Finite Group Databasebeta

← #21447502

Subgroups — #21447502

Order 7808.

250 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 65 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#16840308C211yesmaximal, characteristic
2#16839746C211yesmaximal, characteristic, complemented
3#16839560C212yesmaximal, complemented
4#16839558C212yesmaximal, complemented
5C61×#413C211yesmaximal, characteristic, complemented
6C2×#11758222C411yescharacteristic
7C2×#11758194—21no—
8#14519775C2211yescharacteristic
9#14519773C411yescharacteristic
10#14519766C2211yescharacteristic
11#14519764C411yescharacteristic
12#14519749—21no—
13#14519749—21no—
14C4×C22⋊D61—21no—
15C4×C22⋊D61—21no—
16C2×C4×Dic61C411yescharacteristic
17#14519696C2212yes—
18#14519694—21no—
19C2×#41×C61C2211yescharacteristic
20C2×M16×C61—21no—
21#101×C61C2212yes—
22#100×C61—21no—
23#41×C61—41no—
24#41×C61—41no—
25C2×Q8×C61C2311yescharacteristic
26C2×D4×C61C2×C411yescharacteristic
27C2×D4×C61D411yescharacteristic
28C2×D4×C61D411yescharacteristic
29C22×C4×C61C2×C411yescharacteristic
30C22×C4×C61D411yescharacteristic
31C22×C4×C61D411yescharacteristic
32C2×C22⋊D61—21no—
33C2×C22⋊D61—21no—
34C2×C22⋊D61—21no—
35C22×Dic61—21no—
36#11758222—41no—
37#11758222—41no—
38C2×D244C2×C411yescharacteristic
39C2×C4×D61—21no—
40C2×Dic122C2×C411yescharacteristic
41M16×C61—22no—
42M16×C61—41no—
43C2×C8×C61—41no—
44C22⋊Dic61—21no—
45C22⋊Dic61—21no—
46#11758198—21no—
47#11758198—21no—
48#11758196—21no—
49#11758196—21no—
50C4×Dic61—21no—
51C4×Dic61C2×C411yescharacteristic
52C4×Dic61C2×C411yescharacteristic
53#11758194—22no—
54#11758194—41no—
55C2×#92418—41no—
56C23×C61C22⋊C411yescharacteristic
57C23×C61C22⋊C411yescharacteristic
58C23×C61C22⋊C411yescharacteristic
59C22×D61—21no—
60Q8×C61—41no—
61D4×C61—41no—
62D4×C61—41no—
63D4×C61—41no—
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61C22⋊C411yescharacteristic
71C2×C4×C61C22×C411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C22⋊D61—42no—
75C22⋊D61—42no—
76C22⋊D61—42no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—42no—
81D244—41no—
82C4×D61—41no—
83C4×D61—41no—
84Dic122—41no—
85C8×C61—42no—
86#92418—42no—
87C22×C61—21no—
88C22×C61—21no—
89C22×C61—21no—
90C22×C61—41no—
91C22×C61—41no—
92C22×C61—41no—
93C22×C61C2×C22⋊C411yescharacteristic
94C2×D61—41no—
95C2×D61—41no—
96C2×D61—41no—
97C4×C61—21no—
98C4×C61—21no—
99C4×C61—21no—
100C4×C61#9911yescharacteristic
101C4×C61#9911yescharacteristic
102Dic61—22no—
103Dic61—41no—
104Dic61—41no—
105#2132—611nomaximal, Sylow
106C2×C61—21no—
107C2×C61—41no—
108C2×C61—41no—
109C2×C61—41no—
110C2×C61C2×#9911yescharacteristic
111D61—81no—
112#532—611no—
113#413—611no—
114#413D6111yescharacteristic, complemented
115#356—612no—
116#355—612no—
117C61#213211yescharacteristic, complemented, Sylow
118C2×#41—611no—
119C2×#41C2×D6111yescharacteristic
120C2×M16—21no—
121C2×M16—1221no—
122C4⋊Q8—611no—
123#127—611no—
124#124—611no—
125#124—611no—
126#121—1221no—
127#121—1221no—
128C4×D4—1221no—
129C4×D4—1221no—
130C2×C42—611no—
131#101—612no—
132#101C2×D6112yes—
133#100—21no—
134#100—1221no—
135#41—41no—
136#41—41no—
137#41—2441no—
138#41—2441no—
139C2×Q8—611no—
140C2×Q8C22×D6111yescharacteristic
141C2×D4—611no—
142C2×D4—1221no—
143C2×D4—1221no—
144C2×D4—1221no—
145C2×D4C4×D6111yescharacteristic
146C2×D4D24411yescharacteristic
147C2×D4C22⋊D6111yescharacteristic
148C22×C4—1221no—
149C22×C4—1221no—
150C22×C4C4×D6111yescharacteristic
151C22×C4D24411yescharacteristic
152C22×C4C22⋊D6111yescharacteristic
153M16—22no—
154M16—41no—
155M16—1222no—
156M16—2441no—
157C2×C8—41no—
158C2×C8—2441no—
159C4⋊C4—1221no—
160C4⋊C4—1221no—
161C22⋊C4—1221no—
162C22⋊C4—1221no—
163C22⋊C4—1221no—
164C22⋊C4—1221no—
165C42—611no—
166C42—611no—
167C42—1221no—
168C23—1221no—
169C23#1175819811yescharacteristic
170C23#1175819811yescharacteristic
171C23#1175819811yescharacteristic
172Q8—41no—
173Q8—2441no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—2441no—
178D4—2442no—
179D4—2442no—
180D4—2442no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—1221no—
188C2×C4—1221no—
189C2×C4—1221no—
190C2×C4—2442no—
191C2×C4—2441no—
192C2×C4—2441no—
193C2×C4#1175819811yescharacteristic
194C2×C4C2×C4×D6111yescharacteristic
195C2×C4C2×D24411yescharacteristic
196C2×C4C2×C22⋊D6111yescharacteristic
197C8—42no—
198C8—2442no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—2441no—
206C22—2441no—
207C22—2441no—
208C22C2×#1175819811yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—1222no—
213C4—2441no—
214C4—2441no—
215C4#1451969111yescharacteristic
216C4#1451969111yescharacteristic
217C2—21no—
218C2—41no—
219C2—41no—
220C2—41no—
221C2—4881no—
222C2C2×#1451969111yescharacteristic
subgroupG/H
centerC4#14519691
commutatorC2×C4×C61C22×C4
FrattiniC2×Q8C22×D61
FittingC61×#413C2
socleC2×C61C2×#99
hypercenter#413D61
hypocenterC61#2132
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #16839746C2semidirect
3. #16839560C2semidirect
4. #16839558C2semidirect
5. C61×#413C2semidirect
114. #413D61semidirect
117. C61#2132semidirect