Finite Group Databasebeta

← #21447121

Subgroups — #21447121

Order 7808.

262 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C2×#14519810C211yesmaximal, characteristic
2C2×#14519712C211yesmaximal, characteristic, complemented
3#16839761C211yesmaximal, characteristic
4C2×#14519700C211yesmaximal, characteristic, complemented
5C2×#14519695C211yesmaximal, characteristic, complemented
6#16839730C211yesmaximal, characteristic
7C61×#343C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×Dic122C2211yescharacteristic
10#14519810—22no—
11#14519810—22no—
12C2×Dic244—21no—
13C2×#11758190—21no—
14C2×#11758194C2211yescharacteristic
15C22×#92418C2211yescharacteristic
16#14519712—22no—
17#14519700—21no—
18#14519700—22no—
19#14519697—21no—
20#14519695—22no—
21#14519689—22no—
22C2×M16×C61C2211yescharacteristic
23C2×M16×C61C2211yescharacteristic
24C2×C4⋊C4×C61C2211yescharacteristic
25C22×C4×C61—21no—
26C22×C4×C61C2311yescharacteristic
27C2×C22⋊D61—21no—
28C22×Dic61—21no—
29#11758222—21no—
30#11758222—21no—
31#11758222—21no—
32#11758222—21no—
33C2×D244D411yescharacteristic
34C2×C4×D61—21no—
35C2×Dic122—21no—
36C2×Dic122—21no—
37C2×Dic122—21no—
38C2×Dic122—21no—
39C2×Dic122—21no—
40C2×Dic122D412yes—
41C2×Dic122D411yescharacteristic
42M16×C61—21no—
43M16×C61—21no—
44M16×C61—21no—
45M16×C61D412yes—
46C2×C8×C61—21no—
47C2×C8×C61—21no—
48C4⋊C4×C61—21no—
49C4⋊C4×C61—21no—
50#11758194—21no—
51#11758194—21no—
52C2×#92418—21no—
53C2×#92418—21no—
54C2×#92418—21no—
55C2×#92418D412yes—
56Dic244—24no—
57#11758190—24no—
58C23×C61#4111yescharacteristic
59C22×D61—21no—
60C2×C4×C61—41no—
61C2×C4×C61—81no—
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61#4111yescharacteristic
67C2×C4×C61#4111yescharacteristic
68C22⋊D61—41no—
69C22⋊D61—41no—
70C2×Dic61—21no—
71C2×Dic61—22no—
72C2×Dic61—41no—
73C2×Dic61—41no—
74D244—21no—
75D244—21no—
76C4×D61—41no—
77C4×D61—41no—
78Dic122—22no—
79Dic122—21no—
80Dic122—22no—
81Dic122—21no—
82Dic122—41no—
83Dic122—41no—
84C8×C61—22no—
85C8×C61—41no—
86#92418—22no—
87#92418—41no—
88C22×C61—21no—
89C22×C61—21no—
90C22×C61#12111yescharacteristic
91C22×C61#12311yescharacteristic
92C22×C61#12411yescharacteristic
93C2×D61—41no—
94C2×D61—41no—
95C2×D61—41no—
96C4×C61—81no—
97C4×C61#12011yescharacteristic
98C4×C61#12111yescharacteristic
99C4×C61#12111yescharacteristic
100C4×C61#12311yescharacteristic
101Dic61—42no—
102Dic61—41no—
103#2052—611nomaximal, Sylow
104C2×C61—21no—
105C2×C61—21no—
106C2×C61#39411yescharacteristic
107C2×C61#47111yescharacteristic
108C2×C61#47311yescharacteristic
109D61—81no—
110C2×#137—611no—
111C2×#108—611no—
112#417—611no—
113C2×#103—611no—
114C2×#101—611no—
115#408—611no—
116#343D6111yescharacteristic, complemented
117C61#205211yescharacteristic, complemented, Sylow
118C2×#41—611no—
119C22×Q8—611no—
120#137—1222no—
121#137—1222no—
122C2×Q16—1221no—
123C2×SD16—1221no—
124C2×M16—611no—
125C2×M16C2×D6111yescharacteristic
126C2×M16C2×D6111yescharacteristic
127C22×C8—611no—
128C2×C4⋊C4C2×D6111yescharacteristic
129#108—1222no—
130#103—1222no—
131#103—1221no—
132#102—1221no—
133#101—1222no—
134C22⋊C8—1222no—
135#41—1221no—
136#41—1221no—
137#41—1221no—
138#41—1221no—
139C2×Q8—612no—
140C2×Q8—611no—
141C2×Q8—1221no—
142C2×Q8—1221no—
143C2×Q8—1221no—
144C2×Q8—1221no—
145C2×Q8—1221no—
146C2×D4—611no—
147C2×D4—1221no—
148C22×C4—21no—
149C22×C4—1221no—
150C22×C4—1221no—
151C22×C4C22×D6111yescharacteristic
152Q16—1224no—
153SD16—1224no—
154M16—21no—
155M16—21no—
156M16—21no—
157M16—1221no—
158M16—1221no—
159M16D24412yes—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—612no—
163C2×C8—1221no—
164C2×C8—1221no—
165C2×C8—1221no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C23—1221no—
169C23#1175822211yescharacteristic
170Q8—1222no—
171Q8—1221no—
172Q8—1222no—
173Q8—1221no—
174Q8—2441no—
175Q8—2441no—
176D4—1221no—
177D4—1221no—
178D4—2441no—
179D4—2441no—
180C2×C4—41no—
181C2×C4—81no—
182C2×C4—1221no—
183C2×C4—1222no—
184C2×C4—2441no—
185C2×C4—2441no—
186C2×C4—2441no—
187C2×C4—2441no—
188C2×C4C2×D24411yescharacteristic
189C2×C4#1175822211yescharacteristic
190C2×C4D4×D6111yescharacteristic
191C2×C4D4×D6111yescharacteristic
192C2×C4D4×D6111yescharacteristic
193C2×C4#1175822611yescharacteristic
194C8—22no—
195C8—41no—
196C8—1222no—
197C8—2441no—
198C22—21no—
199C22—21no—
200C22—2441no—
201C22—2441no—
202C22—2441no—
203C22#1451975011yescharacteristic
204C22#1451976211yescharacteristic
205C22#1451976511yescharacteristic
206C4—81no—
207C4—2441no—
208C4—2442no—
209C4#1451974711yescharacteristic
210C4#1451975011yescharacteristic
211C4#1451975211yescharacteristic
212C4#1451976211yescharacteristic
213C2—21no—
214C2—21no—
215C2—4881no—
216C2#1683968011yescharacteristic
217C2#1684002411yescharacteristic
218C2#1684003611yescharacteristic
subgroupG/H
centerC22#14519750
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#343C2
socleC22×C61#121
hypercenter#343D61
hypocenterC61#2052
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
2. C2×#14519712C2semidirect
4. C2×#14519700C2semidirect
5. C2×#14519695C2semidirect
7. C61×#343C2semidirect
116. #343D61semidirect
117. C61#2052semidirect