Finite Group Databasebeta

← #14927197

Subgroups — #14927197

Order 2816.

1964 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076998C211yesmaximal, characteristic, complemented
2#13076988C211yesmaximal, characteristic, complemented
3#13076955C211yesmaximal, characteristic, complemented
4#13076917C211yesmaximal, characteristic, complemented
5#13074673C212yesmaximal, complemented
6#13074628C212yesmaximal, complemented
7#13073884C212yesmaximal, complemented
8#13073860C212yesmaximal, complemented
9#13073224C211yesmaximal, characteristic, complemented
10#13073170C212yesmaximal, complemented
11#13072957C211yesmaximal, characteristic, complemented
12#13072403C211yesmaximal, characteristic, complemented
13#13072360C212yesmaximal, complemented
14#13072340C211yesmaximal, characteristic, complemented
15#13072274C211yesmaximal, characteristic, complemented
16#13072193C211yesmaximal, characteristic, complemented
17#13072056C211yesmaximal, characteristic
18#13071981C211yesmaximal, characteristic, complemented
19#13071314C212yesmaximal, complemented
20#13071243C212yesmaximal, complemented
21C4×#66983C211yesmaximal, characteristic, complemented
22C2×#10622542C211yesmaximal, characteristic, complemented
23C42×D4×C11C211yesmaximal, characteristic, complemented
24C23×Dic22C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C22×C42×C11C2211yescharacteristic
29C22×C42×C11C2211yescharacteristic
30C2×#66992C2212yes—
31C2×#66983C2211yescharacteristic
32C2×#66983C2211yescharacteristic
33C2×C4×C22⋊D11C2212yes—
34C22×C4⋊Dic11C2211yescharacteristic
35C2×#66977C2211yescharacteristic
36C2×#66977C2211yescharacteristic
37C2×#66928C2211yescharacteristic
38C2×#66928C2211yescharacteristic
39C2×C4×D44C2211yescharacteristic
40C2×#66923C2211yescharacteristic
41C4×C11×C4⋊C4C2211yescharacteristic
42C4×C11×C4⋊C4C2211yescharacteristic
43C4×C11×C4⋊C4C2211yescharacteristic
44C4×C11×C22⋊C4C2211yescharacteristic
45C4×C11×C22⋊C4C2211yescharacteristic
46C4×C11×C22⋊C4C2211yescharacteristic
47C4×C11×C22⋊C4C2211yescharacteristic
48C4×C11×C22⋊C4C2211yescharacteristic
49C4×C11×C22⋊C4C2211yescharacteristic
50C43×C11C2211yescharacteristic
51#10622833C2212yes—
52#10622826C2212yes—
53#10622826C2212yes—
54#10622826C2212yes—
55#10622825C2211yescharacteristic
56#10622825C2211yescharacteristic
57#10622824C2212yes—
58#10622823C2212yes—
59C2×C11⋊#95C2212yes—
60C2×C11⋊#95C2212yes—
61#10622607C2212yes—
62#10622606C2212yes—
63#10622602C2212yes—
64#10622595C2212yes—
65#10622592C2212yes—
66#10622591C2212yes—
67#10622574C2212yes—
68#10622572C2212yes—
69#10622571C2212yes—
70#10622571C2212yes—
71#10622571C2212yes—
72#10622569C2212yes—
73#10622565C2212yes—
74#10622560C2212yes—
75#10622559C2212yes—
76#10622559C2212yes—
77#10622557C2212yes—
78#10622555C2212yes—
79#10622553C2212yes—
80#10622553C2212yes—
81#10622553C2212yes—
82#10622553C2212yes—
83#10622553C2212yes—
84#10622553C2212yes—
85#10622553C2212yes—
86#10622552C2211yescharacteristic
87#10622552C2211yescharacteristic
88C4×(C2×D11)⋊C4C2212yes—
89#10622550C2212yes—
90#10622549C2211yescharacteristic
91C4×C4⋊Dic11C2211yescharacteristic
92#10622546C2212yes—
93#10622546C2212yes—
94#10622546C2212yes—
95#10622546C2212yes—
96#10622546C2212yes—
97#10622542C2211yescharacteristic
98#10622542C2211yescharacteristic
99#10622542C2211yescharacteristic
100#10622542C2211yescharacteristic
101#10622542C2211yescharacteristic
102#10622542C2211yescharacteristic
103#10622542C2211yescharacteristic
104#10622542C2212yes—
105#10622542C2212yes—
106#10622542C2211yescharacteristic
107#10622541C2211yescharacteristic
108#10622541C2211yescharacteristic
109#10622541C2211yescharacteristic
110#10622541C2211yescharacteristic
111#10622288C2212yes—
112#10622288C2212yes—
113#10622286C2212yes—
114#10622286C2212yes—
115#10622280C2212yes—
116#10622277C2212yes—
117C11⋊#401C2212yes—
118#10622273C2212yes—
119#10622271C2212yes—
120#10622270C2212yes—
121#10622264C2212yes—
122#10622263C2212yes—
123C22×D4×C11C2311yescharacteristic
124C23×C4×C11C2311yescharacteristic
125C23×C4×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C22×C22⋊D11C2312yes—
131C22×C22⋊D11C2312yes—
132C23×Dic11C2312yes—
133C23×Dic11C2312yes—
134C22×D44C2311yescharacteristic
135C22×C4×D11C2312yes—
136C22×Dic22—24no—
137C22×Dic22—42no—
138C22×Dic22—42no—
139C22×Dic22C2311yescharacteristic
140C22×Dic22C2311yescharacteristic
141C22×Dic22C2312yes—
142C4×D4×C11—24no—
143C4×D4×C11—24no—
144C4×D4×C11—24no—
145C2×C11×C4⋊C4C2311yescharacteristic
146C2×C11×C4⋊C4C2311yescharacteristic
147C2×C11×C4⋊C4C2311yescharacteristic
148C2×C11×C22⋊C4C2311yescharacteristic
149C2×C11×C22⋊C4C2311yescharacteristic
150C2×C11×C22⋊C4C2311yescharacteristic
151C2×C11×C22⋊C4C2311yescharacteristic
152C2×C11×C22⋊C4C2311yescharacteristic
153C2×C11×C22⋊C4C2311yescharacteristic
154C2×C42×C11—42no—
155C2×C42×C11—42no—
156C2×C42×C11C2311yescharacteristic
157C2×C42×C11C2311yescharacteristic
158C2×C42×C11C2311yescharacteristic
159C2×C42×C11C2311yescharacteristic
160C2×C42×C11C2311yescharacteristic
161C2×C42×C11C2311yescharacteristic
162C2×C42×C11C2311yescharacteristic
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2311yescharacteristic
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173#66992—28no—
174#66983—24no—
175#66983—42no—
176C4×C22⋊D11—28no—
177C2×(C2×D11)⋊C4C2312yes—
178C2×(C2×D11)⋊C4C2312yes—
179C2×(C2×D11)⋊C4C2312yes—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×C4⋊Dic11—42no—
189C2×C4⋊Dic11C2311yescharacteristic
190C2×C4⋊Dic11C2311yescharacteristic
191C2×C4⋊Dic11C2311yescharacteristic
192C2×C4⋊Dic11C2311yescharacteristic
193C2×C4⋊Dic11C2311yescharacteristic
194C2×C4⋊Dic11C2312yes—
195#66977—42no—
196#66977—42no—
197C2×Dic11⋊C4C2312yes—
198C2×Dic11⋊C4C2312yes—
199C2×Dic11⋊C4C2312yes—
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2312yes—
202C2×Dic11⋊C4C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×C4×Dic11C2312yes—
206#66928—42no—
207#66928—42no—
208C4×D44—42no—
209#66923—42no—
210C11×#95C2311yescharacteristic
211C11×#95C2311yescharacteristic
212C11×#95C2311yescharacteristic
213C11×#95C2311yescharacteristic
214C11×#95C2311yescharacteristic
215C11×#95C2311yescharacteristic
216C11⋊#95C2312yes—
217C11⋊#95C2312yes—
218C11⋊#95C2312yes—
219C11⋊#95C2312yes—
220C11⋊#95C2312yes—
221C11⋊#95C2312yes—
222C11⋊#95C2312yes—
223C11⋊#95C2312yes—
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241#35030—111nomaximal, Sylow
242C24×C11C2411yescharacteristic
243C24×C11C2411yescharacteristic
244C23×D11C2412yes—
245C2×D4×C11—22no—
246C2×D4×C11—22no—
247C2×D4×C11#4114yes—
248C22×C4×C11—22no—
249C22×C4×C11—22no—
250C22×C4×C11—22no—
251C22×C4×C11—22no—
252C22×C4×C11—22no—
253C22×C4×C11—22no—
254C22×C4×C11—22no—
255C22×C4×C11—22no—
256C22×C4×C11—22no—
257C22×C4×C11—22no—
258C22×C4×C11—41no—
259C22×C4×C11—41no—
260C22×C4×C11—41no—
261C22×C4×C11—41no—
262C22×C4×C11—41no—
263C22×C4×C11—41no—
264C22×C4×C11#4114yes—
265C22×C4×C11#4114yes—
266C22×C4×C11C2411yescharacteristic
267C22×C4×C11C2411yescharacteristic
268C22×C4×C11C2411yescharacteristic
269C22×C4×C11C2411yescharacteristic
270C22×C4×C11C2411yescharacteristic
271C22×C4×C11C2411yescharacteristic
272C22×C4×C11C2411yescharacteristic
273C22×C4×C11C2411yescharacteristic
274C22×C4×C11C2411yescharacteristic
275C22×C4×C11C2411yescharacteristic
276C22×C4×C11C2411yescharacteristic
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C2411yescharacteristic
279C2×C22⋊D11—24no—
280C2×C22⋊D11—24no—
281C2×C22⋊D11—24no—
282C2×C22⋊D11—24no—
283C2×C22⋊D11—42no—
284C2×C22⋊D11—42no—
285C22×Dic11—24no—
286C22×Dic11—24no—
287C22×Dic11—42no—
288C22×Dic11—42no—
289C22×Dic11—42no—
290C22×Dic11—42no—
291C22×Dic11C2412yes—
292C22×Dic11C2412yes—
293C22×Dic11C2412yes—
294C22×Dic11C2412yes—
295C22×Dic11C2412yes—
296C22×Dic11C2412yes—
297C22×Dic11C2412yes—
298C2×D44—22no—
299C2×D44—22no—
300C2×D44—22no—
301C2×C4×D11—24no—
302C2×C4×D11—42no—
303C2×C4×D11—42no—
304C2×Dic22—24no—
305C2×Dic22—22no—
306C2×Dic22—22no—
307C2×Dic22—22no—
308C2×Dic22—22no—
309C2×Dic22—22no—
310C2×Dic22—22no—
311C2×Dic22—42no—
312C2×Dic22—42no—
313C2×Dic22—416no—
314C11×C4⋊C4—22no—
315C11×C4⋊C4—22no—
316C11×C4⋊C4—22no—
317C11×C22⋊C4—22no—
318C11×C22⋊C4—22no—
319C11×C22⋊C4—22no—
320C11×C22⋊C4—22no—
321C11×C22⋊C4—22no—
322C11×C22⋊C4—22no—
323C42×C11—22no—
324C42×C11—22no—
325C42×C11—22no—
326C42×C11—22no—
327C42×C11—22no—
328C42×C11—22no—
329C42×C11—22no—
330C42×C11—22no—
331C42×C11—41no—
332C42×C11—41no—
333C42×C11—41no—
334C42×C11—41no—
335C42×C11—41no—
336C22⋊Dic11—24no—
337C22⋊Dic11—24no—
338C22⋊Dic11—42no—
339C22⋊Dic11—42no—
340(C2×D11)⋊C4—24no—
341(C2×D11)⋊C4—24no—
342(C2×D11)⋊C4—24no—
343(C2×D11)⋊C4—24no—
344(C2×D11)⋊C4—42no—
345(C2×D11)⋊C4—42no—
346(C2×D11)⋊C4—42no—
347(C2×D11)⋊C4—42no—
348(C2×D11)⋊C4—42no—
349(C2×D11)⋊C4—42no—
350(C2×D11)⋊C4—42no—
351C4⋊Dic11—22no—
352C4⋊Dic11—22no—
353C4⋊Dic11—22no—
354C4⋊Dic11—22no—
355C4⋊Dic11—22no—
356C4⋊Dic11—42no—
357Dic11⋊C4—24no—
358Dic11⋊C4—24no—
359Dic11⋊C4—42no—
360Dic11⋊C4—42no—
361Dic11⋊C4—42no—
362Dic11⋊C4—42no—
363Dic11⋊C4—42no—
364Dic11⋊C4—42no—
365C4×Dic11—24no—
366#2863—111no—
367#2861—111no—
368#2855—111no—
369#2850—111no—
370#2653—112no—
371#2650—112no—
372#2574—112no—
373#2572—112no—
374#2514—111no—
375#2510—112no—
376#2489—111no—
377#2447—111no—
378#2444—112no—
379#2442—111no—
380#2436—111no—
381#2427—111no—
382#2416—111no—
383#2409—111no—
384#2325—112no—
385#2318—112no—
386C4×#121—111no—
387C2×#391—111no—
388C42×D4D1111yescharacteristic, complemented
389C23×C11—21no—
390C23×C11—21no—
391C23×C11—21no—
392C23×C11—21no—
393C23×C11—21no—
394C23×C11—21no—
395C23×C11—21no—
396C23×C11—21no—
397C23×C11—21no—
398C23×C11—21no—
399C23×C11C2×#4112yes—
400C23×C11C2×#4112yes—
401C23×C11C2×#4112yes—
402C23×C11C2×#4112yes—
403C23×C11C2511yescharacteristic
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—22no—
408C22×D11—22no—
409C22×D11—22no—
410C22×D11—22no—
411D4×C11—28no—
412C2×C4×C11—21no—
413C2×C4×C11—21no—
414C2×C4×C11—21no—
415C2×C4×C11—21no—
416C2×C4×C11—21no—
417C2×C4×C11—21no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—21no—
421C2×C4×C11—21no—
422C2×C4×C11—28no—
423C2×C4×C11—21no—
424C2×C4×C11—21no—
425C2×C4×C11—21no—
426C2×C4×C11—21no—
427C2×C4×C11—21no—
428C2×C4×C11—21no—
429C2×C4×C11—21no—
430C2×C4×C11—21no—
431C2×C4×C11—21no—
432C2×C4×C11—21no—
433C2×C4×C11—21no—
434C2×C4×C11—21no—
435C2×C4×C11—21no—
436C2×C4×C11—21no—
437C2×C4×C11—21no—
438C2×C4×C11—21no—
439C2×C4×C11—21no—
440C2×C4×C11—21no—
441C2×C4×C11—21no—
442C2×C4×C11—21no—
443C2×C4×C11—21no—
444C2×C4×C11—44no—
445C2×C4×C11—44no—
446C2×C4×C11—44no—
447C2×C4×C11—44no—
448C2×C4×C11—44no—
449C2×C4×C11C2×#4112yes—
450C2×C4×C11C2×#4112yes—
451C2×C4×C11C2×#4112yes—
452C2×C4×C11C2×#4112yes—
453C2×C4×C11C2×#4112yes—
454C2×C4×C11H(5,𝔽2)12yes—
455C2×C4×C11H(5,𝔽2)12yes—
456C2×C4×C112−1+412yes—
457C22⋊D11—48no—
458C22⋊D11—84no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—48no—
481C2×Dic11—84no—
482D44—44no—
483C4×D11—84no—
484Dic22—48no—
485Dic22—44no—
486Dic22—44no—
487C23×Q8—111no—
488C2×#125—111no—
489C2×#124—111no—
490C2×#124—111no—
491C2×C22⋊Q8—111no—
492C2×C22⋊Q8—111no—
493C2×#121—112no—
494C2×#121—111no—
495C2×#121—111no—
496C2×C4×D4—112no—
497C2×C4×D4—111no—
498C2×C4×D4C2×D1111yescharacteristic
499C2×C4×D4C2×D1111yescharacteristic
500C2×C4×D4C2×D1111yescharacteristic
501C22×C4⋊C4—111no—
502C22×C42C2×D1111yescharacteristic
503C22×C42C2×D1111yescharacteristic
504#401—112no—
505#400—112no—
506#400—112no—
507#400—112no—
508#398—112no—
509#397—112no—
510#397—112no—
511#397—112no—
512#397—112no—
513#396—112no—
514#395—112no—
515#394—112no—
516#394—112no—
517#393—112no—
518#393—112no—
519#393—112no—
520#391—112no—
521#391—111no—
522#391—111no—
523#391—111no—
524#391—111no—
525#391—111no—
526#391—111no—
527#391—112no—
528#391—111no—
529#391—111no—
530#390—111no—
531#390—111no—
532#389—111no—
533#389—111no—
534#389—111no—
535#389—111no—
536#388—112no—
537#388—112no—
538#388—112no—
539#388—112no—
540#388—112no—
541#388—112no—
542#388—112no—
543#388—112no—
544#387—112no—
545#387—112no—
546#387—112no—
547#387—112no—
548#387—112no—
549#387—112no—
550#386—112no—
551#386—112no—
552#386—112no—
553#386—112no—
554#386—112no—
555#386—112no—
556#386—112no—
557#386—112no—
558#385—112no—
559#385—112no—
560#385—112no—
561#385—112no—
562#383—112no—
563#383—112no—
564#382—111no—
565#382—112no—
566#381—112no—
567#381—112no—
568#380—111no—
569#380—111no—
570#380—112no—
571#380—112no—
572C4×C4⋊C4—111no—
573C4×C4⋊C4C2×D1111yescharacteristic
574C4×C4⋊C4C2×D1111yescharacteristic
575C4×C4⋊C4C2×D1111yescharacteristic
576C4×C22⋊C4—112no—
577C4×C22⋊C4C2×D1111yescharacteristic
578C4×C22⋊C4C2×D1111yescharacteristic
579C4×C22⋊C4C2×D1111yescharacteristic
580C4×C22⋊C4C2×D1111yescharacteristic
581C4×C22⋊C4C2×D1111yescharacteristic
582C4×C22⋊C4C2×D1111yescharacteristic
583C2×#95—112no—
584C2×#95—112no—
585C43C2×D1111yescharacteristic
586C22×C11—22no—
587C22×C11—22no—
588C22×C11—22no—
589C22×C11—22no—
590C22×C11—22no—
591C22×C11—22no—
592C22×C11—22no—
593C22×C11—22no—
594C22×C11—22no—
595C22×C11—41no—
596C22×C11—41no—
597C22×C11—41no—
598C22×C11—41no—
599C22×C11#52914yes—
600C22×C11C22×#4111yescharacteristic
601C22×C11C22×#4111yescharacteristic
602C22×C11C22×#4111yescharacteristic
603C22×C11C2×H(5,𝔽2)11yescharacteristic
604C22×C11C2×H(5,𝔽2)11yescharacteristic
605C22×C11C2×2−1+411yescharacteristic
606C22×C11#58511yescharacteristic
607C2×D11—42no—
608C2×D11—42no—
609C2×D11—42no—
610C2×D11—42no—
611C2×D11—42no—
612C2×D11—42no—
613C2×D11—42no—
614C4×C11—22no—
615C4×C11—22no—
616C4×C11—22no—
617C4×C11—22no—
618C4×C11—22no—
619C4×C11—41no—
620C4×C11—41no—
621C4×C11—41no—
622C4×C11—41no—
623C4×C11—41no—
624C4×C11—41no—
625C4×C11—41no—
626C4×C11#53814yes—
627Dic11—42no—
628Dic11—42no—
629Dic11—42no—
630Dic11—42no—
631Dic11—42no—
632Dic11—42no—
633Dic11—42no—
634C22×Q8—111no—
635C22×Q8—111no—
636C22×Q8—112no—
637C22×Q8—224no—
638C22×Q8—442no—
639C22×Q8—442no—
640C22×D4—112no—
641C22×D4—112no—
642C22×D4—111no—
643C22×D4C22×D1111yescharacteristic
644C23×C4—112no—
645C23×C4—112no—
646C23×C4—112no—
647C23×C4C22×D1111yescharacteristic
648C23×C4C22×D1111yescharacteristic
649C23×C4C22×D1111yescharacteristic
650C23×C4C22×D1111yescharacteristic
651C23×C4C22×D1111yescharacteristic
652C23×C4C22×D1111yescharacteristic
653#125—442no—
654#124—442no—
655#124—442no—
656C22⋊Q8—442no—
657C22⋊Q8—442no—
658#121—228no—
659#121—224no—
660#121—442no—
661C4×D4—24no—
662C4×D4—24no—
663C4×D4—24no—
664C4×D4—228no—
665C4×D4—442no—
666C2×C4⋊C4—111no—
667C2×C4⋊C4—111no—
668C2×C4⋊C4—111no—
669C2×C4⋊C4—112no—
670C2×C4⋊C4—111no—
671C2×C4⋊C4—112no—
672C2×C4⋊C4—111no—
673C2×C4⋊C4—112no—
674C2×C4⋊C4—112no—
675C2×C4⋊C4—112no—
676C2×C4⋊C4—112no—
677C2×C4⋊C4—112no—
678C2×C4⋊C4—112no—
679C2×C4⋊C4—112no—
680C2×C4⋊C4—442no—
681C2×C4⋊C4C22×D1111yescharacteristic
682C2×C4⋊C4C22×D1111yescharacteristic
683C2×C4⋊C4C22×D1111yescharacteristic
684C2×C22⋊C4—112no—
685C2×C22⋊C4—112no—
686C2×C22⋊C4—112no—
687C2×C22⋊C4—112no—
688C2×C22⋊C4—112no—
689C2×C22⋊C4—112no—
690C2×C22⋊C4—112no—
691C2×C22⋊C4—112no—
692C2×C22⋊C4—112no—
693C2×C22⋊C4—112no—
694C2×C22⋊C4—112no—
695C2×C22⋊C4—112no—
696C2×C22⋊C4—112no—
697C2×C22⋊C4—112no—
698C2×C22⋊C4—112no—
699C2×C22⋊C4C22×D1111yescharacteristic
700C2×C22⋊C4C22×D1111yescharacteristic
701C2×C22⋊C4C22×D1111yescharacteristic
702C2×C22⋊C4C22×D1111yescharacteristic
703C2×C22⋊C4C22×D1111yescharacteristic
704C2×C22⋊C4C22×D1111yescharacteristic
705C2×C42—42no—
706C2×C42—42no—
707C2×C42—112no—
708C2×C42C22×D1111yescharacteristic
709C2×C42C22×D1111yescharacteristic
710C2×C42C22×D1111yescharacteristic
711C2×C42C22×D1111yescharacteristic
712C2×C42C22×D1111yescharacteristic
713C2×C42C22×D1111yescharacteristic
714C2×C42C22×D1111yescharacteristic
715C2×C42C22×D1111yescharacteristic
716C2×C42C22×D1111yescharacteristic
717C2×C42C22×D1111yescharacteristic
718C2×C42C22×D1111yescharacteristic
719C2×C42C22×D1111yescharacteristic
720C2×C42C22×D1111yescharacteristic
721#95—112no—
722#95—112no—
723#95—112no—
724#95—112no—
725#95—112no—
726#95—112no—
727#95—112no—
728#95—112no—
729#95—112no—
730#95—112no—
731#95—112no—
732#95—112no—
733#95—112no—
734#95—112no—
735#95—112no—
736#95—112no—
737#95—112no—
738#95—112no—
739#95—112no—
740#95—112no—
741#95—112no—
742#95—112no—
743#95—112no—
744#95—112no—
745#95—112no—
746#95C22×D1111yescharacteristic
747#95C22×D1111yescharacteristic
748#95C22×D1111yescharacteristic
749#95C22×D1111yescharacteristic
750#95C22×D1111yescharacteristic
751#95C22×D1111yescharacteristic
752C2×C11—24no—
753C2×C11—42no—
754C2×C11C2×#52911yescharacteristic
755C2×C11C2×#53811yescharacteristic
756C2×C11#346111yescharacteristic
757C2×C11#350511yescharacteristic
758C2×C11#351111yescharacteristic
759C2×C11#351411yescharacteristic
760C2×C11#352011yescharacteristic
761D11—82no—
762C24—112no—
763C24C23×D1111yescharacteristic
764C24C23×D1111yescharacteristic
765C2×Q8—224no—
766C2×Q8—222no—
767C2×Q8—222no—
768C2×Q8—222no—
769C2×Q8—222no—
770C2×Q8—222no—
771C2×Q8—222no—
772C2×Q8—442no—
773C2×Q8—442no—
774C2×Q8—4416no—
775C2×D4—22no—
776C2×D4—22no—
777C2×D4—224no—
778C2×D4—224no—
779C2×D4—224no—
780C2×D4—224no—
781C2×D4—222no—
782C2×D4—222no—
783C2×D4—222no—
784C2×D4—442no—
785C2×D4—442no—
786C2×D4#433914yes—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—41no—
798C22×C4—41no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4—112no—
804C22×C4—112no—
805C22×C4—112no—
806C22×C4—112no—
807C22×C4—112no—
808C22×C4—112no—
809C22×C4—112no—
810C22×C4—224no—
811C22×C4—224no—
812C22×C4—224no—
813C22×C4—442no—
814C22×C4—442no—
815C22×C4—442no—
816C22×C4—442no—
817C22×C4—442no—
818C22×C4—442no—
819C22×C4#433914yes—
820C22×C4#433914yes—
821C22×C4C23×D1111yescharacteristic
822C22×C4C23×D1111yescharacteristic
823C22×C4C23×D1111yescharacteristic
824C22×C4C23×D1111yescharacteristic
825C22×C4C23×D1111yescharacteristic
826C22×C4C23×D1111yescharacteristic
827C22×C4C23×D1111yescharacteristic
828C22×C4C23×D1111yescharacteristic
829C22×C4C23×D1111yescharacteristic
830C22×C4C23×D1111yescharacteristic
831C22×C4C23×D1111yescharacteristic
832C22×C4C23×D1111yescharacteristic
833C22×C4C23×D1111yescharacteristic
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—224no—
838C4⋊C4—224no—
839C4⋊C4—222no—
840C4⋊C4—222no—
841C4⋊C4—222no—
842C4⋊C4—222no—
843C4⋊C4—222no—
844C4⋊C4—442no—
845C4⋊C4—442no—
846C4⋊C4—442no—
847C4⋊C4—442no—
848C4⋊C4—442no—
849C4⋊C4—442no—
850C4⋊C4—442no—
851C22⋊C4—22no—
852C22⋊C4—22no—
853C22⋊C4—22no—
854C22⋊C4—22no—
855C22⋊C4—22no—
856C22⋊C4—22no—
857C22⋊C4—224no—
858C22⋊C4—224no—
859C22⋊C4—224no—
860C22⋊C4—224no—
861C22⋊C4—224no—
862C22⋊C4—224no—
863C22⋊C4—442no—
864C22⋊C4—442no—
865C22⋊C4—442no—
866C22⋊C4—442no—
867C22⋊C4—442no—
868C22⋊C4—442no—
869C22⋊C4—442no—
870C22⋊C4—442no—
871C22⋊C4—442no—
872C42—22no—
873C42—22no—
874C42—22no—
875C42—22no—
876C42—22no—
877C42—22no—
878C42—22no—
879C42—22no—
880C42—41no—
881C42—41no—
882C42—41no—
883C42—41no—
884C42—41no—
885C42—224no—
886C11#3503011yescharacteristic, complemented, Sylow
887C23—21no—
888C23—21no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—21no—
896C23—21no—
897C23—222no—
898C23—222no—
899C23—222no—
900C23—222no—
901C23—222no—
902C23—222no—
903C23—222no—
904C23C2×#433912yes—
905C23C2×#433912yes—
906C23C2×#433912yes—
907C23C2×#433912yes—
908C23C24×D1111yescharacteristic
909Q8—448no—
910Q8—444no—
911Q8—444no—
912D4—28no—
913D4—448no—
914D4—444no—
915D4—884no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—28no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—44no—
949C2×C4—44no—
950C2×C4—44no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—222no—
954C2×C4—222no—
955C2×C4—222no—
956C2×C4—222no—
957C2×C4—222no—
958C2×C4—222no—
959C2×C4—222no—
960C2×C4—222no—
961C2×C4—222no—
962C2×C4—222no—
963C2×C4—222no—
964C2×C4—222no—
965C2×C4—222no—
966C2×C4—222no—
967C2×C4—222no—
968C2×C4—222no—
969C2×C4—222no—
970C2×C4—222no—
971C2×C4—222no—
972C2×C4—222no—
973C2×C4—222no—
974C2×C4—448no—
975C2×C4—884no—
976C2×C4—884no—
977C2×C4C2×#433912yes—
978C2×C4C2×#433912yes—
979C2×C4C2×#433912yes—
980C2×C4C2×#433912yes—
981C2×C4C2×#433912yes—
982C2×C4#6703712yes—
983C2×C4#6704212yes—
984C2×C4#6704312yes—
985C22—22no—
986C22—22no—
987C22—22no—
988C22—22no—
989C22—22no—
990C22—22no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—442no—
999C22—442no—
1000C22—442no—
1001C22—442no—
1002C22—442no—
1003C22—442no—
1004C22—442no—
1005C22#1062301014yes—
1006C22C22×#433911yescharacteristic
1007C22C22×#433911yescharacteristic
1008C22C22×#433911yescharacteristic
1009C22C2×#6703711yescharacteristic
1010C22C2×#6704211yescharacteristic
1011C22C2×#6704311yescharacteristic
1012C22#1062345311yescharacteristic
1013C4—22no—
1014C4—22no—
1015C4—22no—
1016C4—22no—
1017C4—22no—
1018C4—41no—
1019C4—41no—
1020C4—41no—
1021C4—41no—
1022C4—41no—
1023C4—41no—
1024C4—41no—
1025C4—442no—
1026C4—442no—
1027C4—442no—
1028C4—442no—
1029C4—442no—
1030C4—442no—
1031C4—442no—
1032C4#1062309114yes—
1033C2—24no—
1034C2—42no—
1035C2—882no—
1036C2C2×#1062301011yescharacteristic
1037C2C2×#1062309111yescharacteristic
1038C2#1308204311yescharacteristic
1039C2#1308245511yescharacteristic
1040C2#1308252711yescharacteristic
1041C2#1308257711yescharacteristic
1042C2#1308266511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC42×D4×C11C2
prime radical#13072056C2
hypercenterC42×D4D11
hypocenterC11#35030
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
1. #13076998C2semidirect
2. #13076988C2semidirect
3. #13076955C2semidirect
4. #13076917C2semidirect
5. #13074673C2semidirect
6. #13074628C2semidirect
7. #13073884C2semidirect
8. #13073860C2semidirect
9. #13073224C2semidirect
10. #13073170C2semidirect
11. #13072957C2semidirect
12. #13072403C2semidirect
13. #13072360C2semidirect
14. #13072340C2semidirect
15. #13072274C2semidirect
16. #13072193C2semidirect
18. #13071981C2semidirect
19. #13071314C2semidirect
20. #13071243C2semidirect
21. C4×#66983C2semidirect
22. C2×#10622542C2semidirect
23. C42×D4×C11C2semidirect
388. C42×D4D11semidirect
886. C11#35030semidirect

Maximal subgroups

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

subgroupindex
#130769982
#130769882
#130769552
#130769172
#130746732
#130746282
#130738842
#130738602
#130732242
#130731702
#130729572
#130724032
#130723602
#130723402
#130722742
#130721932
#130720562
#130719812
#130713142
#130712432
C4×#669832
C2×#106225422
C42×D4×C112
#3503011