Finite Group Databasebeta

← #21447037

Subgroups — #21447037

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#16840336C211yesmaximal, characteristic
2#16839804C211yesmaximal, characteristic, complemented
3C2×#14519703C211yesmaximal, characteristic
4#16839764C211yesmaximal, characteristic
5#16839669C211yesmaximal, characteristic, complemented
6#16839523C211yesmaximal, characteristic, complemented
7C2×#101×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519775—21no—
10#14519766—21no—
11#14519760—22no—
12#14519753—21no—
13#14519753—21no—
14#14519736C2211yescharacteristic
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4×Dic61C2211yescharacteristic
17#14519711—21no—
18#14519709—21no—
19#14519703—22no—
20#14519702—21no—
21#14519699—21no—
22#14519684—22no—
23C22×Q8×C61C2211yescharacteristic
24C2×M16×C61C2211yescharacteristic
25C2×M16×C61C2211yescharacteristic
26#101×C61—22no—
27C2×Q8×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61—21no—
31C2×Q8×C61—21no—
32C2×Q8×C61—21no—
33C22×C4×C61D412yes—
34C22×C4×C61C2311yescharacteristic
35C2×C22⋊D61—21no—
36C22×Dic61—21no—
37C22×Dic61—21no—
38#11758222—21no—
39#11758222—21no—
40#11758222—21no—
41#11758222—21no—
42C2×D244D411yescharacteristic
43C2×C4×D61—21no—
44C2×Dic122D411yescharacteristic
45M16×C61—21no—
46M16×C61—21no—
47M16×C61—21no—
48M16×C61D412yes—
49C2×C8×C61—21no—
50C2×C8×C61—21no—
51C22⋊Dic61—21no—
52#11758198—22no—
53#11758198—22no—
54C4⋊Dic61—21no—
55C4⋊Dic61—21no—
56C4⋊Dic61D411yescharacteristic
57C4⋊Dic61D411yescharacteristic
58#11758196—22no—
59#11758196—22no—
60C4×Dic61—21no—
61C4×Dic61—21no—
62C4×Dic61—21no—
63C23×C61C2×D411yescharacteristic
64C22×D61—21no—
65Q8×C61—41no—
66Q8×C61—41no—
67Q8×C61—41no—
68Q8×C61—41no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61#4111yescharacteristic
76C2×C4×C61#4111yescharacteristic
77C2×C4×C61#4111yescharacteristic
78C22⋊D61—41no—
79C22⋊D61—41no—
80C2×Dic61—22no—
81C2×Dic61—21no—
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61—41no—
85C2×Dic61—41no—
86C2×Dic61—42no—
87C2×Dic61—41no—
88D244—21no—
89D244—21no—
90C4×D61—41no—
91C4×D61—41no—
92Dic122—21no—
93Dic122—21no—
94C8×C61—22no—
95C8×C61—41no—
96C22×C61—21no—
97C22×C61—21no—
98C22×C61#12011yescharacteristic
99C22×C61#12111yescharacteristic
100C22×C61#12311yescharacteristic
101C2×D61—41no—
102C2×D61—41no—
103C2×D61—41no—
104C4×C61—42no—
105C4×C61#12111yescharacteristic
106C4×C61#12111yescharacteristic
107C4×C61#12311yescharacteristic
108C4×C61#12411yescharacteristic
109Dic61—42no—
110Dic61—41no—
111Dic61—41no—
112Dic61—41no—
113Dic61—81no—
114#2038—611nomaximal, Sylow
115C2×C61—21no—
116C2×C61—21no—
117C2×C61#39411yescharacteristic
118C2×C61#45411yescharacteristic
119C2×C61#45611yescharacteristic
120D61—81no—
121#536—611no—
122#428—611no—
123C2×#104—611no—
124#417—611no—
125C2×#101D6111yescharacteristic, complemented
126#391—611no—
127#339—611no—
128C61#203811yescharacteristic, complemented, Sylow
129C2×#41—611no—
130C22×Q8C2×D6111yescharacteristic
131C2×M16C2×D6111yescharacteristic
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×C42—611no—
141#107—1221no—
142#106—1221no—
143#104—1222no—
144#103—1221no—
145#102—1221no—
146#101—22no—
147#95—1222no—
148#41—1221no—
149#41—1221no—
150#41—1221no—
151#41—1221no—
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—21no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—611no—
159C2×D4—611no—
160C2×D4—1221no—
161C22×C4—1221no—
162C22×C4—1221no—
163C22×C4—1221no—
164C22×C4D24412yes—
165C22×C4C22×D6111yescharacteristic
166M16—21no—
167M16—21no—
168M16—21no—
169M16C22⋊D6112yes—
170C2×C8—21no—
171C2×C8—21no—
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—1221no—
182C42—1221no—
183C42—1221no—
184C23—1221no—
185C23C2×D24411yescharacteristic
186Q8—41no—
187Q8—41no—
188Q8—41no—
189Q8—41no—
190Q8—1221no—
191Q8—1221no—
192D4—1221no—
193D4—1221no—
194D4—2441no—
195D4—2441no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—1222no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—1221no—
203C2×C4—2442no—
204C2×C4—2441no—
205C2×C4—2441no—
206C2×C4—2441no—
207C2×C4—2441no—
208C2×C4—2441no—
209C2×C4#1175822211yescharacteristic
210C2×C4D4×D6111yescharacteristic
211C2×C4D4×D6111yescharacteristic
212C2×C4#1175822411yescharacteristic
213C2×C4#1175822411yescharacteristic
214C2×C4C2×C22⋊D6111yescharacteristic
215C8—22no—
216C8—41no—
217C22—21no—
218C22—21no—
219C22—2441no—
220C22—2441no—
221C22—2441no—
222C22#1451974711yescharacteristic
223C22#1451975111yescharacteristic
224C22#1451976111yescharacteristic
225C4—42no—
226C4—4881no—
227C4—2442no—
228C4—2441no—
229C4—2441no—
230C4—2441no—
231C4#1451974811yescharacteristic
232C4#1451974911yescharacteristic
233C4#1451975911yescharacteristic
234C4#1451976311yescharacteristic
235C2—21no—
236C2—21no—
237C2—4881no—
238C2#1683967811yescharacteristic
239C2#1683993711yescharacteristic
240C2#1683994711yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#101×C61C2
socleC22×C61#120
hypercenterC2×#101D61
hypocenterC61#2038
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #16839804C2semidirect
5. #16839669C2semidirect
6. #16839523C2semidirect
7. C2×#101×C61C2semidirect
125. C2×#101D61semidirect
128. C61#2038semidirect