Finite Group Databasebeta

← #21458605

Subgroups — #21458605

Order 7808.

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

normal subgroups only

This group has 340 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, complemented
2#16840473C211yesmaximal, characteristic
3#16840129C212yesmaximal, complemented
4#16840067C212yesmaximal, complemented
5#16840054C211yesmaximal, characteristic, complemented
6#16839966C212yesmaximal
7#16839964C211yesmaximal, characteristic
8#16839892C211yesmaximal, characteristic, complemented
9#16839865C212yesmaximal
10C4×#11758190C211yesmaximal, characteristic
11C61×#487C211yesmaximal, characteristic, complemented
12C2×#11758190C2211yescharacteristic
13C2×#11758201C2212yes—
14#14519775C2212yes—
15#14519768—21no—
16#14519768C2212yes—
17#14519767—22no—
18#14519757—21no—
19#14519753—22no—
20Q8×Dic61C2212yes—
21C4×Dic122C2211yescharacteristic
22C4×Dic122C2211yescharacteristic
23#14519742—21no—
24C4×D244C2211yescharacteristic
25#14519739C2212yes—
26C4⋊C4×D61—21no—
27#14519710C2212yes—
28#14519709C2211yescharacteristic
29C4⋊#92418C2211yescharacteristic
30#14519706C2212yes—
31#14519702C2211yescharacteristic
32#14519701C2212yes—
33#14519700C2212yes—
34#14519699C2211yescharacteristic
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×D244C2311yescharacteristic
44C2×C4×D61—21no—
45C2×C4×D61—22no—
46C2×Dic122D411yescharacteristic
47C2×Dic122C2311yescharacteristic
48C2×C8×C61C2311yescharacteristic
49C2×C8×C61C2311yescharacteristic
50C4⋊C4×C61—21no—
51C4⋊C4×C61—21no—
52C4⋊C4×C61—21no—
53C4⋊C4×C61C2312yes—
54C42×C61C2311yescharacteristic
55#11758201—24no—
56#11758198—21no—
57#11758198—22no—
58C4⋊Dic61—22no—
59C4⋊Dic61—22no—
60C4⋊Dic61D411yescharacteristic
61C4⋊Dic61C2311yescharacteristic
62C4⋊Dic61C2311yescharacteristic
63#11758196—21no—
64#11758196—22no—
65#11758196—22no—
66#11758196—22no—
67#11758196D412yes—
68C4×Dic61—21no—
69C4×Dic61—22no—
70C4×Dic61C2312yes—
71C2×#92418C2312yes—
72#11758190—22no—
73C22×D61—21no—
74Q8×C61—22no—
75Q8×C61—22no—
76Q8×C61—81no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2411yescharacteristic
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61C2×D412yes—
86C2×Dic61C2×D412yes—
87D244—21no—
88D244#4112yes—
89C4×D61—42no—
90C4×D61—82no—
91Dic122—22no—
92Dic122—21no—
93Dic122—21no—
94C8×C61—21no—
95C8×C61—21no—
96#92418—22no—
97C22×C61C22×D411yescharacteristic
98C2×D61—22no—
99C2×D61—41no—
100C2×D61—41no—
101C4×C61—21no—
102C4×C61—42no—
103C4×C61—42no—
104C4×C61#13712yes—
105C4×C61C2×#4111yescharacteristic
106C4×C612−1+411yescharacteristic
107Dic61—22no—
108Dic61—22no—
109Dic61—41no—
110Dic61—41no—
111Dic61—41no—
112#3372—611nomaximal, Sylow
113C2×C61#54811yescharacteristic
114C2×C61C2×#13711yescharacteristic
115C2×C61#57711yescharacteristic
116D61—42no—
117#557—611no—
118#554—611no—
119#491—612no—
120#487D6111yescharacteristic, complemented
121#479—612no—
122#477—611no—
123#461—611no—
124#461—612no—
125#446—611no—
126#440—612no—
127C4×SD16—611no—
128C61#337211yescharacteristic, complemented, Sylow
129C2×SD16—612no—
130C2×SD16—611no—
131C4⋊Q8—612no—
132C4⋊Q8C2×D6111yescharacteristic
133C4⋊Q8C2×D6111yescharacteristic
134#125—612no—
135#125—1222no—
136#125—1221no—
137C22⋊Q8—1221no—
138C22⋊Q8—1222no—
139C4×Q8—611no—
140C4×Q8—612no—
141C4×Q8—611no—
142C4×Q8—1221no—
143C4×D4—612no—
144C4×D4—611no—
145C2×C4⋊C4—1221no—
146#107—612no—
147#106—611no—
148C4⋊C8—612no—
149C4⋊C8—611no—
150#103—612no—
151#103—611no—
152#103—612no—
153#103C2×D6112yes—
154#103C2×D6112yes—
155#102—611no—
156#97—612no—
157C4×C8C2×D6111yescharacteristic
158C2×Q8—21no—
159C2×Q8—611no—
160C2×Q8—611no—
161C2×Q8C22×D6112yes—
162C2×D4—611no—
163C22×C4—1222no—
164C22×C4—1221no—
165SD16—1222no—
166SD16—1224no—
167C2×C8—612no—
168C2×C8C22×D6111yescharacteristic
169C2×C8C22×D6111yescharacteristic
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—611no—
174C4⋊C4—612no—
175C4⋊C4—611no—
176C4⋊C4—611no—
177C4⋊C4—1222no—
178C4⋊C4—1222no—
179C4⋊C4—1222no—
180C4⋊C4—1222no—
181C4⋊C4—1222no—
182C4⋊C4—1221no—
183C4⋊C4C22×D6112yes—
184C22⋊C4—1222no—
185C22⋊C4—1221no—
186C42—612no—
187C42—1222no—
188C42—1221no—
189C42C22×D6111yescharacteristic
190C23—1221no—
191Q8—22no—
192Q8—22no—
193Q8—81no—
194Q8—1222no—
195Q8—1221no—
196Q8—1221no—
197D4—612no—
198D4—1221no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—612no—
202C2×C4—612no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—1221no—
206C2×C4—4882no—
207C2×C4—2442no—
208C2×C4D4×D6111yescharacteristic
209C2×C4D4×D6111yescharacteristic
210C2×C4C23×D6111yescharacteristic
211C8—21no—
212C8—21no—
213C8—1222no—
214C22—1222no—
215C22—2441no—
216C22—2441no—
217C22C2×D4×D6111yescharacteristic
218C4—21no—
219C4—42no—
220C4—42no—
221C4—1222no—
222C4—1222no—
223C4—2441no—
224C4—2441no—
225C4—2441no—
226C4#1451980912yes—
227C4#41×D6111yescharacteristic
228C4#1451982411yescharacteristic
229C2—2442no—
230C2#1684042011yescharacteristic
231C2C2×#1451980911yescharacteristic
232C2#1684056811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#487C2
socleC22×C61C22×D4
hypercenter#487D61
hypocenterC61#3372
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
1. #16840487C2semidirect
3. #16840129C2semidirect
4. #16840067C2semidirect
5. #16840054C2semidirect
8. #16839892C2semidirect
11. C61×#487C2semidirect
120. #487D61semidirect
128. C61#3372semidirect