Finite Group Databasebeta

← #21446857

Subgroups — #21446857

Order 7808.

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

normal subgroups only

This group has 362 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
2#16840336C211yesmaximal, characteristic
3C2×#14519775C211yesmaximal, characteristic, complemented
4C2×#14519703C211yesmaximal, characteristic
5#16839772C211yesmaximal, characteristic, complemented
6#16839523C211yesmaximal, characteristic, complemented
7C2×#101×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×Dic122C2211yescharacteristic
10#14519810—22no—
11#14519810—22no—
12C2×Dic244—21no—
13C2×#11758190—21no—
14#14519775—22no—
15#14519775—21no—
16#14519775—22no—
17#14519766—21no—
18#14519760—22no—
19#14519753—22no—
20#14519736C2211yescharacteristic
21C2×#11758196—22no—
22C2×C4×Dic61C2211yescharacteristic
23#14519703—22no—
24#14519702—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×C61—21no—
35C22×C4×C61D412yes—
36C22×C4×C61C2311yescharacteristic
37C2×C22⋊D61—21no—
38C22×Dic61—21no—
39C22×Dic61—21no—
40#11758222—21no—
41#11758222—21no—
42#11758222—21no—
43#11758222—21no—
44C2×D244D411yescharacteristic
45C2×C4×D61—21no—
46C2×Dic122—21no—
47C2×Dic122—21no—
48C2×Dic122—21no—
49C2×Dic122—21no—
50C2×Dic122—21no—
51C2×Dic122D412yes—
52C2×Dic122D411yescharacteristic
53M16×C61—21no—
54M16×C61—21no—
55M16×C61—21no—
56M16×C61D412yes—
57C2×C8×C61—21no—
58C2×C8×C61—21no—
59C22⋊Dic61—21no—
60#11758198—24no—
61C4⋊Dic61D412yes—
62#11758196—28no—
63#11758196—24no—
64C4×Dic61—21no—
65C4×Dic61—21no—
66C4×Dic61D412yes—
67Dic244—24no—
68#11758190—24no—
69C23×C61C2×D411yescharacteristic
70C22×D61—21no—
71Q8×C61—41no—
72Q8×C61—41no—
73Q8×C61—41no—
74Q8×C61—41no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61#4111yescharacteristic
84C22⋊D61—41no—
85C22⋊D61—41no—
86C2×Dic61—24no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—21no—
91C2×Dic61—41no—
92C2×Dic61—41no—
93D244—21no—
94D244—21no—
95C4×D61—41no—
96C4×D61—41no—
97Dic122—22no—
98Dic122—21no—
99Dic122—22no—
100Dic122—21no—
101Dic122—41no—
102Dic122—41no—
103C8×C61—22no—
104C8×C61—41no—
105C22×C61—22no—
106C22×C61#12011yescharacteristic
107C22×C61#12011yescharacteristic
108C22×C61#12111yescharacteristic
109C2×D61—41no—
110C2×D61—42no—
111C4×C61—42no—
112C4×C61#12011yescharacteristic
113C4×C61#12111yescharacteristic
114C4×C61#12111yescharacteristic
115C4×C61#12711yescharacteristic
116Dic61—24no—
117Dic61—42no—
118Dic61—41no—
119Dic61—42no—
120#2005—611nomaximal, Sylow
121C2×C61—21no—
122C2×C61—21no—
123C2×C61#39211yescharacteristic
124C2×C61#45612yes—
125D61—81no—
126C2×#137—611no—
127#536—611no—
128C2×C4⋊Q8—611no—
129C2×#104—611no—
130#419—611no—
131C2×#101D6111yescharacteristic, complemented
132#339—611no—
133C61#200511yescharacteristic, complemented, Sylow
134C2×#41—611no—
135C22×Q8—611no—
136C22×Q8C2×D6111yescharacteristic
137#137—1222no—
138#137—1222no—
139C2×Q16—1221no—
140C2×SD16—1221no—
141C2×M16C2×D6111yescharacteristic
142C2×M16C2×D6111yescharacteristic
143C4⋊Q8—1222no—
144C4⋊Q8—1222no—
145C4⋊Q8—1221no—
146#124—1221no—
147#123—1222no—
148C22⋊Q8—1222no—
149#117—611no—
150C2×C4⋊C4—1222no—
151C2×C42—611no—
152#104—1222no—
153#103—1222no—
154#101—22no—
155#41—1221no—
156#41—1221no—
157#41—1221no—
158#41—1221no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—611no—
166C2×Q8—612no—
167C2×Q8—1221no—
168C2×Q8—1221no—
169C2×Q8—1221no—
170C2×Q8—1221no—
171C2×Q8—1221no—
172C2×D4—611no—
173C2×D4—1221no—
174C22×C4—1221no—
175C22×C4—1221no—
176C22×C4—1221no—
177C22×C4D24412yes—
178C22×C4C22×D6111yescharacteristic
179Q16—1224no—
180SD16—1224no—
181M16—21no—
182M16—21no—
183M16—21no—
184M16C22⋊D6112yes—
185C2×C8—21no—
186C2×C8—21no—
187C4⋊C4—612no—
188C4⋊C4—1228no—
189C4⋊C4—1224no—
190C22⋊C4—1224no—
191C22⋊C4—1221no—
192C42—612no—
193C42—1221no—
194C42—1221no—
195C23—1221no—
196C23C2×D24411yescharacteristic
197Q8—41no—
198Q8—41no—
199Q8—41no—
200Q8—41no—
201Q8—1222no—
202Q8—1221no—
203Q8—1222no—
204Q8—1221no—
205Q8—2441no—
206Q8—2441no—
207D4—1221no—
208D4—1221no—
209D4—2441no—
210D4—2441no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—1224no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1221no—
219C2×C4—2441no—
220C2×C4—2441no—
221C2×C4—2441no—
222C2×C4—2441no—
223C2×C4#1175822211yescharacteristic
224C2×C4D4×D6111yescharacteristic
225C2×C4D4×D6111yescharacteristic
226C2×C4D4×D6111yescharacteristic
227C2×C4D4×D6111yescharacteristic
228C2×C4C2×C22⋊D6111yescharacteristic
229C8—22no—
230C8—41no—
231C22—22no—
232C22—2442no—
233C22—2441no—
234C22#1451974711yescharacteristic
235C22#1451974711yescharacteristic
236C22#1451975111yescharacteristic
237C4—42no—
238C4—1224no—
239C4—2442no—
240C4—2441no—
241C4—2442no—
242C4#1451974511yescharacteristic
243C4#1451975011yescharacteristic
244C4#1451975011yescharacteristic
245C4#1451977311yescharacteristic
246C2—21no—
247C2—21no—
248C2—4881no—
249C2#1683967111yescharacteristic
250C2#1683994712yes—
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#101×C61C2
socleC22×C61#120
hypercenterC2×#101D61
hypocenterC61#2005
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. C2×#14519775C2semidirect
5. #16839772C2semidirect
6. #16839523C2semidirect
7. C2×#101×C61C2semidirect
131. C2×#101D61semidirect
133. C61#2005semidirect