Finite Group Databasebeta

← #21451542

Subgroups — #21451542

Order 7808.

932 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 932 conjugacy classes of subgroups — too many to draw. Only its 153 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×#14519750C211yesmaximal, characteristic, complemented
3C2×#14519749C212yesmaximal, complemented
4#16839675C211yesmaximal, characteristic, complemented
5#16839674C211yesmaximal, characteristic, complemented
6#16839671C212yesmaximal, complemented
7#16839670C212yesmaximal, complemented
8#16839670C211yesmaximal, characteristic, complemented
9#16839621C211yesmaximal, characteristic, complemented
10#16839620C212yesmaximal, complemented
11C61×#392C211yesmaximal, characteristic, complemented
12C2×#11758224—28no—
13C2×#11758224—24no—
14C22×Dic122C2211yescharacteristic
15C22×D244C2211yescharacteristic
16C22×C22⋊D61C2211yescharacteristic
17C22×C22⋊D61C2212yes—
18C22×C22⋊D61C2212yes—
19C22×C22⋊D61C2211yescharacteristic
20C23×Dic61C2212yes—
21C22×C4×D61C2211yescharacteristic
22#14519750—24no—
23#14519749—28no—
24C2×#11758196C2212yes—
25C2×#11758196C2211yescharacteristic
26C2×C22⋊Dic61C2212yes—
27C2×C22⋊Dic61C2212yes—
28C2×#11758198C2212yes—
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2212yes—
31#14519684C2212yes—
32#14519684C2212yes—
33#14519684C2211yescharacteristic
34C22×D4×C61C2211yescharacteristic
35C22×D4×C61C2212yes—
36C2×C22⋊C4×C61C2211yescharacteristic
37C2×C22⋊C4×C61C2212yes—
38#95×C61C2211yescharacteristic
39C24×C61C2311yescharacteristic
40C24×C61C2312yes—
41C23×D61C2311yescharacteristic
42C23×D61C2311yescharacteristic
43C2×D4×C61—24no—
44C2×D4×C61—24no—
45C2×D4×C61—22no—
46C2×D4×C61—42no—
47C2×D4×C61—42no—
48C22×C4×C61C2311yescharacteristic
49C22×C4×C61C2312yes—
50C22×C4×C61C2311yescharacteristic
51C2×C22⋊D61—24no—
52C2×C22⋊D61—24no—
53C2×C22⋊D61—24no—
54C2×C22⋊D61—22no—
55C2×C22⋊D61—24no—
56C2×C22⋊D61—24no—
57C2×C22⋊D61—22no—
58C2×C22⋊D61—42no—
59C2×C22⋊D61—42no—
60C2×C22⋊D61—42no—
61C22×Dic61—24no—
62C22×Dic61—24no—
63C22×Dic61D418yescomplemented
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2312yes—
66C22×Dic61C2312yes—
67C22×Dic61C2311yescharacteristic
68#11758224—232no—
69C2×D244—22no—
70C2×D244—42no—
71C2×C4×D61—24no—
72C2×C4×D61D414yescomplemented
73C2×Dic122—22no—
74C2×Dic122—24no—
75C22⋊C4×C61—22no—
76C22⋊C4×C61—42no—
77C22⋊Dic61—24no—
78C22⋊Dic61—42no—
79#11758198—22no—
80#11758198—24no—
81#11758198—42no—
82#11758196—24no—
83#11758196—22no—
84C23×C61—22no—
85C23×C61—22no—
86C23×C61—22no—
87C23×C61—22no—
88C23×C61—22no—
89C23×C61—22no—
90C23×C61—22no—
91C23×C61—21no—
92C23×C61—22no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61C2×D414yes—
96C23×C61C2411yescharacteristic
97C22×D61—22no—
98C22×D61—21no—
99C22×D61—22no—
100C22×D61—21no—
101C22×D61—21no—
102C22×D61—22no—
103C22×D61—22no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61C2×D412yes—
107D4×C61—28no—
108D4×C61—48no—
109C2×C4×C61—22no—
110C2×C4×C61—22no—
111C2×C4×C61—21no—
112C2×C4×C61—22no—
113C2×C4×C61—22no—
114C2×C4×C61—22no—
115C2×C4×C61C2×D412yes—
116C22⋊D61—216no—
117C22⋊D61—44no—
118C22⋊D61—48no—
119C22⋊D61—44no—
120C2×Dic61—22no—
121C2×Dic61—22no—
122C2×Dic61—216no—
123C2×Dic61—21no—
124C2×Dic61—22no—
125C2×Dic61—22no—
126C2×Dic61—22no—
127C2×Dic61—22no—
128C2×Dic61C2×D414yes—
129C2×Dic61C2×D414yes—
130C2×Dic61C2×D412yes—
131D244—44no—
132C4×D61—28no—
133Dic122—28no—
134C22×C61—24no—
135C22×C61—24no—
136C22×C61—24no—
137C22×C61—42no—
138C22×C61—42no—
139C22×C61—42no—
140C22×C61—42no—
141C22×C61—41no—
142C22×C61—41no—
143C22×C61—42no—
144C22×C61—42no—
145C22×C61—41no—
146C22×C61C22×D411yescharacteristic
147C22×C61C22×D412yes—
148C22×C61H(5,𝔽2)12yes—
149C22×C61H(5,𝔽2)11yescharacteristic
150C22×C612−1+411yescharacteristic
151C2×D61—22no—
152C2×D61—22no—
153C2×D61—22no—
154C2×D61—42no—
155C2×D61—42no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—42no—
159C2×D61—42no—
160C2×D61—41no—
161C4×C61—22no—
162C4×C61—41no—
163C4×C61—42no—
164Dic61—24no—
165Dic61—41no—
166Dic61—42no—
167Dic61#12014yes—
168#2615—611nomaximal, Sylow
169C2×C61—44no—
170C2×C61—81no—
171C2×C61C2×#12011yescharacteristic
172C2×C61#53511yescharacteristic
173C2×C61#53512yes—
174C2×C61#53712yes—
175C2×C61#53711yescharacteristic
176D61—42no—
177D61—81no—
178C22×#41—611no—
179C2×#121—612no—
180C2×#121—611no—
181#393—611no—
182#393—611no—
183#392—612no—
184#392—611no—
185#392—612no—
186#392D6111yescharacteristic, complemented
187#380—612no—
188#380—611no—
189C61#261511yescharacteristic, complemented, Sylow
190C2×#41—1228no—
191C2×#41—1224no—
192C22×Q8—611no—
193C22×D4—611no—
194C22×D4—612no—
195C22×D4—611no—
196C22×D4—612no—
197C22×D4—611no—
198C22×D4C2×D6111yescharacteristic
199C22×D4C2×D6112yes—
200C23×C4—612no—
201C23×C4—611no—
202#121—1224no—
203#121—1228no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—612no—
206C2×C22⋊C4—612no—
207C2×C22⋊C4—612no—
208C2×C22⋊C4—611no—
209C2×C22⋊C4—612no—
210C2×C22⋊C4—612no—
211C2×C22⋊C4C2×D6111yescharacteristic
212C2×C22⋊C4C2×D6112yes—
213#95—612no—
214#95—612no—
215#95—611no—
216#95C2×D6111yescharacteristic
217C24—611no—
218C24—611no—
219C24C22×D6111yescharacteristic
220C24C22×D6112yes—
221#41—12232no—
222C2×Q8—1224no—
223C2×Q8—1222no—
224C2×D4—24no—
225C2×D4—24no—
226C2×D4—22no—
227C2×D4—42no—
228C2×D4—42no—
229C2×D4—1222no—
230C2×D4—1224no—
231C2×D4—1222no—
232C2×D4—1224no—
233C2×D4—1224no—
234C2×D4—1224no—
235C2×D4—1222no—
236C2×D4—1224no—
237C2×D4—2442no—
238C2×D4—2442no—
239C2×D4—2442no—
240C2×D4—2442no—
241C22×C4—611no—
242C22×C4—618no—
243C22×C4—612no—
244C22×C4—614no—
245C22×C4—612no—
246C22×C4—611no—
247C22×C4—1224no—
248C22×C4—1224no—
249C22×C4—1224no—
250C22×C4C22×D6111yescharacteristic
251C22×C4C22×D6112yes—
252C22×C4C22×D6111yescharacteristic
253C4⋊C4—1222no—
254C4⋊C4—1224no—
255C22⋊C4—22no—
256C22⋊C4—42no—
257C22⋊C4—1224no—
258C22⋊C4—1224no—
259C22⋊C4—1222no—
260C22⋊C4—2442no—
261C22⋊C4—2442no—
262C23—22no—
263C23—22no—
264C23—22no—
265C23—22no—
266C23—22no—
267C23—22no—
268C23—21no—
269C23—22no—
270C23—21no—
271C23—22no—
272C23—21no—
273C23—612no—
274C23—1222no—
275C23—1221no—
276C23—1222no—
277C23—1221no—
278C23—1221no—
279C23—1222no—
280C23—1222no—
281C23—1221no—
282C23—1221no—
283C23D4×D6114yes—
284C23C23×D6111yescharacteristic
285Q8—1228no—
286D4—28no—
287D4—48no—
288D4—12216no—
289D4—2444no—
290D4—2444no—
291D4—2448no—
292D4—2444no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—612no—
300C2×C4—614no—
301C2×C4—614no—
302C2×C4—1228no—
303C2×C4—12216no—
304C2×C4—1222no—
305C2×C4—1222no—
306C2×C4—1221no—
307C2×C4—1222no—
308C2×C4—1222no—
309C2×C4—1222no—
310C2×C4—1222no—
311C2×C4D4×D6112yes—
312C22—24no—
313C22—24no—
314C22—24no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—42no—
319C22—41no—
320C22—41no—
321C22—42no—
322C22—42no—
323C22—41no—
324C22—1222no—
325C22—1222no—
326C22—1222no—
327C22—2441no—
328C22—2441no—
329C22—2442no—
330C22—2442no—
331C22—2441no—
332C22—2442no—
333C22—2442no—
334C22C2×D4×D6111yescharacteristic
335C22C2×D4×D6112yes—
336C22#1451982212yes—
337C22#1451982211yescharacteristic
338C22#1451982411yescharacteristic
339C4—22no—
340C4—41no—
341C4—42no—
342C4—614no—
343C4—1224no—
344C4—2441no—
345C4—2442no—
346C2—44no—
347C2—81no—
348C2—4881no—
349C2—2442no—
350C2#120×D6111yescharacteristic
351C2#1684032511yescharacteristic
352C2#1684032712yes—
353C2#1684033912yes—
354C2#1684034111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#392C2
hypercenter#392D61
hypocenterC61#2615
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×#11758224C2semidirect
2. C2×#14519750C2semidirect
3. C2×#14519749C2semidirect
4. #16839675C2semidirect
5. #16839674C2semidirect
6. #16839671C2semidirect
7. #16839670C2semidirect
8. #16839670C2semidirect
9. #16839621C2semidirect
10. #16839620C2semidirect
11. C61×#392C2semidirect
63. C22×Dic61D4semidirect
72. C2×C4×D61D4semidirect
186. #392D61semidirect
189. C61#2615semidirect