Finite Group Databasebeta

← #24907482

Subgroups — #24907482

Order 10624.

312 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 87 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#19128169C211yesmaximal, characteristic
2#19127724C211yesmaximal, characteristic, complemented
3C2×#14581720C211yesmaximal, characteristic
4C2×#14581718C211yesmaximal, characteristic
5C4×Dic83⋊C4C211yesmaximal, characteristic, complemented
6#19127460C211yesmaximal, characteristic, complemented
7#339×C83C211yesmaximal, characteristic, complemented
8C2×#13050590C2211yescharacteristic
9C2×#13050574C2211yescharacteristic
10#14581757C411yescharacteristic, complemented
11#14581757C411yescharacteristic, complemented
12#14581754C411yescharacteristic, complemented
13#14581754C411yescharacteristic, complemented
14(C22⋊D83)⋊C4—21no—
15(C22⋊D83)⋊C4—21no—
16#14581749—21no—
17C2×Dic83⋊C4—21no—
18C2×C4×Dic83C2211yescharacteristic
19C2×C4×Dic83C2211yescharacteristic
20C42×D83—21no—
21Dic83⋊C8—21no—
22Dic83⋊C8—21no—
23#14581720—22no—
24#14581718—22no—
25C83⋊#95—21no—
26C2×M16×C83C2211yescharacteristic
27#117×C83C2211yescharacteristic
28C2×C42×C83C2211yescharacteristic
29#13050590—21no—
30#13050590—21no—
31#13050590D412yes—
32#13050590Q812yes—
33C2×Dic166C2×C411yescharacteristic
34C2×D332C2×C411yescharacteristic
35C2×C22⋊D83—21no—
36C22×Dic83—21no—
37C22×Dic83D411yescharacteristic
38C22×Dic83D411yescharacteristic
39C2×C4×D83—21no—
40C2×C4×D83—21no—
41C2×C4×D83—21no—
42#13050574—21no—
43#13050574—21no—
44C2×C83⋊C8—21no—
45Dic83⋊C4—24no—
46Dic83⋊C4—21no—
47Dic83⋊C4—21no—
48(C2×D83)⋊C4—21no—
49(C2×D83)⋊C4—21no—
50C4×Dic83—21no—
51C4×Dic83—21no—
52C4×Dic83—21no—
53C4×Dic83—21no—
54C4×Dic83C2×C411yescharacteristic
55C4×Dic83C2×C411yescharacteristic
56C4×Dic83D411yescharacteristic
57C4×Dic83D411yescharacteristic
58C22×C4×C83—21no—
59C22×C4×C83C2311yescharacteristic
60M16×C83—21no—
61M16×C83—21no—
62C2×C8×C83—21no—
63C4⋊C4×C83C2×C411yescharacteristic
64C4⋊C4×C83C2×C411yescharacteristic
65C22⋊C4×C83—21no—
66C42×C83—21no—
67C42×C83—21no—
68C42×C83—21no—
69C23×C83C2×D411yescharacteristic
70C22×D83—21no—
71C2×C4×C83—22no—
72C2×C4×C83—21no—
73C2×C4×C83—21no—
74C2×C4×C83—41no—
75C2×C4×C83—41no—
76C2×C4×C83C22×C411yescharacteristic
77C2×C4×C83C2×D411yescharacteristic
78C2×C4×C83C2×D411yescharacteristic
79C2×C4×C83C2×Q811yescharacteristic
80C2×C4×C83#4111yescharacteristic
81C2×C4×C83#4111yescharacteristic
82C22⋊D83—22no—
83C22⋊D83—22no—
84C2×Dic83—21no—
85C2×Dic83—22no—
86C2×Dic83—22no—
87C2×Dic83—41no—
88C2×Dic83—41no—
89C2×Dic83—41no—
90C2×Dic83C22⋊C411yescharacteristic
91C2×Dic83C22⋊C411yescharacteristic
92C2×Dic83C22⋊C411yescharacteristic
93C2×Dic83C22⋊C411yescharacteristic
94D332—21no—
95D332C4⋊C412yescomplemented
96C4×D83—22no—
97C4×D83—22no—
98C4×D83—42no—
99C4×D83—42no—
100Dic166—21no—
101Dic166C4⋊C412yescomplemented
102C8×C83—41no—
103C83⋊C8—41no—
104C22×C83—21no—
105C22×C83—21no—
106C22×C83C2×C22⋊C411yescharacteristic
107C22×C83#12111yescharacteristic
108C22×C83C22⋊Q811yescharacteristic
109C2×D83—22no—
110C2×D83—41no—
111C2×D83—41no—
112C4×C83—42no—
113C4×C83—41no—
114C4×C83—41no—
115C4×C83C2×C4⋊C411yescharacteristic
116C4×C83#11711yescharacteristic
117C4×C83#12111yescharacteristic
118C4×C83C22⋊Q811yescharacteristic
119Dic83—22no—
120Dic83—21no—
121Dic83—21no—
122Dic83—21no—
123Dic83—42no—
124Dic83#10412yescomplemented
125C2×C83—21no—
126C2×C83—21no—
127C2×C83#38011yescharacteristic
128C2×C83C2×#10411yescharacteristic
129C2×C83#42111yescharacteristic
130D83—42no—
131#1806—831nomaximal, Sylow
132C83#180611yescharacteristic, complemented, Sylow
133C4×#41—831no—
134#423—831no—
135C2×#104—831no—
136C2×#104—831no—
137C4×C4⋊C4—831no—
138#339—831no—
139#339D8311yescharacteristic, complemented
140C2×#41—831no—
141C2×M16—831no—
142C2×M16C2×D8311yescharacteristic
143C4×Q8—831no—
144C4×Q8—831no—
145C4×D4—831no—
146C4×D4—831no—
147C4×D4—1661no—
148C4×D4—1661no—
149#117—1661no—
150#117C2×D8311yescharacteristic
151C2×C4⋊C4—1661no—
152C2×C42—831no—
153C2×C42—831no—
154C2×C42—1661no—
155C2×C42C2×D8311yescharacteristic
156C4⋊C8—1661no—
157C4⋊C8—1661no—
158#104—1662no—
159#104—1662no—
160#95—1661no—
161#41—832no—
162#41—832no—
163#41—1661no—
164#41—1661no—
165C2×Q8—831no—
166C2×D4—831no—
167C2×D4—1661no—
168C22×C4—21no—
169C22×C4—831no—
170C22×C4—831no—
171C22×C4—1661no—
172C22×C4—1661no—
173C22×C4—1661no—
174C22×C4—1661no—
175C22×C4C22×D8311yescharacteristic
176M16—21no—
177M16—21no—
178M16—1661no—
179M16—1661no—
180C2×C8—21no—
181C2×C8—1661no—
182C4⋊C4—1661no—
183C4⋊C4—1661no—
184C4⋊C4—1664no—
185C4⋊C4C4×D8311yescharacteristic
186C4⋊C4C4×D8311yescharacteristic
187C22⋊C4—21no—
188C22⋊C4—1661no—
189C22⋊C4—1661no—
190C42—21no—
191C42—21no—
192C42—21no—
193C42—831no—
194C42—831no—
195C42—831no—
196C42—831no—
197C42—1661no—
198C42—1661no—
199C42—1661no—
200C42—1661no—
201C23—1661no—
202C23D4×D8311yescharacteristic
203Q8—832no—
204Q8—1661no—
205D4—832no—
206D4—1662no—
207D4—1662no—
208D4—1661no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—3322no—
215C2×C4—3322no—
216C2×C4—3321no—
217C2×C4—3321no—
218C2×C4—3321no—
219C2×C4—831no—
220C2×C4—831no—
221C2×C4—831no—
222C2×C4—831no—
223C2×C4—1662no—
224C2×C4—1662no—
225C2×C4—1661no—
226C2×C4—1662no—
227C2×C4—1662no—
228C2×C4C2×C4×D8311yescharacteristic
229C2×C4D4×D8311yescharacteristic
230C2×C4D4×D8311yescharacteristic
231C2×C4Q8×D8311yescharacteristic
232C2×C4#1305059011yescharacteristic
233C2×C4#1305059011yescharacteristic
234C8—41no—
235C8—3321no—
236C22—21no—
237C22—21no—
238C22—3321no—
239C22—3321no—
240C22—1662no—
241C22C22⋊C4×D8311yescharacteristic
242C22#1458176511yescharacteristic
243C22#1458177011yescharacteristic
244C4—42no—
245C4—41no—
246C4—41no—
247C4—3322no—
248C4—832no—
249C4—1662no—
250C4—1661no—
251C4—1661no—
252C4—1661no—
253C4C4⋊C4×D8311yescharacteristic
254C4#1458174911yescharacteristic
255C4#1458176511yescharacteristic
256C4#1458177011yescharacteristic
257C2—21no—
258C2—21no—
259C2—3322no—
260C2#1912756011yescharacteristic
261C2#104×D8311yescharacteristic
262C2#1912771611yescharacteristic
subgroupG/H
centerC2×C4D4×D83
commutatorC2×C4×C83C22×C4
FrattiniC22×C4C22×D83
Fitting#339×C83C2
socleC22×C83C2×C22⋊C4
prime radicalC2×#13050590C22
cosocleC22×C4×C83C23
hypercenter#339D83
hypocenterC83#1806
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #19127724C2semidirect
5. C4×Dic83⋊C4C2semidirect
6. #19127460C2semidirect
7. #339×C83C2semidirect
10. #14581757C4semidirect
11. #14581757C4semidirect
12. #14581754C4semidirect
13. #14581754C4semidirect
95. D332C4⋊C4semidirect
101. Dic166C4⋊C4semidirect
124. Dic83#104semidirect
132. C83#1806semidirect
139. #339D83semidirect

Maximal subgroups

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

subgroupindex
#191281692
#191277242
C2×#145817202
C2×#145817182
C4×Dic83⋊C42
#191274602
#339×C832
#180683