Finite Group Databasebeta

← #21449439

Subgroups — #21449439

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×#11758222C211yesmaximal, characteristic, complemented
2C2×#14519773C211yesmaximal, characteristic, complemented
3C2×#14519764C211yesmaximal, characteristic, complemented
4#16839670C214yesmaximal, complemented
5#16839667C211yesmaximal, characteristic, complemented
6#16839663C211yesmaximal, characteristic, complemented
7#16839638C214yesmaximal, complemented
8C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
9C2×#121×C61C211yesmaximal, characteristic, complemented
10C2×#11758222—24no—
11C2×#11758222—24no—
12C2×#11758222—24no—
13C22×Dic122C2211yescharacteristic
14C22×D244C2211yescharacteristic
15C22×C22⋊D61C2212yes—
16C22×C22⋊D61C2214yes—
17C22×C4×D61C2212yes—
18#14519773—24no—
19#14519764—24no—
20C2×C22⋊Dic61C2214yes—
21C2×C22⋊Dic61C2212yes—
22C2×#11758198C2214yes—
23C2×C4×Dic61C2211yescharacteristic
24C2×C4×Dic61C2211yescharacteristic
25#14519684C2212yes—
26#14519684C2214yes—
27C22×D4×C61C2211yescharacteristic
28C22×D4×C61C2212yes—
29C23×C4×C61C2211yescharacteristic
30#121×C61—24no—
31C2×C4⋊C4×C61C2211yescharacteristic
32C2×C22⋊C4×C61C2212yes—
33C24×C61C2312yes—
34C24×C61C2311yescharacteristic
35C23×D61C2312yes—
36C2×D4×C61—24no—
37C2×D4×C61—22no—
38C2×D4×C61—22no—
39C2×D4×C61—22no—
40C2×D4×C61—44no—
41C22×C4×C61—22no—
42C22×C4×C61—22no—
43C22×C4×C61D414yescomplemented
44C22×C4×C61C2312yes—
45C22×C4×C61C2311yescharacteristic
46C22×C4×C61C2311yescharacteristic
47C2×C22⋊D61—24no—
48C2×C22⋊D61—24no—
49C2×C22⋊D61—28no—
50C2×C22⋊D61—24no—
51C2×C22⋊D61—28no—
52C2×C22⋊D61—44no—
53C22×Dic61C2312yes—
54C22×Dic61C2312yes—
55C22×Dic61C2312yes—
56#11758222—232no—
57C2×D244—22no—
58C2×D244—22no—
59C2×D244D414yescomplemented
60C2×C4×D61—24no—
61C2×C4×D61—24no—
62C2×C4×D61—24no—
63C2×Dic122—22no—
64C2×Dic122—22no—
65C2×Dic122D414yescomplemented
66C4⋊C4×C61—22no—
67C22⋊C4×C61—24no—
68C22⋊Dic61—28no—
69C22⋊Dic61—24no—
70#11758198—44no—
71C4×Dic61—22no—
72C4×Dic61—22no—
73C23×C61—21no—
74C23×C61—21no—
75C23×C61—22no—
76C23×C61—22no—
77C23×C61—22no—
78C23×C61—22no—
79C23×C61—22no—
80C23×C61—24no—
81C23×C61—24no—
82C23×C61C2×D412yes—
83C23×C61C2411yescharacteristic
84C22×D61—22no—
85C22×D61—22no—
86C22×D61—24no—
87C22×D61—24no—
88C22×D61C2×D414yes—
89D4×C61—48no—
90D4×C61—44no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—28no—
94C2×C4×C61—22no—
95C2×C4×C61—24no—
96C2×C4×C61C2×D412yes—
97C2×C4×C61C2×D412yes—
98C2×C4×C61C2×D412yes—
99C2×C4×C61C2×D412yes—
100C22⋊D61—216no—
101C22⋊D61—416no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61C2×D414yes—
110C2×Dic61#4114yescomplemented
111D244—28no—
112C4×D61—216no—
113Dic122—28no—
114C22×C61—22no—
115C22×C61—22no—
116C22×C61—22no—
117C22×C61—42no—
118C22×C61—42no—
119C22×C61—42no—
120C22×C61—42no—
121C22×C61—42no—
122C22×C61—44no—
123C22×C61—44no—
124C22×C61C22×D411yescharacteristic
125C22×C61C22×D411yescharacteristic
126C22×C61C22×D411yescharacteristic
127C22×C61C2×#4112yes—
128C22×C61H(5,𝔽2)12yes—
129C2×D61—24no—
130C2×D61—28no—
131C2×D61—42no—
132C2×D61—42no—
133C2×D61—44no—
134C4×C61—22no—
135C4×C61—42no—
136C4×C61#12014yes—
137Dic61—24no—
138Dic61—24no—
139Dic61—42no—
140#2431—611nomaximal, Sylow
141C2×C61—42no—
142C2×C61—82no—
143C2×C61C2×#12011yescharacteristic
144C2×C61#53211yescharacteristic
145C2×C61#53511yescharacteristic
146C2×C61#54612yes—
147C2×C61#55012yes—
148D61—44no—
149C22×#41—611no—
150C2×#127—611no—
151C2×#124—611no—
152C2×#121D6111yescharacteristic, complemented
153#392—614no—
154#391—611no—
155#390—611no—
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×D4C2×D6111yescharacteristic
167C22×D4C2×D6112yes—
168C23×C4—612no—
169C23×C4C2×D6111yescharacteristic
170#127—1224no—
171#124—1224no—
172#121—24no—
173C2×C4⋊C4C2×D6111yescharacteristic
174C2×C22⋊C4—614no—
175C2×C22⋊C4—612no—
176C2×C22⋊C4—614no—
177C2×C22⋊C4C2×D6112yes—
178C2×C42—611no—
179C2×C42—611no—
180#95—612no—
181#95—614no—
182C24—612no—
183C24C22×D6112yes—
184C24C22×D6111yescharacteristic
185#41—12232no—
186C2×Q8—614no—
187C2×Q8—1222no—
188C2×Q8—1222no—
189C2×D4—24no—
190C2×D4—22no—
191C2×D4—22no—
192C2×D4—22no—
193C2×D4—44no—
194C2×D4—614no—
195C2×D4—1224no—
196C2×D4—1228no—
197C2×D4—1224no—
198C2×D4—1224no—
199C2×D4—1228no—
200C2×D4—1222no—
201C2×D4—1222no—
202C2×D4—2444no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—612no—
206C22×C4—612no—
207C22×C4—612no—
208C22×C4—1224no—
209C22×C4—1224no—
210C22×C4—1224no—
211C22×C4C22⋊D6114yescomplemented
212C22×C4C22×D6112yes—
213C22×C4C22×D6111yescharacteristic
214C22×C4C22×D6111yescharacteristic
215C4⋊C4—22no—
216C22⋊C4—24no—
217C22⋊C4—1224no—
218C22⋊C4—1228no—
219C22⋊C4—2444no—
220C42—1222no—
221C42—1222no—
222C23—21no—
223C23—21no—
224C23—22no—
225C23—22no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23—24no—
230C23—24no—
231C23—614no—
232C23—1222no—
233C23—1222no—
234C23—1224no—
235C23—1224no—
236C23C2×C22⋊D6112yes—
237C23C23×D6111yescharacteristic
238Q8—1228no—
239D4—48no—
240D4—44no—
241D4—12216no—
242D4—1228no—
243D4—24416no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—28no—
247C2×C4—22no—
248C2×C4—24no—
249C2×C4—614no—
250C2×C4—614no—
251C2×C4—12216no—
252C2×C4—1222no—
253C2×C4—1222no—
254C2×C4—1222no—
255C2×C4—1222no—
256C2×C4—1222no—
257C2×C4—1222no—
258C2×C4—1222no—
259C2×C4D4×D6112yes—
260C2×C4D4×D6112yes—
261C2×C4C2×C22⋊D6112yes—
262C2×C4C2×C22⋊D6112yes—
263C22—22no—
264C22—22no—
265C22—22no—
266C22—42no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—44no—
272C22—44no—
273C22—1224no—
274C22—1228no—
275C22—2442no—
276C22—2442no—
277C22—2444no—
278C22C2×D4×D6111yescharacteristic
279C22C2×D4×D6111yescharacteristic
280C22C22×C22⋊D6111yescharacteristic
281C22#41×D6112yes—
282C22#1451982212yes—
283C4—22no—
284C4—42no—
285C4—1224no—
286C4—1224no—
287C4—2442no—
288C4#1451974514yes—
289C2—42no—
290C2—82no—
291C2—2444no—
292C2C2×#1451974511yescharacteristic
293C2#1684030811yescharacteristic
294C2#1684032911yescharacteristic
295C2#1684040912yes—
296C2#1684043012yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#121×C61C2
hypercenterC2×#121D61
hypocenterC61#2431
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#11758222C2semidirect
2. C2×#14519773C2semidirect
3. C2×#14519764C2semidirect
4. #16839670C2semidirect
5. #16839667C2semidirect
6. #16839663C2semidirect
7. #16839638C2semidirect
8. C4×C22⋊Dic61C2semidirect
9. C2×#121×C61C2semidirect
43. C22×C4×C61D4semidirect
59. C2×D244D4semidirect
65. C2×Dic122D4semidirect
110. C2×Dic61#41semidirect
152. C2×#121D61semidirect
158. C61#2431semidirect
211. C22×C4C22⋊D61semidirect