Finite Group Databasebeta

← #14677162

Subgroups — #14677162

Order 2816.

1810 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic11C211yesmaximal, characteristic
2C2×#10622843C211yesmaximal, characteristic
3C2×#10622541C211yesmaximal, characteristic
4C2×C4×Dic11⋊C4C211yesmaximal, characteristic
5#13066880C212yesmaximal
6#13066872C212yesmaximal
7#13066847C212yesmaximal
8#13066847C212yesmaximal
9#13066845C211yesmaximal, characteristic
10#13066845C211yesmaximal, characteristic
11C2×C11×#391C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C2×Q8×Dic11—24no—
16C2×Q8×Dic11—24no—
17C2×Q8×Dic11—24no—
18C22×C4⋊Dic11C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×Dic11⋊C4C2211yescharacteristic
22C22×Dic11⋊C4C2212yes—
23C22×Dic11⋊C4C2211yescharacteristic
24C22×C4×Dic11C2212yes—
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C11×#391—24no—
28C2×C11×#95C2212yes—
29C2×C11×#95C2212yes—
30#10622843C418yescomplemented
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C4×Dic11⋊C4—24no—
41#10622541—24no—
42C22×Q8×C11—22no—
43C22×Q8×C11—22no—
44C22×Q8×C11—22no—
45C22×Q8×C11—22no—
46C22×Q8×C11C2×C414yes—
47C22×Q8×C11D414yes—
48C22×Q8×C11Q814yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2312yes—
56C23×Dic11C2312yes—
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C42×C11—22no—
64C2×C42×C11—22no—
65C2×C42×C11—22no—
66Q8×Dic11—232no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—24no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—24no—
73C2×C4⋊Dic11—24no—
74C2×C4⋊Dic11C2×C414yes—
75C2×C4⋊Dic11D414yes—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4—22no—
81C2×Dic11⋊C4—24no—
82C2×Dic11⋊C4—24no—
83C2×Dic11⋊C4—42no—
84C2×Dic11⋊C4Q814yescomplemented
85C2×C4×Dic11—22no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—24no—
88C2×C4×Dic11—22no—
89C2×C4×Dic11—22no—
90C2×C4×Dic11—24no—
91C2×C4×Dic11—24no—
92C2×C4×Dic11C2×C414yes—
93C2×C4×Dic11D414yes—
94C11×#95—24no—
95C11×#95—24no—
96C11⋊#95—24no—
97C11⋊#95—22no—
98C11⋊#95—22no—
99C11⋊#95—24no—
100C11⋊#95—24no—
101C11⋊#95—42no—
102C11⋊#95—42no—
103C11⋊#95C2×C418yes—
104C11⋊#95C2×C418yes—
105#14017—111nomaximal, Sylow
106C24×C11C2411yescharacteristic
107C2×Q8×C11—28no—
108C2×Q8×C11—28no—
109C2×Q8×C11—28no—
110C2×Q8×C11—28no—
111C2×Q8×C11—28no—
112C2×Q8×C11—28no—
113C2×Q8×C11C4⋊C4116yescomplemented
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11C22×C414yes—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C2×D414yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×Q812yes—
144C22×C4×C11C2×Q814yes—
145C22×C4×C11C2×Q812yes—
146C22×C4×C11#4112yes—
147C22×C4×C11#4112yes—
148C22×C4×C11#4112yes—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—21no—
156C22×Dic11—22no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—21no—
164C22×Dic11—22no—
165C22×Dic11—21no—
166C22×Dic11—22no—
167C22×Dic11—21no—
168C22×Dic11—22no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—22no—
178C22×Dic11—21no—
179C22×Dic11—22no—
180C22×Dic11—21no—
181C22×Dic11C22×C412yes—
182C22×Dic11C22×C414yes—
183C22×Dic11C22×C412yes—
184C22×Dic11C2×D414yes—
185C22×Dic11C2×D412yes—
186C22×Dic11C2×D412yes—
187C22×Dic11C2×Q812yes—
188C22×Dic11C2×Q812yes—
189C22×Dic11#4112yes—
190C22×Dic11#4112yes—
191C11×C4⋊C4—44no—
192C42×C11—44no—
193C4⋊Dic11—216no—
194C4⋊Dic11—28no—
195C4⋊Dic11—28no—
196Dic11⋊C4—28no—
197Dic11⋊C4—28no—
198Dic11⋊C4—48no—
199C4×Dic11—216no—
200C4×Dic11—28no—
201C4×Dic11—28no—
202C22×C4×Q8—111no—
203C2×#391—111no—
204C2×#391D1111yescharacteristic
205C2×#389—111no—
206C2×C4×C4⋊C4—111no—
207#1444—112no—
208#1442—112no—
209#1436—112no—
210#1436—112no—
211C4⋊#95—111no—
212C4⋊#95—111no—
213C23×C11C23×C411yescharacteristic
214C23×C11C22×D411yescharacteristic
215C23×C11C22×D411yescharacteristic
216C23×C11C22×D411yescharacteristic
217C23×C11C22×Q811yescharacteristic
218C23×C11C22×Q811yescharacteristic
219C23×C11C2×#4111yescharacteristic
220C23×C11C2×#4111yescharacteristic
221C23×C11C2×#4111yescharacteristic
222C23×C11C2×#4111yescharacteristic
223C23×C11C2×#4111yescharacteristic
224C23×C11H(5,𝔽2)11yescharacteristic
225C23×C112−1+411yescharacteristic
226C23×C112−1+411yescharacteristic
227C23×C112−1+411yescharacteristic
228Q8×C11—232no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11C2×C4⋊C418yes—
257C2×C4×C11C2×C4⋊C414yes—
258C2×C4×C11C4×D414yes—
259C2×C4×C11C4×D414yes—
260C2×C4×C11#12014yes—
261C2×C4×C11C22⋊Q814yes—
262C2×C4×C11C22⋊Q814yes—
263C2×C4×C11#12314yes—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—24no—
282C2×Dic11—24no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—24no—
287C2×Dic11—24no—
288C2×Dic11—42no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—42no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—42no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—42no—
299C2×Dic11—42no—
300C2×Dic11—42no—
301C2×Dic11—41no—
302C2×Dic11—42no—
303C2×Dic11—42no—
304C2×Dic11C4×Q814yescomplemented
305C2×Dic11C22⋊Q814yes—
306C23×Q8C2×D1111yescharacteristic
307C2×C4×Q8—224no—
308C2×C4×Q8—224no—
309C2×C4×Q8—224no—
310C22×C4⋊C4—111no—
311C22×C4⋊C4—111no—
312C22×C4⋊C4—111no—
313C22×C4⋊C4—111no—
314C22×C4⋊C4—112no—
315C22×C4⋊C4—112no—
316C22×C4⋊C4C2×D1111yescharacteristic
317C22×C42—111no—
318C22×C42—111no—
319C22×C42—112no—
320C22×C42C2×D1111yescharacteristic
321#391—24no—
322#391—118no—
323#389—224no—
324C4×C4⋊C4—224no—
325C2×#95—112no—
326C2×#95—112no—
327C2×#95—112no—
328C2×#95—112no—
329C2×#95—111no—
330C2×#95—112no—
331C2×#95—111no—
332C2×#95—112no—
333C2×#95—112no—
334C2×#95C2×D1112yes—
335C2×#95C2×D1112yes—
336C22×C11C22×C4⋊C411yescharacteristic
337C22×C11C2×C4×D411yescharacteristic
338C22×C11C2×C4×D411yescharacteristic
339C22×C11C2×C4×Q811yescharacteristic
340C22×C11C4×#4111yescharacteristic
341C22×C11#51911yescharacteristic
342C22×C11#52011yescharacteristic
343C22×C11C2×#12011yescharacteristic
344C22×C11C2×C22⋊Q811yescharacteristic
345C22×C11C2×C22⋊Q811yescharacteristic
346C22×C11C2×C22⋊Q811yescharacteristic
347C22×C11C2×#12311yescharacteristic
348C22×C11#52511yescharacteristic
349C22×C11#52911yescharacteristic
350C22×C11#53311yescharacteristic
351C22×C11#53611yescharacteristic
352C22×C11#53711yescharacteristic
353C22×C11#54111yescharacteristic
354C22×C11#54211yescharacteristic
355C22×C11#54611yescharacteristic
356C22×C11#54711yescharacteristic
357C22×C11#54811yescharacteristic
358C22×C11#54811yescharacteristic
359C22×C11#54811yescharacteristic
360C22×C11D4×Q811yescharacteristic
361C22×C11D4×Q811yescharacteristic
362C22×C11#55011yescharacteristic
363C22×C11#55611yescharacteristic
364C22×C11#55611yescharacteristic
365C22×C11#55711yescharacteristic
366C22×C11#55711yescharacteristic
367C22×C11#55711yescharacteristic
368C22×C11#55711yescharacteristic
369C22×C11Q8211yescharacteristic
370C22×C11#55911yescharacteristic
371C4×C11—28no—
372C4×C11—42no—
373C4×C11—42no—
374C4×C11—82no—
375C4×C11#38518yes—
376Dic11—24no—
377Dic11—24no—
378Dic11—42no—
379Dic11—44no—
380Dic11—42no—
381Dic11—44no—
382C22×Q8—22no—
383C22×Q8—22no—
384C22×Q8—22no—
385C22×Q8—22no—
386C22×Q8Dic2214yes—
387C22×Q8C4×D1114yes—
388C22×Q8C22⋊D1114yes—
389C23×C4—111no—
390C23×C4—111no—
391C23×C4—111no—
392C23×C4—112no—
393C23×C4—112no—
394C23×C4—111no—
395C23×C4C22×D1112yes—
396C23×C4C22×D1111yescharacteristic
397C23×C4C22×D1111yescharacteristic
398C23×C4C22×D1112yes—
399C23×C4C22×D1111yescharacteristic
400C4×Q8—2232no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—114no—
405C2×C4⋊C4—114no—
406C2×C4⋊C4—114no—
407C2×C4⋊C4—224no—
408C2×C4⋊C4—224no—
409C2×C4⋊C4—222no—
410C2×C4⋊C4—222no—
411C2×C4⋊C4—222no—
412C2×C4⋊C4—222no—
413C2×C4⋊C4—222no—
414C2×C4⋊C4—222no—
415C2×C4⋊C4—222no—
416C2×C4⋊C4—222no—
417C2×C4⋊C4—224no—
418C2×C4⋊C4—222no—
419C2×C4⋊C4—224no—
420C2×C4⋊C4—224no—
421C2×C4⋊C4—442no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—114no—
426C2×C42—114no—
427C2×C42—224no—
428C2×C42—224no—
429C2×C42—222no—
430C2×C42—222no—
431C2×C42—222no—
432C2×C42—224no—
433C2×C42—222no—
434#95—24no—
435#95—24no—
436#95—118no—
437#95—118no—
438#95—224no—
439#95—224no—
440#95—222no—
441#95—222no—
442#95—224no—
443#95—442no—
444#95—442no—
445C2×C11C2×#38511yescharacteristic
446C2×C11C4×C22⋊Q811yescharacteristic
447C2×C11#232311yescharacteristic
448C2×C11Q8×C4⋊C411yescharacteristic
449C2×C11#235111yescharacteristic
450C2×C11#236511yescharacteristic
451C2×C11#236711yescharacteristic
452C2×C11#240711yescharacteristic
453C2×C11#240911yescharacteristic
454C2×C11#244611yescharacteristic
455C2×C11#244811yescharacteristic
456C2×C11#245111yescharacteristic
457C2×C11#245311yescharacteristic
458C2×C11#258111yescharacteristic
459C2×C11#258211yescharacteristic
460C24C23×D1111yescharacteristic
461C2×Q8—28no—
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—28no—
467C2×Q8Dic11⋊C4116yescomplemented
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—112no—
492C22×C4—112no—
493C22×C4—112no—
494C22×C4—112no—
495C22×C4—112no—
496C22×C4—112no—
497C22×C4—112no—
498C22×C4—114no—
499C22×C4—112no—
500C22×C4—114no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—221no—
517C22×C4—222no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—222no—
521C22×C4—221no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—221no—
526C22×C4—221no—
527C22×C4—221no—
528C22×C4—222no—
529C22×C4—222no—
530C22×C4—221no—
531C22×C4—222no—
532C22×C4—221no—
533C22×C4C2×Dic2214yes—
534C22×C4C2×Dic2212yes—
535C22×C4C2×C4×D1114yes—
536C22×C4C2×C4×D1112yes—
537C22×C4D4×D1112yes—
538C22×C4D4×D1112yes—
539C22×C4#434112yes—
540C22×C4#434112yes—
541C22×C4Q8×D1112yes—
542C22×C4#434312yes—
543C22×C4C2×C22⋊D1114yes—
544C22×C4C2×C22⋊D1112yes—
545C4⋊C4—44no—
546C4⋊C4—228no—
547C4⋊C4—2216no—
548C4⋊C4—228no—
549C4⋊C4—228no—
550C4⋊C4—228no—
551C4⋊C4—448no—
552C42—44no—
553C42—2216no—
554C42—228no—
555C42—228no—
556C11#1401711yescharacteristic, complemented, Sylow
557C23C22×Dic2211yescharacteristic
558C23C22×C4×D1111yescharacteristic
559C23C2×D4×D1111yescharacteristic
560C23C2×D4×D1111yescharacteristic
561C23C2×#434111yescharacteristic
562C23C2×#434111yescharacteristic
563C23C2×Q8×D1111yescharacteristic
564C23C2×#434311yescharacteristic
565C23#6704011yescharacteristic
566C23#6704011yescharacteristic
567C23#41×D1111yescharacteristic
568C23#41×D1111yescharacteristic
569C23#6704211yescharacteristic
570C23#6704311yescharacteristic
571C23C22×C22⋊D1111yescharacteristic
572Q8—232no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—114no—
601C2×C4—114no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—224no—
616C2×C4—224no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—224no—
620C2×C4—224no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—222no—
624C2×C4—224no—
625C2×C4—224no—
626C2×C4—441no—
627C2×C4—442no—
628C2×C4—441no—
629C2×C4—442no—
630C2×C4—442no—
631C2×C4—441no—
632C2×C4—442no—
633C2×C4—441no—
634C2×C4—442no—
635C2×C4—441no—
636C2×C4—442no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—442no—
640C2×C4—442no—
641C2×C4—441no—
642C2×C4#6693114yes—
643C2×C4#6693114yes—
644C2×C4(C22⋊D11)⋊C414yes—
645C2×C4(C22⋊D11)⋊C414yes—
646C2×C4C2×Dic11⋊C418yes—
647C2×C4C2×Dic11⋊C414yes—
648C2×C4#6698814yes—
649C2×C4#6699014yes—
650C22C2×#6693111yescharacteristic
651C22C2×#6693111yescharacteristic
652C22C2×(C22⋊D11)⋊C411yescharacteristic
653C22C2×(C22⋊D11)⋊C411yescharacteristic
654C22Q8×Dic2211yescharacteristic
655C22#1062310011yescharacteristic
656C22#1062310011yescharacteristic
657C22#1062310111yescharacteristic
658C22C4×Q8×D1111yescharacteristic
659C22#1062310311yescharacteristic
660C22C4×#434311yescharacteristic
661C22#1062310511yescharacteristic
662C22D11×C22⋊Q811yescharacteristic
663C22#1062315811yescharacteristic
664C22#1062315911yescharacteristic
665C22#1062316011yescharacteristic
666C22#1062316111yescharacteristic
667C22#1062316211yescharacteristic
668C22#1062316311yescharacteristic
669C22#1062316411yescharacteristic
670C22#1062320211yescharacteristic
671C22#1062321111yescharacteristic
672C22#1062321211yescharacteristic
673C22#1062321311yescharacteristic
674C22#1062325211yescharacteristic
675C22#1062325911yescharacteristic
676C22#1062326211yescharacteristic
677C22#1062326311yescharacteristic
678C22C22×Dic11⋊C411yescharacteristic
679C22C2×#6698811yescharacteristic
680C22C2×#6699011yescharacteristic
681C22Q8×C22⋊D1111yescharacteristic
682C22#1062334811yescharacteristic
683C22#1062336211yescharacteristic
684C22#1062336511yescharacteristic
685C4—28no—
686C4—42no—
687C4—42no—
688C4—82no—
689C4—224no—
690C4—224no—
691C4—444no—
692C4—442no—
693C4—444no—
694C4—442no—
695C4#1062255918yes—
696C2C2×#1062255911yescharacteristic
697C2#1307115411yescharacteristic
698C2#1307130111yescharacteristic
699C2Q8×Dic11⋊C411yescharacteristic
700C2#1307153411yescharacteristic
701C2#1307167311yescharacteristic
702C2#1307169211yescharacteristic
703C2#1307196311yescharacteristic
704C2#1307197711yescharacteristic
705C2#1307238811yescharacteristic
706C2#1307241011yescharacteristic
707C2#1307245711yescharacteristic
708C2#1307247911yescharacteristic
709C2#1307398011yescharacteristic
710C2#1307398711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#391C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#391D11
hypocenterC11#14017
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
30. #10622843C4semidirect
84. C2×Dic11⋊C4Q8semidirect
113. C2×Q8×C11C4⋊C4semidirect
304. C2×Dic11C4×Q8semidirect
467. C2×Q8Dic11⋊C4semidirect
556. C11#14017semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic112
C2×#106228432
C2×#106225412
C2×C4×Dic11⋊C42
#130668802
#130668722
#130668472
#130668452
C2×C11×#3912
#1401711