Finite Group Databasebeta

← #21444752

Subgroups — #21444752

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#16839896C211yesmaximal, characteristic, complemented
3#16839676C211yesmaximal, characteristic, complemented
4#16839497C211yesmaximal, characteristic, complemented
5#16839496C211yesmaximal, characteristic, complemented
6#16839487C211yesmaximal, characteristic, complemented
7C61×#447C211yesmaximal, characteristic, complemented
8C2×#11758224—21no—
9C2×#11758199—21no—
10#14519755—21no—
11#14519754—21no—
12#14519751C2211yescharacteristic
13#14519750—21no—
14#14519749—21no—
15#14519749—21no—
16C2×#11758196C2211yescharacteristic
17C2×C22⋊Dic61—21no—
18C2×C22⋊Dic61—21no—
19#14519698—21no—
20C22⋊#92418C2211yescharacteristic
21#14519684C2211yescharacteristic
22C22×D4×C61C2211yescharacteristic
23C2×D8×C61—21no—
24#121×C61C2211yescharacteristic
25#102×C61—21no—
26C22⋊C8×C61C2211yescharacteristic
27C24×C61—21no—
28C2×D4×C61—21no—
29C2×D4×C61—21no—
30C2×D4×C61—21no—
31C2×D4×C61—42no—
32C2×D4×C61D411yescharacteristic
33C22×C4×C61C2311yescharacteristic
34C2×C22⋊D61—21no—
35C2×C22⋊D61—21no—
36C2×C22⋊D61—21no—
37C22×Dic61—21no—
38C22×Dic61—21no—
39C22×Dic61D411yescharacteristic
40C22×Dic61D411yescharacteristic
41#11758224—42no—
42#11758224—42no—
43C2×D244D411yescharacteristic
44C2×C4×D61—21no—
45C2×Dic122—21no—
46D8×C61—42no—
47C2×C8×C61—21no—
48C4⋊C4×C61D411yescharacteristic
49C22⋊C4×C61—21no—
50C22⋊Dic61—21no—
51C22⋊Dic61—42no—
52C22⋊Dic61—42no—
53#11758199—42no—
54#11758198—21no—
55#11758198—21no—
56C4⋊Dic61D411yescharacteristic
57#11758196—21no—
58#11758196—21no—
59#11758196—21no—
60C2×#92418—21no—
61C23×C61—22no—
62C23×C61—21no—
63C23×C61—41no—
64C23×C61—41no—
65C23×C61—41no—
66C23×C61—41no—
67C23×C61—41no—
68C23×C61—41no—
69C23×C61C2×D411yescharacteristic
70C22×D61—21no—
71D4×C61—22no—
72D4×C61—22no—
73D4×C61—41no—
74D4×C61—41no—
75D4×C61—41no—
76D4×C61—41no—
77D4×C61—41no—
78C2×C4×C61—21no—
79C2×C4×C61—41no—
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C22⋊D61—42no—
83C22⋊D61—41no—
84C22⋊D61—41no—
85C22⋊D61—81no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—42no—
91C2×Dic61—41no—
92C2×Dic61—41no—
93C2×Dic61—41no—
94C2×Dic61—41no—
95C2×Dic61D812yescomplemented
96D244—41no—
97C4×D61—42no—
98Dic122—42no—
99C8×C61—41no—
100#92418—41no—
101C22×C61—21no—
102C22×C61—21no—
103C22×C61—42no—
104C22×C61—42no—
105C22×C61—41no—
106C22×C61—41no—
107C22×C61—41no—
108C22×C61—42no—
109C22×C61—81no—
110C22×C61—81no—
111C22×C61—81no—
112C22×C61—81no—
113C22×C61#12011yescharacteristic
114C22×C61C2×D811yescharacteristic
115C22×C61AGL(1,ℤ/8)11yescharacteristic
116C2×D61—41no—
117C2×D61—41no—
118C2×D61—41no—
119C4×C61—21no—
120C4×C61—21no—
121C4×C61—41no—
122Dic61—22no—
123Dic61—41no—
124Dic61—41no—
125Dic61—81no—
126#1598—611nomaximal, Sylow
127C2×C61—21no—
128C2×C61—21no—
129C2×C61—81no—
130C2×C61—82no—
131C2×C61#44711yescharacteristic
132C2×C61#45411yescharacteristic
133C2×C61B(4,𝔽2)11yescharacteristic
134D61—81no—
135#537—611no—
136#447—611no—
137#447D6111yescharacteristic, complemented
138#394—611no—
139#327—611no—
140#327—611no—
141#324—611no—
142C61#159811yescharacteristic, complemented, Sylow
143C2×#41—1221no—
144C22×D4C2×D6111yescharacteristic
145C2×D8—21no—
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—21no—
158#102—1221no—
159C22⋊C8—611no—
160C22⋊C8C2×D6111yescharacteristic
161#95—611no—
162C24—21no—
163#41—2442no—
164#41—2442no—
165C2×Q8—1221no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—42no—
170C2×D4—611no—
171C2×D4—1221no—
172C2×D4—1221no—
173C2×D4—1221no—
174C2×D4C22⋊D6111yescharacteristic
175C22×C4—611no—
176C22×C4—611no—
177C22×C4—1221no—
178C22×C4—1221no—
179C22×C4—1221no—
180C22×C4C22×D6111yescharacteristic
181D8—42no—
182D8—2442no—
183C2×C8—21no—
184C2×C8—1221no—
185C4⋊C4—611no—
186C4⋊C4—1221no—
187C4⋊C4—1221no—
188C4⋊C4—1221no—
189C4⋊C4C22⋊D6111yescharacteristic
190C22⋊C4—21no—
191C22⋊C4—1221no—
192C22⋊C4—1221no—
193C22⋊C4—1221no—
194C22⋊C4—2442no—
195C22⋊C4—2442no—
196C23—22no—
197C23—21no—
198C23—41no—
199C23—41no—
200C23—41no—
201C23—41no—
202C23—41no—
203C23—41no—
204C23—1221no—
205C23D4×D6111yescharacteristic
206Q8—2442no—
207D4—22no—
208D4—22no—
209D4—41no—
210D4—41no—
211D4—41no—
212D4—41no—
213D4—41no—
214D4—4881no—
215D4—2441no—
216D4—2442no—
217D4—2441no—
218D4—2441no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—612no—
222C2×C4—1221no—
223C2×C4—1221no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—2442no—
227C2×C4—2442no—
228C2×C4—2441no—
229C2×C4—2441no—
230C2×C4—2441no—
231C2×C4—2441no—
232C2×C4D4×D6111yescharacteristic
233C2×C4C2×C22⋊D6111yescharacteristic
234C8—41no—
235C8—2441no—
236C22—21no—
237C22—21no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—81no—
245C22—81no—
246C22—81no—
247C22—81no—
248C22—2441no—
249C22—2441no—
250C22—2441no—
251C22#1451974511yescharacteristic
252C22D8×D6111yescharacteristic
253C22#1451980111yescharacteristic
254C4—21no—
255C4—21no—
256C4—41no—
257C4—1222no—
258C4—4881no—
259C4—2441no—
260C4—2441no—
261C2—21no—
262C2—21no—
263C2—82no—
264C2—81no—
265C2—4881no—
266C2#1683989411yescharacteristic
267C2#1683993311yescharacteristic
268C2#1683994811yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#447C2
socleC22×C61#120
hypercenter#447D61
hypocenterC61#1598
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #16840339C2semidirect
2. #16839896C2semidirect
3. #16839676C2semidirect
4. #16839497C2semidirect
5. #16839496C2semidirect
6. #16839487C2semidirect
7. C61×#447C2semidirect
95. C2×Dic61D8semidirect
137. #447D61semidirect
142. C61#1598semidirect