Finite Group Databasebeta

← #14676322

Subgroups — #14676322

Order 2816.

2374 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622570C212yesmaximal
3C2×#10622263C211yesmaximal, characteristic, complemented
4C2×#10622262C211yesmaximal, characteristic, complemented
5#13066860C212yesmaximal, complemented
6#13066859C212yesmaximal, complemented
7Dic11⋊#95C212yesmaximal, complemented
8#13066839C211yesmaximal, characteristic, complemented
9(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
11C11×C22⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C2×C4×C22⋊D11—24no—
19C2×C4×C22⋊D11—24no—
20C2×C4×C22⋊D11C418yescomplemented
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2211yescharacteristic
27C22×C4×Dic11C2212yes—
28C22×C4×Dic11C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622570—28no—
39#10622263—24no—
40#10622262—24no—
41C25×C11C2311yescharacteristic
42C24×D11C2311yescharacteristic
43C23×C4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11—42no—
46C23×C4×C11—42no—
47C23×C4×C11C2×C414yes—
48C23×C4×C11C2312yes—
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11—22no—
53C22×C22⋊D11—22no—
54C22×C22⋊D11—22no—
55C22×C22⋊D11—22no—
56C22×C22⋊D11C2×C414yes—
57C22×C22⋊D11D414yes—
58C22×C22⋊D11Q814yes—
59C23×Dic11C2312yes—
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2312yes—
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C22×C4×D11—22no—
65C22×C4×D11—22no—
66C22×C4×D11—42no—
67C22×C4×D11—42no—
68C22×C4×D11C2×C414yes—
69C2×C11×C22⋊C4—24no—
70C2×C11×C22⋊C4—24no—
71C2×C11×C22⋊C4—42no—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—24no—
76C2×C22⋊Dic11—42no—
77C2×C22⋊Dic11C2×C414yes—
78C4×C22⋊D11—232no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—24no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—24no—
85C2×(C2×D11)⋊C4—42no—
86C2×(C2×D11)⋊C4—42no—
87C2×(C2×D11)⋊C4C2×C414yes—
88C2×Dic11⋊C4—24no—
89C2×Dic11⋊C4—24no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—22no—
92C2×Dic11⋊C4—24no—
93C2×Dic11⋊C4—24no—
94C2×Dic11⋊C4—24no—
95C2×Dic11⋊C4—24no—
96C2×Dic11⋊C4C2×C414yes—
97C2×C4×Dic11—24no—
98C2×C4×Dic11—24no—
99C2×C4×Dic11—24no—
100C2×C4×Dic11C2×C414yes—
101C2×C4×Dic11D414yes—
102C2×C4×Dic11D414yes—
103C11×#95—22no—
104C11×#95—22no—
105C11×#95—42no—
106C11⋊#95—22no—
107C11⋊#95—22no—
108C11⋊#95—24no—
109C11⋊#95—42no—
110C11⋊#95—42no—
111C11⋊#95—42no—
112#13941—111nomaximal, Sylow
113C24×C11—21no—
114C24×C11—21no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—21no—
118C24×C11—21no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11C22×C412yes—
122C24×C11C2×D412yes—
123C24×C11C2×Q812yes—
124C24×C11C2411yescharacteristic
125C23×D11—21no—
126C23×D11—21no—
127C23×D11—22no—
128C23×D11—22no—
129C23×D11—21no—
130C23×D11—21no—
131C23×D11—22no—
132C23×D11—22no—
133C23×D11C22×C412yes—
134C23×D11C2×D412yes—
135C23×D11C2×Q812yes—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—28no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—44no—
157C22×C4×C11—44no—
158C22×C4×C11—48no—
159C22×C4×C11—48no—
160C22×C4×C11C22×C412yes—
161C22×C4×C11C22×C412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D412yes—
164C22×C4×C11#4114yes—
165C2×C22⋊D11—28no—
166C2×C22⋊D11—28no—
167C2×C22⋊D11—28no—
168C2×C22⋊D11—28no—
169C2×C22⋊D11—28no—
170C2×C22⋊D11—28no—
171C2×C22⋊D11C4⋊C4116yescomplemented
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11C22×C412yes—
192C22×Dic11C22×C412yes—
193C22×Dic11C22×C412yes—
194C22×Dic11C2×D412yes—
195C22×Dic11C2×D412yes—
196C22×Dic11C2×D412yes—
197C22×Dic11C2×D412yes—
198C22×Dic11C2×D412yes—
199C22×Dic11C2×Q812yes—
200C22×Dic11#4114yes—
201C22×Dic11#4112yes—
202C22×Dic11#4112yes—
203C2×C4×D11—28no—
204C2×C4×D11—44no—
205C2×C4×D11—44no—
206C2×C4×D11—48no—
207C2×C4×D11—48no—
208C11×C22⋊C4—48no—
209C22⋊Dic11—28no—
210C22⋊Dic11—48no—
211(C2×D11)⋊C4—28no—
212(C2×D11)⋊C4—48no—
213(C2×D11)⋊C4—48no—
214Dic11⋊C4—216no—
215Dic11⋊C4—28no—
216Dic11⋊C4—48no—
217C4×Dic11—48no—
218C4×Dic11C22⋊C4116yescomplemented
219C22×C4×D4—111no—
220C2×#390—112no—
221C2×#382—111no—
222C2×C4×C4⋊C4—111no—
223#1439—112no—
224#1439—112no—
225C4⋊#95—112no—
226C22⋊#95—111no—
227C22⋊#95—111no—
228C22⋊#95—111no—
229C22⋊#95D1111yescharacteristic, complemented
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11—24no—
241C23×C11—24no—
242C23×C11—24no—
243C23×C11—24no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11—42no—
249C23×C11—42no—
250C23×C11—42no—
251C23×C11—42no—
252C23×C11C2×C4⋊C414yes—
253C23×C11C23×C411yescharacteristic
254C23×C11C22×D411yescharacteristic
255C23×C11C22×D411yescharacteristic
256C23×C11C22×D411yescharacteristic
257C23×C11C22×Q811yescharacteristic
258C23×C11C2×#4112yes—
259C23×C11C2×#4111yescharacteristic
260C23×C11C2×#4111yescharacteristic
261C23×C11C2×#4112yes—
262C23×C11H(5,𝔽2)12yes—
263C23×C11H(5,𝔽2)12yes—
264C22×D11—22no—
265C22×D11—22no—
266C22×D11—22no—
267C22×D11—22no—
268C22×D11—22no—
269C22×D11—22no—
270C22×D11—22no—
271C22×D11—22no—
272C22×D11—22no—
273C22×D11—22no—
274C22×D11—24no—
275C22×D11—24no—
276C22×D11—24no—
277C22×D11—24no—
278C22×D11—42no—
279C22×D11—42no—
280C22×D11—42no—
281C22×D11—42no—
282C22×D11—42no—
283C22×D11—42no—
284C22×D11—42no—
285C22×D11—42no—
286C22×D11C2×C4⋊C414yes—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—24no—
290C2×C4×C11—24no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
296C2×C4×C11—24no—
297C2×C4×C11—416no—
298C2×C4×C11—42no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11—42no—
305C2×C4×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11C2×C22⋊C414yes—
312C22⋊D11—232no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—24no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—42no—
324C2×Dic11—42no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11C2×C22⋊C414yes—
337C2×Dic11C2×C22⋊C414yes—
338C2×Dic11C2×C4⋊C414yes—
339C2×Dic11#11714yes—
340C2×Dic11#12114yes—
341C2×Dic11#12114yes—
342C2×Dic11C22⋊Q814yes—
343C2×Dic11C22⋊Q814yes—
344C4×D11—416no—
345C23×D4—111no—
346C24×C4—111no—
347C24×C4C2×D1111yescharacteristic
348C2×C4×D4—118no—
349C2×C4×D4—224no—
350C2×C4×D4—224no—
351C22×C4⋊C4—111no—
352C22×C4⋊C4—112no—
353C22×C4⋊C4—112no—
354C22×C22⋊C4—111no—
355C22×C22⋊C4—111no—
356C22×C22⋊C4—112no—
357C22×C22⋊C4—112no—
358C22×C22⋊C4—112no—
359C22×C22⋊C4C2×D1112yes—
360C22×C42—111no—
361C22×C42—112no—
362#390—228no—
363#382—224no—
364C4×C4⋊C4—224no—
365C2×#95—111no—
366C2×#95—111no—
367C2×#95—112no—
368C2×#95—112no—
369C2×#95—112no—
370C2×#95—112no—
371C2×#95C2×D1111yescharacteristic
372C2×#95C2×D1111yescharacteristic
373C2×#95C2×D1112yes—
374C22×C11—24no—
375C22×C11—24no—
376C22×C11—24no—
377C22×C11—42no—
378C22×C11—44no—
379C22×C11—44no—
380C22×C11—42no—
381C22×C11—42no—
382C22×C11—44no—
383C22×C11—44no—
384C22×C11—42no—
385C22×C11C22×C22⋊C411yescharacteristic
386C22×C11C22×C4⋊C411yescharacteristic
387C22×C11C2×#11711yescharacteristic
388C22×C11C4×#4111yescharacteristic
389C22×C11C4×#4111yescharacteristic
390C22×C11#51811yescharacteristic
391C22×C11#51811yescharacteristic
392C22×C11C2×#12111yescharacteristic
393C22×C11C2×#12111yescharacteristic
394C22×C11C2×C22⋊Q811yescharacteristic
395C22×C11C2×C22⋊Q811yescharacteristic
396C22×C11#52512yes—
397C22×C11#53212yes—
398C22×C11#53512yes—
399C22×C11#53512yes—
400C22×C11#54612yes—
401C22×C11#54612yes—
402C22×C11#55312yes—
403C22×C11#55312yes—
404C22×C11#55412yes—
405C22×C11#55412yes—
406C22×C11#55912yes—
407C22×C11#55912yes—
408C2×D11—24no—
409C2×D11—24no—
410C2×D11—24no—
411C2×D11—42no—
412C2×D11—44no—
413C2×D11—44no—
414C2×D11—42no—
415C2×D11—42no—
416C2×D11—44no—
417C2×D11—44no—
418C2×D11—42no—
419C4×C11—24no—
420C4×C11—42no—
421C4×C11—44no—
422C4×C11—82no—
423Dic11—24no—
424Dic11—42no—
425Dic11—44no—
426Dic11—82no—
427Dic11#38018yes—
428C25—111no—
429C25C22×D1111yescharacteristic
430C22×D4—114no—
431C22×D4—114no—
432C22×D4—114no—
433C22×D4—222no—
434C22×D4—222no—
435C22×D4—222no—
436C22×D4—222no—
437C23×C4—22no—
438C23×C4—22no—
439C23×C4—42no—
440C23×C4—42no—
441C23×C4—111no—
442C23×C4—111no—
443C23×C4—112no—
444C23×C4—111no—
445C23×C4—114no—
446C23×C4—112no—
447C23×C4—222no—
448C23×C4—222no—
449C23×C4—442no—
450C23×C4—442no—
451C23×C4C4×D1114yes—
452C23×C4C22×D1112yes—
453C23×C4C22×D1111yescharacteristic
454C23×C4C22×D1112yes—
455C23×C4C22×D1111yescharacteristic
456C4×D4—2232no—
457C2×C4⋊C4—114no—
458C2×C4⋊C4—222no—
459C2×C4⋊C4—222no—
460C2×C4⋊C4—224no—
461C2×C4⋊C4—224no—
462C2×C4⋊C4—224no—
463C2×C4⋊C4—224no—
464C2×C4⋊C4—224no—
465C2×C4⋊C4—224no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—114no—
470C2×C22⋊C4—114no—
471C2×C22⋊C4—222no—
472C2×C22⋊C4—222no—
473C2×C22⋊C4—222no—
474C2×C22⋊C4—222no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4—224no—
477C2×C22⋊C4—224no—
478C2×C22⋊C4—224no—
479C2×C22⋊C4—224no—
480C2×C22⋊C4—224no—
481C2×C22⋊C4—442no—
482C2×C22⋊C4—442no—
483C2×C22⋊C4—442no—
484C2×C42—114no—
485C2×C42—114no—
486C2×C42—114no—
487C2×C42—224no—
488C2×C42—224no—
489C2×C42—224no—
490#95—22no—
491#95—22no—
492#95—42no—
493#95—224no—
494#95—222no—
495#95—222no—
496#95—442no—
497#95—442no—
498#95—442no—
499C2×C11—44no—
500C2×C11C2×#38011yescharacteristic
501C2×C11#229711yescharacteristic
502C2×C11#230911yescharacteristic
503C2×C11#234911yescharacteristic
504C2×C11#234911yescharacteristic
505C2×C11#235711yescharacteristic
506C2×C11#235711yescharacteristic
507C2×C11#253512yes—
508C2×C11#254412yes—
509C2×C11#256612yes—
510C2×C11#258012yes—
511D11—44no—
512C24—22no—
513C24—21no—
514C24—21no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—21no—
519C24—21no—
520C24—112no—
521C24—112no—
522C24—112no—
523C24—222no—
524C24—221no—
525C24—221no—
526C24—222no—
527C24—222no—
528C24—222no—
529C24—221no—
530C24—221no—
531C24C2×C4×D1112yes—
532C24D4×D1112yes—
533C24Q8×D1112yes—
534C24C23×D1111yescharacteristic
535C2×D4—1116no—
536C2×D4—228no—
537C2×D4—228no—
538C2×D4—228no—
539C2×D4—228no—
540C2×D4—228no—
541C2×D4—228no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—28no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—112no—
567C22×C4—112no—
568C22×C4—112no—
569C22×C4—112no—
570C22×C4—112no—
571C22×C4—112no—
572C22×C4—112no—
573C22×C4—112no—
574C22×C4—112no—
575C22×C4—112no—
576C22×C4—112no—
577C22×C4—114no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—228no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—444no—
599C22×C4—444no—
600C22×C4—448no—
601C22×C4—448no—
602C22×C4C2×C4×D1112yes—
603C22×C4C2×C4×D1112yes—
604C22×C4#433914yes—
605C22×C4D4×D1112yes—
606C22×C4D4×D1112yes—
607C4⋊C4—228no—
608C4⋊C4—2216no—
609C4⋊C4—448no—
610C22⋊C4—48no—
611C22⋊C4—228no—
612C22⋊C4—228no—
613C22⋊C4—448no—
614C22⋊C4—448no—
615C22⋊C4—448no—
616C42—1116no—
617C42—448no—
618C11#1394111yescharacteristic, complemented, Sylow
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—24no—
624C23—24no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—24no—
630C23—22no—
631C23—22no—
632C23—24no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—114no—
642C23—222no—
643C23—222no—
644C23—222no—
645C23—222no—
646C23—224no—
647C23—224no—
648C23—222no—
649C23—222no—
650C23—222no—
651C23—222no—
652C23—224no—
653C23—222no—
654C23—222no—
655C23—224no—
656C23—442no—
657C23—442no—
658C23—442no—
659C23—442no—
660C23—442no—
661C23—442no—
662C23—442no—
663C23—442no—
664C23C4⋊C4×D1114yes—
665C23C22×C4×D1111yescharacteristic
666C23C2×#433912yes—
667C23C2×D4×D1111yescharacteristic
668C23C2×D4×D1111yescharacteristic
669C23C2×D4×D1111yescharacteristic
670C23#6703712yes—
671C23#6703712yes—
672C23C2×Q8×D1111yescharacteristic
673C23#41×D1111yescharacteristic
674C23#41×D1111yescharacteristic
675C23#41×D1112yes—
676D4—2232no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—416no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—114no—
702C2×C4—114no—
703C2×C4—114no—
704C2×C4—114no—
705C2×C4—114no—
706C2×C4—114no—
707C2×C4—114no—
708C2×C4—114no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—224no—
712C2×C4—224no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—224no—
717C2×C4—224no—
718C2×C4—224no—
719C2×C4—4416no—
720C2×C4—442no—
721C2×C4—442no—
722C2×C4—442no—
723C2×C4—442no—
724C2×C4—442no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4—442no—
732C2×C4—442no—
733C2×C4C22⋊C4×D1114yes—
734C22—24no—
735C22—24no—
736C22—24no—
737C22—44no—
738C22—42no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—224no—
746C22—224no—
747C22—224no—
748C22—444no—
749C22—442no—
750C22—444no—
751C22—444no—
752C22—444no—
753C22—442no—
754C22—442no—
755C22—442no—
756C22C4×#433911yescharacteristic
757C22C2×C22⋊C4×D1111yescharacteristic
758C22#1062301711yescharacteristic
759C22#1062301711yescharacteristic
760C22#1062302112yes—
761C22C2×C4⋊C4×D1111yescharacteristic
762C22#1062304212yes—
763C22D11×#11711yescharacteristic
764C22#1062305311yescharacteristic
765C22#1062307112yes—
766C22#1062307812yes—
767C22#1062307912yes—
768C22#1062309012yes—
769C22#1062312312yes—
770C22#1062312312yes—
771C22D11×#12111yescharacteristic
772C22D11×#12111yescharacteristic
773C22#1062314112yes—
774C22D11×C22⋊Q811yescharacteristic
775C22D11×C22⋊Q811yescharacteristic
776C22#1062316712yes—
777C22#1062319212yes—
778C22#1062319512yes—
779C4—24no—
780C4—42no—
781C4—44no—
782C4—82no—
783C4—118no—
784C4—224no—
785C4—442no—
786C4—444no—
787C4—882no—
788C2—44no—
789C2—444no—
790C2D11×#38011yescharacteristic
791C2#1307110211yescharacteristic
792C2#1307119711yescharacteristic
793C2#1307152011yescharacteristic
794C2#1307152311yescharacteristic
795C2#1307158411yescharacteristic
796C2#1307159011yescharacteristic
797C2#1307351612yes—
798C2#1307358512yes—
799C2#1307381412yes—
800C2#1307397312yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22⋊#95D11
hypocenterC11#13941
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#10622263C2semidirect
4. C2×#10622262C2semidirect
5. #13066860C2semidirect
6. #13066859C2semidirect
7. Dic11⋊#95C2semidirect
8. #13066839C2semidirect
9. (C2×D11)⋊#95C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C11×C22⋊#95C2semidirect
20. C2×C4×C22⋊D11C4semidirect
171. C2×C22⋊D11C4⋊C4semidirect
218. C4×Dic11C22⋊C4semidirect
229. C22⋊#95D11semidirect
618. C11#13941semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×#106225702
C2×#106222632
C2×#106222622
#130668602
#130668592
Dic11⋊#952
#130668392
(C2×D11)⋊#952
C11×C22⋊#952
#1394111