Finite Group Databasebeta

← #21446358

Subgroups — #21446358

Order 7808.

380 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 79 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#16840321C211yesmaximal, characteristic
2#16840235C211yesmaximal, characteristic, complemented
3C2×#14519692C211yesmaximal, characteristic, complemented
4C2×#14519691C211yesmaximal, characteristic, complemented
5#16839529C211yesmaximal, characteristic, complemented
6#16839528C211yesmaximal, characteristic, complemented
7C2×#99×C61C211yesmaximal, characteristic, complemented
8C22×C22⋊D61C2211yescharacteristic
9#14519760C412yescomplemented
10#14519758—21no—
11#14519749—22no—
12#14519746C412yescomplemented
13#14519745—21no—
14C4×C22⋊D61—22no—
15#14519737—22no—
16#14519733—21no—
17C2×C22⋊Dic61C2211yescharacteristic
18C2×C22⋊Dic61C2211yescharacteristic
19C2×C22⋊Dic61C2211yescharacteristic
20C22⋊C4×D61—21no—
21#14519692—22no—
22#14519691—22no—
23C22×D4×C61C2211yescharacteristic
24C2×C22⋊C4×C61C2211yescharacteristic
25C2×C22⋊C4×C61C2211yescharacteristic
26#99×C61—22no—
27C24×C61C2×C411yescharacteristic, complemented
28C24×C61C2311yescharacteristic
29C23×D61D411yescharacteristic
30C2×D4×C61—21no—
31C2×D4×C61—21no—
32C2×D4×C61—21no—
33C2×D4×C61—21no—
34C2×D4×C61—21no—
35C2×D4×C61—21no—
36C22×C4×C61—21no—
37C22×C4×C61—21no—
38C22×C4×C61C2×C411yescharacteristic, complemented
39C2×C22⋊D61—21no—
40C2×C22⋊D61—21no—
41C2×C22⋊D61—21no—
42C2×C22⋊D61—21no—
43C2×C22⋊D61—22no—
44C2×C22⋊D61C2×C412yes—
45C2×C22⋊D61D412yes—
46C22×Dic61—21no—
47C22×Dic61—21no—
48C22×Dic61—21no—
49C22×Dic61D411yescharacteristic
50C2×C4×D61—22no—
51C22⋊C4×C61—21no—
52C22⋊C4×C61—21no—
53C22⋊C4×C61—21no—
54C22⋊C4×C61D412yescomplemented
55C22⋊Dic61—21no—
56C22⋊Dic61—21no—
57C22⋊Dic61—22no—
58C22⋊Dic61—21no—
59C22⋊Dic61—21no—
60C22⋊Dic61C2×C412yescomplemented
61C22⋊Dic61D412yescomplemented
62#11758198—22no—
63#11758198—22no—
64#11758196—22no—
65#11758196—22no—
66C4×Dic61—22no—
67C23×C61—21no—
68C23×C61—21no—
69C23×C61—21no—
70C23×C61—81no—
71C23×C61—81no—
72C23×C61C22×C411yescharacteristic
73C23×C61C2×D411yescharacteristic
74C23×C61C2×D411yescharacteristic
75C23×C61C2×D411yescharacteristic
76C23×C61C2×D411yescharacteristic
77C23×C61#4111yescharacteristic
78C23×C61#4111yescharacteristic
79C22×D61—21no—
80C22×D61—21no—
81C22×D61—81no—
82C22×D61C22⋊C412yes—
83D4×C61—41no—
84D4×C61—41no—
85D4×C61—41no—
86D4×C61—41no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—22no—
91C2×C4×C61—41no—
92C2×C4×C61—81no—
93C2×C4×C61—81no—
94C22⋊D61—22no—
95C22⋊D61—22no—
96C22⋊D61—22no—
97C22⋊D61—22no—
98C22⋊D61—82no—
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—41no—
104C2×Dic61—81no—
105C2×Dic61—81no—
106C2×Dic61—81no—
107C2×Dic61C22⋊C412yes—
108C4×D61—82no—
109C22×C61—41no—
110C22×C61—41no—
111C22×C61—41no—
112C22×C61—41no—
113C22×C61—41no—
114C22×C61—41no—
115C22×C61—41no—
116C22×C61—42no—
117C22×C61—41no—
118C22×C61—81no—
119C22×C61—81no—
120C22×C61C2×C22⋊C411yescharacteristic
121C22×C61C4×D411yescharacteristic
122C22×C61C4×D411yescharacteristic
123C22×C61#12011yescharacteristic
124C22×C61#12111yescharacteristic
125C22×C61#12111yescharacteristic
126C22×C61#12311yescharacteristic
127C2×D61—22no—
128C2×D61—42no—
129C2×D61—42no—
130C2×D61—81no—
131C4×C61—42no—
132C4×C61—41no—
133C4×C61—81no—
134Dic61—22no—
135Dic61—42no—
136Dic61—42no—
137Dic61—81no—
138#1913—611nomaximal, Sylow
139C2×C61—21no—
140C2×C61—21no—
141C2×C61—21no—
142C2×C61—21no—
143C2×C61—21no—
144C2×C61—21no—
145C2×C61—21no—
146C2×C61—81no—
147C2×C61#38611yescharacteristic
148D61—42no—
149#534—611no—
150#518—611no—
151C2×#99—611no—
152C2×#99—611no—
153C2×#99D6111yescharacteristic, complemented
154#342—611no—
155#342—611no—
156C61#191311yescharacteristic, complemented, Sylow
157C22×D4—611no—
158C22×D4C2×D6111yescharacteristic
159#123—612no—
160#123—1221no—
161#121—1222no—
162#120—612no—
163#120—1221no—
164C4×D4—1222no—
165C4×D4—1222no—
166#117—1221no—
167C2×C22⋊C4—611no—
168C2×C22⋊C4—611no—
169C2×C22⋊C4—611no—
170C2×C22⋊C4—1221no—
171C2×C22⋊C4C2×D6111yescharacteristic
172C2×C22⋊C4C2×D6111yescharacteristic
173#99—22no—
174#99—1222no—
175#99—1222no—
176C24—611no—
177C24C4×D6111yescharacteristic, complemented
178C24C22×D6111yescharacteristic
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—21no—
184C2×D4—21no—
185C2×D4—612no—
186C2×D4—612no—
187C2×D4—1221no—
188C2×D4—1221no—
189C2×D4—1221no—
190C2×D4—1221no—
191C2×D4—1222no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—611no—
195C22×C4—1222no—
196C22×C4—1221no—
197C22×C4—1221no—
198C22×C4—1221no—
199C22×C4C4×D6111yescharacteristic, complemented
200C4⋊C4—1222no—
201C4⋊C4—1222no—
202C22⋊C4—21no—
203C22⋊C4—21no—
204C22⋊C4—21no—
205C22⋊C4—612no—
206C22⋊C4—612no—
207C22⋊C4—1222no—
208C22⋊C4—1222no—
209C22⋊C4—1222no—
210C22⋊C4—1221no—
211C22⋊C4—1221no—
212C22⋊C4—1221no—
213C22⋊C4—1221no—
214C22⋊C4C22⋊D6112yescomplemented
215C42—1222no—
216C23—21no—
217C23—21no—
218C23—21no—
219C23—81no—
220C23—81no—
221C23—612no—
222C23—1221no—
223C23—1221no—
224C23—4881no—
225C23C2×C4×D6111yescharacteristic
226C23#1175822211yescharacteristic
227C23D4×D6111yescharacteristic
228C23D4×D6111yescharacteristic
229C23D4×D6111yescharacteristic
230C23#1175822411yescharacteristic
231C23C2×C22⋊D6111yescharacteristic
232D4—41no—
233D4—41no—
234D4—41no—
235D4—41no—
236D4—1222no—
237D4—1222no—
238D4—1222no—
239D4—1222no—
240D4—4882no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—612no—
249C2×C4—1221no—
250C2×C4—1221no—
251C2×C4—1222no—
252C2×C4—1222no—
253C2×C4—4882no—
254C2×C4—4881no—
255C2×C4—4881no—
256C2×C4—4881no—
257C2×C4—2441no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—41no—
263C22—41no—
264C22—41no—
265C22—42no—
266C22—41no—
267C22—81no—
268C22—81no—
269C22—1222no—
270C22—4881no—
271C22—2442no—
272C22—2442no—
273C22C22⋊C4×D6111yescharacteristic
274C22#1451973711yescharacteristic
275C22C4×C22⋊D6111yescharacteristic
276C22#1451974511yescharacteristic
277C22#1451974811yescharacteristic
278C22#1451975011yescharacteristic
279C22#1451975911yescharacteristic
280C4—42no—
281C4—41no—
282C4—81no—
283C4—1222no—
284C4—4881no—
285C4—2442no—
286C4—2442no—
287C2—21no—
288C2—21no—
289C2—21no—
290C2—21no—
291C2—21no—
292C2—21no—
293C2—21no—
294C2—81no—
295C2—2442no—
296C2#1683963811yescharacteristic
subgroupG/H
centerC2#16839638
commutatorC23×C61C22×C4
FrattiniC24C22×D61
FittingC2×#99×C61C2
socleC2×C61#386
hypercenterC2×#99D61
hypocenterC61#1913
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. #16840235C2semidirect
3. C2×#14519692C2semidirect
4. C2×#14519691C2semidirect
5. #16839529C2semidirect
6. #16839528C2semidirect
7. C2×#99×C61C2semidirect
9. #14519760C4semidirect
12. #14519746C4semidirect
27. C24×C61C2×C4semidirect
38. C22×C4×C61C2×C4semidirect
54. C22⋊C4×C61D4semidirect
60. C22⋊Dic61C2×C4semidirect
61. C22⋊Dic61D4semidirect
153. C2×#99D61semidirect
156. C61#1913semidirect
177. C24C4×D61semidirect
199. C22×C4C4×D61semidirect
214. C22⋊C4C22⋊D61semidirect