Finite Group Databasebeta

← #14959834

Subgroups — #14959834

Order 2816.

2082 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077008C212yesmaximal, complemented
2#13077005C212yesmaximal, complemented
3#13077003C211yesmaximal, characteristic, complemented
4#13076998C211yesmaximal, characteristic, complemented
5#13076988C211yesmaximal, characteristic, complemented
6#13076983C211yesmaximal, characteristic, complemented
7#13076955C211yesmaximal, characteristic, complemented
8#13076947C211yesmaximal, characteristic
9#13076938C212yesmaximal, complemented
10#13076931C212yesmaximal, complemented
11#13076926C211yesmaximal, characteristic, complemented
12#13076917C211yesmaximal, characteristic
13C4×#66923C211yesmaximal, characteristic, complemented
14C4×#66929C212yesmaximal, complemented
15C4×#66928C211yesmaximal, characteristic, complemented
16C4×#66977C211yesmaximal, characteristic, complemented
17C4×#66982C212yesmaximal, complemented
18C4×#66983C211yesmaximal, characteristic
19#13071113C212yesmaximal, complemented
20#13071093C211yesmaximal, characteristic, complemented
21#13071080C211yesmaximal, characteristic, complemented
22#13071059C212yesmaximal, complemented
23C2×C43×C11C211yesmaximal, characteristic, complemented
24C22×C42×C11C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C22×C42×C11C2211yescharacteristic
27C22×C42×C11C2211yescharacteristic
28C22×C42×C11C2211yescharacteristic
29C22×C42×C11C2211yescharacteristic
30C22×C42×C11C2211yescharacteristic
31C2×#66983C2211yescharacteristic
32C2×#66982C2212yes—
33C2×C4×C22⋊D11C2212yes—
34C2×#66977C2211yescharacteristic
35C2×#66929C2212yes—
36C2×#66928C2211yescharacteristic
37C2×C4×D44C2211yescharacteristic
38C2×#66925C2212yes—
39C2×#66923C2211yescharacteristic
40C2×C4×Dic22C2211yescharacteristic
41C43×C11C2211yescharacteristic
42C43×C11C2211yescharacteristic
43C43×C11C2211yescharacteristic
44C43×C11C2211yescharacteristic
45C43×C11C2211yescharacteristic
46C43×C11C2211yescharacteristic
47C43×C11C2211yescharacteristic
48C43×C11C2211yescharacteristic
49#10622826C2212yes—
50#10622826C2212yes—
51#10622826C2212yes—
52#10622826C2212yes—
53#10622825C2211yescharacteristic
54#10622825C2211yescharacteristic
55#10622824C2212yes—
56#10622823C2212yes—
57#10622823C2212yes—
58#10622823C2212yes—
59#10622823C2212yes—
60C4×C22⋊Dic11C2212yes—
61#10622553C2212yes—
62#10622553C2212yes—
63#10622553C2212yes—
64#10622553C2212yes—
65#10622553C2212yes—
66#10622553C2212yes—
67#10622553C2212yes—
68#10622553C2212yes—
69#10622553C2212yes—
70#10622553C2212yes—
71#10622553C2212yes—
72#10622553C2212yes—
73#10622553C2212yes—
74#10622553C2212yes—
75#10622553C2212yes—
76#10622553C2212yes—
77#10622552C2211yescharacteristic
78#10622552C2211yescharacteristic
79#10622552C2211yescharacteristic
80#10622552C2211yescharacteristic
81C4×(C2×D11)⋊C4C2212yes—
82C4×(C2×D11)⋊C4C2212yes—
83C4×(C2×D11)⋊C4C2212yes—
84C4×(C2×D11)⋊C4C2212yes—
85#10622550C2212yes—
86#10622549C2211yescharacteristic
87#10622549C2211yescharacteristic
88C4×C4⋊Dic11C2211yescharacteristic
89C4×C4⋊Dic11C2211yescharacteristic
90#10622546C2212yes—
91#10622546C2212yes—
92#10622546C2212yes—
93#10622546C2212yes—
94#10622546C2212yes—
95#10622546C2212yes—
96#10622546C2212yes—
97#10622546C2212yes—
98#10622546C2212yes—
99#10622546C2212yes—
100#10622546C2212yes—
101#10622546C2212yes—
102#10622546C2212yes—
103#10622546C2212yes—
104#10622546C2212yes—
105#10622546C2212yes—
106#10622545C2212yes—
107C4×Dic11⋊C4C2212yes—
108C4×Dic11⋊C4C2212yes—
109C4×Dic11⋊C4C2212yes—
110C4×Dic11⋊C4C2212yes—
111#10622542C2211yescharacteristic
112#10622542C2211yescharacteristic
113#10622542C2211yescharacteristic
114#10622542C2211yescharacteristic
115#10622541C2211yescharacteristic
116#10622541C2211yescharacteristic
117#10622541C2211yescharacteristic
118#10622541C2211yescharacteristic
119#10622541C2211yescharacteristic
120#10622541C2211yescharacteristic
121#10622541C2211yescharacteristic
122#10622541C2211yescharacteristic
123C23×C4×C11C2311yescharacteristic
124C23×C4×C11C2311yescharacteristic
125C23×C4×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C22×C22⋊D11C2312yes—
131C22×D44C2311yescharacteristic
132C22×C4×D11C2312yes—
133C22×Dic22C2311yescharacteristic
134C2×C42×C11—24no—
135C2×C42×C11—24no—
136C2×C42×C11—24no—
137C2×C42×C11—24no—
138C2×C42×C11—24no—
139C2×C42×C11—24no—
140C2×C42×C11—24no—
141C2×C42×C11C2311yescharacteristic
142C2×C42×C11C2311yescharacteristic
143C2×C42×C11C2311yescharacteristic
144C2×C42×C11C2311yescharacteristic
145C2×C42×C11C2311yescharacteristic
146C2×C42×C11C2311yescharacteristic
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2311yescharacteristic
149C2×C42×C11C2311yescharacteristic
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2311yescharacteristic
152C2×C42×C11C2311yescharacteristic
153C2×C42×C11C2311yescharacteristic
154C2×C42×C11C2311yescharacteristic
155C2×C42×C11C2311yescharacteristic
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—
172#66983—24no—
173#66982—28no—
174C4×C22⋊D11—28no—
175C2×(C2×D11)⋊C4C2312yes—
176C2×(C2×D11)⋊C4C2312yes—
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×C4⋊Dic11C2311yescharacteristic
188C2×C4⋊Dic11C2311yescharacteristic
189C2×C4⋊Dic11C2311yescharacteristic
190C2×C4⋊Dic11C2311yescharacteristic
191C2×C4⋊Dic11C2311yescharacteristic
192C2×C4⋊Dic11C2311yescharacteristic
193#66977—24no—
194C2×Dic11⋊C4C2312yes—
195C2×Dic11⋊C4C2312yes—
196C2×Dic11⋊C4C2312yes—
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×Dic11⋊C4C2312yes—
206C2×C4×Dic11C2312yes—
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2312yes—
209#66929—28no—
210#66928—24no—
211C4×D44—24no—
212#66925—28no—
213#66923—24no—
214C4×Dic22—24no—
215C11⋊#95C2312yes—
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—
239#36638—111nomaximal, Sylow
240C24×C11C2411yescharacteristic
241C23×D11C2412yes—
242C22×C4×C11—22no—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11—22no—
246C22×C4×C11—22no—
247C22×C4×C11—22no—
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—22no—
259C22×C4×C11—22no—
260C22×C4×C11#4114yes—
261C22×C4×C11#4114yes—
262C22×C4×C11#4114yes—
263C22×C4×C11C2411yescharacteristic
264C22×C4×C11C2411yescharacteristic
265C22×C4×C11C2411yescharacteristic
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
277C2×C22⋊D11—24no—
278C2×C22⋊D11—24no—
279C2×C22⋊D11—24no—
280C22×Dic11C2412yes—
281C22×Dic11C2412yes—
282C22×Dic11C2412yes—
283C22×Dic11C2412yes—
284C22×Dic11C2412yes—
285C22×Dic11C2412yes—
286C22×Dic11C2412yes—
287C2×D44—22no—
288C2×D44—22no—
289C2×D44—22no—
290C2×C4×D11—24no—
291C2×C4×D11—24no—
292C2×C4×D11—24no—
293C2×Dic22—22no—
294C2×Dic22—22no—
295C2×Dic22—22no—
296C42×C11—22no—
297C42×C11—22no—
298C42×C11—22no—
299C42×C11—22no—
300C42×C11—22no—
301C42×C11—22no—
302C42×C11—22no—
303C42×C11—22no—
304C42×C11—22no—
305C42×C11—22no—
306C42×C11—22no—
307C42×C11—22no—
308C42×C11—22no—
309C42×C11—22no—
310C42×C11—22no—
311C42×C11—22no—
312C42×C11—22no—
313C42×C11—22no—
314C42×C11—22no—
315C42×C11—22no—
316C42×C11—22no—
317C42×C11—22no—
318C42×C11—22no—
319C42×C11—22no—
320C42×C11#4114yes—
321C42×C11#4114yes—
322C42×C11#4114yes—
323C42×C11#4114yes—
324C22⋊Dic11—24no—
325C22⋊Dic11—24no—
326C22⋊Dic11—24no—
327(C2×D11)⋊C4—24no—
328(C2×D11)⋊C4—24no—
329(C2×D11)⋊C4—24no—
330(C2×D11)⋊C4—24no—
331(C2×D11)⋊C4—24no—
332(C2×D11)⋊C4—24no—
333(C2×D11)⋊C4—24no—
334(C2×D11)⋊C4—24no—
335(C2×D11)⋊C4—24no—
336(C2×D11)⋊C4—24no—
337(C2×D11)⋊C4—24no—
338(C2×D11)⋊C4—24no—
339C4⋊Dic11—22no—
340C4⋊Dic11—22no—
341C4⋊Dic11—22no—
342C4⋊Dic11—22no—
343C4⋊Dic11—22no—
344C4⋊Dic11—22no—
345Dic11⋊C4—24no—
346Dic11⋊C4—24no—
347Dic11⋊C4—24no—
348Dic11⋊C4—24no—
349Dic11⋊C4—24no—
350Dic11⋊C4—24no—
351Dic11⋊C4—24no—
352Dic11⋊C4—24no—
353Dic11⋊C4—24no—
354Dic11⋊C4—24no—
355Dic11⋊C4—24no—
356Dic11⋊C4—24no—
357C4×Dic11—24no—
358C4×Dic11—24no—
359C4×Dic11—24no—
360#2866—112no—
361#2865—112no—
362#2864—111no—
363#2863—111no—
364#2861—111no—
365#2860—111no—
366#2855—111no—
367#2854—111no—
368#2853—112no—
369#2852—112no—
370#2851—111no—
371#2850—111no—
372C4×#125—111no—
373C4×#126—112no—
374C4×#124—111no—
375C4×C22⋊Q8—111no—
376C4×#123—112no—
377C4×#121—111no—
378#2298—112no—
379#2295—111no—
380#2293—111no—
381#2290—112no—
382C2×C43D1111yescharacteristic, complemented
383C23×C11—21no—
384C23×C11—21no—
385C23×C11—21no—
386C23×C11—21no—
387C23×C11C2×#4112yes—
388C23×C11C2×#4112yes—
389C23×C11C2×#4112yes—
390C23×C11C2511yescharacteristic
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—22no—
397C22×D11—22no—
398C2×C4×C11—28no—
399C2×C4×C11—28no—
400C2×C4×C11—28no—
401C2×C4×C11—28no—
402C2×C4×C11—28no—
403C2×C4×C11—21no—
404C2×C4×C11—21no—
405C2×C4×C11—21no—
406C2×C4×C11—21no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—21no—
411C2×C4×C11—21no—
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—21no—
423C2×C4×C11—21no—
424C2×C4×C11—21no—
425C2×C4×C11—21no—
426C2×C4×C11—21no—
427C2×C4×C11—28no—
428C2×C4×C11—28no—
429C2×C4×C11C2×#4112yes—
430C2×C4×C11C2×#4112yes—
431C2×C4×C11C2×#4112yes—
432C2×C4×C11C2×#4112yes—
433C2×C4×C11C2×#4112yes—
434C2×C4×C11C2×#4112yes—
435C2×C4×C11C2×#4112yes—
436C2×C4×C11C2×#4112yes—
437C2×C4×C11C2×#4112yes—
438C2×C4×C11C2×#4112yes—
439C2×C4×C11C2×#4112yes—
440C2×C4×C11C2×#4112yes—
441C2×C4×C11C2×#4112yes—
442C2×C4×C11C2×#4112yes—
443C2×C4×C11C2×#4112yes—
444C2×C4×C11C2×#4112yes—
445C2×C4×C11C2×#4112yes—
446C2×C4×C11C2×#4112yes—
447C22⋊D11—48no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
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—
469D44—44no—
470C4×D11—48no—
471Dic22—44no—
472C2×#126—112no—
473C2×#125—111no—
474C2×#124—111no—
475C2×#123—112no—
476C2×C22⋊Q8—111no—
477C2×#121—111no—
478C2×C4×Q8—111no—
479C2×C4×D4—112no—
480C2×C4×D4—111no—
481C2×#117—112no—
482C22×C42C2×D1111yescharacteristic
483C22×C42C2×D1111yescharacteristic
484C22×C42C2×D1111yescharacteristic
485C22×C42C2×D1111yescharacteristic
486C22×C42C2×D1111yescharacteristic
487C22×C42C2×D1111yescharacteristic
488C22×C42C2×D1111yescharacteristic
489#391—111no—
490#391—111no—
491#391—111no—
492#391—111no—
493#390—111no—
494#390—111no—
495#390—111no—
496#390—111no—
497#389—111no—
498#389—111no—
499#389—111no—
500#389—111no—
501#389—111no—
502#389—111no—
503#389—111no—
504#389—111no—
505#388—112no—
506#388—112no—
507#388—112no—
508#388—112no—
509#388—112no—
510#388—112no—
511#388—112no—
512#388—112no—
513#388—112no—
514#388—112no—
515#388—112no—
516#388—112no—
517#388—112no—
518#388—112no—
519#388—112no—
520#388—112no—
521#387—112no—
522#387—112no—
523#387—112no—
524#387—112no—
525#387—112no—
526#387—112no—
527#387—112no—
528#387—112no—
529#387—112no—
530#387—112no—
531#387—112no—
532#387—112no—
533#387—112no—
534#387—112no—
535#387—112no—
536#387—112no—
537#386—112no—
538#386—112no—
539#386—112no—
540#386—112no—
541#385—112no—
542#385—112no—
543#385—112no—
544#385—112no—
545#383—112no—
546#382—111no—
547#382—111no—
548#381—112no—
549#380—111no—
550#380—111no—
551C4×C4⋊C4—112no—
552C4×C4⋊C4—112no—
553C4×C4⋊C4—112no—
554C4×C4⋊C4—112no—
555C4×C4⋊C4—111no—
556C4×C4⋊C4—111no—
557C4×C22⋊C4—112no—
558C4×C22⋊C4—112no—
559C4×C22⋊C4—112no—
560C4×C22⋊C4—112no—
561C4×C22⋊C4—112no—
562#376—112no—
563C43C2×D1111yescharacteristic
564C43C2×D1111yescharacteristic
565C43C2×D1111yescharacteristic
566C43C2×D1111yescharacteristic
567C43C2×D1111yescharacteristic
568C43C2×D1111yescharacteristic
569C43C2×D1111yescharacteristic
570C43C2×D1111yescharacteristic
571C22×C11—22no—
572C22×C11—22no—
573C22×C11—22no—
574C22×C11—22no—
575C22×C11—22no—
576C22×C11—22no—
577C22×C11#52914yes—
578C22×C11C22×#4111yescharacteristic
579C22×C11C22×#4111yescharacteristic
580C22×C11C22×#4111yescharacteristic
581C22×C11C22×#4111yescharacteristic
582C22×C11C22×#4111yescharacteristic
583C22×C11C22×#4111yescharacteristic
584C22×C11C22×#4111yescharacteristic
585C2×D11—42no—
586C2×D11—42no—
587C2×D11—42no—
588C2×D11—42no—
589C2×D11—42no—
590C2×D11—42no—
591C2×D11—42no—
592C4×C11—22no—
593C4×C11—22no—
594C4×C11—22no—
595C4×C11—22no—
596C4×C11—22no—
597C4×C11—22no—
598C4×C11—22no—
599C4×C11—22no—
600C4×C11—22no—
601C4×C11—22no—
602C4×C11—22no—
603C4×C11—22no—
604C4×C11#52914yes—
605C4×C11#52914yes—
606Dic11—42no—
607Dic11—42no—
608Dic11—42no—
609Dic11—42no—
610Dic11—42no—
611Dic11—42no—
612Dic11—42no—
613C22×Q8—111no—
614C22×D4—112no—
615C22×D4—111no—
616C23×C4—112no—
617C23×C4C22×D1111yescharacteristic
618C23×C4C22×D1111yescharacteristic
619C23×C4C22×D1111yescharacteristic
620C23×C4C22×D1111yescharacteristic
621C23×C4C22×D1111yescharacteristic
622C23×C4C22×D1111yescharacteristic
623C23×C4C22×D1111yescharacteristic
624#126—228no—
625#125—224no—
626#124—224no—
627#123—228no—
628C22⋊Q8—224no—
629#121—224no—
630C4×Q8—224no—
631C4×D4—228no—
632C4×D4—224no—
633#117—228no—
634C2×C4⋊C4—112no—
635C2×C4⋊C4—112no—
636C2×C4⋊C4—111no—
637C2×C4⋊C4—112no—
638C2×C4⋊C4—111no—
639C2×C4⋊C4—112no—
640C2×C4⋊C4—111no—
641C2×C4⋊C4—111no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—112no—
644C2×C4⋊C4—112no—
645C2×C4⋊C4—111no—
646C2×C4⋊C4—111no—
647C2×C4⋊C4—112no—
648C2×C4⋊C4—112no—
649C2×C4⋊C4—112no—
650C2×C4⋊C4—112no—
651C2×C4⋊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×C42—24no—
668C2×C42—24no—
669C2×C42—24no—
670C2×C42—24no—
671C2×C42—24no—
672C2×C42—24no—
673C2×C42—24no—
674C2×C42—112no—
675C2×C42—112no—
676C2×C42—112no—
677C2×C42C22×D1111yescharacteristic
678C2×C42C22×D1111yescharacteristic
679C2×C42C22×D1111yescharacteristic
680C2×C42C22×D1111yescharacteristic
681C2×C42C22×D1111yescharacteristic
682C2×C42C22×D1111yescharacteristic
683C2×C42C22×D1111yescharacteristic
684C2×C42C22×D1111yescharacteristic
685C2×C42C22×D1111yescharacteristic
686C2×C42C22×D1111yescharacteristic
687C2×C42C22×D1111yescharacteristic
688C2×C42C22×D1111yescharacteristic
689C2×C42C22×D1111yescharacteristic
690C2×C42C22×D1111yescharacteristic
691C2×C42C22×D1111yescharacteristic
692C2×C42C22×D1111yescharacteristic
693C2×C42C22×D1111yescharacteristic
694C2×C42C22×D1111yescharacteristic
695C2×C42C22×D1111yescharacteristic
696C2×C42C22×D1111yescharacteristic
697C2×C42C22×D1111yescharacteristic
698C2×C42C22×D1111yescharacteristic
699C2×C42C22×D1111yescharacteristic
700C2×C42C22×D1111yescharacteristic
701C2×C42C22×D1111yescharacteristic
702C2×C42C22×D1111yescharacteristic
703C2×C42C22×D1111yescharacteristic
704C2×C42C22×D1111yescharacteristic
705#95—112no—
706#95—112no—
707#95—112no—
708#95—112no—
709#95—112no—
710#95—112no—
711#95—112no—
712#95—112no—
713#95—112no—
714#95—112no—
715#95—112no—
716#95—112no—
717#95—112no—
718#95—112no—
719#95—112no—
720#95—112no—
721#95—112no—
722#95—112no—
723#95—112no—
724#95—112no—
725#95—112no—
726#95—112no—
727#95—112no—
728#95—112no—
729C2×C11—24no—
730C2×C11C2×#52911yescharacteristic
731C2×C11C2×#52911yescharacteristic
732C2×C11C2×#52911yescharacteristic
733C2×C11#344411yescharacteristic
734C2×C11#344411yescharacteristic
735C2×C11#344411yescharacteristic
736C2×C11#344411yescharacteristic
737D11—82no—
738C24—112no—
739C24C23×D1111yescharacteristic
740C2×Q8—222no—
741C2×Q8—222no—
742C2×Q8—222no—
743C2×D4—224no—
744C2×D4—224no—
745C2×D4—224no—
746C2×D4—222no—
747C2×D4—222no—
748C2×D4—222no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—112no—
768C22×C4—112no—
769C22×C4—112no—
770C22×C4—112no—
771C22×C4—112no—
772C22×C4—112no—
773C22×C4—112no—
774C22×C4—224no—
775C22×C4—224no—
776C22×C4—224no—
777C22×C4#433914yes—
778C22×C4#433914yes—
779C22×C4#433914yes—
780C22×C4C23×D1111yescharacteristic
781C22×C4C23×D1111yescharacteristic
782C22×C4C23×D1111yescharacteristic
783C22×C4C23×D1111yescharacteristic
784C22×C4C23×D1111yescharacteristic
785C22×C4C23×D1111yescharacteristic
786C22×C4C23×D1111yescharacteristic
787C22×C4C23×D1111yescharacteristic
788C22×C4C23×D1111yescharacteristic
789C22×C4C23×D1111yescharacteristic
790C22×C4C23×D1111yescharacteristic
791C22×C4C23×D1111yescharacteristic
792C22×C4C23×D1111yescharacteristic
793C22×C4C23×D1111yescharacteristic
794C4⋊C4—224no—
795C4⋊C4—224no—
796C4⋊C4—224no—
797C4⋊C4—222no—
798C4⋊C4—224no—
799C4⋊C4—222no—
800C4⋊C4—222no—
801C4⋊C4—224no—
802C4⋊C4—222no—
803C4⋊C4—224no—
804C4⋊C4—224no—
805C4⋊C4—224no—
806C4⋊C4—224no—
807C4⋊C4—222no—
808C4⋊C4—222no—
809C4⋊C4—224no—
810C4⋊C4—224no—
811C4⋊C4—224no—
812C22⋊C4—224no—
813C22⋊C4—224no—
814C22⋊C4—224no—
815C22⋊C4—224no—
816C22⋊C4—224no—
817C22⋊C4—224no—
818C22⋊C4—224no—
819C22⋊C4—224no—
820C22⋊C4—224no—
821C22⋊C4—224no—
822C22⋊C4—224no—
823C22⋊C4—224no—
824C22⋊C4—224no—
825C22⋊C4—224no—
826C22⋊C4—224no—
827C42—22no—
828C42—22no—
829C42—22no—
830C42—22no—
831C42—22no—
832C42—22no—
833C42—22no—
834C42—22no—
835C42—22no—
836C42—22no—
837C42—22no—
838C42—22no—
839C42—22no—
840C42—22no—
841C42—22no—
842C42—22no—
843C42—22no—
844C42—22no—
845C42—22no—
846C42—22no—
847C42—22no—
848C42—22no—
849C42—22no—
850C42—22no—
851C42—224no—
852C42—224no—
853C42—224no—
854C42#433914yes—
855C42#433914yes—
856C42#433914yes—
857C42#433914yes—
858C11#3663811yescharacteristic, complemented, Sylow
859C23—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—222no—
864C23—222no—
865C23—222no—
866C23—222no—
867C23—222no—
868C23—222no—
869C23—222no—
870C23C2×#433912yes—
871C23C2×#433912yes—
872C23C2×#433912yes—
873C23C24×D1111yescharacteristic
874Q8—444no—
875D4—448no—
876D4—444no—
877C2×C4—28no—
878C2×C4—28no—
879C2×C4—28no—
880C2×C4—28no—
881C2×C4—28no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—21no—
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—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—28no—
907C2×C4—28no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—222no—
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—448no—
930C2×C4C2×#433912yes—
931C2×C4C2×#433912yes—
932C2×C4C2×#433912yes—
933C2×C4C2×#433912yes—
934C2×C4C2×#433912yes—
935C2×C4C2×#433912yes—
936C2×C4C2×#433912yes—
937C2×C4C2×#433912yes—
938C2×C4C2×#433912yes—
939C2×C4C2×#433912yes—
940C2×C4C2×#433912yes—
941C2×C4C2×#433912yes—
942C2×C4C2×#433912yes—
943C2×C4C2×#433912yes—
944C2×C4C2×#433912yes—
945C2×C4C2×#433912yes—
946C2×C4C2×#433912yes—
947C2×C4C2×#433912yes—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—442no—
955C22—442no—
956C22—442no—
957C22—442no—
958C22—442no—
959C22—442no—
960C22—442no—
961C22#1062301014yes—
962C22C22×#433911yescharacteristic
963C22C22×#433911yescharacteristic
964C22C22×#433911yescharacteristic
965C22C22×#433911yescharacteristic
966C22C22×#433911yescharacteristic
967C22C22×#433911yescharacteristic
968C22C22×#433911yescharacteristic
969C4—22no—
970C4—22no—
971C4—22no—
972C4—22no—
973C4—22no—
974C4—22no—
975C4—22no—
976C4—22no—
977C4—22no—
978C4—22no—
979C4—22no—
980C4—22no—
981C4—442no—
982C4—442no—
983C4—442no—
984C4—442no—
985C4—442no—
986C4—442no—
987C4—442no—
988C4#1062301014yes—
989C4#1062301014yes—
990C2—24no—
991C2—882no—
992C2C2×#1062301011yescharacteristic
993C2C2×#1062301011yescharacteristic
994C2C2×#1062301011yescharacteristic
995C2#1308191211yescharacteristic
996C2#1308191211yescharacteristic
997C2#1308191211yescharacteristic
998C2#1308191211yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C43×C11C2
prime radicalC2×#66983C22
hypercenterC2×C43D11
hypocenterC11#36638
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C43

Complements

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

NH ≅ G/Ntype
1. #13077008C2semidirect
2. #13077005C2semidirect
3. #13077003C2semidirect
4. #13076998C2semidirect
5. #13076988C2semidirect
6. #13076983C2semidirect
7. #13076955C2semidirect
9. #13076938C2semidirect
10. #13076931C2semidirect
11. #13076926C2semidirect
13. C4×#66923C2semidirect
14. C4×#66929C2semidirect
15. C4×#66928C2semidirect
16. C4×#66977C2semidirect
17. C4×#66982C2semidirect
19. #13071113C2semidirect
20. #13071093C2semidirect
21. #13071080C2semidirect
22. #13071059C2semidirect
23. C2×C43×C11C2semidirect
382. C2×C43D11semidirect
858. C11#36638semidirect

Maximal subgroups

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

subgroupindex
#130770082
#130770052
#130770032
#130769982
#130769882
#130769832
#130769552
#130769472
#130769382
#130769312
#130769262
#130769172
C4×#669232
C4×#669292
C4×#669282
C4×#669772
C4×#669822
C4×#669832
#130711132
#130710932
#130710802
#130710592
C2×C43×C112
#3663811