Finite Group Databasebeta

← #21447116

Subgroups — #21447116

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×#14519807C211yesmaximal, characteristic
2C2×#14519712C211yesmaximal, characteristic, complemented
3C2×#14519700C211yesmaximal, characteristic, complemented
4C2×#14519695C211yesmaximal, characteristic, complemented
5#16839729C211yesmaximal, characteristic
6#16839531C211yesmaximal, characteristic, complemented
7C61×#417C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9#14519807—22no—
10#14519807—22no—
11C2×#11758202—21no—
12C2×#11758200—21no—
13C2×#11758194C2211yescharacteristic
14C2×#11758194C2211yescharacteristic
15C22×#92418C2211yescharacteristic
16#14519712—22no—
17#14519700—22no—
18#14519695—22no—
19C22⋊#92418—22no—
20C2×#41×C61C2211yescharacteristic
21C2×M16×C61C2211yescharacteristic
22C2×C4⋊C4×C61C2211yescharacteristic
23#103×C61—21no—
24#102×C61—21no—
25#41×C61—21no—
26#41×C61—21no—
27#41×C61—21no—
28#41×C61—21no—
29C2×Q8×C61D411yescharacteristic
30C2×D4×C61—21no—
31C2×D4×C61D411yescharacteristic
32C22×C4×C61—21no—
33C22×C4×C61—21no—
34C22×C4×C61C2311yescharacteristic
35C22×Dic61—21no—
36C2×Dic122—21no—
37C2×Dic122—21no—
38C2×Dic122—21no—
39C2×Dic122—21no—
40C2×Dic122—21no—
41C2×Dic122D412yes—
42M16×C61—21no—
43M16×C61—21no—
44C2×C8×C61—21no—
45C4⋊C4×C61—21no—
46C4⋊C4×C61—21no—
47#11758202—24no—
48#11758200—24no—
49#11758194—21no—
50#11758194—21no—
51#11758194—21no—
52#11758194D412yes—
53C2×#92418—21no—
54C2×#92418—21no—
55C2×#92418—21no—
56C2×#92418—21no—
57C2×#92418D412yes—
58C23×C61—21no—
59C23×C61#4111yescharacteristic
60Q8×C61—21no—
61Q8×C61—21no—
62D4×C61—21no—
63D4×C61—21no—
64D4×C61—41no—
65D4×C61—41no—
66C2×C4×C61—21no—
67C2×C4×C61—41no—
68C2×C4×C61—41no—
69C2×C4×C61—41no—
70C2×C4×C61—81no—
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61#4111yescharacteristic
76C2×C4×C61#4111yescharacteristic
77C2×Dic61—22no—
78C2×Dic61—41no—
79C2×Dic61—41no—
80Dic122—22no—
81Dic122—22no—
82Dic122—41no—
83Dic122—41no—
84C8×C61—41no—
85#92418—22no—
86#92418—22no—
87#92418—41no—
88C22×C61—21no—
89C22×C61—21no—
90C22×C61—41no—
91C22×C61—41no—
92C22×C61—41no—
93C22×C61#12111yescharacteristic
94C22×C61#12311yescharacteristic
95C22×C61#12411yescharacteristic
96C4×C61—41no—
97C4×C61—81no—
98C4×C61#12011yescharacteristic
99C4×C61#12111yescharacteristic
100C4×C61#12111yescharacteristic
101C4×C61#12311yescharacteristic
102Dic61—42no—
103#2052—611nomaximal, Sylow
104C2×C61—21no—
105C2×C61—21no—
106C2×C61—81no—
107C2×C61#39411yescharacteristic
108C2×C61#47111yescharacteristic
109C2×C61#47311yescharacteristic
110C2×#137—611no—
111C2×#108—611no—
112#417D6111yescharacteristic
113C2×#103—611no—
114C2×#101—611no—
115#408—611no—
116#343—611no—
117C61#205211yescharacteristic, complemented, Sylow
118C2×#41C2×D6111yescharacteristic
119C22×Q8—611no—
120#137—1222no—
121#137—1222no—
122C2×Q16—1221no—
123C2×SD16—1221no—
124C2×M16—611no—
125C2×M16—611no—
126C2×M16C2×D6111yescharacteristic
127C22×C8—611no—
128C2×C4⋊C4C2×D6111yescharacteristic
129#108—1222no—
130#103—21no—
131#103—1222no—
132#102—21no—
133#101—1222no—
134C22⋊C8—1222no—
135#41—21no—
136#41—21no—
137#41—21no—
138#41—21no—
139C2×Q8—612no—
140C2×Q8—1221no—
141C2×Q8—1221no—
142C2×Q8—1221no—
143C2×Q8—1221no—
144C2×Q8—1221no—
145C2×Q8C22⋊D6111yescharacteristic
146C2×D4—21no—
147C2×D4C22⋊D6111yescharacteristic
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—1221no—
151C22×C4C22×D6111yescharacteristic
152Q16—1224no—
153SD16—1224no—
154M16—21no—
155M16—21no—
156M16—612no—
157M16—1221no—
158M16—1221no—
159M16—1221no—
160C2×C8—21no—
161C2×C8—612no—
162C2×C8—1221no—
163C2×C8—1221no—
164C2×C8—1221no—
165C2×C8—1221no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C23—21no—
169C23#1175822411yescharacteristic
170Q8—21no—
171Q8—21no—
172Q8—1222no—
173Q8—1222no—
174Q8—2441no—
175Q8—2441no—
176D4—21no—
177D4—21no—
178D4—41no—
179D4—41no—
180C2×C4—21no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—81no—
185C2×C4—1222no—
186C2×C4—2441no—
187C2×C4—2441no—
188C2×C4#1175822211yescharacteristic
189C2×C4#1175822211yescharacteristic
190C2×C4D4×D6111yescharacteristic
191C2×C4D4×D6111yescharacteristic
192C2×C4D4×D6111yescharacteristic
193C2×C4C2×C22⋊D6111yescharacteristic
194C8—41no—
195C8—1222no—
196C8—1222no—
197C8—2441no—
198C22—21no—
199C22—21no—
200C22—41no—
201C22—41no—
202C22—41no—
203C22#1451974911yescharacteristic
204C22#1451975911yescharacteristic
205C22#1451976311yescharacteristic
206C4—41no—
207C4—81no—
208C4—2442no—
209C4#1451974511yescharacteristic
210C4#1451975011yescharacteristic
211C4#1451975011yescharacteristic
212C4#1451976011yescharacteristic
213C2—21no—
214C2—21no—
215C2—81no—
216C2#1683967711yescharacteristic
217C2#1684002311yescharacteristic
218C2#1684003511yescharacteristic
subgroupG/H
centerC22#14519749
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#417C2
socleC22×C61#121
hypercenter#417D61
hypocenterC61#2052
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#14519712C2semidirect
3. C2×#14519700C2semidirect
4. C2×#14519695C2semidirect
6. #16839531C2semidirect
117. C61#2052semidirect