Finite Group Databasebeta

← #21445851

Subgroups — #21445851

Order 7808.

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

normal subgroups only

This group has 316 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
1C22×#11758189C211yesmaximal, characteristic
2C2×#14519710C211yesmaximal, characteristic, complemented
3C2×#14519708C211yesmaximal, characteristic, complemented
4#16839619C211yesmaximal, characteristic
5#16839619C211yesmaximal, characteristic
6#16839525C211yesmaximal, characteristic, complemented
7C61×#340C211yesmaximal, characteristic, complemented
8C22×C4×D61C2211yescharacteristic
9C2×#11758189—22no—
10C2×#11758189—22no—
11C2×#11758189C414yescomplemented
12C22×#92418C2211yescharacteristic
13C2×C4⋊Dic61C2211yescharacteristic
14C2×C4⋊Dic61C2211yescharacteristic
15C2×#11758198—21no—
16C2×#11758198—21no—
17#14519710—22no—
18#14519708—22no—
19#14519684—21no—
20#14519684—21no—
21C22×C8×C61C2211yescharacteristic
22C2×C4⋊C4×C61C2211yescharacteristic
23C2×C4⋊C4×C61C2211yescharacteristic
24C23×D61D411yescharacteristic
25C22×C4×C61—21no—
26C22×C4×C61—21no—
27C22×C4×C61C2311yescharacteristic
28C22×Dic61—21no—
29C22×Dic61—21no—
30C22×Dic61D411yescharacteristic
31C2×C4×D61—21no—
32C2×C4×D61—21no—
33C2×C4×D61—21no—
34C2×C4×D61—21no—
35C2×C4×D61C2×C412yes—
36C2×C4×D61Q812yes—
37C2×C8×C61—21no—
38C2×C8×C61—21no—
39C2×C8×C61C2×C412yes—
40C4⋊C4×C61—21no—
41C4⋊C4×C61—21no—
42C4⋊C4×C61—21no—
43C4⋊C4×C61—21no—
44#11758198—42no—
45#11758198—42no—
46C4⋊Dic61—21no—
47C4⋊Dic61—21no—
48C4⋊Dic61—21no—
49C4⋊Dic61—21no—
50C2×#92418C2×C412yes—
51C2×#92418D412yes—
52C2×#92418D412yes—
53#11758189—28no—
54C23×C61C2×D411yescharacteristic
55C22×D61—21no—
56C22×D61—21no—
57C22×D61—21no—
58C22×D61—21no—
59C22×D61—21no—
60C22×D61—21no—
61C22×D61C4⋊C412yes—
62C2×C4×C61—41no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61—41no—
68C2×C4×C61C22×C411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×Q811yescharacteristic
72C2×C4×C61#4111yescharacteristic
73C2×C4×C61#4111yescharacteristic
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—41no—
77C2×Dic61—41no—
78C2×Dic61—41no—
79C2×Dic61—41no—
80C2×Dic61—41no—
81C2×Dic61—41no—
82C2×Dic61C4⋊C412yes—
83C4×D61—22no—
84C4×D61—22no—
85C4×D61—22no—
86C4×D61—22no—
87C8×C61—22no—
88#92418C22⋊C414yescomplemented
89C22×C61C2×C4⋊C411yescharacteristic
90C22×C61#12111yescharacteristic
91C22×C61#12111yescharacteristic
92C22×C61AGL(1,ℤ/8)11yescharacteristic
93C22×C61AGL(1,ℤ/8)11yescharacteristic
94C22×C61#13711yescharacteristic
95C22×C61#13711yescharacteristic
96C2×D61—22no—
97C2×D61—22no—
98C2×D61—22no—
99C2×D61—41no—
100C2×D61—41no—
101C2×D61—41no—
102C2×D61—41no—
103C4×C61—81no—
104C4×C61—81no—
105C4×C61C2×C22⋊C411yescharacteristic
106C4×C61#11711yescharacteristic
107C4×C61C22⋊Q811yescharacteristic
108C4×C61C22⋊Q811yescharacteristic
109Dic61—22no—
110Dic61—81no—
111Dic61—81no—
112#1809—611nomaximal, Sylow
113C2×C61#38011yescharacteristic
114C2×C61#42811yescharacteristic
115C2×C61#42811yescharacteristic
116C2×C61#46811yescharacteristic
117C2×C61#46811yescharacteristic
118C2×C61#46911yescharacteristic
119C2×C61#47011yescharacteristic
120D61—42no—
121C22×M16—611no—
122C2×#107—611no—
123C2×#106—611no—
124#380—611no—
125#380—611no—
126#340—611no—
127#340D6111yescharacteristic, complemented
128C61#180911yescharacteristic, complemented, Sylow
129C23×C4—611no—
130C2×M16—614no—
131C2×M16—1222no—
132C2×M16—1222no—
133C22×C8—611no—
134C22×C8C2×D6111yescharacteristic
135C2×C4⋊C4—611no—
136C2×C4⋊C4—611no—
137C2×C4⋊C4C2×D6111yescharacteristic
138C2×C4⋊C4C2×D6111yescharacteristic
139C2×C22⋊C4—1221no—
140C2×C22⋊C4—1221no—
141#107—1222no—
142#106—1222no—
143#95—1221no—
144#95—1221no—
145C24—611no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—611no—
149C22×C4—612no—
150C22×C4—612no—
151C22×C4—1221no—
152C22×C4—1221no—
153C22×C4—1221no—
154C22×C4—1221no—
155C22×C4—1221no—
156C22×C4—1221no—
157C22×C4C22×D6111yescharacteristic
158M16—1228no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—612no—
162C2×C8—612no—
163C2×C8—612no—
164C2×C8C4×D6112yes—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—1221no—
170C4⋊C4—1221no—
171C4⋊C4—1221no—
172C4⋊C4—1221no—
173C22⋊C4—2442no—
174C22⋊C4—2442no—
175C23—612no—
176C23—1221no—
177C23—1221no—
178C23—1221no—
179C23—1221no—
180C23—1221no—
181C23—1221no—
182C23D4×D6111yescharacteristic
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—612no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—1222no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4—2441no—
197C2×C4—2441no—
198C2×C4—2441no—
199C2×C4—2441no—
200C2×C4—2441no—
201C2×C4—2441no—
202C2×C4C2×C4×D6111yescharacteristic
203C2×C4#1175822211yescharacteristic
204C2×C4#1175822211yescharacteristic
205C2×C4D4×D6111yescharacteristic
206C2×C4D4×D6111yescharacteristic
207C2×C4Q8×D6111yescharacteristic
208C8—22no—
209C8—614no—
210C22—1222no—
211C22—1222no—
212C22—1222no—
213C22—2441no—
214C22—2441no—
215C22—2441no—
216C22—2441no—
217C22C4⋊C4×D6111yescharacteristic
218C22#1451975011yescharacteristic
219C22#1451975011yescharacteristic
220C22#1451980111yescharacteristic
221C22#1451980411yescharacteristic
222C22#1451980611yescharacteristic
223C22#1451980911yescharacteristic
224C4—81no—
225C4—81no—
226C4—1222no—
227C4—4881no—
228C4—4881no—
229C4C22⋊C4×D6111yescharacteristic
230C4#1451973411yescharacteristic
231C4#1451975511yescharacteristic
232C4#1451975511yescharacteristic
233C2—2442no—
234C2#1683962111yescharacteristic
235C2#1683980111yescharacteristic
236C2#1683980311yescharacteristic
237C2#1684000711yescharacteristic
238C2#1684001111yescharacteristic
239C2#1684001411yescharacteristic
240C2#1684001911yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#340C2
socleC23×C61C2×D4
hypercenter#340D61
hypocenterC61#1809
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×#14519710C2semidirect
3. C2×#14519708C2semidirect
6. #16839525C2semidirect
7. C61×#340C2semidirect
11. C2×#11758189C4semidirect
88. #92418C22⋊C4semidirect
127. #340D61semidirect
128. C61#1809semidirect