Finite Group Databasebeta

← #21447211

Subgroups — #21447211

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×#14519710C211yesmaximal, characteristic
2C2×C4⋊#92418C211yesmaximal, characteristic
3C2×#14519700C211yesmaximal, characteristic
4C2×#14519700C211yesmaximal, characteristic
5#16839668C211yesmaximal, characteristic
6#16839524C211yesmaximal, characteristic
7C61×#389C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10C22×#92418C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12#14519710—22no—
13C4⋊#92418—22no—
14#14519700—22no—
15#14519700—22no—
16#14519684—21no—
17#14519684—21no—
18C2×C4⋊C4×C61—21no—
19C2×C4⋊C4×C61C2211yescharacteristic
20C2×C4⋊C4×C61C2211yescharacteristic
21C2×C42×C61C2211yescharacteristic
22#95×C61—21no—
23C22×C4×C61—21no—
24C22×C4×C61—21no—
25C22×C4×C61D411yescharacteristic
26C22×C4×C61D411yescharacteristic
27C22×C4×C61C2311yescharacteristic
28C22×Dic61—21no—
29C22×Dic61—21no—
30C2×Dic122—21no—
31C2×Dic122—21no—
32C2×Dic122—21no—
33C2×Dic122—21no—
34C2×Dic122—21no—
35C2×Dic122Q812yes—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61—21no—
39C4⋊C4×C61—42no—
40C4⋊C4×C61D412yes—
41C42×C61—21no—
42C42×C61—21no—
43C4⋊Dic61—21no—
44C4⋊Dic61—21no—
45C2×#92418—21no—
46C2×#92418—21no—
47C2×#92418—21no—
48C2×#92418—21no—
49C2×#92418—21no—
50C2×#92418D412yes—
51C23×C61C2×D411yescharacteristic
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—22no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—41no—
59C2×C4×C61—41no—
60C2×C4×C61—41no—
61C2×C4×C61—41no—
62C2×C4×C61—41no—
63C2×C4×C61Q1612yes—
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×Q811yescharacteristic
67C2×C4×C61#4111yescharacteristic
68C2×C4×C61#4111yescharacteristic
69C2×C4×C61#4111yescharacteristic
70C2×Dic61—22no—
71C2×Dic61—41no—
72C2×Dic61—41no—
73C2×Dic61—41no—
74C2×Dic61—41no—
75C2×Dic61—41no—
76Dic122—22no—
77Dic122—22no—
78Dic122—41no—
79Dic122—41no—
80#92418—22no—
81#92418—41no—
82C22×C61#12111yescharacteristic
83C22×C61#12111yescharacteristic
84C22×C61C22⋊Q811yescharacteristic
85C22×C61C2×Q1611yescharacteristic
86C22×C61#13511yescharacteristic
87C22×C61AGL(1,ℤ/8)11yescharacteristic
88C22×C61#13711yescharacteristic
89C4×C61—22no—
90C4×C61—42no—
91C4×C61—41no—
92C4×C61—81no—
93C4×C61#12111yescharacteristic
94C4×C61C22⋊Q811yescharacteristic
95C4×C61C22⋊Q811yescharacteristic
96C4×C61#12611yescharacteristic
97Dic61—42no—
98Dic61—81no—
99#2068—611nomaximal, Sylow
100C2×C61#39611yescharacteristic
101C2×C61#46211yescharacteristic
102C2×C61#46311yescharacteristic
103C2×C61#46711yescharacteristic
104C2×C61#46811yescharacteristic
105C2×C61#47711yescharacteristic
106C2×C61#47911yescharacteristic
107C2×#107—611no—
108C2×C4⋊C8—611no—
109C2×#103—611no—
110C2×#103—611no—
111#391—611no—
112#389D6111yescharacteristic
113#340—611no—
114C61#206811yescharacteristic, complemented, Sylow
115C22×Q8—611no—
116C22×C8—611no—
117C22×C8—611no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—611no—
120C2×C4⋊C4C2×D6111yescharacteristic
121C2×C4⋊C4C2×D6111yescharacteristic
122C2×C42C2×D6111yescharacteristic
123#107—1222no—
124C4⋊C8—1222no—
125#103—1222no—
126#103—1222no—
127#95—21no—
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—1221no—
139C22×C4—1221no—
140C22×C4C22⋊D6111yescharacteristic
141C22×C4C22⋊D6111yescharacteristic
142C22×C4C22×D6111yescharacteristic
143C2×C8—612no—
144C2×C8—1221no—
145C2×C8—1221no—
146C2×C8—1221no—
147C2×C8—1221no—
148C2×C8—1221no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—42no—
153C4⋊C4—1221no—
154C4⋊C4—1221no—
155C4⋊C4D24412yes—
156C42—21no—
157C42—21no—
158C23C2×C22⋊D6111yescharacteristic
159Q8—1222no—
160Q8—1222no—
161Q8—2441no—
162Q8—2441no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—1222no—
175C2×C4—2441no—
176C2×C4—2441no—
177C2×C4—2441no—
178C2×C4—2441no—
179C2×C4—2441no—
180C2×C4#1175820212yes—
181C2×C4C2×D24411yescharacteristic
182C2×C4#1175822211yescharacteristic
183C2×C4D4×D6111yescharacteristic
184C2×C4#1175822411yescharacteristic
185C2×C4Q8×D6111yescharacteristic
186C2×C4#1175822611yescharacteristic
187C8—1222no—
188C8—2441no—
189C22#1451974911yescharacteristic
190C22#1451975111yescharacteristic
191C22#1451975311yescharacteristic
192C22C2×#1175820211yescharacteristic
193C22#1451979711yescharacteristic
194C22#1451980311yescharacteristic
195C22#1451980711yescharacteristic
196C4—22no—
197C4—42no—
198C4—41no—
199C4—81no—
200C4—4881no—
201C4—2442no—
202C4#1451975211yescharacteristic
203C4#1451975511yescharacteristic
204C4#1451975711yescharacteristic
205C4#1451977211yescharacteristic
206C2#1683968411yescharacteristic
207C2#1683997211yescharacteristic
208C2#1683997711yescharacteristic
209C2#1684000111yescharacteristic
210C2#1684000611yescharacteristic
211C2#1684005411yescharacteristic
212C2#1684006611yescharacteristic
subgroupG/H
centerC23C2×C22⋊D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#389C2
socleC23×C61C2×D4
hypercenter#389D61
hypocenterC61#2068
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
114. C61#2068semidirect