Finite Group Databasebeta

← #21447096

Subgroups — #21447096

Order 7808.

254 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 67 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#16839810C211yesmaximal, characteristic, complemented
2#16839779C211yesmaximal, characteristic
3#16839771C211yesmaximal, characteristic, complemented
4#16839746C211yesmaximal, characteristic
5C2×#14519696C211yesmaximal, characteristic, complemented
6#16839534C211yesmaximal, characteristic, complemented
7C2×#137×C61C211yesmaximal, characteristic
8C2×#11758194C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C2×#11758194C2211yescharacteristic
11#14519736C2211yescharacteristic
12#14519712—22no—
13#14519704—22no—
14#14519701—22no—
15#14519696—21no—
16#14519696—22no—
17#14519694—21no—
18C2×#41×C61C2211yescharacteristic
19C22×Q8×C61C2211yescharacteristic
20#137×C61—22no—
21#137×C61—22no—
22C2×Q16×C61—21no—
23C2×SD16×C61—21no—
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×C61—21no—
33C2×Q8×C61—21no—
34C2×Q8×C61D411yescharacteristic
35C2×Q8×C61D412yes—
36C2×D4×C61—21no—
37C2×D4×C61D411yescharacteristic
38C22×C4×C61—21no—
39C22×C4×C61—21no—
40C22×C4×C61C2311yescharacteristic
41Q16×C61—24no—
42SD16×C61—24no—
43M16×C61—21no—
44M16×C61D412yes—
45C2×C8×C61—21no—
46C22⋊Dic61—21no—
47C4⋊Dic61—21no—
48C4×Dic61—21no—
49#11758194—21no—
50#11758194—21no—
51#11758194—21no—
52#11758194—21no—
53#11758194—21no—
54#11758194D412yes—
55C2×#92418—21no—
56C2×#92418—21no—
57C2×#92418—21no—
58C23×C61—21no—
59C23×C61#4111yescharacteristic
60Q8×C61—22no—
61Q8×C61—21no—
62Q8×C61—21no—
63Q8×C61—22no—
64Q8×C61—41no—
65Q8×C61—41no—
66D4×C61—21no—
67D4×C61—21no—
68D4×C61—41no—
69D4×C61—41no—
70C2×C4×C61—22no—
71C2×C4×C61—21no—
72C2×C4×C61—41no—
73C2×C4×C61—41no—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61#4111yescharacteristic
81C2×C4×C61#4111yescharacteristic
82C2×Dic61—41no—
83C8×C61—22no—
84#92418—22no—
85#92418—41no—
86#92418—41no—
87C22×C61—41no—
88C22×C61—41no—
89C22×C61—81no—
90C22×C61#12111yescharacteristic
91C22×C61#12311yescharacteristic
92C22×C61#12411yescharacteristic
93C4×C61—41no—
94C4×C61—42no—
95C4×C61#12011yescharacteristic
96C4×C61#12111yescharacteristic
97C4×C61#12111yescharacteristic
98C4×C61#12311yescharacteristic
99Dic61—81no—
100#2049—611nomaximal, Sylow
101C2×C61—21no—
102C2×C61—21no—
103C2×C61—21no—
104C2×C61—81no—
105C2×C61#39411yescharacteristic
106C2×#137D6111yescharacteristic
107#430—611no—
108#421—611no—
109#419—611no—
110#413—611no—
111C2×#101—611no—
112#344—611no—
113C61#204911yescharacteristic, complemented, Sylow
114C2×#41C2×D6111yescharacteristic
115C22×Q8C2×D6111yescharacteristic
116#137—22no—
117#137—22no—
118C2×Q16—21no—
119C2×SD16—21no—
120C2×M16—611no—
121C2×M16—611no—
122C2×M16—611no—
123C2×M16C2×D6111yescharacteristic
124#117—611no—
125#108—1222no—
126#104—1222no—
127#103—1222no—
128#101—1222no—
129#101—1221no—
130#100—1221no—
131#41—21no—
132#41—21no—
133#41—21no—
134#41—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8C22⋊D6111yescharacteristic
141C2×Q8C22⋊D6112yes—
142C2×D4—21no—
143C2×D4C22⋊D6111yescharacteristic
144C22×C4—21no—
145C22×C4—21no—
146C22×C4C22×D6111yescharacteristic
147Q16—24no—
148SD16—24no—
149M16—21no—
150M16—612no—
151M16—1221no—
152M16—1221no—
153M16—1221no—
154M16—1221no—
155M16—1221no—
156M16C22⋊D6112yes—
157C2×C8—21no—
158C2×C8—1221no—
159C2×C8—1221no—
160C2×C8—1221no—
161C4⋊C4—1221no—
162C22⋊C4—1221no—
163C42—1221no—
164C23—21no—
165C23#1175822411yescharacteristic
166Q8—22no—
167Q8—21no—
168Q8—21no—
169Q8—22no—
170Q8—41no—
171Q8—41no—
172D4—21no—
173D4—21no—
174D4—41no—
175D4—41no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—2441no—
183C2×C4D4×D6111yescharacteristic
184C2×C4#1175822411yescharacteristic
185C2×C4#1175822411yescharacteristic
186C2×C4C2×C22⋊D6111yescharacteristic
187C2×C4C2×C22⋊D6111yescharacteristic
188C2×C4C2×C22⋊D6111yescharacteristic
189C8—22no—
190C8—1222no—
191C8—2441no—
192C8—2441no—
193C22—41no—
194C22—41no—
195C22—81no—
196C22#1451974911yescharacteristic
197C22#1451975811yescharacteristic
198C22#1451976411yescharacteristic
199C4—41no—
200C4—42no—
201C4—4881no—
202C4#1451974611yescharacteristic
203C4#1451974811yescharacteristic
204C4#1451974911yescharacteristic
205C4#1451975811yescharacteristic
206C2—21no—
207C2—21no—
208C2—21no—
209C2—81no—
210C2#1683967611yescharacteristic
subgroupG/H
centerC2#16839676
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#137×C61C2
socleC2×C61#394
hypercenterC2×#137D61
hypocenterC61#2049
LCSG ▷ C22×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. #16839810C2semidirect
3. #16839771C2semidirect
5. C2×#14519696C2semidirect
6. #16839534C2semidirect
113. C61#2049semidirect