Finite Group Databasebeta

← #21458618

Subgroups — #21458618

Order 7808.

326 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 123 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#16840490C211yesmaximal, characteristic
2#16840130C212yesmaximal
3#16840112C211yesmaximal, characteristic
4#16840069C212yesmaximal
5#16840047C211yesmaximal, characteristic
6#16839969C211yesmaximal, characteristic
7#16839969C212yesmaximal
8#16839893C211yesmaximal, characteristic
9#16839867C212yesmaximal
10C4×#11758202C211yesmaximal, characteristic
11C61×#557C211yesmaximal, characteristic
12C2×#11758202C2211yescharacteristic
13C2×#11758202C2212yes—
14#14519777C2211yescharacteristic
15#14519775—21no—
16#14519769C2212yes—
17#14519767—22no—
18C4×Dic122C2211yescharacteristic
19C4×Dic122C2212yes—
20#14519742—21no—
21#14519710C2211yescharacteristic
22#14519708C2212yes—
23C4⋊#92418C2211yescharacteristic
24C4⋊#92418C2212yes—
25#14519701C2212yes—
26#14519701C2212yes—
27#14519701C2212yes—
28#14519701C2211yescharacteristic
29#14519701C2212yes—
30#14519700C2211yescharacteristic
31#14519688C2212yes—
32C4×#92418C2211yescharacteristic
33C4⋊Q8×C61C2211yescharacteristic
34C4⋊Q8×C61C2212yes—
35#125×C61—21no—
36#125×C61—22no—
37C4×Q8×C61—21no—
38C4×Q8×C61C2211yescharacteristic
39C4×Q8×C61C2212yes—
40C4×Q8×C61C2211yescharacteristic
41C2×Q8×C61D411yescharacteristic
42C2×Q8×C61C2311yescharacteristic
43C2×Q8×C61C2312yes—
44C2×Dic122—21no—
45C2×Dic122C2311yescharacteristic
46C4⋊C4×C61—22no—
47C4⋊C4×C61—21no—
48C4⋊C4×C61—22no—
49C4⋊C4×C61—21no—
50C4⋊C4×C61—22no—
51C4⋊C4×C61—21no—
52C4⋊C4×C61D411yescharacteristic
53C4⋊C4×C61D412yes—
54C4⋊C4×C61C2311yescharacteristic
55C42×C61—22no—
56C42×C61—21no—
57C42×C61C2311yescharacteristic
58C42×C61C2312yes—
59#11758202—22no—
60#11758202—24no—
61C4⋊Dic61—21no—
62C4⋊Dic61C2312yes—
63C4⋊Dic61C2311yescharacteristic
64#11758196—22no—
65#11758196—21no—
66#11758196—22no—
67#11758196—22no—
68C4×Dic61—22no—
69C4×Dic61—21no—
70C2×#92418C2311yescharacteristic
71C2×#92418C2311yescharacteristic
72C2×#92418C2312yes—
73Q8×C61—22no—
74Q8×C61—21no—
75Q8×C61—22no—
76Q8×C61—21no—
77Q8×C61—22no—
78C2×C4×C61—21no—
79C2×C4×C61—22no—
80C2×C4×C61—21no—
81C2×C4×C61C2×D412yes—
82C2×C4×C61C2×D412yes—
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2411yescharacteristic
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—22no—
89Dic122—21no—
90Dic122—42no—
91Dic122#4112yes—
92#92418—21no—
93#92418—22no—
94#92418—21no—
95C22×C61C22×D411yescharacteristic
96C4×C61—22no—
97C4×C61—22no—
98C4×C61—21no—
99C4×C61—42no—
100C4×C61—41no—
101C4×C61—41no—
102C4×C61#13712yes—
103C4×C61C2×#4111yescharacteristic
104C4×C612−1+411yescharacteristic
105Dic61—22no—
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—611no—
127C4⋊Q8—1221no—
128C4⋊Q8C2×D6111yescharacteristic
129C4⋊Q8C2×D6112yes—
130#125—21no—
131#125—22no—
132#125—612no—
133#125—1222no—
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—612no—
147#103—612no—
148#103—612no—
149#103—612no—
150#103—611no—
151#97—612no—
152C4×C8—611no—
153C2×Q8—611no—
154C2×Q8—1221no—
155C2×Q8C22⋊D6111yescharacteristic
156C2×Q8C22×D6111yescharacteristic
157C2×Q8C22×D6112yes—
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—21no—
169C4⋊C4—612no—
170C4⋊C4—611no—
171C4⋊C4—1221no—
172C4⋊C4—1222no—
173C4⋊C4—1222no—
174C4⋊C4—1222no—
175C4⋊C4—1221no—
176C4⋊C4C22⋊D6111yescharacteristic
177C4⋊C4C22⋊D6112yes—
178C4⋊C4C22×D6111yescharacteristic
179C42—22no—
180C42—21no—
181C42—1222no—
182C42—1221no—
183C42C22×D6111yescharacteristic
184C42C22×D6112yes—
185Q8—22no—
186Q8—21no—
187Q8—22no—
188Q8—21no—
189Q8—22no—
190Q8—612no—
191Q8—1221no—
192Q8—2442no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—1222no—
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—41no—
212C4—42no—
213C4—41no—
214C4—1222no—
215C4—2442no—
216C4—2441no—
217C4#1451980812yes—
218C4#41×D6111yescharacteristic
219C4#1451982411yescharacteristic
220C2#1684041911yescharacteristic
221C2C2×#1451980811yescharacteristic
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