Finite Group Databasebeta

← #21444887

Subgroups — #21444887

Order 7808.

278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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#16840433C211yesmaximal, characteristic, complemented
2#16840139C211yesmaximal, characteristic, complemented
3#16839963C211yesmaximal, characteristic, complemented
4#16839957C211yesmaximal, characteristic, complemented
5#16839505C211yesmaximal, characteristic, complemented
6#16839494C211yesmaximal, characteristic, complemented
7C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#11758222—21no—
9C2×#11758190—21no—
10C2×D488—22no—
11C2×#11758199—21no—
12#14519774C2211yescharacteristic
13#14519774C2211yescharacteristic
14#14519773—21no—
15#14519751—21no—
16#14519750—22no—
17C4×Dic122C2211yescharacteristic
18#14519739—21no—
19C4⋊#92418C2211yescharacteristic
20#14519699—21no—
21#14519697—21no—
22C4×D4×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4×C8×C61C2211yescharacteristic
25C2×D4×C61D411yescharacteristic
26C22×C4×C61—21no—
27C2×C22⋊D61—22no—
28C2×C22⋊D61—22no—
29#11758222—42no—
30#11758222—42no—
31C2×D244—21no—
32C2×D244—21no—
33C2×D244—21no—
34C2×D244—21no—
35C2×D244—21no—
36C2×D244D412yes—
37C2×C4×D61—22no—
38C2×Dic122D411yescharacteristic
39C2×C8×C61—21no—
40C2×C8×C61—21no—
41C4⋊C4×C61D411yescharacteristic
42C22⋊C4×C61—21no—
43C42×C61C2311yescharacteristic
44#11758199—42no—
45#11758198—22no—
46C4⋊Dic61D411yescharacteristic
47#11758196—21no—
48C4×Dic61—21no—
49C2×#92418—21no—
50D488—44no—
51#11758190—42no—
52C23×C61—21no—
53C22×D61—22no—
54C22×D61—41no—
55D4×C61—21no—
56D4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—41no—
59C2×C4×C61—41no—
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C22⋊D61—44no—
64C22⋊D61—82no—
65C2×Dic61—21no—
66C2×Dic61—21no—
67D244—42no—
68D244—42no—
69D244—41no—
70D244—41no—
71D244—41no—
72D244—41no—
73D244—41no—
74D244—41no—
75D244—41no—
76D244—41no—
77C4×D61—44no—
78Dic122—21no—
79Dic122D812yescomplemented
80C8×C61—22no—
81C8×C61—41no—
82#92418—41no—
83C22×C61—41no—
84C22×C61—41no—
85C22×C61—41no—
86C22×C61#12011yescharacteristic
87C2×D61—42no—
88C2×D61—42no—
89C2×D61—42no—
90C2×D61—81no—
91C2×D61—81no—
92C2×D61—81no—
93C4×C61—21no—
94C4×C61—41no—
95C4×C61C2×D811yescharacteristic
96C4×C61#13511yescharacteristic
97C4×C61AGL(1,ℤ/8)11yescharacteristic
98C4×C61AGL(1,ℤ/8)11yescharacteristic
99Dic61—22no—
100Dic61—41no—
101#1621—611nomaximal, Sylow
102C2×C61—81no—
103C2×C61#44711yescharacteristic
104C2×C61#44911yescharacteristic
105C2×C61#45311yescharacteristic
106D61—82no—
107D61—161no—
108#550—611no—
109#493—611no—
110#460—611no—
111#459—611no—
112#331—611no—
113Q8⋊C8—611no—
114D4⋊C8D6111yescharacteristic, complemented
115C61#162111yescharacteristic, complemented, Sylow
116C2×#41—1221no—
117C2×SD16—1221no—
118C2×D8—1222no—
119C2×D8—1221no—
120#127—611no—
121#127—611no—
122#127—1221no—
123#121—1222no—
124#121—1221no—
125C4×Q8—611no—
126C4×D4—1221no—
127C4×D4C2×D6111yescharacteristic
128C4⋊C8—611no—
129C4⋊C8C2×D6111yescharacteristic
130#102—1221no—
131#102—1221no—
132C4×C8C2×D6111yescharacteristic
133#41—2442no—
134#41—2442no—
135C2×Q8—611no—
136C2×D4—612no—
137C2×D4—1222no—
138C2×D4—1222no—
139C2×D4—1221no—
140C2×D4—1221no—
141C2×D4—1221no—
142C2×D4—1221no—
143C2×D4—1221no—
144C2×D4D24411yescharacteristic
145C22×C4—21no—
146C22×C4—1222no—
147SD16—2442no—
148D8—2444no—
149D8—2442no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—1221no—
153C4⋊C4—611no—
154C4⋊C4—1221no—
155C4⋊C4D24411yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—1222no—
158C42—1221no—
159C42C22×D6111yescharacteristic
160C23—21no—
161C23—1222no—
162C23—2441no—
163Q8—612no—
164Q8—1221no—
165D4—21no—
166D4—21no—
167D4—4882no—
168D4—2442no—
169D4—2442no—
170D4—2444no—
171D4—2441no—
172D4—2441no—
173D4—2441no—
174D4—2441no—
175D4—2441no—
176D4—2441no—
177D4—2441no—
178D4—2441no—
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—1221no—
183C2×C4—1221no—
184C2×C4—2444no—
185C2×C4C2×D24411yescharacteristic
186C2×C4D4×D6111yescharacteristic
187C2×C4D4×D6111yescharacteristic
188C8—22no—
189C8—41no—
190C8—2441no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—4881no—
195C22—4881no—
196C22—4881no—
197C22—2442no—
198C22—2442no—
199C22—2442no—
200C22#1451974711yescharacteristic
201C4—21no—
202C4—41no—
203C4—1222no—
204C4—2441no—
205C4D8×D6111yescharacteristic
206C4#1451979911yescharacteristic
207C4#1451980411yescharacteristic
208C4#1451980511yescharacteristic
209C2—81no—
210C2—9761no—
211C2—4882no—
212C2#1683989711yescharacteristic
213C2#1683990911yescharacteristic
214C2#1683993111yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×D4⋊C8C2
socleC22×C61#120
hypercenterD4⋊C8D61
hypocenterC61#1621
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. #16840433C2semidirect
2. #16840139C2semidirect
3. #16839963C2semidirect
4. #16839957C2semidirect
5. #16839505C2semidirect
6. #16839494C2semidirect
7. C61×D4⋊C8C2semidirect
79. Dic122D8semidirect
114. D4⋊C8D61semidirect
115. C61#1621semidirect