Finite Group Databasebeta

← #21446725

Subgroups — #21446725

Order 7808.

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

normal subgroups only

This group has 296 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
1C22×#11758200C211yesmaximal, characteristic
2C2×#14519712C211yesmaximal, characteristic, complemented
3#16839770C211yesmaximal, characteristic, complemented
4C2×#14519695C211yesmaximal, characteristic, complemented
5C2×#14519694C211yesmaximal, characteristic
6#16839718C211yesmaximal, characteristic, complemented
7C61×#418C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C2×#11758200—21no—
10C2×#11758200—21no—
11C2×#11758200—22no—
12C2×#11758200C414yescomplemented
13C2×#11758194C2211yescharacteristic
14C2×#11758194C2211yescharacteristic
15C22×#92418C2211yescharacteristic
16#14519712—22no—
17#14519700—22no—
18#14519695—22no—
19#14519694—22no—
20#14519688—21no—
21C4×#92418—21no—
22C22×D4×C61C2211yescharacteristic
23C2×M16×C61C2211yescharacteristic
24#117×C61C2211yescharacteristic
25#102×C61—22no—
26C24×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29C2×D4×C61—21no—
30C2×D4×C61—21no—
31C2×D4×C61—21no—
32C2×D4×C61C2×C412yes—
33C22×C4×C61C2311yescharacteristic
34C22×Dic61—21no—
35C2×Dic122—21no—
36C2×Dic122—21no—
37C2×Dic122—21no—
38C2×Dic122—21no—
39C2×Dic122—21no—
40C2×Dic122C2×C412yes—
41M16×C61—21no—
42M16×C61—21no—
43C2×C8×C61—21no—
44C4⋊C4×C61D412yes—
45C22⋊C4×C61—21no—
46C42×C61—21no—
47#11758200—24no—
48#11758200—24no—
49#11758194—21no—
50#11758194—21no—
51#11758194—21no—
52#11758194D412yes—
53C2×#92418—21no—
54C2×#92418—21no—
55C2×#92418C2×C412yes—
56C2×#92418D411yescharacteristic
57C2×#92418D411yescharacteristic
58C2×#92418D412yes—
59C23×C61—22no—
60C23×C61—41no—
61C23×C61—41no—
62C23×C61—82no—
63C23×C61#4111yescharacteristic
64D4×C61—22no—
65D4×C61—22no—
66D4×C61—41no—
67D4×C61—41no—
68C2×C4×C61—22no—
69C2×C4×C61C22×C411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61#4111yescharacteristic
75C2×Dic61—22no—
76C2×Dic61—41no—
77C2×Dic61—41no—
78Dic122—22no—
79Dic122—22no—
80Dic122—41no—
81Dic122—41no—
82C8×C61—41no—
83#92418—22no—
84#92418—41no—
85#92418C22⋊C412yes—
86#92418C22⋊C412yes—
87C22×C61—22no—
88C22×C61—42no—
89C22×C61—82no—
90C22×C61—82no—
91C22×C61—82no—
92C22×C61C4×D411yescharacteristic
93C22×C61#12111yescharacteristic
94C22×C61#12411yescharacteristic
95C4×C61—42no—
96C4×C61C2×C22⋊C411yescharacteristic
97C4×C61C4×D411yescharacteristic
98C4×C61#12111yescharacteristic
99C4×C61#12711yescharacteristic
100Dic61—42no—
101#1977—611nomaximal, Sylow
102C2×C61—21no—
103C2×C61—21no—
104C2×C61—82no—
105C2×C61#39011yescharacteristic
106C2×C61#47112yes—
107C22×SD16—611no—
108C2×#108—611no—
109#419—611no—
110#418D6111yescharacteristic
111C2×#101—611no—
112C2×#100—611no—
113#405—611no—
114C61#197711yescharacteristic, complemented, Sylow
115C22×Q8—611no—
116C22×D4C2×D6111yescharacteristic
117C2×SD16—614no—
118C2×SD16—1221no—
119C2×SD16—1221no—
120C2×SD16—1222no—
121C2×M16—611no—
122C2×M16—611no—
123C2×M16C2×D6111yescharacteristic
124C22×C8—611no—
125#117C2×D6111yescharacteristic
126#108—1222no—
127#103—1222no—
128#102—22no—
129#101—1222no—
130#100—1222no—
131#97—1221no—
132C4×C8—1221no—
133C24—21no—
134C2×Q8—612no—
135C2×Q8—1221no—
136C2×Q8—1221no—
137C2×Q8—1221no—
138C2×Q8—1221no—
139C2×Q8—1221no—
140C2×D4—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4C4×D6112yes—
146C22×C4—1221no—
147C22×C4C22×D6111yescharacteristic
148SD16—1224no—
149SD16—1224no—
150M16—21no—
151M16—21no—
152M16—612no—
153M16—1221no—
154M16—1221no—
155M16—1221no—
156C2×C8—21no—
157C2×C8—612no—
158C2×C8—611no—
159C2×C8—611no—
160C2×C8—612no—
161C2×C8—1221no—
162C2×C8—1221no—
163C4⋊C4C22⋊D6112yes—
164C22⋊C4—21no—
165C42—21no—
166C23—22no—
167C23—41no—
168C23—41no—
169C23—82no—
170C23#1175822411yescharacteristic
171Q8—1222no—
172Q8—1222no—
173Q8—2441no—
174Q8—2441no—
175D4—22no—
176D4—22no—
177D4—41no—
178D4—41no—
179C2×C4—22no—
180C2×C4—1222no—
181C2×C4—2441no—
182C2×C4—2441no—
183C2×C4C2×C4×D6111yescharacteristic
184C2×C4#1175822211yescharacteristic
185C2×C4D4×D6111yescharacteristic
186C2×C4D4×D6111yescharacteristic
187C2×C4D4×D6111yescharacteristic
188C2×C4C2×C22⋊D6111yescharacteristic
189C8—41no—
190C8—612no—
191C8—612no—
192C8—1222no—
193C8—2441no—
194C22—22no—
195C22—42no—
196C22—82no—
197C22—82no—
198C22—82no—
199C22#1451973711yescharacteristic
200C22#1451974911yescharacteristic
201C22#1451976311yescharacteristic
202C4—42no—
203C4—2442no—
204C4C22⋊C4×D6111yescharacteristic
205C4C4×C22⋊D6111yescharacteristic
206C4#1451975011yescharacteristic
207C4#1451977311yescharacteristic
208C2—21no—
209C2—21no—
210C2—82no—
211C2#1683966211yescharacteristic
212C2#1684002312yes—
subgroupG/H
centerC22#14519749
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#418C2
socleC22×C61#121
hypercenter#418D61
hypocenterC61#1977
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. C2×#14519712C2semidirect
3. #16839770C2semidirect
4. C2×#14519695C2semidirect
6. #16839718C2semidirect
12. C2×#11758200C4semidirect
114. C61#1977semidirect