Finite Group Databasebeta

← #21444755

Subgroups — #21444755

Order 7808.

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

normal subgroups only

This group has 310 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, complemented
2#16839898C211yesmaximal, characteristic, complemented
3#16839895C211yesmaximal, characteristic, complemented
4#16839680C211yesmaximal, characteristic, complemented
5#16839495C211yesmaximal, characteristic, complemented
6#16839487C211yesmaximal, characteristic, complemented
7C61×#327C211yesmaximal, characteristic, complemented
8C2×#11758224—21no—
9C22×D244C2211yescharacteristic
10C2×D488—21no—
11C2×#11758199—21no—
12#14519755—21no—
13#14519754—21no—
14#14519751C2211yescharacteristic
15#14519750—21no—
16#14519749—21no—
17#14519749—21no—
18C2×#11758196C2211yescharacteristic
19C2×#11758198—21no—
20C2×#11758198—21no—
21#14519699—21no—
22#14519697—21no—
23C22⋊#92418C2211yescharacteristic
24#121×C61C2211yescharacteristic
25C22⋊C8×C61C2211yescharacteristic
26#95×C61C2211yescharacteristic
27C23×D61—21no—
28C2×D4×C61—21no—
29C2×D4×C61D411yescharacteristic
30C22×C4×C61—21no—
31C22×C4×C61C2311yescharacteristic
32C2×C22⋊D61—21no—
33C2×C22⋊D61—21no—
34C2×C22⋊D61—21no—
35C22×Dic61—21no—
36C22×Dic61D411yescharacteristic
37C22×Dic61D411yescharacteristic
38#11758224—42no—
39#11758224—42no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244—42no—
43C2×D244D411yescharacteristic
44C2×C4×D61—21no—
45C2×Dic122—21no—
46C2×C8×C61—21no—
47C4⋊C4×C61D411yescharacteristic
48C22⋊C4×C61—21no—
49C22⋊Dic61—21no—
50#11758199—42no—
51#11758198—21no—
52#11758198—21no—
53#11758198—42no—
54#11758198—42no—
55C4⋊Dic61D411yescharacteristic
56#11758196—21no—
57#11758196—21no—
58#11758196—21no—
59C2×#92418—21no—
60D488—42no—
61C23×C61—21no—
62C23×C61C2×D411yescharacteristic
63C22×D61—22no—
64C22×D61—21no—
65C22×D61—41no—
66C22×D61—41no—
67C22×D61—41no—
68C22×D61—41no—
69C22×D61—41no—
70C22×D61—41no—
71D4×C61—41no—
72D4×C61—41no—
73D4×C61—41no—
74C2×C4×C61—21no—
75C2×C4×C61—41no—
76C2×C4×C61—41no—
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C22⋊D61—42no—
82C22⋊D61—41no—
83C22⋊D61—41no—
84C22⋊D61—81no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—42no—
90C2×Dic61—41no—
91C2×Dic61D812yescomplemented
92D244—22no—
93D244—22no—
94D244—41no—
95D244—41no—
96D244—41no—
97C4×D61—42no—
98Dic122—42no—
99C8×C61—41no—
100#92418—41no—
101C22×C61—21no—
102C22×C61—21no—
103C22×C61—41no—
104C22×C61—41no—
105C22×C61—41no—
106C22×C61#12011yescharacteristic
107C22×C61C2×D811yescharacteristic
108C22×C61AGL(1,ℤ/8)11yescharacteristic
109C2×D61—42no—
110C2×D61—42no—
111C2×D61—41no—
112C2×D61—41no—
113C2×D61—42no—
114C2×D61—41no—
115C2×D61—81no—
116C2×D61—81no—
117C2×D61—81no—
118C2×D61—81no—
119C4×C61—21no—
120C4×C61—21no—
121C4×C61—41no—
122C4×C61—81no—
123Dic61—22no—
124Dic61—41no—
125Dic61—41no—
126#1598—611nomaximal, Sylow
127C2×C61—21no—
128C2×C61—21no—
129C2×C61—81no—
130C2×C61#44711yescharacteristic
131C2×C61#45411yescharacteristic
132C2×C61B(4,𝔽2)11yescharacteristic
133D61—81no—
134D61—82no—
135#537—611no—
136#447—611no—
137#447—611no—
138#394—611no—
139#327—611no—
140#327D6111yescharacteristic, complemented
141#324—611no—
142C61#159811yescharacteristic, complemented, Sylow
143C2×#41—1221no—
144C22×D4—611no—
145C2×D8—1221no—
146C2×D8—1221no—
147C22⋊Q8—1221no—
148C22⋊Q8—1221no—
149#121—611no—
150#121—1221no—
151#121—1221no—
152#121—1221no—
153#121C2×D6111yescharacteristic
154C2×C4⋊C4—611no—
155C2×C22⋊C4—1221no—
156C2×C22⋊C4—1221no—
157#102—1221no—
158#102—1221no—
159C22⋊C8—611no—
160C22⋊C8C2×D6111yescharacteristic
161#95C2×D6111yescharacteristic
162C24—1221no—
163#41—2442no—
164#41—2442no—
165C2×Q8—1221no—
166C2×D4—21no—
167C2×D4—611no—
168C2×D4—1221no—
169C2×D4—1221no—
170C2×D4—1221no—
171C2×D4—1221no—
172C2×D4—1221no—
173C2×D4—2442no—
174C2×D4D24411yescharacteristic
175C22×C4—21no—
176C22×C4—611no—
177C22×C4—611no—
178C22×C4—1221no—
179C22×C4—1221no—
180C22×C4C22×D6111yescharacteristic
181D8—2442no—
182D8—2442no—
183C2×C8—21no—
184C2×C8—1221no—
185C4⋊C4—611no—
186C4⋊C4—1221no—
187C4⋊C4—1221no—
188C4⋊C4—1221no—
189C4⋊C4D24411yescharacteristic
190C22⋊C4—21no—
191C22⋊C4—1221no—
192C22⋊C4—1221no—
193C22⋊C4—1221no—
194C22⋊C4—2442no—
195C22⋊C4—2442no—
196C23—21no—
197C23—1222no—
198C23—1221no—
199C23—2441no—
200C23—2441no—
201C23—2441no—
202C23—2441no—
203C23—2441no—
204C23—2441no—
205C23D4×D6111yescharacteristic
206Q8—2442no—
207D4—41no—
208D4—41no—
209D4—41no—
210D4—1222no—
211D4—1222no—
212D4—4881no—
213D4—2441no—
214D4—2441no—
215D4—2441no—
216D4—2442no—
217D4—2441no—
218D4—2441no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—612no—
225C2×C4—1221no—
226C2×C4—1221no—
227C2×C4—1221no—
228C2×C4—1221no—
229C2×C4—2442no—
230C2×C4—2442no—
231C2×C4—2441no—
232C2×C4C2×D24411yescharacteristic
233C2×C4D4×D6111yescharacteristic
234C8—41no—
235C8—2441no—
236C22—21no—
237C22—21no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—4881no—
242C22—4881no—
243C22—4881no—
244C22—4881no—
245C22—2442no—
246C22—2442no—
247C22—2441no—
248C22—2442no—
249C22—2441no—
250C22—2441no—
251C22#1451974711yescharacteristic
252C22D8×D6111yescharacteristic
253C22#1451980411yescharacteristic
254C4—21no—
255C4—21no—
256C4—41no—
257C4—81no—
258C4—1222no—
259C4—2441no—
260C4—2441no—
261C2—21no—
262C2—21no—
263C2—81no—
264C2—4882no—
265C2—4881no—
266C2#1683989711yescharacteristic
267C2#1683993611yescharacteristic
268C2#1683995011yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#327C2
socleC22×C61#120
hypercenter#327D61
hypocenterC61#1598
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
1. #16840339C2semidirect
2. #16839898C2semidirect
3. #16839895C2semidirect
4. #16839680C2semidirect
5. #16839495C2semidirect
6. #16839487C2semidirect
7. C61×#327C2semidirect
91. C2×Dic61D8semidirect
140. #327D61semidirect
142. C61#1598semidirect