Finite Group Databasebeta

← #21447482

Subgroups — #21447482

Order 7808.

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

normal subgroups only

This group has 258 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#16839736C211yesmaximal, characteristic, complemented
3#16839556C212yesmaximal, complemented
4#16839554C212yesmaximal, complemented
5C61×#410C211yesmaximal, characteristic, complemented
6C2×#11758222C411yescharacteristic, complemented
7#14519775C411yescharacteristic, complemented
8#14519773C2211yescharacteristic
9#14519766C411yescharacteristic, complemented
10#14519764C2211yescharacteristic
11#14519749—21no—
12#14519749—21no—
13C4×C22⋊D61—21no—
14C4×C22⋊D61—21no—
15#14519736—21no—
16C2×C4×Dic61C411yescharacteristic, complemented
17#14519692—21no—
18#14519692C2212yes—
19C2×#41×C61C2211yescharacteristic
20#117×C61—21no—
21#99×C61—21no—
22#99×C61C2212yes—
23#41×C61—41no—
24#41×C61—41no—
25C2×Q8×C61C2×C411yescharacteristic
26C2×D4×C61D411yescharacteristic
27C2×D4×C61D411yescharacteristic
28C2×D4×C61C2311yescharacteristic
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
41C4⋊C4×C61—41no—
42C22⋊C4×C61—22no—
43C42×C61—41no—
44C22⋊Dic61—21no—
45C22⋊Dic61—21no—
46C22⋊Dic61—22no—
47#11758198—21no—
48#11758198—21no—
49C4⋊Dic61—41no—
50#11758196—21no—
51#11758196—21no—
52C4×Dic61—21no—
53C4×Dic61—41no—
54C4×Dic61C2×C411yescharacteristic
55C4×Dic61C2×C411yescharacteristic
56C23×C61C22⋊C411yescharacteristic
57C23×C61C2×D411yescharacteristic
58C23×C61C2×D411yescharacteristic
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×C61—42no—
71C2×C4×C61C22⋊C411yescharacteristic
72C2×C4×C61C22⋊C411yescharacteristic
73C2×C4×C61C22⋊C411yescharacteristic
74C2×C4×C61C22×C411yescharacteristic
75C22⋊D61—42no—
76C22⋊D61—42no—
77C22⋊D61—42no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—42no—
82C2×Dic61—42no—
83D244—41no—
84C4×D61—41no—
85C4×D61—41no—
86Dic122—41no—
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—82no—
101C4×C61#9911yescharacteristic
102C4×C61#9911yescharacteristic
103Dic61—22no—
104Dic61—41no—
105Dic61—41no—
106Dic61—82no—
107#2126—611nomaximal, Sylow
108C2×C61—21no—
109C2×C61—41no—
110C2×C61—41no—
111C2×C61—41no—
112C2×C61C2×#9911yescharacteristic
113D61—81no—
114#532—611no—
115#410—611no—
116#410D6111yescharacteristic, complemented
117#354—612no—
118#353—612no—
119C61#212611yescharacteristic, complemented, Sylow
120C2×#41—611no—
121C2×#41C2×D6111yescharacteristic
122C4⋊Q8—611no—
123#127—611no—
124#124—611no—
125#124—611no—
126#121—1221no—
127#121—1221no—
128C4×D4—1221no—
129C4×D4—1221no—
130#117—21no—
131#117—1221no—
132C2×C42—611no—
133#99—21no—
134#99—612no—
135#99—1221no—
136#99C2×D6112yes—
137#41—41no—
138#41—41no—
139#41—2441no—
140#41—2441no—
141C2×Q8—611no—
142C2×Q8C4×D6111yescharacteristic
143C2×D4—611no—
144C2×D4—1221no—
145C2×D4—1221no—
146C2×D4—1221no—
147C2×D4D24411yescharacteristic
148C2×D4C22⋊D6111yescharacteristic
149C2×D4C22×D6111yescharacteristic
150C22×C4—1221no—
151C22×C4—1221no—
152C22×C4C4×D6111yescharacteristic
153C22×C4D24411yescharacteristic
154C22×C4C22⋊D6111yescharacteristic
155C4⋊C4—41no—
156C4⋊C4—1221no—
157C4⋊C4—1221no—
158C4⋊C4—2441no—
159C22⋊C4—22no—
160C22⋊C4—1221no—
161C22⋊C4—1221no—
162C22⋊C4—1221no—
163C22⋊C4—1221no—
164C22⋊C4—1222no—
165C42—41no—
166C42—611no—
167C42—611no—
168C42—1221no—
169C42—2441no—
170C23—1221no—
171C23#1175819811yescharacteristic
172C23C2×D24411yescharacteristic
173C23C2×C22⋊D6111yescharacteristic
174Q8—41no—
175Q8—2441no—
176D4—41no—
177D4—41no—
178D4—41no—
179D4—2441no—
180D4—2442no—
181D4—2442no—
182D4—2442no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—2442no—
194C2×C4—2442no—
195C2×C4—2441no—
196C2×C4—2441no—
197C2×C4#1175819811yescharacteristic
198C2×C4#1175819811yescharacteristic
199C2×C4#1175819811yescharacteristic
200C2×C4C2×C4×D6111yescharacteristic
201C22—21no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—2441no—
208C22—2441no—
209C22—2441no—
210C22C2×#1175819811yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—82no—
215C4—1222no—
216C4—4882no—
217C4—2441no—
218C4—2441no—
219C4#1451969111yescharacteristic
220C4#1451969111yescharacteristic
221C2—21no—
222C2—41no—
223C2—41no—
224C2—41no—
225C2—4881no—
226C2C2×#1451969111yescharacteristic
subgroupG/H
centerC4#14519691
commutatorC2×C4×C61C22×C4
FrattiniC2×D4C22×D61
FittingC61×#410C2
socleC2×C61C2×#99
hypercenter#410D61
hypocenterC61#2126
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #16839736C2semidirect
3. #16839556C2semidirect
4. #16839554C2semidirect
5. C61×#410C2semidirect
6. C2×#11758222C4semidirect
7. #14519775C4semidirect
9. #14519766C4semidirect
16. C2×C4×Dic61C4semidirect
116. #410D61semidirect
119. C61#2126semidirect