Finite Group Databasebeta

← #14675955

Subgroups — #14675955

Order 2816.

2690 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622826C212yesmaximal
3C2×#10622823C212yesmaximal, complemented
4C2×#10622280C211yesmaximal, characteristic, complemented
5#13066867C212yesmaximal, complemented
6#13066860C212yesmaximal, complemented
7Dic11⋊#95C211yesmaximal, characteristic, complemented
8#13066841C211yesmaximal, characteristic, complemented
9#13066839C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
11C22×C11×#95C211yesmaximal, characteristic, complemented
12C24×C4×C11C2212yes—
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C2×C4×C22⋊D11—28no—
19C2×C4×C22⋊D11C418yescomplemented
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×Dic11⋊C4C2212yes—
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C2×C11×#95—24no—
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2212yes—
30C2×C11×#95C2211yescharacteristic
31#10622826—28no—
32#10622823—28no—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40#10622280—24no—
41C25×C11C2311yescharacteristic
42C24×D11C2311yescharacteristic
43C23×C4×C11—24no—
44C23×C4×C11—24no—
45C23×C4×C11—24no—
46C23×C4×C11—22no—
47C23×C4×C11—24no—
48C23×C4×C11—22no—
49C23×C4×C11—24no—
50C23×C4×C11—24no—
51C23×C4×C11—42no—
52C23×C4×C11—42no—
53C23×C4×C11—42no—
54C23×C4×C11C2×C414yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2312yes—
57C23×C4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—24no—
60C22×C22⋊D11—24no—
61C22×C22⋊D11C2×C414yes—
62C22×C22⋊D11D414yes—
63C22×C22⋊D11Q814yes—
64C23×Dic11C2312yes—
65C23×Dic11C2312yes—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C22×C4×D11—22no—
70C22×C4×D11—22no—
71C22×C4×D11—24no—
72C22×C4×D11—42no—
73C22×C4×D11C2×C414yescomplemented
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—24no—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11C2×C414yes—
78C2×C22⋊Dic11D418yes—
79C4×C22⋊D11—232no—
80C2×(C2×D11)⋊C4—24no—
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×C414yescomplemented
88C2×Dic11⋊C4—24no—
89C2×Dic11⋊C4—24no—
90C2×Dic11⋊C4—24no—
91C2×Dic11⋊C4—24no—
92C2×Dic11⋊C4—24no—
93C2×Dic11⋊C4—42no—
94C2×Dic11⋊C4—42no—
95C2×Dic11⋊C4C2×C414yescomplemented
96C2×C4×Dic11—24no—
97C2×C4×Dic11C2×C414yescomplemented
98C11×#95—24no—
99C11×#95—22no—
100C11×#95D414yescomplemented
101C11⋊#95—22no—
102C11⋊#95—22no—
103C11⋊#95—24no—
104C11⋊#95—24no—
105C11⋊#95—24no—
106C11⋊#95—24no—
107C11⋊#95—42no—
108#13899—111nomaximal, Sylow
109C24×C11—21no—
110C24×C11—21no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—21no—
114C24×C11—21no—
115C24×C11C22×C412yes—
116C24×C11C2×D414yes—
117C24×C11C2×D412yes—
118C24×C11C2×Q812yes—
119C24×C11#4114yes—
120C24×C11C2411yescharacteristic
121C23×D11—21no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—21no—
125C23×D11—22no—
126C23×D11—21no—
127C23×D11—22no—
128C23×D11—21no—
129C23×D11C22×C412yes—
130C23×D11C2×D412yes—
131C23×D11C2×Q812yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—216no—
135C22×C4×C11—28no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—28no—
153C22×C4×C11—44no—
154C22×C4×C11—48no—
155C22×C4×C11—48no—
156C22×C4×C11—48no—
157C22×C4×C11—48no—
158C22×C4×C11—48no—
159C22×C4×C11—48no—
160C22×C4×C11—48no—
161C22×C4×C11—48no—
162C22×C4×C11C22×C412yes—
163C22×C4×C11C22×C412yes—
164C22×C4×C11C2×D414yes—
165C22×C4×C11C2×D412yes—
166C22×C4×C11#4114yes—
167C22×C4×C11#4112yes—
168C2×C22⋊D11—28no—
169C2×C22⋊D11—28no—
170C2×C22⋊D11—216no—
171C2×C22⋊D11—216no—
172C2×C22⋊D11C4⋊C4116yescomplemented
173C22×Dic11—22no—
174C22×Dic11—21no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—21no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—21no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—21no—
194C22×Dic11—22no—
195C22×Dic11C22×C412yes—
196C22×Dic11C22×C412yes—
197C22×Dic11C22×C412yes—
198C22×Dic11C2×D414yes—
199C22×Dic11C2×D414yes—
200C22×Dic11C2×D412yes—
201C22×Dic11C2×Q812yes—
202C2×C4×D11—28no—
203C2×C4×D11—28no—
204C2×C4×D11—44no—
205C2×C4×D11—48no—
206C2×C4×D11—48no—
207C22⋊Dic11—48no—
208C22⋊Dic11C22⋊C4116yescomplemented
209(C2×D11)⋊C4—28no—
210(C2×D11)⋊C4—48no—
211(C2×D11)⋊C4—48no—
212Dic11⋊C4—28no—
213Dic11⋊C4—48no—
214Dic11⋊C4—48no—
215C4×Dic11—28no—
216C22×C4×D4—111no—
217C2×#386—112no—
218C2×#385—112no—
219C2×#380—111no—
220C22×#95D1111yescharacteristic, complemented
221#1441—112no—
222#1439—112no—
223C4⋊#95—111no—
224#1434—111no—
225C22⋊#95—111no—
226C22⋊#95—111no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—24no—
232C23×C11—24no—
233C23×C11—24no—
234C23×C11—24no—
235C23×C11—24no—
236C23×C11—22no—
237C23×C11—24no—
238C23×C11—24no—
239C23×C11—24no—
240C23×C11—24no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—24no—
245C23×C11C2×C22⋊C414yes—
246C23×C11C2×C4⋊C414yes—
247C23×C11#11714yes—
248C23×C11#12118yes—
249C23×C11C22⋊Q818yes—
250C23×C11C23×C411yescharacteristic
251C23×C11C22×D412yes—
252C23×C11C22×D411yescharacteristic
253C23×C11C22×D411yescharacteristic
254C23×C11C22×Q811yescharacteristic
255C23×C11C2×#4112yes—
256C23×C11C2×#4111yescharacteristic
257C23×C11C2×#4112yes—
258C23×C11H(5,𝔽2)12yes—
259C23×C11H(5,𝔽2)11yescharacteristic
260C23×C112−1+411yescharacteristic
261C22×D11—22no—
262C22×D11—22no—
263C22×D11—22no—
264C22×D11—22no—
265C22×D11—22no—
266C22×D11—22no—
267C22×D11—24no—
268C22×D11—24no—
269C22×D11—22no—
270C22×D11—24no—
271C22×D11—22no—
272C22×D11—22no—
273C22×D11—22no—
274C22×D11—24no—
275C22×D11—42no—
276C22×D11—42no—
277C22×D11—42no—
278C22×D11—42no—
279C22×D11—42no—
280C22×D11—42no—
281C22×D11—42no—
282C22×D11—42no—
283C22×D11C2×C4⋊C414yes—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—24no—
287C2×C4×C11—24no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—24no—
292C2×C4×C11—24no—
293C2×C4×C11—24no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
296C2×C4×C11—24no—
297C2×C4×C11—416no—
298C2×C4×C11—432no—
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×C11C4×D414yes—
310C22⋊D11—232no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—24no—
318C2×Dic11—24no—
319C2×Dic11—24no—
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×Dic11—42no—
337C2×Dic11C2×C22⋊C414yes—
338C2×Dic11C2×C22⋊C414yes—
339C2×Dic11C2×C4⋊C414yes—
340C4×D11—416no—
341C23×D4—111no—
342C24×C4—111no—
343C24×C4C2×D1112yes—
344C24×C4C2×D1111yescharacteristic
345C2×C4×D4—118no—
346C2×C4×D4—228no—
347C22×C4⋊C4—111no—
348C22×C4⋊C4—112no—
349C22×C4⋊C4—112no—
350C22×C22⋊C4—111no—
351C22×C22⋊C4—111no—
352C22×C22⋊C4—112no—
353C22×C22⋊C4—112no—
354C22×C22⋊C4—112no—
355C22×C42—111no—
356#386—228no—
357#385—228no—
358#380—224no—
359C2×#95—24no—
360C2×#95—111no—
361C2×#95—111no—
362C2×#95—112no—
363C2×#95—112no—
364C2×#95—112no—
365C2×#95—112no—
366C2×#95—112no—
367C2×#95C2×D1111yescharacteristic
368C2×#95C2×D1112yes—
369C2×#95C2×D1111yescharacteristic
370C22×C11—24no—
371C22×C11—24no—
372C22×C11—24no—
373C22×C11—24no—
374C22×C11—24no—
375C22×C11—28no—
376C22×C11—28no—
377C22×C11—28no—
378C22×C11—28no—
379C22×C11—24no—
380C22×C11#38018yescomplemented
381C22×C11C22×C22⋊C411yescharacteristic
382C22×C11C22×C4⋊C411yescharacteristic
383C22×C11C2×#11711yescharacteristic
384C22×C11C2×C4×D411yescharacteristic
385C22×C11C4×#4111yescharacteristic
386C22×C11#51811yescharacteristic
387C22×C11#52011yescharacteristic
388C22×C11C2×#12112yes—
389C22×C11C2×C22⋊Q812yes—
390C22×C11#52512yes—
391C22×C11#52912yes—
392C22×C11#53812yes—
393C22×C11#53912yes—
394C22×C11D4212yes—
395C22×C11D4211yescharacteristic
396C22×C11#54612yes—
397C22×C11#54612yes—
398C22×C11#54612yes—
399C22×C11#54712yes—
400C22×C11#54711yescharacteristic
401C22×C11D4×Q811yescharacteristic
402C22×C11#55411yescharacteristic
403C22×C11#55412yes—
404C2×D11—24no—
405C2×D11—24no—
406C2×D11—24no—
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—44no—
411C2×D11—44no—
412C2×D11—44no—
413C2×D11—44no—
414C2×D11—42no—
415C4×C11—24no—
416C4×C11—42no—
417C4×C11—44no—
418C4×C11—44no—
419Dic11—24no—
420Dic11—24no—
421Dic11—24no—
422Dic11—82no—
423Dic11—82no—
424C25—111no—
425C25C22×D1111yescharacteristic
426C22×D4—114no—
427C22×D4—114no—
428C22×D4—114no—
429C22×D4—224no—
430C22×D4—224no—
431C23×C4—24no—
432C23×C4—24no—
433C23×C4—24no—
434C23×C4—22no—
435C23×C4—24no—
436C23×C4—22no—
437C23×C4—24no—
438C23×C4—24no—
439C23×C4—42no—
440C23×C4—42no—
441C23×C4—42no—
442C23×C4—111no—
443C23×C4—111no—
444C23×C4—111no—
445C23×C4—114no—
446C23×C4—112no—
447C23×C4—112no—
448C23×C4—224no—
449C23×C4—222no—
450C23×C4—222no—
451C23×C4—442no—
452C23×C4C4×D1114yes—
453C23×C4C22×D1111yescharacteristic
454C23×C4C22×D1112yes—
455C23×C4C22×D1112yes—
456C23×C4C22×D1111yescharacteristic
457C4×D4—2232no—
458C2×C4⋊C4—114no—
459C2×C4⋊C4—224no—
460C2×C4⋊C4—224no—
461C2×C4⋊C4—224no—
462C2×C4⋊C4—224no—
463C2×C4⋊C4—224no—
464C2×C4⋊C4—442no—
465C2×C4⋊C4—442no—
466C2×C22⋊C4—114no—
467C2×C22⋊C4—118no—
468C2×C22⋊C4—114no—
469C2×C22⋊C4—224no—
470C2×C22⋊C4—224no—
471C2×C22⋊C4—224no—
472C2×C22⋊C4—224no—
473C2×C22⋊C4—224no—
474C2×C22⋊C4—224no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4—224no—
477C2×C22⋊C4—442no—
478C2×C22⋊C4—442no—
479C2×C42—114no—
480C2×C42—224no—
481#95—24no—
482#95—22no—
483#95—224no—
484#95—224no—
485#95—224no—
486#95—224no—
487#95—222no—
488#95—222no—
489#95—442no—
490#95C22⋊D1114yescomplemented
491C2×C11—28no—
492C2×C11C2×#38011yescharacteristic
493C2×C11#229011yescharacteristic
494C2×C11#231811yescharacteristic
495C2×C11D4×C22⋊C411yescharacteristic
496C2×C11#233911yescharacteristic
497C2×C11D4×C4⋊C411yescharacteristic
498C2×C11#234911yescharacteristic
499C2×C11#242412yes—
500C2×C11#242512yes—
501C2×C11#244912yes—
502C2×C11#245012yes—
503D11—44no—
504C24—22no—
505C24—21no—
506C24—22no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—112no—
511C24—112no—
512C24—112no—
513C24—222no—
514C24—221no—
515C24—222no—
516C24—222no—
517C24—221no—
518C24—222no—
519C24—221no—
520C24—221no—
521C24C2×C4×D1112yes—
522C24#433914yes—
523C24D4×D1114yes—
524C24D4×D1112yes—
525C24Q8×D1112yes—
526C24C23×D1111yescharacteristic
527C2×D4—1116no—
528C2×D4—228no—
529C2×D4—228no—
530C2×D4—2216no—
531C2×D4—2216no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—216no—
535C22×C4—28no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—28no—
553C22×C4—44no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—112no—
563C22×C4—112no—
564C22×C4—112no—
565C22×C4—112no—
566C22×C4—114no—
567C22×C4—114no—
568C22×C4—112no—
569C22×C4—228no—
570C22×C4—222no—
571C22×C4—221no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—221no—
575C22×C4—222no—
576C22×C4—221no—
577C22×C4—221no—
578C22×C4—228no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—444no—
594C22×C4—448no—
595C22×C4—448no—
596C22×C4C2×C4×D1112yes—
597C22×C4C2×C4×D1112yes—
598C22×C4#433914yes—
599C22×C4#433912yes—
600C22×C4C2×C22⋊D1114yes—
601C22×C4C2×C22⋊D1112yes—
602C4⋊C4—228no—
603C4⋊C4—448no—
604C4⋊C4—448no—
605C22⋊C4—1116no—
606C22⋊C4—228no—
607C22⋊C4—448no—
608C22⋊C4—448no—
609C22⋊C4—448no—
610C42—228no—
611C11#1389911yescharacteristic, complemented, Sylow
612C23—22no—
613C23—24no—
614C23—22no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—22no—
620C23—22no—
621C23—24no—
622C23—24no—
623C23—22no—
624C23—24no—
625C23—22no—
626C23—24no—
627C23—22no—
628C23—24no—
629C23—22no—
630C23—114no—
631C23—222no—
632C23—222no—
633C23—222no—
634C23—222no—
635C23—224no—
636C23—224no—
637C23—222no—
638C23—222no—
639C23—224no—
640C23—222no—
641C23—224no—
642C23—222no—
643C23—222no—
644C23—222no—
645C23—442no—
646C23—442no—
647C23—442no—
648C23—442no—
649C23—442no—
650C23—442no—
651C23—442no—
652C23—442no—
653C23#6692514yes—
654C23C22⋊C4×D1114yes—
655C23#6693718yes—
656C23C4⋊C4×D1114yes—
657C23#6694918yes—
658C23C22×C4×D1111yescharacteristic
659C23C2×#433912yes—
660C23C2×#433912yes—
661C23C2×#433911yescharacteristic
662C23C2×D4×D1112yes—
663C23C2×D4×D1111yescharacteristic
664C23#6703712yes—
665C23#6703711yescharacteristic
666C23C2×Q8×D1111yescharacteristic
667C23#6704011yescharacteristic
668C23C22×C22⋊D1111yescharacteristic
669D4—2232no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—416no—
684C2×C4—432no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—114no—
696C2×C4—114no—
697C2×C4—114no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—224no—
703C2×C4—224no—
704C2×C4—224no—
705C2×C4—222no—
706C2×C4—224no—
707C2×C4—224no—
708C2×C4—222no—
709C2×C4—224no—
710C2×C4—4416no—
711C2×C4—442no—
712C2×C4—442no—
713C2×C4—442no—
714C2×C4—442no—
715C2×C4—442no—
716C2×C4—442no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—442no—
721C2×C4—442no—
722C2×C4—442no—
723C2×C4—442no—
724C2×C4—442no—
725C2×C4C4×C22⋊D1114yes—
726C22—28no—
727C22—28no—
728C22—28no—
729C22—28no—
730C22—24no—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—24no—
735C22—24no—
736C22—224no—
737C22—224no—
738C22—224no—
739C22—444no—
740C22—444no—
741C22—444no—
742C22—444no—
743C22—442no—
744C22—442no—
745C22—442no—
746C22—442no—
747C22#1062228018yescomplemented
748C22C2×#6692511yescharacteristic
749C22C4×#433911yescharacteristic
750C22#1062301012yes—
751C22C2×C22⋊C4×D1111yescharacteristic
752C22#1062301711yescharacteristic
753C22C2×#6693712yes—
754C22#1062302112yes—
755C22#1062302112yes—
756C22#1062302112yes—
757C22#1062302512yes—
758C22C2×C4⋊C4×D1111yescharacteristic
759C22#1062303511yescharacteristic
760C22#1062303811yescharacteristic
761C22#1062303812yes—
762C22C2×#6694912yes—
763C22#1062304212yes—
764C22#1062304211yescharacteristic
765C22#1062304612yes—
766C22C2×C4×C22⋊D1111yescharacteristic
767C22#1062332212yes—
768C22D4×C22⋊D1111yescharacteristic
769C22D4×C22⋊D1112yes—
770C22Q8×C22⋊D1111yescharacteristic
771C4—24no—
772C4—44no—
773C4—44no—
774C4—42no—
775C4—224no—
776C4—224no—
777C4—224no—
778C4—882no—
779C4—882no—
780C2—28no—
781C2—444no—
782C2C2×#1062228011yescharacteristic
783C2#1307105911yescharacteristic
784C2#1307125011yescharacteristic
785C2C22⋊C4×C22⋊D1111yescharacteristic
786C2#1307144311yescharacteristic
787C2C4⋊C4×C22⋊D1111yescharacteristic
788C2#1307152311yescharacteristic
789C2#1307215212yes—
790C2#1307216712yes—
791C2#1307242512yes—
792C2#1307244012yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×#95C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22×#95D11
hypocenterC11#13899
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
3. C2×#10622823C2semidirect
4. C2×#10622280C2semidirect
5. #13066867C2semidirect
6. #13066860C2semidirect
7. Dic11⋊#95C2semidirect
8. #13066841C2semidirect
9. #13066839C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C22×C11×#95C2semidirect
19. C2×C4×C22⋊D11C4semidirect
73. C22×C4×D11C2×C4semidirect
87. C2×(C2×D11)⋊C4C2×C4semidirect
95. C2×Dic11⋊C4C2×C4semidirect
97. C2×C4×Dic11C2×C4semidirect
100. C11×#95D4semidirect
172. C2×C22⋊D11C4⋊C4semidirect
208. C22⋊Dic11C22⋊C4semidirect
220. C22×#95D11semidirect
380. C22×C11#380semidirect
490. #95C22⋊D11semidirect
611. C11#13899semidirect
747. C22#10622280semidirect

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×#106228262
C2×#106228232
C2×#106222802
#130668672
#130668602
Dic11⋊#952
#130668412
#130668392
(C2×D11)⋊#952
C22×C11×#952
#1389911