Finite Group Databasebeta

← #21446330

Subgroups — #21446330

Order 7808.

332 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#14519803C211yesmaximal, characteristic
2C2×#14519783C211yesmaximal, characteristic, complemented
3#16839761C211yesmaximal, characteristic, complemented
4C2×#14519694C211yesmaximal, characteristic, complemented
5#16839531C211yesmaximal, characteristic, complemented
6#16839527C211yesmaximal, characteristic, complemented
7C2×#102×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519803—22no—
10#14519803C414yescomplemented
11C2×#11758200—21no—
12C2×#11758199—21no—
13#14519783—22no—
14#14519783—22no—
15C2×#11758194C2211yescharacteristic
16C2×#11758194C2211yescharacteristic
17C2×#11758194C2211yescharacteristic
18C2×#11758189—21no—
19C2×C8×D61—21no—
20#14519700—21no—
21#14519697—21no—
22#14519694—22no—
23C22×D4×C61C2211yescharacteristic
24C22×C8×C61C2211yescharacteristic
25C2×C4⋊C4×C61C2211yescharacteristic
26#102×C61—21no—
27#102×C61—21no—
28C24×C61—21no—
29C2×D4×C61—21no—
30C2×D4×C61—21no—
31C2×D4×C61—21no—
32C2×D4×C61—21no—
33C2×D4×C61—21no—
34C2×D4×C61C2×C412yes—
35C22×C4×C61—21no—
36C22×C4×C61C2311yescharacteristic
37C2×C22⋊D61—21no—
38#11758222—21no—
39#11758222—21no—
40#11758222C2×C412yes—
41#11758222D412yes—
42C2×D244D411yescharacteristic
43C2×C4×D61—21no—
44C2×Dic122D411yescharacteristic
45C2×C8×C61—21no—
46C2×C8×C61—21no—
47C2×C8×C61D411yescharacteristic
48C2×C8×C61D411yescharacteristic
49C4⋊C4×C61—21no—
50C4⋊C4×C61—21no—
51#11758200—24no—
52#11758199—24no—
53#11758194—21no—
54#11758194—21no—
55#11758194—21no—
56#11758194—21no—
57#11758194C2×C412yes—
58#11758194D412yes—
59C2×#92418—21no—
60C2×#92418—21no—
61C2×#92418—21no—
62#11758189—24no—
63C8×D61—24no—
64C23×C61—22no—
65C23×C61—41no—
66C23×C61—41no—
67C23×C61—81no—
68C23×C61—81no—
69C23×C61#4111yescharacteristic
70C22×D61—21no—
71D4×C61—22no—
72D4×C61—22no—
73D4×C61—41no—
74D4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61—81no—
77C2×C4×C61C22×C411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61#4111yescharacteristic
83C22⋊D61—22no—
84C22⋊D61—22no—
85C2×Dic61—21no—
86D244—21no—
87D244C22⋊C412yes—
88C4×D61—22no—
89C4×D61—22no—
90Dic122—21no—
91Dic122C22⋊C412yes—
92C8×C61—21no—
93C8×C61—21no—
94#92418—22no—
95#92418—22no—
96#92418—41no—
97C22×C61—21no—
98C22×C61—21no—
99C22×C61—42no—
100C22×C61—82no—
101C22×C61—82no—
102C22×C61—81no—
103C22×C61—81no—
104C22×C61C4×D411yescharacteristic
105C22×C61#12111yescharacteristic
106C22×C61#12311yescharacteristic
107C2×D61—22no—
108C2×D61—41no—
109C2×D61—41no—
110C4×C61—81no—
111C4×C61C2×C22⋊C411yescharacteristic
112C4×C61C4×D411yescharacteristic
113C4×C61#12011yescharacteristic
114C4×C61#12111yescharacteristic
115Dic61—22no—
116#1907—611nomaximal, Sylow
117C2×C61—21no—
118C2×C61—21no—
119C2×C61—82no—
120C2×C61#38611yescharacteristic
121C2×C61#47111yescharacteristic
122C2×C61#47211yescharacteristic
123D61—42no—
124C2×AGL(1,ℤ/8)—611no—
125C2×#131—611no—
126#417—611no—
127C2×#102D6111yescharacteristic, complemented
128C2×#100—611no—
129#343—611no—
130#341—611no—
131C61#190711yescharacteristic, complemented, Sylow
132C2×#41—611no—
133C22×D4C2×D6111yescharacteristic
134AGL(1,ℤ/8)—614no—
135AGL(1,ℤ/8)—1222no—
136C2×SD16—1221no—
137C2×D8—1221no—
138#131—1222no—
139#131—1222no—
140C2×M16—611no—
141C2×M16—611no—
142C2×M16—611no—
143C2×M16—1221no—
144C22×C8—1221no—
145C22×C8C2×D6111yescharacteristic
146C2×C4⋊C4C2×D6111yescharacteristic
147#103—1221no—
148#102—21no—
149#102—21no—
150#102—1221no—
151#100—1222no—
152C24—21no—
153#41—612no—
154#41—612no—
155#41—1221no—
156#41—1221no—
157C2×Q8—611no—
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—21no—
163C2×D4—611no—
164C2×D4—1221no—
165C2×D4C4×D6112yes—
166C22×C4—21no—
167C22×C4—1221no—
168C22×C4C22×D6111yescharacteristic
169SD16—1224no—
170D8—1224no—
171M16—612no—
172M16—612no—
173M16—1224no—
174M16—1221no—
175M16—1221no—
176M16—1221no—
177M16—1221no—
178C2×C8—21no—
179C2×C8—21no—
180C2×C8—1224no—
181C2×C8—1221no—
182C2×C8—1221no—
183C2×C8—1221no—
184C2×C8C22⋊D6111yescharacteristic
185C2×C8C22⋊D6111yescharacteristic
186C4⋊C4—21no—
187C4⋊C4—21no—
188C23—22no—
189C23—41no—
190C23—41no—
191C23—81no—
192C23—81no—
193C23—1221no—
194C23#1175822411yescharacteristic
195Q8—612no—
196Q8—1221no—
197D4—22no—
198D4—22no—
199D4—41no—
200D4—41no—
201D4—612no—
202D4—1222no—
203D4—1222no—
204D4—1221no—
205C2×C4—41no—
206C2×C4—81no—
207C2×C4—1221no—
208C2×C4—1222no—
209C2×C4—1222no—
210C2×C4C2×C4×D6111yescharacteristic
211C2×C4#1175822211yescharacteristic
212C2×C4D4×D6111yescharacteristic
213C2×C4D4×D6111yescharacteristic
214C2×C4D4×D6111yescharacteristic
215C2×C4C2×C22⋊D6111yescharacteristic
216C8—21no—
217C8—21no—
218C8—1222no—
219C8—1222no—
220C8—2441no—
221C22—21no—
222C22—21no—
223C22—42no—
224C22—82no—
225C22—82no—
226C22—81no—
227C22—81no—
228C22—1222no—
229C22—2441no—
230C22—2441no—
231C22#1451973711yescharacteristic
232C22#1451974811yescharacteristic
233C22#1451975911yescharacteristic
234C4—81no—
235C4—1222no—
236C4C22⋊C4×D6111yescharacteristic
237C4C4×C22⋊D6111yescharacteristic
238C4#1451974511yescharacteristic
239C4#1451975011yescharacteristic
240C2—21no—
241C2—21no—
242C2—82no—
243C2—2442no—
244C2#1683963811yescharacteristic
245C2#1684002211yescharacteristic
246C2#1684002911yescharacteristic
subgroupG/H
centerC22#14519748
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#102×C61C2
socleC22×C61#121
hypercenterC2×#102D61
hypocenterC61#1907
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#14519783C2semidirect
3. #16839761C2semidirect
4. C2×#14519694C2semidirect
5. #16839531C2semidirect
6. #16839527C2semidirect
7. C2×#102×C61C2semidirect
10. #14519803C4semidirect
127. C2×#102D61semidirect
131. C61#1907semidirect