Finite Group Databasebeta

← #21444823

Subgroups — #21444823

Order 7808.

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

normal subgroups only

This group has 254 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#16840076C211yesmaximal, characteristic, complemented
3#16840073C211yesmaximal, characteristic, complemented
4#16839694C211yesmaximal, 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⋊Dic61—21no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196C2211yescharacteristic
18#14519711—21no—
19#14519710—21no—
20#14519699—21no—
21#14519698—21no—
22C22⋊#92418C2211yescharacteristic
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⋊Dic61—42no—
52C4⋊Dic61D411yescharacteristic
53#11758196—21no—
54#11758196—21no—
55#11758196—21no—
56C2×#92418—21no—
57C23×C61—21no—
58C23×C61C2×D411yescharacteristic
59C22×D61—21no—
60D4×C61—41no—
61D4×C61—41no—
62D4×C61—41no—
63C2×C4×C61—22no—
64C2×C4×C61—21no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61—41no—
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C22⋊D61—42no—
71C22⋊D61—41no—
72C22⋊D61—41no—
73C22⋊D61—81no—
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—42no—
79C2×Dic61—41no—
80C2×Dic61—41no—
81C2×Dic61—41no—
82C2×Dic61—41no—
83C2×Dic61D812yes—
84D244—41no—
85C4×D61—42no—
86Dic122—42no—
87C8×C61—41no—
88#92418—41no—
89C22×C61—21no—
90C22×C61—21no—
91C22×C61—41no—
92C22×C61—41no—
93C22×C61—41no—
94C22×C61#12011yescharacteristic
95C22×C61C2×D811yescharacteristic
96C22×C61AGL(1,ℤ/8)11yescharacteristic
97C2×D61—41no—
98C2×D61—41no—
99C2×D61—41no—
100C4×C61—21no—
101C4×C61—21no—
102C4×C61—42no—
103C4×C61—41no—
104Dic61—22no—
105Dic61—41no—
106Dic61—41no—
107Dic61—81no—
108#1610—611nomaximal, Sylow
109C2×C61—21no—
110C2×C61—21no—
111C2×C61—81no—
112C2×C61#44711yescharacteristic
113C2×C61#45611yescharacteristic
114C2×C61#45811yescharacteristic
115D61—81no—
116#537—611no—
117#480—611no—
118#480—611no—
119#398—611no—
120#327—611no—
121#327D6111yescharacteristic, complemented
122#324—611no—
123C61#161011yescharacteristic, complemented, Sylow
124C2×#41—1221no—
125C22⋊Q8—1221no—
126C22⋊Q8—1221no—
127#121—611no—
128#121—1221no—
129#121—1221no—
130#121—1221no—
131#121C2×D6111yescharacteristic
132C2×C4⋊C4—611no—
133C2×C4⋊C4—611no—
134C2×C4⋊C4—1221no—
135#107—1221no—
136#107—1221no—
137#102—1221no—
138#102—1221no—
139C22⋊C8—611no—
140C22⋊C8C2×D6111yescharacteristic
141#95—1221no—
142#95C2×D6111yescharacteristic
143#41—2442no—
144#41—2442no—
145C2×Q8—1221no—
146C2×D4—21no—
147C2×D4—611no—
148C2×D4—1221no—
149C2×D4—1221no—
150C2×D4—1221no—
151C2×D4D24411yescharacteristic
152C22×C4—21no—
153C22×C4—611no—
154C22×C4—611no—
155C22×C4—1221no—
156C22×C4—1221no—
157C22×C4—1221no—
158C22×C4C22×D6111yescharacteristic
159C2×C8—21no—
160C2×C8—1221no—
161C4⋊C4—611no—
162C4⋊C4—1221no—
163C4⋊C4—1221no—
164C4⋊C4—1221no—
165C4⋊C4—1221no—
166C4⋊C4—1221no—
167C4⋊C4—2442no—
168C4⋊C4D24411yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—1221no—
171C22⋊C4—1221no—
172C22⋊C4—1221no—
173C23—21no—
174C23—1221no—
175C23D4×D6111yescharacteristic
176Q8—2442no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—4881no—
181D4—2441no—
182D4—2442no—
183D4—2441no—
184D4—2441no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—612no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—1221no—
195C2×C4—2442no—
196C2×C4—2442no—
197C2×C4—2441no—
198C2×C4—2441no—
199C2×C4—2441no—
200C2×C4—2441no—
201C2×C4C2×D24411yescharacteristic
202C2×C4D4×D6111yescharacteristic
203C8—41no—
204C8—2441no—
205C22—21no—
206C22—21no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—2441no—
211C22—2441no—
212C22—2441no—
213C22#1451974711yescharacteristic
214C22D8×D6111yescharacteristic
215C22#1451980411yescharacteristic
216C4—21no—
217C4—21no—
218C4—42no—
219C4—41no—
220C4—1222no—
221C4—4881no—
222C4—2441no—
223C4—2441no—
224C2—21no—
225C2—21no—
226C2—81no—
227C2—4881no—
228C2#1683989711yescharacteristic
229C2#1683994611yescharacteristic
230C2#1683995311yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#327C2
socleC22×C61#120
hypercenter#327D61
hypocenterC61#1610
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. #16840076C2semidirect
3. #16840073C2semidirect
4. #16839694C2semidirect
5. #16839495C2semidirect
6. #16839487C2semidirect
7. C61×#327C2semidirect
121. #327D61semidirect
123. C61#1610semidirect