Finite Group Databasebeta

← #21457202

Subgroups — #21457202

Order 7808.

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

normal subgroups only

This group has 386 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#16840312C211yesmaximal, characteristic
2#16840057C212yesmaximal, complemented
3#16840039C212yesmaximal, complemented
4#16840010C214yesmaximal, complemented
5#16839964C212yesmaximal, complemented
6#16839962C212yesmaximal, complemented
7#16839786C211yesmaximal, characteristic, complemented
8C61×#533C211yesmaximal, characteristic, complemented
9C2×#11758222—21no—
10C2×#11758201C2214yes—
11C2×#11758194C2212yes—
12#14519777C2211yescharacteristic
13#14519774C2211yescharacteristic
14#14519765—21no—
15#14519751—21no—
16#14519751C2212yes—
17C4×D244—21no—
18C4×D244C2212yes—
19#14519710C2214yes—
20C4⋊#92418C2212yes—
21C4⋊#92418C2212yes—
22#14519701C2214yes—
23#14519697C2214yes—
24C4⋊Q8×C61C2211yescharacteristic
25C4⋊Q8×C61C2211yescharacteristic
26#125×C61—21no—
27C22⋊Q8×C61—21no—
28C22⋊Q8×C61C2212yes—
29C4×Q8×C61—21no—
30C4×Q8×C61C2212yes—
31#117×C61—21no—
32C2×C42×C61C2211yescharacteristic
33C2×Q8×C61—21no—
34C2×Q8×C61C2312yes—
35C22×C4×C61D411yescharacteristic
36C22×C4×C61D411yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C2×C22⋊D61—22no—
39#11758222—44no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244C2312yes—
43C2×C4×D61—22no—
44C2×Dic122—21no—
45C4⋊C4×C61—21no—
46C4⋊C4×C61—21no—
47C4⋊C4×C61—21no—
48C4⋊C4×C61—22no—
49C4⋊C4×C61—22no—
50C4⋊C4×C61C2312yes—
51C22⋊C4×C61—22no—
52C42×C61—22no—
53C42×C61D411yescharacteristic
54C42×C61D411yescharacteristic
55C42×C61C2311yescharacteristic
56C42×C61C2311yescharacteristic
57#11758201—44no—
58#11758198—22no—
59#11758198—22no—
60C4⋊Dic61—21no—
61C4⋊Dic61C2312yes—
62#11758194—42no—
63C2×#92418C2314yes—
64C23×C61C2×D411yescharacteristic
65C22×D61—22no—
66Q8×C61—22no—
67Q8×C61—22no—
68Q8×C61—42no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2411yescharacteristic
81C22⋊D61—44no—
82C2×Dic61—22no—
83D244—22no—
84D244—22no—
85D244—42no—
86D244—42no—
87C4×D61—44no—
88Dic122—42no—
89#92418—24no—
90C22×C61—21no—
91C22×C61—21no—
92C22×C61—21no—
93C22×C61C22×D411yescharacteristic
94C2×D61—42no—
95C2×D61—42no—
96C2×D61—42no—
97C4×C61—21no—
98C4×C61—21no—
99C4×C61—21no—
100C4×C61—42no—
101C4×C61—42no—
102C4×C61AGL(1,ℤ/8)12yes—
103C4×C61#13712yes—
104C4×C61H(5,𝔽2)11yescharacteristic
105C4×C612−1+411yescharacteristic
106Dic61—42no—
107#3254—611nomaximal, Sylow
108C2×C61—41no—
109C2×C61#53711yescharacteristic
110C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C61C2×#13711yescharacteristic
112D61—82no—
113#533D6111yescharacteristic, complemented
114#532—611no—
115#477—612no—
116#474—612no—
117#468—614no—
118#461—612no—
119#460—612no—
120#423—611no—
121C61#325411yescharacteristic, complemented, Sylow
122C2×#41—1221no—
123C2×SD16—614no—
124C2×M16—612no—
125C4⋊Q8—611no—
126C4⋊Q8C2×D6111yescharacteristic
127C4⋊Q8C2×D6111yescharacteristic
128#127—611no—
129#125—21no—
130#124—1221no—
131C22⋊Q8—21no—
132C22⋊Q8C2×D6112yes—
133#121—612no—
134#121—1221no—
135C4×Q8—21no—
136C4×Q8C2×D6112yes—
137C4×D4—612no—
138C4×D4—1221no—
139#117—21no—
140C2×C42C2×D6111yescharacteristic
141#107—614no—
142C4⋊C8—612no—
143C4⋊C8—612no—
144#103—614no—
145#102—614no—
146#41—2444no—
147C2×Q8—21no—
148C2×Q8—1221no—
149C2×Q8C22×D6112yes—
150C2×D4—612no—
151C2×D4—1222no—
152C2×D4—1221no—
153C2×D4—1221no—
154C22×C4—1222no—
155C22×C4C22⋊D6111yescharacteristic
156C22×C4C22⋊D6111yescharacteristic
157C22×C4C22×D6111yescharacteristic
158SD16—2444no—
159M16—2442no—
160C2×C8—614no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—22no—
165C4⋊C4—22no—
166C4⋊C4—612no—
167C4⋊C4—1221no—
168C4⋊C4C22×D6112yes—
169C22⋊C4—22no—
170C22⋊C4—1222no—
171C22⋊C4—1222no—
172C42—22no—
173C42C22⋊D6111yescharacteristic
174C42C22⋊D6111yescharacteristic
175C42C22×D6111yescharacteristic
176C42C22×D6111yescharacteristic
177C23—1222no—
178C23C2×C22⋊D6111yescharacteristic
179Q8—22no—
180Q8—22no—
181Q8—42no—
182Q8—2442no—
183D4—1222no—
184D4—1222no—
185D4—2442no—
186D4—2444no—
187D4—2442no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—1222no—
195C2×C4—2444no—
196C2×C4C2×C22⋊D6111yescharacteristic
197C2×C4C2×C22⋊D6111yescharacteristic
198C2×C4C2×C22⋊D6111yescharacteristic
199C2×C4C2×C22⋊D6111yescharacteristic
200C2×C4C2×C22⋊D6111yescharacteristic
201C2×C4C23×D6111yescharacteristic
202C8—1224no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—2442no—
207C22—2442no—
208C22—2442no—
209C22C22×C22⋊D6111yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—42no—
214C4—42no—
215C4—2442no—
216C4#1451980212yes—
217C4#1451980812yes—
218C4#1451982311yescharacteristic
219C4#1451982411yescharacteristic
220C2—41no—
221C2—4882no—
222C2#1684034011yescharacteristic
223C2C2×#1451980211yescharacteristic
224C2C2×#1451980811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#533C2
socleC22×C61C22×D4
hypercenter#533D61
hypocenterC61#3254
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #16840057C2semidirect
3. #16840039C2semidirect
4. #16840010C2semidirect
5. #16839964C2semidirect
6. #16839962C2semidirect
7. #16839786C2semidirect
8. C61×#533C2semidirect
113. #533D61semidirect
121. C61#3254semidirect