Finite Group Databasebeta

← #24920140

Subgroups — #24920140

Order 10624.

336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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#19128431C211yesmaximal, characteristic
2#19128429C211yesmaximal, characteristic
3#19128053C211yesmaximal, characteristic
4#19128050C212yesmaximal
5#19127995C212yesmaximal
6#19127912C211yesmaximal, characteristic
7#19127910C212yesmaximal
8#19127825C211yesmaximal, characteristic
9#19127795C212yesmaximal
10C4×#13050580C211yesmaximal, characteristic
11#477×C83C211yesmaximal, characteristic
12C2×Dic332C2212yes—
13C2×#13050580C2211yescharacteristic
14#14581792C2211yescharacteristic
15#14581791—21no—
16#14581791C2212yes—
17#14581790—22no—
18#14581790C2212yes—
19#14581784—21no—
20#14581782—22no—
21C4×Dic166—21no—
22C4×Dic166C2211yescharacteristic
23C4×Dic166C2211yescharacteristic
24#14581757—21no—
25#14581757C2212yes—
26#14581757C2212yes—
27#14581725C2211yescharacteristic
28Dic83⋊C8C2212yes—
29#14581717C2212yes—
30#14581716C2211yescharacteristic
31#14581715C2212yes—
32#14581715C2211yescharacteristic
33#14581715C2212yes—
34C4×C83⋊C8C2211yescharacteristic
35C8×Dic83C2212yes—
36C4⋊Q8×C83C2211yescharacteristic
37C4×Q8×C83C2211yescharacteristic
38#107×C83C2212yes—
39C4⋊C8×C83C2211yescharacteristic
40#103×C83C2212yes—
41C2×Dic166—22no—
42C2×Dic166D411yescharacteristic
43C2×Dic166C2312yes—
44C2×Dic166C2311yescharacteristic
45Dic332—24no—
46#13050580—22no—
47C2×C83⋊C8C2311yescharacteristic
48C2×C83⋊C8C2311yescharacteristic
49C4⋊Dic83—21no—
50C4⋊Dic83—21no—
51C4⋊Dic83D411yescharacteristic
52C4⋊Dic83C2311yescharacteristic
53Dic83⋊C4—21no—
54Dic83⋊C4—22no—
55Dic83⋊C4—22no—
56Dic83⋊C4—22no—
57Dic83⋊C4—22no—
58Dic83⋊C4—22no—
59Dic83⋊C4D412yes—
60C4×Dic83—21no—
61C4×Dic83—22no—
62C4×Dic83—22no—
63C4×Dic83C2312yes—
64C2×Q8×C83—21no—
65C2×Q8×C83C2311yescharacteristic
66C2×C8×C83C2312yes—
67C4⋊C4×C83—21no—
68C4⋊C4×C83—21no—
69C4⋊C4×C83C2312yes—
70C4⋊C4×C83C2311yescharacteristic
71C42×C83—21no—
72C42×C83C2311yescharacteristic
73Q8×C83—21no—
74Q8×C83—21no—
75Q8×C83—81no—
76C2×C4×C83—21no—
77C2×C4×C83—21no—
78C2×C4×C83—22no—
79C2×C4×C83C2×D411yescharacteristic
80C2×C4×C83C2×D411yescharacteristic
81C2×C4×C83C2411yescharacteristic
82C2×Dic83—21no—
83C2×Dic83—22no—
84C2×Dic83—21no—
85C2×Dic83C2×D412yes—
86C2×Dic83C2×D412yes—
87Dic166—21no—
88Dic166—22no—
89Dic166—22no—
90Dic166—82no—
91Dic166Q1614yescomplemented
92Dic166#4112yes—
93C8×C83—22no—
94C83⋊C8—21no—
95C83⋊C8—21no—
96C22×C83C22×D411yescharacteristic
97C4×C83—21no—
98C4×C83—41no—
99C4×C83—42no—
100C4×C83—41no—
101C4×C83C2×Q1612yes—
102C4×C83C2×#4111yescharacteristic
103C4×C832−1+411yescharacteristic
104Dic83—22no—
105Dic83—22no—
106Dic83—42no—
107Dic83—41no—
108Dic83C2×Q1614yes—
109C2×C83#54811yescharacteristic
110C2×C83C22×Q1611yescharacteristic
111C2×C83#57711yescharacteristic
112#3363—831nomaximal, Sylow
113C83#336311yescharacteristic, complemented, Sylow
114Q82—831no—
115#557—831no—
116#487—831no—
117#487—832no—
118#477—832no—
119#477D8311yescharacteristic
120#462—831no—
121#462—832no—
122C8×Q8—831no—
123C4×Q16—831no—
124C4×Q16—832no—
125C2×Q16—831no—
126C2×Q16—832no—
127C4⋊Q8—832no—
128C4⋊Q8—832no—
129C4⋊Q8—831no—
130C4⋊Q8—1661no—
131C4⋊Q8—1662no—
132C4⋊Q8C2×D8311yescharacteristic
133#125—1661no—
134#125—1662no—
135C4×Q8—831no—
136C4×Q8—832no—
137C4×Q8—832no—
138C4×Q8—831no—
139C4×Q8—1661no—
140C4×Q8—1661no—
141C4×Q8C2×D8311yescharacteristic
142#107—831no—
143#107C2×D8312yes—
144C4⋊C8—832no—
145C4⋊C8C2×D8311yescharacteristic
146#103—831no—
147#103—832no—
148#103—831no—
149#103—832no—
150#103—832no—
151#103C2×D8312yes—
152C4×C8—832no—
153C4×C8—831no—
154C2×Q8—21no—
155C2×Q8—831no—
156C2×Q8—831no—
157C2×Q8—832no—
158C2×Q8—1662no—
159C2×Q8C22×D8311yescharacteristic
160Q16—1664no—
161Q16—1662no—
162C2×C8—831no—
163C2×C8—831no—
164C2×C8C22×D8312yes—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—832no—
168C4⋊C4—831no—
169C4⋊C4—831no—
170C4⋊C4—1662no—
171C4⋊C4—1662no—
172C4⋊C4—1662no—
173C4⋊C4—1662no—
174C4⋊C4—1662no—
175C4⋊C4—1661no—
176C4⋊C4—1661no—
177C4⋊C4—1661no—
178C4⋊C4C22×D8312yes—
179C4⋊C4C22×D8311yescharacteristic
180C42—21no—
181C42—832no—
182C42—1662no—
183C42—1662no—
184C42—1661no—
185C42C22×D8311yescharacteristic
186Q8—21no—
187Q8—21no—
188Q8—81no—
189Q8—834no—
190Q8—832no—
191Q8—6642no—
192Q8—1662no—
193Q8—1662no—
194Q8—1661no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—832no—
199C2×C4—832no—
200C2×C4—1661no—
201C2×C4—1662no—
202C2×C4—1661no—
203C2×C4D4×D8311yescharacteristic
204C2×C4D4×D8311yescharacteristic
205C2×C4C23×D8311yescharacteristic
206C8—22no—
207C8—1661no—
208C8—1661no—
209C22C2×D4×D8311yescharacteristic
210C4—21no—
211C4—41no—
212C4—42no—
213C4—41no—
214C4—3322no—
215C4—3321no—
216C4—834no—
217C4—1662no—
218C4—1662no—
219C4Q16×D8312yes—
220C4#41×D8311yescharacteristic
221C4#1458184011yescharacteristic
222C2#1912836111yescharacteristic
223C2C2×Q16×D8311yescharacteristic
224C2#1912851111yescharacteristic
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#477×C83C2
socle, prime radicalC22×C83C22×D4
hypercenter#477D83
hypocenterC83#3363
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
91. Dic166Q16semidirect
113. C83#3363semidirect

Maximal subgroups

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

subgroupindex
#191284312
#191284292
#191280532
#191280502
#191279952
#191279122
#191279102
#191278252
#191277952
C4×#130505802
#477×C832
#336383