Finite Group Databasebeta

← #21444875

Subgroups — #21444875

Order 7808.

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

normal subgroups only

This group has 336 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, complemented
2#16840139C211yesmaximal, characteristic, complemented
3#16839958C211yesmaximal, characteristic, complemented
4#16839957C211yesmaximal, characteristic, complemented
5#16839505C211yesmaximal, characteristic, complemented
6#16839491C211yesmaximal, characteristic, complemented
7C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C22×D244—21no—
9C2×D4×D61—21no—
10C2×D488—21no—
11C2×D488—22no—
12C2×#11758199—21no—
13#14519774C2211yescharacteristic
14#14519774C2211yescharacteristic, complemented
15#14519752—21no—
16#14519751—21no—
17#14519747—22no—
18C4×D244C2211yescharacteristic
19C4⋊#92418C2211yescharacteristic, complemented
20#14519699—21no—
21#14519697—21no—
22C4×D4×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic, complemented
24C4×C8×C61C2211yescharacteristic, complemented
25C23×D61—22no—
26C2×D4×C61D411yescharacteristic
27C22×C4×C61—21no—
28C2×C22⋊D61—22no—
29D4×D61—42no—
30D4×D61—42no—
31C2×D244—22no—
32C2×D244—21no—
33C2×D244—21no—
34C2×D244—21no—
35C2×D244—21no—
36C2×D244—21no—
37C2×D244—42no—
38C2×D244—42no—
39C2×D244D411yescharacteristic
40C2×D244D412yes—
41C2×C4×D61—21no—
42C2×C8×C61—21no—
43C2×C8×C61—21no—
44C4⋊C4×C61D411yescharacteristic
45C22⋊C4×C61—21no—
46C42×C61C2311yescharacteristic
47#11758199—42no—
48#11758198—22no—
49#11758198—21no—
50C4⋊Dic61D411yescharacteristic
51C2×#92418—21no—
52D488—44no—
53D488—42no—
54C23×C61—21no—
55C22×D61—21no—
56C22×D61—22no—
57C22×D61—44no—
58C22×D61—44no—
59C22×D61—41no—
60C22×D61—82no—
61D4×C61—21no—
62D4×C61D812yescomplemented
63C2×C4×C61—21no—
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—42no—
74D244—44no—
75D244—41no—
76D244—41no—
77D244—41no—
78D244—41no—
79D244—41no—
80D244—41no—
81D244—41no—
82D244—41no—
83D244D812yescomplemented
84C4×D61—41no—
85C4×D61—41no—
86C8×C61—22no—
87C8×C61—41no—
88#92418—41no—
89C22×C61—22no—
90C22×C61—41no—
91C22×C61—41no—
92C22×C61#12011yescharacteristic
93C2×D61—22no—
94C2×D61—41no—
95C2×D61—41no—
96C2×D61—42no—
97C2×D61—42no—
98C2×D61—42no—
99C2×D61—88no—
100C2×D61—81no—
101C2×D61—81no—
102C2×D61—81no—
103C4×C61—21no—
104C4×C61—41no—
105C4×C61C2×D811yescharacteristic
106C4×C61C2×D811yescharacteristic
107C4×C61AGL(1,ℤ/8)11yescharacteristic
108C4×C61AGL(1,ℤ/8)11yescharacteristic
109Dic61—41no—
110#1619—611nomaximal, Sylow
111C2×C61—42no—
112C2×C61#44711yescharacteristic
113C2×C61#44711yescharacteristic
114C2×C61#45311yescharacteristic
115D61—42no—
116D61—82no—
117D61—161no—
118D42—611no—
119#493—611no—
120#459—611no—
121#459—611no—
122#331—611no—
123D4⋊C8—611no—
124D4⋊C8D6111yescharacteristic, complemented
125C61#161911yescharacteristic, complemented, Sylow
126C22×D4—1221no—
127C22×D4—1221no—
128C2×D8—1221no—
129C2×D8—1222no—
130C2×D8—1221no—
131#127—611no—
132#127—611no—
133#121—1221no—
134#121—1221no—
135#120—1222no—
136C4×D4—611no—
137C4×D4C2×D6111yescharacteristic
138C4⋊C8—611no—
139C4⋊C8C2×D6111yescharacteristic, complemented
140#102—1221no—
141#102—1221no—
142C4×C8C2×D6111yescharacteristic, complemented
143C24—1222no—
144C2×D4—611no—
145C2×D4—612no—
146C2×D4—1222no—
147C2×D4—1222no—
148C2×D4—1221no—
149C2×D4—1221no—
150C2×D4—1221no—
151C2×D4—1221no—
152C2×D4—1221no—
153C2×D4—2442no—
154C2×D4—2442no—
155C2×D4—2442no—
156C2×D4—2442no—
157C2×D4D24411yescharacteristic
158C22×C4—21no—
159C22×C4—1221no—
160D8—2444no—
161D8—2442no—
162D8—2442no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—1221no—
166C4⋊C4—611no—
167C4⋊C4D24411yescharacteristic
168C22⋊C4—21no—
169C22⋊C4—1222no—
170C22⋊C4—1221no—
171C42C22×D6111yescharacteristic
172C23—21no—
173C23—1221no—
174C23—1222no—
175C23—4882no—
176C23—2444no—
177C23—2444no—
178C23—2441no—
179D4—21no—
180D4—612no—
181D4—1221no—
182D4—2442no—
183D4—2442no—
184D4—2444no—
185D4—2444no—
186D4—2441no—
187D4—2441no—
188D4—2441no—
189D4—2441no—
190D4—2441no—
191D4—2441no—
192D4—2441no—
193D4—2441no—
194D4D48812yescomplemented
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—1221no—
199C2×C4—2441no—
200C2×C4—2441no—
201C2×C4C2×D24411yescharacteristic
202C2×C4D4×D6111yescharacteristic
203C2×C4D4×D6111yescharacteristic
204C8—22no—
205C8—41no—
206C8—2441no—
207C22—22no—
208C22—41no—
209C22—41no—
210C22—1222no—
211C22—4888no—
212C22—4881no—
213C22—4881no—
214C22—4881no—
215C22—2442no—
216C22—2442no—
217C22—2442no—
218C22—2441no—
219C22—2441no—
220C22#1451974711yescharacteristic
221C4—21no—
222C4—41no—
223C4—2441no—
224C4D8×D6111yescharacteristic
225C4C2×D48811yescharacteristic
226C4#1451980411yescharacteristic
227C4#1451980511yescharacteristic
228C2—42no—
229C2—9761no—
230C2—4882no—
231C2—2442no—
232C2#1683989711yescharacteristic
233C2#1683989811yescharacteristic
234C2#1683993111yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×D4⋊C8C2
socleC22×C61#120
hypercenterD4⋊C8D61
hypocenterC61#1619
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. D4×D244C2semidirect
2. #16840139C2semidirect
3. #16839958C2semidirect
4. #16839957C2semidirect
5. #16839505C2semidirect
6. #16839491C2semidirect
7. C61×D4⋊C8C2semidirect
14. #14519774C22semidirect
19. C4⋊#92418C22semidirect
23. C4⋊C8×C61C22semidirect
24. C4×C8×C61C22semidirect
62. D4×C61D8semidirect
83. D244D8semidirect
124. D4⋊C8D61semidirect
125. C61#1619semidirect
139. C4⋊C8C2×D61semidirect
142. C4×C8C2×D61semidirect
194. D4D488semidirect