Finite Group Databasebeta

← #21446468

Subgroups — #21446468

Order 7808.

224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 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×#14519713C211yesmaximal, characteristic, complemented
2C2×#14519705C211yesmaximal, characteristic
3#16839759C211yesmaximal, characteristic
4#16839728C211yesmaximal, characteristic
5#16839717C211yesmaximal, characteristic, complemented
6#16839522C211yesmaximal, characteristic, complemented
7C61×#336C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C2×#11758194C2211yescharacteristic
11#14519736C2211yescharacteristic
12#14519713—22no—
13#14519705—22no—
14#14519702C411yescharacteristic, complemented
15#14519702C411yescharacteristic, complemented
16#14519699C411yescharacteristic, complemented
17#14519699C411yescharacteristic, complemented
18#14519689—21no—
19#14519689—21no—
20#14519687—21no—
21C8×Dic61—21no—
22C22×C8×C61C2211yescharacteristic
23C22×C8×C61C2211yescharacteristic
24C2×C42×C61C2211yescharacteristic
25C22×C4×C61—21no—
26C22×C4×C61C2311yescharacteristic
27C2×C22⋊D61—21no—
28#11758222—21no—
29#11758222—21no—
30#11758222—21no—
31#11758222—21no—
32C2×D244C2×C411yescharacteristic
33C2×C4×D61—21no—
34C2×Dic122C2×C411yescharacteristic
35C2×C8×C61—21no—
36C2×C8×C61—21no—
37C2×C8×C61—21no—
38C2×C8×C61—21no—
39C2×C8×C61C2×C411yescharacteristic
40C2×C8×C61C2×C411yescharacteristic
41C2×C8×C61D411yescharacteristic
42C2×C8×C61D411yescharacteristic
43C42×C61—21no—
44C42×C61—21no—
45C22⋊Dic61—21no—
46C4⋊Dic61C2×C411yescharacteristic
47C4⋊Dic61C2×C411yescharacteristic
48C4×Dic61—21no—
49#11758194—21no—
50#11758194—21no—
51#11758194—21no—
52#11758194D412yes—
53C2×#92418—21no—
54C2×#92418—21no—
55C23×C61#4111yescharacteristic
56C22×D61—21no—
57C2×C4×C61—22no—
58C2×C4×C61—41no—
59C2×C4×C61—41no—
60C2×C4×C61C22×C411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61#4111yescharacteristic
64C2×C4×C61#4111yescharacteristic
65C2×C4×C61#4111yescharacteristic
66C22⋊D61—41no—
67C22⋊D61—41no—
68C2×Dic61—21no—
69C2×Dic61—21no—
70C2×Dic61—21no—
71D244—21no—
72D244—21no—
73C4×D61—41no—
74C4×D61—41no—
75Dic122—21no—
76Dic122—21no—
77C8×C61—21no—
78C8×C61—21no—
79C8×C61—21no—
80C8×C61—21no—
81#92418—22no—
82#92418—41no—
83C22×C61—21no—
84C22×C61—21no—
85C22×C61C4×D411yescharacteristic
86C22×C61#12411yescharacteristic
87C22×C61#12611yescharacteristic
88C2×D61—41no—
89C2×D61—41no—
90C2×D61—41no—
91C4×C61—42no—
92C4×C61#11711yescharacteristic
93C4×C61C4×D411yescharacteristic
94C4×C61#12111yescharacteristic
95C4×C61#12311yescharacteristic
96Dic61—41no—
97Dic61—41no—
98Dic61—41no—
99#1929—611nomaximal, Sylow
100C2×C61—21no—
101C2×C61—21no—
102C2×C61#38811yescharacteristic
103C2×C61#44311yescharacteristic
104C2×C61#44411yescharacteristic
105D61—81no—
106C2×#108—611no—
107C2×#104—611no—
108#416—611no—
109#408—611no—
110#405—611no—
111#339—611no—
112#336D6111yescharacteristic, complemented
113C61#192911yescharacteristic, complemented, Sylow
114C2×#41—611no—
115C2×M16—611no—
116C2×M16—611no—
117C22×C8C2×D6111yescharacteristic
118C22×C8C2×D6111yescharacteristic
119#117—611no—
120C2×C42C2×D6111yescharacteristic
121#108—1222no—
122#104—1222no—
123#103—611no—
124#103—611no—
125#102—611no—
126#102—611no—
127C22⋊C8—1221no—
128C22⋊C8—1221no—
129#97—1221no—
130C4×C8—1221no—
131#41—1221no—
132#41—1221no—
133#41—1221no—
134#41—1221no—
135C2×Q8—611no—
136C2×D4—611no—
137C2×D4—1221no—
138C22×C4—21no—
139C22×C4—1221no—
140C22×C4C22×D6111yescharacteristic
141M16—612no—
142M16—1221no—
143M16—1221no—
144M16—1221no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—1221no—
150C2×C8—1221no—
151C2×C8C4×D6111yescharacteristic
152C2×C8C4×D6111yescharacteristic
153C2×C8D24411yescharacteristic
154C2×C8D24411yescharacteristic
155C4⋊C4—611no—
156C4⋊C4—611no—
157C22⋊C4—1221no—
158C42—21no—
159C42—21no—
160C42—1221no—
161C23—1221no—
162C23#1175822211yescharacteristic
163Q8—1221no—
164Q8—1221no—
165D4—1221no—
166D4—1221no—
167D4—2441no—
168D4—2441no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—1221no—
173C2×C4—1221no—
174C2×C4—1221no—
175C2×C4—2441no—
176C2×C4—2441no—
177C2×C4C2×C4×D6111yescharacteristic
178C2×C4C2×D24411yescharacteristic
179C2×C4D4×D6111yescharacteristic
180C2×C4#1175822411yescharacteristic
181C2×C4#1175822411yescharacteristic
182C2×C4#1175822611yescharacteristic
183C8—21no—
184C8—21no—
185C8—21no—
186C8—21no—
187C8—1222no—
188C8—2441no—
189C22—21no—
190C22—21no—
191C22—2441no—
192C22—2441no—
193C22—2441no—
194C22C4×D24411yescharacteristic
195C22#1451976311yescharacteristic
196C22#1451977211yescharacteristic
197C4—42no—
198C4—2441no—
199C4—2441no—
200C4—2441no—
201C4#1451973511yescharacteristic
202C4#1451973711yescharacteristic
203C4#1451975211yescharacteristic
204C4#1451976111yescharacteristic
205C2—21no—
206C2—21no—
207C2—4881no—
208C2#1683965411yescharacteristic
209C2#1683988011yescharacteristic
210C2#1683988511yescharacteristic
subgroupG/H
centerC2×C4C2×D244
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#336C2
socleC22×C61C4×D4
hypercenter#336D61
hypocenterC61#1929
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #336

Complements

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

NH ≅ G/Ntype
1. C2×#14519713C2semidirect
5. #16839717C2semidirect
6. #16839522C2semidirect
7. C61×#336C2semidirect
14. #14519702C4semidirect
15. #14519702C4semidirect
16. #14519699C4semidirect
17. #14519699C4semidirect
112. #336D61semidirect
113. C61#1929semidirect