Finite Group Databasebeta

← #14676874

Subgroups — #14676874

Order 2816.

1802 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622541C211yesmaximal, characteristic, complemented
2C2×#10622557C212yesmaximal
3C2×#10622825C211yesmaximal, characteristic
4C2×#10622825C211yesmaximal, characteristic
5C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
6#13066871C212yesmaximal, complemented
7#13066863C212yesmaximal
8#13066846C211yesmaximal, characteristic, complemented
9#13066846C211yesmaximal, characteristic, complemented
10#13066840C212yesmaximal, complemented
11C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2212yes—
24C22×C4×Dic11C2212yes—
25C4×C11×C22⋊C4—24no—
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28#10622825—24no—
29#10622825C418yescomplemented
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622557—28no—
39C4×C4⋊Dic11—24no—
40#10622541—24no—
41C25×C11C2311yescharacteristic
42C23×C4×C11—22no—
43C23×C4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11C2×C414yes—
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×Dic11C2312yes—
56C23×Dic11C2312yes—
57C23×Dic11C2312yes—
58C23×Dic11C2312yes—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4D414yes—
65C2×C42×C11—22no—
66C2×C42×C11—22no—
67C2×C42×C11—22no—
68C2×C42×C11—22no—
69C2×C42×C11—22no—
70C2×C42×C11D414yes—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—42no—
76C2×C22⋊Dic11C2×C418yes—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11C2×C414yes—
87C2×C4⋊Dic11C2×C414yes—
88C2×C4⋊Dic11D414yes—
89C2×Dic11⋊C4—24no—
90C2×Dic11⋊C4—24no—
91C2×Dic11⋊C4—42no—
92C2×C4×Dic11—24no—
93C2×C4×Dic11—24no—
94C2×C4×Dic11—24no—
95C11×#95—22no—
96C11×#95—22no—
97C11⋊#95—24no—
98C11⋊#95—24no—
99C11⋊#95—24no—
100C11⋊#95—24no—
101C11⋊#95—24no—
102C11⋊#95—24no—
103C11⋊#95—42no—
104C11⋊#95C2×C418yes—
105#13994—111nomaximal, Sylow
106C24×C11—21no—
107C24×C11—21no—
108C24×C11—21no—
109C24×C11—21no—
110C24×C11—21no—
111C24×C11—21no—
112C24×C11—21no—
113C24×C11—21no—
114C24×C11—21no—
115C24×C11—21no—
116C24×C11—21no—
117C24×C11—21no—
118C24×C11C22×C412yes—
119C24×C11C2×D412yes—
120C24×C11#4112yes—
121C24×C11C2411yescharacteristic
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—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—28no—
151C22×C4×C11—28no—
152C22×C4×C11—28no—
153C22×C4×C11—44no—
154C22×C4×C11—44no—
155C22×C4×C11—44no—
156C22×C4×C11—44no—
157C22×C4×C11C22×C412yes—
158C22×C4×C11C22×C412yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D412yes—
165C22×C4×C11#4112yes—
166C22×C4×C11#4112yes—
167C22×C4×C11#4112yes—
168C22×C4×C11#4112yes—
169C22×C4×C11#4112yes—
170C22×C4×C11#4112yes—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
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—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11C22×C414yes—
197C22×Dic11C22×C414yes—
198C22×Dic11C2×D414yes—
199C11×C22⋊C4—28no—
200C11×C22⋊C4—28no—
201C42×C11—28no—
202C42×C11—44no—
203C22⋊Dic11—216no—
204C22⋊Dic11—48no—
205C4⋊Dic11—28no—
206C4⋊Dic11—28no—
207C4⋊Dic11—28no—
208C4⋊Dic11—44no—
209Dic11⋊C4—48no—
210C4×Dic11—48no—
211C2×#389—111no—
212C2×#388—112no—
213C2×#380—111no—
214C2×#380—111no—
215C2×C4×C4⋊C4—111no—
216C2×C4×C22⋊C4D1111yescharacteristic
217#1442—112no—
218#1440—112no—
219C4⋊#95—111no—
220C4⋊#95—111no—
221#1434—112no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11C4×D414yes—
257C23×C11C23×C411yescharacteristic
258C23×C11C22×D411yescharacteristic
259C23×C11C22×D411yescharacteristic
260C23×C11C22×D411yescharacteristic
261C23×C11C2×#4111yescharacteristic
262C23×C11C2×#4111yescharacteristic
263C23×C11C2×#4111yescharacteristic
264C23×C11C2×#4111yescharacteristic
265C23×C11C2×#4111yescharacteristic
266C23×C11C2×#4111yescharacteristic
267C23×C11C2×#4111yescharacteristic
268C23×C11H(5,𝔽2)11yescharacteristic
269C23×C112−1+411yescharacteristic
270C23×C112−1+411yescharacteristic
271C23×C112−1+411yescharacteristic
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—416no—
307C2×C4×C11#11714yes—
308C2×C4×C11C4×D414yes—
309C2×C4×C11C4×D414yes—
310C2×C4×C11#12114yes—
311C2×C4×C11#12114yes—
312C2×C4×C11#12314yes—
313C2×C4×C11#12414yes—
314C2×C4×C11#12614yes—
315C2×Dic11—24no—
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—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×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C24×C4C2×D1111yescharacteristic
344C22×C4⋊C4—111no—
345C22×C4⋊C4—111no—
346C22×C4⋊C4—111no—
347C22×C4⋊C4—111no—
348C22×C4⋊C4—112no—
349C22×C22⋊C4—112no—
350C22×C22⋊C4—112no—
351C22×C22⋊C4C2×D1111yescharacteristic
352C22×C22⋊C4C2×D1111yescharacteristic
353C22×C42—112no—
354C22×C42C2×D1111yescharacteristic
355C22×C42C2×D1111yescharacteristic
356#389—224no—
357#388—228no—
358#380—118no—
359#380—224no—
360C4×C4⋊C4—224no—
361C4×C22⋊C4—24no—
362C2×#95—112no—
363C2×#95—112no—
364C2×#95—112no—
365C2×#95—112no—
366C2×#95—112no—
367C2×#95—112no—
368C2×#95—112no—
369C2×#95—112no—
370C2×#95C2×D1111yescharacteristic
371C2×#95C2×D1111yescharacteristic
372C22×C11—24no—
373C22×C11—24no—
374C22×C11—24no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11—42no—
378C22×C11—42no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—42no—
382C22×C11—42no—
383C22×C11—42no—
384C22×C11—42no—
385C22×C11—42no—
386C22×C11—42no—
387C22×C11C2×#11711yescharacteristic
388C22×C11C2×C4×D411yescharacteristic
389C22×C11C2×C4×D411yescharacteristic
390C22×C11C2×C4×D411yescharacteristic
391C22×C11C4×#4111yescharacteristic
392C22×C11#51911yescharacteristic
393C22×C11#52011yescharacteristic
394C22×C11C2×#12111yescharacteristic
395C22×C11C2×#12111yescharacteristic
396C22×C11C2×#12311yescharacteristic
397C22×C11#52511yescharacteristic
398C22×C11C2×#12411yescharacteristic
399C22×C11C2×#12611yescharacteristic
400C22×C11#52911yescharacteristic
401C22×C11#53211yescharacteristic
402C22×C11#53611yescharacteristic
403C22×C11#53711yescharacteristic
404C22×C11#54111yescharacteristic
405C22×C11#54211yescharacteristic
406C22×C11D4211yescharacteristic
407C22×C11#54711yescharacteristic
408C22×C11#54711yescharacteristic
409C22×C11#54711yescharacteristic
410C22×C11#54711yescharacteristic
411C22×C11#54811yescharacteristic
412C22×C11#54811yescharacteristic
413C22×C11#55211yescharacteristic
414C22×C11#55211yescharacteristic
415C22×C11#55211yescharacteristic
416C22×C11#55211yescharacteristic
417C22×C11#55211yescharacteristic
418C22×C11#55311yescharacteristic
419C22×C11#55511yescharacteristic
420C22×C11#55511yescharacteristic
421C22×C11#55611yescharacteristic
422C4×C11—24no—
423C4×C11—42no—
424C4×C11—42no—
425C4×C11—42no—
426C4×C11—42no—
427C4×C11#38818yescomplemented
428Dic11—44no—
429Dic11—44no—
430Dic11—44no—
431Dic11—82no—
432C25C22×D1111yescharacteristic
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—22no—
439C23×C4—112no—
440C23×C4—112no—
441C23×C4—112no—
442C23×C4—112no—
443C23×C4C4×D1114yes—
444C23×C4C22×D1111yescharacteristic
445C23×C4C22×D1111yescharacteristic
446C23×C4C22×D1111yescharacteristic
447C23×C4C22×D1111yescharacteristic
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1111yescharacteristic
450C2×C4⋊C4—114no—
451C2×C4⋊C4—114no—
452C2×C4⋊C4—114no—
453C2×C4⋊C4—222no—
454C2×C4⋊C4—222no—
455C2×C4⋊C4—222no—
456C2×C4⋊C4—222no—
457C2×C4⋊C4—222no—
458C2×C4⋊C4—222no—
459C2×C4⋊C4—224no—
460C2×C4⋊C4—224no—
461C2×C4⋊C4—222no—
462C2×C4⋊C4—222no—
463C2×C4⋊C4—222no—
464C2×C4⋊C4—442no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—118no—
471C2×C22⋊C4—224no—
472C2×C22⋊C4—224no—
473C2×C22⋊C4—224no—
474C2×C22⋊C4—224no—
475C2×C22⋊C4—442no—
476C2×C22⋊C4D4414yes—
477C2×C42—22no—
478C2×C42—22no—
479C2×C42—22no—
480C2×C42—22no—
481C2×C42—22no—
482C2×C42—224no—
483C2×C42—224no—
484C2×C42—224no—
485C2×C42C22⋊D1114yes—
486#95—22no—
487#95—22no—
488#95—118no—
489#95—224no—
490#95—224no—
491#95—224no—
492#95—224no—
493#95—224no—
494#95—224no—
495#95—442no—
496C2×C11—44no—
497C2×C11C2×#38811yescharacteristic
498C2×C11C4×#12111yescharacteristic
499C2×C11#232311yescharacteristic
500C2×C11#234411yescharacteristic
501C2×C11#234611yescharacteristic
502C2×C11#236111yescharacteristic
503C2×C11#236211yescharacteristic
504C2×C11#248511yescharacteristic
505C2×C11#248611yescharacteristic
506C2×C11#248911yescharacteristic
507C2×C11#249111yescharacteristic
508C2×C11#249511yescharacteristic
509C2×C11#249611yescharacteristic
510C2×C11#253611yescharacteristic
511C2×C11#253711yescharacteristic
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24C2×C4×D1112yes—
525C24C2×D4412yes—
526C24#433912yes—
527C24C23×D1111yescharacteristic
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—28no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—114no—
564C22×C4—114no—
565C22×C4—114no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—222no—
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—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4C2×C4×D1112yes—
592C22×C4C2×C4×D1112yes—
593C22×C4C2×D4412yes—
594C22×C4C2×D4412yes—
595C22×C4#433912yes—
596C22×C4#433912yes—
597C22×C4#433912yes—
598C22×C4D4×D1112yes—
599C22×C4#434112yes—
600C22×C4#434112yes—
601C22×C4#434112yes—
602C22×C4C2×C22⋊D1112yes—
603C22×C4C2×C22⋊D1112yes—
604C22×C4C2×C22⋊D1112yes—
605C4⋊C4—228no—
606C4⋊C4—228no—
607C4⋊C4—228no—
608C4⋊C4—448no—
609C4⋊C4—444no—
610C22⋊C4—28no—
611C22⋊C4—28no—
612C22⋊C4—2216no—
613C22⋊C4—448no—
614C42—28no—
615C42—44no—
616C42—448no—
617C11#1399411yescharacteristic, complemented, Sylow
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23C4×D4414yes—
653C23C22×C4×D1111yescharacteristic
654C23C22×D4411yescharacteristic
655C23C2×#433911yescharacteristic
656C23C2×#433911yescharacteristic
657C23C2×#433911yescharacteristic
658C23C2×#433911yescharacteristic
659C23C2×D4×D1111yescharacteristic
660C23C2×#434111yescharacteristic
661C23C2×#434111yescharacteristic
662C23C2×#434111yescharacteristic
663C23#6704211yescharacteristic
664C23#6704311yescharacteristic
665C23#6704311yescharacteristic
666C23#6704311yescharacteristic
667C23C22×C22⋊D1111yescharacteristic
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—416no—
703C2×C4—224no—
704C2×C4—224no—
705C2×C4—224no—
706C2×C4—224no—
707C2×C4—224no—
708C2×C4—224no—
709C2×C4—224no—
710C2×C4—224no—
711C2×C4—224no—
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×C4—442no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4#6693014yes—
732C2×C4#6693214yes—
733C2×C4(C22⋊D11)⋊C414yes—
734C2×C4#6693814yes—
735C2×C4C4×C22⋊D1114yes—
736C2×C4#6698314yes—
737C2×C4#6698814yes—
738C2×C4#6699114yes—
739C22—24no—
740C22—24no—
741C22—24no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22C2×C4×D4411yescharacteristic
755C22C4×#433911yescharacteristic
756C22#1062300811yescharacteristic
757C22#1062301011yescharacteristic
758C22C2×#6693011yescharacteristic
759C22C2×#6693211yescharacteristic
760C22C2×(C22⋊D11)⋊C411yescharacteristic
761C22C2×#6693811yescharacteristic
762C22#1062304711yescharacteristic
763C22#1062304911yescharacteristic
764C22#1062305411yescharacteristic
765C22#1062306511yescharacteristic
766C22#1062307211yescharacteristic
767C22#1062307211yescharacteristic
768C22#1062307211yescharacteristic
769C22#1062307211yescharacteristic
770C22#1062307211yescharacteristic
771C22#1062307311yescharacteristic
772C22D4×D4411yescharacteristic
773C22#1062308211yescharacteristic
774C22#1062308311yescharacteristic
775C22#1062308311yescharacteristic
776C22#1062308611yescharacteristic
777C22#1062308611yescharacteristic
778C22#1062308611yescharacteristic
779C22#1062309411yescharacteristic
780C22#1062309411yescharacteristic
781C22#1062309611yescharacteristic
782C22C2×C4×C22⋊D1111yescharacteristic
783C22C2×#6698311yescharacteristic
784C22#1062332211yescharacteristic
785C22C2×#6698811yescharacteristic
786C22C2×#6699111yescharacteristic
787C22#1062335611yescharacteristic
788C22#1062336411yescharacteristic
789C4—24no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—42no—
794C4—444no—
795C4—444no—
796C4—444no—
797C4—882no—
798C4#1062255718yescomplemented
799C2—44no—
800C2C2×#1062255711yescharacteristic
801C2C4×#6698311yescharacteristic
802C2#1307129811yescharacteristic
803C2#1307148311yescharacteristic
804C2#1307149911yescharacteristic
805C2#1307163011yescharacteristic
806C2#1307164111yescharacteristic
807C2#1307291311yescharacteristic
808C2#1307292411yescharacteristic
809C2#1307295711yescharacteristic
810C2#1307297911yescharacteristic
811C2#1307302711yescharacteristic
812C2#1307303811yescharacteristic
813C2#1307352511yescharacteristic
814C2#1307352911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#13994
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622541C2semidirect
5. C2×C4×C4⋊Dic11C2semidirect
6. #13066871C2semidirect
8. #13066846C2semidirect
9. #13066846C2semidirect
10. #13066840C2semidirect
29. #10622825C4semidirect
427. C4×C11#388semidirect
617. C11#13994semidirect
798. C4#10622557semidirect

Maximal subgroups

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

subgroupindex
C2×#106225412
C2×#106225572
C2×#106228252
C2×C4×C4⋊Dic112
#130668712
#130668632
#130668462
#130668402
C2×C4×C11×C22⋊C42
#1399411