Finite Group Databasebeta

← #21446338

Subgroups — #21446338

Order 7808.

312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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#16840528C211yesmaximal, characteristic
2#16840336C211yesmaximal, characteristic
3#16839771C211yesmaximal, characteristic, complemented
4#16839735C211yesmaximal, characteristic
5#16839519C211yesmaximal, characteristic, complemented
6#16839518C211yesmaximal, characteristic, complemented
7C61×#419C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519785—22no—
10#14519783—22no—
11C2×#11758194C2211yescharacteristic
12M16×D61—22no—
13#14519775C412yescomplemented
14#14519766C412yescomplemented
15#14519760—22no—
16#14519753—22no—
17#14519736C2211yescharacteristic
18#14519736C2211yescharacteristic
19#14519701—22no—
20#14519691—22no—
21C22×Q8×C61C2211yescharacteristic
22C2×M16×C61C2211yescharacteristic
23#117×C61C2211yescharacteristic
24#103×C61—22no—
25C2×Q8×C61—21no—
26C2×Q8×C61—21no—
27C2×Q8×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61C2×C412yes—
31C22×C4×C61—21no—
32C22×C4×C61C2311yescharacteristic
33C2×C22⋊D61D412yes—
34#11758222—21no—
35#11758222—21no—
36#11758222—21no—
37#11758222—21no—
38C2×D244C2×C411yescharacteristic
39C2×C4×D61D412yes—
40C2×Dic122C2×C411yescharacteristic
41M16×C61—21no—
42M16×C61—21no—
43C2×C8×C61D412yes—
44C4⋊C4×C61—21no—
45C22⋊C4×C61—21no—
46C42×C61—21no—
47C22⋊Dic61—21no—
48C22⋊Dic61—21no—
49#11758198—24no—
50C4⋊Dic61—21no—
51C4⋊Dic61—21no—
52#11758196—24no—
53C4×Dic61—21no—
54C4×Dic61C2×C412yes—
55#11758194—21no—
56#11758194—21no—
57C2×#92418D412yes—
58#11758189—24no—
59C8×D61—24no—
60C23×C61C2×D411yescharacteristic
61C22×D61C22⋊C412yes—
62Q8×C61—22no—
63Q8×C61—22no—
64Q8×C61—41no—
65Q8×C61—41no—
66C2×C4×C61—22no—
67C2×C4×C61—41no—
68C2×C4×C61—41no—
69C2×C4×C61—41no—
70C2×C4×C61C22×C411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61#4111yescharacteristic
75C2×C4×C61#4111yescharacteristic
76C22⋊D61—22no—
77C22⋊D61—22no—
78C2×Dic61—22no—
79C2×Dic61—41no—
80C2×Dic61C22⋊C412yes—
81D244—21no—
82D244—21no—
83C4×D61—22no—
84C4×D61—22no—
85Dic122—21no—
86Dic122—21no—
87C8×C61—22no—
88#92418—22no—
89C22×C61—41no—
90C22×C61C2×C22⋊C411yescharacteristic
91C22×C61#12111yescharacteristic
92C22×C61#12111yescharacteristic
93C2×D61—22no—
94C2×D61—42no—
95C4×C61—42no—
96C4×C61—81no—
97C4×C61C4×D411yescharacteristic
98C4×C61C4×D411yescharacteristic
99C4×C61#12011yescharacteristic
100C4×C61#12311yescharacteristic
101Dic61—22no—
102Dic61—42no—
103Dic61—81no—
104#1909—611nomaximal, Sylow
105C2×C61—21no—
106C2×C61—21no—
107C2×C61—21no—
108C2×C61#38611yescharacteristic
109D61—42no—
110#568—611no—
111#536—611no—
112#419—611no—
113#419D6111yescharacteristic, complemented
114#410—611no—
115H(3,ℤ/4)—611no—
116H(3,ℤ/4)—611no—
117C61#190911yescharacteristic, complemented, Sylow
118C2×#41—611no—
119C22×Q8C2×D6111yescharacteristic
120#131—1222no—
121#131—1222no—
122C2×M16—611no—
123C2×M16—1222no—
124C2×M16C2×D6111yescharacteristic
125C4⋊Q8—612no—
126#124—612no—
127#123—1222no—
128C22⋊Q8—1222no—
129#117—611no—
130#117—611no—
131#117C2×D6111yescharacteristic
132#103—22no—
133#103—1222no—
134#99—1222no—
135#41—1221no—
136#41—1221no—
137#41—1221no—
138#41—1221no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8—611no—
145C2×Q8C4×D6112yes—
146C2×D4—612no—
147C2×D4—611no—
148C22×C4—21no—
149C22×C4—612no—
150C22×C4C22×D6111yescharacteristic
151M16—21no—
152M16—21no—
153M16—1224no—
154M16—1221no—
155M16—1221no—
156C2×C8—612no—
157C2×C8—1224no—
158C2×C8C22⋊D6112yes—
159C4⋊C4—21no—
160C4⋊C4—1224no—
161C4⋊C4—1221no—
162C4⋊C4—1221no—
163C22⋊C4—21no—
164C22⋊C4—1224no—
165C22⋊C4—1221no—
166C22⋊C4—1221no—
167C42—21no—
168C42—612no—
169C42—1221no—
170C23—612no—
171C23D4×D6111yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—41no—
175Q8—41no—
176Q8—1221no—
177Q8—1221no—
178D4—1222no—
179D4—1222no—
180D4—1221no—
181D4—1221no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—612no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4—1222no—
190C2×C4—2441no—
191C2×C4C2×C4×D6111yescharacteristic
192C2×C4#1175822211yescharacteristic
193C2×C4D4×D6111yescharacteristic
194C2×C4D4×D6111yescharacteristic
195C2×C4#1175822411yescharacteristic
196C2×C4C2×C22⋊D6111yescharacteristic
197C8—22no—
198C8—1222no—
199C22—41no—
200C22—1222no—
201C22—2442no—
202C22C22⋊C4×D6111yescharacteristic
203C22#1451974811yescharacteristic
204C22#1451975011yescharacteristic
205C4—42no—
206C4—81no—
207C4—1222no—
208C4—4881no—
209C4—2442no—
210C4#1451973711yescharacteristic
211C4C4×C22⋊D6111yescharacteristic
212C4#1451974511yescharacteristic
213C4#1451975911yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—2442no—
218C2#1683963811yescharacteristic
subgroupG/H
centerC2#16839638
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#419C2
socleC2×C61#386
hypercenter#419D61
hypocenterC61#1909
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #16839771C2semidirect
5. #16839519C2semidirect
6. #16839518C2semidirect
7. C61×#419C2semidirect
13. #14519775C4semidirect
14. #14519766C4semidirect
113. #419D61semidirect
117. C61#1909semidirect