Finite Group Databasebeta

← #21446164

Subgroups — #21446164

Order 7808.

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

normal subgroups only

This group has 438 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×#11758199C211yesmaximal, characteristic
2C2×#14519739C211yesmaximal, characteristic, complemented
3C2×#14519699C211yesmaximal, characteristic, complemented
4#16839665C211yesmaximal, characteristic, complemented
5#16839524C211yesmaximal, characteristic, complemented
6#16839516C211yesmaximal, characteristic, complemented
7C2×#102×C61C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C22×C4×D61—21no—
10C2×#11758199—22no—
11C2×#11758199—22no—
12C2×#11758199C414yescomplemented
13C22×#92418C2211yescharacteristic
14#14519739—22no—
15#14519739—22no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×C22⋊Dic61—21no—
18C2×C22⋊Dic61—21no—
19C2×#11758198—21no—
20C2×C4×Dic61C2211yescharacteristic
21#14519699—22no—
22C22×D4×C61C2211yescharacteristic
23C22×C8×C61C2211yescharacteristic
24C2×C4⋊C4×C61C2211yescharacteristic
25#102×C61—22no—
26C24×C61—21no—
27C23×D61—21no—
28C2×D4×C61—21no—
29C2×D4×C61—21no—
30C2×D4×C61—21no—
31C2×D4×C61—21no—
32C2×D4×C61—21no—
33C2×D4×C61C2×C412yescomplemented
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—
53C22⋊Dic61—42no—
54C22⋊Dic61—42no—
55#11758199—28no—
56#11758198—24no—
57C4⋊Dic61—21no—
58C4⋊Dic61—21no—
59C4×Dic61—21no—
60C4×Dic61—21no—
61C2×#92418—21no—
62C2×#92418—21no—
63C2×#92418C2×C412yescomplemented
64C23×C61—22no—
65C23×C61—41no—
66C23×C61—41no—
67C23×C61—41no—
68C23×C61—41no—
69C23×C61—41no—
70C23×C61—41no—
71C23×C61C2×D411yescharacteristic
72C22×D61—22no—
73C22×D61—22no—
74C22×D61—22no—
75C22×D61—41no—
76C22×D61—41no—
77C22×D61—41no—
78C22×D61—41no—
79D4×C61—22no—
80D4×C61—22no—
81D4×C61—41no—
82D4×C61—41no—
83C2×C4×C61—22no—
84C2×C4×C61—41no—
85C2×C4×C61—41no—
86C2×C4×C61C22×C411yescharacteristic
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61#4111yescharacteristic
91C2×C4×C61#4111yescharacteristic
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—41no—
98C2×Dic61—41no—
99C2×Dic61—41no—
100C2×Dic61D812yescomplemented
101D244—22no—
102D244—22no—
103D244—22no—
104D244C22⋊C414yescomplemented
105C4×D61—48no—
106C8×C61—41no—
107#92418—22no—
108C22×C61—42no—
109C22×C61—42no—
110C22×C61—42no—
111C22×C61—81no—
112C22×C61—81no—
113C22×C61—81no—
114C22×C61—81no—
115C22×C61C4×D411yescharacteristic
116C22×C61#12011yescharacteristic
117C22×C61#12111yescharacteristic
118C22×C61C2×D811yescharacteristic
119C22×C61#13511yescharacteristic
120C22×C61AGL(1,ℤ/8)11yescharacteristic
121C22×C61AGL(1,ℤ/8)11yescharacteristic
122C2×D61—24no—
123C2×D61—42no—
124C2×D61—42no—
125C2×D61—42no—
126C2×D61—42no—
127C2×D61—42no—
128C2×D61—42no—
129C4×C61—42no—
130C4×C61C2×C22⋊C411yescharacteristic
131C4×C61C4×D411yescharacteristic
132C4×C61#12111yescharacteristic
133C4×C61#12311yescharacteristic
134Dic61—22no—
135Dic61—41no—
136Dic61—81no—
137#1879—611nomaximal, Sylow
138C2×C61—82no—
139C2×C61#38611yescharacteristic
140C2×C61C4×D811yescharacteristic
141C2×C61#44211yescharacteristic
142C2×C61#44711yescharacteristic
143C2×C61#44911yescharacteristic
144C2×C61#45911yescharacteristic
145C2×C61#46311yescharacteristic
146D61—44no—
147C22×D8—611no—
148C2×C4×D4—611no—
149C2×#102—611no—
150C2×#102D6111yescharacteristic, complemented
151#390—611no—
152#340—611no—
153#336—611no—
154C61#187911yescharacteristic, complemented, Sylow
155C22×D4—611no—
156C22×D4C2×D6111yescharacteristic
157C23×C4—1221no—
158C2×D8—614no—
159C2×D8—1222no—
160C2×D8—1222no—
161C22×C8—611no—
162C22×C8C2×D6111yescharacteristic
163C4×D4—1222no—
164C4×D4—1222no—
165C2×C4⋊C4—611no—
166C2×C4⋊C4C2×D6111yescharacteristic
167C2×C22⋊C4—1221no—
168C2×C22⋊C4—1221no—
169C2×C22⋊C4—1221no—
170C2×C42—611no—
171#102—22no—
172#102—1222no—
173C24—21no—
174C24—1221no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—612no—
181C2×D4—612no—
182C2×D4—612no—
183C2×D4—1221no—
184C2×D4—1221no—
185C2×D4—1221no—
186C2×D4C4×D6112yescomplemented
187C22×C4—21no—
188C22×C4—611no—
189C22×C4—611no—
190C22×C4—1224no—
191C22×C4—1221no—
192C22×C4—2442no—
193C22×C4—2442no—
194C22×C4C22×D6111yescharacteristic
195D8—1228no—
196C2×C8—21no—
197C2×C8—21no—
198C2×C8—21no—
199C2×C8—612no—
200C2×C8—1221no—
201C2×C8—1221no—
202C4⋊C4—21no—
203C4⋊C4—1221no—
204C4⋊C4—1221no—
205C4⋊C4C22⋊D6112yes—
206C22⋊C4—1224no—
207C22⋊C4—2442no—
208C22⋊C4—2442no—
209C42—1221no—
210C42—1221no—
211C23—22no—
212C23—41no—
213C23—41no—
214C23—41no—
215C23—41no—
216C23—41no—
217C23—41no—
218C23—1222no—
219C23—1222no—
220C23—1222no—
221C23—2441no—
222C23—2441no—
223C23—2441no—
224C23—2441no—
225C23D4×D6111yescharacteristic
226D4—22no—
227D4—22no—
228D4—41no—
229D4—41no—
230D4—614no—
231D4—1222no—
232D4—1222no—
233D4—1222no—
234C2×C4—22no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—612no—
238C2×C4—1221no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—1221no—
242C2×C4—1221no—
243C2×C4—2448no—
244C2×C4—2441no—
245C2×C4—2441no—
246C2×C4—2441no—
247C2×C4C2×C4×D6111yescharacteristic
248C2×C4#1175822211yescharacteristic
249C2×C4D4×D6111yescharacteristic
250C2×C4D4×D6111yescharacteristic
251C2×C4#1175822411yescharacteristic
252C2×C4C2×C22⋊D6111yescharacteristic
253C8—41no—
254C8—1222no—
255C22—42no—
256C22—42no—
257C22—42no—
258C22—81no—
259C22—81no—
260C22—81no—
261C22—81no—
262C22—1224no—
263C22—2442no—
264C22—2442no—
265C22—2442no—
266C22—2442no—
267C22—2442no—
268C22—2442no—
269C22#1451973711yescharacteristic
270C22#1451974511yescharacteristic
271C22#1451975011yescharacteristic
272C22D8×D6111yescharacteristic
273C22#1451979811yescharacteristic
274C22#1451980111yescharacteristic
275C22#1451980411yescharacteristic
276C4—42no—
277C4—1222no—
278C4—4881no—
279C4—2441no—
280C4C22⋊C4×D6111yescharacteristic
281C4C4×C22⋊D6111yescharacteristic
282C4#1451974811yescharacteristic
283C4#1451975911yescharacteristic
284C2—82no—
285C2—2444no—
286C2#1683963811yescharacteristic
287C2#1683984211yescharacteristic
288C2#1683987111yescharacteristic
289C2#1683989411yescharacteristic
290C2#1683990611yescharacteristic
291C2#1683995611yescharacteristic
292C2#1683997611yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#102×C61C2
socleC23×C61C2×D4
hypercenterC2×#102D61
hypocenterC61#1879
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#14519739C2semidirect
3. C2×#14519699C2semidirect
4. #16839665C2semidirect
5. #16839524C2semidirect
6. #16839516C2semidirect
7. C2×#102×C61C2semidirect
12. C2×#11758199C4semidirect
33. C2×D4×C61C2×C4semidirect
63. C2×#92418C2×C4semidirect
100. C2×Dic61D8semidirect
104. D244C22⋊C4semidirect
150. C2×#102D61semidirect
154. C61#1879semidirect
186. C2×D4C4×D61semidirect