Finite Group Databasebeta

← #21444865

Subgroups — #21444865

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#16840350C211yesmaximal, characteristic
2#16840097C211yesmaximal, characteristic, complemented
3#16840080C211yesmaximal, characteristic, complemented
4#16839498C211yesmaximal, characteristic, complemented
5#16839495C211yesmaximal, characteristic, complemented
6#16839486C211yesmaximal, characteristic, complemented
7C61×#399C211yesmaximal, 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×C61—21no—
23C2×C4⋊C4×C61C2211yescharacteristic
24C2×C22⋊C4×C61—21no—
25C2×C22⋊C4×C61C2211yescharacteristic
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—
40C4⋊C4×C61—42no—
41C22⋊C4×C61—21no—
42C22⋊C4×C61—21no—
43C22⋊C4×C61—42no—
44C22⋊Dic61—21no—
45C22⋊Dic61—21no—
46C22⋊Dic61—21no—
47#11758198—21no—
48#11758198—21no—
49C4⋊Dic61D411yescharacteristic
50C4⋊Dic61D411yescharacteristic
51#11758196—21no—
52#11758196—21no—
53C4×Dic61—21no—
54C2×#92418—21no—
55C2×#92418—21no—
56C23×C61—21no—
57C23×C61—21no—
58C23×C61—21no—
59C23×C61—41no—
60C23×C61—41no—
61C23×C61C2×D411yescharacteristic
62C22×D61—21no—
63C2×C4×C61—22no—
64C2×C4×C61—21no—
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×C61—41no—
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C22⋊D61—41no—
75C22⋊D61—41no—
76C22⋊D61—81no—
77C22⋊D61—81no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81D244—41no—
82C4×D61—81no—
83Dic122—41no—
84#92418—41no—
85#92418—41no—
86C22×C61—21no—
87C22×C61—21no—
88C22×C61—42no—
89C22×C61—41no—
90C22×C61—41no—
91C22×C61—41no—
92C22×C61—81no—
93C22×C61#12011yescharacteristic
94C22×C61#13511yescharacteristic
95C22×C61#13711yescharacteristic
96C2×D61—41no—
97C2×D61—41no—
98C2×D61—41no—
99C4×C61—21no—
100C4×C61—21no—
101C4×C61—42no—
102C4×C61—41no—
103C4×C61—81no—
104Dic61—41no—
105Dic61—41no—
106Dic61—41no—
107#1618—611nomaximal, Sylow
108C2×C61—21no—
109C2×C61—21no—
110C2×C61—81no—
111C2×C61#45211yescharacteristic
112C2×C61#45311yescharacteristic
113C2×C61#45811yescharacteristic
114D61—81no—
115#538—611no—
116#484—611no—
117#481—611no—
118#399D6111yescharacteristic, complemented
119#328—611no—
120#327—611no—
121#323—611no—
122C61#161811yescharacteristic, complemented, Sylow
123#126—1221no—
124#124—1221no—
125#123—1221no—
126C22⋊Q8—611no—
127#121—611no—
128#121—1221no—
129#120—1221no—
130C4×D4—1221no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4C2×D6111yescharacteristic
133C2×C22⋊C4—21no—
134C2×C22⋊C4C2×D6111yescharacteristic
135#107—1221no—
136#106—1221no—
137#103—1221no—
138#102—1221no—
139C22⋊C8—611no—
140C22⋊C8—611no—
141#95C2×D6111yescharacteristic
142C24C22⋊D6111yescharacteristic
143C2×Q8—611no—
144C2×D4—611no—
145C2×D4—1221no—
146C2×D4—1221no—
147C2×D4—1221no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—1221no—
151C22×C4C22⋊D6111yescharacteristic
152C22×C4C22×D6111yescharacteristic
153C2×C8—1221no—
154C2×C8—1221no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—42no—
158C4⋊C4—611no—
159C4⋊C4—611no—
160C4⋊C4—1221no—
161C4⋊C4—1221no—
162C22⋊C4—21no—
163C22⋊C4—21no—
164C22⋊C4—42no—
165C22⋊C4—1221no—
166C22⋊C4—1221no—
167C22⋊C4—1221no—
168C22⋊C4—1221no—
169C22⋊C4—1221no—
170C42—1221no—
171C23—21no—
172C23—21no—
173C23—21no—
174C23—41no—
175C23—41no—
176C23—1221no—
177C23C2×C22⋊D6111yescharacteristic
178Q8—2441no—
179D4—4881no—
180D4—4881no—
181D4—2441no—
182D4—2441no—
183D4—2441no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—1221no—
194C2×C4—1221no—
195C2×C4—1221no—
196C2×C4—4881no—
197C2×C4D4×D6111yescharacteristic
198C2×C4D4×D6111yescharacteristic
199C8—2441no—
200C8—2441no—
201C22—21no—
202C22—21no—
203C22—42no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—81no—
208C22—2441no—
209C22—2441no—
210C22—2441no—
211C22#1451974511yescharacteristic
212C22#1451979711yescharacteristic
213C22#1451980811yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—41no—
218C4—81no—
219C4—2441no—
220C4—2441no—
221C4—2441no—
222C2—21no—
223C2—21no—
224C2—81no—
225C2—4881no—
226C2#1683992211yescharacteristic
227C2#1683992911yescharacteristic
228C2#1683995111yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#399C2
socleC22×C61#120
hypercenter#399D61
hypocenterC61#1618
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #399

Complements

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

NH ≅ G/Ntype
2. #16840097C2semidirect
3. #16840080C2semidirect
4. #16839498C2semidirect
5. #16839495C2semidirect
6. #16839486C2semidirect
7. C61×#399C2semidirect
118. #399D61semidirect
122. C61#1618semidirect