4C22⋊Dic11116yes—
544C42—28no—
545C42—228no—
546C42—448no—
547C42—444no—
548C11#1405311yescharacteristic, complemented, Sylow
549C23C2×D4×D1111yescharacteristic
550C23C2×#434111yescharacteristic
551C23#6703711yescharacteristic
552C23#6703711yescharacteristic
553C23C2×Q8×D1111yescharacteristic
554C23C2×Q8×D1111yescharacteristic
555C23C2×Q8×D1111yescharacteristic
556C23C2×#434311yescharacteristic
557C23C2×#434311yescharacteristic
558C23C2×#434311yescharacteristic
559C23#6704011yescharacteristic
560C23#6704011yescharacteristic
561C23C23×Dic1111yescharacteristic
562C23C22×C22⋊D1111yescharacteristic
563C23C22×C22⋊D1111yescharacteristic
564Q8—432no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—114no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—224no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—224no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—224no—
608C2×C4—222no—
609C2×C4—442no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—442no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—442no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—442no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—442no—
626C2×C4—442no—
627C2×C4—442no—
628C2×C4—442no—
629C2×C4—442no—
630C2×C4—442no—
631C2×C4—442no—
632C2×C4D4×Dic1114yes—
633C2×C4#6699714yes—
634C2×C4Q8×Dic1114yes—
635C2×C4Q8×Dic1114yes—
636C2×C4Q8×Dic1114yes—
637C2×C4#6699914yes—
638C2×C4#6699914yes—
639C2×C4#6700014yes—
640C2×C4C2×C22⋊Dic1118yes—
641C2×C4C2×C22⋊Dic1114yes—
642C22#1062325211yescharacteristic
643C22#1062325311yescharacteristic
644C22D11×C4⋊Q811yescharacteristic
645C22#1062325611yescharacteristic
646C22#1062325711yescharacteristic
647C22#1062325811yescharacteristic
648C22#1062325911yescharacteristic
649C22#1062325911yescharacteristic
650C22#1062326011yescharacteristic
651C22#1062326011yescharacteristic
652C22#1062326111yescharacteristic
653C22#1062326111yescharacteristic
654C22#1062326311yescharacteristic
655C22#1062326411yescharacteristic
656C22#1062326411yescharacteristic
657C22#1062326511yescharacteristic
658C22C2×D4×Dic1111yescharacteristic
659C22#1062332911yescharacteristic
660C22D4×C22⋊D1111yescharacteristic
661C22D4×C22⋊D1111yescharacteristic
662C22#1062333711yescharacteristic
663C22#1062333711yescharacteristic
664C22C2×#6699711yescharacteristic
665C22C2×Q8×Dic1111yescharacteristic
666C22C2×Q8×Dic1111yescharacteristic
667C22C2×Q8×Dic1111yescharacteristic
668C22#1062334311yescharacteristic
669C22C2×#6699911yescharacteristic
670C22C2×#6699911yescharacteristic
671C22C2×#6700011yescharacteristic
672C22Q8×C22⋊D1111yescharacteristic
673C22Q8×C22⋊D1111yescharacteristic
674C22#1062334811yescharacteristic
675C22#1062334811yescharacteristic
676C22C22×C22⋊Dic1111yescharacteristic
677C4—24no—
678C4—28no—
679C4—24no—
680C4—44no—
681C4—224no—
682C4—444no—
683C4—442no—
684C4—442no—
685C4—442no—
686C4—882no—
687C4#1062284318yescomplemented
688C2C2×#1062284311yescharacteristic
689C2C4⋊Q8×Dic1111yescharacteristic
690C2#1307136511yescharacteristic
691C2D4×C22⋊Dic1111yescharacteristic
692C2Q8×C22⋊Dic1111yescharacteristic
693C2#1307167611yescharacteristic
694C2#1307170611yescharacteristic
695C2#1307230311yescharacteristic
696C2#1307231411yescharacteristic
697C2#1307245111yescharacteristic
698C2#1307246211yescharacteristic
699C2#1307298211yescharacteristic
700C2#1307299311yescharacteristic
701C2#1307363311yescharacteristic
702C2#1307364311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×C4⋊Q8C2
socle, prime radical, cosocleC24×C11C24
hypercenterC22×C4⋊Q8D11
hypocenterC11#14053
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
15. C2×C11×C4⋊Q8C4semidirect
80. C2×C4⋊Dic11Q8semidirect
89. C2×C4×Dic11Q8semidirect
101. C11⋊#95Q8semidirect
301. C2×Dic11C4⋊Q8semidirect
305. C2×C4⋊Q8Dic11semidirect
370. C4×C11#391semidirect
548. C11#14053semidirect
687. C4#10622843semidirect

Maximal subgroups

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

subgroupindex
C2×#106228432
C2×#106225982
C2×C4⋊C4×Dic112
#130668872
#130668692
#130668482
#130668462
#130668452
C4×C11⋊#952
C22×C11×C4⋊Q82
#1405311