Finite Group Databasebeta

← #14661661

Subgroups — #14661661

Order 2816.

1194 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622559C211yesmaximal, characteristic
2C2×#10622555C211yesmaximal, characteristic
3C2×#10622164C211yesmaximal, characteristic
4C2×#10622165C211yesmaximal, characteristic
5C2×#10622165C211yesmaximal, characteristic
6#13066838C211yesmaximal, characteristic
7C2×C11×#342C211yesmaximal, characteristic
8C24×Dic11C2211yescharacteristic
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×C11×C22⋊C4C2211yescharacteristic
12C22×C22⋊Dic11C2211yescharacteristic
13C22×C22⋊Dic11C2211yescharacteristic
14C22×C22⋊Dic11C2211yescharacteristic
15C22×Dic11⋊C4—21no—
16C22×Dic11⋊C4C412yescomplemented
17C2×C11⋊#95—21no—
18C2×C11⋊#95—22no—
19C2×C11⋊#95C412yescomplemented
20#10622559—21no—
21#10622559—22no—
22#10622559—21no—
23#10622555—22no—
24#10622555—22no—
25C11×#342—22no—
26#10622165—22no—
27#10622165—22no—
28#10622164—22no—
29C25×C11C2311yescharacteristic
30C23×C4×C11—21no—
31C23×C4×C11—21no—
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11C2×C411yescharacteristic
34C23×Dic11—21no—
35C23×Dic11—21no—
36C23×Dic11—21no—
37C23×Dic11—21no—
38C23×Dic11—21no—
39C23×Dic11—21no—
40C23×Dic11—44no—
41C23×Dic11C2×C412yes—
42C23×Dic11C2×C412yes—
43C23×Dic11D411yescharacteristic
44C23×Dic11D412yes—
45C23×Dic11D411yescharacteristic
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4—21no—
54C2×C11×C22⋊C4—21no—
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—21no—
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4D412yes—
63C2×C11×C22⋊C4Q812yes—
64C2×C22⋊Dic11—21no—
65C2×C22⋊Dic11—21no—
66C2×C22⋊Dic11—21no—
67C2×C22⋊Dic11—21no—
68C2×C22⋊Dic11—21no—
69C2×C22⋊Dic11—21no—
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—21no—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11D412yes—
79C2×C22⋊Dic11D412yes—
80C2×C22⋊Dic11Q812yes—
81C2×C22⋊Dic11Q812yes—
82C2×Dic11⋊C4—24no—
83C2×Dic11⋊C4—22no—
84C2×Dic11⋊C4—22no—
85C2×Dic11⋊C4—44no—
86C2×Dic11⋊C4—44no—
87C11⋊#95—24no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90C11⋊#95—44no—
91#11203—111nomaximal, Sylow
92C24×C11—42no—
93C24×C11—42no—
94C24×C11C22×C411yescharacteristic
95C24×C11C2×D411yescharacteristic
96C24×C11C2×D411yescharacteristic
97C24×C11C2×D411yescharacteristic
98C24×C11C2×D411yescharacteristic
99C24×C11C2×D411yescharacteristic
100C24×C11C2×Q811yescharacteristic
101C24×C11C2×Q811yescharacteristic
102C24×C11C2×Q811yescharacteristic
103C24×C11#4111yescharacteristic
104C24×C11#4111yescharacteristic
105C24×C11#4111yescharacteristic
106C24×C11#4111yescharacteristic
107C24×C11#4111yescharacteristic
108C24×C11#4111yescharacteristic
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11—41no—
122C22×C4×C11—41no—
123C22×C4×C11—41no—
124C22×C4×C11—41no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×Dic11—24no—
128C22×Dic11—24no—
129C22×Dic11—24no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—42no—
143C22×Dic11—42no—
144C22×Dic11—42no—
145C22×Dic11—42no—
146C22×Dic11—42no—
147C22×Dic11—42no—
148C22×Dic11—42no—
149C22×Dic11—42no—
150C22×Dic11—42no—
151C22×Dic11—44no—
152C22×Dic11—44no—
153C22×Dic11—44no—
154C22×Dic11—44no—
155C22×Dic11—41no—
156C22×Dic11—41no—
157C22×Dic11—41no—
158C22×Dic11—41no—
159C22×Dic11C22⋊C412yes—
160C22×Dic11C22⋊C412yes—
161C22×Dic11C4⋊C414yescomplemented
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—41no—
167C11×C22⋊C4—41no—
168C11×C22⋊C4—41no—
169C11×C22⋊C4—41no—
170C11×C22⋊C4—41no—
171C11×C22⋊C4—41no—
172C11×C22⋊C4—41no—
173C11×C22⋊C4—41no—
174C22⋊Dic11—22no—
175C22⋊Dic11—22no—
176C22⋊Dic11—22no—
177C22⋊Dic11—22no—
178C22⋊Dic11—22no—
179C22⋊Dic11—22no—
180C22⋊Dic11—22no—
181C22⋊Dic11—22no—
182C22⋊Dic11—41no—
183C22⋊Dic11—41no—
184C22⋊Dic11—41no—
185C22⋊Dic11—41no—
186Dic11⋊C4—48no—
187Dic11⋊C4—44no—
188Dic11⋊C4—44no—
189C2×#385—111no—
190C2×#380—111no—
191C2×#342—111no—
192C2×#342—111no—
193C2×#342—111no—
194C2×#342D1111yescharacteristic
195C22⋊#95—111no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—42no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—41no—
215C23×C11—42no—
216C23×C11—41no—
217C23×C11—42no—
218C23×C11C2×C22⋊C411yescharacteristic
219C23×C11C2×C4⋊C411yescharacteristic
220C23×C11#11711yescharacteristic
221C23×C11C4×D411yescharacteristic
222C23×C11C4×D411yescharacteristic
223C23×C11C4×Q811yescharacteristic
224C23×C11C4×Q811yescharacteristic
225C23×C11#12011yescharacteristic
226C23×C11#12111yescharacteristic
227C23×C11#12111yescharacteristic
228C23×C11#12111yescharacteristic
229C23×C11#12111yescharacteristic
230C23×C11#12111yescharacteristic
231C23×C11#12111yescharacteristic
232C23×C11C22⋊Q811yescharacteristic
233C23×C11C22⋊Q811yescharacteristic
234C23×C11C22⋊Q811yescharacteristic
235C23×C11C22⋊Q811yescharacteristic
236C23×C11C22⋊Q811yescharacteristic
237C23×C11C22⋊Q811yescharacteristic
238C23×C11C22⋊Q811yescharacteristic
239C23×C11C22⋊Q811yescharacteristic
240C23×C11#12311yescharacteristic
241C23×C11#12311yescharacteristic
242C23×C11#12311yescharacteristic
243C23×C11#12411yescharacteristic
244C23×C11#12511yescharacteristic
245C23×C11#12511yescharacteristic
246C23×C11#12511yescharacteristic
247C23×C11#12511yescharacteristic
248C23×C11#12611yescharacteristic
249C23×C11#12611yescharacteristic
250C23×C11C4⋊Q811yescharacteristic
251C23×C11C4⋊Q811yescharacteristic
252C23×C11C4⋊Q811yescharacteristic
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—44no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—82no—
263C2×C4×C11—82no—
264C2×C4×C11—81no—
265C2×C4×C11—81no—
266C2×C4×C11—82no—
267C2×C4×C11—81no—
268C2×C4×C11—81no—
269C2×C4×C11—81no—
270C2×C4×C11—81no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—44no—
280C2×Dic11—44no—
281C2×Dic11—44no—
282C2×Dic11—44no—
283C2×Dic11—44no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11—44no—
289C2×Dic11—42no—
290C2×Dic11—42no—
291C2×Dic11—44no—
292C2×Dic11—42no—
293C2×Dic11—42no—
294C2×Dic11—82no—
295C2×Dic11—82no—
296C2×Dic11—81no—
297C2×Dic11—81no—
298C2×Dic11—82no—
299C2×Dic11#9914yes—
300C24×C4—111no—
301C22×C4⋊C4—112no—
302C22×C4⋊C4—221no—
303C22×C22⋊C4—111no—
304C22×C22⋊C4—111no—
305C22×C22⋊C4—111no—
306C22×C22⋊C4C2×D1111yescharacteristic
307C22×C22⋊C4C2×D1111yescharacteristic
308C22×C22⋊C4C2×D1111yescharacteristic
309#385—221no—
310#385—222no—
311#385—221no—
312#380—222no—
313#380—222no—
314C2×#95—112no—
315C2×#95—221no—
316C2×#95—222no—
317#342—22no—
318#342—222no—
319#342—222no—
320#342—222no—
321C22×C11—22no—
322C22×C11—22no—
323C22×C11—22no—
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—22no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—21no—
339C22×C11—22no—
340C22×C11—22no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—22no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11#38011yescharacteristic
362C22×C11#38611yescharacteristic
363C22×C11#38711yescharacteristic
364C22×C11#38711yescharacteristic
365C22×C11#38911yescharacteristic
366C22×C11#38911yescharacteristic
367C22×C11#39111yescharacteristic
368C22×C11#39411yescharacteristic
369C22×C11#39511yescharacteristic
370C22×C11#39611yescharacteristic
371C22×C11#39611yescharacteristic
372C22×C11#39811yescharacteristic
373C22×C11#39811yescharacteristic
374C22×C11#39811yescharacteristic
375C22×C11#40011yescharacteristic
376C22×C11C2×#9912yes—
377C22×C11#41012yes—
378C4×C11—82no—
379C4×C11—82no—
380C4×C11—81no—
381C4×C11—81no—
382Dic11—24no—
383Dic11—44no—
384Dic11—42no—
385Dic11—82no—
386Dic11—82no—
387C25C22×D1111yescharacteristic
388C23×C4—21no—
389C23×C4—21no—
390C23×C4—111no—
391C23×C4—112no—
392C23×C4—112no—
393C23×C4—112no—
394C23×C4—111no—
395C23×C4—221no—
396C23×C4—221no—
397C23×C4—221no—
398C23×C4—221no—
399C23×C4—221no—
400C23×C4—221no—
401C23×C4—444no—
402C23×C4C4×D1111yescharacteristic
403C23×C4C4×D1111yescharacteristic
404C2×C4⋊C4—222no—
405C2×C4⋊C4—222no—
406C2×C4⋊C4—224no—
407C2×C4⋊C4—444no—
408C2×C4⋊C4—444no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—112no—
426C2×C22⋊C4—112no—
427C2×C22⋊C4—112no—
428C2×C22⋊C4—112no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4Dic2212yes—
444C2×C22⋊C4C22⋊D1112yes—
445#95—222no—
446#95—222no—
447#95—224no—
448#95—444no—
449C2×C11—21no—
450C2×C11—21no—
451C2×C11—21no—
452C2×C11—21no—
453C2×C11—21no—
454C2×C11—21no—
455C2×C11—21no—
456C2×C11—21no—
457C2×C11—21no—
458C2×C11—21no—
459C2×C11—21no—
460C2×C11—21no—
461C2×C11#144111yescharacteristic
462C2×C11#179912yes—
463C2×C11#189811yescharacteristic
464C2×C11#189911yescharacteristic
465C2×C11#199612yes—
466C24—42no—
467C24—42no—
468C24C2×Dic2211yescharacteristic
469C24C2×C4×D1111yescharacteristic
470C24#433911yescharacteristic
471C24#433911yescharacteristic
472C24#433911yescharacteristic
473C24#433911yescharacteristic
474C24D4×D1111yescharacteristic
475C24D4×D1111yescharacteristic
476C24D4×D1111yescharacteristic
477C24D4×D1111yescharacteristic
478C24#434111yescharacteristic
479C24#434111yescharacteristic
480C24Q8×D1111yescharacteristic
481C24Q8×D1111yescharacteristic
482C24C2×C22⋊D1111yescharacteristic
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—112no—
502C22×C4—112no—
503C22×C4—114no—
504C22×C4—224no—
505C22×C4—224no—
506C22×C4—224no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—221no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—221no—
516C22×C4—222no—
517C22×C4—222no—
518C22×C4—222no—
519C22×C4—442no—
520C22×C4—442no—
521C22×C4—442no—
522C22×C4—444no—
523C22×C4—444no—
524C22×C4—444no—
525C22×C4—444no—
526C22×C4—442no—
527C22×C4—442no—
528C22×C4—442no—
529C22×C4—442no—
530C22×C4—442no—
531C22×C4—442no—
532C22×C4—441no—
533C22×C4—441no—
534C22×C4—441no—
535C22×C4—441no—
536C4⋊C4—444no—
537C4⋊C4—448no—
538C4⋊C4—444no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—41no—
544C22⋊C4—41no—
545C22⋊C4—41no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—41no—
549C22⋊C4—41no—
550C22⋊C4—41no—
551C22⋊C4—222no—
552C22⋊C4—222no—
553C22⋊C4—222no—
554C22⋊C4—222no—
555C22⋊C4—222no—
556C22⋊C4—222no—
557C22⋊C4—222no—
558C22⋊C4—222no—
559C22⋊C4—441no—
560C22⋊C4—441no—
561C22⋊C4—441no—
562C22⋊C4—441no—
563C11#1120311yescharacteristic, complemented, Sylow
564C23—22no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—22no—
569C23—22no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—42no—
575C23—41no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—41no—
580C23—42no—
581C23—41no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—41no—
586C23C4×Dic2211yescharacteristic
587C23#6692311yescharacteristic
588C23#6692511yescharacteristic
589C23#6692911yescharacteristic
590C23#6693111yescharacteristic
591C23#6693111yescharacteristic
592C23#6693211yescharacteristic
593C23C22⋊C4×D1111yescharacteristic
594C23(C22⋊D11)⋊C411yescharacteristic
595C23#6693611yescharacteristic
596C23#6693611yescharacteristic
597C23#6693711yescharacteristic
598C23#6693711yescharacteristic
599C23#6693711yescharacteristic
600C23#6693711yescharacteristic
601C23#6693811yescharacteristic
602C23#6694011yescharacteristic
603C23#6694111yescharacteristic
604C23#6694111yescharacteristic
605C23#6694211yescharacteristic
606C23#6694211yescharacteristic
607C23#6694211yescharacteristic
608C23C4⋊C4×D1111yescharacteristic
609C23#6694911yescharacteristic
610C23#6694911yescharacteristic
611C23#6694911yescharacteristic
612C23#6694911yescharacteristic
613C23#6694911yescharacteristic
614C23#6697711yescharacteristic
615C23C4×C22⋊D1111yescharacteristic
616C23#6698211yescharacteristic
617C23#6699011yescharacteristic
618C23#6699111yescharacteristic
619C23#6699211yescharacteristic
620C23#6699711yescharacteristic
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—44no—
624C2×C4—42no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—81no—
631C2×C4—81no—
632C2×C4—82no—
633C2×C4—82no—
634C2×C4—82no—
635C2×C4—81no—
636C2×C4—81no—
637C2×C4—81no—
638C2×C4—81no—
639C2×C4—114no—
640C2×C4—224no—
641C2×C4—224no—
642C2×C4—222no—
643C2×C4—222no—
644C2×C4—224no—
645C2×C4—222no—
646C2×C4—222no—
647C2×C4—222no—
648C2×C4—444no—
649C2×C4—444no—
650C2×C4—444no—
651C2×C4—444no—
652C2×C4—442no—
653C2×C4—442no—
654C2×C4—444no—
655C2×C4—442no—
656C2×C4—442no—
657C2×C4—444no—
658C2×C4—442no—
659C2×C4—442no—
660C2×C4—444no—
661C2×C4—442no—
662C2×C4—442no—
663C2×C4—881no—
664C2×C4—881no—
665C2×C4—882no—
666C2×C4—882no—
667C2×C4—882no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22#1062225911yescharacteristic
709C22#1062226011yescharacteristic
710C22#1062226511yescharacteristic
711C22#1062227011yescharacteristic
712C22#1062227011yescharacteristic
713C22#1062227111yescharacteristic
714C22#1062228011yescharacteristic
715C22#1062228911yescharacteristic
716C22#1062235312yes—
717C22D11×#9912yes—
718C22#1062254611yescharacteristic
719C22#1062256111yescharacteristic
720C22#1062256911yescharacteristic
721C22#1062257211yescharacteristic
722C22#1062258511yescharacteristic
723C22#1062259211yescharacteristic
724C22#1062259311yescharacteristic
725C4—82no—
726C4—82no—
727C4—81no—
728C4—81no—
729C4—224no—
730C4—442no—
731C4—444no—
732C4—882no—
733C4—882no—
734C2—21no—
735C2—21no—
736C2—21no—
737C2—21no—
738C2—21no—
739C2—21no—
740C2—21no—
741C2—21no—
742C2—21no—
743C2—21no—
744C2—21no—
745C2—21no—
746C2#1306686711yescharacteristic
747C2#1306860312yes—
748C2#1306906611yescharacteristic
749C2#1306907111yescharacteristic
750C2#1306959912yes—
subgroupG/H
centerC23C22⋊C4×D11
commutatorC24×C11C22×C4
FrattiniC25C22×D11
FittingC2×C11×#342C2
socleC23×C11C2×C22⋊C4
prime radical, cosocleC25×C11C23
hypercenterC2×#342D11
hypocenterC11#11203
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
16. C22×Dic11⋊C4C4semidirect
19. C2×C11⋊#95C4semidirect
161. C22×Dic11C4⋊C4semidirect
563. C11#11203semidirect

Maximal subgroups

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

subgroupindex
C2×#106225592
C2×#106225552
C2×#106221642
C2×#106221652
#130668382
C2×C11×#3422
#1120311