Finite Group Databasebeta

← #21444797

Subgroups — #21444797

Order 7808.

260 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 49 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#16840350C211yesmaximal, characteristic
2#16839918C211yesmaximal, characteristic, complemented
3#16839901C211yesmaximal, characteristic, complemented
4#16839498C211yesmaximal, characteristic, complemented
5#16839495C211yesmaximal, characteristic, complemented
6#16839486C211yesmaximal, characteristic, complemented
7C61×#393C211yesmaximal, characteristic, complemented
8C2×#11758202—21no—
9C2×#11758201—21no—
10#14519770—21no—
11#14519763—21no—
12#14519759—21no—
13#14519756C2211yescharacteristic
14#14519751C2211yescharacteristic
15#14519750—21no—
16#14519746—21no—
17C4×C22⋊D61—21no—
18#14519701—21no—
19#14519701—21no—
20C22⋊#92418C2211yescharacteristic
21C22⋊#92418C2211yescharacteristic
22C22×Q8×C61C2211yescharacteristic
23C2×C22⋊C4×C61—21no—
24C2×C22⋊C4×C61C2211yescharacteristic
25#95×C61—21no—
26#95×C61C2211yescharacteristic
27C24×C61D411yescharacteristic
28C2×Q8×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61—42no—
31C22×C4×C61—21no—
32C22×C4×C61—21no—
33C22×C4×C61D411yescharacteristic
34C22×C4×C61C2311yescharacteristic
35C2×C22⋊D61—21no—
36C2×C22⋊D61—21no—
37C2×C22⋊D61—21no—
38C2×D244D411yescharacteristic
39C2×C4×D61—21no—
40C2×Dic122D411yescharacteristic
41C22⋊C4×C61—21no—
42C22⋊C4×C61—21no—
43C22⋊C4×C61—42no—
44C22⋊Dic61—21no—
45C22⋊Dic61—21no—
46C22⋊Dic61—21no—
47#11758202—42no—
48#11758201—42no—
49#11758198—21no—
50#11758198—21no—
51C4⋊Dic61D411yescharacteristic
52C4⋊Dic61D411yescharacteristic
53#11758196—21no—
54#11758196—21no—
55C4×Dic61—21no—
56C2×#92418—21no—
57C2×#92418—21no—
58C23×C61—21no—
59C23×C61—21no—
60C23×C61—21no—
61C23×C61—41no—
62C23×C61—41no—
63C23×C61C2×D411yescharacteristic
64C22×D61—21no—
65Q8×C61—22no—
66Q8×C61—22no—
67Q8×C61—41no—
68Q8×C61—41no—
69C2×C4×C61—22no—
70C2×C4×C61—21no—
71C2×C4×C61—41no—
72C2×C4×C61—41no—
73C2×C4×C61—41no—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61—41no—
77C2×C4×C61—41no—
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C22⋊D61—41no—
81C22⋊D61—41no—
82C22⋊D61—81no—
83C22⋊D61—81no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87D244—41no—
88C4×D61—81no—
89Dic122—41no—
90#92418—41no—
91#92418—41no—
92C22×C61—21no—
93C22×C61—21no—
94C22×C61—42no—
95C22×C61—41no—
96C22×C61—41no—
97C22×C61—41no—
98C22×C61—81no—
99C22×C61#12011yescharacteristic
100C22×C61#13511yescharacteristic
101C22×C61#13711yescharacteristic
102C2×D61—41no—
103C2×D61—41no—
104C2×D61—41no—
105C4×C61—21no—
106C4×C61—21no—
107C4×C61—41no—
108C4×C61—42no—
109C4×C61—81no—
110Dic61—41no—
111Dic61—41no—
112Dic61—41no—
113#1606—611nomaximal, Sylow
114C2×C61—21no—
115C2×C61—21no—
116C2×C61—81no—
117C2×C61#45211yescharacteristic
118C2×C61#45511yescharacteristic
119C2×C61B(4,𝔽2)11yescharacteristic
120D61—81no—
121#538—611no—
122#451—611no—
123#448—611no—
124#393D6111yescharacteristic, complemented
125#328—611no—
126#327—611no—
127#323—611no—
128C61#160611yescharacteristic, complemented, Sylow
129C22×Q8C2×D6111yescharacteristic
130C2×Q16—1221no—
131C2×SD16—1221no—
132#126—1221no—
133#124—1221no—
134#123—1221no—
135C22⋊Q8—611no—
136#121—611no—
137#121—1221no—
138#120—1221no—
139C4×D4—1221no—
140C2×C22⋊C4—21no—
141C2×C22⋊C4C2×D6111yescharacteristic
142#103—1221no—
143#103—1221no—
144C22⋊C8—611no—
145C22⋊C8—611no—
146#95—21no—
147#95C2×D6111yescharacteristic
148C24C22⋊D6111yescharacteristic
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—42no—
152C2×Q8—611no—
153C2×D4—611no—
154C2×D4—1221no—
155C2×D4—1221no—
156C2×D4—1221no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—1221no—
160C22×C4C22⋊D6111yescharacteristic
161C22×C4C22×D6111yescharacteristic
162Q16—2442no—
163SD16—2442no—
164C2×C8—1221no—
165C2×C8—1221no—
166C4⋊C4—611no—
167C4⋊C4—611no—
168C4⋊C4—1221no—
169C4⋊C4—1221no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—42no—
173C22⋊C4—1221no—
174C22⋊C4—1221no—
175C22⋊C4—1221no—
176C22⋊C4—1221no—
177C22⋊C4—1221no—
178C42—1221no—
179C23—21no—
180C23—21no—
181C23—21no—
182C23—41no—
183C23—41no—
184C23—1221no—
185C23C2×C22⋊D6111yescharacteristic
186Q8—22no—
187Q8—22no—
188Q8—41no—
189Q8—41no—
190Q8—2441no—
191D4—4881no—
192D4—4881no—
193D4—2441no—
194D4—2441no—
195D4—2441no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—1221no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—4881no—
209C2×C4D4×D6111yescharacteristic
210C2×C4D4×D6111yescharacteristic
211C8—2441no—
212C8—2441no—
213C22—21no—
214C22—21no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22—41no—
219C22—81no—
220C22—2441no—
221C22—2441no—
222C22—2441no—
223C22#1451974511yescharacteristic
224C22#1451979711yescharacteristic
225C22#1451980811yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—42no—
230C4—81no—
231C4—2441no—
232C4—2441no—
233C4—2441no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—4881no—
238C2#1683992211yescharacteristic
239C2#1683993911yescharacteristic
240C2#1683994811yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#393C2
socleC22×C61#120
hypercenter#393D61
hypocenterC61#1606
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #393

Complements

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

NH ≅ G/Ntype
2. #16839918C2semidirect
3. #16839901C2semidirect
4. #16839498C2semidirect
5. #16839495C2semidirect
6. #16839486C2semidirect
7. C61×#393C2semidirect
124. #393D61semidirect
128. C61#1606semidirect