Finite Group Databasebeta

← #21456119

Subgroups — #21456119

Order 7808.

358 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840374C211yesmaximal, characteristic
2#16840103C212yesmaximal
3#16840069C212yesmaximal, complemented
4#16839972C212yesmaximal, complemented
5#16839918C212yesmaximal
6#16839867C212yesmaximal, complemented
7C4×#11758202C212yesmaximal, complemented
8#16839823C211yesmaximal, characteristic
9C61×#519C211yesmaximal, characteristic
10C2×#11758202C2212yes—
11C2×#11758202C2212yes—
12#14519777C2211yescharacteristic
13#14519770—22no—
14#14519769C2211yescharacteristic
15#14519767—22no—
16#14519756C2212yes—
17C4×Dic122C2212yes—
18#14519710C2212yes—
19#14519708C2212yes—
20C4⋊#92418C2212yes—
21#14519701C2212yes—
22#14519701C2212yes—
23#14519700C2212yes—
24#14519700C2212yes—
25C22⋊#92418C2212yes—
26#14519688C2211yescharacteristic
27C4×#92418C2211yescharacteristic
28C22×Q8×C61C2211yescharacteristic
29C4×Q8×C61—22no—
30C4×Q8×C61C2212yes—
31C4×Q8×C61C2212yes—
32#117×C61—22no—
33#117×C61C2211yescharacteristic
34#117×C61C2211yescharacteristic
35C2×Q8×C61—24no—
36C2×Q8×C61—21no—
37C2×Q8×C61C2312yes—
38C22×C4×C61—21no—
39C22×C4×C61C2311yescharacteristic
40C2×Dic122C2312yes—
41C4⋊C4×C61—22no—
42C4⋊C4×C61—22no—
43C4⋊C4×C61D412yes—
44C4⋊C4×C61C2312yes—
45C22⋊C4×C61—21no—
46C22⋊C4×C61D412yes—
47C42×C61—22no—
48C42×C61—22no—
49C42×C61—21no—
50C42×C61C2311yescharacteristic
51C42×C61C2311yescharacteristic
52C22⋊Dic61—22no—
53#11758202—24no—
54#11758202—24no—
55C4⋊Dic61—22no—
56C4⋊Dic61C2312yes—
57#11758196—22no—
58#11758196—22no—
59#11758196—22no—
60C4×Dic61—22no—
61C2×#92418C2312yes—
62C2×#92418C2312yes—
63C23×C61C2×D411yescharacteristic
64Q8×C61—24no—
65Q8×C61—22no—
66Q8×C61#4114yes—
67C2×C4×C61—24no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61C2×D412yes—
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D412yes—
74C2×C4×C61C2411yescharacteristic
75C2×Dic61—22no—
76C2×Dic61—22no—
77Dic122—22no—
78Dic122—22no—
79#92418—22no—
80#92418—22no—
81C22×C61—21no—
82C22×C61—22no—
83C22×C61C22×D411yescharacteristic
84C4×C61—24no—
85C4×C61—21no—
86C4×C61—22no—
87C4×C61—22no—
88C4×C61—42no—
89C4×C61C2×#4112yes—
90Dic61—42no—
91Dic61—42no—
92#3127—611nomaximal, Sylow
93C2×C61—41no—
94C2×C61#52511yescharacteristic
95C2×C61#57812yes—
96#541—611no—
97#519D6111yescharacteristic
98#485—612no—
99#479—612no—
100#462—612no—
101#451—612no—
102#441—612no—
103C4×Q16—612no—
104#433—611no—
105C61#312711yescharacteristic, complemented, Sylow
106C22×Q8C2×D6111yescharacteristic
107C2×Q16—612no—
108C2×Q16—612no—
109C4⋊Q8—611no—
110#126—1222no—
111#125—611no—
112#125—1222no—
113C22⋊Q8—612no—
114C4×Q8—22no—
115C4×Q8—612no—
116C4×Q8C2×D6112yes—
117C4×Q8C2×D6112yes—
118#117—22no—
119#117C2×D6111yescharacteristic
120#117C2×D6111yescharacteristic
121#107—612no—
122#106—612no—
123C4⋊C8—612no—
124#103—612no—
125#103—612no—
126#103—612no—
127#103—612no—
128C22⋊C8—612no—
129#97—611no—
130C4×C8—611no—
131C2×Q8—24no—
132C2×Q8—21no—
133C2×Q8—612no—
134C2×Q8C22×D6112yes—
135C22×C4—21no—
136C22×C4C22×D6111yescharacteristic
137Q16—1224no—
138Q16—1224no—
139C2×C8—612no—
140C2×C8—612no—
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—612no—
144C4⋊C4—1222no—
145C4⋊C4—1222no—
146C4⋊C4—1222no—
147C4⋊C4—1222no—
148C4⋊C4C22⋊D6112yes—
149C4⋊C4C22×D6112yes—
150C22⋊C4—21no—
151C22⋊C4—1222no—
152C22⋊C4C22⋊D6112yes—
153C42—22no—
154C42—22no—
155C42—21no—
156C42—1222no—
157C42C22×D6111yescharacteristic
158C42C22×D6111yescharacteristic
159C23C2×C22⋊D6111yescharacteristic
160Q8—24no—
161Q8—22no—
162Q8—1222no—
163Q8—1222no—
164Q8#1175822214yes—
165C2×C4—24no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—1222no—
170C2×C4—1222no—
171C2×C4C2×C22⋊D6112yes—
172C2×C4C2×C22⋊D6112yes—
173C2×C4C2×C22⋊D6111yescharacteristic
174C2×C4C23×D6111yescharacteristic
175C8—1222no—
176C8—1222no—
177C22—21no—
178C22—22no—
179C22C22×C22⋊D6111yescharacteristic
180C4—24no—
181C4—21no—
182C4—22no—
183C4—22no—
184C4—42no—
185C4—2442no—
186C4—2442no—
187C4C2×#1175822212yes—
188C2—41no—
189C2#1684027311yescharacteristic
190C2#1684057712yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#519C2
socleC22×C61C22×D4
hypercenter#519D61
hypocenterC61#3127
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
3. #16840069C2semidirect
4. #16839972C2semidirect
6. #16839867C2semidirect
7. C4×#11758202C2semidirect
105. C61#3127semidirect