Finite Group Databasebeta

← #21444831

Subgroups — #21444831

Order 7808.

232 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 49 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#16840350C211yesmaximal, characteristic
2#16840092C211yesmaximal, characteristic, complemented
3#16840075C211yesmaximal, characteristic, complemented
4#16839498C211yesmaximal, characteristic, complemented
5#16839495C211yesmaximal, characteristic, complemented
6#16839486C211yesmaximal, characteristic, complemented
7C61×#397C211yesmaximal, characteristic, complemented
8#14519770—21no—
9#14519763—21no—
10#14519759—21no—
11#14519756C2211yescharacteristic
12#14519751C2211yescharacteristic
13#14519750—21no—
14#14519746—21no—
15C4×C22⋊D61—21no—
16#14519710—21no—
17#14519708—21no—
18#14519700—21no—
19#14519697—21no—
20C22⋊#92418C2211yescharacteristic
21C22⋊#92418C2211yescharacteristic
22C2×C4⋊C4×C61C2211yescharacteristic
23C2×C22⋊C4×C61—21no—
24C2×C22⋊C4×C61C2211yescharacteristic
25#95×C61—21no—
26#95×C61C2211yescharacteristic
27C24×C61D411yescharacteristic
28C22×C4×C61—21no—
29C22×C4×C61—21no—
30C22×C4×C61D411yescharacteristic
31C22×C4×C61C2311yescharacteristic
32C2×C22⋊D61—21no—
33C2×C22⋊D61—21no—
34C2×C22⋊D61—21no—
35C2×D244D411yescharacteristic
36C2×C4×D61—21no—
37C2×Dic122D411yescharacteristic
38C4⋊C4×C61—21no—
39C4⋊C4×C61—21no—
40C22⋊C4×C61—21no—
41C22⋊C4×C61—21no—
42C22⋊C4×C61—42no—
43C22⋊Dic61—21no—
44C22⋊Dic61—21no—
45C22⋊Dic61—21no—
46#11758198—21no—
47#11758198—21no—
48C4⋊Dic61D411yescharacteristic
49C4⋊Dic61D411yescharacteristic
50#11758196—21no—
51#11758196—21no—
52C4×Dic61—21no—
53C2×#92418—21no—
54C2×#92418—21no—
55C23×C61—21no—
56C23×C61—21no—
57C23×C61—21no—
58C23×C61—41no—
59C23×C61—41no—
60C23×C61C2×D411yescharacteristic
61C22×D61—21no—
62C2×C4×C61—21no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61—41no—
68C2×C4×C61—41no—
69C2×C4×C61—41no—
70C2×C4×C61—41no—
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C22⋊D61—41no—
74C22⋊D61—41no—
75C22⋊D61—81no—
76C22⋊D61—81no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80D244—41no—
81C4×D61—81no—
82Dic122—41no—
83#92418—41no—
84#92418—41no—
85C22×C61—21no—
86C22×C61—21no—
87C22×C61—42no—
88C22×C61—41no—
89C22×C61—41no—
90C22×C61—41no—
91C22×C61—81no—
92C22×C61#12011yescharacteristic
93C22×C61#13511yescharacteristic
94C22×C61AGL(1,ℤ/8)11yescharacteristic
95C2×D61—41no—
96C2×D61—41no—
97C2×D61—41no—
98C4×C61—21no—
99C4×C61—21no—
100C4×C61—41no—
101C4×C61—81no—
102C4×C61—81no—
103Dic61—41no—
104Dic61—41no—
105Dic61—41no—
106#1612—611nomaximal, Sylow
107C2×C61—21no—
108C2×C61—21no—
109C2×C61—81no—
110C2×C61#44911yescharacteristic
111C2×C61#45511yescharacteristic
112C2×C61#45811yescharacteristic
113D61—81no—
114#538—611no—
115#483—611no—
116#480—611no—
117#397D6111yescharacteristic, complemented
118#328—611no—
119#327—611no—
120#323—611no—
121C61#161211yescharacteristic, complemented, Sylow
122#126—1221no—
123#124—1221no—
124#123—1221no—
125C22⋊Q8—611no—
126#121—611no—
127#121—1221no—
128#120—1221no—
129C4×D4—1221no—
130C2×C4⋊C4C2×D6111yescharacteristic
131C2×C22⋊C4—21no—
132C2×C22⋊C4C2×D6111yescharacteristic
133#107—1221no—
134#106—1221no—
135#103—1221no—
136#102—1221no—
137C22⋊C8—611no—
138C22⋊C8—611no—
139#95—21no—
140#95C2×D6111yescharacteristic
141C24C22⋊D6111yescharacteristic
142C2×Q8—611no—
143C2×D4—611no—
144C2×D4—1221no—
145C2×D4—1221no—
146C2×D4—1221no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—1221no—
150C22×C4C22⋊D6111yescharacteristic
151C22×C4C22×D6111yescharacteristic
152C2×C8—1221no—
153C2×C8—1221no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—611no—
157C4⋊C4—611no—
158C4⋊C4—1221no—
159C4⋊C4—1221no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—42no—
163C22⋊C4—1221no—
164C22⋊C4—1221no—
165C22⋊C4—1221no—
166C22⋊C4—1221no—
167C22⋊C4—1221no—
168C42—1221no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—1221no—
175C23C2×C22⋊D6111yescharacteristic
176Q8—2441no—
177D4—4881no—
178D4—4881no—
179D4—2441no—
180D4—2441no—
181D4—2441no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—4881no—
195C2×C4D4×D6111yescharacteristic
196C2×C4D4×D6111yescharacteristic
197C8—2441no—
198C8—2441no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—81no—
206C22—2441no—
207C22—2441no—
208C22—2441no—
209C22#1451974511yescharacteristic
210C22#1451979711yescharacteristic
211C22#1451980311yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—81no—
217C4—2441no—
218C4—2441no—
219C4—2441no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—4881no—
224C2#1683990511yescharacteristic
225C2#1683993911yescharacteristic
226C2#1683995111yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#397C2
socleC22×C61#120
hypercenter#397D61
hypocenterC61#1612
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #16840092C2semidirect
3. #16840075C2semidirect
4. #16839498C2semidirect
5. #16839495C2semidirect
6. #16839486C2semidirect
7. C61×#397C2semidirect
117. #397D61semidirect
121. C61#1612semidirect