Finite Group Databasebeta

← #14682188

Subgroups — #14682188

Order 2816.

2118 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622552C211yesmaximal, characteristic
2C2×#10622278C212yesmaximal
3C2×#10622281C212yesmaximal, complemented
4C2×#10622602C212yesmaximal, complemented
5#13066868C212yesmaximal, complemented
6#13066862C212yesmaximal, complemented
7#13066858C212yesmaximal, complemented
8#13066846C211yesmaximal, characteristic, complemented
9C11×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×C4×D11C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2212yes—
24C2×C11×#95C2212yes—
25C2×C11×#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31#10622602—28no—
32#10622552C418yescomplemented
33#10622281—28no—
34#10622278—28no—
35C24×D11C2312yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C23×Dic11C2312yes—
44C22×D44—41no—
45C22×D44—41no—
46C22×D44—41no—
47C22×D44—41no—
48C22×D44C2×C414yes—
49C22×D44D414yes—
50C22×D44Q814yes—
51C22×C4×D11—24no—
52C22×C4×D11—24no—
53C22×C4×D11—24no—
54C22×C4×D11—42no—
55C22×C4×D11—42no—
56C22×C4×D11—42no—
57C22×C4×D11—42no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—41no—
60C2×C11×C4⋊C4—41no—
61C2×C11×C4⋊C4—41no—
62C2×C11×C4⋊C4—41no—
63C2×C11×C4⋊C4D414yescomplemented
64C2×C42×C11—41no—
65C2×C42×C11—41no—
66C2×C42×C11C2×C414yescomplemented
67C2×(C2×D11)⋊C4—24no—
68C2×(C2×D11)⋊C4—24no—
69C2×(C2×D11)⋊C4—24no—
70C2×(C2×D11)⋊C4—24no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—42no—
77C2×(C2×D11)⋊C4—42no—
78C2×(C2×D11)⋊C4—42no—
79C2×(C2×D11)⋊C4—42no—
80C2×(C2×D11)⋊C4C2×C418yescomplemented
81C2×(C2×D11)⋊C4C2×C418yescomplemented
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—41no—
84C2×C4⋊Dic11—41no—
85C2×C4⋊Dic11—41no—
86C2×C4⋊Dic11—41no—
87C2×C4⋊Dic11—41no—
88C2×C4⋊Dic11—41no—
89C2×C4⋊Dic11C2×C414yescomplemented
90C2×C4⋊Dic11D414yescomplemented
91C2×Dic11⋊C4—24no—
92C2×Dic11⋊C4—24no—
93C2×Dic11⋊C4—42no—
94C11×#95—24no—
95C11×#95—24no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95—24no—
99C11⋊#95—24no—
100C11⋊#95—42no—
101#14440—111nomaximal, Sylow
102C24×C11C2411yescharacteristic
103C23×D11—22no—
104C23×D11—22no—
105C23×D11—22no—
106C23×D11—22no—
107C23×D11—22no—
108C23×D11—22no—
109C23×D11—22no—
110C23×D11—22no—
111C23×D11—22no—
112C23×D11—22no—
113C23×D11—22no—
114C23×D11—22no—
115C23×D11C22×C414yes—
116C23×D11C2×D414yes—
117C23×D11C2×Q814yes—
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×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11C22×C412yes—
144C22×C4×C11C22×C412yes—
145C22×C4×C11C22×C412yes—
146C22×C4×C11C2×D414yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×Q812yes—
151C22×C4×C11#4112yes—
152C22×C4×C11#4112yes—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11C22×C414yes—
173C22×Dic11C2×D414yes—
174C2×D44—44no—
175C2×D44—44no—
176C2×D44—44no—
177C2×D44—44no—
178C2×D44—44no—
179C2×D44—44no—
180C2×D44C4⋊C4116yescomplemented
181C2×C4×D11—48no—
182C2×C4×D11—48no—
183C2×C4×D11—48no—
184C2×C4×D11—48no—
185C2×C4×D11—48no—
186C2×C4×D11—48no—
187C2×C4×D11—48no—
188C11×C4⋊C4—44no—
189C11×C4⋊C4—44no—
190C42×C11—44no—
191(C2×D11)⋊C4—216no—
192(C2×D11)⋊C4—216no—
193(C2×D11)⋊C4—48no—
194(C2×D11)⋊C4—48no—
195(C2×D11)⋊C4—48no—
196C4⋊Dic11—44no—
197C4⋊Dic11—44no—
198C4⋊Dic11—44no—
199Dic11⋊C4—48no—
200C2×#390—111no—
201C2×#386—112no—
202C2×#385—112no—
203C2×#385—112no—
204#1441—112no—
205#1439—112no—
206#1439—112no—
207C4⋊#95—111no—
208C4⋊#95D1111yescharacteristic, complemented
209C23×C11C23×C411yescharacteristic
210C23×C11C22×D411yescharacteristic
211C23×C11C22×D411yescharacteristic
212C23×C11C22×D411yescharacteristic
213C23×C11C22×Q811yescharacteristic
214C23×C11C2×#4111yescharacteristic
215C23×C11C2×#4111yescharacteristic
216C23×C11H(5,𝔽2)11yescharacteristic
217C23×C11H(5,𝔽2)11yescharacteristic
218C23×C11H(5,𝔽2)11yescharacteristic
219C23×C11H(5,𝔽2)11yescharacteristic
220C23×C11H(5,𝔽2)11yescharacteristic
221C23×C11H(5,𝔽2)11yescharacteristic
222C23×C112−1+411yescharacteristic
223C23×C112−1+411yescharacteristic
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—24no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—24no—
231C22×D11—24no—
232C22×D11—24no—
233C22×D11—24no—
234C22×D11—24no—
235C22×D11—24no—
236C22×D11—24no—
237C22×D11—24no—
238C22×D11—24no—
239C22×D11—24no—
240C22×D11—24no—
241C22×D11—24no—
242C22×D11—42no—
243C22×D11—42no—
244C22×D11—42no—
245C22×D11—42no—
246C22×D11—42no—
247C22×D11—42no—
248C22×D11—42no—
249C22×D11—42no—
250C22×D11—42no—
251C22×D11—42no—
252C22×D11—42no—
253C22×D11—42no—
254C22×D11—42no—
255C22×D11—42no—
256C22×D11—42no—
257C22×D11—42no—
258C22×D11C2×C4⋊C418yes—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—24no—
278C2×C4×C11—24no—
279C2×C4×C11—24no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—42no—
283C2×C4×C11—42no—
284C2×C4×C11—42no—
285C2×C4×C11—42no—
286C2×C4×C11—42no—
287C2×C4×C11—42no—
288C2×C4×C11—42no—
289C2×C4×C11—42no—
290C2×C4×C11—42no—
291C2×C4×C11C2×C4⋊C414yes—
292C2×C4×C11C4×D414yes—
293C2×C4×C11C4×D414yes—
294C2×Dic11—24no—
295C2×Dic11—24no—
296C2×Dic11—24no—
297C2×Dic11—24no—
298C2×Dic11—24no—
299C2×Dic11—24no—
300C2×Dic11—42no—
301C2×Dic11—42no—
302C2×Dic11—42no—
303C2×Dic11—42no—
304C2×Dic11—42no—
305C2×Dic11—42no—
306C2×Dic11—42no—
307C2×Dic11—42no—
308C2×Dic11—42no—
309C2×Dic11—42no—
310C2×Dic11—42no—
311C2×Dic11—42no—
312C2×Dic11—42no—
313C2×Dic11—42no—
314C2×Dic11—42no—
315D44—416no—
316C4×D11—432no—
317C23×D4—111no—
318C24×C4—112no—
319C22×C4⋊C4—111no—
320C22×C4⋊C4—111no—
321C22×C4⋊C4—112no—
322C22×C4⋊C4—111no—
323C22×C4⋊C4C2×D1111yescharacteristic
324C22×C4⋊C4C2×D1111yescharacteristic
325C22×C22⋊C4—112no—
326C22×C22⋊C4—112no—
327C22×C22⋊C4—112no—
328C22×C22⋊C4—112no—
329C22×C22⋊C4—112no—
330C22×C42C2×D1111yescharacteristic
331#390—118no—
332#386—228no—
333#385—228no—
334#385—228no—
335C2×#95—112no—
336C2×#95—112no—
337C2×#95—112no—
338C2×#95—112no—
339C2×#95—112no—
340C2×#95C2×D1112yes—
341C2×#95C2×D1112yes—
342C22×C11C22×C4⋊C411yescharacteristic
343C22×C11C2×C4×D411yescharacteristic
344C22×C11C2×C4×D411yescharacteristic
345C22×C11#51811yescharacteristic
346C22×C11#51811yescharacteristic
347C22×C11#52011yescharacteristic
348C22×C11#52011yescharacteristic
349C22×C11#53411yescharacteristic
350C22×C11#53411yescharacteristic
351C22×C11#53411yescharacteristic
352C22×C11#53411yescharacteristic
353C22×C11#53711yescharacteristic
354C22×C11#53711yescharacteristic
355C22×C11#53811yescharacteristic
356C22×C11#53811yescharacteristic
357C22×C11#53911yescharacteristic
358C22×C11#53911yescharacteristic
359C22×C11#54311yescharacteristic
360C22×C11#54311yescharacteristic
361C22×C11D4211yescharacteristic
362C22×C11D4211yescharacteristic
363C22×C11D4211yescharacteristic
364C22×C11#54711yescharacteristic
365C22×C11#54711yescharacteristic
366C22×C11D4×Q811yescharacteristic
367C22×C11D4×Q811yescharacteristic
368C22×C11#55011yescharacteristic
369C22×C11#55011yescharacteristic
370C22×C11#55411yescharacteristic
371C22×C11#55411yescharacteristic
372C22×C11#55911yescharacteristic
373C22×C11H(3,𝔽4)11yescharacteristic
374C22×C11#56211yescharacteristic
375C22×C11#56211yescharacteristic
376C22×C11#56311yescharacteristic
377C2×D11—28no—
378C2×D11—28no—
379C2×D11—28no—
380C2×D11—44no—
381C2×D11—44no—
382C2×D11—44no—
383C2×D11—44no—
384C2×D11—44no—
385C2×D11—44no—
386C2×D11—44no—
387C2×D11—44no—
388C2×D11—44no—
389C2×D11—44no—
390C2×D11—44no—
391C2×D11—44no—
392C4×C11—24no—
393C4×C11—24no—
394C4×C11—24no—
395C4×C11—44no—
396C4×C11—82no—
397Dic11—44no—
398Dic11—44no—
399Dic11—82no—
400C25—112no—
401C22×D4—114no—
402C22×D4—114no—
403C22×D4—114no—
404C22×D4—441no—
405C22×D4—441no—
406C22×D4—441no—
407C22×D4—441no—
408C23×C4—112no—
409C23×C4—112no—
410C23×C4—112no—
411C23×C4—224no—
412C23×C4—224no—
413C23×C4—224no—
414C23×C4—442no—
415C23×C4—442no—
416C23×C4—442no—
417C23×C4—442no—
418C23×C4C22×D1112yes—
419C23×C4C22×D1112yes—
420C23×C4C22×D1111yescharacteristic
421C23×C4C22×D1111yescharacteristic
422C23×C4C22×D1111yescharacteristic
423C2×C4⋊C4—22no—
424C2×C4⋊C4—41no—
425C2×C4⋊C4—41no—
426C2×C4⋊C4—41no—
427C2×C4⋊C4—41no—
428C2×C4⋊C4—114no—
429C2×C4⋊C4—114no—
430C2×C4⋊C4—224no—
431C2×C4⋊C4—224no—
432C2×C4⋊C4—222no—
433C2×C4⋊C4—442no—
434C2×C4⋊C4—441no—
435C2×C4⋊C4—441no—
436C2×C4⋊C4—441no—
437C2×C4⋊C4—441no—
438C2×C4⋊C4—441no—
439C2×C4⋊C4—441no—
440C2×C4⋊C4D4414yescomplemented
441C2×C22⋊C4—118no—
442C2×C22⋊C4—118no—
443C2×C22⋊C4—224no—
444C2×C22⋊C4—224no—
445C2×C22⋊C4—224no—
446C2×C22⋊C4—224no—
447C2×C22⋊C4—224no—
448C2×C22⋊C4—224no—
449C2×C22⋊C4—224no—
450C2×C22⋊C4—224no—
451C2×C22⋊C4—224no—
452C2×C22⋊C4—442no—
453C2×C22⋊C4—442no—
454C2×C22⋊C4—442no—
455C2×C22⋊C4—442no—
456C2×C42—41no—
457C2×C42—41no—
458C2×C42C4×D1114yescomplemented
459#95—24no—
460#95—24no—
461#95—224no—
462#95—224no—
463#95—224no—
464#95—224no—
465#95—442no—
466C2×C11#231511yescharacteristic
467C2×C11#232511yescharacteristic
468C2×C11#232511yescharacteristic
469C2×C11D4×C4⋊C411yescharacteristic
470C2×C11D4×C4⋊C411yescharacteristic
471C2×C11#236611yescharacteristic
472C2×C11#237911yescharacteristic
473C2×C11#267911yescharacteristic
474C2×C11#268211yescharacteristic
475C2×C11#268211yescharacteristic
476C2×C11#268311yescharacteristic
477C2×C11#272411yescharacteristic
478C2×C11#273211yescharacteristic
479C2×C11#273211yescharacteristic
480C2×C11#280411yescharacteristic
481D11—48no—
482C24—114no—
483C24—114no—
484C24—114no—
485C24—222no—
486C24—222no—
487C24—222no—
488C24—222no—
489C24—222no—
490C24—222no—
491C24—222no—
492C24—222no—
493C24—222no—
494C24—222no—
495C24—222no—
496C24—222no—
497C24C23×D1111yescharacteristic
498C2×D4—1116no—
499C2×D4—444no—
500C2×D4—444no—
501C2×D4—444no—
502C2×D4—444no—
503C2×D4—444no—
504C2×D4—444no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—114no—
531C22×C4—114no—
532C22×C4—222no—
533C22×C4—222no—
534C22×C4—222no—
535C22×C4—222no—
536C22×C4—222no—
537C22×C4—222no—
538C22×C4—222no—
539C22×C4—222no—
540C22×C4—222no—
541C22×C4—222no—
542C22×C4—222no—
543C22×C4—222no—
544C22×C4—222no—
545C22×C4—222no—
546C22×C4—222no—
547C22×C4—222no—
548C22×C4—222no—
549C22×C4—222no—
550C22×C4—222no—
551C22×C4—448no—
552C22×C4—448no—
553C22×C4—448no—
554C22×C4—448no—
555C22×C4—448no—
556C22×C4—448no—
557C22×C4—448no—
558C22×C4C2×C4×D1112yes—
559C22×C4C2×C4×D1112yes—
560C22×C4C2×C4×D1112yes—
561C22×C4C2×D4414yes—
562C22×C4C2×D4412yes—
563C22×C4#433912yes—
564C22×C4D4×D1112yes—
565C22×C4D4×D1112yes—
566C22×C4Q8×D1112yes—
567C22×C4#434312yes—
568C4⋊C4—44no—
569C4⋊C4—44no—
570C4⋊C4—444no—
571C4⋊C4—444no—
572C4⋊C4—448no—
573C4⋊C4—444no—
574C22⋊C4—2216no—
575C22⋊C4—2216no—
576C22⋊C4—448no—
577C22⋊C4—448no—
578C22⋊C4—448no—
579C42—44no—
580C11#1444011yescharacteristic, complemented, Sylow
581C23—118no—
582C23—224no—
583C23—224no—
584C23—224no—
585C23—224no—
586C23—224no—
587C23—224no—
588C23—224no—
589C23—224no—
590C23—224no—
591C23—224no—
592C23—224no—
593C23—224no—
594C23—224no—
595C23—224no—
596C23—224no—
597C23—224no—
598C23—224no—
599C23—224no—
600C23—442no—
601C23—442no—
602C23—442no—
603C23—442no—
604C23—442no—
605C23—442no—
606C23—442no—
607C23—442no—
608C23—442no—
609C23—442no—
610C23—442no—
611C23—442no—
612C23—442no—
613C23—442no—
614C23—442no—
615C23—442no—
616C23C22×C4×D1111yescharacteristic
617C23C22×D4411yescharacteristic
618C23C2×#433911yescharacteristic
619C23C2×D4×D1111yescharacteristic
620C23C2×D4×D1111yescharacteristic
621C23#6703711yescharacteristic
622C23#6703711yescharacteristic
623C23#6703711yescharacteristic
624C23C2×Q8×D1111yescharacteristic
625C23C2×#434311yescharacteristic
626C23#6704011yescharacteristic
627C23#6704211yescharacteristic
628C23#6704211yescharacteristic
629C23#6704211yescharacteristic
630C23#6704311yescharacteristic
631D4—4416no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—224no—
665C2×C4—224no—
666C2×C4—224no—
667C2×C4—224no—
668C2×C4—224no—
669C2×C4—224no—
670C2×C4—4432no—
671C2×C4—442no—
672C2×C4—442no—
673C2×C4—442no—
674C2×C4—442no—
675C2×C4—442no—
676C2×C4—442no—
677C2×C4—442no—
678C2×C4—442no—
679C2×C4—442no—
680C2×C4—442no—
681C2×C4—442no—
682C2×C4—442no—
683C2×C4—442no—
684C2×C4—442no—
685C2×C4—442no—
686C2×C4C4×D4414yes—
687C2×C4C4⋊C4×D1114yes—
688C2×C4#6694614yes—
689C22—228no—
690C22—228no—
691C22—228no—
692C22—444no—
693C22—444no—
694C22—444no—
695C22—444no—
696C22—444no—
697C22—444no—
698C22—444no—
699C22—444no—
700C22—444no—
701C22—444no—
702C22—444no—
703C22—444no—
704C22C2×C4×D4411yescharacteristic
705C22#1062301711yescharacteristic
706C22#1062302411yescharacteristic
707C22#1062302511yescharacteristic
708C22C2×C4⋊C4×D1111yescharacteristic
709C22C2×#6694611yescharacteristic
710C22#1062303511yescharacteristic
711C22#1062304111yescharacteristic
712C22#1062304611yescharacteristic
713C22#1062305211yescharacteristic
714C22#1062305411yescharacteristic
715C22D4×D4411yescharacteristic
716C22D4×D4411yescharacteristic
717C22#1062308211yescharacteristic
718C22#1062308411yescharacteristic
719C22Q8×D4411yescharacteristic
720C22#1062310811yescharacteristic
721C22#1062311011yescharacteristic
722C22#1062311611yescharacteristic
723C22#1062312811yescharacteristic
724C22#1062313611yescharacteristic
725C22#1062313611yescharacteristic
726C22#1062313611yescharacteristic
727C22#1062316511yescharacteristic
728C22#1062316511yescharacteristic
729C22#1062317511yescharacteristic
730C22#1062317611yescharacteristic
731C22#1062321411yescharacteristic
732C22#1062321511yescharacteristic
733C22#1062323011yescharacteristic
734C22#1062323111yescharacteristic
735C22#1062324811yescharacteristic
736C22#1062325711yescharacteristic
737C22#1062325811yescharacteristic
738C22#1062326111yescharacteristic
739C4—24no—
740C4—24no—
741C4—24no—
742C4—44no—
743C4—82no—
744C4—444no—
745C4—444no—
746C4—882no—
747C2—448no—
748C2#1307122911yescharacteristic
749C2#1307131611yescharacteristic
750C2#1307131911yescharacteristic
751C2#1307151611yescharacteristic
752C2C4⋊C4×D4411yescharacteristic
753C2#1307168011yescharacteristic
754C2#1307178711yescharacteristic
755C2#1307495111yescharacteristic
756C2#1307497811yescharacteristic
757C2#1307497911yescharacteristic
758C2#1307498711yescharacteristic
759C2#1307554511yescharacteristic
760C2#1307563211yescharacteristic
761C2#1307563411yescharacteristic
762C2#1307656011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC4⋊#95D11
hypocenterC11#14440
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#10622281C2semidirect
4. C2×#10622602C2semidirect
5. #13066868C2semidirect
6. #13066862C2semidirect
7. #13066858C2semidirect
8. #13066846C2semidirect
9. C11×C4⋊#95C2semidirect
32. #10622552C4semidirect
63. C2×C11×C4⋊C4D4semidirect
66. C2×C42×C11C2×C4semidirect
80. C2×(C2×D11)⋊C4C2×C4semidirect
81. C2×(C2×D11)⋊C4C2×C4semidirect
89. C2×C4⋊Dic11C2×C4semidirect
90. C2×C4⋊Dic11D4semidirect
180. C2×D44C4⋊C4semidirect
208. C4⋊#95D11semidirect
440. C2×C4⋊C4D44semidirect
458. C2×C42C4×D11semidirect
580. C11#14440semidirect

Maximal subgroups

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

subgroupindex
C2×#106225522
C2×#106222782
C2×#106222812
C2×#106226022
#130668682
#130668622
#130668582
#130668462
C11×C4⋊#952
#1444011