Finite Group Databasebeta

← #21444857

Subgroups — #21444857

Order 7808.

246 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 51 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#16840339C211yesmaximal, characteristic
2#16840081C211yesmaximal, characteristic, complemented
3#16840078C211yesmaximal, characteristic, complemented
4#16839702C211yesmaximal, characteristic, complemented
5#16839495C211yesmaximal, characteristic, complemented
6#16839487C211yesmaximal, characteristic, complemented
7C61×#327C211yesmaximal, characteristic, complemented
8C2×#11758224—21no—
9#14519755—21no—
10#14519754—21no—
11#14519751C2211yescharacteristic
12#14519750—21no—
13#14519749—21no—
14#14519749—21no—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×#11758196C2211yescharacteristic
17#14519709—21no—
18#14519708—21no—
19#14519699—21no—
20#14519698—21no—
21C22⋊#92418C2211yescharacteristic
22#14519684—21no—
23#14519684—21no—
24#121×C61C2211yescharacteristic
25C22⋊C8×C61C2211yescharacteristic
26#95×C61C2211yescharacteristic
27C2×D4×C61—21no—
28C2×D4×C61D411yescharacteristic
29C22×C4×C61—21no—
30C22×C4×C61C2311yescharacteristic
31C2×C22⋊D61—21no—
32C2×C22⋊D61—21no—
33C2×C22⋊D61—21no—
34C22×Dic61—21no—
35C22×Dic61—21no—
36C22×Dic61D411yescharacteristic
37C22×Dic61D411yescharacteristic
38#11758224—42no—
39#11758224—42no—
40C2×D244D411yescharacteristic
41C2×C4×D61—21no—
42C2×Dic122—21no—
43C2×C8×C61—21no—
44C4⋊C4×C61D411yescharacteristic
45C22⋊C4×C61—21no—
46C22⋊Dic61—21no—
47#11758198—21no—
48#11758198—21no—
49C4⋊Dic61—21no—
50C4⋊Dic61—21no—
51C4⋊Dic61D411yescharacteristic
52#11758196—21no—
53#11758196—21no—
54#11758196—21no—
55C2×#92418—21no—
56C23×C61—21no—
57C23×C61C2×D411yescharacteristic
58C22×D61—21no—
59D4×C61—41no—
60D4×C61—41no—
61D4×C61—41no—
62C2×C4×C61—21no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C22⋊D61—42no—
70C22⋊D61—41no—
71C22⋊D61—41no—
72C22⋊D61—81no—
73C2×Dic61—21no—
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—42no—
78C2×Dic61—41no—
79C2×Dic61—42no—
80C2×Dic61—41no—
81C2×Dic61SD1612yes—
82D244—41no—
83C4×D61—42no—
84Dic122—42no—
85C8×C61—41no—
86#92418—41no—
87C22×C61—21no—
88C22×C61—21no—
89C22×C61—41no—
90C22×C61—41no—
91C22×C61—41no—
92C22×C61#12011yescharacteristic
93C22×C61C2×SD1611yescharacteristic
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—
102Dic61—22no—
103Dic61—41no—
104Dic61—41no—
105Dic61—81no—
106#1616—611nomaximal, Sylow
107C2×C61—21no—
108C2×C61—21no—
109C2×C61—81no—
110C2×C61#45011yescharacteristic
111C2×C61#45411yescharacteristic
112C2×C61#45811yescharacteristic
113D61—81no—
114#537—611no—
115#481—611no—
116#481—611no—
117#400—611no—
118#327—611no—
119#327D6111yescharacteristic, complemented
120#324—611no—
121C61#161611yescharacteristic, complemented, Sylow
122C2×#41—1221no—
123C22⋊Q8—1221no—
124C22⋊Q8—1221no—
125#121—611no—
126#121—1221no—
127#121—1221no—
128#121—1221no—
129#121C2×D6111yescharacteristic
130C2×C4⋊C4—611no—
131C2×C4⋊C4—611no—
132#106—1221no—
133#106—1221no—
134#102—1221no—
135#102—1221no—
136C22⋊C8—611no—
137C22⋊C8C2×D6111yescharacteristic
138#95—1221no—
139#95—1221no—
140#95C2×D6111yescharacteristic
141#41—2442no—
142#41—2442no—
143C2×Q8—1221no—
144C2×D4—21no—
145C2×D4—611no—
146C2×D4—1221no—
147C2×D4—1221no—
148C2×D4—1221no—
149C2×D4D24411yescharacteristic
150C22×C4—21no—
151C22×C4—611no—
152C22×C4—611no—
153C22×C4—1221no—
154C22×C4—1221no—
155C22×C4—1221no—
156C22×C4C22×D6111yescharacteristic
157C2×C8—21no—
158C2×C8—1221no—
159C4⋊C4—611no—
160C4⋊C4—1221no—
161C4⋊C4—1221no—
162C4⋊C4—1221no—
163C4⋊C4—1221no—
164C4⋊C4—1221no—
165C4⋊C4D24411yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—1221no—
168C22⋊C4—1221no—
169C22⋊C4—1221no—
170C23—21no—
171C23—1221no—
172C23D4×D6111yescharacteristic
173Q8—2442no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—4881no—
178D4—2441no—
179D4—2442no—
180D4—2441no—
181D4—2441no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—612no—
188C2×C4—1221no—
189C2×C4—1221no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—2442no—
193C2×C4—2442no—
194C2×C4—2442no—
195C2×C4—2441no—
196C2×C4—2441no—
197C2×C4C2×D24411yescharacteristic
198C2×C4D4×D6111yescharacteristic
199C8—41no—
200C8—2441no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—2441no—
207C22—2441no—
208C22—2441no—
209C22#1451974711yescharacteristic
210C22SD16×D6111yescharacteristic
211C22#1451980111yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—1222no—
217C4—4881no—
218C4—2441no—
219C4—2441no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—4881no—
224C2#1683991411yescharacteristic
225C2#1683993611yescharacteristic
226C2#1683995311yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#327C2
socleC22×C61#120
hypercenter#327D61
hypocenterC61#1616
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. #16840081C2semidirect
3. #16840078C2semidirect
4. #16839702C2semidirect
5. #16839495C2semidirect
6. #16839487C2semidirect
7. C61×#327C2semidirect
119. #327D61semidirect
121. C61#1616semidirect