Finite Group Databasebeta

← #14774041

Subgroups — #14774041

Order 2816.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622840C211yesmaximal, characteristic
2C2×#10622639C211yesmaximal, characteristic, complemented
3C22×#66899C211yesmaximal, characteristic, complemented
4#13071630C211yesmaximal, characteristic
5#13069500C211yesmaximal, characteristic, complemented
6#13069309C211yesmaximal, characteristic, complemented
7#13069254C211yesmaximal, characteristic, complemented
8#13069042C211yesmaximal, characteristic
9#13068971C211yesmaximal, characteristic, complemented
10#13068953C211yesmaximal, characteristic, complemented
11#13068870C211yesmaximal, characteristic, complemented
12#13068803C211yesmaximal, characteristic, complemented
13#13068446C211yesmaximal, characteristic, complemented
14#13068394C211yesmaximal, characteristic, complemented
15Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C2×#66983C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C23×C11⋊C8C2211yescharacteristic
24C2×(C22⋊D11)⋊C4—21no—
25C2×C4×D44C2211yescharacteristic
26C11×#391—21no—
27C11×#391—21no—
28C11×#391C2211yescharacteristic
29C11×#391C2211yescharacteristic
30C11×#380—21no—
31C11×#380C2211yescharacteristic
32C4×C11×C22⋊C4—21no—
33C4×C11×C22⋊C4C2211yescharacteristic
34#10622840C418yescomplemented
35C2×#66899—24no—
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×#66899C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43#10622639—24no—
44C2×#66873C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48#10622571—21no—
49#10622552C2211yescharacteristic
50C4×C4⋊Dic11C2211yescharacteristic
51#10622541C2211yescharacteristic
52C2×#66867C2211yescharacteristic
53C2×#66867C2211yescharacteristic
54#10622283—21no—
55#10622281—21no—
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61#10622162C2211yescharacteristic
62C22×Q8×C11—21no—
63C22×Q8×C11—22no—
64C22×Q8×C11—22no—
65C22×Q8×C11—22no—
66C22×Q8×C11—41no—
67C22×Q8×C11—41no—
68C22×Q8×C11C2×C414yescomplemented
69C22×Q8×C11C2311yescharacteristic
70C22×Q8×C11C2311yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11C2311yescharacteristic
73C22×C22⋊D11—21no—
74C23×Dic11—21no—
75C22×D44C2311yescharacteristic
76C22×C4×D11—21no—
77C4×Q8×C11—22no—
78C4×Q8×C11—22no—
79C4×Q8×C11—41no—
80C4×Q8×C11—41no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4D411yescharacteristic
87C2×C11×C22⋊C4D411yescharacteristic
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×#4325—22no—
93C2×#4325—22no—
94C2×#4325—41no—
95C2×#4325—41no—
96C2×#4325C2×C414yescomplemented
97C2×#4325C2×C414yescomplemented
98#66983—22no—
99#66983C2×C414yes—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11—21no—
106C2×C4⋊Dic11—41no—
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110C2×Dic11⋊C4—21no—
111C2×C4×Dic11—21no—
112C22×C11⋊C8—22no—
113C22×C11⋊C8—22no—
114C22×C11⋊C8—41no—
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119(C22⋊D11)⋊C4—44no—
120C4×D44—22no—
121C4×D44—41no—
122C11×#95—21no—
123C11×#95—21no—
124C11×#95—21no—
125C11×#95—21no—
126C11×#95—21no—
127C11×#95D411yescharacteristic
128C11×#95D411yescharacteristic
129#66899—22no—
130#66899—22no—
131#66899—22no—
132#66899C2×C414yescomplemented
133#66899C2×C414yescomplemented
134#66899D414yescomplemented
135C11⋊#95—21no—
136C11⋊#95—21no—
137C22⋊(C11⋊C8)C2×C414yescomplemented
138#66873—22no—
139#66873—41no—
140#66871—22no—
141#66871—41no—
142#66867—22no—
143#66867—41no—
144#22855—111nomaximal, Sylow
145C24×C11C2×D411yescharacteristic
146C23×D11—21no—
147C2×Q8×C11—24no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—28no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—42no—
158C2×Q8×C11—42no—
159C2×Q8×C11—44no—
160C2×Q8×C11—44no—
161C2×Q8×C11—44no—
162C2×Q8×C11C22×C412yes—
163C2×Q8×C11C22×C412yes—
164C2×Q8×C11C2×D412yes—
165C2×Q8×C11#4112yes—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—24no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—42no—
176C22×C4×C11—42no—
177C22×C4×C11C22×C412yes—
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11#4112yes—
184C22×C4×C11C2411yescharacteristic
185C2×C22⋊D11—24no—
186C2×C22⋊D11—42no—
187C2×C22⋊D11—42no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—42no—
192C22×Dic11—42no—
193C22×Dic11—81no—
194C2×D44—21no—
195C2×D44—21no—
196C2×D44—21no—
197C2×D44—21no—
198C2×D44—21no—
199C2×D44C22×C412yes—
200C2×C4×D11—42no—
201C2×C4×D11—42no—
202C2×C4×D11—81no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—42no—
208C11×C4⋊C4—42no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—42no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—42no—
217C42×C11—42no—
218#4325—28no—
219#4325—44no—
220(C2×D11)⋊C4—24no—
221(C2×D11)⋊C4—42no—
222(C2×D11)⋊C4—42no—
223(C2×D11)⋊C4—81no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—42no—
229C4⋊Dic11C22×C412yes—
230C4⋊Dic11C2×D412yes—
231Dic11⋊C4—42no—
232C4×Dic11—42no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—44no—
243C2×C11⋊C8C22×C412yes—
244C2×C11⋊C8C22×C412yes—
245C2×C11⋊C8C2×D412yes—
246C2×#448—111no—
247C2×#440—111no—
248C22×#103—111no—
249#2361—111no—
250Q8×C22⋊C4D1111yescharacteristic, complemented
251#1973—111no—
252#1935—111no—
253#1928—111no—
254#1893—111no—
255#1880—111no—
256#1877—111no—
257#1863—111no—
258#1852—111no—
259#1763—111no—
260#1752—111no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11C4×D412yes—
266C23×C11AGL(1,ℤ/8)12yes—
267C23×C11#13712yes—
268C23×C11C22×D411yescharacteristic
269C22×D11—22no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276Q8×C11—22no—
277Q8×C11—22no—
278Q8×C11—22no—
279Q8×C11—22no—
280Q8×C11—22no—
281Q8×C11—48no—
282Q8×C11—41no—
283Q8×C11—41no—
284Q8×C11C4×D414yescomplemented
285C2×C4×C11—22no—
286C2×C4×C11—21no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—21no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—48no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11C4×D412yes—
317C2×C4×C11C23×C411yescharacteristic
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C2×#4111yescharacteristic
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C2×C4×C11H(5,𝔽2)11yescharacteristic
323C22⋊D11—48no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—84no—
334D44—22no—
335D44—22no—
336D44—41no—
337D44—41no—
338C4×D11—84no—
339C11⋊C8—22no—
340C11⋊C8—22no—
341C11⋊C8—22no—
342C11⋊C8—41no—
343C23×Q8C2×D1111yescharacteristic
344C22×SD16—111no—
345C22×SD16—111no—
346C23×C8—111no—
347C2×#121—111no—
348C2×C4×Q8C2×D1111yescharacteristic
349C2×C4×Q8C2×D1111yescharacteristic
350C2×C4×D4—111no—
351C2×C4×D4—221no—
352C22×C4⋊C4—111no—
353#448—118no—
354#440—224no—
355C2×#107—111no—
356C2×#107—111no—
357C2×#103—111no—
358C2×#103—111no—
359C2×#103—111no—
360C2×#103—111no—
361C2×#103—111no—
362C2×#103—111no—
363C2×#103—224no—
364C2×#102—111no—
365C2×#102—111no—
366C2×C22⋊C8—111no—
367C2×#97—111no—
368C2×#97—111no—
369#391—21no—
370#391—21no—
371#391C2×D1111yescharacteristic
372#391C2×D1111yescharacteristic
373#390—111no—
374#389—111no—
375#388—221no—
376#386—221no—
377#385—221no—
378#380—21no—
379#380C2×D1111yescharacteristic
380C4×C4⋊C4—111no—
381C4×C22⋊C4—21no—
382C4×C22⋊C4C2×D1111yescharacteristic
383#340—111no—
384#340—111no—
385#340—111no—
386#340—111no—
387#336—111no—
388#336—111no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11#44014yescomplemented
396C22×C11C2×C4×D411yescharacteristic
397C22×C11D4211yescharacteristic
398C22×C11#54611yescharacteristic
399C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
400C22×C11C2×#13711yescharacteristic
401C22×C11#57711yescharacteristic
402C22×C11#57811yescharacteristic
403C2×D11—42no—
404C2×D11—42no—
405C2×D11—42no—
406C2×D11—81no—
407C2×D11—81no—
408C2×D11—81no—
409C2×D11—81no—
410C4×C11—22no—
411C4×C11—24no—
412C4×C11—42no—
413C4×C11—41no—
414C4×C11—41no—
415C4×C11—41no—
416C4×C11—41no—
417C4×C11—81no—
418C4×C11—81no—
419C4×C11C2×C4×D411yescharacteristic
420C4×C11#51811yescharacteristic
421C4×C11#54611yescharacteristic
422C4×C11#55111yescharacteristic
423Dic11—42no—
424Dic11—42no—
425Dic11—81no—
426C22×Q8—22no—
427C22×Q8—21no—
428C22×Q8—22no—
429C22×Q8—22no—
430C22×Q8—41no—
431C22×Q8—41no—
432C22×Q8C4×D1114yescomplemented
433C22×Q8C22×D1111yescharacteristic
434C22×Q8C22×D1111yescharacteristic
435C22×D4—111no—
436C22×D4—221no—
437C23×C4—21no—
438C23×C4—221no—
439C23×C4—221no—
440C23×C4C22×D1111yescharacteristic
441C2×SD16—114no—
442C2×SD16—114no—
443C2×SD16—222no—
444C2×SD16—222no—
445C2×SD16—441no—
446C2×SD16—441no—
447C22×C8—111no—
448C22×C8—111no—
449C22×C8—111no—
450C22×C8—111no—
451C22×C8—222no—
452C22×C8—222no—
453C22×C8—441no—
454#121—114no—
455#121—222no—
456C4×Q8—22no—
457C4×Q8—22no—
458C4×Q8—41no—
459C4×Q8—41no—
460C4×D4—222no—
461C4×D4—441no—
462C4×D4—444no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—222no—
469C2×C4⋊C4—221no—
470C2×C4⋊C4—221no—
471C2×C4⋊C4—441no—
472C2×C4⋊C4C22×D1111yescharacteristic
473C2×C4⋊C4C22×D1111yescharacteristic
474C2×C22⋊C4—21no—
475C2×C22⋊C4—221no—
476C2×C22⋊C4—221no—
477C2×C22⋊C4—221no—
478C2×C22⋊C4—221no—
479C2×C22⋊C4C22⋊D1111yescharacteristic
480C2×C22⋊C4C22⋊D1111yescharacteristic
481C2×C42—21no—
482C2×C42—21no—
483C2×C42—221no—
484C2×C42C22×D1111yescharacteristic
485C2×C42C22×D1111yescharacteristic
486#107—222no—
487#107—441no—
488#103—114no—
489#103—114no—
490#103—114no—
491#103—222no—
492#103—222no—
493#103—222no—
494#102—222no—
495#102—441no—
496C22⋊C8—114no—
497#97—222no—
498#97—441no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—221no—
505#95—221no—
506#95C22⋊D1111yescharacteristic
507#95C22⋊D1111yescharacteristic
508C2×C11—24no—
509C2×C11#235811yescharacteristic
510C2×C11C2×#44011yescharacteristic
511C2×C11#294711yescharacteristic
512C2×C11#326511yescharacteristic
513C2×C11#327011yescharacteristic
514C2×C11#330811yescharacteristic
515C2×C11#332011yescharacteristic
516D11—82no—
517C24—221no—
518C24C2×C22⋊D1111yescharacteristic
519C2×Q8—24no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—28no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—42no—
530C2×Q8—42no—
531C2×Q8—44no—
532C2×Q8—44no—
533C2×Q8—44no—
534C2×Q8C2×C4×D1112yes—
535C2×Q8C2×C4×D1112yes—
536C2×Q8D4×D1112yes—
537C2×Q8#434112yes—
538C2×D4—112no—
539C2×D4—224no—
540C2×D4—221no—
541C2×D4—221no—
542C2×D4—221no—
543C2×D4—221no—
544C2×D4—221no—
545C2×D4—442no—
546C2×D4—442no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—442no—
562C22×C4—442no—
563C22×C4—442no—
564C22×C4—442no—
565C22×C4—881no—
566C22×C4—881no—
567C22×C4C2×C4×D1112yes—
568C22×C4#433912yes—
569C22×C4C2×C22⋊D1111yescharacteristic
570C22×C4C2×C22⋊D1111yescharacteristic
571C22×C4C2×C22⋊D1111yescharacteristic
572C22×C4C2×C22⋊D1111yescharacteristic
573C22×C4C2×C22⋊D1111yescharacteristic
574C22×C4C23×D1111yescharacteristic
575SD16—228no—
576SD16—444no—
577C2×C8—112no—
578C2×C8—112no—
579C2×C8—112no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C2×C8—221no—
588C2×C8—221no—
589C2×C8—444no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—112no—
597C4⋊C4—112no—
598C4⋊C4—221no—
599C4⋊C4—221no—
600C4⋊C4—221no—
601C4⋊C4—221no—
602C4⋊C4—442no—
603C4⋊C4—442no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—42no—
607C22⋊C4—224no—
608C22⋊C4—442no—
609C22⋊C4—442no—
610C22⋊C4—881no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—42no—
616C42—42no—
617C42—442no—
618C11#2285511yescharacteristic, complemented, Sylow
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—222no—
624C23—441no—
625C23—441no—
626C23—441no—
627C23—441no—
628C23—441no—
629C23—441no—
630C23C4×C22⋊D1112yes—
631C23#6699512yes—
632C23#6700212yes—
633C23C22×C22⋊D1111yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—48no—
640Q8—41no—
641Q8—41no—
642Q8(C22⋊D11)⋊C414yescomplemented
643D4—222no—
644D4—222no—
645D4—448no—
646D4—441no—
647D4—441no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—48no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—441no—
682C2×C4—441no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—884no—
689C2×C4—884no—
690C2×C4C4×C22⋊D1112yes—
691C2×C4C22×C4×D1111yescharacteristic
692C2×C4C2×#433911yescharacteristic
693C2×C4C2×D4×D1111yescharacteristic
694C2×C4C2×#434111yescharacteristic
695C2×C4#6703711yescharacteristic
696C2×C4#6703711yescharacteristic
697C8—222no—
698C8—222no—
699C8—222no—
700C8—441no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—442no—
708C22—442no—
709C22—442no—
710C22—881no—
711C22—881no—
712C22—881no—
713C22—881no—
714C22#1062263914yescomplemented
715C22C2×C4×C22⋊D1111yescharacteristic
716C22D4×C22⋊D1111yescharacteristic
717C22#1062333711yescharacteristic
718C22C2×#6699511yescharacteristic
719C22C2×#6700211yescharacteristic
720C22#1062336811yescharacteristic
721C22#1062336911yescharacteristic
722C4—22no—
723C4—24no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—42no—
729C4—81no—
730C4—81no—
731C4—442no—
732C4—442no—
733C4—881no—
734C4C2×(C22⋊D11)⋊C411yescharacteristic
735C4#1062301711yescharacteristic
736C4#1062302111yescharacteristic
737C4#1062302611yescharacteristic
738C2—24no—
739C2—882no—
740C2#1307159511yescharacteristic
741C2C2×#1062263911yescharacteristic
742C2#1307745911yescharacteristic
743C2#1308011211yescharacteristic
744C2#1308018711yescharacteristic
745C2#1308060711yescharacteristic
746C2#1308078711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingQ8×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenterQ8×C22⋊C4D11
hypocenterC11#22855
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622639C2semidirect
3. C22×#66899C2semidirect
5. #13069500C2semidirect
6. #13069309C2semidirect
7. #13069254C2semidirect
9. #13068971C2semidirect
10. #13068953C2semidirect
11. #13068870C2semidirect
12. #13068803C2semidirect
13. #13068446C2semidirect
14. #13068394C2semidirect
15. Q8×C11×C22⋊C4C2semidirect
34. #10622840C4semidirect
68. C22×Q8×C11C2×C4semidirect
96. C2×#4325C2×C4semidirect
97. C2×#4325C2×C4semidirect
132. #66899C2×C4semidirect
133. #66899C2×C4semidirect
134. #66899D4semidirect
137. C22⋊(C11⋊C8)C2×C4semidirect
250. Q8×C22⋊C4D11semidirect
284. Q8×C11C4×D4semidirect
395. C22×C11#440semidirect
432. C22×Q8C4×D11semidirect
618. C11#22855semidirect
642. Q8(C22⋊D11)⋊C4semidirect
714. C22#10622639semidirect

Maximal subgroups

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

subgroupindex
C2×#106228402
C2×#106226392
C22×#668992
#130716302
#130695002
#130693092
#130692542
#130690422
#130689712
#130689532
#130688702
#130688032
#130684462
#130683942
Q8×C11×C22⋊C42
#2285511