Finite Group Databasebeta

← #35303759

Subgroups — #35303759

Order 21248.

394 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24917973C211yesmaximal, characteristic
2#24907332C211yesmaximal, characteristic
3#24906209C211yesmaximal, characteristic
4#24905961C211yesmaximal, characteristic
5#24905867C211yesmaximal, characteristic
6#24905866C211yesmaximal, characteristic
7C83×#1503C211yesmaximal, characteristic
8#19128258C2211yescharacteristic
9#19128104C411yescharacteristic, complemented
10#19128104C411yescharacteristic, complemented
11#19128100—21no—
12#19128100—21no—
13#19128097C411yescharacteristic, complemented
14#19128097C411yescharacteristic, complemented
15#19127754C2211yescharacteristic
16#19127737—21no—
17#19127737—21no—
18C2×C4⋊(C83⋊C8)C2211yescharacteristic
19C2×#14581703—21no—
20C2×C4×C83⋊C8C2211yescharacteristic
21#19127456—21no—
22#19127453—21no—
23#19127451—21no—
24#19127437—22no—
25#19127433—22no—
26Q8⋊(C83⋊C8)—22no—
27#533×C83C2211yescharacteristic
28#431×C83C2211yescharacteristic
29C4×C4⋊C4×C83C2211yescharacteristic
30#328×C83—22no—
31C22×C83⋊C8—21no—
32C22×C83⋊C8D411yescharacteristic
33C22×C83⋊C8D411yescharacteristic
34#14581792C2×C411yescharacteristic
35#14581792C2×C411yescharacteristic
36#14581784—21no—
37#14581771—21no—
38#14581771—21no—
39C4×Dic166—21no—
40C4×Dic166—21no—
41#14581751—21no—
42#14581725—21no—
43#14581725—21no—
44#14581725—21no—
45#14581725—21no—
46#14581723—21no—
47#14581723—21no—
48#14581723—21no—
49#14581723—21no—
50C4⋊(C83⋊C8)—21no—
51C4⋊(C83⋊C8)—21no—
52C4⋊(C83⋊C8)D412yes—
53C22⋊(C83⋊C8)—21no—
54#14581703—42no—
55C4×C83⋊C8—21no—
56C4×C83⋊C8C2×C411yescharacteristic
57C4×C83⋊C8C2×C411yescharacteristic
58C4×C83⋊C8D411yescharacteristic
59C4×C83⋊C8D411yescharacteristic
60C4⋊Q8×C83C2×C411yescharacteristic
61C4⋊Q8×C83C2×C411yescharacteristic
62#125×C83—21no—
63C22⋊Q8×C83—21no—
64C22⋊Q8×C83—21no—
65C4×Q8×C83—21no—
66C4×Q8×C83—21no—
67#117×C83—21no—
68C2×C4⋊C4×C83—21no—
69C2×C42×C83—21no—
70C2×C42×C83C2311yescharacteristic
71C4⋊C8×C83—21no—
72C22⋊C8×C83—21no—
73C4×C8×C83—21no—
74#95×C83D412yes—
75C2×Dic166—21no—
76C2×Dic166—21no—
77C2×C83⋊C8—21no—
78C2×C83⋊C8—21no—
79C2×C83⋊C8—22no—
80C2×C83⋊C8—41no—
81C2×C83⋊C8—41no—
82C2×C83⋊C8—41no—
83C2×C83⋊C8C22⋊C411yescharacteristic
84C2×C83⋊C8C22⋊C411yescharacteristic
85C2×C83⋊C8C22⋊C411yescharacteristic
86C2×C83⋊C8C22⋊C411yescharacteristic
87C2×C83⋊C8SD1612yes—
88C2×C83⋊C8Q1612yes—
89C4⋊Dic83—21no—
90C4⋊Dic83—21no—
91C4⋊Dic83—21no—
92C4⋊Dic83—21no—
93Dic83⋊C4—41no—
94Dic83⋊C4—41no—
95C22⋊Dic83—41no—
96C4×Dic83—41no—
97C2×Q8×C83—21no—
98C2×Q8×C83—21no—
99C22×C4×C83—22no—
100C22×C4×C83C2×D411yescharacteristic
101C22×C4×C83C2×D411yescharacteristic
102C22×C4×C83#4111yescharacteristic
103C2×C8×C83—41no—
104C4⋊C4×C83—21no—
105C4⋊C4×C83—21no—
106C4⋊C4×C83—21no—
107C4⋊C4×C83—21no—
108C4⋊C4×C83—42no—
109C4⋊C4×C83—41no—
110C4⋊C4×C83—41no—
111C22⋊C4×C83—41no—
112C42×C83—41no—
113C42×C83—41no—
114C42×C83—41no—
115C42×C83C22×C411yescharacteristic
116C42×C83C2×D411yescharacteristic
117C42×C83C2×D411yescharacteristic
118C42×C83#4111yescharacteristic
119C23×C83#12111yescharacteristic
120Q8×C83—42no—
121Q8×C83—81no—
122C2×C4×C83—22no—
123C2×C4×C83—41no—
124C2×C4×C83—42no—
125C2×C4×C83—42no—
126C2×C4×C83—41no—
127C2×C4×C83—41no—
128C2×C4×C83—42no—
129C2×C4×C83C2×C22⋊C411yescharacteristic
130C2×C4×C83C4×D411yescharacteristic
131C2×C4×C83C4×D411yescharacteristic
132C2×C4×C83#12111yescharacteristic
133C2×C4×C83#12411yescharacteristic
134C2×C4×C83#12711yescharacteristic
135C2×C4×C83C2×SD1611yescharacteristic
136C2×C4×C83C2×Q1611yescharacteristic
137C2×C4×C83#13711yescharacteristic
138C2×C4×C83#13711yescharacteristic
139C2×Dic83—41no—
140C2×Dic83—41no—
141Dic166—42no—
142Dic166—81no—
143C8×C83—81no—
144C83⋊C8—21no—
145C83⋊C8—21no—
146C83⋊C8—42no—
147C83⋊C8—81no—
148C83⋊C8#10312yes—
149C83⋊C8#10312yes—
150C22×C83—21no—
151C22×C83—21no—
152C22×C83#39011yescharacteristic
153C22×C83#46111yescharacteristic
154C22×C83#46211yescharacteristic
155C4×C83—21no—
156C4×C83—21no—
157C4×C83—21no—
158C4×C83—82no—
159C4×C83—81no—
160C4×C83—81no—
161C4×C83C2×#10311yescharacteristic
162C4×C83#41911yescharacteristic
163C4×C83#44412yes—
164C4×C83#46111yescharacteristic
165C4×C83#46211yescharacteristic
166Dic83—81no—
167Dic83—81no—
168#9752—831nomaximal, Sylow
169C2×C83—21no—
170C2×C83—21no—
171C2×C83#197511yescharacteristic
172C2×C83#197611yescharacteristic
173C2×C83#198111yescharacteristic
174#3160—831no—
175#1770—831no—
176#1564—831no—
177#1503—831no—
178#1503D8311yescharacteristic
179#1481—831no—
180#1481—831no—
181C83#975211yescharacteristic, complemented, Sylow
182#533—831no—
183#533C2×D8311yescharacteristic
184#500—831no—
185#500—831no—
186#499—1661no—
187#499—1661no—
188#498—831no—
189#498—831no—
190#431—831no—
191#431C2×D8311yescharacteristic
192#427—1661no—
193#427—1661no—
194C2×C4⋊C8—831no—
195C2×#97—1661no—
196C2×C4×C8—831no—
197C4×C4⋊C4C2×D8311yescharacteristic
198#336—1661no—
199#335—1661no—
200#334—1661no—
201#328—22no—
202#328—1662no—
203Q8⋊C8—1662no—
204Q8⋊C8—1662no—
205C22×C8—831no—
206C22×C8—831no—
207C22×C8—1661no—
208C4⋊Q8—831no—
209C4⋊Q8—831no—
210C4⋊Q8C4×D8311yescharacteristic
211C4⋊Q8C4×D8311yescharacteristic
212#125—21no—
213#125—1661no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216C22⋊Q8—1661no—
217C22⋊Q8—1661no—
218C4×Q8—21no—
219C4×Q8—21no—
220C4×Q8—1661no—
221C4×Q8—1661no—
222#117—21no—
223#117—1661no—
224C2×C4⋊C4—21no—
225C2×C42—21no—
226C2×C42C22×D8311yescharacteristic
227#107—1661no—
228#107—1661no—
229#107—1661no—
230#107—1661no—
231#106—1661no—
232#106—1661no—
233#106—1661no—
234#106—1661no—
235C4⋊C8—21no—
236C4⋊C8—832no—
237C4⋊C8—1661no—
238C4⋊C8—1661no—
239C22⋊C8—21no—
240C22⋊C8—1661no—
241#97—3322no—
242C4×C8—21no—
243C4×C8—831no—
244C4×C8—831no—
245C4×C8—831no—
246C4×C8—831no—
247C4×C8—1661no—
248#95C22⋊D8312yes—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—1661no—
252C2×Q8—1661no—
253C22×C4—22no—
254C22×C4D4×D8311yescharacteristic
255C22×C4C2×C22⋊D8311yescharacteristic
256C22×C4#1305058911yescharacteristic
257C2×C8—41no—
258C2×C8—3321no—
259C2×C8—3321no—
260C2×C8—3321no—
261C2×C8—832no—
262C2×C8—832no—
263C2×C8—831no—
264C2×C8—831no—
265C2×C8—831no—
266C2×C8—831no—
267C2×C8—1662no—
268C2×C8—1661no—
269C2×C8—1661no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—42no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—3321no—
278C4⋊C4—3321no—
279C4⋊C4—1661no—
280C4⋊C4—1661no—
281C4⋊C4—1661no—
282C4⋊C4—1661no—
283C22⋊C4—41no—
284C22⋊C4—3321no—
285C42—41no—
286C42—41no—
287C42—41no—
288C42—3321no—
289C42C2×C4×D8311yescharacteristic
290C42D4×D8311yescharacteristic
291C42D4×D8311yescharacteristic
292C42#1305059011yescharacteristic
293C23#1458176411yescharacteristic
294Q8—42no—
295Q8—81no—
296Q8—3322no—
297Q8—6641no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—3321no—
306C2×C4—3321no—
307C2×C4C22⋊C4×D8311yescharacteristic
308C2×C4(C22⋊D83)⋊C411yescharacteristic
309C2×C4C4×C22⋊D8311yescharacteristic
310C2×C4#1458176511yescharacteristic
311C2×C4#1458177811yescharacteristic
312C2×C4#1458178811yescharacteristic
313C2×C4SD16×D8311yescharacteristic
314C2×C4Q16×D8311yescharacteristic
315C2×C4#1458182111yescharacteristic
316C2×C4#1458182411yescharacteristic
317C8—81no—
318C8—3322no—
319C8—832no—
320C8—832no—
321C8—6641no—
322C8—1661no—
323C8—1661no—
324C22—21no—
325C22—21no—
326C22#1912760111yescharacteristic
327C22#1912790411yescharacteristic
328C22#1912790911yescharacteristic
329C4—21no—
330C4—21no—
331C4—21no—
332C4—82no—
333C4—81no—
334C4—81no—
335C4—6641no—
336C4—6641no—
337C4#103×D8311yescharacteristic
338C4#1912770811yescharacteristic
339C4#1912782012yes—
340C4#1912790511yescharacteristic
341C4#1912791011yescharacteristic
342C2—21no—
343C2—21no—
344C2#2490835311yescharacteristic
345C2#2490835811yescharacteristic
346C2#2490838411yescharacteristic
subgroupG/H
centerC2×C4#14581765
commutatorC42×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1503C2
socleC22×C83#390
prime radicalC23×C83#121
cosocleC2×C42×C83C23
hypercenter#1503D83
hypocenterC83#9752
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
9. #19128104C4semidirect
10. #19128104C4semidirect
13. #19128097C4semidirect
14. #19128097C4semidirect
181. C83#9752semidirect

Maximal subgroups

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

subgroupindex
#249179732
#249073322
#249062092
#249059612
#249058672
#249058662
C83×#15032
#975283