Finite Group Databasebeta

← #14685192

Subgroups — #14685192

Order 2816.

2494 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66931C211yesmaximal, characteristic
2C23×C4⋊Dic11C211yesmaximal, characteristic
3C2×#10622269C212yesmaximal, complemented
4C2×#10622563C211yesmaximal, characteristic
5C2×#10622559C211yesmaximal, characteristic
6#13066881C212yesmaximal, complemented
7#13066880C212yesmaximal, complemented
8#13066868C212yesmaximal, complemented
9#13066839C211yesmaximal, characteristic
10#13066838C211yesmaximal, characteristic
11C11×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C23×Dic22C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11—24no—
21C22×C4⋊Dic11—28no—
22C22×C4⋊Dic11C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2212yes—
25C22×C4⋊Dic11C2212yes—
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2212yes—
29C2×#66931—24no—
30C2×#66931—24no—
31C2×#66931—24no—
32C2×C11×#95C2212yes—
33C2×C11×#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40#10622563—24no—
41#10622559—24no—
42#10622269—28no—
43C25×C11C2311yescharacteristic
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—24no—
47C23×C4×C11—24no—
48C23×C4×C11Q814yescomplemented
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
53C23×Dic11—22no—
54C23×Dic11—22no—
55C23×Dic11—22no—
56C23×Dic11—24no—
57C23×Dic11—24no—
58C23×Dic11—22no—
59C23×Dic11—22no—
60C23×Dic11—42no—
61C23×Dic11—42no—
62C23×Dic11D414yes—
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2312yes—
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2312yes—
68C23×Dic11C2311yescharacteristic
69C22×Dic22—22no—
70C22×Dic22—22no—
71C22×Dic22—22no—
72C22×Dic22—24no—
73C22×Dic22—42no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4D414yes—
79C2×C11×C22⋊C4Q814yescomplemented
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11D414yes—
85C2×C22⋊Dic11Q814yescomplemented
86C2×C4⋊Dic11—232no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—24no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—24no—
92C2×C4⋊Dic11—24no—
93C2×C4⋊Dic11—24no—
94C2×C4⋊Dic11—24no—
95C2×C4⋊Dic11—24no—
96C2×C4⋊Dic11—24no—
97C2×C4⋊Dic11—42no—
98C2×C4⋊Dic11D418yes—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—22no—
104C2×Dic11⋊C4—22no—
105C2×Dic11⋊C4—24no—
106C2×Dic11⋊C4—24no—
107C2×Dic11⋊C4—42no—
108#66931—232no—
109C11×#95—24no—
110C11×#95—24no—
111C11⋊#95—24no—
112C11⋊#95—24no—
113C11⋊#95—24no—
114C11⋊#95—24no—
115C11⋊#95—24no—
116C11⋊#95—42no—
117#14720—111nomaximal, Sylow
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11C2×D412yes—
123C24×C11C2×D412yes—
124C24×C11C2×D412yes—
125C24×C11C2×Q812yes—
126C24×C11C2×Q812yes—
127C24×C11C2×Q812yes—
128C24×C11#4112yes—
129C24×C11C2411yescharacteristic
130C22×C4×C11—28no—
131C22×C4×C11—216no—
132C22×C4×C11—28no—
133C22×C4×C11—28no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—216no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
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×C11C2×D412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D414yes—
156C22×C4×C11C2×Q814yes—
157C22×C4×C11C2×Q814yes—
158C22×C4×C11#4114yes—
159C22×Dic11—28no—
160C22×Dic11—28no—
161C22×Dic11—28no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—21no—
177C22×Dic11—21no—
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—44no—
190C22×Dic11—48no—
191C22×Dic11—48no—
192C22×Dic11—48no—
193C22×Dic11—48no—
194C22×Dic11—44no—
195C22×Dic11—44no—
196C22×Dic11C2×D412yes—
197C22×Dic11C2×D412yes—
198C22×Dic11C2×D414yes—
199C22×Dic11C2×D412yes—
200C22×Dic11C2×D414yes—
201C22×Dic11C2×D412yes—
202C22×Dic11C2×Q814yes—
203C2×Dic22—28no—
204C2×Dic22—48no—
205C2×Dic22—48no—
206C2×Dic22—44no—
207C2×Dic22—44no—
208C11×C22⋊C4—28no—
209C11×C22⋊C4—28no—
210C22⋊Dic11—28no—
211C22⋊Dic11—28no—
212C4⋊Dic11—28no—
213C4⋊Dic11—216no—
214C4⋊Dic11—216no—
215C4⋊Dic11—48no—
216Dic11⋊C4—28no—
217Dic11⋊C4—28no—
218Dic11⋊C4—48no—
219C22×C22⋊Q8—111no—
220C23×C4⋊C4—111no—
221C2×#395—112no—
222C2×#385—111no—
223C2×#385—111no—
224#1444—112no—
225#1444—112no—
226#1441—112no—
227C22⋊#95—111no—
228C22⋊#95—111no—
229C22⋊#95D1111yescharacteristic
230C23×C11—22no—
231C23×C11—24no—
232C23×C11—22no—
233C23×C11—24no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—24no—
237C23×C11—24no—
238C23×C11—24no—
239C23×C11—24no—
240C23×C11—24no—
241C23×C11—24no—
242C23×C11—24no—
243C23×C11—24no—
244C23×C11—24no—
245C23×C11—24no—
246C23×C11#12014yes—
247C23×C11C22⋊Q814yes—
248C23×C11C22⋊Q814yes—
249C23×C11C22⋊Q814yes—
250C23×C11C4⋊Q814yes—
251C23×C11C4⋊Q814yes—
252C23×C11C4⋊Q814yes—
253C23×C11C22×D411yescharacteristic
254C23×C11C22×D411yescharacteristic
255C23×C11C22×D412yes—
256C23×C11C22×D411yescharacteristic
257C23×C11C22×Q811yescharacteristic
258C23×C11C22×Q811yescharacteristic
259C23×C11C22×Q811yescharacteristic
260C23×C11C2×#4111yescharacteristic
261C23×C11C2×#4112yes—
262C23×C11H(5,𝔽2)12yes—
263C23×C112−1+412yes—
264C2×C4×C11—232no—
265C2×C4×C11—24no—
266C2×C4×C11—24no—
267C2×C4×C11—24no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—24no—
274C2×C4×C11—24no—
275C2×C4×C11—24no—
276C2×C4×C11—24no—
277C2×C4×C11—24no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—42no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—42no—
284C2×C4×C11—42no—
285C2×C4×C11—42no—
286C2×C4×C11—42no—
287C2×C4×C11—42no—
288C2×C4×C11C22⋊Q818yescomplemented
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—24no—
292C2×Dic11—24no—
293C2×Dic11—22no—
294C2×Dic11—22no—
295C2×Dic11—22no—
296C2×Dic11—24no—
297C2×Dic11—22no—
298C2×Dic11—24no—
299C2×Dic11—22no—
300C2×Dic11—24no—
301C2×Dic11—24no—
302C2×Dic11—24no—
303C2×Dic11—24no—
304C2×Dic11—24no—
305C2×Dic11—24no—
306C2×Dic11—416no—
307C2×Dic11—416no—
308C2×Dic11—41no—
309C2×Dic11—42no—
310C2×Dic11—41no—
311C2×Dic11—42no—
312C2×Dic11—41no—
313C2×Dic11—42no—
314C2×Dic11—41no—
315C2×Dic11—42no—
316C2×Dic11—42no—
317C2×Dic11—42no—
318C2×Dic11—42no—
319C2×Dic11—42no—
320C2×Dic11—42no—
321C2×Dic11—42no—
322C2×Dic11—42no—
323C2×Dic11—42no—
324C2×Dic11#12014yes—
325Dic22—416no—
326C23×Q8—111no—
327C24×C4—111no—
328C24×C4—111no—
329C24×C4C2×D1111yescharacteristic
330C2×C22⋊Q8—224no—
331C2×C22⋊Q8—224no—
332C2×C22⋊Q8—224no—
333C22×C4⋊C4—112no—
334C22×C4⋊C4—111no—
335C22×C4⋊C4—111no—
336C22×C4⋊C4—112no—
337C22×C4⋊C4—111no—
338C22×C4⋊C4—112no—
339C22×C4⋊C4—112no—
340C22×C4⋊C4—228no—
341C22×C4⋊C4—224no—
342C22×C22⋊C4—111no—
343C22×C22⋊C4—111no—
344C22×C22⋊C4C2×D1111yescharacteristic
345C22×C22⋊C4C2×D1111yescharacteristic
346#395—228no—
347#385—224no—
348#385—224no—
349C2×#95—112no—
350C2×#95—112no—
351C2×#95—112no—
352C2×#95—112no—
353C2×#95—112no—
354C2×#95—112no—
355C2×#95C2×D1112yes—
356C2×#95C2×D1112yes—
357C22×C11—24no—
358C22×C11—24no—
359C22×C11—24no—
360C22×C11—24no—
361C22×C11—24no—
362C22×C11—24no—
363C22×C11—28no—
364C22×C11—28no—
365C22×C11—28no—
366C22×C11—28no—
367C22×C11#39518yescomplemented
368C22×C11C2×#12011yescharacteristic
369C22×C11C2×#12011yescharacteristic
370C22×C11C2×C22⋊Q811yescharacteristic
371C22×C11C2×C22⋊Q812yes—
372C22×C11C2×C22⋊Q811yescharacteristic
373C22×C11C2×C22⋊Q811yescharacteristic
374C22×C11#52511yescharacteristic
375C22×C11#52512yes—
376C22×C11C2×C4⋊Q811yescharacteristic
377C22×C11C2×C4⋊Q811yescharacteristic
378C22×C11C2×C4⋊Q811yescharacteristic
379C22×C11#53411yescharacteristic
380C22×C11#53611yescharacteristic
381C22×C11#53912yes—
382C22×C11#54412yes—
383C22×C11D4212yes—
384C22×C11D4212yes—
385C22×C11#54712yes—
386C22×C11#54712yes—
387C22×C11D4×Q812yes—
388C22×C11D4×Q812yes—
389C22×C11#55412yes—
390C22×C11#55412yes—
391C4×C11—28no—
392C4×C11—42no—
393C4×C11—42no—
394C4×C11—44no—
395Dic11—24no—
396Dic11—42no—
397Dic11—42no—
398Dic11—44no—
399Dic11—42no—
400Dic11—44no—
401C25C22×D1111yescharacteristic
402C22×Q8—222no—
403C22×Q8—222no—
404C22×Q8—224no—
405C22×Q8—222no—
406C22×Q8—442no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—24no—
410C23×C4—24no—
411C23×C4—111no—
412C23×C4—111no—
413C23×C4—111no—
414C23×C4—112no—
415C23×C4—112no—
416C23×C4—111no—
417C23×C4—114no—
418C23×C4—224no—
419C23×C4—224no—
420C23×C4—222no—
421C23×C4—222no—
422C23×C4—222no—
423C23×C4—222no—
424C23×C4—222no—
425C23×C4—442no—
426C23×C4—442no—
427C23×C4Dic2214yescomplemented
428C23×C4C22×D1112yes—
429C23×C4C22×D1111yescharacteristic
430C23×C4C22×D1111yescharacteristic
431C23×C4C22×D1112yes—
432C22⋊Q8—2232no—
433C2×C4⋊C4—118no—
434C2×C4⋊C4—224no—
435C2×C4⋊C4—224no—
436C2×C4⋊C4—224no—
437C2×C4⋊C4—224no—
438C2×C4⋊C4—222no—
439C2×C4⋊C4—222no—
440C2×C4⋊C4—222no—
441C2×C4⋊C4—222no—
442C2×C4⋊C4—222no—
443C2×C4⋊C4—222no—
444C2×C4⋊C4—2232no—
445C2×C4⋊C4—222no—
446C2×C4⋊C4—222no—
447C2×C4⋊C4—222no—
448C2×C4⋊C4—224no—
449C2×C4⋊C4—224no—
450C2×C4⋊C4—224no—
451C2×C4⋊C4—224no—
452C2×C4⋊C4—224no—
453C2×C4⋊C4—442no—
454C2×C4⋊C4—442no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—114no—
460C2×C22⋊C4—114no—
461C2×C22⋊C4—222no—
462C2×C22⋊C4—222no—
463C2×C22⋊C4—222no—
464C2×C22⋊C4—222no—
465C2×C22⋊C4Dic2214yescomplemented
466C2×C22⋊C4D4414yes—
467#95—24no—
468#95—24no—
469#95—224no—
470#95—224no—
471#95—224no—
472#95—224no—
473#95—224no—
474#95—442no—
475C2×C11—28no—
476C2×C11C2×#39511yescharacteristic
477C2×C11#240311yescharacteristic
478C2×C11#240611yescharacteristic
479C2×C11#243411yescharacteristic
480C2×C11#244012yes—
481C2×C11#244012yes—
482C2×C11#244912yes—
483C2×C11#244912yes—
484C2×C11#258311yescharacteristic
485C2×C11#262711yescharacteristic
486C2×C11#284811yescharacteristic
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24C2×Dic2212yes—
492C24C2×Dic2212yes—
493C24C2×D4412yes—
494C24D4×D1112yes—
495C24D4×D1112yes—
496C24#434112yes—
497C24Q8×D1112yes—
498C24C23×D1111yescharacteristic
499C2×Q8—228no—
500C2×Q8—448no—
501C2×Q8—444no—
502C2×Q8—448no—
503C2×Q8—444no—
504C22×C4—28no—
505C22×C4—216no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—216no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—114no—
528C22×C4—112no—
529C22×C4—112no—
530C22×C4—112no—
531C22×C4—114no—
532C22×C4—112no—
533C22×C4—114no—
534C22×C4—228no—
535C22×C4—221no—
536C22×C4—221no—
537C22×C4—222no—
538C22×C4—228no—
539C22×C4—228no—
540C22×C4—222no—
541C22×C4—222no—
542C22×C4—221no—
543C22×C4—221no—
544C22×C4—221no—
545C22×C4—222no—
546C22×C4—222no—
547C22×C4—222no—
548C22×C4—221no—
549C22×C4—221no—
550C22×C4—221no—
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—222no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—444no—
565C22×C4—448no—
566C22×C4—448no—
567C22×C4—448no—
568C22×C4—448no—
569C22×C4—444no—
570C22×C4—444no—
571C22×C4C2×Dic2214yes—
572C22×C4C2×Dic2214yes—
573C22×C4C2×D4412yes—
574C22×C4C2×D4412yes—
575C22×C4D4×D1114yes—
576C22×C4#434114yes—
577C4⋊C4—2216no—
578C4⋊C4—2216no—
579C4⋊C4—228no—
580C4⋊C4—228no—
581C4⋊C4—228no—
582C4⋊C4—448no—
583C4⋊C4—448no—
584C22⋊C4—28no—
585C22⋊C4—28no—
586C22⋊C4—228no—
587C22⋊C4—228no—
588C11#1472011yescharacteristic, complemented, Sylow
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—22no—
596C23—24no—
597C23—22no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—22no—
603C23—22no—
604C23—24no—
605C23#6692214yes—
606C23#6693114yes—
607C23#6693114yes—
608C23#6693514yes—
609C23#6694114yes—
610C23#6694114yes—
611C23#6695014yes—
612C23C22×Dic2211yescharacteristic
613C23C22×Dic2211yescharacteristic
614C23C22×D4411yescharacteristic
615C23C2×D4×D1111yescharacteristic
616C23C2×D4×D1111yescharacteristic
617C23C2×D4×D1112yes—
618C23C2×#434111yescharacteristic
619C23C2×#434112yes—
620C23C2×Q8×D1111yescharacteristic
621C23#6704212yes—
622C23#6704312yes—
623Q8—4416no—
624C2×C4—232no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—42no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—42no—
648C2×C4—114no—
649C2×C4—222no—
650C2×C4—224no—
651C2×C4—224no—
652C2×C4—222no—
653C2×C4—222no—
654C2×C4—222no—
655C2×C4—222no—
656C2×C4—224no—
657C2×C4—224no—
658C2×C4—224no—
659C2×C4—222no—
660C2×C4—224no—
661C2×C4—224no—
662C2×C4—224no—
663C2×C4—224no—
664C2×C4—224no—
665C2×C4—222no—
666C2×C4—4416no—
667C2×C4—4416no—
668C2×C4—442no—
669C2×C4—442no—
670C2×C4—442no—
671C2×C4—442no—
672C2×C4—442no—
673C2×C4—442no—
674C2×C4—442no—
675C2×C4—442no—
676C2×C4—441no—
677C2×C4—441no—
678C2×C4—442no—
679C2×C4—442no—
680C2×C4—441no—
681C2×C4—442no—
682C2×C4—441no—
683C2×C4—442no—
684C2×C4#6693118yescomplemented
685C22—24no—
686C22—28no—
687C22—28no—
688C22—24no—
689C22—24no—
690C22—24no—
691C22—24no—
692C22—24no—
693C22—28no—
694C22—28no—
695C22#1062226918yescomplemented
696C22C2×#6692211yescharacteristic
697C22C2×#6693111yescharacteristic
698C22C2×#6693111yescharacteristic
699C22C2×#6693112yes—
700C22C2×#6693511yescharacteristic
701C22C2×#6694111yescharacteristic
702C22C2×#6694111yescharacteristic
703C22C2×#6695011yescharacteristic
704C22#1062305012yes—
705C22D4×Dic2212yes—
706C22#1062307412yes—
707C22D4×D4412yes—
708C22#1062308612yes—
709C22#1062311712yes—
710C22#1062311711yescharacteristic
711C22D11×#12011yescharacteristic
712C22#1062314012yes—
713C22#1062314212yes—
714C22#1062316312yes—
715C22#1062316612yes—
716C22#1062317911yescharacteristic
717C22#1062318411yescharacteristic
718C22#1062319612yes—
719C4—28no—
720C4—44no—
721C4—42no—
722C4—42no—
723C4—224no—
724C4—444no—
725C4—442no—
726C4—444no—
727C4—442no—
728C4—442no—
729C2—28no—
730C2C2×#1062226911yescharacteristic
731C2#1307192811yescharacteristic
732C2#1307195011yescharacteristic
733C2#1307225811yescharacteristic
734C2#1307231812yes—
735C2#1307231912yes—
736C2#1307242312yes—
737C2#1307243112yes—
738C2#1307399311yescharacteristic
739C2#1307443311yescharacteristic
740C2#1307690111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×C22⋊#95C2
prime radicalC25×C11C23
hypercenterC22⋊#95D11
hypocenterC11#14720
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#10622269C2semidirect
6. #13066881C2semidirect
7. #13066880C2semidirect
8. #13066868C2semidirect
48. C23×C4×C11Q8semidirect
79. C2×C11×C22⋊C4Q8semidirect
85. C2×C22⋊Dic11Q8semidirect
288. C2×C4×C11C22⋊Q8semidirect
367. C22×C11#395semidirect
427. C23×C4Dic22semidirect
465. C2×C22⋊C4Dic22semidirect
588. C11#14720semidirect
684. C2×C4#66931semidirect
695. C22#10622269semidirect

Maximal subgroups

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

subgroupindex
C22×#669312
C23×C4⋊Dic112
C2×#106222692
C2×#106225632
C2×#106225592
#130668812
#130668802
#130668682
#130668392
#130668382
C11×C22⋊#952
#1472011