Finite Group Databasebeta

← #21446074

Subgroups — #21446074

Order 7808.

298 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 101 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×#14519742C211yesmaximal, characteristic
2C2×#14519710C211yesmaximal, characteristic
3C2×#14519702C211yesmaximal, characteristic
4C2×#14519700C211yesmaximal, characteristic
5#16839661C211yesmaximal, characteristic
6#16839516C211yesmaximal, characteristic
7C61×#340C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10#14519742—22no—
11#14519742—22no—
12C2×C4⋊Dic61—21no—
13C2×C4⋊Dic61C2211yescharacteristic
14C2×#11758196—21no—
15C2×C4×Dic61—21no—
16C2×C4×Dic61C2211yescharacteristic
17#14519710—22no—
18#14519702—22no—
19#14519700C414yescomplemented
20#14519684—21no—
21C22×C8×C61C2211yescharacteristic
22C2×C4⋊C4×C61C2211yescharacteristic
23C2×C4⋊C4×C61C2211yescharacteristic
24C22×C4×C61—21no—
25C22×C4×C61—21no—
26C22×C4×C61C2311yescharacteristic
27C22×Dic61—21no—
28C22×Dic61—21no—
29C22×Dic61D411yescharacteristic
30C22×Dic61D411yescharacteristic
31C2×Dic122—21no—
32C2×Dic122—21no—
33C2×Dic122—21no—
34C2×Dic122C2×C412yes—
35C2×Dic122D412yes—
36C2×Dic122Q812yes—
37C2×C8×C61—21no—
38C2×C8×C61—21no—
39C2×C8×C61—21no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61—21no—
42C4⋊C4×C61C2×C412yes—
43C4⋊C4×C61D412yes—
44C4⋊Dic61—21no—
45C4⋊Dic61—21no—
46C4⋊Dic61—42no—
47#11758196—24no—
48C4×Dic61—24no—
49C4×Dic61—21no—
50C4×Dic61—21no—
51C2×#92418—21no—
52C2×#92418—21no—
53C2×#92418C2×C412yes—
54C23×C61C2×D411yescharacteristic
55C2×C4×C61—22no—
56C2×C4×C61—22no—
57C2×C4×C61—41no—
58C2×C4×C61—41no—
59C2×C4×C61—41no—
60C2×C4×C61—41no—
61C2×C4×C61C22×C411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61C2×Q811yescharacteristic
65C2×C4×C61#4111yescharacteristic
66C2×C4×C61#4111yescharacteristic
67C2×Dic61—22no—
68C2×Dic61—21no—
69C2×Dic61—22no—
70C2×Dic61—22no—
71C2×Dic61—21no—
72C2×Dic61—21no—
73C2×Dic61—21no—
74C2×Dic61—21no—
75C2×Dic61—41no—
76C2×Dic61—41no—
77C2×Dic61—41no—
78C2×Dic61Q1612yes—
79Dic122—22no—
80Dic122—22no—
81Dic122—22no—
82Dic122C4⋊C414yescomplemented
83C8×C61—41no—
84#92418—22no—
85C22×C61C4×D411yescharacteristic
86C22×C61#12011yescharacteristic
87C22×C61C22⋊Q811yescharacteristic
88C22×C61C2×Q1611yescharacteristic
89C22×C61#13511yescharacteristic
90C22×C61AGL(1,ℤ/8)11yescharacteristic
91C22×C61#13711yescharacteristic
92C4×C61—42no—
93C4×C61—42no—
94C4×C61C2×C4⋊C411yescharacteristic
95C4×C61C4×D411yescharacteristic
96C4×C61C22⋊Q811yescharacteristic
97C4×C61#12311yescharacteristic
98Dic61—24no—
99Dic61—22no—
100Dic61—41no—
101Dic61—81no—
102#1863—611nomaximal, Sylow
103C2×C61#38511yescharacteristic
104C2×C61C4×Q1611yescharacteristic
105C2×C61#44011yescharacteristic
106C2×C61#44911yescharacteristic
107C2×C61#45111yescharacteristic
108C2×C61#47711yescharacteristic
109C2×C61#47911yescharacteristic
110C2×C4×Q8—611no—
111C2×#107—611no—
112C2×#103—611no—
113C2×#103—611no—
114#389—611no—
115#340D6111yescharacteristic
116#336—611no—
117C61#186311yescharacteristic, complemented, Sylow
118C22×Q8—611no—
119C22×C8—611no—
120C22×C8C2×D6111yescharacteristic
121C4×Q8—1222no—
122C4×Q8—1222no—
123C2×C4⋊C4—611no—
124C2×C4⋊C4—1221no—
125C2×C4⋊C4—1221no—
126C2×C4⋊C4C2×D6111yescharacteristic
127C2×C4⋊C4C2×D6111yescharacteristic
128C2×C42—611no—
129C2×C42—1221no—
130#107—1222no—
131#103—614no—
132#103—1222no—
133#95—1221no—
134C2×Q8—612no—
135C2×Q8—612no—
136C2×Q8—612no—
137C2×Q8—1221no—
138C2×Q8—1221no—
139C2×Q8—1221no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—611no—
143C22×C4—611no—
144C22×C4—1221no—
145C22×C4—1221no—
146C22×C4C22×D6111yescharacteristic
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—612no—
151C2×C8—1221no—
152C2×C8—1221no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—1224no—
156C4⋊C4—1221no—
157C4⋊C4—1221no—
158C4⋊C4—2442no—
159C4⋊C4C4×D6112yes—
160C4⋊C4D24412yes—
161C42—1224no—
162C42—1221no—
163C42—1221no—
164C23D4×D6111yescharacteristic
165Q8—614no—
166Q8—1222no—
167Q8—1222no—
168Q8—1222no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—612no—
176C2×C4—1222no—
177C2×C4—1221no—
178C2×C4—1222no—
179C2×C4—1222no—
180C2×C4—1221no—
181C2×C4—1221no—
182C2×C4—1221no—
183C2×C4—1221no—
184C2×C4—2441no—
185C2×C4—2441no—
186C2×C4—2441no—
187C2×C4C2×C4×D6111yescharacteristic
188C2×C4C2×D24411yescharacteristic
189C2×C4#1175822211yescharacteristic
190C2×C4D4×D6111yescharacteristic
191C2×C4#1175822411yescharacteristic
192C2×C4Q8×D6111yescharacteristic
193C8—41no—
194C8—1222no—
195C22#1451973711yescharacteristic
196C22#1451974711yescharacteristic
197C22#1451975511yescharacteristic
198C22Q16×D6111yescharacteristic
199C22#1451979811yescharacteristic
200C22#1451980111yescharacteristic
201C22#1451980611yescharacteristic
202C4—42no—
203C4—42no—
204C4—1224no—
205C4—1222no—
206C4—4881no—
207C4—2441no—
208C4C4⋊C4×D6111yescharacteristic
209C4C4×D24411yescharacteristic
210C4#1451975711yescharacteristic
211C4#1451975911yescharacteristic
212C2#1683963611yescharacteristic
213C2#1683985411yescharacteristic
214C2#1683985911yescharacteristic
215C2#1683990811yescharacteristic
216C2#1683991911yescharacteristic
217C2#1684005611yescharacteristic
218C2#1684007211yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#340C2
socleC23×C61C2×D4
hypercenter#340D61
hypocenterC61#1863
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
19. #14519700C4semidirect
82. Dic122C4⋊C4semidirect
117. C61#1863semidirect