Finite Group Databasebeta

← #21444796

Subgroups — #21444796

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#16840349C211yesmaximal, characteristic
2#16839918C211yesmaximal, characteristic, complemented
3#16839673C211yesmaximal, characteristic, complemented
4#16839500C211yesmaximal, characteristic, complemented
5#16839496C211yesmaximal, characteristic, complemented
6#16839485C211yesmaximal, characteristic, complemented
7C61×#448C211yesmaximal, characteristic, complemented
8C2×#11758202—21no—
9#14519772—21no—
10#14519763—21no—
11#14519761—21no—
12#14519756C2211yescharacteristic
13#14519749—21no—
14#14519745—21no—
15D4×Dic61—21no—
16C2×#11758198—21no—
17C2×#11758198C2211yescharacteristic
18#14519701—21no—
19C22⋊#92418C2211yescharacteristic
20#14519684—21no—
21#14519684C2211yescharacteristic
22C22×Q8×C61C2211yescharacteristic
23C2×SD16×C61—21no—
24#121×C61C2211yescharacteristic
25#103×C61—21no—
26C22⋊C8×C61C2211yescharacteristic
27C23×D61D411yescharacteristic
28C2×Q8×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61—42no—
31C2×D4×C61—21no—
32C2×D4×C61D411yescharacteristic
33C22×C4×C61—21no—
34C22×C4×C61C2311yescharacteristic
35C2×C22⋊D61—21no—
36C2×C22⋊D61—21no—
37C22×Dic61—21no—
38C22×Dic61—21no—
39C22×Dic61D411yescharacteristic
40C2×Dic122D411yescharacteristic
41SD16×C61—42no—
42C2×C8×C61—21no—
43C4⋊C4×C61D411yescharacteristic
44C22⋊C4×C61—21no—
45C22⋊Dic61—21no—
46C22⋊Dic61—21no—
47#11758202—42no—
48#11758198—21no—
49#11758198—21no—
50#11758198—21no—
51#11758198—21no—
52#11758198—42no—
53C4⋊Dic61—21no—
54C4⋊Dic61D411yescharacteristic
55#11758196—21no—
56C4×Dic61—21no—
57C2×#92418—21no—
58C23×C61—21no—
59C23×C61C2×D411yescharacteristic
60C22×D61—21no—
61C22×D61—21no—
62C22×D61—21no—
63C22×D61—41no—
64C22×D61—41no—
65Q8×C61—22no—
66Q8×C61—22no—
67Q8×C61—41no—
68Q8×C61—41no—
69D4×C61—41no—
70D4×C61—41no—
71D4×C61—41no—
72C2×C4×C61—22no—
73C2×C4×C61—21no—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61—41no—
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C22⋊D61—81no—
80C22⋊D61—81no—
81C2×Dic61—21no—
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61—41no—
85C2×Dic61—41no—
86C2×Dic61—41no—
87C2×Dic61—41no—
88C2×Dic61—81no—
89Dic122—41no—
90C8×C61—41no—
91#92418—41no—
92C22×C61—21no—
93C22×C61—21no—
94C22×C61—41no—
95C22×C61—41no—
96C22×C61—41no—
97C22×C61#12011yescharacteristic
98C22×C61#13511yescharacteristic
99C22×C61#13711yescharacteristic
100C2×D61—42no—
101C2×D61—41no—
102C2×D61—41no—
103C2×D61—41no—
104C2×D61—81no—
105C4×C61—21no—
106C4×C61—21no—
107C4×C61—41no—
108C4×C61—42no—
109Dic61—41no—
110Dic61—41no—
111Dic61—41no—
112Dic61—81no—
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#448D6111yescharacteristic, complemented
124#393—611no—
125#328—611no—
126#327—611no—
127#323—611no—
128C61#160611yescharacteristic, complemented, Sylow
129C22×Q8C2×D6111yescharacteristic
130C2×Q16—1221no—
131C2×SD16—21no—
132#126—1221no—
133#124—1221no—
134#123—1221no—
135C22⋊Q8—611no—
136#121—1221no—
137#121C2×D6111yescharacteristic
138#120—1221no—
139C4×D4—1221no—
140C2×C22⋊C4—611no—
141C2×C22⋊C4—1221no—
142#103—21no—
143#103—1221no—
144C22⋊C8—611no—
145C22⋊C8C2×D6111yescharacteristic
146#95—611no—
147#95—1221no—
148C24—611no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—42no—
152C2×Q8—611no—
153C2×D4—21no—
154C2×D4—1221no—
155C2×D4—1221no—
156C2×D4C22⋊D6111yescharacteristic
157C22×C4—21no—
158C22×C4—611no—
159C22×C4—1221no—
160C22×C4—1221no—
161C22×C4C22×D6111yescharacteristic
162Q16—2442no—
163SD16—42no—
164C2×C8—21no—
165C2×C8—1221no—
166C4⋊C4—611no—
167C4⋊C4—1221no—
168C4⋊C4—1221no—
169C4⋊C4C22⋊D6111yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—1221no—
172C22⋊C4—1221no—
173C22⋊C4—1221no—
174C22⋊C4—1221no—
175C22⋊C4—1221no—
176C22⋊C4—1221no—
177C22⋊C4—2442no—
178C42—1221no—
179C23—21no—
180C23—1221no—
181C23—1221no—
182C23—1221no—
183C23—2441no—
184C23—2441no—
185C23D4×D6111yescharacteristic
186Q8—22no—
187Q8—22no—
188Q8—41no—
189Q8—41no—
190Q8—2441no—
191D4—41no—
192D4—41no—
193D4—41no—
194D4—4881no—
195D4—4881no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—1221no—
202C2×C4—1221no—
203C2×C4—1221no—
204C2×C4—4881no—
205C2×C4—2441no—
206C2×C4—2441no—
207C2×C4—2441no—
208C2×C4—2441no—
209C2×C4D4×D6111yescharacteristic
210C2×C4C2×C22⋊D6111yescharacteristic
211C8—41no—
212C8—2441no—
213C22—21no—
214C22—21no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—4881no—
219C22—2442no—
220C22—2441no—
221C22—2441no—
222C22—2441no—
223C22#1451974511yescharacteristic
224C22#1451979811yescharacteristic
225C22#1451980611yescharacteristic
226C4—21no—
227C4—21no—
228C4—42no—
229C4—41no—
230C4—4881no—
231C4—2441no—
232C4—2441no—
233C4—2441no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—4881no—
238C2#1683992111yescharacteristic
239C2#1683993811yescharacteristic
240C2#1683994811yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#448C2
socleC22×C61#120
hypercenter#448D61
hypocenterC61#1606
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. #16839918C2semidirect
3. #16839673C2semidirect
4. #16839500C2semidirect
5. #16839496C2semidirect
6. #16839485C2semidirect
7. C61×#448C2semidirect
123. #448D61semidirect
128. C61#1606semidirect