Finite Group Databasebeta

← #14806876

Subgroups — #14806876

Order 2816.

1178 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623072C211yesmaximal, characteristic, complemented
2C2×#10622648C211yesmaximal, characteristic, complemented
3C2×#10622655C211yesmaximal, characteristic, complemented
4#13069954C211yesmaximal, characteristic, complemented
5#13069812C211yesmaximal, characteristic, complemented
6#13069762C211yesmaximal, characteristic, complemented
7#13069619C211yesmaximal, characteristic, complemented
8#13068974C211yesmaximal, characteristic, complemented
9#13068934C211yesmaximal, characteristic, complemented
10#13068923C211yesmaximal, characteristic, complemented
11#13068914C211yesmaximal, characteristic, complemented
12#13068869C211yesmaximal, characteristic, complemented
13#13068803C211yesmaximal, characteristic, complemented
14#13068335C211yesmaximal, characteristic, complemented
15C11×#2416C211yesmaximal, characteristic
16C2×C11×#121—21no—
17C2×C11×#121C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C2×#66988—21no—
22C22×#4324C2211yescharacteristic
23C2×#66979C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26C2×#66977C2211yescharacteristic
27C22×#4318C2211yescharacteristic
28#10623072—24no—
29#10623072—24no—
30C2×#66942—21no—
31C2×#66932—21no—
32C2×#66930—21no—
33C2×#66923C2211yescharacteristic
34C2×C4×Dic22C2211yescharacteristic
35C11×#396—21no—
36C11×#394—21no—
37C11×#390C2211yescharacteristic
38C11×#389C2211yescharacteristic
39C11×#386—21no—
40C11×#380C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43C2×#66896C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46C2×C22⋊(C11⋊C8)C2211yescharacteristic
47#10622655—24no—
48#10622648—24no—
49C2×#66874C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51C2×#66874C2211yescharacteristic
52C2×#66872C2211yescharacteristic
53C2×#66871C2211yescharacteristic
54C2×#66871C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11—21no—
65C22×D4×C11D411yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×Dic11—21no—
71C22×Dic22C2311yescharacteristic
72C11×#121—22no—
73C11×#121—22no—
74C11×#121—22no—
75C11×#121—41no—
76C11×#121—44no—
77C4×D4×C11—22no—
78C4×D4×C11—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—41no—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11—21no—
97C2×C22⋊Dic11—21no—
98#66988—28no—
99C2×#4324—22no—
100C2×#4324—22no—
101C2×#4324—41no—
102#66979—22no—
103#66979D414yescomplemented
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11—22no—
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110#66977—22no—
111#66977—22no—
112#66977—22no—
113#66977D414yescomplemented
114C2×Dic11⋊C4—21no—
115C2×Dic11⋊C4—21no—
116C2×Dic11⋊C4—21no—
117C2×Dic11⋊C4—21no—
118C2×Dic11⋊C4—21no—
119C2×C4×Dic11—21no—
120C2×C4×Dic11—21no—
121C2×#4318—22no—
122C2×#4318—22no—
123C2×#4318—41no—
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128#66942—28no—
129#66932—28no—
130#66930—28no—
131#66923—22no—
132#66923—22no—
133C4×Dic22—22no—
134C4×Dic22—22no—
135C11×#95—21no—
136C11×#95—21no—
137#66896—22no—
138#66896—22no—
139#66896—22no—
140C22⋊(C11⋊C8)—22no—
141C22⋊(C11⋊C8)—22no—
142C22⋊(C11⋊C8)—41no—
143#66874—22no—
144#66874—22no—
145#66874—41no—
146#66872—22no—
147#66871—22no—
148#66871—22no—
149#25560—111nomaximal, Sylow
150C24×C11—21no—
151C24×C11C2×D411yescharacteristic
152C24×C11C2×D411yescharacteristic
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—41no—
162C2×D4×C11—42no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11—81no—
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—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—42no—
182C22×C4×C11—42no—
183C22×C4×C11—81no—
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D412yes—
189C22×C4×C11C2×D412yes—
190C22×C4×C11C2411yescharacteristic
191C22×Dic11—24no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—42no—
197C22×Dic11—42no—
198C2×Dic22—21no—
199C2×Dic22—21no—
200C2×Dic22—21no—
201C2×Dic22—21no—
202C2×Dic22—21no—
203C2×Dic22C2×D412yes—
204C11×C4⋊C4—22no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—42no—
211C11×C4⋊C4—42no—
212C11×C4⋊C4#4112yes—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—22no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—42no—
217C11×C22⋊C4—42no—
218C11×C22⋊C4—42no—
219C11×C22⋊C4—81no—
220C42×C11—21no—
221C42×C11—21no—
222C22⋊Dic11—24no—
223C22⋊Dic11—24no—
224C22⋊Dic11—24no—
225#4324—44no—
226C4⋊Dic11—24no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11C2×D412yes—
231C4⋊Dic11C2×D412yes—
232C4⋊Dic11C2×D412yes—
233Dic11⋊C4—24no—
234Dic11⋊C4—24no—
235Dic11⋊C4—24no—
236Dic11⋊C4—24no—
237Dic11⋊C4—24no—
238C4×Dic11—24no—
239C4×Dic11—24no—
240#4318—44no—
241C2×C11⋊C8—21no—
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#4112yes—
253C2×#552—111no—
254C2×#482—111no—
255C2×#468—111no—
256#2416D1111yescharacteristic
257#2059—111no—
258#2035—111no—
259#2025—111no—
260#2000—111no—
261#1880—111no—
262#1874—111no—
263#1872—111no—
264#1870—111no—
265#1863—111no—
266#1852—111no—
267#1736—111no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11#12012yes—
288C23×C11AGL(1,ℤ/8)12yes—
289C23×C11C22×D411yescharacteristic
290D4×C11—44no—
291D4×C11—41no—
292D4×C11—41no—
293D4×C11—41no—
294D4×C11—41no—
295D4×C11—84no—
296D4×C11—84no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—22no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
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—41no—
324C2×C4×C11—41no—
325C2×C4×C11—84no—
326C2×C4×C11#12012yes—
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
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—48no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346Dic22—22no—
347Dic22—22no—
348Dic22—41no—
349Dic22—41no—
350C11⋊C8—22no—
351C11⋊C8—41no—
352C11⋊C8—41no—
353C11⋊C8—41no—
354C22×SD16—111no—
355C22×M16—111no—
356#552—224no—
357#552—224no—
358C2×#126—221no—
359C2×#125—111no—
360C2×#125—221no—
361C2×#123—221no—
362C2×C22⋊Q8—111no—
363C2×C22⋊Q8—111no—
364C2×#121—21no—
365C2×#121C2×D1111yescharacteristic
366C2×#121C2×D1111yescharacteristic
367C2×C4×Q8—111no—
368C2×C4×D4C2×D1111yescharacteristic
369C2×#117—111no—
370C2×#117—221no—
371C22×C4⋊C4—111no—
372C22×C4⋊C4C2×D1111yescharacteristic
373#482—224no—
374#468—224no—
375C2×#107—111no—
376C2×#107—111no—
377C2×#106—111no—
378C2×#103—111no—
379C2×#103—111no—
380C2×#103—111no—
381C2×#102—111no—
382C2×#102—111no—
383C2×#102—111no—
384C2×C22⋊C8—111no—
385C2×C22⋊C8—111no—
386C2×C22⋊C8—111no—
387#396—21no—
388#394—21no—
389#390C2×D1111yescharacteristic
390#389C2×D1111yescharacteristic
391#386—21no—
392#380C2×D1111yescharacteristic
393#340—111no—
394#340—111no—
395#340—111no—
396#340—111no—
397#340—111no—
398#340—111no—
399#336—111no—
400#336—111no—
401C22×C11—22no—
402C22×C11—22no—
403C22×C11—22no—
404C22×C11—22no—
405C22×C11—22no—
406C22×C11—22no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—81no—
416C22×C11—81no—
417C22×C11—81no—
418C22×C11—81no—
419C22×C11—81no—
420C22×C11—81no—
421C22×C11—81no—
422C22×C11C2×#12011yescharacteristic
423C22×C11#54611yescharacteristic
424C22×C11#54711yescharacteristic
425C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
426C22×C11#57511yescharacteristic
427C22×C11#57711yescharacteristic
428C22×C11#57811yescharacteristic
429C4×C11—22no—
430C4×C11—41no—
431C4×C11—41no—
432C4×C11—41no—
433C4×C11—42no—
434C4×C11—81no—
435C4×C11—81no—
436C4×C11#53211yescharacteristic
437C4×C11#53711yescharacteristic
438C4×C11#54611yescharacteristic
439C4×C11#54711yescharacteristic
440Dic11—42no—
441Dic11—42no—
442Dic11—42no—
443Dic11—42no—
444C22×Q8—111no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4C22⋊D1111yescharacteristic
448C22×D4C22×D1111yescharacteristic
449C23×C4—21no—
450C23×C4—221no—
451C23×C4C22×D1111yescharacteristic
452C23×C4C22×D1111yescharacteristic
453C2×SD16—222no—
454C2×SD16—222no—
455C2×SD16—441no—
456C2×M16—222no—
457C2×M16—222no—
458C2×M16—441no—
459C22×C8—111no—
460C22×C8—111no—
461C22×C8—111no—
462C22×C8—111no—
463#126—228no—
464#125—222no—
465#125—222no—
466#125—228no—
467#123—228no—
468C22⋊Q8—114no—
469C22⋊Q8—222no—
470C22⋊Q8—222no—
471C22⋊Q8—222no—
472#121—22no—
473#121—22no—
474#121—22no—
475#121—41no—
476#121—44no—
477C4×Q8—222no—
478C4×Q8—222no—
479C4×D4—22no—
480C4×D4—22no—
481#117—114no—
482#117—228no—
483#117—222no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—41no—
488C2×C4⋊C4—111no—
489C2×C4⋊C4—111no—
490C2×C4⋊C4—111no—
491C2×C4⋊C4—222no—
492C2×C4⋊C4—222no—
493C2×C4⋊C4—221no—
494C2×C4⋊C4—221no—
495C2×C4⋊C4—221no—
496C2×C4⋊C4—221no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4—221no—
499C2×C4⋊C4C22⋊D1111yescharacteristic
500C2×C4⋊C4C22×D1111yescharacteristic
501C2×C4⋊C4C22×D1111yescharacteristic
502C2×C4⋊C4C22×D1111yescharacteristic
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—221no—
509C2×C22⋊C4—221no—
510C2×C22⋊C4—221no—
511C2×C22⋊C4C22⋊D1111yescharacteristic
512C2×C22⋊C4C22⋊D1111yescharacteristic
513C2×C42—221no—
514C2×C42—221no—
515C2×C42C22×D1111yescharacteristic
516#107—222no—
517#107—222no—
518#106—222no—
519#103—222no—
520#103—222no—
521#103—441no—
522#102—222no—
523#102—222no—
524#102—222no—
525C22⋊C8—222no—
526C22⋊C8—222no—
527C22⋊C8—441no—
528#95—21no—
529#95—21no—
530C2×C11—42no—
531C2×C11—42no—
532C2×C11—161no—
533C2×C11#243011yescharacteristic
534C2×C11#300611yescharacteristic
535C2×C11#301311yescharacteristic
536C2×C11#331011yescharacteristic
537C2×C11#332711yescharacteristic
538C2×C11#334311yescharacteristic
539C2×C11#335111yescharacteristic
540C24—21no—
541C24C2×C22⋊D1111yescharacteristic
542C24C2×C22⋊D1111yescharacteristic
543C2×Q8—112no—
544C2×Q8—221no—
545C2×Q8—221no—
546C2×Q8—221no—
547C2×Q8—221no—
548C2×Q8—221no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—41no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—81no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—81no—
580C22×C4—224no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—442no—
586C22×C4—442no—
587C22×C4D4×D1112yes—
588C22×C4D4×D1112yes—
589C22×C4C2×C22⋊D1111yescharacteristic
590C22×C4C2×C22⋊D1111yescharacteristic
591C22×C4C2×C22⋊D1111yescharacteristic
592C22×C4C2×C22⋊D1111yescharacteristic
593C22×C4C23×D1111yescharacteristic
594SD16—444no—
595M16—444no—
596C2×C8—112no—
597C2×C8—221no—
598C2×C8—221no—
599C2×C8—221no—
600C2×C8—221no—
601C2×C8—221no—
602C2×C8—221no—
603C2×C8—221no—
604C2×C8—221no—
605C2×C8—221no—
606C2×C8—221no—
607C2×C8—221no—
608C4⋊C4—22no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—112no—
617C4⋊C4—112no—
618C4⋊C4—112no—
619C4⋊C4—224no—
620C4⋊C4—224no—
621C4⋊C4—224no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4—221no—
626C4⋊C4—221no—
627C4⋊C4—221no—
628C4⋊C4#434112yes—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—81no—
636C22⋊C4—224no—
637C22⋊C4—224no—
638C22⋊C4—224no—
639C42—21no—
640C42—21no—
641C42—224no—
642C42—224no—
643C11#2556011yescharacteristic, complemented, Sylow
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23#6698512yes—
664C23#6699012yes—
665C23C22×C22⋊D1111yescharacteristic
666Q8—222no—
667Q8—222no—
668Q8—441no—
669Q8—441no—
670D4—44no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—84no—
676D4—84no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
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—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—84no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—448no—
711C2×C4—441no—
712C2×C4—441no—
713C2×C4—441no—
714C2×C4—441no—
715C2×C4—441no—
716C2×C4—441no—
717C2×C4—441no—
718C2×C4—441no—
719C2×C4#6699012yes—
720C2×C4C2×D4×D1111yescharacteristic
721C2×C4C2×D4×D1111yescharacteristic
722C2×C4C2×#434111yescharacteristic
723C2×C4#6703711yescharacteristic
724C2×C4#41×D1111yescharacteristic
725C2×C4#6704311yescharacteristic
726C8—222no—
727C8—441no—
728C8—441no—
729C8—441no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22C2×#6698511yescharacteristic
752C22C2×#6699011yescharacteristic
753C22#1062333711yescharacteristic
754C22#1062335311yescharacteristic
755C22#1062335511yescharacteristic
756C22#1062336711yescharacteristic
757C22#1062336911yescharacteristic
758C4—22no—
759C4—42no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—81no—
764C4—81no—
765C4—442no—
766C4—442no—
767C4—442no—
768C4—442no—
769C4#1062312711yescharacteristic
770C4#1062312811yescharacteristic
771C4#1062314111yescharacteristic
772C4#1062314211yescharacteristic
773C2—42no—
774C2—42no—
775C2—161no—
776C2#1307222211yescharacteristic
777C2#1307786611yescharacteristic
778C2#1307792811yescharacteristic
779C2#1308063711yescharacteristic
780C2#1308088411yescharacteristic
781C2#1308105011yescharacteristic
782C2#1308117011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2416C2
socleC23×C11C22×D4
hypercenter#2416D11
hypocenterC11#25560
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2416

Complements

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

NH ≅ G/Ntype
1. C2×#10623072C2semidirect
2. C2×#10622648C2semidirect
3. C2×#10622655C2semidirect
4. #13069954C2semidirect
5. #13069812C2semidirect
6. #13069762C2semidirect
7. #13069619C2semidirect
8. #13068974C2semidirect
9. #13068934C2semidirect
10. #13068923C2semidirect
11. #13068914C2semidirect
12. #13068869C2semidirect
13. #13068803C2semidirect
14. #13068335C2semidirect
103. #66979D4semidirect
113. #66977D4semidirect
643. C11#25560semidirect

Maximal subgroups

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

subgroupindex
C2×#106230722
C2×#106226482
C2×#106226552
#130699542
#130698122
#130697622
#130696192
#130689742
#130689342
#130689232
#130689142
#130688692
#130688032
#130683352
C11×#24162
#2556011