Finite Group Databasebeta

← #21458627

Subgroups — #21458627

Order 7808.

326 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 115 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#16840487C211yesmaximal, characteristic
2#16840487C211yesmaximal, characteristic
3#16840129C212yesmaximal
4#16840071C212yesmaximal
5#16840044C211yesmaximal, characteristic
6#16839971C212yesmaximal
7#16839969C211yesmaximal, characteristic
8#16839892C211yesmaximal, characteristic
9#16839866C212yesmaximal
10C4×Dic244C211yesmaximal, characteristic
11C61×#487C211yesmaximal, characteristic
12C2×Dic244C2211yescharacteristic
13C2×#11758202C2212yes—
14#14519775—21no—
15#14519775C2212yes—
16#14519768—21no—
17#14519768C2212yes—
18#14519767—22no—
19#14519767—22no—
20Q8×Dic61—21no—
21Q8×Dic61C2212yes—
22C4×Dic122C2211yescharacteristic
23C4×Dic122C2211yescharacteristic
24C4×Dic122C2211yescharacteristic
25#14519742—21no—
26#14519742C2212yes—
27#14519711C2211yescharacteristic
28#14519708C2212yes—
29C4⋊#92418C2211yescharacteristic
30#14519706C2212yes—
31#14519702C2211yescharacteristic
32#14519702C2211yescharacteristic
33#14519701C2212yes—
34#14519700C2212yes—
35#14519687C2212yes—
36C4⋊Q8×C61C2211yescharacteristic
37C4⋊Q8×C61C2211yescharacteristic
38#103×C61C2212yes—
39#103×C61C2212yes—
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61—21no—
42C2×Q8×C61C2312yes—
43C2×Dic122D411yescharacteristic
44C2×Dic122C2311yescharacteristic
45C2×Dic122C2311yescharacteristic
46C2×C8×C61C2311yescharacteristic
47C2×C8×C61C2311yescharacteristic
48C4⋊C4×C61—21no—
49C4⋊C4×C61—21no—
50C4⋊C4×C61—21no—
51C4⋊C4×C61C2312yes—
52C42×C61C2311yescharacteristic
53#11758202—24no—
54C4⋊Dic61—22no—
55C4⋊Dic61—22no—
56C4⋊Dic61D411yescharacteristic
57C4⋊Dic61C2311yescharacteristic
58C4⋊Dic61C2311yescharacteristic
59#11758196—21no—
60#11758196—21no—
61#11758196—22no—
62#11758196—22no—
63#11758196—22no—
64#11758196—22no—
65#11758196D412yes—
66C4×Dic61—21no—
67C4×Dic61—21no—
68C4×Dic61—22no—
69C4×Dic61—22no—
70C4×Dic61C2312yes—
71C2×#92418C2312yes—
72Dic244—22no—
73Q8×C61—22no—
74Q8×C61—22no—
75Q8×C61—42no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2411yescharacteristic
81C2×Dic61—21no—
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61C2×D412yes—
86C2×Dic61C2×D412yes—
87Dic122—22no—
88Dic122—21no—
89Dic122—21no—
90Dic122—21no—
91Dic122#4112yes—
92C8×C61—21no—
93C8×C61—21no—
94#92418—22no—
95C22×C61C22×D411yescharacteristic
96C4×C61—21no—
97C4×C61—42no—
98C4×C61—42no—
99C4×C61#13712yes—
100C4×C61C2×#4111yescharacteristic
101C4×C612−1+411yescharacteristic
102Dic61—22no—
103Dic61—22no—
104Dic61—22no—
105Dic61—41no—
106Dic61—41no—
107Dic61—41no—
108#3374—611nomaximal, Sylow
109C2×C61#54811yescharacteristic
110C2×C61C2×#13711yescharacteristic
111C2×C61#57811yescharacteristic
112#557—611no—
113#557—611no—
114#491—612no—
115#487D6111yescharacteristic
116#479—612no—
117#475—611no—
118#462—611no—
119#462—612no—
120#446—611no—
121#441—612no—
122C4×Q16—611no—
123C61#337411yescharacteristic, complemented, Sylow
124C2×Q16—612no—
125C2×Q16—611no—
126C4⋊Q8—612no—
127C4⋊Q8—1221no—
128C4⋊Q8C2×D6111yescharacteristic
129C4⋊Q8C2×D6111yescharacteristic
130#125—612no—
131#125—1222no—
132#125—1222no—
133#125—1221no—
134C4×Q8—611no—
135C4×Q8—612no—
136C4×Q8—612no—
137C4×Q8—611no—
138C4×Q8—611no—
139C4×Q8—1221no—
140C4×Q8—1221no—
141#107—611no—
142#106—612no—
143C4⋊C8—612no—
144C4⋊C8—611no—
145#103—612no—
146#103—611no—
147#103—611no—
148#103—612no—
149#103C2×D6112yes—
150#103C2×D6112yes—
151#97—612no—
152C4×C8C2×D6111yescharacteristic
153C2×Q8—21no—
154C2×Q8—611no—
155C2×Q8—611no—
156C2×Q8—611no—
157C2×Q8C22×D6112yes—
158Q16—1222no—
159Q16—1224no—
160C2×C8—612no—
161C2×C8C22×D6111yescharacteristic
162C2×C8C22×D6111yescharacteristic
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—612no—
167C4⋊C4—611no—
168C4⋊C4—611no—
169C4⋊C4—611no—
170C4⋊C4—1222no—
171C4⋊C4—1222no—
172C4⋊C4—1222no—
173C4⋊C4—1222no—
174C4⋊C4—1222no—
175C4⋊C4—1222no—
176C4⋊C4—1221no—
177C4⋊C4—1221no—
178C4⋊C4C22×D6112yes—
179C42—612no—
180C42—1222no—
181C42—1222no—
182C42—1221no—
183C42—1221no—
184C42C22×D6111yescharacteristic
185Q8—22no—
186Q8—22no—
187Q8—42no—
188Q8—612no—
189Q8—1221no—
190Q8—1222no—
191Q8—1221no—
192Q8—1221no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—612no—
196C2×C4—612no—
197C2×C4—1221no—
198C2×C4—1221no—
199C2×C4—1221no—
200C2×C4—1221no—
201C2×C4D4×D6111yescharacteristic
202C2×C4D4×D6111yescharacteristic
203C2×C4C23×D6111yescharacteristic
204C8—21no—
205C8—21no—
206C8—1222no—
207C22C2×D4×D6111yescharacteristic
208C4—21no—
209C4—42no—
210C4—42no—
211C4—1222no—
212C4—1222no—
213C4—1222no—
214C4—2441no—
215C4—2441no—
216C4—2441no—
217C4#1451980612yes—
218C4#41×D6111yescharacteristic
219C4#1451982411yescharacteristic
220C2#1684042011yescharacteristic
221C2C2×#1451980611yescharacteristic
222C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#487C2
socleC22×C61C22×D4
hypercenter#487D61
hypocenterC61#3374
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
123. C61#3374semidirect