Finite Group Databasebeta

← #21447201

Subgroups — #21447201

Order 7808.

248 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14519708C211yesmaximal, characteristic
2C2×#14519706C211yesmaximal, characteristic
3C2×#14519702C211yesmaximal, characteristic
4C2×#14519700C211yesmaximal, characteristic
5#16839667C211yesmaximal, characteristic
6#16839658C211yesmaximal, characteristic
7C61×#340C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×#11758196—21no—
12C2×C4×Dic61C2211yescharacteristic
13#14519708—22no—
14#14519706—22no—
15#14519702—22no—
16#14519700—22no—
17#14519684—21no—
18#14519684—21no—
19#14519684—21no—
20C22×C8×C61C2211yescharacteristic
21C2×C4⋊C4×C61C2211yescharacteristic
22C2×C4⋊C4×C61C2211yescharacteristic
23C22×C4×C61—21no—
24C22×C4×C61—21no—
25C22×C4×C61C2311yescharacteristic
26C22×Dic61—21no—
27C22×Dic61—21no—
28C22×Dic61D411yescharacteristic
29C22×Dic61D411yescharacteristic
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—
39C4⋊C4×C61—21no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61—21no—
42C4⋊C4×C61—21no—
43C4⋊Dic61—21no—
44C4⋊Dic61D412yes—
45#11758196—42no—
46C4×Dic61—21no—
47C4×Dic61—21no—
48C2×#92418—21no—
49C2×#92418—21no—
50C2×#92418D412yes—
51C23×C61C2×D411yescharacteristic
52C2×C4×C61—41no—
53C2×C4×C61—41no—
54C2×C4×C61—41no—
55C2×C4×C61—41no—
56C2×C4×C61—41no—
57C2×C4×C61—41no—
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—21no—
65C2×Dic61—21no—
66C2×Dic61—21no—
67C2×Dic61—22no—
68C2×Dic61—22no—
69C2×Dic61—21no—
70C2×Dic61—21no—
71C2×Dic61—41no—
72C2×Dic61—41no—
73C2×Dic61—41no—
74C2×Dic61—41no—
75C2×Dic61SD1612yes—
76Dic122—22no—
77Dic122—22no—
78Dic122—41no—
79Dic122—41no—
80C8×C61—41no—
81#92418—22no—
82C22×C61#12111yescharacteristic
83C22×C61#12111yescharacteristic
84C22×C61C22⋊Q811yescharacteristic
85C22×C61C2×SD1611yescharacteristic
86C22×C61#13511yescharacteristic
87C22×C61#13711yescharacteristic
88C22×C61#13711yescharacteristic
89C4×C61—81no—
90C4×C61—81no—
91C4×C61#12111yescharacteristic
92C4×C61C22⋊Q811yescharacteristic
93C4×C61C22⋊Q811yescharacteristic
94C4×C61#12611yescharacteristic
95Dic61—22no—
96Dic61—42no—
97Dic61—42no—
98Dic61—41no—
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⋊C8—611no—
109C2×#103—611no—
110C2×#103—611no—
111#391—611no—
112#389—611no—
113#340D6111yescharacteristic
114C61#206611yescharacteristic, complemented, Sylow
115C22×Q8—611no—
116C22×C8—611no—
117C22×C8C2×D6111yescharacteristic
118C2×C4⋊C4—611no—
119C2×C4⋊C4—1221no—
120C2×C4⋊C4C2×D6111yescharacteristic
121C2×C4⋊C4C2×D6111yescharacteristic
122C2×C42—611no—
123#106—1222no—
124C4⋊C8—1222no—
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—21no—
137C22×C4—21no—
138C22×C4—611no—
139C22×C4—611no—
140C22×C4—1221no—
141C22×C4—1221no—
142C22×C4C22×D6111yescharacteristic
143C2×C8—21no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—612no—
147C2×C8—1221no—
148C2×C8—1221no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—612no—
154C4⋊C4—1221no—
155C4⋊C4—2442no—
156C42—1221no—
157C42—1221no—
158C23D4×D6111yescharacteristic
159Q8—1222no—
160Q8—1222no—
161Q8—2441no—
162Q8—2441no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—612no—
170C2×C4—1221no—
171C2×C4—1221no—
172C2×C4—1221no—
173C2×C4—1221no—
174C2×C4—1222no—
175C2×C4—1222no—
176C2×C4—1221no—
177C2×C4—2441no—
178C2×C4—2441no—
179C2×C4—2441no—
180C2×C4—2441no—
181C2×C4#1175822211yescharacteristic
182C2×C4#1175822211yescharacteristic
183C2×C4#1175822211yescharacteristic
184C2×C4D4×D6111yescharacteristic
185C2×C4D4×D6111yescharacteristic
186C2×C4Q8×D6111yescharacteristic
187C8—41no—
188C8—1222no—
189C22#1451975011yescharacteristic
190C22#1451975011yescharacteristic
191C22#1451975511yescharacteristic
192C22SD16×D6111yescharacteristic
193C22#1451979611yescharacteristic
194C22#1451980611yescharacteristic
195C22#1451980911yescharacteristic
196C4—81no—
197C4—81no—
198C4—1222no—
199C4—2442no—
200C4—2442no—
201C4—2441no—
202C4#1451975011yescharacteristic
203C4#1451975511yescharacteristic
204C4#1451975511yescharacteristic
205C4#1451977111yescharacteristic
206C2#1683968611yescharacteristic
207C2#1683996611yescharacteristic
208C2#1683998311yescharacteristic
209C2#1683999011yescharacteristic
210C2#1684001911yescharacteristic
211C2#1684004611yescharacteristic
212C2#1684006811yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#340C2
socleC23×C61C2×D4
hypercenter#340D61
hypocenterC61#2066
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
114. C61#2066semidirect