Finite Group Databasebeta

← #14737330

Subgroups — #14737330

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079538C211yesmaximal, characteristic, complemented
2#13079009C211yesmaximal, characteristic, complemented
3#13077360C211yesmaximal, characteristic, complemented
4#13068175C212yesmaximal, complemented
5#13068161C212yesmaximal, complemented
6#13068051C212yesmaximal, complemented
7#13068037C212yesmaximal, complemented
8#13067366C211yesmaximal, characteristic, complemented
9#13067265C211yesmaximal, characteristic, complemented
10C2×#10622120C211yesmaximal, characteristic, complemented
11C11×#3245C211yesmaximal, characteristic
12C11×#532C2211yescharacteristic
13C11×#532C2211yescharacteristic
14C2×#67001—21no—
15C2×#66922C2211yescharacteristic
16C11×#474—21no—
17C11×#474C2212yes—
18C11×#466—22no—
19C11×#459—21no—
20C11×#459C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22#10622847—21no—
23#10622845—21no—
24#10622845—21no—
25#10622706—21no—
26#10622694C2212yes—
27#10622689—21no—
28#10622683C2212yes—
29#10622668—22no—
30#10622653—22no—
31#10622632C2212yes—
32#10622632C2212yes—
33#10622625C2212yes—
34#10622624—22no—
35D4×C11⋊C8C2212yes—
36#10622538C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C4×#4318C2211yescharacteristic
39#10622185C2211yescharacteristic
40#10622185C2211yescharacteristic
41#10622182C2211yescharacteristic
42#10622182C2211yescharacteristic
43#10622120C2212yes—
44#10622120C2212yes—
45#10622118C2212yes—
46#10622117C2212yes—
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C22×Dic22—21no—
50C2×C11×D8—22no—
51C22×C8×C11—21no—
52C11×C4⋊Q8D411yescharacteristic
53C11×C4⋊Q8C2311yescharacteristic
54C11×#127D411yescharacteristic
55C11×#127C2311yescharacteristic
56C11×#124—21no—
57C11×#124—21no—
58C11×#121—21no—
59C11×#121—21no—
60C11×#121—21no—
61C11×#121D412yes—
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C4×D4×C11—21no—
65C4×D4×C11C2312yes—
66C2×C42×C11C2311yescharacteristic
67#67001—44no—
68C2×#4324—22no—
69C2×#4324—22no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×#4318—22no—
73C2×#4318D411yescharacteristic
74C2×#4318D411yescharacteristic
75C22×C11⋊C8—21no—
76C22×C11⋊C8—22no—
77#66922—21no—
78#66922—21no—
79#66922—21no—
80#66922C2312yes—
81C11×#107—22no—
82C11×C4⋊C8—21no—
83C11×C4⋊C8C2312yes—
84C11×#102—22no—
85C11×#102—22no—
86#66899—22no—
87#66899—22no—
88#66896—22no—
89#66896—22no—
90C22⋊(C11⋊C8)—21no—
91C22⋊(C11⋊C8)—22no—
92C22⋊(C11⋊C8)—22no—
93#66874—22no—
94#66874—22no—
95C4⋊(C11⋊C8)—21no—
96C4⋊(C11⋊C8)C2311yescharacteristic
97C4⋊(C11⋊C8)C2311yescharacteristic
98C4⋊(C11⋊C8)C2311yescharacteristic
99C4⋊(C11⋊C8)C2311yescharacteristic
100#66867D412yes—
101C4×C11⋊C8—21no—
102C4×C11⋊C8C2312yes—
103#19237—111nomaximal, Sylow
104C11×#41—42no—
105C11×#41—42no—
106C11×#41—42no—
107C11×#41—42no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×D4×C11—22no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—41no—
117C2×D4×C11C2×D412yes—
118C22×C4×C11—22no—
119C22×C4×C11—41no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C22×Dic11—41no—
124C2×Dic22—22no—
125C2×Dic22—41no—
126C2×Dic22—81no—
127C2×Dic22—81no—
128C11×D8—82no—
129C2×C8×C11—22no—
130C2×C8×C11—81no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4C2×D412yes—
135C11×C22⋊C4—22no—
136C11×C22⋊C4—22no—
137C11×C22⋊C4—41no—
138C11×C22⋊C4—41no—
139C42×C11C2×D411yescharacteristic
140C42×C11C2×D411yescharacteristic
141C42×C11#4111yescharacteristic
142C42×C11C2411yescharacteristic
143#4324—82no—
144#4324—82no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11—41no—
148C4⋊Dic11—41no—
149#4318—22no—
150#4318—22no—
151#4318—44no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—44no—
157C2×C11⋊C8—42no—
158C2×C11⋊C8C2×D412yes—
159C2×C11⋊C8C2×D412yes—
160#3245D1111yescharacteristic
161#3206—111no—
162#3141—111no—
163#2935—111no—
164#1701—112no—
165#1699—112no—
166#1681—112no—
167#1679—112no—
168#1565—111no—
169#1540—111no—
170C2×#332—111no—
171C23×C11—22no—
172C23×C11—41no—
173C23×C11#12111yescharacteristic
174Q8×C11—42no—
175Q8×C11—41no—
176Q8×C11—41no—
177D4×C11—22no—
178D4×C11—22no—
179D4×C11—44no—
180D4×C11—41no—
181D4×C11—41no—
182D4×C11—41no—
183D4×C11—41no—
184D4×C11—42no—
185D4×C11—81no—
186D4×C11—81no—
187D4×C11—82no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—22no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—41no—
195C2×C4×C11—82no—
196C2×C4×C11#12111yescharacteristic
197C2×C4×C11#12111yescharacteristic
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11#13512yes—
200C2×C4×C11AGL(1,ℤ/8)12yes—
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×Dic11—42no—
205C2×Dic11—82no—
206Dic22—42no—
207Dic22—42no—
208Dic22—82no—
209C8×C11—42no—
210C11⋊C8—22no—
211C11⋊C8—22no—
212C11⋊C8—41no—
213C11⋊C8—41no—
214C11⋊C8—41no—
215C11⋊C8—41no—
216C2×#131—221no—
217#532C2×D1111yescharacteristic
218#532C2×D1111yescharacteristic
219C2×C4⋊Q8—111no—
220#492—221no—
221#489—222no—
222#487—112no—
223#487—221no—
224#486—112no—
225#474—21no—
226#474C2×D1112yes—
227#466—22no—
228#461—112no—
229#461—112no—
230#459—21no—
231#459C2×D1112yes—
232#448—222no—
233#436—112no—
234#435—222no—
235C8×D4—112no—
236#431—111no—
237C2×C4⋊C8—111no—
238C2×C4⋊C8C2×D1111yescharacteristic
239#417—221no—
240#417—221no—
241#408—221no—
242C4×M16—111no—
243#335—112no—
244#334—112no—
245#332—111no—
246#332—111no—
247#332—112no—
248#332—112no—
249#331—111no—
250#331—111no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—42no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—81no—
257C22×C11—81no—
258C22×C11—81no—
259C22×C11#46312yes—
260C22×C11C2×#12111yescharacteristic
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—42no—
265C4×C11—81no—
266C4×C11#46312yes—
267C4×C11C2×#13511yescharacteristic
268C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
269C4×C11#57611yescharacteristic
270C4×C11#57711yescharacteristic
271Dic11—82no—
272C2×#41—21no—
273C2×#41—21no—
274C22×Q8—221no—
275C2×SD16—222no—
276C2×SD16—222no—
277C2×D8—22no—
278#131—444no—
279C2×M16—111no—
280C2×M16—111no—
281C2×M16—222no—
282C22×C8—21no—
283C22×C8—222no—
284C22×C8—221no—
285C4⋊Q8—112no—
286C4⋊Q8—221no—
287C4⋊Q8—221no—
288C4⋊Q8—221no—
289C4⋊Q8C22⋊D1111yescharacteristic
290C4⋊Q8C22×D1111yescharacteristic
291#127C22⋊D1111yescharacteristic
292#127C22×D1111yescharacteristic
293#124—21no—
294#124—21no—
295#121—21no—
296#121—21no—
297#121—21no—
298#121C22⋊D1112yes—
299C4×D4—21no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4C22×D1112yes—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—221no—
305C2×C42C22×D1111yescharacteristic
306#107—22no—
307C4⋊C8—21no—
308C4⋊C8—111no—
309C4⋊C8—111no—
310C4⋊C8—111no—
311C4⋊C8—111no—
312C4⋊C8—221no—
313C4⋊C8C22×D1112yes—
314#103—222no—
315#103—222no—
316#103—222no—
317#103—222no—
318#102—22no—
319#102—22no—
320#102—222no—
321#102—222no—
322C22⋊C8—222no—
323C22⋊C8—222no—
324C22⋊C8—221no—
325#97—112no—
326C4×C8—112no—
327C4×C8—221no—
328C2×C11—22no—
329C2×C11—82no—
330C2×C11—161no—
331C2×C11C2×#46311yescharacteristic
332C2×C11#306211yescharacteristic
333C2×C11#306911yescharacteristic
334#41—42no—
335#41—42no—
336#41—42no—
337#41—42no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—222no—
341C2×Q8—441no—
342C2×Q8—881no—
343C2×Q8—881no—
344C2×D4—22no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—41no—
351C2×D4C2×C22⋊D1112yes—
352C22×C4—22no—
353C22×C4—41no—
354C22×C4—441no—
355C22×C4D4×D1111yescharacteristic
356C22×C4#434111yescharacteristic
357C22×C4C2×C22⋊D1111yescharacteristic
358SD16—882no—
359SD16—882no—
360D8—82no—
361M16—222no—
362M16—222no—
363M16—444no—
364C2×C8—22no—
365C2×C8—81no—
366C2×C8—112no—
367C2×C8—112no—
368C2×C8—221no—
369C2×C8—221no—
370C2×C8—221no—
371C2×C8—221no—
372C2×C8—444no—
373C2×C8—442no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—222no—
378C4⋊C4—222no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C4⋊C4C2×C22⋊D1112yes—
382C22⋊C4—22no—
383C22⋊C4—22no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C42D4×D1111yescharacteristic
387C42#434111yescharacteristic
388C42C2×C22⋊D1111yescharacteristic
389C42C23×D1111yescharacteristic
390C11#1923711yescharacteristic, complemented, Sylow
391C23—22no—
392C23—41no—
393C23#6699211yescharacteristic
394Q8—42no—
395Q8—41no—
396Q8—41no—
397Q8—442no—
398Q8—442no—
399Q8—882no—
400D4—22no—
401D4—22no—
402D4—44no—
403D4—42no—
404D4—41no—
405D4—41no—
406D4—41no—
407D4—41no—
408D4—81no—
409D4—81no—
410D4—82no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—82no—
419C2×C4—442no—
420C2×C4—882no—
421C2×C4#6696412yes—
422C2×C4#6696512yes—
423C2×C4#6699211yescharacteristic
424C2×C4#6699211yescharacteristic
425C2×C4#6699211yescharacteristic
426C2×C4C2×D4×D1111yescharacteristic
427C2×C4C2×#434111yescharacteristic
428C2×C4C22×C22⋊D1111yescharacteristic
429C8—42no—
430C8—222no—
431C8—222no—
432C8—441no—
433C8—441no—
434C8—441no—
435C8—441no—
436C22—21no—
437C22—21no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22#1062276612yes—
445C22C2×#6699211yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—42no—
450C4—81no—
451C4—882no—
452C4#1062276612yes—
453C4C2×#6696411yescharacteristic
454C4C2×#6696511yescharacteristic
455C4#1062336611yescharacteristic
456C4#1062336811yescharacteristic
457C2—22no—
458C2—82no—
459C2—161no—
460C2C2×#1062276611yescharacteristic
461C2#1307829811yescharacteristic
462C2#1307835511yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3245C2
socleC22×C11C2×#121
hypercenter#3245D11
hypocenterC11#19237
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3245

Complements

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

NH ≅ G/Ntype
1. #13079538C2semidirect
2. #13079009C2semidirect
3. #13077360C2semidirect
4. #13068175C2semidirect
5. #13068161C2semidirect
6. #13068051C2semidirect
7. #13068037C2semidirect
8. #13067366C2semidirect
9. #13067265C2semidirect
10. C2×#10622120C2semidirect
390. C11#19237semidirect

Maximal subgroups

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

subgroupindex
#130795382
#130790092
#130773602
#130681752
#130681612
#130680512
#130680372
#130673662
#130672652
C2×#106221202
C11×#32452
#1923711