Finite Group Databasebeta

← #21458674

Subgroups — #21458674

Order 7808.

370 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 133 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#16840492C211yesmaximal, characteristic, complemented
2D4×Dic122C211yesmaximal, characteristic
3#16840159C212yesmaximal, complemented
4#16840158C211yesmaximal, characteristic, complemented
5#16840050C212yesmaximal
6#16840048C211yesmaximal, characteristic, complemented
7#16840046C212yesmaximal, complemented
8#16839886C211yesmaximal, characteristic, complemented
9#16839853C212yesmaximal
10C4×#11758200C211yesmaximal, characteristic
11C61×#476C211yesmaximal, characteristic
12C22×Dic122—21no—
13C2×#11758200C2211yescharacteristic
14#14519777C2211yescharacteristic
15#14519776—21no—
16#14519776C2212yes—
17#14519776C2212yes—
18#14519775—22no—
19#14519756—21no—
20#14519754—22no—
21C4×Dic122C2211yescharacteristic
22C4×Dic122C2211yescharacteristic
23#14519742—21no—
24#14519742C2212yes—
25D4×Dic61C2212yes—
26#14519709C2212yes—
27#14519708C2212yes—
28#14519708C2211yescharacteristic
29#14519708C2212yes—
30#14519706C2212yes—
31#14519702C2212yes—
32#14519700C2211yescharacteristic
33#14519698C2211yescharacteristic
34C4×#92418C2211yescharacteristic
35C8×Dic61C2212yes—
36C4⋊Q8×C61C2211yescharacteristic
37C4×D4×C61C2211yescharacteristic
38#106×C61C2212yes—
39C4⋊C8×C61C2211yescharacteristic
40#102×C61C2212yes—
41C2×Q8×C61—21no—
42C2×D4×C61C2311yescharacteristic
43C22×C4×C61—21no—
44C22×Dic61—22no—
45C2×Dic122—21no—
46C2×Dic122—22no—
47C2×Dic122—22no—
48C2×Dic122—44no—
49C2×Dic122D411yescharacteristic
50C2×Dic122C2311yescharacteristic
51C2×C8×C61C2312yes—
52C4⋊C4×C61—21no—
53C4⋊C4×C61C2312yes—
54C4⋊C4×C61C2311yescharacteristic
55C22⋊C4×C61—21no—
56C42×C61C2311yescharacteristic
57C22⋊Dic61—22no—
58#11758200Q814yescomplemented
59C4⋊Dic61—21no—
60C4⋊Dic61D411yescharacteristic
61C4⋊Dic61C2311yescharacteristic
62C4⋊Dic61C2312yes—
63#11758196—21no—
64#11758196—22no—
65#11758196—22no—
66#11758196—22no—
67#11758196D412yes—
68C4×Dic61—21no—
69C4×Dic61—22no—
70C4×Dic61C2312yes—
71C2×#92418C2311yescharacteristic
72C2×#92418C2311yescharacteristic
73C23×C61—21no—
74Q8×C61—81no—
75D4×C61—21no—
76D4×C61C2×Q812yes—
77C2×C4×C61—22no—
78C2×C4×C61—21no—
79C2×C4×C61—42no—
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2411yescharacteristic
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—22no—
86C2×Dic61—44no—
87C2×Dic61C2×D412yes—
88C2×Dic61C2×D412yes—
89Dic122—21no—
90Dic122—42no—
91Dic122—44no—
92Dic122—82no—
93Dic122SD1614yescomplemented
94Dic122C2×Q812yescomplemented
95C8×C61—22no—
96#92418—21no—
97#92418C2×Q812yescomplemented
98C22×C61—22no—
99C22×C61—41no—
100C22×C61—41no—
101C22×C61C22×D411yescharacteristic
102C4×C61—21no—
103C4×C61—41no—
104C4×C61—42no—
105C4×C61C2×SD1612yes—
106C4×C61C22×Q811yescharacteristic
107C4×C612−1+411yescharacteristic
108Dic61—22no—
109Dic61—22no—
110Dic61—42no—
111Dic61—41no—
112Dic61C2×SD1614yes—
113Q8×SD16—611nomaximal, Sylow
114C2×C61—42no—
115C2×C61D4×Q811yescharacteristic
116C2×C61C22×SD1611yescharacteristic
117C2×C61#57711yescharacteristic
118Q82—611no—
119D4×Q8—611no—
120#498—611no—
121#498—612no—
122#476—612no—
123#476D6111yescharacteristic
124#475—612no—
125#475—611no—
126C8×Q8—611no—
127C4×SD16—611no—
128C4×SD16—612no—
129C61Q8×SD1611yescharacteristic, complemented, Sylow
130C22×Q8—1221no—
131C2×SD16—611no—
132C4⋊Q8—612no—
133C4⋊Q8—612no—
134C4⋊Q8—611no—
135C4⋊Q8—1221no—
136C4⋊Q8—1222no—
137C4⋊Q8C2×D6111yescharacteristic
138C22⋊Q8—1222no—
139C22⋊Q8—1221no—
140C4×Q8—611no—
141C4×Q8—612no—
142C4×Q8—611no—
143C4×Q8—1221no—
144C4×D4—612no—
145C4×D4C2×D6111yescharacteristic
146#106—612no—
147#106—611no—
148#106—612no—
149#106—612no—
150#106C2×D6112yes—
151C4⋊C8—612no—
152C4⋊C8C2×D6111yescharacteristic
153#103—612no—
154#103—611no—
155#102—611no—
156#102C2×D6112yes—
157C4×C8—612no—
158C4×C8—611no—
159C2×Q8—21no—
160C2×Q8—611no—
161C2×Q8—611no—
162C2×Q8—1222no—
163C2×Q8—1222no—
164C2×Q8—1221no—
165C2×Q8—2444no—
166C2×D4C22×D6111yescharacteristic
167C22×C4—21no—
168C22×C4—1222no—
169SD16—614no—
170C2×C8—611no—
171C2×C8—611no—
172C2×C8C22×D6112yes—
173C4⋊C4—21no—
174C4⋊C4—612no—
175C4⋊C4—611no—
176C4⋊C4—611no—
177C4⋊C4—612no—
178C4⋊C4—1222no—
179C4⋊C4—1222no—
180C4⋊C4—1222no—
181C4⋊C4—1221no—
182C4⋊C4—1221no—
183C4⋊C4C22×D6112yes—
184C4⋊C4C22×D6111yescharacteristic
185C22⋊C4—21no—
186C22⋊C4—1222no—
187C42—612no—
188C42—1222no—
189C42—1221no—
190C42C22×D6111yescharacteristic
191C23—21no—
192Q8—81no—
193Q8—614no—
194Q8—612no—
195Q8—1221no—
196Q8—4882no—
197Q8—2444no—
198Q8—2442no—
199D4—21no—
200D4Q8×D6112yes—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—42no—
204C2×C4—612no—
205C2×C4—612no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—1222no—
209C2×C4—2444no—
210C2×C4D4×D6111yescharacteristic
211C2×C4D4×D6111yescharacteristic
212C2×C4C23×D6111yescharacteristic
213C8—22no—
214C8—612no—
215C8—1221no—
216C22—22no—
217C22—41no—
218C22—41no—
219C22C2×D4×D6111yescharacteristic
220C4—21no—
221C4—41no—
222C4—42no—
223C4—614no—
224C4—1222no—
225C4—1222no—
226C4—2442no—
227C4—2441no—
228C4SD16×D6112yes—
229C4C2×Q8×D6111yescharacteristic
230C4#1451982411yescharacteristic
231C2—42no—
232C2#1684042511yescharacteristic
233C2C2×SD16×D6111yescharacteristic
234C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#476C2
socleC22×C61C22×D4
hypercenter#476D61
hypocenterC61Q8×SD16
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #16840492C2semidirect
3. #16840159C2semidirect
4. #16840158C2semidirect
6. #16840048C2semidirect
7. #16840046C2semidirect
8. #16839886C2semidirect
58. #11758200Q8semidirect
93. Dic122SD16semidirect
94. Dic122C2×Q8semidirect
97. #92418C2×Q8semidirect
129. C61Q8×SD16semidirect