Finite Group Databasebeta

← #21451567

Subgroups — #21451567

Order 7808.

632 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519761C211yesmaximal, characteristic, complemented
2C2×#14519758C211yesmaximal, characteristic, complemented
3C2×#14519749C211yesmaximal, characteristic
4C22×#11758196C211yesmaximal, characteristic, complemented
5#16839696C212yesmaximal, complemented
6#16839686C212yesmaximal, complemented
7#16839685C212yesmaximal, complemented
8#16839677C212yesmaximal, complemented
9#16839641C211yesmaximal, characteristic, complemented
10#16839620C211yesmaximal, characteristic, complemented
11C61×#386C211yesmaximal, characteristic, complemented
12C22×C22⋊D61C2211yescharacteristic
13C22×C22⋊D61C2211yescharacteristic
14C23×Dic61C2211yescharacteristic
15C23×Dic61C2211yescharacteristic
16#14519761—24no—
17#14519758—24no—
18#14519749—24no—
19C2×C4⋊Dic61C2212yes—
20C2×#11758196—24no—
21C2×#11758196C2212yes—
22C2×#11758196C2212yes—
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2212yes—
25C2×#11758196C2212yes—
26C2×C22⋊Dic61C2211yescharacteristic
27C2×C22⋊Dic61C2212yes—
28C2×C22⋊Dic61C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2212yes—
31C2×#11758198C2212yes—
32#14519684C2212yes—
33#14519684C2212yes—
34C22×D4×C61C2211yescharacteristic
35C23×C4×C61C2211yescharacteristic
36C2×C22⋊C4×C61C2211yescharacteristic
37C2×C22⋊C4×C61C2212yes—
38#95×C61C2212yes—
39C24×C61C2311yescharacteristic
40C24×C61C2311yescharacteristic
41C23×D61C2311yescharacteristic
42C2×D4×C61—22no—
43C2×D4×C61—22no—
44C2×D4×C61—22no—
45C22×C4×C61—22no—
46C22×C4×C61—42no—
47C22×C4×C61C2311yescharacteristic
48C22×C4×C61C2312yes—
49C22×C4×C61C2312yes—
50C2×C22⋊D61—22no—
51C2×C22⋊D61—22no—
52C2×C22⋊D61—22no—
53C2×C22⋊D61—22no—
54C2×C22⋊D61—42no—
55C22×Dic61—22no—
56C22×Dic61—22no—
57C22×Dic61—42no—
58C22×Dic61D414yes—
59C22×Dic61D414yescomplemented
60C22×Dic61C2311yescharacteristic
61C22×Dic61C2312yes—
62C22×Dic61C2311yescharacteristic
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2312yes—
65C22⋊C4×C61—22no—
66C22⋊C4×C61—42no—
67C22⋊Dic61—22no—
68C22⋊Dic61—22no—
69C22⋊Dic61—24no—
70#11758198—22no—
71#11758198—24no—
72#11758198—42no—
73C4⋊Dic61—24no—
74#11758196—24no—
75#11758196—24no—
76#11758196—22no—
77#11758196—24no—
78#11758196—42no—
79C23×C61—22no—
80C23×C61—22no—
81C23×C61—21no—
82C23×C61—21no—
83C23×C61—21no—
84C23×C61—22no—
85C23×C61—22no—
86C23×C61C2×D412yes—
87C23×C61C2×D412yes—
88C23×C61#4112yes—
89C23×C61C2411yescharacteristic
90C22×D61—21no—
91C22×D61—21no—
92C22×D61—21no—
93C22×D61—22no—
94C22×D61—22no—
95D4×C61—44no—
96C2×C4×C61—22no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—22no—
100C2×C4×C61—21no—
101C2×C4×C61—22no—
102C2×C4×C61—22no—
103C2×C4×C61—22no—
104C2×C4×C61—22no—
105C2×C4×C61—44no—
106C22⋊D61—44no—
107C22⋊D61—44no—
108C2×Dic61—28no—
109C2×Dic61—22no—
110C2×Dic61—22no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—22no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—22no—
118C2×Dic61—22no—
119C2×Dic61—44no—
120C2×Dic61C2×D412yes—
121C2×Dic61C2×D412yes—
122C2×Dic61C2×D414yes—
123C22×C61—22no—
124C22×C61—22no—
125C22×C61—24no—
126C22×C61—24no—
127C22×C61—41no—
128C22×C61—41no—
129C22×C61—41no—
130C22×C61—42no—
131C22×C61—42no—
132C22×C61#12114yes—
133C22×C61C22×D411yescharacteristic
134C22×C61C22×D411yescharacteristic
135C22×C61C2×#4111yescharacteristic
136C22×C61H(5,𝔽2)12yes—
137C22×C612−1+412yes—
138C2×D61—41no—
139C2×D61—41no—
140C2×D61—41no—
141C2×D61—42no—
142C2×D61—42no—
143C4×C61—41no—
144C4×C61—42no—
145C4×C61—42no—
146Dic61—24no—
147Dic61—22no—
148Dic61—22no—
149Dic61—41no—
150Dic61—42no—
151#2618—611nomaximal, Sylow
152C2×C61—24no—
153C2×C61—81no—
154C2×C61C2×#12111yescharacteristic
155C2×C61#53411yescharacteristic
156C2×C61#53611yescharacteristic
157C2×C61#53712yes—
158C2×C61#53912yes—
159D61—81no—
160C2×#123—611no—
161C2×#123—611no—
162C2×#121—611no—
163C22×C4⋊C4—611no—
164#398—612no—
165#396—612no—
166#396—612no—
167#394—612no—
168#386—611no—
169#386D6111yescharacteristic, complemented
170#380—611no—
171C61#261811yescharacteristic, complemented, Sylow
172C22×D4—611no—
173C22×D4—611no—
174C22×D4C2×D6111yescharacteristic
175C23×C4—611no—
176C23×C4—611no—
177C23×C4C2×D6111yescharacteristic
178#123—1224no—
179#123—1224no—
180#121—1224no—
181C2×C4⋊C4—612no—
182C2×C4⋊C4—612no—
183C2×C4⋊C4—611no—
184C2×C4⋊C4—612no—
185C2×C4⋊C4—612no—
186C2×C4⋊C4—612no—
187C2×C4⋊C4—1224no—
188C2×C22⋊C4—611no—
189C2×C22⋊C4—611no—
190C2×C22⋊C4—612no—
191C2×C22⋊C4—611no—
192C2×C22⋊C4—612no—
193C2×C22⋊C4—612no—
194C2×C22⋊C4C2×D6111yescharacteristic
195C2×C22⋊C4C2×D6112yes—
196#95—612no—
197#95—612no—
198#95C2×D6112yes—
199C24—611no—
200C24C22×D6111yescharacteristic
201C24C22×D6111yescharacteristic
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—1222no—
206C2×D4—1222no—
207C2×D4—1222no—
208C2×D4—1222no—
209C2×D4—2442no—
210C22×C4—22no—
211C22×C4—42no—
212C22×C4—614no—
213C22×C4—611no—
214C22×C4—612no—
215C22×C4—611no—
216C22×C4—614no—
217C22×C4—612no—
218C22×C4—611no—
219C22×C4—1222no—
220C22×C4—1222no—
221C22×C4—2442no—
222C22×C4C22×D6112yes—
223C22×C4C22×D6112yes—
224C22×C4C22×D6111yescharacteristic
225C4⋊C4—1224no—
226C4⋊C4—1224no—
227C4⋊C4—1222no—
228C4⋊C4—1224no—
229C4⋊C4—1224no—
230C4⋊C4—2442no—
231C22⋊C4—22no—
232C22⋊C4—42no—
233C22⋊C4—1222no—
234C22⋊C4—1224no—
235C22⋊C4—1222no—
236C22⋊C4—1224no—
237C22⋊C4—1222no—
238C22⋊C4—2442no—
239C23—22no—
240C23—22no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—22no—
245C23—22no—
246C23—1221no—
247C23—1221no—
248C23—1221no—
249C23—1222no—
250C23—1222no—
251C23#1175822212yes—
252C23D4×D6112yes—
253C23D4×D6112yes—
254C23C23×D6111yescharacteristic
255D4—44no—
256D4—2444no—
257D4—2444no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—44no—
268C2×C4—614no—
269C2×C4—612no—
270C2×C4—612no—
271C2×C4—1222no—
272C2×C4—1222no—
273C2×C4—1222no—
274C2×C4—1222no—
275C2×C4—1228no—
276C2×C4—1222no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—1222no—
281C2×C4—1222no—
282C2×C4—2444no—
283C22—22no—
284C22—22no—
285C22—24no—
286C22—24no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—42no—
291C22—42no—
292C22—2441no—
293C22—2441no—
294C22—2441no—
295C22—2442no—
296C22—2442no—
297C22#1451975014yes—
298C22C2×D4×D6111yescharacteristic
299C22C2×D4×D6111yescharacteristic
300C22C2×#1175822211yescharacteristic
301C22#1451982212yes—
302C22#1451982412yes—
303C4—41no—
304C4—42no—
305C4—42no—
306C4—1224no—
307C4—1222no—
308C4—1222no—
309C4—2441no—
310C4—2442no—
311C2—24no—
312C2—81no—
313C2—4881no—
314C2C2×#1451975011yescharacteristic
315C2#1684032211yescharacteristic
316C2#1684033411yescharacteristic
317C2#1684033912yes—
318C2#1684035412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#386C2
hypercenter#386D61
hypocenterC61#2618
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#14519761C2semidirect
2. C2×#14519758C2semidirect
4. C22×#11758196C2semidirect
5. #16839696C2semidirect
6. #16839686C2semidirect
7. #16839685C2semidirect
8. #16839677C2semidirect
9. #16839641C2semidirect
10. #16839620C2semidirect
11. C61×#386C2semidirect
59. C22×Dic61D4semidirect
169. #386D61semidirect
171. C61#2618semidirect