Finite Group Databasebeta

← #21446315

Subgroups — #21446315

Order 7808.

310 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 93 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#16840240C211yesmaximal, characteristic, complemented
2#16839779C211yesmaximal, characteristic
3#16839771C211yesmaximal, characteristic, complemented
4#16839736C211yesmaximal, characteristic
5#16839533C211yesmaximal, characteristic, complemented
6#16839519C211yesmaximal, characteristic, complemented
7C2×#137×C61C211yesmaximal, characteristic
8C2×#11758194C2211yescharacteristic
9Q8×Dic61—22no—
10Q8×Dic61—22no—
11#14519736—22no—
12#14519736C2211yescharacteristic
13#14519736C2211yescharacteristic
14#14519736C2211yescharacteristic
15#14519704—22no—
16#14519701—22no—
17#14519692—22no—
18C2×#41×C61C2211yescharacteristic
19C22×Q8×C61C2211yescharacteristic
20#137×C61—22no—
21#137×C61—22no—
22C2×Q16×C61C412yescomplemented
23C2×SD16×C61C412yescomplemented
24C2×M16×C61C2211yescharacteristic
25#41×C61—21no—
26#41×C61—21no—
27#41×C61—21no—
28#41×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61—21no—
31C2×Q8×C61—21no—
32C2×Q8×C61C2×C411yescharacteristic
33C2×Q8×C61C2×C412yes—
34C2×Q8×C61D412yes—
35C2×Q8×C61D412yes—
36C2×D4×C61—21no—
37C2×D4×C61C2×C411yescharacteristic
38C22×C4×C61—21no—
39C22×C4×C61—21no—
40C22×C4×C61C2311yescharacteristic
41Q16×C61—24no—
42SD16×C61—24no—
43M16×C61—21no—
44M16×C61—21no—
45C2×C8×C61C2×C412yes—
46C22⋊Dic61—21no—
47C22⋊Dic61—21no—
48C22⋊Dic61D412yes—
49C4⋊Dic61—24no—
50C4⋊Dic61—21no—
51C4⋊Dic61—21no—
52C4⋊Dic61—21no—
53C4×Dic61—24no—
54C4×Dic61—21no—
55C4×Dic61—21no—
56C4×Dic61D412yes—
57#11758194—21no—
58#11758194—21no—
59C2×#92418—21no—
60C23×C61—21no—
61C23×C61C2×D411yescharacteristic
62Q8×C61—22no—
63Q8×C61—22no—
64Q8×C61—22no—
65Q8×C61—21no—
66Q8×C61—21no—
67Q8×C61C22⋊C414yes—
68D4×C61—21no—
69D4×C61—21no—
70D4×C61—41no—
71D4×C61—41no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—21no—
76C2×C4×C61—41no—
77C2×C4×C61—41no—
78C2×C4×C61C22×C411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61#4111yescharacteristic
83C2×C4×C61#4111yescharacteristic
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—41no—
87C8×C61—22no—
88#92418—41no—
89C22×C61—41no—
90C22×C61—41no—
91C22×C61—81no—
92C22×C61C4×D411yescharacteristic
93C22×C61#12011yescharacteristic
94C22×C61#12111yescharacteristic
95C4×C61—24no—
96C4×C61—41no—
97C4×C61C2×C22⋊C411yescharacteristic
98C4×C61C4×D411yescharacteristic
99C4×C61#12111yescharacteristic
100C4×C61#12311yescharacteristic
101Dic61—42no—
102Dic61—42no—
103Dic61—81no—
104#1905—611nomaximal, Sylow
105C2×C61—21no—
106C2×C61—21no—
107C2×C61—21no—
108C2×C61—81no—
109C2×C61#38611yescharacteristic
110C2×#137D6111yescharacteristic
111#519—611no—
112#421—611no—
113#419—611no—
114#410—611no—
115#344—611no—
116H(3,ℤ/4)—611no—
117C61#190511yescharacteristic, complemented, Sylow
118C2×#41C2×D6111yescharacteristic
119C22×Q8C2×D6111yescharacteristic
120#137—22no—
121#137—22no—
122C2×Q16Dic6112yescomplemented
123C2×SD16Dic6112yescomplemented
124C2×M16—611no—
125C2×M16C2×D6111yescharacteristic
126C4×Q8—1222no—
127C4×Q8—1222no—
128#117—611no—
129#117—611no—
130#117—611no—
131#117—1222no—
132#104—1222no—
133#103—1222no—
134#99—1222no—
135#41—21no—
136#41—21no—
137#41—21no—
138#41—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8C2×Dic6111yescharacteristic
143C2×Q8C2×Dic6112yes—
144C2×Q8C22⋊D6112yes—
145C2×Q8C22⋊D6112yes—
146C2×D4—21no—
147C2×D4C2×Dic6111yescharacteristic
148C22×C4—21no—
149C22×C4—21no—
150C22×C4C22×D6111yescharacteristic
151Q16—24no—
152SD16—24no—
153M16—21no—
154M16—21no—
155M16—1221no—
156M16—1221no—
157C2×C8—1221no—
158C2×C8C2×Dic6112yes—
159C4⋊C4—1224no—
160C4⋊C4—1221no—
161C4⋊C4—1221no—
162C4⋊C4—1221no—
163C22⋊C4—612no—
164C22⋊C4—1221no—
165C22⋊C4—1221no—
166C42—612no—
167C42—1224no—
168C42—1221no—
169C42—1221no—
170C23—21no—
171C23D4×D6111yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—22no—
175Q8—21no—
176Q8—21no—
177Q8C22⋊Dic6114yes—
178D4—21no—
179D4—21no—
180D4—41no—
181D4—41no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—1222no—
189C2×C4—1222no—
190C2×C4—2441no—
191C2×C4D4×D6111yescharacteristic
192C2×C4#1175822411yescharacteristic
193C2×C4#1175822411yescharacteristic
194C2×C4C22×Dic6111yescharacteristic
195C2×C4C2×C22⋊D6111yescharacteristic
196C2×C4C2×C22⋊D6111yescharacteristic
197C8—22no—
198C8—2441no—
199C22—41no—
200C22—41no—
201C22—81no—
202C22D4×Dic6111yescharacteristic
203C22#1451974511yescharacteristic
204C22#1451974911yescharacteristic
205C4—24no—
206C4—41no—
207C4—4881no—
208C4—2442no—
209C4—2442no—
210C4C2×C22⋊Dic6111yescharacteristic
211C4D4×Dic6111yescharacteristic
212C4#1451974911yescharacteristic
213C4#1451975811yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—81no—
218C2#1683964211yescharacteristic
subgroupG/H
centerC2#16839642
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#137×C61C2
socleC2×C61#386
hypercenterC2×#137D61
hypocenterC61#1905
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. #16840240C2semidirect
3. #16839771C2semidirect
5. #16839533C2semidirect
6. #16839519C2semidirect
22. C2×Q16×C61C4semidirect
23. C2×SD16×C61C4semidirect
117. C61#1905semidirect
122. C2×Q16Dic61semidirect
123. C2×SD16Dic61semidirect