Finite Group Databasebeta

← #21446293

Subgroups — #21446293

Order 7808.

304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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×#14519810C211yesmaximal, characteristic
2#16840528C211yesmaximal, characteristic
3#16839778C211yesmaximal, characteristic
4#16839772C211yesmaximal, characteristic, complemented
5C2×#14519695C211yesmaximal, characteristic, complemented
6#16839533C211yesmaximal, characteristic, complemented
7C61×#338C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×Dic122C2211yescharacteristic
10#14519810—22no—
11#14519810—22no—
12C2×Dic244C412yescomplemented
13C2×#11758190C412yescomplemented
14#14519785—22no—
15#14519783—22no—
16C2×#11758194C2211yescharacteristic
17M16×D61—22no—
18#14519736C2211yescharacteristic
19#14519703—22no—
20#14519702—22no—
21#14519695—22no—
22C2×M16×C61C2211yescharacteristic
23C2×M16×C61C2211yescharacteristic
24C2×M16×C61C2211yescharacteristic
25C22×C4×C61C2311yescharacteristic
26C2×C22⋊D61—21no—
27C22×Dic61—21no—
28#11758222—21no—
29#11758222—21no—
30#11758222D412yes—
31#11758222D412yes—
32C2×D244C2×C411yescharacteristic
33C2×C4×D61—21no—
34C2×Dic122—21no—
35C2×Dic122—21no—
36C2×Dic122—21no—
37C2×Dic122—21no—
38C2×Dic122—21no—
39C2×Dic122C2×C412yes—
40C2×Dic122C2×C411yescharacteristic
41M16×C61—21no—
42M16×C61—21no—
43M16×C61—21no—
44M16×C61—21no—
45M16×C61—21no—
46M16×C61—21no—
47C2×C8×C61—21no—
48C2×C8×C61C2×C412yes—
49C2×C8×C61D412yes—
50C22⋊Dic61—21no—
51C4⋊Dic61—21no—
52C4×Dic61—21no—
53#11758194—21no—
54#11758194D412yes—
55C2×#92418—21no—
56Dic244—24no—
57#11758190—24no—
58#11758189—24no—
59C8×D61—24no—
60C23×C61#4111yescharacteristic
61C22×D61—21no—
62C2×C4×C61C22×C411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61#4111yescharacteristic
68C22⋊D61—22no—
69C22⋊D61—22no—
70C2×Dic61—21no—
71C2×Dic61—22no—
72C2×Dic61—41no—
73C2×Dic61—41no—
74C2×Dic61—41no—
75D244—21no—
76D244C22⋊C412yes—
77C4×D61—22no—
78C4×D61—22no—
79Dic122—21no—
80Dic122—22no—
81Dic122—22no—
82Dic122—41no—
83Dic122—41no—
84Dic122C22⋊C412yes—
85C8×C61—22no—
86C8×C61—22no—
87C8×C61—41no—
88#92418—22no—
89C22×C61—41no—
90C22×C61C4×D411yescharacteristic
91C22×C61#12111yescharacteristic
92C22×C61#12311yescharacteristic
93C2×D61—22no—
94C2×D61—81no—
95C4×C61C2×C22⋊C411yescharacteristic
96C4×C61C4×D411yescharacteristic
97C4×C61#12011yescharacteristic
98C4×C61#12111yescharacteristic
99Dic61—22no—
100Dic61—42no—
101Dic61—81no—
102#1902—611nomaximal, Sylow
103C2×C61—21no—
104C2×C61—21no—
105C2×C61—21no—
106C2×C61#38611yescharacteristic
107D61—42no—
108C2×#137—611no—
109#568—611no—
110#421—611no—
111#419—611no—
112C2×#101—611no—
113#344—611no—
114#338D6111yescharacteristic, complemented
115C61#190211yescharacteristic, complemented, Sylow
116C2×#41—611no—
117C22×Q8—611no—
118#137—1222no—
119#137—1222no—
120C2×Q16—612no—
121C2×SD16—612no—
122#131—1222no—
123#131—1222no—
124C2×M16—611no—
125C2×M16—1222no—
126C2×M16C2×D6111yescharacteristic
127C2×M16C2×D6111yescharacteristic
128C2×M16C2×D6111yescharacteristic
129#117—611no—
130#104—1222no—
131#103—1222no—
132#101—1222no—
133#41—612no—
134#41—612no—
135#41—1221no—
136#41—1221no—
137C2×Q8—611no—
138C2×Q8—612no—
139C2×Q8—1221no—
140C2×Q8—1221no—
141C2×Q8—1221no—
142C2×Q8—1221no—
143C2×Q8—1221no—
144C2×D4—611no—
145C2×D4—1221no—
146C22×C4—1221no—
147C22×C4—1221no—
148C22×C4C22×D6111yescharacteristic
149Q16—1224no—
150SD16—1224no—
151M16—21no—
152M16—21no—
153M16—21no—
154M16—21no—
155M16—21no—
156M16—21no—
157M16—612no—
158M16—1224no—
159M16—1221no—
160C2×C8—21no—
161C2×C8—1224no—
162C2×C8—1221no—
163C2×C8C4×D6112yes—
164C2×C8D24412yes—
165C4⋊C4—1221no—
166C22⋊C4—1221no—
167C42—1221no—
168C23—1221no—
169C23#1175822611yescharacteristic
170Q8—612no—
171Q8—1221no—
172Q8—1222no—
173Q8—1222no—
174Q8—2441no—
175Q8—2441no—
176D4—612no—
177D4—1222no—
178D4—1222no—
179D4—1221no—
180C2×C4—1221no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—1222no—
184C2×C4—2441no—
185C2×C4—2441no—
186C2×C4—2441no—
187C2×C4C2×C4×D6111yescharacteristic
188C2×C4C2×D24411yescharacteristic
189C2×C4#1175822211yescharacteristic
190C2×C4D4×D6111yescharacteristic
191C2×C4D4×D6111yescharacteristic
192C2×C4D4×D6111yescharacteristic
193C8—22no—
194C8—22no—
195C8—41no—
196C8—1222no—
197C22—41no—
198C22—1222no—
199C22—4881no—
200C22#1451973911yescharacteristic
201C22#1451975211yescharacteristic
202C22#1451976211yescharacteristic
203C4—1222no—
204C4—4881no—
205C4—2442no—
206C4C22⋊C4×D6111yescharacteristic
207C4C4×D24411yescharacteristic
208C4#1451974711yescharacteristic
209C4#1451975011yescharacteristic
210C2—21no—
211C2—21no—
212C2—21no—
213C2—2442no—
214C2#1683964011yescharacteristic
subgroupG/H
centerC2#16839640
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#338C2
socleC2×C61#386
hypercenter#338D61
hypocenterC61#1902
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #338

Complements

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

NH ≅ G/Ntype
4. #16839772C2semidirect
5. C2×#14519695C2semidirect
6. #16839533C2semidirect
7. C61×#338C2semidirect
12. C2×Dic244C4semidirect
13. C2×#11758190C4semidirect
114. #338D61semidirect
115. C61#1902semidirect