Finite Group Databasebeta

← #21446313

Subgroups — #21446313

Order 7808.

310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14519808C211yesmaximal, characteristic
2#16839780C211yesmaximal, characteristic
3#16839771C211yesmaximal, characteristic, complemented
4#16839735C211yesmaximal, characteristic
5#16839532C211yesmaximal, characteristic, complemented
6#16839518C211yesmaximal, characteristic, complemented
7C61×#519C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519808—22no—
10#14519808—22no—
11C2×#11758202C412yescomplemented
12C2×#11758201C412yescomplemented
13C2×#11758194C2211yescharacteristic
14C2×#11758194C2211yescharacteristic
15#14519736C2211yescharacteristic
16#14519705—22no—
17#14519701—22no—
18#14519691—22no—
19C22×Q8×C61C2211yescharacteristic
20C4×Q8×C61—22no—
21C4×Q8×C61—22no—
22#117×C61—22no—
23#117×C61C2211yescharacteristic
24#117×C61C2211yescharacteristic
25C2×Q8×C61—21no—
26C2×Q8×C61—21no—
27C2×Q8×C61—21no—
28C2×Q8×C61C2×C412yes—
29C2×Q8×C61D412yes—
30C2×Q8×C61D412yes—
31C22×C4×C61—21no—
32C22×C4×C61C2311yescharacteristic
33C2×C22⋊D61—21no—
34#11758222—21no—
35#11758222—21no—
36#11758222—21no—
37#11758222—21no—
38C2×D244C2×C411yescharacteristic
39C2×C4×D61—21no—
40C2×Dic122C2×C411yescharacteristic
41C4⋊C4×C61—24no—
42C4⋊C4×C61—21no—
43C4⋊C4×C61—21no—
44C22⋊C4×C61—21no—
45C22⋊C4×C61D412yes—
46C42×C61—24no—
47C42×C61—21no—
48C42×C61D412yes—
49C22⋊Dic61—21no—
50#11758202—24no—
51#11758201—24no—
52C4⋊Dic61—21no—
53C4×Dic61—21no—
54#11758194—21no—
55#11758194—21no—
56#11758194—21no—
57#11758194—21no—
58C2×#92418—21no—
59C2×#92418C2×C412yes—
60C23×C61C2×D411yescharacteristic
61C22×D61—21no—
62Q8×C61—22no—
63Q8×C61—22no—
64Q8×C61—22no—
65Q8×C61C22⋊C414yes—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61C22×C411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61#4111yescharacteristic
76C2×C4×C61#4111yescharacteristic
77C22⋊D61—41no—
78C22⋊D61—41no—
79C2×Dic61—21no—
80C2×Dic61—41no—
81D244—21no—
82D244—21no—
83C4×D61—41no—
84C4×D61—41no—
85Dic122—21no—
86Dic122—21no—
87#92418—22no—
88#92418—41no—
89C22×C61—41no—
90C22×C61C4×D411yescharacteristic
91C22×C61#12011yescharacteristic
92C22×C61#12111yescharacteristic
93C2×D61—41no—
94C2×D61—81no—
95C4×C61—24no—
96C4×C61—42no—
97C4×C61—42no—
98C4×C61C2×C22⋊C411yescharacteristic
99C4×C61C4×D411yescharacteristic
100C4×C61#12111yescharacteristic
101C4×C61#12311yescharacteristic
102Dic61—41no—
103Dic61—81no—
104#1905—611nomaximal, Sylow
105C2×C61—21no—
106C2×C61—21no—
107C2×C61—21no—
108C2×C61#38611yescharacteristic
109D61—81no—
110C2×#137—611no—
111#519D6111yescharacteristic, complemented
112#421—611no—
113#419—611no—
114#410—611no—
115#344—611no—
116H(3,ℤ/4)—611no—
117C61#190511yescharacteristic, complemented, Sylow
118C2×#41—611no—
119C22×Q8C2×D6111yescharacteristic
120#137—1222no—
121#137—1222no—
122C2×Q16—612no—
123C2×SD16—612no—
124C2×M16—611no—
125C2×M16—611no—
126C4×Q8—22no—
127C4×Q8—22no—
128#117—22no—
129#117—611no—
130#117C2×D6111yescharacteristic
131#117C2×D6111yescharacteristic
132#104—1222no—
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—611no—
143C2×Q8C4×D6112yes—
144C2×Q8D24412yes—
145C2×Q8C22⋊D6112yes—
146C2×D4—611no—
147C2×D4—1221no—
148C22×C4—21no—
149C22×C4—1221no—
150C22×C4C22×D6111yescharacteristic
151Q16—1224no—
152SD16—1224no—
153M16—1221no—
154M16—1221no—
155M16—1221no—
156M16—1221no—
157C2×C8—612no—
158C2×C8—1221no—
159C4⋊C4—24no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—1221no—
163C22⋊C4—21no—
164C22⋊C4—1221no—
165C22⋊C4C22⋊D6112yes—
166C42—24no—
167C42—21no—
168C42—1221no—
169C42C22⋊D6112yes—
170C23—1221no—
171C23C2×C22⋊D6111yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—22no—
175Q8—1221no—
176Q8—1221no—
177Q8#1175819814yes—
178D4—1221no—
179D4—1221no—
180D4—2441no—
181D4—2441no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—1221no—
188C2×C4—2441no—
189C2×C4—2441no—
190C2×C4—2441no—
191C2×C4C2×C4×D6111yescharacteristic
192C2×C4C2×D24411yescharacteristic
193C2×C4#1175822211yescharacteristic
194C2×C4#1175822211yescharacteristic
195C2×C4C2×C22⋊D6111yescharacteristic
196C2×C4C2×C22⋊D6111yescharacteristic
197C8—1222no—
198C8—2441no—
199C22—41no—
200C22—4881no—
201C22—2441no—
202C22C4×C22⋊D6111yescharacteristic
203C22#1451974611yescharacteristic
204C22#1451975111yescharacteristic
205C4—24no—
206C4—42no—
207C4—42no—
208C4—4881no—
209C4—2441no—
210C4C2×#1175819811yescharacteristic
211C4C4×C22⋊D6111yescharacteristic
212C4#1451975111yescharacteristic
213C4#1451976011yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—4881no—
218C2#1683964111yescharacteristic
subgroupG/H
centerC2#16839641
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#519C2
socleC2×C61#386
hypercenter#519D61
hypocenterC61#1905
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #519

Complements

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

NH ≅ G/Ntype
3. #16839771C2semidirect
5. #16839532C2semidirect
6. #16839518C2semidirect
7. C61×#519C2semidirect
11. C2×#11758202C4semidirect
12. C2×#11758201C4semidirect
111. #519D61semidirect
117. C61#1905semidirect