Finite Group Databasebeta

← #21444834

Subgroups — #21444834

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#16840349C211yesmaximal, characteristic
2#16840093C211yesmaximal, characteristic, complemented
3#16840073C211yesmaximal, characteristic, complemented
4#16839689C211yesmaximal, characteristic, complemented
5#16839498C211yesmaximal, characteristic, complemented
6#16839485C211yesmaximal, characteristic, complemented
7C61×#327C211yesmaximal, characteristic, complemented
8#14519772—21no—
9#14519763—21no—
10#14519761—21no—
11#14519756C2211yescharacteristic
12#14519749—21no—
13#14519745—21no—
14D4×Dic61—21no—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×#11758198—21no—
17C2×#11758198C2211yescharacteristic
18#14519710—21no—
19#14519709—21no—
20#14519702—21no—
21#14519698—21no—
22C22⋊#92418C2211yescharacteristic
23#14519684—21no—
24#121×C61C2211yescharacteristic
25C22⋊C8×C61C2211yescharacteristic
26#95×C61C2211yescharacteristic
27C23×D61D411yescharacteristic
28C2×D4×C61—21no—
29C2×D4×C61D411yescharacteristic
30C22×C4×C61—21no—
31C22×C4×C61C2311yescharacteristic
32C2×C22⋊D61—21no—
33C2×C22⋊D61—21no—
34C22×Dic61—21no—
35C22×Dic61—21no—
36C22×Dic61D411yescharacteristic
37C2×Dic122D411yescharacteristic
38C2×C8×C61—21no—
39C4⋊C4×C61D411yescharacteristic
40C22⋊C4×C61—21no—
41C22⋊Dic61—21no—
42C22⋊Dic61—21no—
43#11758198—21no—
44#11758198—21no—
45#11758198—21no—
46#11758198—21no—
47#11758198—42no—
48C4⋊Dic61—21no—
49C4⋊Dic61—21no—
50C4⋊Dic61—21no—
51C4⋊Dic61D411yescharacteristic
52#11758196—21no—
53C4×Dic61—21no—
54C2×#92418—21no—
55C23×C61—21no—
56C23×C61C2×D411yescharacteristic
57C22×D61—21no—
58C22×D61—21no—
59C22×D61—21no—
60C22×D61—41no—
61C22×D61—41no—
62D4×C61—41no—
63D4×C61—41no—
64D4×C61—41no—
65C2×C4×C61—21no—
66C2×C4×C61—41no—
67C2×C4×C61—41no—
68C2×C4×C61—41no—
69C2×C4×C61—41no—
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C22⋊D61—81no—
73C22⋊D61—81no—
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—41no—
78C2×Dic61—41no—
79C2×Dic61—41no—
80C2×Dic61—41no—
81C2×Dic61—81no—
82Dic122—41no—
83C8×C61—41no—
84#92418—41no—
85C22×C61—21no—
86C22×C61—21no—
87C22×C61—41no—
88C22×C61—41no—
89C22×C61—41no—
90C22×C61#12011yescharacteristic
91C22×C61#13511yescharacteristic
92C22×C61AGL(1,ℤ/8)11yescharacteristic
93C2×D61—42no—
94C2×D61—41no—
95C2×D61—41no—
96C2×D61—41no—
97C2×D61—81no—
98C4×C61—21no—
99C4×C61—21no—
100C4×C61—41no—
101C4×C61—81no—
102Dic61—41no—
103Dic61—41no—
104Dic61—41no—
105Dic61—81no—
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#397—611no—
118#328—611no—
119#327D6111yescharacteristic, complemented
120#323—611no—
121C61#161211yescharacteristic, complemented, Sylow
122#126—1221no—
123#124—1221no—
124#123—1221no—
125C22⋊Q8—611no—
126#121—1221no—
127#121C2×D6111yescharacteristic
128#120—1221no—
129C4×D4—1221no—
130C2×C4⋊C4—611no—
131C2×C22⋊C4—611no—
132C2×C22⋊C4—1221no—
133#107—1221no—
134#106—1221no—
135#103—1221no—
136#102—1221no—
137C22⋊C8—611no—
138C22⋊C8C2×D6111yescharacteristic
139#95—1221no—
140#95C2×D6111yescharacteristic
141C24—611no—
142C2×Q8—611no—
143C2×D4—21no—
144C2×D4—1221no—
145C2×D4—1221no—
146C2×D4D24411yescharacteristic
147C22×C4—21no—
148C22×C4—611no—
149C22×C4—1221no—
150C22×C4—1221no—
151C22×C4C22×D6111yescharacteristic
152C2×C8—21no—
153C2×C8—1221no—
154C4⋊C4—611no—
155C4⋊C4—1221no—
156C4⋊C4—1221no—
157C4⋊C4—1221no—
158C4⋊C4—1221no—
159C4⋊C4D24411yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—1221no—
162C22⋊C4—1221no—
163C22⋊C4—1221no—
164C22⋊C4—1221no—
165C22⋊C4—1221no—
166C22⋊C4—1221no—
167C22⋊C4—2442no—
168C42—1221no—
169C23—21no—
170C23—1221no—
171C23—1221no—
172C23—1221no—
173C23—2441no—
174C23—2441no—
175C23D4×D6111yescharacteristic
176Q8—2441no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—4881no—
181D4—4881no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—1221no—
188C2×C4—1221no—
189C2×C4—1221no—
190C2×C4—4881no—
191C2×C4—2441no—
192C2×C4—2441no—
193C2×C4—2441no—
194C2×C4—2441no—
195C2×C4C2×D24411yescharacteristic
196C2×C4D4×D6111yescharacteristic
197C8—41no—
198C8—2441no—
199C22—21no—
200C22—21no—
201C22—41no—
202C22—41no—
203C22—41no—
204C22—4881no—
205C22—2442no—
206C22—2441no—
207C22—2441no—
208C22—2441no—
209C22#1451974711yescharacteristic
210C22#1451979811yescharacteristic
211C22#1451980111yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—4881no—
217C4—2441no—
218C4—2441no—
219C4—2441no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—4881no—
224C2#1683990811yescharacteristic
225C2#1683994111yescharacteristic
226C2#1683995311yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#327C2
socleC22×C61#120
hypercenter#327D61
hypocenterC61#1612
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #16840093C2semidirect
3. #16840073C2semidirect
4. #16839689C2semidirect
5. #16839498C2semidirect
6. #16839485C2semidirect
7. C61×#327C2semidirect
119. #327D61semidirect
121. C61#1612semidirect