Finite Group Databasebeta

← #21458622

Subgroups — #21458622

Order 7808.

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

normal subgroups only

This group has 326 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#16840491C211yesmaximal, characteristic
2#16840132C212yesmaximal
3#16840114C211yesmaximal, characteristic
4#16840066C212yesmaximal
5#16840044C211yesmaximal, characteristic
6#16839972C211yesmaximal, characteristic
7#16839972C212yesmaximal
8#16839893C211yesmaximal, characteristic
9#16839867C212yesmaximal
10C4×#11758202C211yesmaximal, characteristic
11C61×#557C211yesmaximal, characteristic
12C2×#11758202C2211yescharacteristic
13C2×#11758202C2212yes—
14#14519777C2211yescharacteristic
15#14519777C2212yes—
16#14519768—21no—
17#14519768—22no—
18Q8×Dic61—21no—
19C4×Dic122C2211yescharacteristic
20C4×Dic122C2212yes—
21#14519710C2211yescharacteristic
22#14519708C2212yes—
23C4⋊#92418C2211yescharacteristic
24C4⋊#92418C2212yes—
25#14519701C2211yescharacteristic
26#14519700C2212yes—
27#14519700C2212yes—
28#14519700C2212yes—
29#14519700C2211yescharacteristic
30#14519700C2212yes—
31#14519688C2212yes—
32C4×#92418C2211yescharacteristic
33C4⋊Q8×C61—21no—
34C4⋊Q8×C61C2211yescharacteristic
35#125×C61—22no—
36#125×C61C2212yes—
37C4×Q8×C61—21no—
38C4×Q8×C61C2211yescharacteristic
39C4×Q8×C61C2212yes—
40C4×Q8×C61C2211yescharacteristic
41C2×Q8×C61—21no—
42C2×Q8×C61D411yescharacteristic
43C2×Q8×C61C2311yescharacteristic
44C2×Dic122C2311yescharacteristic
45C2×Dic122C2312yes—
46C4⋊C4×C61—22no—
47C4⋊C4×C61—21no—
48C4⋊C4×C61—22no—
49C4⋊C4×C61—21no—
50C4⋊C4×C61—22no—
51C4⋊C4×C61D411yescharacteristic
52C4⋊C4×C61D412yes—
53C4⋊C4×C61C2311yescharacteristic
54C4⋊C4×C61C2312yes—
55C42×C61—22no—
56C42×C61—21no—
57C42×C61C2312yes—
58C42×C61C2311yescharacteristic
59#11758202—22no—
60#11758202—24no—
61C4⋊Dic61—22no—
62C4⋊Dic61—21no—
63C4⋊Dic61—22no—
64C4⋊Dic61—21no—
65C4⋊Dic61C2311yescharacteristic
66#11758196—22no—
67#11758196—21no—
68C4×Dic61—22no—
69C4×Dic61—21no—
70C2×#92418C2311yescharacteristic
71C2×#92418C2311yescharacteristic
72C2×#92418C2312yes—
73Q8×C61—22no—
74Q8×C61—21no—
75Q8×C61—42no—
76Q8×C61#4112yes—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—22no—
80C2×C4×C61C2×D412yes—
81C2×C4×C61C2×D412yes—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2411yescharacteristic
85C2×Dic61—21no—
86C2×Dic61—22no—
87C2×Dic61—21no—
88Dic122—21no—
89Dic122—22no—
90Dic122—21no—
91Dic122—22no—
92#92418—21no—
93#92418—22no—
94#92418—21no—
95C22×C61C22×D411yescharacteristic
96C4×C61—22no—
97C4×C61—22no—
98C4×C61—22no—
99C4×C61—21no—
100C4×C61—42no—
101C4×C61—41no—
102C4×C61#13712yes—
103C4×C61C2×#4111yescharacteristic
104C4×C612−1+411yescharacteristic
105Dic61—41no—
106Dic61—42no—
107Dic61—41no—
108#3374—611nomaximal, Sylow
109C2×C61#54811yescharacteristic
110C2×C61C2×#13711yescharacteristic
111C2×C61#57811yescharacteristic
112#557—611no—
113#557D6111yescharacteristic
114#491—612no—
115#487—611no—
116#479—612no—
117#475—611no—
118#462—612no—
119#462—611no—
120#446—611no—
121#441—612no—
122C4×Q16—611no—
123C61#337411yescharacteristic, complemented, Sylow
124C2×Q16—611no—
125C2×Q16—612no—
126C4⋊Q8—21no—
127C4⋊Q8—611no—
128C4⋊Q8—612no—
129C4⋊Q8C2×D6111yescharacteristic
130#125—22no—
131#125—1221no—
132#125—1222no—
133#125C2×D6112yes—
134C4×Q8—21no—
135C4×Q8—611no—
136C4×Q8—612no—
137C4×Q8—1221no—
138C4×Q8C2×D6111yescharacteristic
139C4×Q8C2×D6112yes—
140C4×Q8C2×D6111yescharacteristic
141#107—611no—
142#106—612no—
143C4⋊C8—611no—
144C4⋊C8—612no—
145#103—611no—
146#103—611no—
147#103—612no—
148#103—612no—
149#103—612no—
150#103—612no—
151#97—612no—
152C4×C8—611no—
153C2×Q8—21no—
154C2×Q8—611no—
155C2×Q8—612no—
156C2×Q8C22⋊D6111yescharacteristic
157C2×Q8C22×D6111yescharacteristic
158Q16—1222no—
159Q16—1224no—
160C2×C8—611no—
161C2×C8—611no—
162C2×C8—612no—
163C4⋊C4—22no—
164C4⋊C4—21no—
165C4⋊C4—22no—
166C4⋊C4—21no—
167C4⋊C4—22no—
168C4⋊C4—611no—
169C4⋊C4—1222no—
170C4⋊C4—1221no—
171C4⋊C4—1222no—
172C4⋊C4—1221no—
173C4⋊C4—1222no—
174C4⋊C4—1221no—
175C4⋊C4C22⋊D6111yescharacteristic
176C4⋊C4C22⋊D6112yes—
177C4⋊C4C22×D6112yes—
178C4⋊C4C22×D6111yescharacteristic
179C42—22no—
180C42—21no—
181C42—1222no—
182C42—1221no—
183C42C22×D6111yescharacteristic
184C42C22×D6112yes—
185Q8—21no—
186Q8—22no—
187Q8—42no—
188Q8—1221no—
189Q8—1222no—
190Q8—1221no—
191Q8—1222no—
192Q8#1175822612yes—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—1221no—
197C2×C4—1222no—
198C2×C4—1221no—
199C2×C4C2×C22⋊D6112yes—
200C2×C4C2×C22⋊D6112yes—
201C2×C4C2×C22⋊D6111yescharacteristic
202C2×C4C2×C22⋊D6111yescharacteristic
203C2×C4C23×D6111yescharacteristic
204C8—1221no—
205C8—1222no—
206C8—1221no—
207C22C22×C22⋊D6111yescharacteristic
208C4—22no—
209C4—22no—
210C4—21no—
211C4—22no—
212C4—42no—
213C4—41no—
214C4—2441no—
215C4—2442no—
216C4—2441no—
217C4#1451980712yes—
218C4C2×#1175822611yescharacteristic
219C4#1451982511yescharacteristic
220C2#1684042311yescharacteristic
221C2C2×#1451980711yescharacteristic
222C2#1684057711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#557C2
socleC22×C61C22×D4
hypercenter#557D61
hypocenterC61#3374
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
123. C61#3374semidirect