Finite Group Databasebeta

← #21447136

Subgroups — #21447136

Order 7808.

324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C22×#11758200C211yesmaximal, characteristic
2C2×C4⋊#92418C211yesmaximal, characteristic, complemented
3C2×#14519700C211yesmaximal, characteristic, complemented
4C2×#14519698C211yesmaximal, characteristic
5#16839668C211yesmaximal, characteristic, complemented
6#16839524C211yesmaximal, characteristic, complemented
7C61×#390C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C2×#11758200—22no—
10C2×#11758200—22no—
11C2×#11758200—22no—
12C22×#92418C2211yescharacteristic
13C22×#92418C2211yescharacteristic
14C2×C4⋊Dic61C2211yescharacteristic
15C4⋊#92418—22no—
16#14519700—22no—
17#14519698—22no—
18#14519684—21no—
19#14519684—21no—
20C22×D4×C61C2211yescharacteristic
21C2×C4⋊C4×C61C2211yescharacteristic
22C2×C22⋊C4×C61—21no—
23C2×C22⋊C4×C61—21no—
24C2×C42×C61C2211yescharacteristic
25C24×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29C2×D4×C61—21no—
30C2×D4×C61—21no—
31C2×D4×C61D412yes—
32C22×C4×C61—21no—
33C22×C4×C61D411yescharacteristic
34C22×C4×C61D411yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C22×Dic61—21no—
37C22×Dic61—21no—
38C2×Dic122—21no—
39C2×Dic122—21no—
40C2×Dic122—21no—
41C2×Dic122—21no—
42C2×Dic122—21no—
43C2×Dic122D412yes—
44C4⋊C4×C61—21no—
45C4⋊C4×C61—21no—
46C22⋊C4×C61—42no—
47C22⋊C4×C61—42no—
48C42×C61—21no—
49C42×C61—21no—
50#11758200—28no—
51C4⋊Dic61—21no—
52C4⋊Dic61—21no—
53C2×#92418—21no—
54C2×#92418—21no—
55C2×#92418—21no—
56C2×#92418—21no—
57C2×#92418—21no—
58C2×#92418D412yes—
59C23×C61—22no—
60C23×C61—41no—
61C23×C61—41no—
62C23×C61—41no—
63C23×C61—41no—
64C23×C61—41no—
65C23×C61—41no—
66C23×C61C2×D411yescharacteristic
67D4×C61—22no—
68D4×C61—22no—
69D4×C61—41no—
70D4×C61—41no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—41no—
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61SD1612yescomplemented
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61#4111yescharacteristic
84C2×C4×C61#4111yescharacteristic
85C2×C4×C61#4111yescharacteristic
86C2×Dic61—22no—
87C2×Dic61—41no—
88C2×Dic61—41no—
89C2×Dic61—41no—
90C2×Dic61—41no—
91C2×Dic61—41no—
92Dic122—22no—
93Dic122—22no—
94Dic122—41no—
95Dic122—41no—
96#92418—22no—
97#92418—41no—
98C22×C61—42no—
99C22×C61—42no—
100C22×C61—42no—
101C22×C61—81no—
102C22×C61—81no—
103C22×C61—81no—
104C22×C61—81no—
105C22×C61#12111yescharacteristic
106C22×C61#12111yescharacteristic
107C22×C61#12111yescharacteristic
108C22×C61C2×SD1611yescharacteristic
109C22×C61#13511yescharacteristic
110C22×C61AGL(1,ℤ/8)11yescharacteristic
111C22×C61#13711yescharacteristic
112C4×C61—22no—
113C4×C61—41no—
114C4×C61—81no—
115C4×C61#12011yescharacteristic
116C4×C61#12311yescharacteristic
117C4×C61#12311yescharacteristic
118C4×C61#12411yescharacteristic
119Dic61—42no—
120Dic61—81no—
121#2055—611nomaximal, Sylow
122C2×C61—82no—
123C2×C61#39411yescharacteristic
124C2×C61#46011yescharacteristic
125C2×C61#46111yescharacteristic
126C2×C61#46311yescharacteristic
127C2×C61#46411yescharacteristic
128C2×C61#46511yescharacteristic
129C2×C61#46811yescharacteristic
130C22×SD16—611no—
131C2×C4⋊C8—611no—
132C2×#103—611no—
133C2×#102—611no—
134#391—611no—
135#390D6111yescharacteristic
136#340—611no—
137C61#205511yescharacteristic, complemented, Sylow
138C22×Q8—611no—
139C22×D4C2×D6111yescharacteristic
140C2×SD16—1222no—
141C2×SD16—1222no—
142C2×SD16—1222no—
143C22×C8—611no—
144C22×C8—611no—
145C2×C4⋊C4—611no—
146C2×C4⋊C4C2×D6111yescharacteristic
147C2×C22⋊C4—21no—
148C2×C22⋊C4—21no—
149C2×C42C2×D6111yescharacteristic
150C4⋊C8—1222no—
151#103—1222no—
152#102—1222no—
153#95—1221no—
154#95—1221no—
155C24—21no—
156C2×Q8—612no—
157C2×Q8—1221no—
158C2×Q8—1221no—
159C2×Q8—1221no—
160C2×Q8—1221no—
161C2×Q8—1221no—
162C2×D4—21no—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4D24412yes—
168C22×C4—21no—
169C22×C4—1221no—
170C22×C4—1221no—
171C22×C4C22⋊D6111yescharacteristic
172C22×C4C22⋊D6111yescharacteristic
173C22×C4C22×D6111yescharacteristic
174SD16—1228no—
175C2×C8—612no—
176C2×C8—1221no—
177C2×C8—1221no—
178C2×C8—1221no—
179C2×C8—1221no—
180C2×C8—1221no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—1221no—
184C4⋊C4—1221no—
185C22⋊C4—42no—
186C22⋊C4—42no—
187C42—21no—
188C42—21no—
189C23—22no—
190C23—41no—
191C23—41no—
192C23—41no—
193C23—41no—
194C23—41no—
195C23—41no—
196C23C2×C22⋊D6111yescharacteristic
197Q8—1222no—
198Q8—1222no—
199Q8—2441no—
200Q8—2441no—
201D4—22no—
202D4—22no—
203D4—41no—
204D4—41no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—1222no—
214C2×C4—2441no—
215C2×C4—2441no—
216C2×C4—2441no—
217C2×C4—2441no—
218C2×C4—2441no—
219C2×C4#1175820012yescomplemented
220C2×C4C2×D24411yescharacteristic
221C2×C4#1175822211yescharacteristic
222C2×C4D4×D6111yescharacteristic
223C2×C4D4×D6111yescharacteristic
224C2×C4#1175822411yescharacteristic
225C2×C4#1175822411yescharacteristic
226C8—1222no—
227C8—2441no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—81no—
232C22—81no—
233C22—81no—
234C22—81no—
235C22#1451974811yescharacteristic
236C22#1451974911yescharacteristic
237C22#1451975111yescharacteristic
238C22C2×#1175820011yescharacteristic
239C22#1451979711yescharacteristic
240C22#1451980311yescharacteristic
241C22#1451980711yescharacteristic
242C4—22no—
243C4—41no—
244C4—81no—
245C4—4881no—
246C4—2442no—
247C4#1451974711yescharacteristic
248C4#1451975911yescharacteristic
249C4#1451976111yescharacteristic
250C4#1451976311yescharacteristic
251C2—82no—
252C2#1683967811yescharacteristic
253C2#1683995911yescharacteristic
254C2#1683996711yescharacteristic
255C2#1683997711yescharacteristic
256C2#1683998111yescharacteristic
257C2#1683998911yescharacteristic
258C2#1684000611yescharacteristic
subgroupG/H
centerC23C2×C22⋊D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#390C2
socleC23×C61C2×D4
hypercenter#390D61
hypocenterC61#2055
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊#92418C2semidirect
3. C2×#14519700C2semidirect
5. #16839668C2semidirect
6. #16839524C2semidirect
79. C2×C4×C61SD16semidirect
137. C61#2055semidirect
219. C2×C4#11758200semidirect