Finite Group Databasebeta

← #21447042

Subgroups — #21447042

Order 7808.

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

normal subgroups only

This group has 306 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#16840340C211yesmaximal, characteristic
2C2×#14519705C211yesmaximal, characteristic, complemented
3#16839764C211yesmaximal, characteristic, complemented
4#16839763C211yesmaximal, characteristic, complemented
5#16839632C211yesmaximal, characteristic, complemented
6#16839530C211yesmaximal, characteristic, complemented
7C2×#104×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10#14519756—21no—
11#14519753—21no—
12#14519751—21no—
13#14519749—22no—
14#14519748—21no—
15C2×C4⋊Dic61—22no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×C4⋊Dic61C2211yescharacteristic
18#14519705—22no—
19#14519702—21no—
20#14519701—21no—
21#14519699—21no—
22#14519698—21no—
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
37C2×C22⋊D61—21no—
38C2×C22⋊D61—22no—
39C22×Dic61—21no—
40C22×Dic61D412yes—
41#11758222—21no—
42#11758222—21no—
43#11758222—21no—
44#11758222—21no—
45C2×D244D411yescharacteristic
46C2×C4×D61—21no—
47C2×Dic122D411yescharacteristic
48M16×C61—21no—
49M16×C61—21no—
50C2×C8×C61—21no—
51C42×C61—21no—
52C42×C61D412yescomplemented
53C22⋊Dic61—22no—
54#11758198—22no—
55C4⋊Dic61—21no—
56C4⋊Dic61—21no—
57C4⋊Dic61—21no—
58C4⋊Dic61—21no—
59C4⋊Dic61—44no—
60#11758196—22no—
61#11758194—21no—
62#11758194—21no—
63C2×#92418—21no—
64C23×C61—21no—
65C23×C61C2×D411yescharacteristic
66C22×D61—21no—
67Q8×C61—21no—
68Q8×C61—21no—
69D4×C61—21no—
70D4×C61—21no—
71D4×C61—41no—
72D4×C61—41no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—21no—
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61#4111yescharacteristic
83C2×C4×C61#4111yescharacteristic
84C2×C4×C61#4111yescharacteristic
85C22⋊D61—41no—
86C22⋊D61—41no—
87C22⋊D61—82no—
88C2×Dic61—21no—
89C2×Dic61—22no—
90C2×Dic61—42no—
91C2×Dic61—42no—
92C2×Dic61—41no—
93D244—21no—
94D244—21no—
95C4×D61—41no—
96C4×D61—41no—
97Dic122—21no—
98Dic122—21no—
99C8×C61—41no—
100#92418—41no—
101C22×C61—21no—
102C22×C61—21no—
103C22×C61—41no—
104C22×C61—41no—
105C22×C61—41no—
106C22×C61#12011yescharacteristic
107C22×C61#12111yescharacteristic
108C22×C61#12411yescharacteristic
109C2×D61—41no—
110C2×D61—41no—
111C2×D61—41no—
112C4×C61—24no—
113C4×C61—41no—
114C4×C61#12111yescharacteristic
115C4×C61#12111yescharacteristic
116C4×C61#12311yescharacteristic
117C4×C61#12311yescharacteristic
118Dic61—41no—
119Dic61—42no—
120Dic61—81no—
121#2039—611nomaximal, Sylow
122C2×C61—21no—
123C2×C61—21no—
124C2×C61—81no—
125C2×C61#39411yescharacteristic
126C2×C61#45311yescharacteristic
127C2×C61#45611yescharacteristic
128D61—81no—
129#537—611no—
130C2×#104—611no—
131C2×#104D6111yescharacteristic, complemented
132#417—611no—
133#417—611no—
134#384—611no—
135#343—611no—
136C61#203911yescharacteristic, complemented, Sylow
137C2×#41—611no—
138C2×#41C2×D6111yescharacteristic
139C2×M16—611no—
140C2×M16C2×D6111yescharacteristic
141C22⋊Q8—1221no—
142C22⋊Q8—1221no—
143#121—1221no—
144#121—1222no—
145#121—1221no—
146C2×C4⋊C4—611no—
147C2×C4⋊C4—611no—
148C2×C4⋊C4—1222no—
149C2×C42C2×D6111yescharacteristic
150#104—22no—
151#104—1222no—
152#103—1221no—
153#103—1221no—
154#102—1221no—
155#102—1221no—
156#41—21no—
157#41—21no—
158#41—21no—
159#41—21no—
160#41—1221no—
161#41—1221no—
162#41—1221no—
163#41—1221no—
164C2×Q8—611no—
165C2×Q8D24411yescharacteristic
166C2×D4—21no—
167C2×D4—611no—
168C2×D4—1222no—
169C2×D4—1221no—
170C2×D4D24411yescharacteristic
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—612no—
174C22×C4—1221no—
175C22×C4—1221no—
176C22×C4C22×D6111yescharacteristic
177M16—21no—
178M16—21no—
179M16—1221no—
180M16—1221no—
181C2×C8—21no—
182C2×C8—1221no—
183C4⋊C4—1222no—
184C4⋊C4—1221no—
185C4⋊C4—1221no—
186C4⋊C4—1221no—
187C4⋊C4—1221no—
188C4⋊C4—2444no—
189C22⋊C4—1222no—
190C22⋊C4—1222no—
191C42—21no—
192C42C22⋊D6112yescomplemented
193C23—21no—
194C23—1221no—
195C23D4×D6111yescharacteristic
196Q8—21no—
197Q8—21no—
198Q8—1221no—
199Q8—1221no—
200D4—21no—
201D4—21no—
202D4—41no—
203D4—41no—
204D4—1221no—
205D4—1221no—
206D4—4882no—
207D4—2441no—
208D4—2441no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—1222no—
216C2×C4—1221no—
217C2×C4—2442no—
218C2×C4—2441no—
219C2×C4—2441no—
220C2×C4—2441no—
221C2×C4—2442no—
222C2×C4C2×D24411yescharacteristic
223C2×C4#1175822211yescharacteristic
224C2×C4D4×D6111yescharacteristic
225C2×C4#1175822411yescharacteristic
226C2×C4#1175822411yescharacteristic
227C2×C4C2×C22⋊D6111yescharacteristic
228C8—41no—
229C8—2441no—
230C22—21no—
231C22—21no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22—2441no—
236C22—2441no—
237C22—2441no—
238C22#1451974711yescharacteristic
239C22#1451974911yescharacteristic
240C22#1451976311yescharacteristic
241C4—24no—
242C4—41no—
243C4—4881no—
244C4—2442no—
245C4—2441no—
246C4#1451974811yescharacteristic
247C4#1451975111yescharacteristic
248C4#1451975911yescharacteristic
249C4#1451976111yescharacteristic
250C2—21no—
251C2—21no—
252C2—81no—
253C2—4881no—
254C2#1683967811yescharacteristic
255C2#1683993111yescharacteristic
256C2#1683994611yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#104×C61C2
socleC22×C61#120
hypercenterC2×#104D61
hypocenterC61#2039
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. C2×#14519705C2semidirect
3. #16839764C2semidirect
4. #16839763C2semidirect
5. #16839632C2semidirect
6. #16839530C2semidirect
7. C2×#104×C61C2semidirect
52. C42×C61D4semidirect
131. C2×#104D61semidirect
136. C61#2039semidirect
192. C42C22⋊D61semidirect