Finite Group Databasebeta

← #14788168

Subgroups — #14788168

Order 2816.

1230 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic, complemented
2C2×#10622622C211yesmaximal, characteristic, complemented
3C2×#10622629C211yesmaximal, characteristic, complemented
4#13069819C211yesmaximal, characteristic, complemented
5#13069805C211yesmaximal, characteristic, complemented
6#13069619C211yesmaximal, characteristic, complemented
7#13069612C211yesmaximal, characteristic
8#13069573C211yesmaximal, characteristic, complemented
9#13069548C211yesmaximal, characteristic, complemented
10#13068974C211yesmaximal, characteristic, complemented
11#13068967C211yesmaximal, characteristic, complemented
12#13068883C211yesmaximal, characteristic, complemented
13#13068862C211yesmaximal, characteristic, complemented
14#13068596C211yesmaximal, characteristic, complemented
15C4×C11×#121C211yesmaximal, characteristic, complemented
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C22×#4323C2211yescharacteristic
22C2×#66983C2211yescharacteristic
23C2×#66982—21no—
24C2×C4×C22⋊D11—21no—
25C2×#66977C2211yescharacteristic
26#10623010—24no—
27#10623010—24no—
28C2×#66929—21no—
29C2×#66928C2211yescharacteristic
30C2×C4×D44C2211yescharacteristic
31C2×#66925—21no—
32C2×#66923C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#390C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#388—21no—
37C11×#386—21no—
38C11×#380C2211yescharacteristic
39C4×C11×C4⋊C4C2211yescharacteristic
40C4×C11×C22⋊C4—21no—
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45#10622629—24no—
46#10622622—24no—
47C2×#66874C2211yescharacteristic
48C2×#66874C2211yescharacteristic
49C2×#66874C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51C2×#66873C2211yescharacteristic
52C2×#66873C2211yescharacteristic
53C2×#66872C2211yescharacteristic
54C2×#66871C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4⋊(C11⋊C8)C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11D411yescharacteristic
67C23×C4×C11D411yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11—21no—
70C22×D44C2311yescharacteristic
71C22×C4×D11—21no—
72C22×Dic22C2311yescharacteristic
73C11×#121—22no—
74C11×#121—22no—
75C4×D4×C11—22no—
76C4×D4×C11—22no—
77C4×D4×C11—44no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C42×C11—22no—
88C2×C42×C11—22no—
89C2×C42×C11—21no—
90C2×C42×C11D411yescharacteristic
91C2×C42×C11D411yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C22⋊Dic11—21no—
95C2×#4324—22no—
96C2×#4324—22no—
97C2×#4324—41no—
98C2×#4323—22no—
99C2×#4323—22no—
100C2×#4323—41no—
101#66983—22no—
102#66983—22no—
103#66982—28no—
104C4×C22⋊D11—28no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111#66977—22no—
112#66977—22no—
113C2×Dic11⋊C4—21no—
114C2×Dic11⋊C4—21no—
115C2×Dic11⋊C4—21no—
116C2×Dic11⋊C4—21no—
117C2×C4×Dic11—21no—
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122#66929—28no—
123#66928—22no—
124#66928D414yescomplemented
125C4×D44—22no—
126C4×D44—22no—
127#66925—28no—
128#66923—22no—
129#66923D414yescomplemented
130C4×Dic22—22no—
131C4×Dic22—22no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135#66896—22no—
136#66896—22no—
137C22⋊(C11⋊C8)—41no—
138C22⋊(C11⋊C8)—41no—
139#66874—22no—
140#66874—22no—
141#66874—41no—
142#66873—22no—
143#66873—22no—
144#66873—41no—
145#66872—22no—
146#66871—22no—
147C4⋊(C11⋊C8)—22no—
148C4⋊(C11⋊C8)—22no—
149#24158—111nomaximal, Sylow
150C24×C11—21no—
151C24×C11C2×D411yescharacteristic
152C23×D11—21no—
153C2×D4×C11—24no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—42no—
160C2×D4×C11—42no—
161C2×D4×C11#4112yes—
162C22×C4×C11—22no—
163C22×C4×C11—21no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—41no—
176C22×C4×C11—41no—
177C22×C4×C11—42no—
178C22×C4×C11—42no—
179C22×C4×C11—42no—
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C2×C22⋊D11—24no—
187C2×C22⋊D11—42no—
188C2×C22⋊D11—42no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C2×D44—21no—
193C2×D44—21no—
194C2×D44—21no—
195C2×D44—21no—
196C2×D44—21no—
197C2×D44C2×D412yes—
198C2×C4×D11—24no—
199C2×C4×D11—42no—
200C2×C4×D11—42no—
201C2×Dic22—21no—
202C2×Dic22—21no—
203C2×Dic22—21no—
204C2×Dic22—21no—
205C2×Dic22—21no—
206C2×Dic22C2×D412yes—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—42no—
213C11×C4⋊C4#4112yes—
214C11×C22⋊C4—24no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—42no—
217C11×C22⋊C4—42no—
218C11×C22⋊C4—42no—
219C42×C11—22no—
220C42×C11—22no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—42no—
224C42×C11C2×D412yes—
225C42×C11C2×D412yes—
226C22⋊Dic11—24no—
227#4324—44no—
228#4323—44no—
229(C2×D11)⋊C4—24no—
230(C2×D11)⋊C4—24no—
231(C2×D11)⋊C4—24no—
232(C2×D11)⋊C4—24no—
233C4⋊Dic11—21no—
234C4⋊Dic11—21no—
235C4⋊Dic11C2×D412yes—
236C4⋊Dic11C2×D412yes—
237Dic11⋊C4—24no—
238Dic11⋊C4—24no—
239Dic11⋊C4—24no—
240Dic11⋊C4—24no—
241C4×Dic11—24no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×#529—111no—
255C2×#478—111no—
256C2×#463—111no—
257C4×#121D1111yescharacteristic, complemented
258#2036—111no—
259#2034—111no—
260#2000—111no—
261#1999—111no—
262#1989—111no—
263#1983—111no—
264#1880—111no—
265#1879—111no—
266#1865—111no—
267#1862—111no—
268#1797—111no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—22no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11#13512yes—
283C23×C11C22×D411yescharacteristic
284C22×D11—22no—
285C22×D11—41no—
286C22×D11—41no—
287C22×D11—41no—
288C22×D11—41no—
289C22×D11—41no—
290C22×D11—41no—
291D4×C11—22no—
292D4×C11—22no—
293D4×C11—48no—
294D4×C11—41no—
295D4×C11—41no—
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—22no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—44no—
310C2×C4×C11—44no—
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×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—84no—
324C2×C4×C11#12012yes—
325C2×C4×C11#12012yes—
326C2×C4×C11AGL(1,ℤ/8)12yes—
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C2×#4111yescharacteristic
330C2×C4×C11C2×#4111yescharacteristic
331C2×C4×C11H(5,𝔽2)11yescharacteristic
332C2×C4×C112−1+411yescharacteristic
333C22⋊D11—48no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343D44—22no—
344D44—22no—
345D44—41no—
346D44—41no—
347C4×D11—48no—
348Dic22—22no—
349Dic22—22no—
350Dic22—41no—
351Dic22—41no—
352C11⋊C8—41no—
353C11⋊C8—41no—
354C11⋊C8—41no—
355C11⋊C8—41no—
356C22×SD16—111no—
357C22×D8—111no—
358#529—224no—
359#529—224no—
360C2×#126—221no—
361C2×#125—111no—
362C2×#124—111no—
363C2×#123—221no—
364C2×C22⋊Q8—111no—
365C2×#121—111no—
366C2×#121C2×D1111yescharacteristic
367C2×C4×Q8—111no—
368C2×C4×D4—21no—
369C2×C4×D4—111no—
370C2×C4×D4—221no—
371C2×C4×D4C2×D1111yescharacteristic
372C2×#117—221no—
373C22×C42C2×D1111yescharacteristic
374#478—224no—
375#463—224no—
376C2×#107—111no—
377C2×#106—111no—
378C2×C4⋊C8—111no—
379C2×C4⋊C8—111no—
380C2×#103—111no—
381C2×#103—111no—
382C2×#103—111no—
383C2×#102—111no—
384C2×#102—111no—
385C2×#102—111no—
386C2×#102—111no—
387C2×#102—111no—
388C2×C22⋊C8—111no—
389C2×C22⋊C8—111no—
390#390C2×D1111yescharacteristic
391#389C2×D1111yescharacteristic
392#388—21no—
393#386—21no—
394#380C2×D1111yescharacteristic
395C4×C4⋊C4C2×D1111yescharacteristic
396C4×C22⋊C4—21no—
397#340—111no—
398#340—111no—
399#340—111no—
400#340—111no—
401#336—111no—
402#336—111no—
403C22×C11—22no—
404C22×C11—22no—
405C22×C11—22no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—42no—
413C22×C11—81no—
414C22×C11—81no—
415C22×C11—81no—
416C22×C11—81no—
417C22×C11C2×#12011yescharacteristic
418C22×C11#52511yescharacteristic
419C22×C11#53711yescharacteristic
420C22×C11C2×#13511yescharacteristic
421C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
422C22×C11#57511yescharacteristic
423C22×C11#57511yescharacteristic
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—42no—
427C2×D11—81no—
428C2×D11—81no—
429C2×D11—81no—
430C2×D11—81no—
431C4×C11—22no—
432C4×C11—22no—
433C4×C11—22no—
434C4×C11—42no—
435C4×C11—41no—
436C4×C11—41no—
437C4×C11—81no—
438C4×C11—81no—
439C4×C11#54611yescharacteristic
440C4×C11#54711yescharacteristic
441C4×C11#54811yescharacteristic
442C4×C11#55011yescharacteristic
443Dic11—42no—
444Dic11—42no—
445Dic11—42no—
446C22×Q8—111no—
447C22×D4—21no—
448C22×D4—111no—
449C22×D4—221no—
450C22×D4C22×D1111yescharacteristic
451C23×C4—21no—
452C23×C4—221no—
453C23×C4C22⋊D1111yescharacteristic
454C23×C4C22⋊D1111yescharacteristic
455C23×C4C22×D1111yescharacteristic
456C2×SD16—222no—
457C2×SD16—222no—
458C2×SD16—441no—
459C2×D8—222no—
460C2×D8—222no—
461C2×D8—441no—
462C22×C8—111no—
463C22×C8—111no—
464C22×C8—111no—
465C22×C8—111no—
466#126—228no—
467#125—114no—
468#125—222no—
469#124—114no—
470#124—222no—
471#123—228no—
472C22⋊Q8—222no—
473C22⋊Q8—222no—
474#121—22no—
475#121—22no—
476#121—222no—
477#121—222no—
478C4×Q8—222no—
479C4×Q8—222no—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—44no—
483C4×D4—222no—
484C4×D4—222no—
485C4×D4—228no—
486#117—228no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—111no—
489C2×C4⋊C4—111no—
490C2×C4⋊C4—221no—
491C2×C4⋊C4—221no—
492C2×C4⋊C4—221no—
493C2×C4⋊C4—221no—
494C2×C4⋊C4C22×D1111yescharacteristic
495C2×C4⋊C4C22×D1111yescharacteristic
496C2×C4⋊C4C22×D1111yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—221no—
503C2×C22⋊C4—221no—
504C2×C22⋊C4—221no—
505C2×C22⋊C4—221no—
506C2×C22⋊C4—221no—
507C2×C42—22no—
508C2×C42—22no—
509C2×C42—21no—
510C2×C42—221no—
511C2×C42C22⋊D1111yescharacteristic
512C2×C42C22⋊D1111yescharacteristic
513C2×C42C22×D1111yescharacteristic
514C2×C42C22×D1111yescharacteristic
515#107—222no—
516#106—222no—
517C4⋊C8—222no—
518C4⋊C8—222no—
519#103—222no—
520#103—222no—
521#103—441no—
522#102—222no—
523#102—222no—
524#102—222no—
525#102—222no—
526#102—441no—
527C22⋊C8—441no—
528C22⋊C8—441no—
529#95—21no—
530#95—21no—
531#95—21no—
532C2×C11—42no—
533C2×C11—82no—
534C2×C11#240711yescharacteristic
535C2×C11#300211yescharacteristic
536C2×C11#300611yescharacteristic
537C2×C11#310511yescharacteristic
538C2×C11#311111yescharacteristic
539C2×C11#325011yescharacteristic
540C2×C11#325111yescharacteristic
541D11—82no—
542C24—21no—
543C24—221no—
544C24C2×C22⋊D1111yescharacteristic
545C2×Q8—112no—
546C2×Q8—221no—
547C2×Q8—221no—
548C2×Q8—221no—
549C2×Q8—221no—
550C2×Q8—221no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—112no—
560C2×D4—224no—
561C2×D4—221no—
562C2×D4—221no—
563C2×D4—221no—
564C2×D4—221no—
565C2×D4—221no—
566C2×D4—442no—
567C2×D4—442no—
568C2×D4#433912yes—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—224no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—442no—
592C22×C4—442no—
593C22×C4C2×C22⋊D1111yescharacteristic
594C22×C4C2×C22⋊D1111yescharacteristic
595C22×C4C2×C22⋊D1111yescharacteristic
596C22×C4C2×C22⋊D1111yescharacteristic
597C22×C4C2×C22⋊D1111yescharacteristic
598C22×C4C23×D1111yescharacteristic
599SD16—444no—
600D8—444no—
601C2×C8—221no—
602C2×C8—221no—
603C2×C8—221no—
604C2×C8—221no—
605C2×C8—221no—
606C2×C8—221no—
607C2×C8—221no—
608C2×C8—221no—
609C2×C8—221no—
610C2×C8—221no—
611C2×C8—221no—
612C2×C8—221no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—42no—
619C4⋊C4—112no—
620C4⋊C4—112no—
621C4⋊C4—224no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4—221no—
626C4⋊C4—221no—
627C4⋊C4#433912yes—
628C22⋊C4—24no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—224no—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C22⋊C4—224no—
637C22⋊C4—224no—
638C42—22no—
639C42—22no—
640C42—21no—
641C42—21no—
642C42—42no—
643C42—224no—
644C42D4×D1112yes—
645C42D4×D1112yes—
646C11#2415811yescharacteristic, complemented, Sylow
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—222no—
661C23—441no—
662C23—441no—
663C23—441no—
664C23—441no—
665C23—441no—
666C23—441no—
667C23#6700312yes—
668C23C22×C22⋊D1111yescharacteristic
669Q8—222no—
670Q8—222no—
671Q8—441no—
672Q8—441no—
673D4—22no—
674D4—22no—
675D4—48no—
676D4—41no—
677D4—41no—
678D4—222no—
679D4—222no—
680D4—448no—
681D4—441no—
682D4—441no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—84no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—448no—
715C2×C4—441no—
716C2×C4—441no—
717C2×C4—441no—
718C2×C4—441no—
719C2×C4—441no—
720C2×C4—441no—
721C2×C4#6698512yes—
722C2×C4#6699012yes—
723C2×C4#6699012yes—
724C2×C4C2×#433911yescharacteristic
725C2×C4C2×#433911yescharacteristic
726C2×C4C2×D4×D1111yescharacteristic
727C2×C4C2×D4×D1111yescharacteristic
728C2×C4#6704211yescharacteristic
729C2×C4#6704311yescharacteristic
730C8—441no—
731C8—441no—
732C8—441no—
733C8—441no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—442no—
749C22—442no—
750C22—442no—
751C22—881no—
752C22—881no—
753C22—881no—
754C22—881no—
755C22#1062332211yescharacteristic
756C22C2×#6698511yescharacteristic
757C22C2×#6699011yescharacteristic
758C22C2×#6700311yescharacteristic
759C22#1062335311yescharacteristic
760C22#1062335311yescharacteristic
761C22#1062336411yescharacteristic
762C4—22no—
763C4—22no—
764C4—22no—
765C4—41no—
766C4—41no—
767C4—42no—
768C4—81no—
769C4—81no—
770C4—442no—
771C4—442no—
772C4—442no—
773C4#1062308111yescharacteristic
774C4#1062308211yescharacteristic
775C4#1062308311yescharacteristic
776C4#1062308411yescharacteristic
777C2—42no—
778C2—82no—
779C2—882no—
780C2#1307196111yescharacteristic
781C2#1307783211yescharacteristic
782C2#1307786611yescharacteristic
783C2#1307866311yescharacteristic
784C2#1307872511yescharacteristic
785C2#1307996311yescharacteristic
786C2#1307997211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#121C2
socleC23×C11C22×D4
prime radical#13069612C2
hypercenterC4×#121D11
hypocenterC11#24158
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10623010C2semidirect
2. C2×#10622622C2semidirect
3. C2×#10622629C2semidirect
4. #13069819C2semidirect
5. #13069805C2semidirect
6. #13069619C2semidirect
8. #13069573C2semidirect
9. #13069548C2semidirect
10. #13068974C2semidirect
11. #13068967C2semidirect
12. #13068883C2semidirect
13. #13068862C2semidirect
14. #13068596C2semidirect
15. C4×C11×#121C2semidirect
124. #66928D4semidirect
129. #66923D4semidirect
257. C4×#121D11semidirect
646. C11#24158semidirect

Maximal subgroups

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

subgroupindex
C2×#106230102
C2×#106226222
C2×#106226292
#130698192
#130698052
#130696192
#130696122
#130695732
#130695482
#130689742
#130689672
#130688832
#130688622
#130685962
C4×C11×#1212
#2415811