Finite Group Databasebeta

← #21446667

Subgroups — #21446667

Order 7808.

312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14519766C211yesmaximal, characteristic
2#16839785C211yesmaximal, characteristic, complemented
3C2×#14519696C211yesmaximal, characteristic, complemented
4C2×#14519693C211yesmaximal, characteristic
5C2×#14519693C211yesmaximal, characteristic
6M16×Dic61C211yesmaximal, characteristic, complemented
7C2×#101×C61C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C2×#11758194C2211yescharacteristic
11#14519766—21no—
12#14519766—21no—
13#14519766—22no—
14C2×#11758198C414yes—
15C2×C4×Dic61C2211yescharacteristic
16#14519706—22no—
17#14519696—22no—
18#14519693—22no—
19#14519693—22no—
20#14519687—21no—
21C8×Dic61—21no—
22C22×Q8×C61C2211yescharacteristic
23C2×M16×C61C2211yescharacteristic
24C2×M16×C61C2211yescharacteristic
25#101×C61—22no—
26C23×D61C2×C412yes—
27C2×Q8×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61—21no—
31C2×Q8×C61—21no—
32C2×Q8×C61—21no—
33C22×C4×C61C2×C412yes—
34C22×C4×C61C2311yescharacteristic
35C22×Dic61C2×C412yes—
36C2×D244—21no—
37C2×D244—21no—
38C2×D244—21no—
39C2×D244—21no—
40C2×D244—21no—
41C2×D244—21no—
42M16×C61—21no—
43M16×C61—21no—
44M16×C61—21no—
45M16×C61D412yes—
46C2×C8×C61—21no—
47C2×C8×C61—21no—
48#11758198—24no—
49#11758198—24no—
50C4×Dic61D411yescharacteristic
51C4×Dic61D411yescharacteristic
52C4×Dic61D412yes—
53#11758194—21no—
54#11758194—21no—
55#11758194—21no—
56#11758194D412yes—
57C2×#92418—21no—
58C2×#92418—21no—
59C23×C61C22×C411yescharacteristic
60C22×D61—22no—
61C22×D61—22no—
62C22×D61—22no—
63C22×D61—44no—
64Q8×C61—41no—
65Q8×C61—41no—
66Q8×C61—41no—
67Q8×C61—41no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
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—42no—
78C2×Dic61C22⋊C412yes—
79C2×Dic61C22⋊C412yes—
80D244—41no—
81D244—41no—
82D244—41no—
83D244—41no—
84C8×C61—22no—
85C8×C61—41no—
86#92418—22no—
87#92418—41no—
88C22×C61—22no—
89C22×C61C2×C22⋊C411yescharacteristic
90C22×C61C4×D411yescharacteristic
91C22×C61C4×D411yescharacteristic
92C2×D61—42no—
93C2×D61—44no—
94C2×D61—82no—
95C2×D61—82no—
96C4×C61—42no—
97C4×C61#12111yescharacteristic
98C4×C61#12111yescharacteristic
99C4×C61#12411yescharacteristic
100C4×C61#12711yescharacteristic
101Dic61—22no—
102Dic61—22no—
103#1967—611nomaximal, Sylow
104C2×C61—21no—
105C2×C61—21no—
106C2×C61#39011yescharacteristic
107C2×C61#41312yes—
108D61—82no—
109C2×#124—611no—
110#423—611no—
111C2×#101—611no—
112C2×#101D6111yescharacteristic, complemented
113C2×#100—611no—
114C2×#100—611no—
115C4×M16—611no—
116C61#196711yescharacteristic, complemented, Sylow
117C22×Q8C2×D6111yescharacteristic
118C22×D4—611no—
119C2×M16—611no—
120C2×M16—611no—
121C2×M16C2×D6111yescharacteristic
122C2×M16C2×D6111yescharacteristic
123#124—1221no—
124#124—1221no—
125#124—1222no—
126C2×C22⋊C4—614no—
127C2×C42—611no—
128C4⋊C8—1222no—
129#101—22no—
130#101—1222no—
131#100—1222no—
132#100—1222no—
133#97—1221no—
134C4×C8—1221no—
135C24—612no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×D4—1221no—
143C2×D4—1221no—
144C2×D4—1221no—
145C2×D4—1221no—
146C2×D4—1221no—
147C2×D4—1221no—
148C22×C4—612no—
149C22×C4C4×D6112yes—
150C22×C4C22×D6111yescharacteristic
151M16—21no—
152M16—21no—
153M16—21no—
154M16—612no—
155M16—1221no—
156M16—1221no—
157M16—1221no—
158M16C22⋊D6112yes—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—1221no—
162C2×C8—1221no—
163C22⋊C4—1224no—
164C22⋊C4—1224no—
165C42—611no—
166C42—611no—
167C42—612no—
168C23—1222no—
169C23—1222no—
170C23—1222no—
171C23—2444no—
172C23C2×C4×D6111yescharacteristic
173Q8—41no—
174Q8—41no—
175Q8—41no—
176Q8—41no—
177D4—2441no—
178D4—2441no—
179D4—2441no—
180D4—2441no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—612no—
185C2×C4—612no—
186C2×C4—2442no—
187C2×C4#1175822211yescharacteristic
188C2×C4D4×D6111yescharacteristic
189C2×C4D4×D6111yescharacteristic
190C2×C4D4×D6111yescharacteristic
191C2×C4#1175822411yescharacteristic
192C2×C4C2×C22⋊D6111yescharacteristic
193C8—22no—
194C8—41no—
195C8—1222no—
196C8—2441no—
197C22—22no—
198C22—4882no—
199C22—4882no—
200C22—2444no—
201C22—2442no—
202C22C22⋊C4×D6111yescharacteristic
203C22#1451973711yescharacteristic
204C22C4×C22⋊D6111yescharacteristic
205C4—42no—
206C4—1222no—
207C4—1222no—
208C4#1451974911yescharacteristic
209C4#1451975011yescharacteristic
210C4#1451976311yescharacteristic
211C4#1451977311yescharacteristic
212C2—21no—
213C2—21no—
214C2—4882no—
215C2#1683966211yescharacteristic
216C2#1683974512yes—
subgroupG/H
centerC22C22⋊C4×D61
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#101×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×#101D61
hypocenterC61#1967
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #16839785C2semidirect
3. C2×#14519696C2semidirect
6. M16×Dic61C2semidirect
7. C2×#101×C61C2semidirect
112. C2×#101D61semidirect
116. C61#1967semidirect