Finite Group Databasebeta

← #14759259

Subgroups — #14759259

Order 2816.

710 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071014C211yesmaximal, characteristic
2#13069232C211yesmaximal, characteristic
3#13069226C211yesmaximal, characteristic
4#13069225C211yesmaximal, characteristic
5#13069219C211yesmaximal, characteristic
6#13069181C211yesmaximal, characteristic, complemented
7#13069179C211yesmaximal, characteristic, complemented
8#13069174C211yesmaximal, characteristic, complemented
9#13069172C211yesmaximal, characteristic, complemented
10#13068474C211yesmaximal, characteristic, complemented
11#13068474C211yesmaximal, characteristic, complemented
12#13068378C211yesmaximal, characteristic
13#13068367C211yesmaximal, characteristic, complemented
14#13068302C211yesmaximal, characteristic, complemented
15C4×C11×C22⋊C8C211yesmaximal, characteristic
16C22×C42×C11C2211yescharacteristic
17C2×C11×C22⋊C8C2211yescharacteristic
18C2×C11×C22⋊C8C2211yescharacteristic
19C2×C4×C8×C11C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21#10622825C411yescharacteristic
22#10622825C411yescharacteristic
23#10622824C411yescharacteristic
24#10622824C411yescharacteristic
25C4×C22⋊Dic11C2211yescharacteristic
26C4×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×#66879C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622550C411yescharacteristic
38#10622550C411yescharacteristic
39#10622549C411yescharacteristic
40#10622549C411yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622545C2211yescharacteristic
44#10622545C2211yescharacteristic
45C2×#66867C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622188C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C23×C4×C11C2×C411yescharacteristic
60C23×C4×C11C2×C411yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C42×C11—22no—
67C2×C42×C11—22no—
68C2×C42×C11C2×C411yescharacteristic
69C2×C42×C11C2×C411yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11C2×C411yescharacteristic
73C2×C22⋊Dic11C2×C411yescharacteristic
74C2×C22⋊Dic11C2×C411yescharacteristic
75C2×C22⋊Dic11C2×C411yescharacteristic
76C2×C4⋊Dic11C2×C411yescharacteristic
77C2×C4⋊Dic11C2×C411yescharacteristic
78C2×C4⋊Dic11C2×C411yescharacteristic
79C2×C4⋊Dic11C2×C411yescharacteristic
80C2×C4×Dic11C2311yescharacteristic
81C2×C4×Dic11C2311yescharacteristic
82C2×C4×Dic11C2311yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85C22×C11⋊C8C2311yescharacteristic
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88C11×C22⋊C8—22no—
89C11×C22⋊C8—22no—
90C4×C8×C11—22no—
91C4×C8×C11—22no—
92C11⋊#95C2×C411yescharacteristic
93C11⋊#95C2×C411yescharacteristic
94C11⋊#95C2×C411yescharacteristic
95C11⋊#95C2×C411yescharacteristic
96C11⋊#95C2×C411yescharacteristic
97C11⋊#95C2×C411yescharacteristic
98C11⋊#95C2×C411yescharacteristic
99C11⋊#95C2×C411yescharacteristic
100C11⋊#95C2×C411yescharacteristic
101C11⋊#95C2×C411yescharacteristic
102C11⋊#95C2×C411yescharacteristic
103C11⋊#95C2×C411yescharacteristic
104C11⋊#95C2×C411yescharacteristic
105C11⋊#95C2×C411yescharacteristic
106C11⋊#95C2×C411yescharacteristic
107C11⋊#95C2×C411yescharacteristic
108C22⋊(C11⋊C8)—22no—
109C22⋊(C11⋊C8)—22no—
110#66879—22no—
111#66879—22no—
112Dic11⋊C8—22no—
113Dic11⋊C8—22no—
114Dic11⋊C8—22no—
115Dic11⋊C8—22no—
116C8×Dic11—22no—
117C8×Dic11—22no—
118#66867—22no—
119#66867—22no—
120#21437—111nomaximal, Sylow
121C24×C11C22×C411yescharacteristic
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—41no—
133C22×C4×C11—41no—
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11C22×C411yescharacteristic
141C22×Dic11C22×C411yescharacteristic
142C22×Dic11C22×C411yescharacteristic
143C22×Dic11C22×C411yescharacteristic
144C22×Dic11C22×C411yescharacteristic
145C22×Dic11C22×C411yescharacteristic
146C22×Dic11C22×C411yescharacteristic
147C22×Dic11C22×C411yescharacteristic
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11#4112yes—
159C2×C8×C11#4112yes—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11#4112yes—
165C42×C11#4112yes—
166C22⋊Dic11—22no—
167C22⋊Dic11—22no—
168C22⋊Dic11—41no—
169C22⋊Dic11—41no—
170C4⋊Dic11—22no—
171C4⋊Dic11—22no—
172C4⋊Dic11—41no—
173C4⋊Dic11—41no—
174C4×Dic11—21no—
175C4×Dic11—21no—
176C4×Dic11—21no—
177C4×Dic11—21no—
178C4×Dic11—21no—
179C4×Dic11—21no—
180C4×Dic11—21no—
181C4×Dic11—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8#4112yes—
193C2×C11⋊C8#4112yes—
194#2283—111no—
195#1924—111no—
196#1924—111no—
197#1923—111no—
198#1923—111no—
199#1917—111no—
200#1917—111no—
201#1916—111no—
202#1916—111no—
203#1768—111no—
204#1768—111no—
205#1749—111no—
206C4×C22⋊C8D1111yescharacteristic
207#1746—111no—
208#1726—111no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11#13112yes—
216C23×C11C23×C411yescharacteristic
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—44no—
230C2×C4×C11—44no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11#11712yes—
236C2×C4×C11#11712yes—
237C2×C4×C11#13112yes—
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C8×C11—22no—
269C8×C11—22no—
270C8×C11—41no—
271C8×C11—41no—
272C11⋊C8—22no—
273C11⋊C8—22no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C22×C42C2×D1111yescharacteristic
277C2×C4⋊C8—111no—
278C2×C4⋊C8—111no—
279C2×C4⋊C8—111no—
280C2×C4⋊C8—111no—
281C2×C22⋊C8—111no—
282C2×C22⋊C8—111no—
283C2×C22⋊C8C2×D1111yescharacteristic
284C2×C22⋊C8C2×D1111yescharacteristic
285C2×#97—111no—
286C2×#97—111no—
287C2×#97—111no—
288C2×#97—111no—
289C2×C4×C8—111no—
290C2×C4×C8—111no—
291C2×C4×C8C2×D1111yescharacteristic
292C2×C4×C8C2×D1111yescharacteristic
293#383—111no—
294#383—111no—
295#382—111no—
296#382—111no—
297#381—111no—
298#381—111no—
299#380—111no—
300#380—111no—
301C4×C4⋊C4—111no—
302C4×C4⋊C4—111no—
303C4×C22⋊C4—111no—
304C4×C22⋊C4—111no—
305#376—111no—
306#376—111no—
307#336—111no—
308#336—111no—
309#336—111no—
310#336—111no—
311#336—111no—
312#336—111no—
313#336—111no—
314#336—111no—
315#336—111no—
316#336—111no—
317#336C2×D1111yescharacteristic
318#336C2×D1111yescharacteristic
319C22×C11—22no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11C2×#11711yescharacteristic
327C22×C11C4×#4111yescharacteristic
328C22×C11C4×#4111yescharacteristic
329C22×C11C2×#13111yescharacteristic
330C22×C11C2×#13111yescharacteristic
331C22×C11#56811yescharacteristic
332C22×C11#56811yescharacteristic
333C4×C11—22no—
334C4×C11—22no—
335C4×C11—22no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11#52911yescharacteristic
339C4×C11#52911yescharacteristic
340C4×C11#52911yescharacteristic
341C4×C11#52911yescharacteristic
342Dic11—41no—
343Dic11—41no—
344Dic11—41no—
345Dic11—41no—
346Dic11—41no—
347Dic11—41no—
348Dic11—41no—
349Dic11—41no—
350C23×C4C4×D1111yescharacteristic
351C23×C4C4×D1111yescharacteristic
352C23×C4C22×D1111yescharacteristic
353C22×C8—111no—
354C22×C8—111no—
355C22×C8—111no—
356C22×C8—111no—
357C22×C8C22×D1111yescharacteristic
358C22×C8C22×D1111yescharacteristic
359C22×C8C22×D1111yescharacteristic
360C22×C8C22×D1111yescharacteristic
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C22⋊C4—111no—
366C2×C22⋊C4—111no—
367C2×C22⋊C4—111no—
368C2×C22⋊C4—111no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—111no—
372C2×C42—111no—
373C2×C42—111no—
374C2×C42—111no—
375C2×C42C4×D1111yescharacteristic
376C2×C42C4×D1111yescharacteristic
377C2×C42C22×D1111yescharacteristic
378C2×C42C22×D1111yescharacteristic
379C4⋊C8—222no—
380C4⋊C8—222no—
381C4⋊C8—222no—
382C4⋊C8—222no—
383C22⋊C8—22no—
384C22⋊C8—22no—
385C22⋊C8—222no—
386C22⋊C8—222no—
387#97—222no—
388#97—222no—
389#97—222no—
390#97—222no—
391C4×C8—22no—
392C4×C8—22no—
393C4×C8—222no—
394C4×C8—222no—
395#95—111no—
396#95—111no—
397#95—111no—
398#95—111no—
399#95—111no—
400#95—111no—
401#95—111no—
402#95—111no—
403#95—111no—
404#95—111no—
405#95—111no—
406#95—111no—
407#95—111no—
408#95—111no—
409#95—111no—
410#95—111no—
411C2×C11—42no—
412C2×C11#229811yescharacteristic
413C2×C11#292411yescharacteristic
414C2×C11#292411yescharacteristic
415C2×C11#296611yescharacteristic
416C2×C11#296711yescharacteristic
417C2×C11#296811yescharacteristic
418C2×C11#296911yescharacteristic
419C24C2×C4×D1111yescharacteristic
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—111no—
433C22×C4—111no—
434C22×C4—111no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—111no—
438C22×C4—111no—
439C22×C4—111no—
440C22×C4C2×C4×D1111yescharacteristic
441C22×C4C2×C4×D1111yescharacteristic
442C22×C4C2×C4×D1111yescharacteristic
443C22×C4C2×C4×D1111yescharacteristic
444C22×C4C2×C4×D1111yescharacteristic
445C22×C4C23×D1111yescharacteristic
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—112no—
457C2×C8—112no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8#433912yes—
469C2×C8#433912yes—
470C4⋊C4—222no—
471C4⋊C4—222no—
472C4⋊C4—441no—
473C4⋊C4—441no—
474C22⋊C4—222no—
475C22⋊C4—222no—
476C22⋊C4—441no—
477C22⋊C4—441no—
478C42—22no—
479C42—22no—
480C42—21no—
481C42—21no—
482C42—221no—
483C42—221no—
484C42—221no—
485C42—221no—
486C42—221no—
487C42—221no—
488C42—221no—
489C42—221no—
490C42#434112yes—
491C42#434112yes—
492C11#2143711yescharacteristic, complemented, Sylow
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23#6695412yes—
500C23C22×C4×D1111yescharacteristic
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—44no—
514C2×C4—44no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4#6693012yes—
544C2×C4#6693012yes—
545C2×C4#6695412yes—
546C2×C4C2×#433911yescharacteristic
547C2×C4C2×#433911yescharacteristic
548C2×C4C2×#434111yescharacteristic
549C2×C4C2×#434111yescharacteristic
550C2×C4#41×D1111yescharacteristic
551C2×C4#41×D1111yescharacteristic
552C8—22no—
553C8—22no—
554C8—41no—
555C8—41no—
556C8—222no—
557C8—222no—
558C8—441no—
559C8—441no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22C4×#433911yescharacteristic
568C22C2×#6693011yescharacteristic
569C22#1062305311yescharacteristic
570C22C2×#6695411yescharacteristic
571C22C2×#6695411yescharacteristic
572C22#1062327611yescharacteristic
573C22#1062327611yescharacteristic
574C4—22no—
575C4—22no—
576C4—22no—
577C4—41no—
578C4—41no—
579C4—441no—
580C4—441no—
581C4—441no—
582C4—441no—
583C4—441no—
584C4—441no—
585C4—441no—
586C4—441no—
587C4#1062306911yescharacteristic
588C4#1062306911yescharacteristic
589C4#1062308811yescharacteristic
590C4#1062308811yescharacteristic
591C2—42no—
592C2#1307111211yescharacteristic
593C2#1307727011yescharacteristic
594C2#1307727011yescharacteristic
595C2#1307759111yescharacteristic
596C2#1307760111yescharacteristic
597C2#1307760511yescharacteristic
598C2#1307761411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC4×C11×C22⋊C8C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenterC4×C22⋊C8D11
hypocenterC11#21437
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
6. #13069181C2semidirect
7. #13069179C2semidirect
8. #13069174C2semidirect
9. #13069172C2semidirect
10. #13068474C2semidirect
11. #13068474C2semidirect
13. #13068367C2semidirect
14. #13068302C2semidirect
492. C11#21437semidirect

Maximal subgroups

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

subgroupindex
#130710142
#130692322
#130692262
#130692252
#130692192
#130691812
#130691792
#130691742
#130691722
#130684742
#130683782
#130683672
#130683022
C4×C11×C22⋊C82
#2143711