Finite Group Databasebeta

← #35314308

Subgroups — #35314308

Order 21248.

322 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24916426C211yesmaximal, characteristic
2#24909264C211yesmaximal, characteristic, complemented
3#24909217C211yesmaximal, characteristic, complemented
4#24905446C211yesmaximal, characteristic, complemented
5#24905444C211yesmaximal, characteristic, complemented
6#24905421C211yesmaximal, characteristic, complemented
7C83×#1330C211yesmaximal, characteristic, complemented
8C4×#13050589C411yescharacteristic
9C2×#14581731—21no—
10#19127831C2211yescharacteristic
11#19127828C411yescharacteristic
12#19127779C411yescharacteristic
13#19127775—21no—
14#19127770—21no—
15#19127753C411yescharacteristic
16#19127751—21no—
17M16×Dic83—21no—
18C4×C8×D83C2211yescharacteristic
19C4⋊(C83⋊C16)C2211yescharacteristic
20Dic83⋊C16—21no—
21Dic83⋊C16—21no—
22(C2×D83)⋊C16—21no—
23#19127477C2211yescharacteristic
24#436×C83C2211yescharacteristic
25C4⋊C16×C83C2211yescharacteristic
26#346×C83C2211yescharacteristic
27C2×#13050589C811yescharacteristic
28C2×#13050574—21no—
29C2×C8×D83D411yescharacteristic
30C2×C8×D83D411yescharacteristic
31C4×Dic166C2×C411yescharacteristic
32#14581757C811yescharacteristic
33D4×Dic83C811yescharacteristic
34C4×C22⋊D83—21no—
35(C22⋊D83)⋊C4—21no—
36#14581750C811yescharacteristic
37#14581748—21no—
38C2×C4×Dic83—21no—
39C42×D83C2×C411yescharacteristic
40#14581731—42no—
41C2×C83⋊C16—21no—
42C2×C83⋊C16—21no—
43C4⋊(C83⋊C8)C2×C411yescharacteristic
44Dic83⋊C8—21no—
45Dic83⋊C8—21no—
46C22⋊(C83⋊C8)—21no—
47(C2×D83)⋊C8—21no—
48#14581702—21no—
49#14581702—21no—
50C4×C83⋊C8C2×C411yescharacteristic
51C8×Dic83—21no—
52C8×Dic83D411yescharacteristic
53C8×Dic83D411yescharacteristic
54C2×M16×C83—21no—
55C4×D4×C83C2×C411yescharacteristic
56C2×C16×C83—21no—
57C2×C16×C83—21no—
58C4⋊C8×C83C2×C411yescharacteristic
59C22⋊C8×C83—21no—
60C4×C8×C83C2311yescharacteristic
61#13050589—42no—
62C2×Dic166C2×C811yescharacteristic
63C2×C22⋊D83—21no—
64C22×Dic83—21no—
65C22×Dic83—21no—
66C2×C4×D83C22⋊C411yescharacteristic
67C2×C4×D83C2×C811yescharacteristic
68C2×C4×D83M1611yescharacteristic
69#13050574—42no—
70C2×C83⋊C8—21no—
71C2×C83⋊C8C22⋊C411yescharacteristic
72C2×C83⋊C8C22⋊C411yescharacteristic
73C8×D83—21no—
74C8×D83—21no—
75C8×D83—41no—
76C4⋊Dic83C2×C811yescharacteristic
77Dic83⋊C4—21no—
78Dic83⋊C4—21no—
79C22⋊Dic83—21no—
80(C2×D83)⋊C4—21no—
81C4×Dic83—21no—
82C4×Dic83—21no—
83C4×Dic83—21no—
84C4×Dic83C22⋊C411yescharacteristic
85C4×Dic83C2×C811yescharacteristic
86C4×Dic83M1611yescharacteristic
87C83⋊C16—41no—
88C83⋊C16—41no—
89C2×D4×C83C2×C811yescharacteristic
90C22×C4×C83—21no—
91M16×C83—41no—
92M16×C83—41no—
93C2×C8×C83—21no—
94C2×C8×C83C2×D411yescharacteristic
95C2×C8×C83C2×D411yescharacteristic
96C4⋊C4×C83C2×C811yescharacteristic
97C22⋊C4×C83—21no—
98C42×C83C22×C411yescharacteristic
99C16×C83—41no—
100C16×C83—41no—
101C23×C83—21no—
102C22×D83C22⋊C811yescharacteristic
103D4×C83—41no—
104C2×C4×C83—21no—
105C2×C4×C83—41no—
106C2×C4×C83—41no—
107C2×C4×C83C2×C22⋊C411yescharacteristic
108C2×C4×C83C22×C811yescharacteristic
109C2×C4×C83C2×M1611yescharacteristic
110C22⋊D83—42no—
111C2×Dic83—21no—
112C2×Dic83—21no—
113C2×Dic83—42no—
114C2×Dic83—42no—
115C2×Dic83C22⋊C811yescharacteristic
116C2×Dic83C22⋊C811yescharacteristic
117C2×Dic83C22⋊C811yescharacteristic
118C4×D83—21no—
119C4×D83—21no—
120C4×D83—22no—
121C4×D83—41no—
122Dic166—41no—
123C8×C83—21no—
124C8×C83—41no—
125C8×C83AGL(1,ℤ/8)11yescharacteristic
126C8×C83#13711yescharacteristic
127C83⋊C8—21no—
128C83⋊C8—21no—
129C83⋊C8—41no—
130C22×C83—41no—
131C22×C83—41no—
132C22×C83—41no—
133C22×C83C2×C22⋊C811yescharacteristic
134C2×D83—21no—
135C2×D83—21no—
136C2×D83—21no—
137C4×C83—21no—
138C4×C83—21no—
139C4×C83—41no—
140C4×C83#41711yescharacteristic
141C4×C83#42111yescharacteristic
142Dic83—21no—
143Dic83—21no—
144Dic83—41no—
145Dic83—41no—
146Dic83#34912yes—
147#11628—831nomaximal, Sylow
148C2×C83—81no—
149C2×C83#147711yescharacteristic
150C2×C83C2×#34911yescharacteristic
151C2×C83#211711yescharacteristic
152D83—41no—
153#2965—831no—
154#2163—831no—
155#2150—831no—
156#1338—831no—
157#1338—831no—
158#1330—831no—
159#1330D8311yescharacteristic, complemented
160C83#1162811yescharacteristic, complemented, Sylow
161C4×#41—831no—
162C2×M32—1661no—
163#446—831no—
164#446—831no—
165#436—831no—
166#436C2×D8311yescharacteristic
167#435—1661no—
168#435—1661no—
169#431—831no—
170#431—1661no—
171C4×M16—1661no—
172C2×C4×C8—831no—
173C4⋊C16—831no—
174C4⋊C16—1661no—
175C4⋊C16—1661no—
176C4⋊C16C2×D8311yescharacteristic
177C22⋊C16—1661no—
178#346—831no—
179#346C2×D8311yescharacteristic
180C2×#41—831no—
181C2×M16—21no—
182C2×M16—1661no—
183C22×C8—831no—
184C22×C8—831no—
185C4×Q8—831no—
186C4×Q8—831no—
187C4×D4—831no—
188C4×D4—1661no—
189C4×D4—1661no—
190C4×D4C4×D8311yescharacteristic
191#117—831no—
192#117—1661no—
193C2×C42—831no—
194C2×C42—1661no—
195M32—3322no—
196C2×C16—21no—
197C2×C16—21no—
198C2×C16—1661no—
199C2×C16—1661no—
200C4⋊C8—831no—
201C4⋊C8—1661no—
202C4⋊C8—1661no—
203C4⋊C8C4×D8311yescharacteristic
204C22⋊C8—21no—
205C22⋊C8—1661no—
206C22⋊C8—1661no—
207#97—1661no—
208#97—1661no—
209C4×C8—831no—
210C4×C8—831no—
211C4×C8—831no—
212C4×C8—1661no—
213C4×C8C22×D8311yescharacteristic
214#41—3322no—
215C2×Q8—831no—
216C2×D4—1661no—
217C2×D4C8×D8311yescharacteristic
218C22×C4—21no—
219C22×C4—831no—
220C22×C4—831no—
221C22×C4—831no—
222C22×C4—1661no—
223C22×C4—1661no—
224M16—41no—
225M16—41no—
226M16—3322no—
227C2×C8—21no—
228C2×C8—3321no—
229C2×C8—831no—
230C2×C8—831no—
231C2×C8—1661no—
232C2×C8—1661no—
233C2×C8—1661no—
234C2×C8D4×D8311yescharacteristic
235C2×C8D4×D8311yescharacteristic
236C4⋊C4—831no—
237C4⋊C4—1661no—
238C4⋊C4—1661no—
239C4⋊C4C8×D8311yescharacteristic
240C22⋊C4—21no—
241C22⋊C4—1661no—
242C22⋊C4—1661no—
243C42—831no—
244C42—831no—
245C42—831no—
246C42—1661no—
247C42—1661no—
248C42—1661no—
249C42C2×C4×D8311yescharacteristic
250C16—41no—
251C16—41no—
252C16—3321no—
253C16—3321no—
254C23—21no—
255C23—831no—
256Q8—3321no—
257D4—41no—
258D4—3322no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—3321no—
263C2×C4—3322no—
264C2×C4—3322no—
265C2×C4—831no—
266C2×C4—831no—
267C2×C4—831no—
268C2×C4—1662no—
269C2×C4—1661no—
270C2×C4—1661no—
271C2×C4—1661no—
272C2×C4—1661no—
273C2×C4C22⋊C4×D8311yescharacteristic
274C2×C4C2×C8×D8311yescharacteristic
275C2×C4M16×D8311yescharacteristic
276C8—21no—
277C8—41no—
278C8—3321no—
279C8—1661no—
280C8—1661no—
281C8#1458181611yescharacteristic
282C8#1458182111yescharacteristic
283C22—41no—
284C22—41no—
285C22—41no—
286C22—1661no—
287C22—1661no—
288C22—1661no—
289C22C22⋊C8×D8311yescharacteristic
290C4—21no—
291C4—21no—
292C4—41no—
293C4—3321no—
294C4—3321no—
295C4—832no—
296C4—1661no—
297C4—1661no—
298C4#1912769911yescharacteristic
299C4#1912771611yescharacteristic
300C2—81no—
301C2—3321no—
302C2#2490584711yescharacteristic
303C2#349×D8311yescharacteristic
304C2#2490908911yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D83
commutatorC2×C4×C83C22×C8
FrattiniC4×C8C22×D83
FittingC83×#1330C2
socleC22×C83C2×C22⋊C8
prime radicalC2×#13050589C8
cosocleC4×C8×C83C23
hypercenter#1330D83
hypocenterC83#11628
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1330

Complements

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

NH ≅ G/Ntype
2. #24909264C2semidirect
3. #24909217C2semidirect
4. #24905446C2semidirect
5. #24905444C2semidirect
6. #24905421C2semidirect
7. C83×#1330C2semidirect
159. #1330D83semidirect
160. C83#11628semidirect

Maximal subgroups

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

subgroupindex
#249164262
#249092642
#249092172
#249054462
#249054442
#249054212
C83×#13302
#1162883