Finite Group Databasebeta

← #21445113

Subgroups — #21445113

Order 7808.

230 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 45 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#16840506C211yesmaximal, characteristic, complemented
2#16840152C211yesmaximal, characteristic, complemented
3#16840151C211yesmaximal, characteristic, complemented
4#16840127C211yesmaximal, characteristic, complemented
5#16839503C211yesmaximal, characteristic, complemented
6#16839501C211yesmaximal, characteristic, complemented
7C61×#329C211yesmaximal, characteristic, complemented
8C2×#11758190—21no—
9C2×#11758201—21no—
10C2×D488—21no—
11C2×#11758199—21no—
12#14519774C2211yescharacteristic
13#14519769C2211yescharacteristic
14#14519765C2211yescharacteristic
15#14519761—21no—
16#14519759—21no—
17#14519754—21no—
18#14519753—21no—
19#14519750—21no—
20#14519749—21no—
21#14519699—21no—
22#14519699—21no—
23#14519688C2211yescharacteristic
24#124×C61C2211yescharacteristic
25#97×C61C2211yescharacteristic
26#97×C61C2211yescharacteristic
27C2×Q8×C61D411yescharacteristic
28C2×D4×C61D411yescharacteristic
29C2×C22⋊D61—21no—
30C2×C22⋊D61—21no—
31C22×Dic61—21no—
32C2×D244—21no—
33C2×D244—21no—
34C2×D244—21no—
35C2×D244D411yescharacteristic
36C2×C4×D61—21no—
37C2×Dic122D411yescharacteristic
38C2×C8×C61—21no—
39C2×C8×C61—21no—
40C22⋊C4×C61—21no—
41C22⋊C4×C61—21no—
42C42×C61C2311yescharacteristic
43C22⋊Dic61—21no—
44#11758201—42no—
45#11758199—42no—
46#11758198—21no—
47#11758198—21no—
48#11758198—21no—
49C4⋊Dic61—21no—
50C4⋊Dic61D411yescharacteristic
51C4⋊Dic61D411yescharacteristic
52#11758196—21no—
53#11758196—21no—
54#11758196—21no—
55C2×#92418—21no—
56D488—42no—
57#11758190—42no—
58C23×C61—21no—
59C22×D61—21no—
60C22×D61—41no—
61Q8×C61—41no—
62D4×C61—41no—
63C2×C4×C61—21no—
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C22⋊D61—81no—
68C22⋊D61—81no—
69C2×Dic61—21no—
70C2×Dic61—21no—
71C2×Dic61—21no—
72C2×Dic61—81no—
73D244—41no—
74D244—41no—
75D244—41no—
76D244—41no—
77D244—41no—
78D244—42no—
79C4×D61—81no—
80Dic122—41no—
81C8×C61—22no—
82C8×C61—41no—
83#92418—22no—
84C22×C61—41no—
85C22×C61—41no—
86C22×C61—41no—
87C22×C61#12011yescharacteristic
88C2×D61—41no—
89C2×D61—41no—
90C2×D61—41no—
91C2×D61—81no—
92C2×D61—81no—
93C2×D61—81no—
94C4×C61—21no—
95C4×C61—21no—
96C4×C61—21no—
97C4×C61—41no—
98Dic61—41no—
99Dic61—41no—
100Dic61—41no—
101#1656—611nomaximal, Sylow
102C2×C61—81no—
103C2×C61#45311yescharacteristic
104C2×C61#45311yescharacteristic
105C2×C61#45411yescharacteristic
106D61—81no—
107D61—161no—
108#562—611no—
109#496—611no—
110#496—611no—
111#490—611no—
112#330—611no—
113#329—611no—
114#329D6111yescharacteristic, complemented
115C61#165611yescharacteristic, complemented, Sylow
116C2×SD16—1221no—
117C2×SD16—1221no—
118C2×D8—1221no—
119C2×D8—1221no—
120#127—611no—
121#125—611no—
122#124—611no—
123#124C2×D6111yescharacteristic
124#123—1221no—
125#123—1221no—
126C22⋊Q8—1221no—
127C22⋊Q8—1221no—
128#121—1221no—
129#121—1221no—
130#102—1221no—
131#102—1221no—
132#97—611no—
133#97C2×D6111yescharacteristic
134#97C2×D6111yescharacteristic
135C2×Q8—611no—
136C2×Q8D24411yescharacteristic
137C2×D4—611no—
138C2×D4—1221no—
139C2×D4—1221no—
140C2×D4—1221no—
141C2×D4—1221no—
142C2×D4—1221no—
143C2×D4D24411yescharacteristic
144C22×C4—1221no—
145C22×C4—1221no—
146SD16—2442no—
147SD16—2442no—
148D8—2442no—
149D8—2442no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—1221no—
153C4⋊C4—611no—
154C4⋊C4—611no—
155C4⋊C4—1221no—
156C4⋊C4—1221no—
157C4⋊C4—1221no—
158C4⋊C4—1221no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—1221no—
162C22⋊C4—1221no—
163C22⋊C4—1221no—
164C22⋊C4—1221no—
165C42C22×D6111yescharacteristic
166C23—21no—
167C23—1221no—
168C23—2441no—
169Q8—41no—
170Q8—2441no—
171D4—41no—
172D4—4881no—
173D4—4881no—
174D4—2441no—
175D4—2441no—
176D4—2441no—
177D4—2441no—
178D4—2442no—
179D4—2441no—
180C2×C4—21no—
181C2×C4—1221no—
182C2×C4—1221no—
183C2×C4—1221no—
184C2×C4—4881no—
185C2×C4—4881no—
186C2×C4C2×D24411yescharacteristic
187C2×C4D4×D6111yescharacteristic
188C2×C4D4×D6111yescharacteristic
189C8—22no—
190C8—41no—
191C8—1222no—
192C22—41no—
193C22—41no—
194C22—41no—
195C22—4881no—
196C22—4881no—
197C22—4881no—
198C22—2441no—
199C22—2441no—
200C22—2441no—
201C22#1451974711yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—2441no—
207C4—2441no—
208C4—2441no—
209C2—81no—
210C2—9761no—
211C2—4881no—
212C2#1683993111yescharacteristic
213C2#1683993211yescharacteristic
214C2#1683993611yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#329C2
socleC22×C61#120
hypercenter#329D61
hypocenterC61#1656
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
1. #16840506C2semidirect
2. #16840152C2semidirect
3. #16840151C2semidirect
4. #16840127C2semidirect
5. #16839503C2semidirect
6. #16839501C2semidirect
7. C61×#329C2semidirect
114. #329D61semidirect
115. C61#1656semidirect