Finite Group Databasebeta

← #21458504

Subgroups — #21458504

Order 7808.

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

normal subgroups only

This group has 336 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#16840485C211yesmaximal, characteristic
2#16840119C212yesmaximal
3#16840114C211yesmaximal, characteristic, complemented
4#16840066C212yesmaximal, complemented
5#16840039C211yesmaximal, characteristic
6#16839984C212yesmaximal
7#16839972C211yesmaximal, characteristic, complemented
8Q8×#92418C211yesmaximal, characteristic, complemented
9C4×#11758202C212yesmaximal, complemented
10C4×#11758201C211yesmaximal, characteristic
11C61×#557C211yesmaximal, characteristic, complemented
12C2×#11758202C2212yes—
13C2×#11758201C2211yescharacteristic
14#14519777C2211yescharacteristic
15#14519772—22no—
16#14519765C2212yes—
17#14519753—21no—
18C4×Dic122C2212yes—
19C4×D244C2211yescharacteristic
20#14519735—21no—
21#14519710C2212yes—
22#14519708C2211yescharacteristic
23C4⋊#92418C2211yescharacteristic
24C4⋊#92418C2212yes—
25#14519701C2211yescharacteristic
26#14519700C2212yes—
27#14519700C2212yes—
28#14519700C2212yes—
29#14519697C2212yes—
30#14519697C2211yescharacteristic
31C4×#92418C2211yescharacteristic
32C4×#92418C2212yes—
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×D244C2311yescharacteristic
45C2×C4×D61—21no—
46C2×Dic122C2312yes—
47C4⋊C4×C61—22no—
48C4⋊C4×C61—21no—
49C4⋊C4×C61—22no—
50C4⋊C4×C61—21no—
51C4⋊C4×C61—22no—
52C4⋊C4×C61D411yescharacteristic
53C4⋊C4×C61D412yes—
54C4⋊C4×C61C2311yescharacteristic
55C4⋊C4×C61C2312yes—
56C42×C61—22no—
57C42×C61—21no—
58C42×C61C2312yes—
59C42×C61C2311yescharacteristic
60#11758202—24no—
61#11758201—22no—
62#11758198—22no—
63#11758198—21no—
64#11758198—22no—
65C4⋊Dic61—21no—
66C4⋊Dic61—21no—
67C4⋊Dic61C2311yescharacteristic
68#11758196—22no—
69C4×Dic61—22no—
70C2×#92418C2311yescharacteristic
71C2×#92418C2312yes—
72C2×#92418C2311yescharacteristic
73C22×D61—21no—
74Q8×C61—22no—
75Q8×C61—21no—
76Q8×C61—42no—
77Q8×C61#4112yes—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61C2×D412yes—
82C2×C4×C61C2×D412yes—
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2411yescharacteristic
86C2×Dic61—21no—
87C2×Dic61—22no—
88D244—21no—
89D244—21no—
90C4×D61—42no—
91Dic122—22no—
92Dic122—22no—
93#92418—21no—
94#92418—22no—
95#92418—21no—
96C22×C61C22×D411yescharacteristic
97C2×D61—41no—
98C2×D61—41no—
99C2×D61—41no—
100C4×C61—22no—
101C4×C61—22no—
102C4×C61—22no—
103C4×C61—21no—
104C4×C61—42no—
105C4×C61—41no—
106C4×C61#13512yes—
107C4×C61C2×#4111yescharacteristic
108C4×C612−1+411yescharacteristic
109Dic61—42no—
110Dic61—41no—
111#3364—611nomaximal, Sylow
112C2×C61#54811yescharacteristic
113C2×C61C2×#13511yescharacteristic
114C2×C61#57811yescharacteristic
115D61—81no—
116#557D6111yescharacteristic, complemented
117#556—611no—
118#488—612no—
119#487—611no—
120#479—612no—
121#474—611no—
122#464—612no—
123#462—611no—
124C8×Q8—611no—
125C4×Q16—612no—
126C4×SD16—611no—
127C61#336411yescharacteristic, complemented, Sylow
128C2×Q16—612no—
129C2×SD16—611no—
130C4⋊Q8—21no—
131C4⋊Q8—611no—
132C4⋊Q8C2×D6111yescharacteristic
133#126—1222no—
134#125—22no—
135#125C2×D6112yes—
136#124—612no—
137C22⋊Q8—1221no—
138C4×Q8—21no—
139C4×Q8—612no—
140C4×Q8C2×D6111yescharacteristic
141C4×Q8C2×D6112yes—
142C4×Q8C2×D6111yescharacteristic
143C4×D4—611no—
144#117—1221no—
145#107—612no—
146#106—611no—
147C4⋊C8—611no—
148C4⋊C8—612no—
149#103—611no—
150#103—612no—
151#103—612no—
152#103—612no—
153#102—611no—
154#102—612no—
155C4×C8—611no—
156C4×C8—612no—
157C2×Q8—21no—
158C2×Q8—612no—
159C2×Q8C22⋊D6111yescharacteristic
160C2×Q8C22×D6111yescharacteristic
161C2×D4—611no—
162C22×C4—1221no—
163Q16—1224no—
164SD16—1222no—
165C2×C8—611no—
166C2×C8—612no—
167C2×C8—611no—
168C4⋊C4—22no—
169C4⋊C4—21no—
170C4⋊C4—22no—
171C4⋊C4—21no—
172C4⋊C4—22no—
173C4⋊C4—611no—
174C4⋊C4—1222no—
175C4⋊C4—1221no—
176C4⋊C4—1221no—
177C4⋊C4C22⋊D6111yescharacteristic
178C4⋊C4C22⋊D6112yes—
179C4⋊C4C22×D6111yescharacteristic
180C4⋊C4C22×D6112yes—
181C22⋊C4—1222no—
182C22⋊C4—1221no—
183C22⋊C4—1222no—
184C42—22no—
185C42—21no—
186C42—1222no—
187C42C22×D6111yescharacteristic
188C42C22×D6112yes—
189C23—1221no—
190Q8—21no—
191Q8—22no—
192Q8—42no—
193Q8—1222no—
194Q8—1222no—
195Q8#1175822612yes—
196D4—1221no—
197D4—1221no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—1221no—
202C2×C4—1222no—
203C2×C4—2442no—
204C2×C4C2×C22⋊D6112yes—
205C2×C4C2×C22⋊D6111yescharacteristic
206C2×C4C2×C22⋊D6112yes—
207C2×C4C2×C22⋊D6111yescharacteristic
208C2×C4C23×D6111yescharacteristic
209C8—1221no—
210C8—1222no—
211C8—1221no—
212C22—2441no—
213C22—2441no—
214C22—2441no—
215C22C22×C22⋊D6111yescharacteristic
216C4—22no—
217C4—22no—
218C4—21no—
219C4—22no—
220C4—42no—
221C4—41no—
222C4—2441no—
223C4—2442no—
224C4#1451979712yes—
225C4C2×#1175822611yescharacteristic
226C4#1451982511yescharacteristic
227C2—4881no—
228C2#1684042311yescharacteristic
229C2C2×#1451979711yescharacteristic
230C2#1684057711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#557C2
socleC22×C61C22×D4
hypercenter#557D61
hypocenterC61#3364
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
3. #16840114C2semidirect
4. #16840066C2semidirect
7. #16839972C2semidirect
8. Q8×#92418C2semidirect
9. C4×#11758202C2semidirect
11. C61×#557C2semidirect
116. #557D61semidirect
127. C61#3364semidirect