Finite Group Databasebeta

← #21446913

Subgroups — #21446913

Order 7808.

390 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C22×#11758202C211yesmaximal, characteristic, complemented
2C22×#11758200C211yesmaximal, characteristic
3C2×#14519701C211yesmaximal, characteristic, complemented
4C2×#14519698C211yesmaximal, characteristic
5#16839668C211yesmaximal, characteristic, complemented
6#16839517C211yesmaximal, characteristic, complemented
7C2×#124×C61C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C2×#11758202—22no—
10C2×#11758202—22no—
11C2×#11758202—22no—
12C2×#11758200—22no—
13C2×#11758200—22no—
14C2×#11758200—22no—
15C22×#92418C2211yescharacteristic
16C22×#92418C2211yescharacteristic
17C2×C4⋊Dic61C2211yescharacteristic
18#14519701—22no—
19#14519698—22no—
20#14519684—22no—
21C22×Q8×C61C2211yescharacteristic
22C22×D4×C61C2211yescharacteristic
23#124×C61—22no—
24#124×C61—22no—
25C2×C22⋊C4×C61—22no—
26C2×C42×C61C2211yescharacteristic
27C24×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61—21no—
31C2×Q8×C61—21no—
32C2×Q8×C61—21no—
33C2×Q8×C61D412yes—
34C2×D4×C61—21no—
35C2×D4×C61—21no—
36C2×D4×C61—21no—
37C2×D4×C61—21no—
38C2×D4×C61—21no—
39C2×D4×C61D412yes—
40C22×C4×C61—21no—
41C22×C4×C61D412yes—
42C22×C4×C61C2311yescharacteristic
43C22×Dic61—21no—
44C22×Dic61—21no—
45C2×Dic122—21no—
46C2×Dic122—21no—
47C2×Dic122—21no—
48C2×Dic122—21no—
49C2×Dic122—21no—
50C2×Dic122D412yes—
51C22⋊C4×C61—28no—
52C42×C61—21no—
53C42×C61—21no—
54#11758202—28no—
55#11758200—28no—
56C4⋊Dic61—21no—
57C4⋊Dic61—21no—
58C2×#92418—21no—
59C2×#92418—21no—
60C2×#92418—21no—
61C2×#92418—21no—
62C2×#92418D412yes—
63C2×#92418D412yes—
64C23×C61—22no—
65C23×C61—41no—
66C23×C61—41no—
67C23×C61—42no—
68C23×C61—42no—
69C23×C61C2×D411yescharacteristic
70Q8×C61—22no—
71Q8×C61—22no—
72Q8×C61—41no—
73Q8×C61—41no—
74D4×C61—22no—
75D4×C61—22no—
76D4×C61—41no—
77D4×C61—41no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—41no—
83C2×C4×C61—41no—
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61#4111yescharacteristic
90C2×Dic61—22no—
91C2×Dic61—41no—
92C2×Dic61—41no—
93C2×Dic61—41no—
94C2×Dic61—42no—
95Dic122—22no—
96Dic122—22no—
97Dic122—41no—
98Dic122—41no—
99#92418—22no—
100#92418—22no—
101C22×C61—42no—
102C22×C61—44no—
103C22×C61—82no—
104C22×C61—81no—
105C22×C61—81no—
106C22×C61#12011yescharacteristic
107C22×C61#12111yescharacteristic
108C22×C61#12711yescharacteristic
109C22×C61#13512yes—
110C22×C61#13712yes—
111C4×C61—42no—
112C4×C61—42no—
113C4×C61#12011yescharacteristic
114C4×C61#12011yescharacteristic
115C4×C61#12111yescharacteristic
116C4×C61#12111yescharacteristic
117Dic61—42no—
118Dic61—81no—
119#2015—611nomaximal, Sylow
120C2×C61—82no—
121C2×C61#39211yescharacteristic
122C2×C61#45212yes—
123C2×C61#46412yes—
124C2×C61#49511yescharacteristic
125C2×C61#49711yescharacteristic
126C22×Q16—611no—
127C22×SD16—611no—
128C2×#124D6111yescharacteristic
129C2×#103—611no—
130C2×#102—611no—
131#391—611no—
132#336—611no—
133C61#201511yescharacteristic, complemented, Sylow
134C22×Q8—611no—
135C22×Q8C2×D6111yescharacteristic
136C22×D4C2×D6111yescharacteristic
137C2×Q16—1222no—
138C2×Q16—1222no—
139C2×Q16—1222no—
140C2×SD16—1222no—
141C2×SD16—1222no—
142C2×SD16—1222no—
143C22×C8—611no—
144C22×C8—611no—
145#124—22no—
146#124—22no—
147C2×C4⋊C4—611no—
148C2×C22⋊C4—22no—
149C2×C42C2×D6111yescharacteristic
150#103—1222no—
151#102—1222no—
152#95—1222no—
153C24—21no—
154C2×Q8—21no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—612no—
160C2×Q8—1221no—
161C2×Q8—1221no—
162C2×Q8—1221no—
163C2×Q8—1221no—
164C2×Q8—1221no—
165C2×Q8C22⋊D6112yes—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4C22⋊D6112yes—
172C22×C4—21no—
173C22×C4—1221no—
174C22×C4—1221no—
175C22×C4C22⋊D6112yes—
176C22×C4C22×D6111yescharacteristic
177Q16—1228no—
178SD16—1228no—
179C2×C8—612no—
180C2×C8—612no—
181C2×C8—1221no—
182C2×C8—1221no—
183C2×C8—1221no—
184C2×C8—1221no—
185C4⋊C4—1221no—
186C4⋊C4—1221no—
187C22⋊C4—28no—
188C42—21no—
189C42—21no—
190C23—22no—
191C23—41no—
192C23—41no—
193C23—42no—
194C23—42no—
195C23C2×C22⋊D6111yescharacteristic
196Q8—22no—
197Q8—22no—
198Q8—41no—
199Q8—41no—
200Q8—1222no—
201Q8—1222no—
202Q8—2441no—
203Q8—2441no—
204D4—22no—
205D4—22no—
206D4—41no—
207D4—41no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—1222no—
215C2×C4—2441no—
216C2×C4—2442no—
217C2×C4—2441no—
218C2×C4—2441no—
219C2×C4D4×D6111yescharacteristic
220C2×C4D4×D6111yescharacteristic
221C2×C4D4×D6111yescharacteristic
222C2×C4#1175822411yescharacteristic
223C2×C4C2×C22⋊D6111yescharacteristic
224C2×C4C2×C22⋊D6111yescharacteristic
225C8—1222no—
226C8—1222no—
227C22—44no—
228C22—42no—
229C22—82no—
230C22—81no—
231C22—81no—
232C22#1451974611yescharacteristic
233C22#1451974811yescharacteristic
234C22#1451977311yescharacteristic
235C22#1451979712yes—
236C22#1451980712yes—
237C4—42no—
238C4—42no—
239C4—4881no—
240C4—2442no—
241C4#1451974511yescharacteristic
242C4#1451974511yescharacteristic
243C4#1451974911yescharacteristic
244C4#1451974911yescharacteristic
245C2—82no—
246C2#1683967011yescharacteristic
247C2#1683992412yes—
248C2#1683998112yes—
249C2#1684014411yescharacteristic
250C2#1684015711yescharacteristic
subgroupG/H
centerC23C2×C22⋊D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#124×C61C2
socleC23×C61C2×D4
hypercenterC2×#124D61
hypocenterC61#2015
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C22×#11758202C2semidirect
3. C2×#14519701C2semidirect
5. #16839668C2semidirect
6. #16839517C2semidirect
133. C61#2015semidirect