Finite Group Databasebeta

← #21446150

Subgroups — #21446150

Order 7808.

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

normal subgroups only

This group has 402 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
1C22×#11758201C211yesmaximal, characteristic
2C2×#14519739C211yesmaximal, characteristic
3C2×#14519699C211yesmaximal, characteristic
4#16839669C211yesmaximal, characteristic, complemented
5#16839524C211yesmaximal, characteristic, complemented
6#16839516C211yesmaximal, characteristic, complemented
7C2×#103×C61C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C22×C4×D61—21no—
10C2×#11758201—22no—
11C2×#11758201—22no—
12C2×#11758201C414yescomplemented
13C22×#92418C2211yescharacteristic
14#14519739—22no—
15#14519739—22no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758198—21no—
18C2×C4×Dic61C2211yescharacteristic
19#14519699—22no—
20#14519684—21no—
21#14519684—21no—
22C22×Q8×C61C2211yescharacteristic
23C22×C8×C61C2211yescharacteristic
24C2×C4⋊C4×C61C2211yescharacteristic
25#103×C61—22no—
26C23×D61—21no—
27C2×Q8×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61—21no—
31C2×Q8×C61—21no—
32C2×Q8×C61C2×C412yescomplemented
33C22×C4×C61—21no—
34C22×C4×C61—21no—
35C22×C4×C61C2311yescharacteristic
36C22×Dic61—21no—
37C22×Dic61D411yescharacteristic
38C22×Dic61D411yescharacteristic
39C2×D244—21no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244C2×C412yes—
43C2×D244D412yes—
44C2×D244D412yes—
45C2×C4×D61—24no—
46C2×C4×D61—42no—
47C2×C4×D61—42no—
48C2×C8×C61—21no—
49C2×C8×C61—21no—
50C2×C8×C61—21no—
51C4⋊C4×C61—21no—
52C4⋊C4×C61D412yes—
53#11758201—28no—
54#11758198—24no—
55C4⋊Dic61—21no—
56C4⋊Dic61—21no—
57C4×Dic61—21no—
58C4×Dic61—21no—
59C2×#92418—21no—
60C2×#92418—21no—
61C2×#92418C2×C412yescomplemented
62C23×C61C2×D411yescharacteristic
63C22×D61—22no—
64C22×D61—22no—
65C22×D61—22no—
66C22×D61—41no—
67C22×D61—41no—
68C22×D61—41no—
69C22×D61—41no—
70Q8×C61—22no—
71Q8×C61—22no—
72Q8×C61—41no—
73Q8×C61—41no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—41no—
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61C22×C411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61#4111yescharacteristic
85C2×C4×C61#4111yescharacteristic
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—41no—
92C2×Dic61—41no—
93C2×Dic61—41no—
94C2×Dic61SD1612yescomplemented
95D244—22no—
96D244—22no—
97D244—22no—
98D244C22⋊C414yes—
99C4×D61—48no—
100C8×C61—41no—
101#92418—22no—
102C22×C61C4×D411yescharacteristic
103C22×C61#12011yescharacteristic
104C22×C61#12111yescharacteristic
105C22×C61C2×SD1611yescharacteristic
106C22×C61#13511yescharacteristic
107C22×C61AGL(1,ℤ/8)11yescharacteristic
108C22×C61#13711yescharacteristic
109C2×D61—24no—
110C2×D61—42no—
111C2×D61—42no—
112C2×D61—42no—
113C2×D61—42no—
114C2×D61—42no—
115C2×D61—42no—
116C4×C61—42no—
117C4×C61—42no—
118C4×C61C2×C22⋊C411yescharacteristic
119C4×C61C4×D411yescharacteristic
120C4×C61#12111yescharacteristic
121C4×C61#12311yescharacteristic
122Dic61—22no—
123Dic61—41no—
124Dic61—81no—
125#1877—611nomaximal, Sylow
126C2×C61#38611yescharacteristic
127C2×C61C4×SD1611yescharacteristic
128C2×C61#44011yescharacteristic
129C2×C61#45011yescharacteristic
130C2×C61#45211yescharacteristic
131C2×C61#46111yescharacteristic
132C2×C61#46311yescharacteristic
133D61—44no—
134C22×SD16—611no—
135C2×C4×D4—611no—
136C2×#103D6111yescharacteristic, complemented
137C2×#102—611no—
138#391—611no—
139#340—611no—
140#336—611no—
141C61#187711yescharacteristic, complemented, Sylow
142C22×Q8C2×D6111yescharacteristic
143C22×D4—611no—
144C23×C4—1221no—
145C2×SD16—614no—
146C2×SD16—1222no—
147C2×SD16—1222no—
148C22×C8—611no—
149C22×C8C2×D6111yescharacteristic
150C4×D4—1222no—
151C4×D4—1222no—
152C2×C4⋊C4—611no—
153C2×C4⋊C4C2×D6111yescharacteristic
154C2×C22⋊C4—1221no—
155C2×C42—611no—
156#103—22no—
157#102—1222no—
158#95—1221no—
159#95—1221no—
160C24—1221no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—21no—
166C2×Q8C4×D6112yescomplemented
167C2×D4—612no—
168C2×D4—612no—
169C2×D4—612no—
170C2×D4—1221no—
171C2×D4—1221no—
172C2×D4—1221no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—611no—
176C22×C4—611no—
177C22×C4—1224no—
178C22×C4—1221no—
179C22×C4—2442no—
180C22×C4—2442no—
181C22×C4C22×D6111yescharacteristic
182SD16—1228no—
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—21no—
186C2×C8—612no—
187C2×C8—1221no—
188C2×C8—1221no—
189C4⋊C4—21no—
190C4⋊C4—1221no—
191C4⋊C4—1221no—
192C4⋊C4C22⋊D6112yes—
193C22⋊C4—1224no—
194C42—1221no—
195C42—1221no—
196C23—1222no—
197C23—1222no—
198C23—1222no—
199C23—2441no—
200C23—2441no—
201C23—2441no—
202C23—2441no—
203C23D4×D6111yescharacteristic
204Q8—22no—
205Q8—22no—
206Q8—41no—
207Q8—41no—
208D4—614no—
209D4—1222no—
210D4—1222no—
211D4—1222no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—612no—
219C2×C4—1221no—
220C2×C4—1221no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—1221no—
224C2×C4—2448no—
225C2×C4—2441no—
226C2×C4—2441no—
227C2×C4—2441no—
228C2×C4C2×C4×D6111yescharacteristic
229C2×C4#1175822211yescharacteristic
230C2×C4D4×D6111yescharacteristic
231C2×C4D4×D6111yescharacteristic
232C2×C4#1175822411yescharacteristic
233C2×C4C2×C22⋊D6111yescharacteristic
234C8—41no—
235C8—1222no—
236C22—1224no—
237C22—2442no—
238C22—2442no—
239C22—2442no—
240C22—2442no—
241C22—2442no—
242C22—2442no—
243C22#1451973711yescharacteristic
244C22#1451974511yescharacteristic
245C22#1451975011yescharacteristic
246C22SD16×D6111yescharacteristic
247C22#1451980011yescharacteristic
248C22#1451980411yescharacteristic
249C22#1451980911yescharacteristic
250C4—42no—
251C4—42no—
252C4—1222no—
253C4—4881no—
254C4—2441no—
255C4C22⋊C4×D6111yescharacteristic
256C4C4×C22⋊D6111yescharacteristic
257C4#1451974811yescharacteristic
258C4#1451975911yescharacteristic
259C2—2444no—
260C2#1683963811yescharacteristic
261C2#1683984711yescharacteristic
262C2#1683986511yescharacteristic
263C2#1683991111yescharacteristic
264C2#1683992311yescharacteristic
265C2#1683996611yescharacteristic
266C2#1683998011yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#103×C61C2
socleC23×C61C2×D4
hypercenterC2×#103D61
hypocenterC61#1877
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
4. #16839669C2semidirect
5. #16839524C2semidirect
6. #16839516C2semidirect
7. C2×#103×C61C2semidirect
12. C2×#11758201C4semidirect
32. C2×Q8×C61C2×C4semidirect
61. C2×#92418C2×C4semidirect
94. C2×Dic61SD16semidirect
136. C2×#103D61semidirect
141. C61#1877semidirect
166. C2×Q8C4×D61semidirect