Finite Group Databasebeta

← #21450754

Subgroups — #21450754

Order 7808.

760 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C2×#14519763C211yesmaximal, characteristic, complemented
2C2×#14519755C212yesmaximal, complemented
3C2×#14519750C212yesmaximal, complemented
4C2×#14519739C211yesmaximal, characteristic, complemented
5#16839697C211yesmaximal, characteristic, complemented
6#16839672C211yesmaximal, characteristic, complemented
7#16839671C211yesmaximal, characteristic, complemented
8#16839663C212yesmaximal, complemented
9#16839662C212yesmaximal, complemented
10#16839613C211yesmaximal, characteristic, complemented
11C61×#399C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×D244C2211yescharacteristic
14C22×D244C2212yes—
15C22×C22⋊D61C2211yescharacteristic
16C22×C22⋊D61C2212yes—
17C22×C4×D61C2212yes—
18#14519763—24no—
19#14519755—28no—
20#14519750—28no—
21#14519739—24no—
22C2×#11758196C2212yes—
23C2×#11758196C2212yes—
24C2×C22⋊Dic61C2211yescharacteristic
25C2×#11758198C2212yes—
26C2×#11758198C2211yescharacteristic
27C2×#11758198C2212yes—
28C2×#11758198C2212yes—
29C2×#11758198C2212yes—
30C2×#11758198C2211yescharacteristic
31C2×C4×Dic61C2212yes—
32C2×C4×Dic61C2211yescharacteristic
33#14519684C2211yescharacteristic
34C2×C4⋊C4×C61C2211yescharacteristic
35C2×C4⋊C4×C61C2212yes—
36C2×C22⋊C4×C61C2212yes—
37C2×C22⋊C4×C61C2211yescharacteristic
38#95×C61C2211yescharacteristic
39C24×C61C2311yescharacteristic
40C23×D61C2311yescharacteristic
41C23×D61C2312yes—
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2311yescharacteristic
45C22×C4×C61C2312yes—
46C2×C22⋊D61—24no—
47C2×C22⋊D61—24no—
48C2×C22⋊D61—24no—
49C2×C22⋊D61—22no—
50C2×C22⋊D61—42no—
51C22×Dic61C2311yescharacteristic
52C22×Dic61C2312yes—
53C22×Dic61C2311yescharacteristic
54C22×Dic61C2311yescharacteristic
55C2×D244—24no—
56C2×D244—22no—
57C2×D244—24no—
58C2×D244—24no—
59C2×D244—42no—
60C2×C4×D61—24no—
61C2×C4×D61—24no—
62C2×C4×D61—24no—
63C2×Dic122—24no—
64C2×Dic122—22no—
65C4⋊C4×C61—22no—
66C4⋊C4×C61—24no—
67C22⋊C4×C61—24no—
68C22⋊C4×C61—22no—
69C22⋊Dic61—22no—
70#11758198—24no—
71#11758198—22no—
72#11758198—24no—
73#11758198—24no—
74#11758198—24no—
75#11758198—22no—
76#11758196—24no—
77#11758196D418yescomplemented
78C4×Dic61—42no—
79C4×Dic61D414yescomplemented
80C23×C61—21no—
81C23×C61—22no—
82C23×C61—22no—
83C23×C61—21no—
84C23×C61—21no—
85C23×C61C2411yescharacteristic
86C22×D61—22no—
87C22×D61—22no—
88C22×D61—22no—
89C22×D61—22no—
90C22×D61—22no—
91C22×D61—22no—
92C22×D61—21no—
93C22×D61—22no—
94C22×D61—22no—
95C22×D61—21no—
96C22×D61—21no—
97C22×D61#4114yes—
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61—22no—
101C2×C4×C61—22no—
102C2×C4×C61—21no—
103C2×C4×C61—22no—
104C2×C4×C61—22no—
105C2×C4×C61—22no—
106C2×C4×C61C2×D412yes—
107C2×C4×C61C2×D414yes—
108C22⋊D61—48no—
109C22⋊D61—44no—
110C2×Dic61—22no—
111C2×Dic61—21no—
112C2×Dic61—22no—
113C2×Dic61—21no—
114C2×Dic61—22no—
115C2×Dic61—21no—
116C2×Dic61C2×D412yes—
117C2×Dic61C2×D414yes—
118C2×Dic61C2×D412yes—
119C2×Dic61C2×D414yes—
120D244—28no—
121D244—48no—
122C4×D61—48no—
123Dic122—44no—
124C22×C61—41no—
125C22×C61—41no—
126C22×C61—41no—
127C22×C61—42no—
128C22×C61—42no—
129C22×C61C22×D411yescharacteristic
130C22×C61C22×D412yes—
131C22×C61C2×#4112yes—
132C22×C61H(5,𝔽2)11yescharacteristic
133C22×C612−1+411yescharacteristic
134C2×D61—24no—
135C2×D61—24no—
136C2×D61—24no—
137C2×D61—42no—
138C2×D61—42no—
139C2×D61—42no—
140C2×D61—42no—
141C2×D61—41no—
142C2×D61—41no—
143C2×D61—41no—
144C2×D61—42no—
145C2×D61—42no—
146C4×C61—22no—
147C4×C61—24no—
148C4×C61—41no—
149C4×C61—42no—
150Dic61—22no—
151Dic61—24no—
152Dic61—41no—
153Dic61#12714yes—
154#2540—611nomaximal, Sylow
155C2×C61—81no—
156C2×C61#52511yescharacteristic
157C2×C61C2×#12711yescharacteristic
158C2×C61#53711yescharacteristic
159C2×C61#54612yes—
160C2×C61#54812yes—
161D61—44no—
162D61—81no—
163C2×#124—611no—
164C2×C22⋊Q8—612no—
165C2×#121—612no—
166C2×C4×D4—611no—
167#399—611no—
168#399D6111yescharacteristic, complemented
169#392—611no—
170#392—611no—
171#390—612no—
172#390—612no—
173C4×C4⋊C4—611no—
174C61#254011yescharacteristic, complemented, Sylow
175C22×Q8—611no—
176C22×D4—611no—
177C22×D4—612no—
178C22×D4—611no—
179C22×D4—612no—
180C23×C4—612no—
181#124—1224no—
182C22⋊Q8—1228no—
183#121—1228no—
184C4×D4—1224no—
185C2×C4⋊C4—612no—
186C2×C4⋊C4—612no—
187C2×C4⋊C4C2×D6111yescharacteristic
188C2×C4⋊C4C2×D6112yes—
189C2×C22⋊C4—611no—
190C2×C22⋊C4—612no—
191C2×C22⋊C4—612no—
192C2×C22⋊C4—612no—
193C2×C22⋊C4—612no—
194C2×C22⋊C4—611no—
195C2×C22⋊C4—611no—
196C2×C22⋊C4C2×D6112yes—
197C2×C22⋊C4C2×D6111yescharacteristic
198C2×C42—611no—
199C2×C42—612no—
200#95—611no—
201#95C2×D6111yescharacteristic
202C24—612no—
203C24—611no—
204C24C22×D6111yescharacteristic
205C2×Q8—1224no—
206C2×Q8—1222no—
207C2×D4—1224no—
208C2×D4—1224no—
209C2×D4—1224no—
210C2×D4—1224no—
211C2×D4—1222no—
212C2×D4—1224no—
213C2×D4—1222no—
214C2×D4—1224no—
215C2×D4—2442no—
216C2×D4—2442no—
217C22×C4—611no—
218C22×C4—612no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—1224no—
222C22×C4—1224no—
223C22×C4—1224no—
224C22×C4C22×D6111yescharacteristic
225C22×C4C22×D6112yes—
226C22×C4C22×D6111yescharacteristic
227C22×C4C22×D6112yes—
228C4⋊C4—22no—
229C4⋊C4—24no—
230C4⋊C4—618no—
231C4⋊C4—1224no—
232C22⋊C4—24no—
233C22⋊C4—22no—
234C22⋊C4—1224no—
235C22⋊C4—1224no—
236C22⋊C4—1224no—
237C22⋊C4—1222no—
238C22⋊C4—1222no—
239C22⋊C4—1224no—
240C22⋊C4—1222no—
241C42—614no—
242C42—2442no—
243C23—21no—
244C23—22no—
245C23—22no—
246C23—21no—
247C23—21no—
248C23—614no—
249C23—1222no—
250C23—1222no—
251C23—1222no—
252C23—1222no—
253C23—1222no—
254C23—1222no—
255C23—1221no—
256C23—1222no—
257C23—1222no—
258C23—1221no—
259C23—1221no—
260C23C23×D6111yescharacteristic
261Q8—2444no—
262D4—1228no—
263D4—2448no—
264D4—2444no—
265D4—2448no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—612no—
275C2×C4—614no—
276C2×C4—612no—
277C2×C4—614no—
278C2×C4—1222no—
279C2×C4—1221no—
280C2×C4—1222no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—1222no—
284C2×C4—2448no—
285C2×C4D4×D6112yes—
286C2×C4D4×D6114yes—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—42no—
291C22—42no—
292C22—1224no—
293C22—1224no—
294C22—1224no—
295C22—2441no—
296C22—2441no—
297C22—2441no—
298C22—2442no—
299C22—2442no—
300C22—2442no—
301C22—2442no—
302C22—2442no—
303C22—2442no—
304C22C2×D4×D6111yescharacteristic
305C22C2×D4×D6112yes—
306C22#41×D6112yes—
307C22#1451982311yescharacteristic
308C22#1451982511yescharacteristic
309C4—22no—
310C4—24no—
311C4—42no—
312C4—41no—
313C4—614no—
314C4—1222no—
315C4—1224no—
316C4—2441no—
317C2—81no—
318C2—4881no—
319C2—2444no—
320C2#1684027011yescharacteristic
321C2#127×D6111yescharacteristic
322C2#1684034211yescharacteristic
323C2#1684040412yes—
324C2#1684042212yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#399C2
hypercenter#399D61
hypocenterC61#2540
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#14519763C2semidirect
2. C2×#14519755C2semidirect
3. C2×#14519750C2semidirect
4. C2×#14519739C2semidirect
5. #16839697C2semidirect
6. #16839672C2semidirect
7. #16839671C2semidirect
8. #16839663C2semidirect
9. #16839662C2semidirect
10. #16839613C2semidirect
11. C61×#399C2semidirect
77. #11758196D4semidirect
79. C4×Dic61D4semidirect
168. #399D61semidirect
174. C61#2540semidirect