Finite Group Databasebeta

← #14961675

Subgroups — #14961675

Order 2816.

2022 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076961C211yesmaximal, characteristic, complemented
2#13076926C211yesmaximal, characteristic, complemented
3#13076552C212yesmaximal, complemented
4#13076476C212yesmaximal, complemented
5#13076425C212yesmaximal, complemented
6#13075897C212yesmaximal, complemented
7#13075881C212yesmaximal, complemented
8#13075377C212yesmaximal, complemented
9#13075226C212yesmaximal, complemented
10#13074883C212yesmaximal, complemented
11#13074350C211yesmaximal, characteristic, complemented
12#13074350C211yesmaximal, characteristic, complemented
13#13072366C212yesmaximal, complemented
14#13072351C212yesmaximal, complemented
15#13072152C212yesmaximal, complemented
16#13072152C212yesmaximal, complemented
17#13071319C211yesmaximal, characteristic, complemented
18#13071319C211yesmaximal, characteristic, complemented
19C2×C11×#388C211yesmaximal, characteristic, complemented
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic
25C2×#67006C2212yes—
26C2×#67006C2212yes—
27C2×#66983C2211yescharacteristic
28C2×#66983C2211yescharacteristic
29C2×#66983C2212yes—
30C2×#66983C2212yes—
31C2×C4×C22⋊D11C2212yes—
32C2×C4×C22⋊D11C2212yes—
33C2×#66947C2212yescomplemented
34C2×#66937C2212yes—
35C2×#66937C2212yes—
36C2×#66927C2211yescharacteristic, complemented
37C2×#66923C2211yescharacteristic, complemented
38C11×#388C2212yes—
39C11×#388C2212yes—
40C11×#388C2212yes—
41C11×#388C2212yes—
42C2×C11×#95C2211yescharacteristic
43C2×C11×#95C2211yescharacteristic
44#10622826C2212yes—
45#10622826C2212yes—
46#10622826C2212yes—
47#10622826C2212yes—
48#10622825C2211yescharacteristic
49#10622825C2211yescharacteristic
50#10622823C2212yes—
51#10622823C2212yes—
52#10622606C2212yescomplemented
53#10622605C2212yescomplemented
54#10622604C2212yescomplemented
55#10622603C2212yescomplemented
56#10622602C2212yescomplemented
57#10622597C2212yescomplemented
58#10622594C2212yescomplemented
59#10622574C2212yes—
60#10622574C2212yes—
61#10622574C2212yes—
62#10622574C2212yes—
63#10622573C2212yes—
64#10622573C2212yes—
65#10622573C2212yes—
66#10622573C2212yes—
67#10622572C2212yes—
68#10622572C2212yes—
69#10622572C2212yes—
70#10622572C2212yes—
71#10622570C2212yes—
72#10622570C2212yes—
73#10622569C2212yes—
74#10622569C2212yes—
75#10622566C2212yes—
76#10622566C2212yes—
77#10622564C2212yes—
78#10622564C2212yes—
79#10622561C2212yes—
80#10622561C2212yes—
81#10622552C2212yescomplemented
82#10622552C2211yescharacteristic, complemented
83#10622552C2212yescomplemented
84#10622552C2211yescharacteristic, complemented
85#10622549C2211yescharacteristic, complemented
86#10622548C2211yescharacteristic, complemented
87#10622546C2212yescomplemented
88#10622546C2212yescomplemented
89#10622541C2211yescharacteristic, complemented
90#10622541C2211yescharacteristic, complemented
91#10622288C2212yescomplemented
92#10622288C2212yescomplemented
93#10622285C2212yescomplemented
94#10622283C2212yescomplemented
95#10622283C2212yescomplemented
96#10622282C2212yescomplemented
97#10622281C2212yescomplemented
98#10622281C2212yescomplemented
99#10622278C2212yescomplemented
100#10622278C2212yescomplemented
101#10622278C2212yescomplemented
102#10622277C2212yescomplemented
103#10622273C2212yescomplemented
104#10622268C2212yescomplemented
105#10622266C2212yescomplemented
106#10622266C2212yescomplemented
107C25×C11C2311yescharacteristic
108C23×C4×C11C2311yescharacteristic
109C23×C4×C11C2311yescharacteristic
110C23×C4×C11C2311yescharacteristic
111C23×C4×C11C2311yescharacteristic
112C23×C4×C11C2311yescharacteristic
113C23×C4×C11C2311yescharacteristic
114C22×C22⋊D11C2312yes—
115C22×C22⋊D11C2312yes—
116C22×C22⋊D11C2312yes—
117C22×C22⋊D11C2312yes—
118C22×C22⋊D11C2312yes—
119C22×C22⋊D11C2312yes—
120C22×D44C2312yes—
121C22×D44C2312yes—
122C22×D44C2311yescharacteristic
123C22×D44C2311yescharacteristic
124C22×C4×D11C2312yes—
125C22×C4×D11C2312yes—
126C2×C11×C4⋊C4—42no—
127C2×C11×C4⋊C4C2312yes—
128C2×C11×C4⋊C4C2312yes—
129C2×C11×C22⋊C4—24no—
130C2×C11×C22⋊C4—42no—
131C2×C11×C22⋊C4—42no—
132C2×C11×C22⋊C4C2312yes—
133C2×C11×C22⋊C4C2312yes—
134C2×C11×C22⋊C4C2312yes—
135C2×C11×C22⋊C4C2312yes—
136C2×C11×C22⋊C4C2312yes—
137C2×C11×C22⋊C4C2312yes—
138C2×C42×C11—42no—
139C2×C42×C11C2311yescharacteristic
140C2×C42×C11C2311yescharacteristic
141C2×C42×C11C2311yescharacteristic
142C2×C42×C11C2311yescharacteristic
143#67006—44no—
144#67006—44no—
145C2×C22⋊Dic11C2312yes—
146C2×C22⋊Dic11C2312yes—
147C2×C22⋊Dic11C2312yes—
148C2×C22⋊Dic11C2312yes—
149C2×C22⋊Dic11C2312yes—
150C2×C22⋊Dic11C2312yes—
151#66983—24no—
152#66983—24no—
153#66983—44no—
154#66983—44no—
155C4×C22⋊D11—44no—
156C4×C22⋊D11—44no—
157C2×(C2×D11)⋊C4C2312yes—
158C2×(C2×D11)⋊C4C2312yes—
159C2×(C2×D11)⋊C4C2312yes—
160C2×(C2×D11)⋊C4C2312yes—
161C2×(C2×D11)⋊C4C2312yes—
162C2×(C2×D11)⋊C4C2312yes—
163C2×(C2×D11)⋊C4C2312yes—
164C2×(C2×D11)⋊C4C2312yes—
165C2×(C2×D11)⋊C4C2312yes—
166C2×(C2×D11)⋊C4C2312yes—
167C2×(C2×D11)⋊C4C2312yes—
168C2×(C2×D11)⋊C4C2312yes—
169C2×(C2×D11)⋊C4C2312yes—
170C2×(C2×D11)⋊C4C2312yes—
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C2312yes—
173C2×C4⋊Dic11C2311yescharacteristic
174C2×C4⋊Dic11C2311yescharacteristic
175C2×C4⋊Dic11C2311yescharacteristic
176C2×C4⋊Dic11C2311yescharacteristic
177C2×C4⋊Dic11C2312yes—
178C2×C4⋊Dic11C2311yescharacteristic
179C2×C4⋊Dic11C2311yescharacteristic
180C2×C4⋊Dic11C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×C4×Dic11C2312yes—
188C2×C4×Dic11C2312yes—
189#66947—44no—
190#66937—44no—
191#66937—44no—
192#66927—42no—
193#66923—42no—
194C11×#95C2312yes—
195C11×#95C2312yes—
196C11×#95C2312yes—
197C11×#95C2312yes—
198C11⋊#95C2312yes—
199C11⋊#95C2312yes—
200C11⋊#95C2312yes—
201C11⋊#95C2312yes—
202C11⋊#95C2312yes—
203C11⋊#95C2312yes—
204C11⋊#95C2312yes—
205C11⋊#95C2312yes—
206C11⋊#95C2312yes—
207C11⋊#95C2312yes—
208C11⋊#95C2312yes—
209C11⋊#95C2312yes—
210C11⋊#95C2312yes—
211C11⋊#95C2312yes—
212#36759—111nomaximal, Sylow
213C24×C11—22no—
214C24×C11—22no—
215C24×C11—22no—
216C24×C11—41no—
217C24×C11—41no—
218C24×C11—41no—
219C24×C11—41no—
220C24×C11C2412yes—
221C24×C11C2411yescharacteristic
222C23×D11C2412yes—
223C23×D11C2412yes—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11—22no—
231C22×C4×C11—41no—
232C22×C4×C11—41no—
233C22×C4×C11—41no—
234C22×C4×C11—41no—
235C22×C4×C11—41no—
236C22×C4×C11—41no—
237C22×C4×C11—41no—
238C22×C4×C11—41no—
239C22×C4×C11—41no—
240C22×C4×C11—41no—
241C22×C4×C11#4114yes—
242C22×C4×C11C2412yes—
243C22×C4×C11C2412yes—
244C22×C4×C11C2412yes—
245C22×C4×C11C2411yescharacteristic
246C22×C4×C11C2411yescharacteristic
247C22×C4×C11C2411yescharacteristic
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C2×C22⋊D11—24no—
252C2×C22⋊D11—24no—
253C2×C22⋊D11—24no—
254C2×C22⋊D11—24no—
255C2×C22⋊D11—24no—
256C2×C22⋊D11—24no—
257C2×C22⋊D11—42no—
258C2×C22⋊D11—42no—
259C2×C22⋊D11—42no—
260C2×C22⋊D11—42no—
261C2×C22⋊D11—42no—
262C2×C22⋊D11—42no—
263C2×C22⋊D11—42no—
264C2×C22⋊D11—42no—
265C2×C22⋊D11—42no—
266C2×C22⋊D11—42no—
267C2×C22⋊D11—42no—
268C2×C22⋊D11—42no—
269C22×Dic11C2412yes—
270C22×Dic11C2412yes—
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C22×Dic11C2412yes—
275C2×D44—22no—
276C2×D44—22no—
277C2×D44—24no—
278C2×D44—24no—
279C2×D44—41no—
280C2×D44—42no—
281C2×D44—41no—
282C2×D44—42no—
283C2×D44—42no—
284C2×D44—42no—
285C2×D44—41no—
286C2×D44—41no—
287C2×C4×D11—42no—
288C2×C4×D11—42no—
289C2×C4×D11—42no—
290C2×C4×D11—42no—
291C2×C4×D11—42no—
292C2×C4×D11—42no—
293C11×C4⋊C4—24no—
294C11×C4⋊C4—42no—
295C11×C22⋊C4—24no—
296C11×C22⋊C4—24no—
297C11×C22⋊C4—24no—
298C11×C22⋊C4—24no—
299C11×C22⋊C4—42no—
300C11×C22⋊C4—42no—
301C42×C11—22no—
302C42×C11—22no—
303C42×C11—41no—
304C42×C11—41no—
305C22⋊Dic11—24no—
306C22⋊Dic11—24no—
307C22⋊Dic11—42no—
308C22⋊Dic11—42no—
309C22⋊Dic11—42no—
310C22⋊Dic11—42no—
311(C2×D11)⋊C4—24no—
312(C2×D11)⋊C4—24no—
313(C2×D11)⋊C4—42no—
314(C2×D11)⋊C4—42no—
315(C2×D11)⋊C4—42no—
316(C2×D11)⋊C4—42no—
317(C2×D11)⋊C4—42no—
318(C2×D11)⋊C4—42no—
319(C2×D11)⋊C4—42no—
320(C2×D11)⋊C4—42no—
321(C2×D11)⋊C4—42no—
322(C2×D11)⋊C4—42no—
323(C2×D11)⋊C4—42no—
324(C2×D11)⋊C4—42no—
325(C2×D11)⋊C4—42no—
326(C2×D11)⋊C4—42no—
327C4⋊Dic11—22no—
328C4⋊Dic11—22no—
329C4⋊Dic11—41no—
330C4⋊Dic11—41no—
331C4⋊Dic11—41no—
332C4⋊Dic11—41no—
333C4⋊Dic11—42no—
334C4⋊Dic11—42no—
335Dic11⋊C4—24no—
336Dic11⋊C4—24no—
337Dic11⋊C4—42no—
338Dic11⋊C4—42no—
339Dic11⋊C4—42no—
340Dic11⋊C4—42no—
341C4×Dic11—42no—
342C4×Dic11—42no—
343#2856—111no—
344#2851—111no—
345#2803—112no—
346#2797—112no—
347#2793—112no—
348#2753—112no—
349#2752—112no—
350#2711—112no—
351#2701—112no—
352#2673—112no—
353#2617—111no—
354#2617—111no—
355#2444—112no—
356#2443—112no—
357#2424—112no—
358#2424—112no—
359#2325—111no—
360#2325—111no—
361C2×#388D1111yescharacteristic, complemented
362C23×C11—21no—
363C23×C11—21no—
364C23×C11—21no—
365C23×C11—21no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—44no—
374C23×C11—44no—
375C23×C11—44no—
376C23×C11—82no—
377C23×C11—82no—
378C23×C11—82no—
379C23×C11—82no—
380C23×C11C2×#4112yes—
381C23×C11H(5,𝔽2)12yes—
382C23×C11H(5,𝔽2)12yes—
383C23×C11C2511yescharacteristic
384C22×D11—22no—
385C22×D11—22no—
386C22×D11—22no—
387C22×D11—22no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—22no—
397C22×D11—22no—
398C2×C4×C11—21no—
399C2×C4×C11—21no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—21no—
404C2×C4×C11—21no—
405C2×C4×C11—21no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—21no—
410C2×C4×C11—21no—
411C2×C4×C11—21no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—21no—
417C2×C4×C11—21no—
418C2×C4×C11—21no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—44no—
422C2×C4×C11—44no—
423C2×C4×C11—44no—
424C2×C4×C11—44no—
425C2×C4×C11—82no—
426C2×C4×C11—82no—
427C2×C4×C11C2×#4112yes—
428C2×C4×C11C2×#4112yes—
429C2×C4×C11H(5,𝔽2)12yes—
430C2×C4×C11H(5,𝔽2)12yes—
431C22⋊D11—48no—
432C22⋊D11—48no—
433C22⋊D11—84no—
434C22⋊D11—84no—
435C22⋊D11—84no—
436C22⋊D11—84no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455D44—82no—
456D44—82no—
457D44—84no—
458D44—84no—
459C4×D11—84no—
460C4×D11—84no—
461C2×#127—111no—
462C2×#125—111no—
463C2×#123—112no—
464C2×#121—111no—
465C2×#121—111no—
466C2×#121—112no—
467C2×#121—112no—
468C2×#121—112no—
469C2×#121—112no—
470C2×#120—112no—
471C2×#120—112no—
472C2×C4×D4—112no—
473C2×C4×D4—112no—
474C22×C4⋊C4C2×D1111yescharacteristic
475C22×C22⋊C4C2×D1111yescharacteristic
476C22×C22⋊C4C2×D1111yescharacteristic
477C22×C22⋊C4C2×D1111yescharacteristic
478C22×C42C2×D1111yescharacteristic
479#400—112no—
480#399—112no—
481#398—112no—
482#397—112no—
483#397—112no—
484#397—112no—
485#397—112no—
486#397—112no—
487#396—112no—
488#396—112no—
489#394—112no—
490#394—112no—
491#394—112no—
492#394—112no—
493#394—112no—
494#394—112no—
495#394—112no—
496#394—112no—
497#394—112no—
498#394—112no—
499#392—112no—
500#392—112no—
501#392—112no—
502#392—112no—
503#390—112no—
504#390—112no—
505#390—112no—
506#390—112no—
507#390—111no—
508#390—111no—
509#389—111no—
510#389—111no—
511#388—112no—
512#388—112no—
513#388—112no—
514#388—112no—
515#388—112no—
516#388—112no—
517#388C2×D1112yes—
518#388C2×D1112yes—
519#388C2×D1112yes—
520#388C2×D1112yes—
521#387—112no—
522#387—112no—
523#387—112no—
524#387—112no—
525#387—112no—
526#387—112no—
527#386—112no—
528#386—112no—
529#386—112no—
530#386—112no—
531#386—112no—
532#386—112no—
533#386—112no—
534#386—112no—
535#386—112no—
536#385—112no—
537#385—112no—
538#385—112no—
539#385—112no—
540#385—112no—
541#384—111no—
542#382—111no—
543#381—112no—
544#380—111no—
545#380—111no—
546C2×#95C2×D1111yescharacteristic
547C2×#95C2×D1111yescharacteristic
548C22×C11—22no—
549C22×C11—22no—
550C22×C11—22no—
551C22×C11—22no—
552C22×C11—22no—
553C22×C11—22no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—42no—
561C22×C11—88no—
562C22×C11#54014yes—
563C22×C11C22×#4111yescharacteristic
564C22×C11C2×H(5,𝔽2)11yescharacteristic
565C22×C11C2×H(5,𝔽2)11yescharacteristic
566C22×C11C2×H(5,𝔽2)11yescharacteristic
567C22×C11C2×H(5,𝔽2)11yescharacteristic
568C22×C11#58511yescharacteristic
569C22×C11#58511yescharacteristic
570C2×D11—42no—
571C2×D11—42no—
572C2×D11—42no—
573C2×D11—42no—
574C2×D11—42no—
575C2×D11—42no—
576C2×D11—42no—
577C2×D11—42no—
578C2×D11—42no—
579C2×D11—42no—
580C2×D11—42no—
581C2×D11—42no—
582C2×D11—42no—
583C2×D11—42no—
584C4×C11—22no—
585C4×C11—22no—
586C4×C11—22no—
587C4×C11—22no—
588C4×C11—42no—
589C4×C11—41no—
590C4×C11—41no—
591C4×C11—42no—
592C4×C11—42no—
593Dic11—42no—
594Dic11—42no—
595Dic11—42no—
596Dic11—42no—
597Dic11—42no—
598Dic11—42no—
599C25C22×D1111yescharacteristic
600C22×D4—112no—
601C22×D4—112no—
602C22×D4—112no—
603C22×D4—112no—
604C22×D4—112no—
605C22×D4—112no—
606C22×D4—112no—
607C22×D4—112no—
608C22×D4—111no—
609C22×D4—111no—
610C23×C4—112no—
611C23×C4—112no—
612C23×C4C22×D1111yescharacteristic
613C23×C4C22×D1111yescharacteristic
614C23×C4C22×D1111yescharacteristic
615C23×C4C22×D1111yescharacteristic
616C23×C4C22×D1111yescharacteristic
617C23×C4C22×D1111yescharacteristic
618#127—442no—
619#125—442no—
620#123—444no—
621#121—224no—
622#121—224no—
623#121—444no—
624#121—444no—
625#121—444no—
626#121—444no—
627#120—444no—
628#120—444no—
629C4×D4—444no—
630C4×D4—444no—
631C2×C4⋊C4—42no—
632C2×C4⋊C4—112no—
633C2×C4⋊C4—112no—
634C2×C4⋊C4—111no—
635C2×C4⋊C4—111no—
636C2×C4⋊C4—112no—
637C2×C4⋊C4—112no—
638C2×C4⋊C4—112no—
639C2×C4⋊C4—112no—
640C2×C4⋊C4—111no—
641C2×C4⋊C4—111no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—111no—
644C2×C4⋊C4—111no—
645C2×C4⋊C4—112no—
646C2×C4⋊C4C22×D1112yes—
647C2×C4⋊C4C22×D1112yes—
648C2×C22⋊C4—24no—
649C2×C22⋊C4—42no—
650C2×C22⋊C4—42no—
651C2×C22⋊C4—112no—
652C2×C22⋊C4—112no—
653C2×C22⋊C4—112no—
654C2×C22⋊C4—112no—
655C2×C22⋊C4—112no—
656C2×C22⋊C4—112no—
657C2×C22⋊C4—112no—
658C2×C22⋊C4—112no—
659C2×C22⋊C4—112no—
660C2×C22⋊C4—112no—
661C2×C22⋊C4—112no—
662C2×C22⋊C4—112no—
663C2×C22⋊C4—112no—
664C2×C22⋊C4—112no—
665C2×C22⋊C4—112no—
666C2×C22⋊C4—112no—
667C2×C22⋊C4—112no—
668C2×C22⋊C4—112no—
669C2×C22⋊C4—112no—
670C2×C22⋊C4—112no—
671C2×C22⋊C4—112no—
672C2×C22⋊C4—112no—
673C2×C22⋊C4C22×D1112yes—
674C2×C22⋊C4C22×D1112yes—
675C2×C22⋊C4C22×D1112yes—
676C2×C22⋊C4C22×D1112yes—
677C2×C22⋊C4C22×D1112yes—
678C2×C22⋊C4C22×D1112yes—
679C2×C42—42no—
680C2×C42—112no—
681C2×C42—112no—
682C2×C42C22×D1111yescharacteristic
683C2×C42C22×D1111yescharacteristic
684C2×C42C22×D1111yescharacteristic
685C2×C42C22×D1111yescharacteristic
686#95—112no—
687#95—112no—
688#95—112no—
689#95—112no—
690#95—112no—
691#95—112no—
692#95—112no—
693#95—112no—
694#95—112no—
695#95—112no—
696#95—112no—
697#95—112no—
698#95—112no—
699#95—112no—
700#95C22×D1112yes—
701#95C22×D1112yes—
702#95C22×D1112yes—
703#95C22×D1112yes—
704C2×C11—24no—
705C2×C11—82no—
706C2×C11C2×#54011yescharacteristic
707C2×C11#350511yescharacteristic
708C2×C11#350611yescharacteristic
709C2×C11#353411yescharacteristic
710C2×C11#353711yescharacteristic
711C2×C11#355811yescharacteristic
712C2×C11#356011yescharacteristic
713D11—82no—
714D11—82no—
715C24—22no—
716C24—22no—
717C24—22no—
718C24—41no—
719C24—41no—
720C24—41no—
721C24—41no—
722C24—112no—
723C24—112no—
724C24C23×D1112yes—
725C24C23×D1111yescharacteristic
726C2×D4—224no—
727C2×D4—224no—
728C2×D4—224no—
729C2×D4—224no—
730C2×D4—224no—
731C2×D4—224no—
732C2×D4—222no—
733C2×D4—222no—
734C2×D4—224no—
735C2×D4—224no—
736C2×D4—442no—
737C2×D4—442no—
738C2×D4—441no—
739C2×D4—442no—
740C2×D4—441no—
741C2×D4—442no—
742C2×D4—441no—
743C2×D4—441no—
744C2×D4—442no—
745C2×D4—442no—
746C2×D4—442no—
747C2×D4—442no—
748C2×D4—442no—
749C2×D4—442no—
750C2×D4—442no—
751C2×D4—442no—
752C2×D4—442no—
753C2×D4—442no—
754C2×D4—442no—
755C2×D4—442no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—41no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—41no—
768C22×C4—41no—
769C22×C4—41no—
770C22×C4—41no—
771C22×C4—41no—
772C22×C4—41no—
773C22×C4—112no—
774C22×C4—112no—
775C22×C4—112no—
776C22×C4—112no—
777C22×C4—112no—
778C22×C4—112no—
779C22×C4—442no—
780C22×C4—442no—
781C22×C4—442no—
782C22×C4—442no—
783C22×C4—442no—
784C22×C4—442no—
785C22×C4#433914yes—
786C22×C4C23×D1112yes—
787C22×C4C23×D1112yes—
788C22×C4C23×D1112yes—
789C22×C4C23×D1111yescharacteristic
790C22×C4C23×D1111yescharacteristic
791C22×C4C23×D1111yescharacteristic
792C22×C4C23×D1111yescharacteristic
793C22×C4C23×D1111yescharacteristic
794C22×C4C23×D1111yescharacteristic
795C4⋊C4—24no—
796C4⋊C4—42no—
797C4⋊C4—222no—
798C4⋊C4—222no—
799C4⋊C4—224no—
800C4⋊C4—224no—
801C4⋊C4—442no—
802C4⋊C4—442no—
803C4⋊C4—442no—
804C4⋊C4—442no—
805C4⋊C4—442no—
806C4⋊C4—441no—
807C4⋊C4—441no—
808C4⋊C4—442no—
809C4⋊C4—441no—
810C4⋊C4—441no—
811C22⋊C4—24no—
812C22⋊C4—24no—
813C22⋊C4—24no—
814C22⋊C4—24no—
815C22⋊C4—42no—
816C22⋊C4—42no—
817C22⋊C4—224no—
818C22⋊C4—224no—
819C22⋊C4—224no—
820C22⋊C4—224no—
821C22⋊C4—442no—
822C22⋊C4—442no—
823C22⋊C4—442no—
824C22⋊C4—442no—
825C22⋊C4—442no—
826C22⋊C4—442no—
827C22⋊C4—442no—
828C22⋊C4—442no—
829C22⋊C4—442no—
830C22⋊C4—442no—
831C22⋊C4—442no—
832C22⋊C4—442no—
833C22⋊C4—442no—
834C22⋊C4—442no—
835C22⋊C4—442no—
836C22⋊C4—442no—
837C22⋊C4—442no—
838C22⋊C4—442no—
839C42—22no—
840C42—22no—
841C42—41no—
842C42—41no—
843C42—442no—
844C42—442no—
845C11#3675911yescharacteristic, complemented, Sylow
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—44no—
858C23—44no—
859C23—44no—
860C23—82no—
861C23—82no—
862C23—82no—
863C23—82no—
864C23—222no—
865C23—222no—
866C23—222no—
867C23—222no—
868C23—222no—
869C23—222no—
870C23—222no—
871C23—222no—
872C23—222no—
873C23—222no—
874C23—222no—
875C23—222no—
876C23—222no—
877C23—222no—
878C23C2×#433912yes—
879C23#6704212yes—
880C23#6704212yes—
881C23C24×D1111yescharacteristic
882D4—448no—
883D4—448no—
884D4—882no—
885D4—882no—
886D4—884no—
887D4—884no—
888D4—884no—
889D4—884no—
890D4—884no—
891D4—884no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—22no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—21no—
915C2×C4—44no—
916C2×C4—44no—
917C2×C4—44no—
918C2×C4—44no—
919C2×C4—82no—
920C2×C4—82no—
921C2×C4—222no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—222no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—222no—
935C2×C4—222no—
936C2×C4—222no—
937C2×C4—222no—
938C2×C4—222no—
939C2×C4—884no—
940C2×C4—884no—
941C2×C4C2×#433912yes—
942C2×C4C2×#433912yes—
943C2×C4#6703712yes—
944C2×C4#6703712yes—
945C22—22no—
946C22—22no—
947C22—22no—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—88no—
959C22—442no—
960C22—442no—
961C22—442no—
962C22—442no—
963C22—442no—
964C22—442no—
965C22—442no—
966C22—442no—
967C22—442no—
968C22—442no—
969C22—442no—
970C22—442no—
971C22—442no—
972C22—442no—
973C22#1062306614yes—
974C22C22×#433911yescharacteristic
975C22C2×#6703711yescharacteristic
976C22C2×#6703711yescharacteristic
977C22C2×#6704211yescharacteristic
978C22C2×#6704211yescharacteristic
979C22#1062345311yescharacteristic
980C22#1062345311yescharacteristic
981C4—22no—
982C4—22no—
983C4—22no—
984C4—22no—
985C4—42no—
986C4—41no—
987C4—41no—
988C4—42no—
989C4—42no—
990C4—442no—
991C4—442no—
992C4—442no—
993C4—442no—
994C4—442no—
995C4—442no—
996C2—24no—
997C2—82no—
998C2—882no—
999C2—882no—
1000C2C2×#1062306611yescharacteristic
1001C2#1308245511yescharacteristic
1002C2#1308246811yescharacteristic
1003C2#1308281011yescharacteristic
1004C2#1308285111yescharacteristic
1005C2#1308313511yescharacteristic
1006C2#1308316811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#388C2
hypercenterC2×#388D11
hypocenterC11#36759
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. #13076961C2semidirect
2. #13076926C2semidirect
3. #13076552C2semidirect
4. #13076476C2semidirect
5. #13076425C2semidirect
6. #13075897C2semidirect
7. #13075881C2semidirect
8. #13075377C2semidirect
9. #13075226C2semidirect
10. #13074883C2semidirect
11. #13074350C2semidirect
12. #13074350C2semidirect
13. #13072366C2semidirect
14. #13072351C2semidirect
15. #13072152C2semidirect
16. #13072152C2semidirect
17. #13071319C2semidirect
18. #13071319C2semidirect
19. C2×C11×#388C2semidirect
33. C2×#66947C22semidirect
36. C2×#66927C22semidirect
37. C2×#66923C22semidirect
52. #10622606C22semidirect
53. #10622605C22semidirect
54. #10622604C22semidirect
55. #10622603C22semidirect
56. #10622602C22semidirect
57. #10622597C22semidirect
58. #10622594C22semidirect
81. #10622552C22semidirect
82. #10622552C22semidirect
83. #10622552C22semidirect
84. #10622552C22semidirect
85. #10622549C22semidirect
86. #10622548C22semidirect
87. #10622546C22semidirect
88. #10622546C22semidirect
89. #10622541C22semidirect
90. #10622541C22semidirect
91. #10622288C22semidirect
92. #10622288C22semidirect
93. #10622285C22semidirect
94. #10622283C22semidirect
95. #10622283C22semidirect
96. #10622282C22semidirect
97. #10622281C22semidirect
98. #10622281C22semidirect
99. #10622278C22semidirect
100. #10622278C22semidirect
101. #10622278C22semidirect
102. #10622277C22semidirect
103. #10622273C22semidirect
104. #10622268C22semidirect
105. #10622266C22semidirect
106. #10622266C22semidirect
361. C2×#388D11semidirect
845. C11#36759semidirect

Maximal subgroups

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

subgroupindex
#130769612
#130769262
#130765522
#130764762
#130764252
#130758972
#130758812
#130753772
#130752262
#130748832
#130743502
#130723662
#130723512
#130721522
#130713192
C2×C11×#3882
#3675911