Finite Group Databasebeta

← #21444866

Subgroups — #21444866

Order 7808.

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

normal subgroups only

This group has 240 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#16840352C211yesmaximal, characteristic
2#16840080C211yesmaximal, characteristic, complemented
3#16839697C211yesmaximal, characteristic, complemented
4#16839499C211yesmaximal, characteristic, complemented
5#16839497C211yesmaximal, characteristic, complemented
6#16839485C211yesmaximal, characteristic, complemented
7C61×#484C211yesmaximal, characteristic, complemented
8#14519772—21no—
9#14519766—21no—
10#14519762—21no—
11#14519752—21no—
12#14519751C2211yescharacteristic
13#14519747—21no—
14#14519737—21no—
15C2×#11758196—21no—
16C2×#11758198—21no—
17C2×#11758198C2211yescharacteristic
18#14519708—21no—
19#14519697—21no—
20C22⋊#92418C2211yescharacteristic
21#14519684C2211yescharacteristic
22C22⋊Q8×C61C2211yescharacteristic
23C2×C4⋊C4×C61C2211yescharacteristic
24#107×C61—21no—
25#103×C61—21no—
26C22⋊C8×C61C2211yescharacteristic
27C23×D61D411yescharacteristic
28C2×Q8×C61D411yescharacteristic
29C22×C4×C61—21no—
30C22×C4×C61C2311yescharacteristic
31C2×C22⋊D61—21no—
32C22×Dic61—21no—
33C22×Dic61D411yescharacteristic
34C2×D244—21no—
35C2×D244—21no—
36C2×D244D411yescharacteristic
37C2×C4×D61—21no—
38C2×C8×C61—21no—
39C4⋊C4×C61—21no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61—21no—
42C4⋊C4×C61D411yescharacteristic
43C22⋊C4×C61—21no—
44#11758198—21no—
45#11758198—21no—
46#11758198—21no—
47#11758198—21no—
48#11758198—21no—
49#11758198—21no—
50#11758198—42no—
51C4⋊Dic61D411yescharacteristic
52#11758196—21no—
53#11758196—42no—
54C4×Dic61—21no—
55C2×#92418—21no—
56C23×C61C2×D411yescharacteristic
57C22×D61—21no—
58C22×D61—21no—
59C22×D61—21no—
60C22×D61—21no—
61C22×D61—41no—
62C22×D61—41no—
63Q8×C61—41no—
64C2×C4×C61—21no—
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—41no—
73C22⋊D61—41no—
74C2×Dic61—22no—
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—41no—
78C2×Dic61—41no—
79C2×Dic61—41no—
80D244—41no—
81D244—81no—
82D244—81no—
83C4×D61—81no—
84C8×C61—41no—
85#92418—41no—
86C22×C61—21no—
87C22×C61—21no—
88C22×C61#12011yescharacteristic
89C22×C61#13511yescharacteristic
90C22×C61#13711yescharacteristic
91C2×D61—42no—
92C2×D61—41no—
93C2×D61—41no—
94C2×D61—41no—
95C2×D61—41no—
96C2×D61—41no—
97C2×D61—41no—
98C2×D61—81no—
99C4×C61—21no—
100C4×C61—21no—
101C4×C61—41no—
102C4×C61—41no—
103C4×C61—81no—
104Dic61—42no—
105Dic61—41no—
106Dic61—41no—
107#1618—611nomaximal, Sylow
108C2×C61—21no—
109C2×C61—21no—
110C2×C61#45211yescharacteristic
111C2×C61#45311yescharacteristic
112C2×C61#45811yescharacteristic
113D61—81no—
114D61—81no—
115#538—611no—
116#484D6111yescharacteristic, complemented
117#481—611no—
118#399—611no—
119#328—611no—
120#327—611no—
121#323—611no—
122C61#161811yescharacteristic, complemented, Sylow
123#126—1221no—
124#124—1221no—
125#123—1221no—
126C22⋊Q8C2×D6111yescharacteristic
127#121—611no—
128#121—1221no—
129#120—1221no—
130C4×D4—1221no—
131C2×C4⋊C4—1221no—
132C2×C4⋊C4C2×D6111yescharacteristic
133C2×C22⋊C4—611no—
134C2×C22⋊C4—1221no—
135#107—21no—
136#106—1221no—
137#103—21no—
138#102—1221no—
139C22⋊C8—611no—
140C22⋊C8C2×D6111yescharacteristic
141#95—611no—
142C24—611no—
143C2×Q8C22⋊D6111yescharacteristic
144C2×D4—611no—
145C2×D4—1221no—
146C2×D4—1221no—
147C2×D4—1221no—
148C22×C4—21no—
149C22×C4—611no—
150C22×C4—1221no—
151C22×C4—1221no—
152C22×C4C22×D6111yescharacteristic
153C2×C8—21no—
154C2×C8—1221no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—611no—
159C4⋊C4—1221no—
160C4⋊C4—2442no—
161C4⋊C4C22⋊D6111yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—1221no—
164C22⋊C4—1221no—
165C22⋊C4—1221no—
166C22⋊C4—1221no—
167C22⋊C4—1221no—
168C22⋊C4—1221no—
169C22⋊C4—2442no—
170C42—1221no—
171C23—1221no—
172C23—1221no—
173C23—1221no—
174C23—1221no—
175C23—2441no—
176C23—2441no—
177C23D4×D6111yescharacteristic
178Q8—41no—
179D4—4881no—
180D4—4881no—
181D4—2441no—
182D4—2441no—
183D4—2441no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—1222no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—4881no—
194C2×C4—2441no—
195C2×C4—2441no—
196C2×C4—2441no—
197C2×C4D4×D6111yescharacteristic
198C2×C4C2×C22⋊D6111yescharacteristic
199C8—41no—
200C8—2441no—
201C22—21no—
202C22—21no—
203C22—4881no—
204C22—2442no—
205C22—2441no—
206C22—2441no—
207C22—2441no—
208C22—2441no—
209C22—2441no—
210C22—2441no—
211C22#1451974511yescharacteristic
212C22#1451980011yescharacteristic
213C22#1451980911yescharacteristic
214C4—21no—
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—2442no—
220C4—2441no—
221C4—2441no—
222C2—21no—
223C2—21no—
224C2—4881no—
225C2—4881no—
226C2#1683992311yescharacteristic
227C2#1683992811yescharacteristic
228C2#1683995111yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#484C2
socleC22×C61#120
hypercenter#484D61
hypocenterC61#1618
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. #16840080C2semidirect
3. #16839697C2semidirect
4. #16839499C2semidirect
5. #16839497C2semidirect
6. #16839485C2semidirect
7. C61×#484C2semidirect
116. #484D61semidirect
122. C61#1618semidirect