Finite Group Databasebeta

← #21444997

Subgroups — #21444997

Order 7808.

308 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×D244C211yesmaximal, characteristic
2#16840110C211yesmaximal, characteristic, complemented
3#16839964C211yesmaximal, characteristic, complemented
4#16839505C211yesmaximal, characteristic, complemented
5D4⋊#92418C211yesmaximal, characteristic, complemented
6#16839489C211yesmaximal, characteristic, complemented
7C61×#474C211yesmaximal, characteristic, complemented
8C22×D244—21no—
9C2×D4×D61—21no—
10C2×#11758201—21no—
11#14519774C2211yescharacteristic
12#14519752—21no—
13#14519751—21no—
14#14519747—22no—
15C4×D244C2211yescharacteristic
16C4⋊#92418C2211yescharacteristic, complemented
17#14519701—21no—
18#14519697—22no—
19C4×#92418C2211yescharacteristic, complemented
20C4⋊Q8×C61C2211yescharacteristic, complemented
21C4×D4×C61C2211yescharacteristic
22#107×C61—21no—
23C4⋊C8×C61C2211yescharacteristic, complemented
24#102×C61—21no—
25C23×D61—22no—
26C2×Q8×C61—21no—
27C2×D4×C61D411yescharacteristic
28C22×C4×C61—21no—
29C2×C22⋊D61—22no—
30D4×D61—42no—
31D4×D61—42no—
32C2×D244—22no—
33C2×D244—21no—
34C2×D244—21no—
35C2×D244—42no—
36C2×D244—42no—
37C2×D244D411yescharacteristic
38C2×D244D412yes—
39C2×C4×D61—21no—
40C2×C8×C61—21no—
41C4⋊C4×C61—21no—
42C4⋊C4×C61—21no—
43C4⋊C4×C61D411yescharacteristic
44C22⋊C4×C61—21no—
45C42×C61C2311yescharacteristic
46#11758201—42no—
47#11758198—22no—
48#11758198—21no—
49C4⋊Dic61D411yescharacteristic
50C2×#92418—21no—
51C2×#92418—21no—
52C23×C61—21no—
53C22×D61—21no—
54C22×D61—22no—
55C22×D61—44no—
56C22×D61—44no—
57C22×D61—82no—
58Q8×C61—41no—
59Q8×C61—41no—
60D4×C61—21no—
61D4×C61SD1612yescomplemented
62C2×C4×C61—21no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C22⋊D61—44no—
70C2×Dic61—21no—
71D244—21no—
72D244—42no—
73D244—44no—
74D244—41no—
75D244—41no—
76D244—41no—
77D244—41no—
78D244D812yes—
79C4×D61—41no—
80C4×D61—41no—
81C8×C61—41no—
82#92418—41no—
83#92418—41no—
84C22×C61—22no—
85C22×C61—41no—
86C22×C61—41no—
87C22×C61#12011yescharacteristic
88C2×D61—22no—
89C2×D61—41no—
90C2×D61—41no—
91C2×D61—42no—
92C2×D61—42no—
93C2×D61—42no—
94C2×D61—88no—
95C4×C61—21no—
96C4×C61—41no—
97C4×C61—81no—
98C4×C61C2×D811yescharacteristic
99C4×C61C2×SD1611yescharacteristic
100C4×C61AGL(1,ℤ/8)11yescharacteristic
101C4×C61AGL(1,ℤ/8)11yescharacteristic
102Dic61—41no—
103#1639—611nomaximal, Sylow
104C2×C61—42no—
105C2×C61#44711yescharacteristic
106C2×C61#45011yescharacteristic
107C2×C61#45511yescharacteristic
108D61—42no—
109D61—82no—
110D42—611no—
111#486—611no—
112#474D6111yescharacteristic, complemented
113#461—611no—
114#331—611no—
115D4⋊C8—611no—
116D4⋊C8—611no—
117C61#163911yescharacteristic, complemented, Sylow
118C22×D4—1221no—
119C22×D4—1221no—
120C2×SD16—1221no—
121C4⋊Q8C2×D6111yescharacteristic, complemented
122#127—611no—
123#121—1221no—
124#121—1221no—
125#120—1222no—
126C4×D4—611no—
127C4×D4C2×D6111yescharacteristic
128#107—21no—
129C4⋊C8—611no—
130C4⋊C8C2×D6111yescharacteristic, complemented
131#103—1221no—
132#102—21no—
133#102—1222no—
134C4×C8—611no—
135C24—1222no—
136C2×Q8—21no—
137C2×D4—611no—
138C2×D4—612no—
139C2×D4—1222no—
140C2×D4—1222no—
141C2×D4—1221no—
142C2×D4—1221no—
143C2×D4—2442no—
144C2×D4—2442no—
145C2×D4—2442no—
146C2×D4—2442no—
147C2×D4C22⋊D6111yescharacteristic
148C22×C4—21no—
149C22×C4—1221no—
150SD16—2442no—
151C2×C8—21no—
152C2×C8—1221no—
153C2×C8—1221no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—611no—
157C4⋊C4C22⋊D6111yescharacteristic
158C22⋊C4—21no—
159C22⋊C4—1222no—
160C22⋊C4—1221no—
161C42C22×D6111yescharacteristic
162C23—21no—
163C23—1221no—
164C23—1222no—
165C23—4882no—
166C23—2444no—
167C23—2444no—
168Q8—41no—
169Q8—41no—
170D4—21no—
171D4—612no—
172D4—1221no—
173D4—2442no—
174D4—2444no—
175D4—2444no—
176D4—2441no—
177D4—2441no—
178D4—2441no—
179D4—2441no—
180D4#1175820112yescomplemented
181C2×C4—21no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—1221no—
186C2×C4—2441no—
187C2×C4—2441no—
188C2×C4D4×D6111yescharacteristic
189C2×C4D4×D6111yescharacteristic
190C2×C4C2×C22⋊D6111yescharacteristic
191C8—41no—
192C8—2441no—
193C8—2441no—
194C22—22no—
195C22—41no—
196C22—41no—
197C22—1222no—
198C22—4888no—
199C22—2442no—
200C22—2442no—
201C22—2442no—
202C22—2441no—
203C22—2441no—
204C22#1451974511yescharacteristic
205C4—21no—
206C4—41no—
207C4—81no—
208C4—2441no—
209C4D8×D6111yescharacteristic
210C4C2×#1175820111yescharacteristic
211C4#1451980111yescharacteristic
212C4#1451980211yescharacteristic
213C2—42no—
214C2—4882no—
215C2—2442no—
216C2#1683989411yescharacteristic
217C2#1683991211yescharacteristic
218C2#1683993811yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#474C2
socleC22×C61#120
hypercenter#474D61
hypocenterC61#1639
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #16840110C2semidirect
3. #16839964C2semidirect
4. #16839505C2semidirect
5. D4⋊#92418C2semidirect
6. #16839489C2semidirect
7. C61×#474C2semidirect
16. C4⋊#92418C22semidirect
19. C4×#92418C22semidirect
20. C4⋊Q8×C61C22semidirect
23. C4⋊C8×C61C22semidirect
61. D4×C61SD16semidirect
112. #474D61semidirect
117. C61#1639semidirect
121. C4⋊Q8C2×D61semidirect
130. C4⋊C8C2×D61semidirect
180. D4#11758201semidirect