Finite Group Databasebeta

← #21447035

Subgroups — #21447035

Order 7808.

278 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 69 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#16840333C211yesmaximal, characteristic
2#16839804C211yesmaximal, characteristic, complemented
3#16839763C211yesmaximal, characteristic
4C2×#14519695C211yesmaximal, characteristic, complemented
5#16839668C211yesmaximal, characteristic, complemented
6#16839522C211yesmaximal, characteristic, complemented
7C2×#104×C61C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10#14519775—21no—
11#14519764—21no—
12#14519758—22no—
13#14519756—21no—
14#14519756—21no—
15#14519736C2211yescharacteristic
16C2×C4⋊Dic61C2211yescharacteristic
17#14519711—21no—
18#14519709—21no—
19#14519701—21no—
20#14519698—21no—
21#14519695—22no—
22#14519684—22no—
23C2×#41×C61C2211yescharacteristic
24C2×M16×C61C2211yescharacteristic
25C2×C42×C61C2211yescharacteristic
26#104×C61—22no—
27#41×C61—21no—
28#41×C61—21no—
29#41×C61—21no—
30#41×C61—21no—
31C2×Q8×C61D411yescharacteristic
32C2×D4×C61—21no—
33C2×D4×C61D411yescharacteristic
34C22×C4×C61—21no—
35C22×C4×C61—21no—
36C22×C4×C61C2311yescharacteristic
37C22×Dic61—21no—
38C22×Dic61D412yes—
39C2×Dic122—21no—
40C2×Dic122—21no—
41C2×Dic122—21no—
42C2×Dic122—21no—
43C2×Dic122—21no—
44C2×Dic122—21no—
45M16×C61—21no—
46M16×C61D412yes—
47C2×C8×C61—21no—
48C42×C61—21no—
49C42×C61—21no—
50C22⋊Dic61—22no—
51C22⋊Dic61—22no—
52C22⋊Dic61—21no—
53C4⋊Dic61—21no—
54C4⋊Dic61—21no—
55C4⋊Dic61D411yescharacteristic
56C4⋊Dic61D411yescharacteristic
57#11758196—22no—
58#11758196—22no—
59C4×Dic61—21no—
60#11758194—21no—
61#11758194—21no—
62C2×#92418—21no—
63C23×C61—21no—
64C23×C61C2×D411yescharacteristic
65Q8×C61—21no—
66Q8×C61—21no—
67D4×C61—21no—
68D4×C61—21no—
69D4×C61—41no—
70D4×C61—41no—
71C2×C4×C61—22no—
72C2×C4×C61—21no—
73C2×C4×C61—41no—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61—41no—
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61#4111yescharacteristic
81C2×C4×C61#4111yescharacteristic
82C2×C4×C61#4111yescharacteristic
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—42no—
89C2×Dic61—41no—
90Dic122—41no—
91Dic122—41no—
92Dic122—41no—
93Dic122—41no—
94C8×C61—22no—
95#92418—41no—
96C22×C61—21no—
97C22×C61—21no—
98C22×C61—41no—
99C22×C61—41no—
100C22×C61—41no—
101C22×C61#12011yescharacteristic
102C22×C61#12111yescharacteristic
103C22×C61#12311yescharacteristic
104C4×C61—42no—
105C4×C61—41no—
106C4×C61#12111yescharacteristic
107C4×C61#12111yescharacteristic
108C4×C61#12311yescharacteristic
109C4×C61#12411yescharacteristic
110Dic61—42no—
111Dic61—41no—
112Dic61—41no—
113Dic61—81no—
114#2038—611nomaximal, Sylow
115C2×C61—21no—
116C2×C61—21no—
117C2×C61—81no—
118C2×C61#39411yescharacteristic
119C2×C61#45411yescharacteristic
120C2×C61#45611yescharacteristic
121#536—611no—
122#428—611no—
123C2×#104D6111yescharacteristic
124#417—611no—
125C2×#101—611no—
126#391—611no—
127#339—611no—
128C61#203811yescharacteristic, complemented, Sylow
129C2×#41C2×D6111yescharacteristic
130C22×Q8—611no—
131C2×M16—611no—
132C2×M16C2×D6111yescharacteristic
133C4⋊Q8—1221no—
134#124—1221no—
135#123—1222no—
136C22⋊Q8—1221no—
137C22⋊Q8—1221no—
138#117—611no—
139C2×C4⋊C4—611no—
140C2×C42C2×D6111yescharacteristic
141#107—1221no—
142#106—1221no—
143#104—22no—
144#103—1221no—
145#102—1221no—
146#101—1222no—
147#95—1222no—
148#41—21no—
149#41—21no—
150#41—21no—
151#41—21no—
152C2×Q8—1221no—
153C2×Q8—1221no—
154C2×Q8—1221no—
155C2×Q8—1221no—
156C2×Q8—1221no—
157C2×Q8—1221no—
158C2×Q8D24411yescharacteristic
159C2×D4—21no—
160C2×D4D24411yescharacteristic
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—612no—
164C22×C4—1221no—
165C22×C4C22×D6111yescharacteristic
166M16—21no—
167M16—1221no—
168M16—1221no—
169M16C22⋊D6112yes—
170C2×C8—21no—
171C2×C8—1221no—
172C4⋊C4—611no—
173C4⋊C4—611no—
174C4⋊C4—1222no—
175C4⋊C4—1222no—
176C4⋊C4—1221no—
177C4⋊C4—1221no—
178C22⋊C4—1222no—
179C22⋊C4—1222no—
180C22⋊C4—1221no—
181C42—21no—
182C42—21no—
183C42—1221no—
184C23—21no—
185C23D4×D6111yescharacteristic
186Q8—21no—
187Q8—21no—
188Q8—2441no—
189Q8—2441no—
190Q8—2441no—
191Q8—2441no—
192D4—21no—
193D4—21no—
194D4—41no—
195D4—41no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—1221no—
203C2×C4—1221no—
204C2×C4—1222no—
205C2×C4—1222no—
206C2×C4—1222no—
207C2×C4—2442no—
208C2×C4—2441no—
209C2×C4C2×D24411yescharacteristic
210C2×C4#1175822211yescharacteristic
211C2×C4D4×D6111yescharacteristic
212C2×C4#1175822411yescharacteristic
213C2×C4#1175822411yescharacteristic
214C2×C4C2×C22⋊D6111yescharacteristic
215C8—22no—
216C8—2441no—
217C22—21no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22#1451974711yescharacteristic
223C22#1451974811yescharacteristic
224C22#1451975911yescharacteristic
225C4—42no—
226C4—41no—
227C4—4881no—
228C4—2441no—
229C4—2441no—
230C4—2442no—
231C4#1451974911yescharacteristic
232C4#1451975111yescharacteristic
233C4#1451976111yescharacteristic
234C4#1451976311yescharacteristic
235C2—21no—
236C2—21no—
237C2—81no—
238C2#1683967811yescharacteristic
239C2#1683993611yescharacteristic
240C2#1683994611yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#104×C61C2
socleC22×C61#120
hypercenterC2×#104D61
hypocenterC61#2038
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #16839804C2semidirect
4. C2×#14519695C2semidirect
5. #16839668C2semidirect
6. #16839522C2semidirect
128. C61#2038semidirect