Finite Group Databasebeta

← #21458728

Subgroups — #21458728

Order 7808.

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

normal subgroups only

This group has 340 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
1Q8×Dic122C211yesmaximal, characteristic, complemented
2#16840473C211yesmaximal, characteristic
3#16840170C212yesmaximal, complemented
4#16840165C211yesmaximal, characteristic, complemented
5#16840067C212yesmaximal, complemented
6#16840053C211yesmaximal, characteristic
7#16840041C212yesmaximal
8#16839889C211yesmaximal, characteristic, complemented
9#16839865C212yesmaximal
10C4×#11758201C211yesmaximal, characteristic
11C61×#477C211yesmaximal, characteristic, complemented
12C2×#11758201C2211yescharacteristic
13#14519777—21no—
14#14519777C2211yescharacteristic
15#14519776—22no—
16#14519776C2212yes—
17#14519768C2212yes—
18#14519757—21no—
19#14519753—22no—
20Q8×Dic61C2212yes—
21C4×Dic122—21no—
22C4×Dic122C2211yescharacteristic
23C4×D244C2211yescharacteristic
24#14519739C2212yes—
25C4⋊C4×D61—21no—
26#14519710C2212yes—
27#14519710C2212yes—
28#14519709C2212yes—
29#14519708C2211yescharacteristic
30#14519706C2212yes—
31#14519701C2211yescharacteristic
32#14519699C2212yes—
33#14519697C2211yescharacteristic
34#14519687C2212yes—
35C4×#92418C2211yescharacteristic
36C4⋊Q8×C61C2211yescharacteristic
37C4×Q8×C61C2211yescharacteristic
38#107×C61C2212yes—
39C4⋊C8×C61C2211yescharacteristic
40#103×C61C2212yes—
41C2×Q8×C61—21no—
42C2×Q8×C61C2311yescharacteristic
43C2×D244C2311yescharacteristic
44C2×C4×D61—21no—
45C2×C4×D61—22no—
46C2×Dic122—21no—
47C2×Dic122—22no—
48C2×Dic122D411yescharacteristic
49C2×C8×C61C2312yes—
50C4⋊C4×C61—21no—
51C4⋊C4×C61—21no—
52C4⋊C4×C61C2312yes—
53C4⋊C4×C61C2311yescharacteristic
54C42×C61—21no—
55C42×C61C2311yescharacteristic
56#11758201Q814yescomplemented
57#11758198—21no—
58#11758198—22no—
59C4⋊Dic61—21no—
60C4⋊Dic61—22no—
61C4⋊Dic61—22no—
62C4⋊Dic61D411yescharacteristic
63C4⋊Dic61C2312yes—
64C4⋊Dic61C2311yescharacteristic
65#11758196—22no—
66#11758196—22no—
67#11758196D412yes—
68C4×Dic61—22no—
69C4×Dic61C2312yes—
70C2×#92418C2311yescharacteristic
71C2×#92418C2311yescharacteristic
72C22×D61—21no—
73Q8×C61—21no—
74Q8×C61—81no—
75Q8×C61C2×Q812yes—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—22no—
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2411yescharacteristic
82C2×Dic61—22no—
83C2×Dic61—21no—
84C2×Dic61C2×D412yes—
85C2×Dic61C2×D412yes—
86D244—21no—
87D244C2×Q812yes—
88C4×D61—42no—
89C4×D61—82no—
90Dic122—22no—
91Dic122—82no—
92Dic122—81no—
93C8×C61—22no—
94#92418—21no—
95#92418C2×Q812yes—
96C22×C61C22×D411yescharacteristic
97C2×D61—22no—
98C2×D61—41no—
99C2×D61—41no—
100C4×C61—22no—
101C4×C61—21no—
102C4×C61—41no—
103C4×C61—42no—
104C4×C61#13712yes—
105C4×C61C22×Q811yescharacteristic
106C4×C612−1+411yescharacteristic
107Dic61—22no—
108Dic61—22no—
109Dic61—41no—
110Dic61—42no—
111#3385—611nomaximal, Sylow
112C2×C61D4×Q811yescharacteristic
113C2×C61C2×#13711yescharacteristic
114C2×C61#57611yescharacteristic
115D61—42no—
116Q82—611no—
117#554—611no—
118#501—612no—
119#500—611no—
120#479—612no—
121#477D6111yescharacteristic, complemented
122#476—611no—
123#474—612no—
124#446—611no—
125#440—612no—
126C4×SD16—611no—
127C61#338511yescharacteristic, complemented, Sylow
128C2×SD16—611no—
129C4⋊Q8—612no—
130C4⋊Q8—611no—
131C4⋊Q8—1221no—
132C4⋊Q8—1222no—
133C4⋊Q8C2×D6111yescharacteristic
134#125—612no—
135C22⋊Q8—1221no—
136C22⋊Q8—1222no—
137C4×Q8—611no—
138C4×Q8—612no—
139C4×Q8—1221no—
140C4×Q8C2×D6111yescharacteristic
141C4×D4—612no—
142C4×D4—611no—
143C2×C4⋊C4—1221no—
144#107—612no—
145#107—612no—
146#107C2×D6112yes—
147#106—612no—
148#106—611no—
149C4⋊C8—612no—
150C4⋊C8C2×D6111yescharacteristic
151#103—611no—
152#103C2×D6112yes—
153#102—612no—
154#102—611no—
155#97—612no—
156C4×C8—611no—
157C2×Q8—21no—
158C2×Q8—611no—
159C2×Q8—1222no—
160C2×Q8—1221no—
161C2×Q8C22×D6111yescharacteristic
162C2×D4—611no—
163C22×C4—1222no—
164C22×C4—1221no—
165SD16—614no—
166C2×C8—611no—
167C2×C8—611no—
168C2×C8C22×D6112yes—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—611no—
172C4⋊C4—612no—
173C4⋊C4—612no—
174C4⋊C4—611no—
175C4⋊C4—1222no—
176C4⋊C4—1222no—
177C4⋊C4—1222no—
178C4⋊C4—1222no—
179C4⋊C4—1221no—
180C4⋊C4C22×D6111yescharacteristic
181C4⋊C4C22×D6112yes—
182C22⋊C4—1222no—
183C22⋊C4—1221no—
184C42—21no—
185C42—612no—
186C42—1222no—
187C42C22×D6111yescharacteristic
188C23—1221no—
189Q8—21no—
190Q8—81no—
191Q8—1222no—
192Q8—4881no—
193Q8—4882no—
194Q8Q8×D6112yes—
195D4—612no—
196D4—1221no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—612no—
201C2×C4—612no—
202C2×C4—1222no—
203C2×C4—1221no—
204C2×C4—4882no—
205C2×C4—2442no—
206C2×C4D4×D6111yescharacteristic
207C2×C4D4×D6111yescharacteristic
208C2×C4C23×D6111yescharacteristic
209C8—22no—
210C8—612no—
211C8—1221no—
212C22—1222no—
213C22—2441no—
214C22—2441no—
215C22C2×D4×D6111yescharacteristic
216C4—21no—
217C4—22no—
218C4—42no—
219C4—41no—
220C4—1222no—
221C4—1222no—
222C4—2441no—
223C4—2442no—
224C4#1451980912yes—
225C4C2×Q8×D6111yescharacteristic
226C4#1451982411yescharacteristic
227C2—2442no—
228C2#1684042511yescharacteristic
229C2C2×#1451980911yescharacteristic
230C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#477C2
socleC22×C61C22×D4
hypercenter#477D61
hypocenterC61#3385
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. Q8×Dic122C2semidirect
3. #16840170C2semidirect
4. #16840165C2semidirect
5. #16840067C2semidirect
8. #16839889C2semidirect
11. C61×#477C2semidirect
56. #11758201Q8semidirect
121. #477D61semidirect
127. C61#3385semidirect