Finite Group Databasebeta

← #21449437

Subgroups — #21449437

Order 7808.

952 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 952 conjugacy classes of subgroups — too many to draw. Only its 169 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×#11758224C211yesmaximal, characteristic, complemented
2C2×#14519773C211yesmaximal, characteristic, complemented
3C2×#14519765C211yesmaximal, characteristic, complemented
4C2×#14519752C211yesmaximal, characteristic, complemented
5#16839671C214yesmaximal, complemented
6#16839667C211yesmaximal, characteristic, complemented
7#16839639C214yesmaximal, complemented
8C4×#11758198C211yesmaximal, characteristic, complemented
9C61×#390C211yesmaximal, characteristic, complemented
10C2×#11758224—24no—
11C2×#11758224—24no—
12C2×#11758224—24no—
13C22×Dic122C2211yescharacteristic
14C22×D244C2211yescharacteristic
15C22×D244C2212yes—
16C22×C22⋊D61C2212yes—
17C22×C22⋊D61C2214yes—
18C23×Dic61C2212yes—
19C22×C4×D61C2211yescharacteristic
20#14519773—24no—
21#14519765—24no—
22#14519752—24no—
23C2×#11758198C2212yes—
24C2×#11758198C2214yes—
25C2×#11758198C2212yes—
26C2×C4×Dic61C2211yescharacteristic
27#14519684C2212yes—
28#14519684C2214yes—
29C22×D4×C61C2211yescharacteristic
30C2×C4⋊C4×C61C2211yescharacteristic
31C2×C22⋊C4×C61C2214yes—
32C2×C42×C61C2211yescharacteristic
33C24×C61C2312yes—
34C23×D61C2312yes—
35C23×D61C2311yescharacteristic
36C2×D4×C61—22no—
37C2×D4×C61—22no—
38C2×D4×C61D414yescomplemented
39C22×C4×C61C2312yes—
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C2×C22⋊D61—24no—
43C2×C22⋊D61—24no—
44C2×C22⋊D61—28no—
45C2×C22⋊D61—24no—
46C2×C22⋊D61—28no—
47C2×C22⋊D61—44no—
48C22×Dic61—24no—
49C22×Dic61—24no—
50C22×Dic61—24no—
51C22×Dic61C2311yescharacteristic
52C22×Dic61C2312yes—
53C22×Dic61C2312yes—
54#11758224—232no—
55C2×D244—24no—
56C2×D244—22no—
57C2×D244—22no—
58C2×D244—22no—
59C2×D244—44no—
60C2×C4×D61—22no—
61C2×C4×D61—22no—
62C2×C4×D61D414yescomplemented
63C2×Dic122—22no—
64C2×Dic122—22no—
65C2×Dic122D414yescomplemented
66C4⋊C4×C61—22no—
67C22⋊C4×C61—44no—
68C42×C61—22no—
69#11758198—24no—
70#11758198—28no—
71#11758198—24no—
72C4×Dic61—22no—
73C23×C61—22no—
74C23×C61—22no—
75C23×C61—24no—
76C23×C61—24no—
77C23×C61C2×D414yes—
78C23×C61C2411yescharacteristic
79C22×D61—21no—
80C22×D61—21no—
81C22×D61—22no—
82C22×D61—22no—
83C22×D61—22no—
84C22×D61—22no—
85C22×D61—22no—
86C22×D61—24no—
87C22×D61—24no—
88C22×D61C2×D412yes—
89D4×C61—28no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—24no—
95C2×C4×C61C2×D412yes—
96C2×C4×C61C2×D412yes—
97C2×C4×C61C2×D412yes—
98C22⋊D61—216no—
99C22⋊D61—416no—
100C2×Dic61—216no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—22no—
107C2×Dic61C2×D414yes—
108C2×Dic61C2×D412yes—
109C2×Dic61#4114yescomplemented
110D244—48no—
111D244—44no—
112C4×D61—28no—
113Dic122—28no—
114C22×C61—24no—
115C22×C61—28no—
116C22×C61—42no—
117C22×C61—42no—
118C22×C61—44no—
119C22×C61C22×D411yescharacteristic
120C22×C61C22×D411yescharacteristic
121C22×C61C22×D411yescharacteristic
122C22×C61C2×#4112yes—
123C22×C61H(5,𝔽2)12yes—
124C2×D61—22no—
125C2×D61—22no—
126C2×D61—22no—
127C2×D61—42no—
128C2×D61—42no—
129C2×D61—42no—
130C2×D61—42no—
131C2×D61—42no—
132C2×D61—44no—
133C2×D61—44no—
134C4×C61—42no—
135C4×C61—42no—
136C4×C61#12014yes—
137Dic61—24no—
138Dic61—22no—
139Dic61—24no—
140#2431—611nomaximal, Sylow
141C2×C61—44no—
142C2×C61C2×#12011yescharacteristic
143C2×C61#53211yescharacteristic
144C2×C61#53511yescharacteristic
145C2×C61#54612yes—
146C2×C61#55012yes—
147D61—42no—
148D61—82no—
149C22×#41—611no—
150C2×#127—611no—
151C2×#124—611no—
152C2×#121—611no—
153#392—614no—
154#391—611no—
155#390D6111yescharacteristic, complemented
156#386—614no—
157C4×C22⋊C4—611no—
158C61#243111yescharacteristic, complemented, Sylow
159C2×#41—1224no—
160C2×#41—1224no—
161C2×#41—1224no—
162C22×Q8—611no—
163C22×D4—612no—
164C22×D4—614no—
165C22×D4—611no—
166C22×D4—612no—
167C22×D4C2×D6111yescharacteristic
168C23×C4—611no—
169C23×C4—612no—
170#127—1224no—
171#124—1224no—
172#121—1224no—
173C2×C4⋊C4C2×D6111yescharacteristic
174C2×C22⋊C4—612no—
175C2×C22⋊C4—614no—
176C2×C22⋊C4—612no—
177C2×C22⋊C4C2×D6114yes—
178C2×C42—611no—
179C2×C42C2×D6111yescharacteristic
180#95—612no—
181#95—614no—
182C24—611no—
183C24—612no—
184C24C22×D6112yes—
185#41—12232no—
186C2×Q8—614no—
187C2×Q8—1222no—
188C2×Q8—1222no—
189C2×D4—22no—
190C2×D4—22no—
191C2×D4—1224no—
192C2×D4—1224no—
193C2×D4—1228no—
194C2×D4—1224no—
195C2×D4—1224no—
196C2×D4—1228no—
197C2×D4—1222no—
198C2×D4—1222no—
199C2×D4—1222no—
200C2×D4—2444no—
201C2×D4—2444no—
202C2×D4D24414yescomplemented
203C22×C4—612no—
204C22×C4—611no—
205C22×C4—612no—
206C22×C4—614no—
207C22×C4—1224no—
208C22×C4—1224no—
209C22×C4—1224no—
210C22×C4—1222no—
211C22×C4—1222no—
212C22×C4C22×D6112yes—
213C22×C4C22×D6112yes—
214C22×C4C22×D6111yescharacteristic
215C4⋊C4—22no—
216C22⋊C4—44no—
217C22⋊C4—1224no—
218C22⋊C4—1224no—
219C22⋊C4—1228no—
220C42—22no—
221C42—1222no—
222C23—22no—
223C23—22no—
224C23—24no—
225C23—24no—
226C23—612no—
227C23—1221no—
228C23—1221no—
229C23—1222no—
230C23—1222no—
231C23—1222no—
232C23—1222no—
233C23—1222no—
234C23—1224no—
235C23—1224no—
236C23C2×D24414yes—
237C23C23×D6111yescharacteristic
238Q8—1228no—
239D4—28no—
240D4—12216no—
241D4—2448no—
242D4—24416no—
243D4—2444no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—24no—
249C2×C4—612no—
250C2×C4—614no—
251C2×C4—614no—
252C2×C4—12216no—
253C2×C4—1221no—
254C2×C4—1222no—
255C2×C4—1222no—
256C2×C4—1221no—
257C2×C4—1222no—
258C2×C4—1222no—
259C2×C4—1228no—
260C2×C4C2×D24412yes—
261C2×C4D4×D6112yes—
262C2×C4D4×D6112yes—
263C22—24no—
264C22—28no—
265C22—42no—
266C22—42no—
267C22—44no—
268C22—1222no—
269C22—1222no—
270C22—1222no—
271C22—2442no—
272C22—2442no—
273C22—2442no—
274C22—2444no—
275C22—2444no—
276C22—2442no—
277C22—2442no—
278C22C2×D4×D6111yescharacteristic
279C22C2×D4×D6111yescharacteristic
280C22C22×D24411yescharacteristic
281C22#41×D6112yes—
282C22#1451982212yes—
283C4—42no—
284C4—42no—
285C4—1222no—
286C4—1224no—
287C4—1224no—
288C4#1451974714yes—
289C2—44no—
290C2—4882no—
291C2—2442no—
292C2C2×#1451974711yescharacteristic
293C2#1684031111yescharacteristic
294C2#1684032511yescharacteristic
295C2#1684040712yes—
296C2#1684043012yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#390C2
hypercenter#390D61
hypocenterC61#2431
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C22×#11758224C2semidirect
2. C2×#14519773C2semidirect
3. C2×#14519765C2semidirect
4. C2×#14519752C2semidirect
5. #16839671C2semidirect
6. #16839667C2semidirect
7. #16839639C2semidirect
8. C4×#11758198C2semidirect
9. C61×#390C2semidirect
38. C2×D4×C61D4semidirect
62. C2×C4×D61D4semidirect
65. C2×Dic122D4semidirect
109. C2×Dic61#41semidirect
155. #390D61semidirect
158. C61#2431semidirect
202. C2×D4D244semidirect