Finite Group Databasebeta

← #24920492

Subgroups — #24920492

Order 10624.

350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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#19128429C211yesmaximal, characteristic, complemented
2#19128421C211yesmaximal, characteristic
3#19128092C212yesmaximal
4#19128081C211yesmaximal, characteristic, complemented
5#19127922C212yesmaximal
6#19127911C211yesmaximal, characteristic, complemented
7#19127910C212yesmaximal, complemented
8#19127906C211yesmaximal, characteristic
9#19127831C211yesmaximal, characteristic, complemented
10#19127807C212yesmaximal, complemented
11C4×SD16×C83C211yesmaximal, characteristic
12C2×Dic332C2212yes—
13C2×Dic332C2212yes—
14C2×#13050580C2212yes—
15C2×#13050578C2212yes—
16#14581792C2211yescharacteristic
17#14581792C2211yescharacteristic
18#14581790C2212yes—
19#14581785—22no—
20#14581784—21no—
21#14581782—22no—
22#14581779C2212yes—
23#14581771—21no—
24C4×Dic166—21no—
25C4×Dic166C2211yescharacteristic
26#14581757C2212yes—
27#14581757C2212yes—
28#14581751—21no—
29C4⋊(C83⋊C8)C2211yescharacteristic
30Dic83⋊C8C2212yes—
31#14581715C2212yes—
32#14581715C2212yes—
33#14581702C2212yes—
34C2×SD16×C83C2211yescharacteristic
35C4×Q8×C83C2211yescharacteristic
36C4×D4×C83C2211yescharacteristic
37#106×C83C2211yescharacteristic
38#103×C83C2211yescharacteristic
39#102×C83C2211yescharacteristic
40C4×C8×C83C2211yescharacteristic
41C2×Dic166D411yescharacteristic
42C2×Dic166C2312yes—
43C2×Dic166C2312yes—
44Dic332—24no—
45Dic332—42no—
46#13050580—42no—
47#13050578—42no—
48C2×C83⋊C8C2312yes—
49C4⋊Dic83—21no—
50C4⋊Dic83—21no—
51C4⋊Dic83—21no—
52C4⋊Dic83—21no—
53C4⋊Dic83D411yescharacteristic
54Dic83⋊C4—22no—
55Dic83⋊C4—22no—
56Dic83⋊C4—22no—
57Dic83⋊C4—22no—
58Dic83⋊C4D412yes—
59C22⋊Dic83—22no—
60C22⋊Dic83—22no—
61C4×Dic83—22no—
62C4×Dic83—22no—
63C4×Dic83C2312yes—
64C2×Q8×C83C2311yescharacteristic
65C2×D4×C83C2311yescharacteristic
66C22×C4×C83—21no—
67SD16×C83—22no—
68C2×C8×C83C2311yescharacteristic
69C2×C8×C83C2311yescharacteristic
70C4⋊C4×C83—21no—
71C4⋊C4×C83C2311yescharacteristic
72C4⋊C4×C83C2311yescharacteristic
73C22⋊C4×C83—21no—
74C42×C83—21no—
75C42×C83C2311yescharacteristic
76C23×C83—21no—
77Q8×C83—21no—
78Q8×C83—21no—
79D4×C83—21no—
80D4×C83—21no—
81C2×C4×C83—21no—
82C2×C4×C83—21no—
83C2×C4×C83—21no—
84C2×C4×C83—42no—
85C2×C4×C83C2×D411yescharacteristic
86C2×C4×C83C2×D411yescharacteristic
87C2×C4×C83C2411yescharacteristic
88C2×Dic83—22no—
89C2×Dic83—22no—
90C2×Dic83C2×D412yes—
91C2×Dic83C2×D412yes—
92Dic166—22no—
93Dic166—22no—
94Dic166—22no—
95Dic166—22no—
96Dic166—22no—
97C8×C83—21no—
98C8×C83#4112yes—
99C83⋊C8—22no—
100C22×C83—41no—
101C22×C83—41no—
102C22×C83—41no—
103C22×C83C22×D411yescharacteristic
104C4×C83—21no—
105C4×C83—41no—
106C4×C83—41no—
107C4×C83—41no—
108C4×C83#13712yes—
109C4×C83C2×#4111yescharacteristic
110C4×C83H(5,𝔽2)11yescharacteristic
111Dic83—22no—
112Dic83—22no—
113Dic83—42no—
114Dic83—42no—
115C2×C83—81no—
116C2×C83#55011yescharacteristic
117C2×C83C2×#13711yescharacteristic
118C2×C83#57811yescharacteristic
119#3398—831nomaximal, Sylow
120C83#339811yescharacteristic, complemented, Sylow
121#557—831no—
122#556—831no—
123#497—832no—
124#494—831no—
125#464—832no—
126#462—831no—
127#462—832no—
128#461—831no—
129#446—831no—
130#441—832no—
131C4×SD16D8311yescharacteristic
132C2×Q16—832no—
133C2×Q16—832no—
134C2×Q16—832no—
135C2×SD16—832no—
136C2×SD16C2×D8311yescharacteristic
137C4⋊Q8—832no—
138C4⋊Q8—831no—
139C4⋊Q8—831no—
140#126—1662no—
141#125—1661no—
142#125—1662no—
143#124—832no—
144C22⋊Q8—1661no—
145C4×Q8—831no—
146C4×Q8—832no—
147C4×Q8—832no—
148C4×Q8—1661no—
149C4×Q8C2×D8311yescharacteristic
150C4×D4C2×D8311yescharacteristic
151#117—1661no—
152#106C2×D8311yescharacteristic
153C4⋊C8—832no—
154C4⋊C8—831no—
155#103—832no—
156#103—832no—
157#103C2×D8311yescharacteristic
158#102C2×D8311yescharacteristic
159#97—832no—
160C4×C8C2×D8311yescharacteristic
161C2×Q8—831no—
162C2×Q8—832no—
163C2×Q8—832no—
164C2×Q8C22×D8311yescharacteristic
165C2×D4C22×D8311yescharacteristic
166C22×C4—21no—
167Q16—3322no—
168Q16—3322no—
169Q16—1664no—
170SD16—22no—
171SD16—3322no—
172C2×C8—832no—
173C2×C8C22×D8311yescharacteristic
174C2×C8C22×D8311yescharacteristic
175C4⋊C4—21no—
176C4⋊C4—831no—
177C4⋊C4—832no—
178C4⋊C4—1662no—
179C4⋊C4—1662no—
180C4⋊C4—1662no—
181C4⋊C4—1662no—
182C4⋊C4—1661no—
183C4⋊C4—1661no—
184C4⋊C4—1661no—
185C4⋊C4—1661no—
186C4⋊C4C22×D8311yescharacteristic
187C4⋊C4C22×D8311yescharacteristic
188C22⋊C4—21no—
189C22⋊C4—1662no—
190C22⋊C4—1662no—
191C42—21no—
192C42—832no—
193C42—1662no—
194C42—1662no—
195C42C22×D8311yescharacteristic
196C23—21no—
197Q8—21no—
198Q8—21no—
199Q8—1662no—
200Q8—1662no—
201Q8—1662no—
202Q8—1662no—
203Q8—1662no—
204D4—21no—
205D4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—42no—
210C2×C4—832no—
211C2×C4—832no—
212C2×C4—1662no—
213C2×C4—1662no—
214C2×C4D4×D8311yescharacteristic
215C2×C4D4×D8311yescharacteristic
216C2×C4C23×D8311yescharacteristic
217C8—21no—
218C8—1662no—
219C8#1305059012yes—
220C22—41no—
221C22—41no—
222C22—41no—
223C22C2×D4×D8311yescharacteristic
224C4—21no—
225C4—41no—
226C4—41no—
227C4—41no—
228C4—3322no—
229C4—3322no—
230C4—1662no—
231C4—1662no—
232C4#1458182112yes—
233C4C2×#1305059011yescharacteristic
234C4#1458183811yescharacteristic
235C2—81no—
236C2#1912837211yescharacteristic
237C2C2×#1458182111yescharacteristic
238C2#1912851511yescharacteristic
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC4×SD16×C83C2
socleC22×C83C22×D4
prime radicalC2×D4×C83C23
hypercenterC4×SD16D83
hypocenterC83#3398
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #19128429C2semidirect
4. #19128081C2semidirect
6. #19127911C2semidirect
7. #19127910C2semidirect
9. #19127831C2semidirect
10. #19127807C2semidirect
120. C83#3398semidirect

Maximal subgroups

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

subgroupindex
#191284292
#191284212
#191280922
#191280812
#191279222
#191279112
#191279102
#191279062
#191278312
#191278072
C4×SD16×C832
#339883