Finite Group Databasebeta

← #21447199

Subgroups — #21447199

Order 7808.

248 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#14519709C211yesmaximal, characteristic
2C2×#14519702C211yesmaximal, characteristic
3C2×#14519702C211yesmaximal, characteristic
4#16839668C211yesmaximal, characteristic
5#16839660C211yesmaximal, characteristic
6#16839525C211yesmaximal, characteristic
7C2×C4⋊C8×C61C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C2×C4⋊Dic61C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758196—21no—
13#14519709—22no—
14#14519702—22no—
15#14519702—22no—
16#14519684—21no—
17#14519684—21no—
18#14519684—21no—
19C22×C8×C61C2211yescharacteristic
20C22×C8×C61C2211yescharacteristic
21C2×C42×C61C2211yescharacteristic
22C4⋊C8×C61—22no—
23C22×C4×C61D411yescharacteristic
24C22×C4×C61D411yescharacteristic
25C22×C4×C61C2311yescharacteristic
26C22×Dic61—21no—
27C22×Dic61—21no—
28C22×Dic61—21no—
29C22×Dic61—21no—
30C2×Dic122—21no—
31C2×Dic122—21no—
32C2×Dic122—21no—
33C2×Dic122—21no—
34C2×Dic122—21no—
35C2×Dic122Q812yes—
36C2×C8×C61—21no—
37C2×C8×C61—21no—
38C2×C8×C61—21no—
39C2×C8×C61—21no—
40C2×C8×C61—21no—
41C2×C8×C61D412yes—
42C42×C61—21no—
43C42×C61—21no—
44C4⋊Dic61—21no—
45C4⋊Dic61—21no—
46C4⋊Dic61—21no—
47C4⋊Dic61—21no—
48C4⋊Dic61—21no—
49C4⋊Dic61D412yes—
50#11758196—42no—
51C23×C61C2×D411yescharacteristic
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61SD1612yes—
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×Q811yescharacteristic
61C2×C4×C61#4111yescharacteristic
62C2×C4×C61#4111yescharacteristic
63C2×C4×C61#4111yescharacteristic
64C2×Dic61—22no—
65C2×Dic61—22no—
66C2×Dic61—41no—
67C2×Dic61—41no—
68C2×Dic61—41no—
69C2×Dic61—41no—
70C2×Dic61—41no—
71C2×Dic61—41no—
72C2×Dic61—41no—
73C2×Dic61—41no—
74C2×Dic61—41no—
75C2×Dic61—41no—
76Dic122—22no—
77Dic122—22no—
78Dic122—41no—
79Dic122—41no—
80C8×C61—22no—
81C8×C61—41no—
82C22×C61#12111yescharacteristic
83C22×C61#12111yescharacteristic
84C22×C61C22⋊Q811yescharacteristic
85C22×C61C2×SD1611yescharacteristic
86C22×C61#13511yescharacteristic
87C22×C61#13711yescharacteristic
88C22×C61#13711yescharacteristic
89C4×C61—22no—
90C4×C61—41no—
91C4×C61#12111yescharacteristic
92C4×C61C22⋊Q811yescharacteristic
93C4×C61C22⋊Q811yescharacteristic
94C4×C61#12611yescharacteristic
95Dic61—42no—
96Dic61—42no—
97Dic61—81no—
98Dic61—81no—
99#2066—611nomaximal, Sylow
100C2×C61#39611yescharacteristic
101C2×C61#46111yescharacteristic
102C2×C61#46411yescharacteristic
103C2×C61#46511yescharacteristic
104C2×C61#47011yescharacteristic
105C2×C61#47511yescharacteristic
106C2×C61#47911yescharacteristic
107C2×#106—611no—
108C2×C4⋊C8D6111yescharacteristic
109C2×#103—611no—
110C2×#103—611no—
111#391—611no—
112#389—611no—
113#340—611no—
114C61#206611yescharacteristic, complemented, Sylow
115C22×Q8—611no—
116C22×C8C2×D6111yescharacteristic
117C22×C8C2×D6111yescharacteristic
118C2×C4⋊C4—611no—
119C2×C4⋊C4—611no—
120C2×C4⋊C4—611no—
121C2×C4⋊C4—1221no—
122C2×C42C2×D6111yescharacteristic
123#106—1222no—
124C4⋊C8—22no—
125#103—1222no—
126#103—1222no—
127#95—1221no—
128#95—1221no—
129#95—1221no—
130C2×Q8—612no—
131C2×Q8—1221no—
132C2×Q8—1221no—
133C2×Q8—1221no—
134C2×Q8—1221no—
135C2×Q8—1221no—
136C22×C4—1221no—
137C22×C4—1221no—
138C22×C4—1221no—
139C22×C4—1221no—
140C22×C4D24411yescharacteristic
141C22×C4D24411yescharacteristic
142C22×C4C22×D6111yescharacteristic
143C2×C8—21no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—21no—
148C2×C8C22⋊D6112yes—
149C4⋊C4—612no—
150C4⋊C4—1221no—
151C4⋊C4—1221no—
152C4⋊C4—1221no—
153C4⋊C4—1221no—
154C4⋊C4—1221no—
155C4⋊C4—2442no—
156C42—21no—
157C42—21no—
158C23C2×D24411yescharacteristic
159Q8—1222no—
160Q8—1222no—
161Q8—2441no—
162Q8—2441no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—1222no—
169C2×C4—1222no—
170C2×C4—2441no—
171C2×C4—2441no—
172C2×C4—2441no—
173C2×C4—2441no—
174C2×C4—2441no—
175C2×C4—2441no—
176C2×C4—2441no—
177C2×C4—2441no—
178C2×C4—2441no—
179C2×C4—2441no—
180C2×C4#1175819012yes—
181C2×C4#1175822211yescharacteristic
182C2×C4D4×D6111yescharacteristic
183C2×C4#1175822411yescharacteristic
184C2×C4Q8×D6111yescharacteristic
185C2×C4#1175822611yescharacteristic
186C2×C4C2×C22⋊D6111yescharacteristic
187C8—22no—
188C8—41no—
189C22#1451975111yescharacteristic
190C22#1451975211yescharacteristic
191C22#1451975711yescharacteristic
192C22C2×#1175819011yescharacteristic
193C22#1451979911yescharacteristic
194C22#1451981011yescharacteristic
195C22#1451981011yescharacteristic
196C4—22no—
197C4—41no—
198C4—4881no—
199C4—4881no—
200C4—2442no—
201C4—2442no—
202C4#1451974911yescharacteristic
203C4#1451975311yescharacteristic
204C4#1451975511yescharacteristic
205C4#1451977211yescharacteristic
206C2#1683968411yescharacteristic
207C2#1683996811yescharacteristic
208C2#1683998511yescharacteristic
209C2#1683999111yescharacteristic
210C2#1684002011yescharacteristic
211C2#1684004811yescharacteristic
212C2#1684007011yescharacteristic
subgroupG/H
centerC23C2×D244
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×C4⋊C8×C61C2
socleC23×C61C2×D4
hypercenterC2×C4⋊C8D61
hypocenterC61#2066
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
114. C61#2066semidirect