Finite Group Databasebeta

← #21446939

Subgroups — #21446939

Order 7808.

342 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 73 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×#14519810C211yesmaximal, characteristic
2C2×#14519808C211yesmaximal, characteristic
3C22×#11758202C211yesmaximal, characteristic, complemented
4C2×#14519695C211yesmaximal, characteristic, complemented
5#16839730C211yesmaximal, characteristic
6#16839526C211yesmaximal, characteristic, complemented
7C2×#101×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×Dic122C2211yescharacteristic
10#14519810—22no—
11#14519810—22no—
12#14519808—22no—
13#14519808—22no—
14C2×Dic244—21no—
15C2×#11758202—22no—
16C2×#11758202—22no—
17C2×#11758202—21no—
18C2×#11758202—22no—
19C2×#11758190—21no—
20C2×#11758201—21no—
21C2×#11758194C2211yescharacteristic
22C22×#92418C2211yescharacteristic
23#14519695—22no—
24#14519689—22no—
25C22×Q8×C61C2211yescharacteristic
26C2×M16×C61C2211yescharacteristic
27C2×M16×C61C2211yescharacteristic
28#101×C61—22no—
29C2×Q8×C61—21no—
30C2×Q8×C61—21no—
31C2×Q8×C61—21no—
32C2×Q8×C61—21no—
33C2×Q8×C61—21no—
34C2×Q8×C61D412yes—
35C22×C4×C61—21no—
36C22×C4×C61C2311yescharacteristic
37C2×C22⋊D61—21no—
38C22×Dic61—21no—
39#11758222—21no—
40#11758222—21no—
41#11758222—21no—
42#11758222—21no—
43C2×D244D411yescharacteristic
44C2×C4×D61—21no—
45C2×Dic122—21no—
46C2×Dic122—21no—
47C2×Dic122—21no—
48C2×Dic122—21no—
49C2×Dic122—21no—
50C2×Dic122D412yes—
51C2×Dic122D411yescharacteristic
52M16×C61—21no—
53M16×C61—21no—
54M16×C61—21no—
55M16×C61D412yes—
56C2×C8×C61—21no—
57C2×C8×C61—21no—
58#11758202—24no—
59#11758202—28no—
60#11758201—24no—
61#11758194—21no—
62#11758194D412yes—
63C2×#92418—21no—
64C2×#92418—21no—
65C2×#92418—21no—
66C2×#92418D412yes—
67Dic244—24no—
68#11758190—24no—
69C23×C61#4111yescharacteristic
70C22×D61—21no—
71Q8×C61—22no—
72Q8×C61—22no—
73Q8×C61—41no—
74Q8×C61—41no—
75C2×C4×C61—22no—
76C2×C4×C61—41no—
77C2×C4×C61—41no—
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C22⋊D61—41no—
85C22⋊D61—41no—
86C2×Dic61—22no—
87C2×Dic61—21no—
88C2×Dic61—41no—
89C2×Dic61—41no—
90D244—21no—
91D244—21no—
92C4×D61—41no—
93C4×D61—41no—
94Dic122—22no—
95Dic122—21no—
96Dic122—22no—
97Dic122—21no—
98Dic122—41no—
99Dic122—41no—
100C8×C61—22no—
101C8×C61—41no—
102#92418—22no—
103#92418—22no—
104C22×C61—22no—
105C22×C61#12111yescharacteristic
106C22×C61#12111yescharacteristic
107C22×C61#12111yescharacteristic
108C2×D61—41no—
109C2×D61—42no—
110C4×C61—42no—
111C4×C61#12011yescharacteristic
112C4×C61#12011yescharacteristic
113C4×C61#12011yescharacteristic
114C4×C61#12711yescharacteristic
115Dic61—42no—
116Dic61—41no—
117#2020—611nomaximal, Sylow
118C2×C61—21no—
119C2×C61—21no—
120C2×C61#39211yescharacteristic
121C2×C61#47312yes—
122D61—81no—
123C2×#137—611no—
124C2×#137—611no—
125C22×Q16—611no—
126C2×#101—611no—
127C2×#101D6111yescharacteristic, complemented
128#408—611no—
129#341—611no—
130C61#202011yescharacteristic, complemented, Sylow
131C2×#41—611no—
132C22×Q8—611no—
133C22×Q8C2×D6111yescharacteristic
134#137—1222no—
135#137—1222no—
136#137—1222no—
137#137—1222no—
138C2×Q16—1221no—
139C2×Q16—1222no—
140C2×Q16—1222no—
141C2×Q16—1221no—
142C2×Q16—1222no—
143C2×SD16—1221no—
144C2×SD16—1221no—
145C2×M16—611no—
146C2×M16C2×D6111yescharacteristic
147C2×M16C2×D6111yescharacteristic
148C22×C8—611no—
149#101—22no—
150#101—1222no—
151C22⋊C8—1222no—
152#41—1221no—
153#41—1221no—
154#41—1221no—
155#41—1221no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—611no—
162C2×Q8—612no—
163C2×Q8—1221no—
164C2×Q8—1221no—
165C2×Q8—1221no—
166C2×Q8—1221no—
167C2×Q8—1221no—
168C2×Q8D24412yes—
169C2×D4—611no—
170C2×D4—1221no—
171C22×C4—21no—
172C22×C4—1221no—
173C22×C4—1221no—
174C22×C4C22×D6111yescharacteristic
175Q16—1224no—
176Q16—1228no—
177Q16—1224no—
178SD16—1224no—
179SD16—1224no—
180M16—21no—
181M16—21no—
182M16—21no—
183M16—612no—
184M16—1221no—
185M16C22⋊D6112yes—
186C2×C8—21no—
187C2×C8—21no—
188C2×C8—612no—
189C2×C8—1221no—
190C2×C8—1221no—
191C2×C8—1221no—
192C23—1221no—
193C23#1175822211yescharacteristic
194Q8—22no—
195Q8—22no—
196Q8—41no—
197Q8—41no—
198Q8—1222no—
199Q8—1221no—
200Q8—1222no—
201Q8—1221no—
202Q8—2441no—
203Q8—2441no—
204D4—1221no—
205D4—1221no—
206D4—2441no—
207D4—2441no—
208C2×C4—22no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—1222no—
212C2×C4—1221no—
213C2×C4—2441no—
214C2×C4—2441no—
215C2×C4—2441no—
216C2×C4—2441no—
217C2×C4C2×D24411yescharacteristic
218C2×C4D4×D6111yescharacteristic
219C2×C4D4×D6111yescharacteristic
220C2×C4D4×D6111yescharacteristic
221C2×C4D4×D6111yescharacteristic
222C2×C4C2×C22⋊D6111yescharacteristic
223C8—22no—
224C8—41no—
225C8—1222no—
226C8—1222no—
227C22—22no—
228C22—2442no—
229C22—2441no—
230C22#1451975011yescharacteristic
231C22#1451975011yescharacteristic
232C22#1451975111yescharacteristic
233C4—42no—
234C4—2441no—
235C4—2442no—
236C4#1451974511yescharacteristic
237C4#1451974711yescharacteristic
238C4#1451974711yescharacteristic
239C4#1451977311yescharacteristic
240C2—21no—
241C2—21no—
242C2—4881no—
243C2#1683967111yescharacteristic
244C2#1684003612yes—
subgroupG/H
centerC22#14519750
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#101×C61C2
socleC22×C61#121
hypercenterC2×#101D61
hypocenterC61#2020
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
3. C22×#11758202C2semidirect
4. C2×#14519695C2semidirect
6. #16839526C2semidirect
7. C2×#101×C61C2semidirect
127. C2×#101D61semidirect
130. C61#2020semidirect