Finite Group Databasebeta

← #21445010

Subgroups — #21445010

Order 7808.

250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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#16840434C211yesmaximal, characteristic
2#16840110C211yesmaximal, characteristic, complemented
3#16840039C211yesmaximal, characteristic, complemented
4#16839505C211yesmaximal, characteristic, complemented
5Q8⋊#92418C211yesmaximal, characteristic, complemented
6#16839489C211yesmaximal, characteristic, complemented
7C61×#462C211yesmaximal, characteristic, complemented
8C2×#11758226—21no—
9#14519774—21no—
10#14519774C2211yescharacteristic
11#14519752—22no—
12#14519752—21no—
13C4×D244—21no—
14C4×D244C2211yescharacteristic
15#14519710—21no—
16C4⋊#92418C2211yescharacteristic
17#14519697—21no—
18#14519697—22no—
19C4×#92418C2211yescharacteristic
20C2×Q16×C61—21no—
21C4⋊Q8×C61C2211yescharacteristic
22C4×Q8×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24#103×C61—21no—
25C2×Q8×C61—21no—
26C2×Q8×C61D411yescharacteristic
27#11758226—42no—
28#11758226—42no—
29C2×D244—22no—
30C2×D244—21no—
31C2×D244—21no—
32C2×D244—22no—
33C2×D244D411yescharacteristic
34C2×D244D412yes—
35C2×C4×D61—22no—
36C2×C4×D61—21no—
37Q16×C61—42no—
38C2×C8×C61—21no—
39C4⋊C4×C61—21no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61—21no—
42C4⋊C4×C61D411yescharacteristic
43C42×C61—21no—
44C42×C61C2311yescharacteristic
45#11758198—22no—
46#11758198—21no—
47C4⋊Dic61D411yescharacteristic
48C2×#92418—21no—
49C2×#92418—21no—
50C22×D61—21no—
51C22×D61—22no—
52Q8×C61—21no—
53Q8×C61—41no—
54Q8×C61—41no—
55Q8×C61D812yes—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—41no—
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C2×Dic61—21no—
63D244—21no—
64D244—21no—
65D244—42no—
66D244—44no—
67D244—41no—
68D244—41no—
69D244—41no—
70D244—41no—
71D244—82no—
72C4×D61—44no—
73C4×D61—41no—
74C4×D61—41no—
75C8×C61—41no—
76#92418—41no—
77#92418—41no—
78C22×C61#12011yescharacteristic
79C2×D61—42no—
80C2×D61—41no—
81C2×D61—41no—
82C2×D61—42no—
83C2×D61—42no—
84C2×D61—41no—
85C4×C61—22no—
86C4×C61—21no—
87C4×C61—41no—
88C4×C61—81no—
89C4×C61C2×D811yescharacteristic
90C4×C61#13511yescharacteristic
91C4×C61AGL(1,ℤ/8)11yescharacteristic
92C4×C61#13711yescharacteristic
93Dic61—41no—
94#1641—611nomaximal, Sylow
95C2×C61#44711yescharacteristic
96C2×C61#45211yescharacteristic
97C2×C61#45511yescharacteristic
98D61—81no—
99D61—82no—
100#550—611no—
101#486—611no—
102#474—611no—
103#462D6111yescharacteristic, complemented
104#331—611no—
105Q8⋊C8—611no—
106D4⋊C8—611no—
107C61#164111yescharacteristic, complemented, Sylow
108C2×#41—1221no—
109C2×Q16—21no—
110C4⋊Q8C2×D6111yescharacteristic
111#127—611no—
112#127—1221no—
113#121—1222no—
114#121—1221no—
115C4×Q8C2×D6111yescharacteristic
116C4×D4—611no—
117C4×D4—1221no—
118#107—1221no—
119C4⋊C8—611no—
120C4⋊C8C2×D6111yescharacteristic
121#103—21no—
122#102—1221no—
123#102—1222no—
124C4×C8—611no—
125#41—2442no—
126#41—2442no—
127C2×Q8—21no—
128C2×Q8C22⋊D6111yescharacteristic
129C2×D4—611no—
130C2×D4—612no—
131C2×D4—1222no—
132C2×D4—1222no—
133C2×D4—1221no—
134C2×D4—1221no—
135C22×C4—1222no—
136C22×C4—1221no—
137Q16—42no—
138C2×C8—21no—
139C2×C8—1221no—
140C2×C8—1221no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—611no—
145C4⋊C4C22⋊D6111yescharacteristic
146C22⋊C4—1222no—
147C22⋊C4—1221no—
148C42—21no—
149C42C22×D6111yescharacteristic
150C23—1221no—
151C23—1222no—
152Q8—21no—
153Q8—41no—
154Q8—41no—
155Q8#1175819912yes—
156D4—1221no—
157D4—1221no—
158D4—4882no—
159D4—2442no—
160D4—2444no—
161D4—2441no—
162D4—2441no—
163D4—2441no—
164D4—2441no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—1221no—
169C2×C4—2444no—
170C2×C4—2441no—
171C2×C4—2441no—
172C2×C4D4×D6111yescharacteristic
173C2×C4D4×D6111yescharacteristic
174C2×C4C2×C22⋊D6111yescharacteristic
175C8—41no—
176C8—2441no—
177C8—2441no—
178C22—2441no—
179C22—2442no—
180C22—2442no—
181C22—2441no—
182C22—2441no—
183C22—2442no—
184C22#1451974511yescharacteristic
185C4—21no—
186C4—22no—
187C4—41no—
188C4—81no—
189C4—2441no—
190C4C2×#1175819911yescharacteristic
191C4#1451980011yescharacteristic
192C4#1451980211yescharacteristic
193C4#1451980911yescharacteristic
194C2—4881no—
195C2—4882no—
196C2#1683989511yescharacteristic
197C2#1683992311yescharacteristic
198C2#1683993811yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#462C2
socleC22×C61#120
hypercenter#462D61
hypocenterC61#1641
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. #16840110C2semidirect
3. #16840039C2semidirect
4. #16839505C2semidirect
5. Q8⋊#92418C2semidirect
6. #16839489C2semidirect
7. C61×#462C2semidirect
103. #462D61semidirect
107. C61#1641semidirect