Finite Group Databasebeta

← #14797690

Subgroups — #14797690

Order 2816.

1148 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622659C211yesmaximal, characteristic
2C2×C4×#4325C211yesmaximal, characteristic, complemented
3C22⋊C4×D44C211yesmaximal, characteristic
4#13070140C211yesmaximal, characteristic, complemented
5#13070052C211yesmaximal, characteristic, complemented
6#13069931C211yesmaximal, characteristic, complemented
7#13069816C211yesmaximal, characteristic, complemented
8#13069298C211yesmaximal, characteristic, complemented
9#13069224C211yesmaximal, characteristic, complemented
10#13068971C211yesmaximal, characteristic, complemented
11#13068953C211yesmaximal, characteristic, complemented
12#13068862C211yesmaximal, characteristic, complemented
13#13068623C211yesmaximal, characteristic, complemented
14#13068546C211yesmaximal, characteristic
15C11×#2421C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic, complemented
19C22×#4325C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C2×C22⋊C4×D11—21no—
22C2×C4×D44C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C11×#400—21no—
25C11×#397—21no—
26C11×#391C2211yescharacteristic, complemented
27C11×#389C2211yescharacteristic, complemented
28C11×#388—21no—
29C11×#387—21no—
30C11×#382C2211yescharacteristic, complemented
31C11×#380C2211yescharacteristic
32C4×C11×C22⋊C4C2211yescharacteristic
33C2×#66899C2211yescharacteristic, complemented
34C2×#66899C2211yescharacteristic, complemented
35#10622825C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38#10622659—24no—
39C4×#4325—24no—
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66872C2211yescharacteristic, complemented
47C2×#66871C2211yescharacteristic, complemented
48#10622568—21no—
49#10622552C2211yescharacteristic
50#10622552C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
52C2×C4×C11⋊C8C2211yescharacteristic, complemented
53#10622278—21no—
54#10622278—21no—
55#10622167C2211yescharacteristic, complemented
56#10622167C2211yescharacteristic, complemented
57#10622167C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622162C2211yescharacteristic, complemented
60#10622162C2211yescharacteristic, complemented
61C24×D11—21no—
62C22×Q8×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×D44—21no—
65C22×D44—22no—
66C22×D44—22no—
67C22×D44—22no—
68C22×D44—22no—
69C22×D44—41no—
70C22×D44—41no—
71C22×D44C2311yescharacteristic
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×C4×D11—21no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—41no—
77C4×Q8×C11—22no—
78C4×Q8×C11—41no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4D411yescharacteristic
88C2×C11×C22⋊C4D411yescharacteristic
89C2×C42×C11—21no—
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C22⋊Dic11—21no—
93C2×#4325—22no—
94C2×#4325—22no—
95C2×#4325—22no—
96C2×#4325—22no—
97C2×#4325—41no—
98C2×#4325D414yes—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22⋊C4×D11—44no—
112C4×D44—22no—
113C4×D44—22no—
114C4×D44—41no—
115C4×D44—41no—
116C11×#95—21no—
117C11×#95—21no—
118C11×#95—21no—
119C11×#95—21no—
120C11×#95—21no—
121C11×#95—21no—
122C11×#95D411yescharacteristic
123C11×#95D411yescharacteristic
124#66899—22no—
125#66899—41no—
126C11⋊#95—21no—
127C22⋊(C11⋊C8)—22no—
128C22⋊(C11⋊C8)—41no—
129#66873—22no—
130#66873—22no—
131#66873—22no—
132#66873—22no—
133#66873—22no—
134#66873—41no—
135#66872—22no—
136#66871—41no—
137C4⋊(C11⋊C8)—41no—
138C4×C11⋊C8—22no—
139#24905—111nomaximal, Sylow
140C24×C11C2×D411yescharacteristic
141C23×D11—21no—
142C23×D11—21no—
143C23×D11—24no—
144C23×D11—42no—
145C23×D11—42no—
146C23×D11—42no—
147C23×D11—42no—
148C23×D11—81no—
149C23×D11—81no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11C2×D412yes—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C22×Dic11—21no—
173C22×Dic11—21no—
174C2×D44—24no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—42no—
184C2×D44—42no—
185C2×D44—44no—
186C2×D44—44no—
187C2×D44—44no—
188C2×D44—44no—
189C2×D44C2×D412yes—
190C2×D44#4112yes—
191C2×D44#4112yes—
192C2×D44#4112yes—
193C2×C4×D11—42no—
194C2×C4×D11—42no—
195C2×C4×D11—42no—
196C2×C4×D11—42no—
197C2×C4×D11—81no—
198C2×C4×D11—81no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—42no—
206C11×C4⋊C4—42no—
207C11×C4⋊C4—42no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—42no—
211C11×C22⋊C4—42no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—42no—
217C22⋊Dic11—42no—
218#4325—28no—
219#4325—44no—
220(C2×D11)⋊C4—42no—
221(C2×D11)⋊C4—42no—
222(C2×D11)⋊C4—42no—
223(C2×D11)⋊C4—42no—
224(C2×D11)⋊C4—81no—
225(C2×D11)⋊C4—81no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
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⋊C8C2×D412yes—
242C2×#450—111no—
243C2×C4×SD16—111no—
244#2421D1111yescharacteristic, complemented
245D4×C22⋊C4—111no—
246#2092—111no—
247#2077—111no—
248#2055—111no—
249#2036—111no—
250#1934—111no—
251#1923—111no—
252#1880—111no—
253#1877—111no—
254#1862—111no—
255#1804—111no—
256#1786—111no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11#13512yes—
264C23×C11C22×D411yescharacteristic
265C22×D11—22no—
266C22×D11—22no—
267C22×D11—22no—
268C22×D11—22no—
269C22×D11—48no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—48no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11—41no—
280C22×D11—41no—
281C22×D11—84no—
282C22×D11—84no—
283C22×D11—84no—
284C22×D11—84no—
285C22×D11—84no—
286Q8×C11—22no—
287Q8×C11—22no—
288Q8×C11—41no—
289Q8×C11—41no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
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—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
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×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11AGL(1,ℤ/8)12yes—
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11C2×#4111yescharacteristic
323C2×C4×C11C2×#4111yescharacteristic
324C2×C4×C11C2×#4111yescharacteristic
325C2×C4×C11H(5,𝔽2)11yescharacteristic
326C2×C4×C11H(5,𝔽2)11yescharacteristic
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333D44—22no—
334D44—22no—
335D44—22no—
336D44—22no—
337D44—22no—
338D44—48no—
339D44—41no—
340D44—41no—
341D44#12314yes—
342C4×D11—84no—
343C4×D11—84no—
344C11⋊C8—22no—
345C11⋊C8—41no—
346C11⋊C8—41no—
347C11⋊C8—41no—
348C23×D4—111no—
349C22×SD16—111no—
350C22×SD16—111no—
351C2×C22⋊Q8C2×D1111yescharacteristic
352C2×C4×Q8C2×D1111yescharacteristic, complemented
353C2×C4×D4—111no—
354C2×C4×D4—111no—
355C22×C22⋊C4—221no—
356#450—224no—
357C4×SD16—224no—
358C2×#107—111no—
359C2×#106—111no—
360C2×C4⋊C8—111no—
361C2×#103—111no—
362C2×#103—111no—
363C2×#102—111no—
364C2×#102—111no—
365C2×#102—111no—
366C2×#102—111no—
367C2×#102—111no—
368C2×#102—111no—
369C2×C22⋊C8—111no—
370C2×C22⋊C8—111no—
371C2×C4×C8—111no—
372#400—21no—
373#397—21no—
374#391C2×D1111yescharacteristic, complemented
375#390—111no—
376#390—111no—
377#389C2×D1111yescharacteristic, complemented
378#388—21no—
379#387—21no—
380#386—221no—
381#386—221no—
382#382C2×D1111yescharacteristic, complemented
383#380—111no—
384#380C2×D1111yescharacteristic
385#379—221no—
386C4×C22⋊C4C2×D1111yescharacteristic
387#340—111no—
388#340—111no—
389#340—111no—
390#340—111no—
391#336—111no—
392#336—111no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—22no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11#52511yescharacteristic
401C22×C11D4211yescharacteristic
402C22×C11#54611yescharacteristic
403C22×C11C2×#13511yescharacteristic
404C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
405C22×C11#57711yescharacteristic
406C22×C11#57711yescharacteristic
407C2×D11—24no—
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—42no—
411C2×D11—42no—
412C2×D11—42no—
413C2×D11—42no—
414C2×D11—42no—
415C2×D11—42no—
416C2×D11—42no—
417C2×D11—816no—
418C2×D11—81no—
419C2×D11—81no—
420C2×D11—81no—
421C2×D11—81no—
422C4×C11—22no—
423C4×C11—41no—
424C4×C11—42no—
425C4×C11—41no—
426C4×C11—41no—
427C4×C11—41no—
428C4×C11—81no—
429C4×C11—81no—
430C4×C11—81no—
431C4×C11C2×#12311yescharacteristic
432C4×C11#53811yescharacteristic
433C4×C11#54611yescharacteristic
434C4×C11#55111yescharacteristic
435Dic11—81no—
436Dic11—81no—
437C25—221no—
438C22×Q8C22×D1111yescharacteristic
439C22×D4—111no—
440C22×D4—111no—
441C22×D4—222no—
442C22×D4—222no—
443C22×D4—222no—
444C22×D4—222no—
445C22×D4—221no—
446C22×D4—441no—
447C22×D4—441no—
448C23×C4—221no—
449C23×C4—221no—
450C23×C4C22×D1111yescharacteristic
451C2×SD16—114no—
452C2×SD16—222no—
453C2×SD16—222no—
454C2×SD16—222no—
455C2×SD16—222no—
456C2×SD16—441no—
457C22×C8—111no—
458C22×C8—111no—
459C22×C8—111no—
460C22×C8—111no—
461C22⋊Q8—22no—
462C22⋊Q8—41no—
463C4×Q8—22no—
464C4×Q8—41no—
465C4×D4—222no—
466C4×D4—222no—
467C4×D4—441no—
468C4×D4—441no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—111no—
473C2×C4⋊C4—111no—
474C2×C4⋊C4C22×D1111yescharacteristic
475C2×C4⋊C4C22×D1111yescharacteristic
476C2×C4⋊C4C22×D1111yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—221no—
480C2×C22⋊C4—221no—
481C2×C22⋊C4—221no—
482C2×C22⋊C4—221no—
483C2×C22⋊C4—221no—
484C2×C22⋊C4—221no—
485C2×C22⋊C4—221no—
486C2×C22⋊C4—444no—
487C2×C22⋊C4C22⋊D1111yescharacteristic
488C2×C22⋊C4C22⋊D1111yescharacteristic
489C2×C42—21no—
490C2×C42C22×D1111yescharacteristic
491C2×C42C22×D1111yescharacteristic
492#107—441no—
493#106—222no—
494C4⋊C8—441no—
495#103—222no—
496#103—441no—
497#102—222no—
498#102—222no—
499#102—222no—
500#102—222no—
501#102—222no—
502#102—441no—
503C22⋊C8—222no—
504C22⋊C8—441no—
505C4×C8—222no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—221no—
513#95C22⋊D1111yescharacteristic
514#95C22⋊D1111yescharacteristic
515C2×C11—42no—
516C2×C11#241811yescharacteristic
517C2×C11#310511yescharacteristic
518C2×C11#312311yescharacteristic
519C2×C11#326511yescharacteristic
520C2×C11#328211yescharacteristic
521C2×C11#329611yescharacteristic
522C2×C11#332411yescharacteristic
523D11—44no—
524D11—82no—
525C24—224no—
526C24—221no—
527C24—221no—
528C24—442no—
529C24—442no—
530C24—442no—
531C24—442no—
532C24—881no—
533C24—881no—
534C24C2×C22⋊D1111yescharacteristic
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8D4×D1112yes—
541C2×D4—112no—
542C2×D4—112no—
543C2×D4—112no—
544C2×D4—112no—
545C2×D4—224no—
546C2×D4—221no—
547C2×D4—221no—
548C2×D4—221no—
549C2×D4—221no—
550C2×D4—221no—
551C2×D4—221no—
552C2×D4—221no—
553C2×D4—221no—
554C2×D4—442no—
555C2×D4—442no—
556C2×D4—444no—
557C2×D4—444no—
558C2×D4—444no—
559C2×D4—444no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—221no—
571C22×C4—221no—
572C22×C4—442no—
573C22×C4—442no—
574C22×C4—442no—
575C22×C4—442no—
576C22×C4—881no—
577C22×C4—881no—
578C22×C4C2×C22⋊D1111yescharacteristic
579C22×C4C2×C22⋊D1111yescharacteristic
580C22×C4C2×C22⋊D1111yescharacteristic
581C22×C4C2×C22⋊D1111yescharacteristic
582C22×C4C2×C22⋊D1111yescharacteristic
583C22×C4C23×D1111yescharacteristic
584SD16—228no—
585SD16—444no—
586C2×C8—112no—
587C2×C8—221no—
588C2×C8—221no—
589C2×C8—221no—
590C2×C8—221no—
591C2×C8—221no—
592C2×C8—221no—
593C2×C8—221no—
594C2×C8—221no—
595C2×C8—221no—
596C2×C8—221no—
597C2×C8—221no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—221no—
608C4⋊C4—221no—
609C4⋊C4—221no—
610C4⋊C4—221no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—442no—
616C22⋊C4—442no—
617C22⋊C4—442no—
618C22⋊C4—442no—
619C22⋊C4—442no—
620C22⋊C4—881no—
621C22⋊C4—881no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—42no—
627C11#2490511yescharacteristic, complemented, Sylow
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—222no—
635C23—222no—
636C23—222no—
637C23—222no—
638C23—448no—
639C23—448no—
640C23—441no—
641C23—441no—
642C23—441no—
643C23—441no—
644C23—441no—
645C23—441no—
646C23—441no—
647C23—441no—
648C23—441no—
649C23—441no—
650C23—884no—
651C23—884no—
652C23—884no—
653C23—884no—
654C23—884no—
655C23#6700312yes—
656C23C22×C22⋊D1111yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—41no—
660Q8—41no—
661D4—114no—
662D4—222no—
663D4—222no—
664D4—222no—
665D4—222no—
666D4—222no—
667D4—448no—
668D4—441no—
669D4—441no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—41no—
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—441no—
701C2×C4—441no—
702C2×C4—441no—
703C2×C4—441no—
704C2×C4—441no—
705C2×C4—441no—
706C2×C4—884no—
707C2×C4—884no—
708C2×C4#6700212yes—
709C2×C4C2×D4×D1111yescharacteristic
710C2×C4#6703711yescharacteristic
711C2×C4#41×D1111yescharacteristic
712C2×C4#41×D1111yescharacteristic
713C2×C4#41×D1111yescharacteristic
714C2×C4#6704211yescharacteristic
715C8—222no—
716C8—441no—
717C8—441no—
718C8—441no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—224no—
727C22—442no—
728C22—442no—
729C22—442no—
730C22—442no—
731C22—442no—
732C22—442no—
733C22—442no—
734C22—442no—
735C22—442no—
736C22—8816no—
737C22—881no—
738C22—881no—
739C22—881no—
740C22—881no—
741C22D4×C22⋊D1111yescharacteristic
742C22C2×#6700211yescharacteristic
743C22C2×#6700311yescharacteristic
744C22#1062335911yescharacteristic
745C22#1062336011yescharacteristic
746C22#1062336811yescharacteristic
747C22#1062336811yescharacteristic
748C4—22no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—42no—
754C4—81no—
755C4—81no—
756C4—81no—
757C4—881no—
758C4—881no—
759C4D11×#12311yescharacteristic
760C4#1062318511yescharacteristic
761C4#1062318811yescharacteristic
762C4#1062319011yescharacteristic
763C2—42no—
764C2—444no—
765C2—882no—
766C2#1307207511yescharacteristic
767C2#1307865911yescharacteristic
768C2#1307886311yescharacteristic
769C2#1308011211yescharacteristic
770C2#1308032411yescharacteristic
771C2#1308044511yescharacteristic
772C2#1308084111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2421C2
socleC23×C11C22×D4
prime radicalC23×D44C22
hypercenter#2421D11
hypocenterC11#24905
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2421

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4325C2semidirect
4. #13070140C2semidirect
5. #13070052C2semidirect
6. #13069931C2semidirect
7. #13069816C2semidirect
8. #13069298C2semidirect
9. #13069224C2semidirect
10. #13068971C2semidirect
11. #13068953C2semidirect
12. #13068862C2semidirect
13. #13068623C2semidirect
15. C11×#2421C2semidirect
18. C2×C4×Q8×C11C22semidirect
26. C11×#391C22semidirect
27. C11×#389C22semidirect
30. C11×#382C22semidirect
33. C2×#66899C22semidirect
34. C2×#66899C22semidirect
46. C2×#66872C22semidirect
47. C2×#66871C22semidirect
51. C2×C4⋊(C11⋊C8)C22semidirect
52. C2×C4×C11⋊C8C22semidirect
55. #10622167C22semidirect
56. #10622167C22semidirect
57. #10622167C22semidirect
58. #10622167C22semidirect
59. #10622162C22semidirect
60. #10622162C22semidirect
244. #2421D11semidirect
352. C2×C4×Q8C2×D11semidirect
374. #391C2×D11semidirect
377. #389C2×D11semidirect
382. #382C2×D11semidirect
627. C11#24905semidirect

Maximal subgroups

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

subgroupindex
C2×#106226592
C2×C4×#43252
C22⋊C4×D442
#130701402
#130700522
#130699312
#130698162
#130692982
#130692242
#130689712
#130689532
#130688622
#130686232
#130685462
C11×#24212
#2490511