Finite Group Databasebeta

← #21445828

Subgroups — #21445828

Order 7808.

356 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 101 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×#14519739C211yesmaximal, characteristic
2C2×#14519706C211yesmaximal, characteristic, complemented
3C2×#14519699C211yesmaximal, characteristic
4C2×#14519697C211yesmaximal, characteristic
5#16839627C211yesmaximal, characteristic, complemented
6#16839524C211yesmaximal, characteristic, complemented
7C61×#340C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C22×C4×D61—21no—
10C22×#92418C2211yescharacteristic
11#14519739—22no—
12#14519739C414yescomplemented
13C2×C4⋊Dic61C2211yescharacteristic
14C2×#11758198—21no—
15C2×C4×Dic61C2211yescharacteristic
16#14519706—22no—
17#14519699—22no—
18#14519697—22no—
19#14519684—21no—
20#14519684—21no—
21C22×C8×C61C2211yescharacteristic
22C2×C4⋊C4×C61C2211yescharacteristic
23C2×C4⋊C4×C61C2211yescharacteristic
24C23×D61—21no—
25C22×C4×C61—21no—
26C22×C4×C61—21no—
27C22×C4×C61C2311yescharacteristic
28C22×Dic61—21no—
29C22×Dic61D411yescharacteristic
30C22×Dic61D411yescharacteristic
31C2×D244—21no—
32C2×D244—21no—
33C2×D244—21no—
34C2×D244C2×C412yes—
35C2×D244D412yes—
36C2×D244Q812yes—
37C2×C4×D61—24no—
38C2×C4×D61—42no—
39C2×C4×D61—42no—
40C2×C8×C61—21no—
41C2×C8×C61—21no—
42C2×C8×C61—21no—
43C4⋊C4×C61—21no—
44C4⋊C4×C61—21no—
45C4⋊C4×C61—21no—
46C4⋊C4×C61C2×C412yes—
47#11758198—24no—
48C4⋊Dic61—21no—
49C4⋊Dic61—21no—
50C4×Dic61C2×C412yes—
51C4×Dic61D412yes—
52C2×#92418—21no—
53C2×#92418—21no—
54C2×#92418—21no—
55C23×C61C2×D411yescharacteristic
56C22×D61—22no—
57C22×D61—22no—
58C22×D61—22no—
59C22×D61—41no—
60C22×D61—41no—
61C22×D61—41no—
62C22×D61—41no—
63C2×C4×C61—22no—
64C2×C4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61—41no—
68C2×C4×C61—41no—
69C2×C4×C61C22×C411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×Q811yescharacteristic
73C2×C4×C61#4111yescharacteristic
74C2×C4×C61#4111yescharacteristic
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—41no—
80C2×Dic61—41no—
81C2×Dic61—41no—
82C2×Dic61C22⋊C412yes—
83C2×Dic61C22⋊C412yes—
84D244—22no—
85D244—22no—
86D244—22no—
87D244C4⋊C414yes—
88C4×D61—48no—
89C8×C61—41no—
90#92418—41no—
91C22×C61C2×C22⋊C411yescharacteristic
92C22×C61#12111yescharacteristic
93C22×C61C22⋊Q811yescharacteristic
94C22×C61#13511yescharacteristic
95C22×C61#13511yescharacteristic
96C22×C61AGL(1,ℤ/8)11yescharacteristic
97C22×C61AGL(1,ℤ/8)11yescharacteristic
98C2×D61—24no—
99C2×D61—42no—
100C2×D61—42no—
101C2×D61—42no—
102C2×D61—42no—
103C2×D61—42no—
104C2×D61—42no—
105C4×C61—42no—
106C4×C61—81no—
107C4×C61C2×C4⋊C411yescharacteristic
108C4×C61#11711yescharacteristic
109C4×C61#12111yescharacteristic
110C4×C61C22⋊Q811yescharacteristic
111Dic61—22no—
112Dic61—22no—
113Dic61—81no—
114#1804—611nomaximal, Sylow
115C2×C61#38011yescharacteristic
116C2×C61#41611yescharacteristic
117C2×C61#41811yescharacteristic
118C2×C61#46311yescharacteristic
119C2×C61#46311yescharacteristic
120C2×C61#47811yescharacteristic
121C2×C61#47811yescharacteristic
122D61—44no—
123C2×C4×D4—611no—
124C2×C4⋊C8—611no—
125C2×#102—611no—
126C2×#102—611no—
127#382—611no—
128#340—611no—
129#340D6111yescharacteristic, complemented
130C61#180411yescharacteristic, complemented, Sylow
131C22×D4—611no—
132C23×C4—1221no—
133C22×C8—611no—
134C22×C8C2×D6111yescharacteristic
135C4×D4—614no—
136C4×D4—1222no—
137C2×C4⋊C4—611no—
138C2×C4⋊C4C2×D6111yescharacteristic
139C2×C4⋊C4C2×D6111yescharacteristic
140C2×C22⋊C4—1221no—
141C2×C42—611no—
142C4⋊C8—1222no—
143#102—1222no—
144#102—1222no—
145#95—1221no—
146#95—1221no—
147C24—1221no—
148C2×D4—612no—
149C2×D4—612no—
150C2×D4—612no—
151C2×D4—1221no—
152C2×D4—1221no—
153C2×D4—1221no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—611no—
157C22×C4—611no—
158C22×C4—1224no—
159C22×C4—1221no—
160C22×C4—2442no—
161C22×C4—2442no—
162C22×C4C22×D6111yescharacteristic
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—1221no—
167C2×C8—1221no—
168C2×C8—1221no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—1221no—
173C4⋊C4—1221no—
174C4⋊C4C4×D6112yes—
175C22⋊C4—1224no—
176C42—612no—
177C42—612no—
178C23—1222no—
179C23—1222no—
180C23—1222no—
181C23—2441no—
182C23—2441no—
183C23—2441no—
184C23—2441no—
185C23D4×D6111yescharacteristic
186D4—614no—
187D4—1222no—
188D4—1222no—
189D4—1222no—
190C2×C4—22no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—612no—
197C2×C4—612no—
198C2×C4—1221no—
199C2×C4—1221no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—2448no—
203C2×C4—2441no—
204C2×C4—2441no—
205C2×C4—2441no—
206C2×C4C2×C4×D6111yescharacteristic
207C2×C4#1175822211yescharacteristic
208C2×C4#1175822211yescharacteristic
209C2×C4D4×D6111yescharacteristic
210C2×C4D4×D6111yescharacteristic
211C2×C4Q8×D6111yescharacteristic
212C8—41no—
213C8—2441no—
214C22—1224no—
215C22—2442no—
216C22—2442no—
217C22—2442no—
218C22—2442no—
219C22—2442no—
220C22—2442no—
221C22C22⋊C4×D6111yescharacteristic
222C22#1451975011yescharacteristic
223C22#1451975511yescharacteristic
224C22#1451979811yescharacteristic
225C22#1451980011yescharacteristic
226C22#1451980111yescharacteristic
227C22#1451980411yescharacteristic
228C4—42no—
229C4—81no—
230C4—1222no—
231C4—1222no—
232C4—4881no—
233C4C4⋊C4×D6111yescharacteristic
234C4#1451973411yescharacteristic
235C4#1451975011yescharacteristic
236C4#1451975511yescharacteristic
237C2—2444no—
238C2#1683962111yescharacteristic
239C2#1683975711yescharacteristic
240C2#1683976511yescharacteristic
241C2#1683997611yescharacteristic
242C2#1683998011yescharacteristic
243C2#1684006111yescharacteristic
244C2#1684006511yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#340C2
socleC23×C61C2×D4
hypercenter#340D61
hypocenterC61#1804
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#14519706C2semidirect
5. #16839627C2semidirect
6. #16839524C2semidirect
7. C61×#340C2semidirect
12. #14519739C4semidirect
129. #340D61semidirect
130. C61#1804semidirect