Finite Group Databasebeta

← #21450296

Subgroups — #21450296

Order 7808.

544 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 169 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×#14519753C211yesmaximal, characteristic
2C2×C4⋊C4×D61C211yesmaximal, characteristic
3#16839696C214yesmaximal, complemented
4#16839669C211yesmaximal, characteristic, complemented
5#16839636C214yesmaximal
6#16839632C211yesmaximal, characteristic, complemented
7#16839631C211yesmaximal, characteristic, complemented
8C4×#11758198C211yesmaximal, characteristic
9C61×#391C211yesmaximal, characteristic, complemented
10C22×C4×D61C2211yescharacteristic
11C22×C4×D61C2212yes—
12#14519753—24no—
13C2×C4⋊Dic61C2211yescharacteristic
14C2×C4⋊Dic61C2211yescharacteristic
15C2×C4⋊Dic61C2214yes—
16C2×#11758196C2212yes—
17C2×#11758196C2212yes—
18C2×#11758196C2214yes—
19C4⋊C4×D61—24no—
20C2×#11758198C2212yes—
21C2×#11758198C2212yes—
22C2×C4×Dic61C2211yescharacteristic
23#14519684C2212yes—
24#14519684C2214yes—
25C22×Q8×C61C2211yescharacteristic
26C2×C4⋊C4×C61C2211yescharacteristic
27C2×C42×C61C2211yescharacteristic
28#95×C61C2214yes—
29C23×D61C2311yescharacteristic
30C2×Q8×C61—22no—
31C2×Q8×C61—22no—
32C2×Q8×C61—22no—
33C22×C4×C61C2312yes—
34C22×C4×C61C2312yes—
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×Dic61C2312yes—
38C22×Dic61C2312yes—
39C22×Dic61C2311yescharacteristic
40C22×Dic61C2312yes—
41C2×C4×D61—22no—
42C2×C4×D61—22no—
43C2×C4×D61—24no—
44C2×C4×D61—44no—
45C2×C4×D61D414yes—
46C4⋊C4×C61—22no—
47C42×C61—22no—
48#11758198—24no—
49#11758198Q818yescomplemented
50C4⋊Dic61—22no—
51C4⋊Dic61—22no—
52C4⋊Dic61—44no—
53#11758196—24no—
54#11758196—24no—
55#11758196—44no—
56C4×Dic61—22no—
57C23×C61C2411yescharacteristic
58C22×D61—21no—
59C22×D61—21no—
60C22×D61—22no—
61C22×D61C2×D412yes—
62C22×D61C2×Q814yes—
63Q8×C61—44no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—24no—
71C2×C4×C61C2×D412yes—
72C2×C4×C61C2×Q814yes—
73C2×C4×C61#4112yes—
74C2×C4×C61#4112yes—
75C2×Dic61—22no—
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—24no—
82C2×Dic61—24no—
83C2×Dic61C2×D412yes—
84C2×Dic61C2×Q814yes—
85C4×D61—28no—
86C4×D61—48no—
87C22×C61C22×D411yescharacteristic
88C22×C61C22×Q812yes—
89C22×C61C2×#4111yescharacteristic
90C22×C61C2×#4111yescharacteristic
91C22×C61H(5,𝔽2)12yes—
92C2×D61—22no—
93C2×D61—22no—
94C2×D61—24no—
95C2×D61—24no—
96C2×D61C4⋊Q814yes—
97C4×C61—24no—
98C4×C61—42no—
99C4×C61—42no—
100C4×C61#12314yes—
101Dic61—22no—
102Dic61—24no—
103Dic61—42no—
104Dic61—42no—
105#2502—611nomaximal, Sylow
106C2×C61C2×#12311yescharacteristic
107C2×C61C2×C4⋊Q811yescharacteristic
108C2×C61#53511yescharacteristic
109C2×C61#55412yes—
110C2×C61#55412yes—
111D61—24no—
112C2×C22⋊Q8—611no—
113C22×C4⋊C4—611no—
114#398—614no—
115#391—611no—
116#391D6111yescharacteristic, complemented
117#385—614no—
118#384—611no—
119#384—611no—
120C4×C22⋊C4—611no—
121C61#250211yescharacteristic, complemented, Sylow
122C22×Q8C2×D6111yescharacteristic
123C23×C4—611no—
124C23×C4—612no—
125C22⋊Q8—1224no—
126C2×C4⋊C4—611no—
127C2×C4⋊C4—612no—
128C2×C4⋊C4—611no—
129C2×C4⋊C4—612no—
130C2×C4⋊C4—614no—
131C2×C4⋊C4—614no—
132C2×C4⋊C4—1224no—
133C2×C4⋊C4C2×D6111yescharacteristic
134C2×C22⋊C4—612no—
135C2×C22⋊C4—612no—
136C2×C42—611no—
137C2×C42C2×D6111yescharacteristic
138#95—612no—
139#95—614no—
140#95C2×D6114yes—
141C24—611no—
142C2×Q8—22no—
143C2×Q8—22no—
144C2×Q8—22no—
145C22×C4—612no—
146C22×C4—611no—
147C22×C4—614no—
148C22×C4—612no—
149C22×C4—612no—
150C22×C4—1224no—
151C22×C4—1222no—
152C22×C4—1222no—
153C22×C4—2444no—
154C22×C4C22×D6112yes—
155C22×C4C22×D6112yes—
156C22×C4C22×D6112yes—
157C22×C4C22×D6111yescharacteristic
158C4⋊C4—22no—
159C4⋊C4—1224no—
160C4⋊C4—1224no—
161C4⋊C4—1222no—
162C4⋊C4—1222no—
163C4⋊C4—2444no—
164C4⋊C4—2444no—
165C22⋊C4—618no—
166C22⋊C4—1224no—
167C42—22no—
168C42—1222no—
169C23—612no—
170C23—614no—
171C23—1221no—
172C23—1221no—
173C23—1222no—
174C23C23×D6111yescharacteristic
175Q8—44no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—612no—
184C2×C4—614no—
185C2×C4—1221no—
186C2×C4—1222no—
187C2×C4—1221no—
188C2×C4—1222no—
189C2×C4—1228no—
190C2×C4—1222no—
191C2×C4—1222no—
192C2×C4—1224no—
193C2×C4—1224no—
194C2×C4—2448no—
195C2×C4#1175822212yes—
196C2×C4D4×D6112yes—
197C2×C4#1175822412yes—
198C2×C4Q8×D6114yes—
199C22—614no—
200C22—1224no—
201C22—1224no—
202C22—1222no—
203C22—1222no—
204C22C2×D4×D6111yescharacteristic
205C22C2×Q8×D6112yes—
206C22C2×#1175822411yescharacteristic
207C22C2×#1175822211yescharacteristic
208C22#1451982312yes—
209C4—24no—
210C4—42no—
211C4—42no—
212C4—1224no—
213C4—1222no—
214C4—2442no—
215C4—2442no—
216C4#1451975914yes—
217C2—1224no—
218C2C2×#1451975911yescharacteristic
219C2C4⋊Q8×D6111yescharacteristic
220C2#1684033011yescharacteristic
221C2#1684047012yes—
222C2#1684047212yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#391C2
hypercenter#391D61
hypocenterC61#2502
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
3. #16839696C2semidirect
4. #16839669C2semidirect
6. #16839632C2semidirect
7. #16839631C2semidirect
9. C61×#391C2semidirect
49. #11758198Q8semidirect
116. #391D61semidirect
121. C61#2502semidirect