Finite Group Databasebeta

← #21447119

Subgroups — #21447119

Order 7808.

262 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 69 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×#14519808C211yesmaximal, characteristic
2C2×#14519713C211yesmaximal, characteristic, complemented
3#16839761C211yesmaximal, characteristic
4C2×#14519696C211yesmaximal, characteristic, complemented
5#16839728C211yesmaximal, characteristic
6#16839531C211yesmaximal, characteristic, complemented
7C2×#103×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519808—22no—
10#14519808—22no—
11C2×#11758202—21no—
12C2×#11758201—21no—
13C2×#11758194C2211yescharacteristic
14C2×#11758194C2211yescharacteristic
15C2×#11758194C2211yescharacteristic
16#14519713—22no—
17#14519700—21no—
18#14519697—21no—
19#14519696—22no—
20#14519689—22no—
21C22×Q8×C61C2211yescharacteristic
22C22×C8×C61C2211yescharacteristic
23C2×C4⋊C4×C61C2211yescharacteristic
24#103×C61—22no—
25C2×Q8×C61—21no—
26C2×Q8×C61—21no—
27C2×Q8×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61D412yes—
31C22×C4×C61—21no—
32C22×C4×C61—21no—
33C22×C4×C61C2311yescharacteristic
34C2×C22⋊D61—21no—
35#11758222—21no—
36#11758222—21no—
37#11758222—21no—
38#11758222—21no—
39C2×D244D411yescharacteristic
40C2×C4×D61—21no—
41C2×Dic122D411yescharacteristic
42C2×C8×C61—21no—
43C2×C8×C61—21no—
44C2×C8×C61D412yes—
45C4⋊C4×C61—21no—
46C4⋊C4×C61—21no—
47#11758202—24no—
48#11758201—24no—
49#11758194—21no—
50#11758194—21no—
51#11758194—21no—
52#11758194—21no—
53#11758194—21no—
54#11758194D412yes—
55C2×#92418—21no—
56C2×#92418—21no—
57C2×#92418—21no—
58C23×C61#4111yescharacteristic
59C22×D61—21no—
60Q8×C61—22no—
61Q8×C61—22no—
62Q8×C61—41no—
63Q8×C61—41no—
64C2×C4×C61—22no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61—41no—
68C2×C4×C61—81no—
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61#4111yescharacteristic
74C2×C4×C61#4111yescharacteristic
75C22⋊D61—41no—
76C22⋊D61—41no—
77C2×Dic61—21no—
78D244—21no—
79D244—21no—
80C4×D61—41no—
81C4×D61—41no—
82Dic122—21no—
83Dic122—21no—
84C8×C61—22no—
85#92418—22no—
86#92418—41no—
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—42no—
97C4×C61—81no—
98C4×C61#12011yescharacteristic
99C4×C61#12111yescharacteristic
100C4×C61#12111yescharacteristic
101C4×C61#12311yescharacteristic
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×#103D6111yescharacteristic, complemented
114C2×#101—611no—
115#408—611no—
116#343—611no—
117C61#205211yescharacteristic, complemented, Sylow
118C2×#41—611no—
119C22×Q8C2×D6111yescharacteristic
120#137—1222no—
121#137—1222no—
122C2×Q16—1221no—
123C2×SD16—1221no—
124C2×M16—611no—
125C2×M16—611no—
126C2×M16—611no—
127C22×C8C2×D6111yescharacteristic
128C2×C4⋊C4C2×D6111yescharacteristic
129#108—1222no—
130#103—22no—
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—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8—611no—
145C2×Q8D24412yes—
146C2×D4—611no—
147C2×D4—1221no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—1221no—
151C22×C4C22×D6111yescharacteristic
152Q16—1224no—
153SD16—1224no—
154M16—612no—
155M16—1221no—
156M16—1221no—
157M16—1221no—
158M16—1221no—
159M16—1221no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—1221no—
163C2×C8—1221no—
164C2×C8—1221no—
165C2×C8C22⋊D6112yes—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C23—1221no—
169C23#1175822411yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—41no—
173Q8—41no—
174Q8—1221no—
175Q8—1221no—
176D4—1221no—
177D4—1221no—
178D4—2441no—
179D4—2441no—
180C2×C4—22no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—81no—
185C2×C4—1221no—
186C2×C4—2441no—
187C2×C4—2441no—
188C2×C4C2×D24411yescharacteristic
189C2×C4#1175822211yescharacteristic
190C2×C4D4×D6111yescharacteristic
191C2×C4D4×D6111yescharacteristic
192C2×C4#1175822411yescharacteristic
193C2×C4C2×C22⋊D6111yescharacteristic
194C8—22no—
195C8—1222no—
196C8—2441no—
197C8—2441no—
198C22—21no—
199C22—21no—
200C22—2441no—
201C22—2441no—
202C22—2441no—
203C22#1451974811yescharacteristic
204C22#1451976111yescharacteristic
205C22#1451976311yescharacteristic
206C4—42no—
207C4—81no—
208C4—2441no—
209C4#1451974711yescharacteristic
210C4#1451974911yescharacteristic
211C4#1451975111yescharacteristic
212C4#1451975911yescharacteristic
213C2—21no—
214C2—21no—
215C2—4881no—
216C2#1683967811yescharacteristic
217C2#1684002211yescharacteristic
218C2#1684003411yescharacteristic
subgroupG/H
centerC22#14519748
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#103×C61C2
socleC22×C61#121
hypercenterC2×#103D61
hypocenterC61#2052
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×#14519713C2semidirect
4. C2×#14519696C2semidirect
6. #16839531C2semidirect
7. C2×#103×C61C2semidirect
113. C2×#103D61semidirect
117. C61#2052semidirect