Finite Group Databasebeta

← #21444785

Subgroups — #21444785

Order 7808.

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

normal subgroups only

This group has 244 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#16840361C211yesmaximal, characteristic
2#16839917C211yesmaximal, characteristic, complemented
3#16839903C211yesmaximal, characteristic
4#16839683C211yesmaximal, characteristic, complemented
5#16839495C211yesmaximal, characteristic
6#16839487C211yesmaximal, characteristic, complemented
7C61×#328C211yesmaximal, characteristic, complemented
8C22×Dic122C2211yescharacteristic
9C2×#11758202—21no—
10C2×#11758190—21no—
11#14519772—21no—
12#14519768—21no—
13#14519762—21no—
14#14519761—21no—
15#14519753—21no—
16#14519751C2211yescharacteristic
17#14519737—21no—
18C2×C4⋊Dic61—21no—
19C2×#11758196C2211yescharacteristic
20#14519702—21no—
21#14519700—21no—
22C22⋊#92418C2211yescharacteristic
23#14519684—21no—
24C22⋊Q8×C61C2211yescharacteristic
25C22⋊C8×C61C2211yescharacteristic
26#95×C61C2211yescharacteristic
27C2×Q8×C61D411yescharacteristic
28C22×C4×C61—21no—
29C22×C4×C61C2311yescharacteristic
30C2×C22⋊D61—21no—
31C22×Dic61—21no—
32C22×Dic61D411yescharacteristic
33C22×Dic61D411yescharacteristic
34C2×D244D411yescharacteristic
35C2×C4×D61—21no—
36C2×Dic122—21no—
37C2×Dic122—21no—
38C2×Dic122—42no—
39C2×C8×C61—21no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61D411yescharacteristic
42C22⋊C4×C61—21no—
43#11758202—42no—
44#11758198—21no—
45#11758198—21no—
46#11758198—21no—
47#11758198—21no—
48C4⋊Dic61—21no—
49C4⋊Dic61—21no—
50C4⋊Dic61—42no—
51C4⋊Dic61D411yescharacteristic
52#11758196—21no—
53#11758196—21no—
54#11758196—21no—
55C4×Dic61—21no—
56C2×#92418—21no—
57#11758190—42no—
58C23×C61C2×D411yescharacteristic
59C22×D61—21no—
60Q8×C61—41no—
61C2×C4×C61—22no—
62C2×C4×C61—21no—
63C2×C4×C61—21no—
64C2×C4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C22⋊D61—41no—
70C22⋊D61—41no—
71C2×Dic61—22no—
72C2×Dic61—21no—
73C2×Dic61—21no—
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—41no—
78C2×Dic61—41no—
79C2×Dic61—41no—
80D244—41no—
81C4×D61—81no—
82Dic122—22no—
83Dic122—22no—
84Dic122—41no—
85Dic122—41no—
86C8×C61—41no—
87#92418—41no—
88C22×C61—21no—
89C22×C61—21no—
90C22×C61#12011yescharacteristic
91C22×C61#13511yescharacteristic
92C22×C61#13711yescharacteristic
93C2×D61—41no—
94C2×D61—41no—
95C2×D61—41no—
96C4×C61—21no—
97C4×C61—21no—
98C4×C61—42no—
99C4×C61—41no—
100C4×C61—41no—
101Dic61—41no—
102Dic61—41no—
103Dic61—42no—
104Dic61—41no—
105#1603—611nomaximal, Sylow
106C2×C61—21no—
107C2×C61—21no—
108C2×C61#45211yescharacteristic
109C2×C61#45611yescharacteristic
110C2×C61B(4,𝔽2)11yescharacteristic
111D61—81no—
112#539—611no—
113#451—611no—
114#448—611no—
115#395—611no—
116#328D6111yescharacteristic, complemented
117#327—611no—
118#324—611no—
119C61#160311yescharacteristic, complemented, Sylow
120C22×Q8—611no—
121C2×Q16—1221no—
122C2×SD16—1221no—
123#126—1221no—
124#125—1221no—
125#123—1221no—
126#123—1221no—
127C22⋊Q8—1221no—
128C22⋊Q8C2×D6111yescharacteristic
129#121—611no—
130C4×D4—1221no—
131C2×C4⋊C4—611no—
132C2×C4⋊C4—1221no—
133#103—1221no—
134#103—1221no—
135C22⋊C8—611no—
136C22⋊C8C2×D6111yescharacteristic
137#95—1221no—
138#95C2×D6111yescharacteristic
139C2×Q8—1221no—
140C2×Q8—1221no—
141C2×Q8—2442no—
142C2×Q8D24411yescharacteristic
143C2×D4—611no—
144C2×D4—1221no—
145C22×C4—21no—
146C22×C4—611no—
147C22×C4—611no—
148C22×C4—1221no—
149C22×C4—1221no—
150C22×C4C22×D6111yescharacteristic
151Q16—2442no—
152SD16—2442no—
153C2×C8—21no—
154C2×C8—1221no—
155C4⋊C4—21no—
156C4⋊C4—611no—
157C4⋊C4—1221no—
158C4⋊C4—1221no—
159C4⋊C4—1221no—
160C4⋊C4—1221no—
161C4⋊C4—1221no—
162C4⋊C4—2442no—
163C4⋊C4D24411yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—1221no—
166C22⋊C4—1221no—
167C22⋊C4—1221no—
168C22⋊C4—1221no—
169C42—1221no—
170C23—1221no—
171C23D4×D6111yescharacteristic
172Q8—41no—
173Q8—1222no—
174Q8—1222no—
175Q8—2441no—
176Q8—2441no—
177D4—2441no—
178D4—2441no—
179D4—2441no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—1222no—
187C2×C4—1221no—
188C2×C4—1221no—
189C2×C4—1221no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—4881no—
193C2×C4—2441no—
194C2×C4—2441no—
195C2×C4—2441no—
196C2×C4C2×D24411yescharacteristic
197C2×C4D4×D6111yescharacteristic
198C8—41no—
199C8—2441no—
200C22—21no—
201C22—21no—
202C22—2441no—
203C22—2441no—
204C22—2441no—
205C22#1451974711yescharacteristic
206C22#1451979811yescharacteristic
207C22#1451980911yescharacteristic
208C4—21no—
209C4—21no—
210C4—42no—
211C4—41no—
212C4—41no—
213C4—2441no—
214C4—2442no—
215C4—2441no—
216C4—2441no—
217C2—21no—
218C2—21no—
219C2—4881no—
220C2#1683992711yescharacteristic
221C2#1683994611yescharacteristic
222C2#1683995011yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#328C2
socleC22×C61#120
hypercenter#328D61
hypocenterC61#1603
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #16839917C2semidirect
4. #16839683C2semidirect
6. #16839487C2semidirect
7. C61×#328C2semidirect
116. #328D61semidirect
119. C61#1603semidirect