Finite Group Databasebeta

← #21446264

Subgroups — #21446264

Order 7808.

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

normal subgroups only

This group has 358 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
1#16840269C211yesmaximal, characteristic
2C2×#14519734C211yesmaximal, characteristic, complemented
3C2×#14519704C211yesmaximal, characteristic, complemented
4#16839725C211yesmaximal, characteristic, complemented
5#16839523C211yesmaximal, characteristic, complemented
6#16839522C211yesmaximal, characteristic, complemented
7C2×#104×C61C211yesmaximal, characteristic, complemented
8C22×C4×D61C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10#14519758—21no—
11#14519753C412yescomplemented
12#14519748C412yescomplemented
13#14519745—21no—
14C4×C22⋊D61—22no—
15#14519736C2211yescharacteristic
16#14519734—22no—
17#14519734—22no—
18C2×#11758196—21no—
19C2×#11758198—21no—
20C2×C4×Dic61C2211yescharacteristic
21#14519704—22no—
22#14519689—22no—
23C2×#41×C61C2211yescharacteristic
24C2×M16×C61C2211yescharacteristic
25C2×C42×C61C2211yescharacteristic
26#104×C61—22no—
27C23×D61D411yescharacteristic
28#41×C61—21no—
29#41×C61—21no—
30#41×C61—21no—
31#41×C61—21no—
32C2×Q8×C61C2×C411yescharacteristic
33C2×D4×C61—21no—
34C2×D4×C61C2×C411yescharacteristic
35C22×C4×C61—21no—
36C22×C4×C61—21no—
37C22×C4×C61C2311yescharacteristic
38C2×C22⋊D61—22no—
39C22×Dic61—21no—
40C22×Dic61D411yescharacteristic
41C2×C4×D61—21no—
42C2×C4×D61—21no—
43C2×C4×D61—21no—
44C2×C4×D61—21no—
45C2×C4×D61C2×C412yes—
46C2×C4×D61D412yes—
47M16×C61—21no—
48M16×C61—21no—
49C2×C8×C61—21no—
50C42×C61—21no—
51C42×C61D412yescomplemented
52C22⋊Dic61—21no—
53C22⋊Dic61—22no—
54#11758198—24no—
55#11758198—22no—
56C4⋊Dic61C2×C412yes—
57#11758196—24no—
58#11758196—22no—
59C4×Dic61—21no—
60C4×Dic61—21no—
61C4×Dic61D412yescomplemented
62#11758194—21no—
63#11758194—21no—
64C2×#92418—21no—
65C23×C61—21no—
66C23×C61C2×D411yescharacteristic
67C22×D61—21no—
68C22×D61—21no—
69C22×D61—42no—
70C22×D61C22⋊C412yes—
71Q8×C61—21no—
72Q8×C61—21no—
73D4×C61—21no—
74D4×C61—21no—
75D4×C61—41no—
76D4×C61—41no—
77C2×C4×C61—21no—
78C2×C4×C61—22no—
79C2×C4×C61—42no—
80C2×C4×C61—41no—
81C2×C4×C61—41no—
82C2×C4×C61C22×C411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61#4111yescharacteristic
87C2×C4×C61#4111yescharacteristic
88C22⋊D61—44no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—42no—
94C2×Dic61C22⋊C412yes—
95C4×D61—22no—
96C4×D61—22no—
97C4×D61—22no—
98C4×D61—22no—
99C8×C61—41no—
100#92418—41no—
101C22×C61—22no—
102C22×C61—41no—
103C22×C61—42no—
104C22×C61C2×C22⋊C411yescharacteristic
105C22×C61#12011yescharacteristic
106C22×C61#12311yescharacteristic
107C2×D61—22no—
108C2×D61—22no—
109C2×D61—22no—
110C2×D61—42no—
111C2×D61—42no—
112C4×C61—42no—
113C4×C61—41no—
114C4×C61C4×D411yescharacteristic
115C4×C61C4×D411yescharacteristic
116C4×C61#12111yescharacteristic
117C4×C61#12111yescharacteristic
118Dic61—22no—
119Dic61—42no—
120Dic61—42no—
121#1897—611nomaximal, Sylow
122C2×C61—21no—
123C2×C61—21no—
124C2×C61—81no—
125C2×C61#38611yescharacteristic
126C2×C61#42112yes—
127D61—42no—
128#525—611no—
129C2×#117—611no—
130C2×#104—611no—
131C2×#104D6111yescharacteristic, complemented
132#407—611no—
133#339—611no—
134#339—611no—
135C61#189711yescharacteristic, complemented, Sylow
136C2×#41C2×D6111yescharacteristic
137C23×C4—611no—
138C2×M16—611no—
139C2×M16C2×D6111yescharacteristic
140#123—1221no—
141C22⋊Q8—612no—
142#121—612no—
143#120—1221no—
144C4×D4—1222no—
145#117—611no—
146#117—1222no—
147#117—1222no—
148C2×C4⋊C4—1221no—
149C2×C22⋊C4—1221no—
150C2×C42—611no—
151C2×C42C2×D6111yescharacteristic
152#104—22no—
153#104—1222no—
154C22⋊C8—1222no—
155C24—611no—
156#41—21no—
157#41—21no—
158#41—21no—
159#41—21no—
160C2×Q8C4×D6111yescharacteristic
161C2×D4—21no—
162C2×D4—1222no—
163C2×D4C4×D6111yescharacteristic
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—611no—
167C22×C4—612no—
168C22×C4—612no—
169C22×C4—1221no—
170C22×C4—1221no—
171C22×C4—1221no—
172C22×C4—1221no—
173C22×C4—1221no—
174C22×C4C22×D6111yescharacteristic
175M16—21no—
176M16—21no—
177M16—1221no—
178M16—1221no—
179C2×C8—21no—
180C2×C8—1221no—
181C4⋊C4—612no—
182C4⋊C4—1222no—
183C4⋊C4—1224no—
184C22⋊C4—1222no—
185C22⋊C4—1224no—
186C22⋊C4—1222no—
187C22⋊C4—1221no—
188C42—21no—
189C42—612no—
190C42—1221no—
191C42—1221no—
192C42C22⋊D6112yescomplemented
193C23—21no—
194C23—612no—
195C23—1221no—
196C23—1221no—
197C23—2442no—
198C23D4×D6111yescharacteristic
199Q8—21no—
200Q8—21no—
201D4—21no—
202D4—21no—
203D4—41no—
204D4—41no—
205D4—2444no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—612no—
212C2×C4—1221no—
213C2×C4—1221no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—2442no—
221C2×C4C2×C4×D6111yescharacteristic
222C2×C4#1175822211yescharacteristic
223C2×C4D4×D6111yescharacteristic
224C2×C4D4×D6111yescharacteristic
225C2×C4#1175822411yescharacteristic
226C2×C4C2×C22⋊D6111yescharacteristic
227C8—41no—
228C8—2441no—
229C22—22no—
230C22—42no—
231C22—41no—
232C22—1222no—
233C22—1222no—
234C22—1222no—
235C22—2442no—
236C22—2442no—
237C22C22⋊C4×D6111yescharacteristic
238C22#1451974511yescharacteristic
239C22#1451975911yescharacteristic
240C4—42no—
241C4—41no—
242C4—1222no—
243C4—2442no—
244C4—2442no—
245C4#1451973711yescharacteristic
246C4C4×C22⋊D6111yescharacteristic
247C4#1451974811yescharacteristic
248C4#1451975011yescharacteristic
249C2—21no—
250C2—21no—
251C2—81no—
252C2—2442no—
253C2#1683963811yescharacteristic
254C2#1683977712yes—
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#104×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×#104D61
hypocenterC61#1897
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#14519734C2semidirect
3. C2×#14519704C2semidirect
4. #16839725C2semidirect
5. #16839523C2semidirect
6. #16839522C2semidirect
7. C2×#104×C61C2semidirect
11. #14519753C4semidirect
12. #14519748C4semidirect
51. C42×C61D4semidirect
61. C4×Dic61D4semidirect
131. C2×#104D61semidirect
135. C61#1897semidirect
192. C42C22⋊D61semidirect