Finite Group Databasebeta

← #21444169

Subgroups — #21444169

Order 7808.

256 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 63 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×#14519763C211yesmaximal, characteristic
2#16839816C211yesmaximal, characteristic, complemented
3#16839812C211yesmaximal, characteristic, complemented
4#16839486C211yesmaximal, characteristic, complemented
5#16839485C211yesmaximal, characteristic, complemented
6#16839485C211yesmaximal, characteristic, complemented
7C61×#323C211yesmaximal, characteristic, complemented
8C22×Dic122C411yescharacteristic
9C22×C22⋊D61C411yescharacteristic
10#14519763—21no—
11#14519763—21no—
12#14519763—21no—
13#14519763—21no—
14C2×C22⋊Dic61C411yescharacteristic
15C2×#11758198C411yescharacteristic
16C2×#11758198C2211yescharacteristic
17C2×C4×Dic61C2211yescharacteristic
18#14519706—21no—
19#14519706—21no—
20C22⋊#92418C2211yescharacteristic
21C22⋊#92418C2211yescharacteristic
22#14519687—21no—
23C8×Dic61—21no—
24C2×C22⋊C4×C61C2211yescharacteristic
25C22⋊C8×C61C2211yescharacteristic
26C22⋊C8×C61C2211yescharacteristic
27C24×C61C2×C411yescharacteristic
28C23×D61C2×C411yescharacteristic
29C22×C4×C61C2×C411yescharacteristic
30C22×C4×C61C2311yescharacteristic
31C2×C22⋊D61—21no—
32C2×C22⋊D61—21no—
33C2×C22⋊D61—42no—
34C22×Dic61C2×C411yescharacteristic
35C22×Dic61C2×C411yescharacteristic
36C22×Dic61C2×C411yescharacteristic
37C2×Dic122—21no—
38C2×Dic122—21no—
39C2×Dic122—42no—
40C2×C8×C61—21no—
41C2×C8×C61—21no—
42C22⋊C4×C61—21no—
43C22⋊C4×C61—21no—
44C22⋊Dic61—21no—
45C22⋊Dic61—21no—
46#11758198—21no—
47#11758198—21no—
48#11758198—21no—
49#11758198—21no—
50C4×Dic61D411yescharacteristic
51C4×Dic61D411yescharacteristic
52C4×Dic61D411yescharacteristic
53C4×Dic61D411yescharacteristic
54C2×#92418—21no—
55C2×#92418—21no—
56C23×C61—21no—
57C23×C61—21no—
58C23×C61—21no—
59C23×C61—41no—
60C23×C61—41no—
61C23×C61C22×C411yescharacteristic
62C22×D61—21no—
63C22×D61—21no—
64C22×D61—21no—
65C22×D61—41no—
66C22×D61—41no—
67C2×C4×C61—21no—
68C2×C4×C61—41no—
69C2×C4×C61—41no—
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C22⋊D61—42no—
73C22⋊D61—42no—
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—22no—
77C2×Dic61—21no—
78C2×Dic61—41no—
79C2×Dic61C22⋊C411yescharacteristic
80C2×Dic61C22⋊C411yescharacteristic
81C2×Dic61C22⋊C411yescharacteristic
82C2×Dic61C22⋊C411yescharacteristic
83Dic122—42no—
84Dic122—42no—
85C8×C61—41no—
86C8×C61—41no—
87#92418—41no—
88#92418—41no—
89C22×C61—21no—
90C22×C61—21no—
91C22×C61—41no—
92C22×C61—41no—
93C22×C61—41no—
94C22×C61—81no—
95C22×C61—81no—
96C22×C61C2×C22⋊C411yescharacteristic
97C22×C61#13111yescharacteristic
98C22×C61#13111yescharacteristic
99C2×D61—41no—
100C2×D61—41no—
101C2×D61—41no—
102C2×D61—81no—
103C2×D61—81no—
104C4×C61—21no—
105C4×C61—21no—
106C4×C61—41no—
107Dic61—21no—
108Dic61—21no—
109Dic61—21no—
110Dic61—41no—
111Dic61#10012yes—
112#1469—611nomaximal, Sylow
113C2×C61—21no—
114C2×C61—21no—
115C2×C61—81no—
116C2×C61#40811yescharacteristic
117C2×C61#41011yescharacteristic
118C2×C61C2×#10011yescharacteristic
119D61—81no—
120C2×#124—611no—
121#432—611no—
122#431—611no—
123#323—611no—
124#323—611no—
125#323—611no—
126#323D6111yescharacteristic, complemented
127C61#146911yescharacteristic, complemented, Sylow
128C22×Q8—611no—
129C22×D4—611no—
130#124—1221no—
131#124—1221no—
132#124—1221no—
133#124—1221no—
134C2×C22⋊C4—611no—
135C2×C22⋊C4—611no—
136C2×C22⋊C4—611no—
137C2×C22⋊C4C2×D6111yescharacteristic
138C2×C42—611no—
139C4⋊C8—1221no—
140C4⋊C8—1221no—
141C22⋊C8—611no—
142C22⋊C8—611no—
143C22⋊C8C2×D6111yescharacteristic
144C22⋊C8C2×D6111yescharacteristic
145#97—1221no—
146C4×C8—1221no—
147C24—611no—
148C24C4×D6111yescharacteristic
149C2×Q8—1221no—
150C2×Q8—1221no—
151C2×Q8—2442no—
152C2×D4—1221no—
153C2×D4—1221no—
154C2×D4—2442no—
155C22×C4—611no—
156C22×C4—611no—
157C22×C4—611no—
158C22×C4C4×D6111yescharacteristic
159C22×C4C22×D6111yescharacteristic
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—1221no—
163C2×C8—1221no—
164C22⋊C4—21no—
165C22⋊C4—21no—
166C22⋊C4—1221no—
167C22⋊C4—1221no—
168C22⋊C4—1221no—
169C22⋊C4—1221no—
170C22⋊C4—1221no—
171C22⋊C4—1221no—
172C42—611no—
173C42—611no—
174C42—611no—
175C42—611no—
176C23—21no—
177C23—21no—
178C23—21no—
179C23—41no—
180C23—41no—
181C23—1221no—
182C23—1221no—
183C23—1221no—
184C23—2441no—
185C23—2441no—
186C23C2×C4×D6111yescharacteristic
187Q8—2442no—
188Q8—2442no—
189D4—2442no—
190D4—2442no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—611no—
195C2×C4—611no—
196C2×C4—611no—
197C2×C4—611no—
198C2×C4—1222no—
199C2×C4—1221no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—2441no—
203C2×C4D4×D6111yescharacteristic
204C2×C4D4×D6111yescharacteristic
205C8—41no—
206C8—41no—
207C8—2441no—
208C8—2441no—
209C22—21no—
210C22—21no—
211C22—41no—
212C22—41no—
213C22—41no—
214C22—81no—
215C22—81no—
216C22—4881no—
217C22—4881no—
218C22—2441no—
219C22—2441no—
220C22—2441no—
221C22C22⋊C4×D6111yescharacteristic
222C22#1451978311yescharacteristic
223C22#1451978511yescharacteristic
224C4—21no—
225C4—21no—
226C4—41no—
227C4—612no—
228C4—1221no—
229C4—1221no—
230C4—1221no—
231C4—2441no—
232C2—21no—
233C2—21no—
234C2—81no—
235C2—4881no—
236C2#1683972711yescharacteristic
237C2#1683973411yescharacteristic
238C2#100×D6111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#323C2
socleC22×C61C2×C22⋊C4
hypercenter#323D61
hypocenterC61#1469
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #16839816C2semidirect
3. #16839812C2semidirect
4. #16839486C2semidirect
5. #16839485C2semidirect
6. #16839485C2semidirect
7. C61×#323C2semidirect
126. #323D61semidirect
127. C61#1469semidirect