Finite Group Databasebeta

← #14675962

Subgroups — #14675962

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×#10622571C212yesmaximal
3C2×#10622559C212yesmaximal, complemented
4C2×#10622280C211yesmaximal, characteristic, complemented
5C22×C11⋊#95C211yesmaximal, characteristic, complemented
6#13066867C212yesmaximal, complemented
7#13066860C212yesmaximal, complemented
8Dic11⋊#95C211yesmaximal, characteristic, complemented
9#13066841C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
11C11×C22⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C24×Dic11C2212yes—
15C23×C4×D11C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
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×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2212yes—
30C2×C11⋊#95—24no—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38#10622571—28no—
39#10622559—28no—
40#10622280—24no—
41C25×C11C2311yescharacteristic
42C24×D11C2311yescharacteristic
43C23×C4×C11—24no—
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—42no—
47C23×C4×C11C2×C414yes—
48C23×C4×C11C2312yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11—24no—
53C22×C22⋊D11—24no—
54C22×C22⋊D11C2×C414yes—
55C22×C22⋊D11D414yes—
56C22×C22⋊D11Q814yes—
57C23×Dic11—24no—
58C23×Dic11—24no—
59C23×Dic11—24no—
60C23×Dic11—24no—
61C23×Dic11—24no—
62C23×Dic11—42no—
63C23×Dic11—42no—
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×C11×C22⋊C4—24no—
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4—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—22no—
99C11×#95—22no—
100C11×#95—42no—
101C11⋊#95—22no—
102C11⋊#95—24no—
103C11⋊#95—24no—
104C11⋊#95—24no—
105C11⋊#95—24no—
106C11⋊#95—24no—
107C11⋊#95D414yescomplemented
108#13899—111nomaximal, Sylow
109C24×C11—21no—
110C24×C11—22no—
111C24×C11—21no—
112C24×C11—21no—
113C24×C11—22no—
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—28no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—28no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
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—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—44no—
155C22×C4×C11—48no—
156C22×C4×C11—48no—
157C22×C4×C11C22×C412yes—
158C22×C4×C11C22×C412yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11#4112yes—
161C2×C22⋊D11—28no—
162C2×C22⋊D11—28no—
163C2×C22⋊D11—216no—
164C2×C22⋊D11—216no—
165C2×C22⋊D11C4⋊C4116yescomplemented
166C22×Dic11—216no—
167C22×Dic11—22no—
168C22×Dic11—21no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—21no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—21no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—21no—
187C22×Dic11—48no—
188C22×Dic11—48no—
189C22×Dic11—48no—
190C22×Dic11—48no—
191C22×Dic11—48no—
192C22×Dic11—48no—
193C22×Dic11C22×C412yes—
194C22×Dic11C22×C412yes—
195C22×Dic11C22×C412yes—
196C22×Dic11C2×D414yes—
197C22×Dic11C2×D414yes—
198C22×Dic11C2×D414yes—
199C22×Dic11C2×D412yes—
200C22×Dic11C2×Q812yes—
201C22×Dic11#4114yes—
202C2×C4×D11—28no—
203C2×C4×D11—28no—
204C2×C4×D11—44no—
205C2×C4×D11—48no—
206C2×C4×D11—48no—
207C11×C22⋊C4—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×#95—111no—
221#1441—112no—
222#1439—112no—
223C4⋊#95—111no—
224#1434—111no—
225C22⋊#95—111no—
226C22⋊#95D1111yescharacteristic, complemented
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—22no—
236C23×C11—24no—
237C23×C11—24no—
238C23×C11—24no—
239C23×C11—24no—
240C23×C11—22no—
241C23×C11—24no—
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—416no—
292C2×C4×C11—42no—
293C2×C4×C11—42no—
294C2×C4×C11—42no—
295C2×C4×C11—42no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
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×C11C4×D414yes—
309C22⋊D11—232no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—24no—
319C2×Dic11—24no—
320C2×Dic11—24no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—24no—
328C2×Dic11—432no—
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×C4—112no—
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⋊C4C2×D1112yes—
355C22×C42—111no—
356#386—228no—
357#385—228no—
358#380—224no—
359C2×#95—111no—
360C2×#95—111no—
361C2×#95—112no—
362C2×#95—112no—
363C2×#95—112no—
364C2×#95—112no—
365C2×#95—112no—
366C2×#95—224no—
367C2×#95C2×D1111yescharacteristic
368C2×#95C2×D1111yescharacteristic
369C2×#95C2×D1112yes—
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#54711yescharacteristic
400C22×C11#54712yes—
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—82no—
418C4×C11—82no—
419Dic11—24no—
420Dic11—24no—
421Dic11—24no—
422Dic11—44no—
423Dic11—44no—
424C25—111no—
425C25C22×D1111yescharacteristic
426C22×D4—114no—
427C22×D4—114no—
428C22×D4—114no—
429C22×D4—224no—
430C22×D4—224no—
431C23×C4—24no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—42no—
435C23×C4—111no—
436C23×C4—111no—
437C23×C4—111no—
438C23×C4—112no—
439C23×C4—112no—
440C23×C4—114no—
441C23×C4—224no—
442C23×C4—224no—
443C23×C4—224no—
444C23×C4—224no—
445C23×C4—222no—
446C23×C4—222no—
447C23×C4—224no—
448C23×C4—224no—
449C23×C4—442no—
450C23×C4—442no—
451C23×C4—442no—
452C23×C4C4×D1114yes—
453C23×C4C22×D1112yes—
454C23×C4C22×D1112yes—
455C23×C4C22×D1111yescharacteristic
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—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—114no—
470C2×C22⋊C4—118no—
471C2×C22⋊C4—114no—
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—22no—
482#95—22no—
483#95—42no—
484#95—114no—
485#95—224no—
486#95—224no—
487#95—224no—
488#95—224no—
489#95—224no—
490#95—222no—
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—21no—
505C24—21no—
506C24—22no—
507C24—22no—
508C24—21no—
509C24—21no—
510C24—112no—
511C24—112no—
512C24—112no—
513C24—222no—
514C24—221no—
515C24—222no—
516C24—221no—
517C24—222no—
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—28no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—28no—
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—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—44no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—112no—
558C22×C4—112no—
559C22×C4—112no—
560C22×C4—112no—
561C22×C4—114no—
562C22×C4—114no—
563C22×C4—112no—
564C22×C4—114no—
565C22×C4—114no—
566C22×C4—228no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—2216no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
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—228no—
589C22×C4—444no—
590C22×C4—448no—
591C22×C4—448no—
592C22×C4—448no—
593C22×C4—448no—
594C22×C4—448no—
595C22×C4—448no—
596C22×C4—448no—
597C22×C4—448no—
598C22×C4C2×C4×D1112yes—
599C22×C4C2×C4×D1112yes—
600C22×C4D4×D1112yes—
601C22×C4#434112yes—
602C4⋊C4—228no—
603C4⋊C4—448no—
604C4⋊C4—448no—
605C22⋊C4—48no—
606C22⋊C4—1116no—
607C22⋊C4—228no—
608C22⋊C4—448no—
609C22⋊C4—448no—
610C42—228no—
611C11#1389911yescharacteristic, complemented, Sylow
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—22no—
623C23—24no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—114no—
631C23—222no—
632C23—222no—
633C23—222no—
634C23—222no—
635C23—224no—
636C23—224no—
637C23—222no—
638C23—222no—
639C23—222no—
640C23—224no—
641C23—222no—
642C23—222no—
643C23—222no—
644C23—224no—
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×D4×D1112yes—
661C23C2×D4×D1111yescharacteristic
662C23C2×D4×D1111yescharacteristic
663C23C2×#434111yescharacteristic
664C23#6703712yes—
665C23C2×Q8×D1111yescharacteristic
666C23#41×D1112yes—
667C23#6704211yescharacteristic
668C23#6704311yescharacteristic
669D4—2232no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—416no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
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—114no—
695C2×C4—114no—
696C2×C4—114no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—224no—
702C2×C4—224no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—224no—
706C2×C4—224no—
707C2×C4—224no—
708C2×C4—224no—
709C2×C4—224no—
710C2×C4—224no—
711C2×C4—224no—
712C2×C4—224no—
713C2×C4—224no—
714C2×C4—224no—
715C2×C4—4416no—
716C2×C4—4432no—
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×C4(C22⋊D11)⋊C414yes—
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
749C22C2×C22⋊C4×D1111yescharacteristic
750C22C2×(C22⋊D11)⋊C411yescharacteristic
751C22#1062301711yescharacteristic
752C22C2×#6693712yes—
753C22C2×C4⋊C4×D1111yescharacteristic
754C22C2×#6694912yes—
755C22#1062305311yescharacteristic
756C22#1062305411yescharacteristic
757C22#1062306912yes—
758C22#1062307812yes—
759C22#1062309112yes—
760C22#1062309512yes—
761C22#1062312112yes—
762C22#1062312212yes—
763C22#1062314011yescharacteristic
764C22#1062314112yes—
765C22#1062314211yescharacteristic
766C22#1062316311yescharacteristic
767C22#1062316611yescharacteristic
768C22#1062316712yes—
769C22#1062318512yes—
770C22#1062318612yes—
771C4—24no—
772C4—42no—
773C4—82no—
774C4—82no—
775C4—224no—
776C4—224no—
777C4—224no—
778C4—444no—
779C4—444no—
780C2—28no—
781C2—444no—
782C2C2×#1062228011yescharacteristic
783C2#1307105511yescharacteristic
784C2#1307124311yescharacteristic
785C2#1307143211yescharacteristic
786C2#1307144011yescharacteristic
787C2#1307151211yescharacteristic
788C2#1307152011yescharacteristic
789C2#1307215412yes—
790C2#1307216912yes—
791C2#1307242712yes—
792C2#1307244212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#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×#10622559C2semidirect
4. C2×#10622280C2semidirect
5. C22×C11⋊#95C2semidirect
6. #13066867C2semidirect
7. #13066860C2semidirect
8. Dic11⋊#95C2semidirect
9. #13066841C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C11×C22⋊#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
107. C11⋊#95D4semidirect
165. C2×C22⋊D11C4⋊C4semidirect
208. C22⋊Dic11C22⋊C4semidirect
226. C22⋊#95D11semidirect
380. C22×C11#380semidirect
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×#106225712
C2×#106225592
C2×#106222802
C22×C11⋊#952
#130668672
#130668602
Dic11⋊#952
#130668412
(C2×D11)⋊#952
C11×C22⋊#952
#1389911