Finite Group Databasebeta

← #21452270

Subgroups — #21452270

Order 7808.

456 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519770C211yesmaximal, characteristic
2C2×#14519756C211yesmaximal, characteristic
3#16839703C211yesmaximal, characteristic, complemented
4#16839703C211yesmaximal, characteristic, complemented
5#16839696C211yesmaximal, characteristic, complemented
6#16839690C211yesmaximal, characteristic
7#16839687C211yesmaximal, characteristic
8#16839683C211yesmaximal, characteristic, complemented
9#16839666C211yesmaximal, characteristic, complemented
10#16839659C211yesmaximal, characteristic, complemented
11#16839659C211yesmaximal, characteristic, complemented
12#16839650C211yesmaximal, characteristic
13#16839649C211yesmaximal, characteristic, complemented
14#16839635C211yesmaximal, characteristic
15C61×#381C211yesmaximal, characteristic
16C22×Dic122C2211yescharacteristic
17#14519770—24no—
18#14519756—24no—
19C2×C4⋊Dic61C2211yescharacteristic
20C2×C4⋊Dic61C2211yescharacteristic
21C2×C4⋊Dic61C2211yescharacteristic
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×#11758196C2211yescharacteristic
29C2×#11758196C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic
32C2×C22⋊Dic61C2211yescharacteristic
33C2×C22⋊Dic61C2211yescharacteristic
34C2×C4×Dic61C2211yescharacteristic
35C2×C4×Dic61C2211yescharacteristic
36#14519684C2211yescharacteristic
37#14519684C2211yescharacteristic
38#14519684C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46C23×C4×C61C2211yescharacteristic
47C2×C22⋊C4×C61C2211yescharacteristic
48C2×C22⋊C4×C61C2211yescharacteristic
49#95×C61C2211yescharacteristic
50#95×C61C2211yescharacteristic
51#95×C61C2211yescharacteristic
52#95×C61C2211yescharacteristic
53C24×C61C2311yescharacteristic
54C22×C4×C61—22no—
55C22×C4×C61—22no—
56C22×C4×C61—41no—
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C22×Dic61C2311yescharacteristic
70C22×Dic61C2311yescharacteristic
71C2×Dic122—22no—
72C2×Dic122—22no—
73C2×Dic122—41no—
74C22⋊C4×C61—22no—
75C22⋊C4×C61—41no—
76C22⋊Dic61—22no—
77C22⋊Dic61—22no—
78C22⋊Dic61—22no—
79C22⋊Dic61D414yes—
80C4⋊Dic61—22no—
81C4⋊Dic61—22no—
82C4⋊Dic61—41no—
83#11758196—22no—
84#11758196—22no—
85#11758196—22no—
86#11758196—22no—
87#11758196—22no—
88#11758196—22no—
89#11758196—22no—
90#11758196—41no—
91C4×Dic61—22no—
92C4×Dic61—41no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61C2×D412yes—
100C23×C61C2411yescharacteristic
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—44no—
119C2×C4×C61#4112yes—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61C2×D412yes—
142C2×Dic61C2×D412yes—
143C2×Dic61#4112yes—
144Dic122—44no—
145C22×C61—22no—
146C22×C61—22no—
147C22×C61—22no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61C22×D411yescharacteristic
153C22×C61C2×#4111yescharacteristic
154C22×C61C2×#4111yescharacteristic
155C22×C61H(5,𝔽2)11yescharacteristic
156C22×C612−1+411yescharacteristic
157C22×C612−1+411yescharacteristic
158C22×C612−1+411yescharacteristic
159C4×C61—22no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61—41no—
165Dic61—22no—
166Dic61—22no—
167Dic61—22no—
168Dic61—41no—
169Dic61—41no—
170Dic61—41no—
171Dic61—41no—
172Dic61—41no—
173#2689—611nomaximal, Sylow
174C2×C61—42no—
175C2×C61#53611yescharacteristic
176C2×C61#53911yescharacteristic
177C2×C61#54111yescharacteristic
178C2×C61#54611yescharacteristic
179C2×C61#54711yescharacteristic
180C2×C61#55611yescharacteristic
181C2×C61#56311yescharacteristic
182C2×#126—611no—
183C2×C22⋊Q8—611no—
184#400—611no—
185#400—611no—
186#398—611no—
187#397—611no—
188#397—611no—
189#395—611no—
190#391—611no—
191#389—611no—
192#389—611no—
193#388—611no—
194#387—611no—
195#385—611no—
196#381D6111yescharacteristic
197C61#268911yescharacteristic, complemented, Sylow
198C22×Q8—611no—
199C23×C4C2×D6111yescharacteristic
200#126—1224no—
201C22⋊Q8—1224no—
202C2×C4⋊C4—611no—
203C2×C4⋊C4—611no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—611no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—611no—
213C2×C22⋊C4—611no—
214C2×C22⋊C4—611no—
215C2×C22⋊C4—611no—
216C2×C22⋊C4—611no—
217C2×C22⋊C4C2×D6111yescharacteristic
218C2×C22⋊C4C2×D6111yescharacteristic
219C2×C42—611no—
220C2×C42—611no—
221#95—611no—
222#95—611no—
223#95—611no—
224#95—611no—
225#95—611no—
226#95—611no—
227#95—611no—
228#95—611no—
229#95—611no—
230#95—611no—
231#95C2×D6111yescharacteristic
232#95C2×D6111yescharacteristic
233#95C2×D6111yescharacteristic
234#95C2×D6111yescharacteristic
235C24C22×D6111yescharacteristic
236C2×Q8—1222no—
237C2×Q8—1222no—
238C2×Q8—2441no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—41no—
242C22×C4—611no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4C22×D6111yescharacteristic
251C22×C4C22×D6111yescharacteristic
252C22×C4C22×D6111yescharacteristic
253C22×C4C22×D6111yescharacteristic
254C22×C4C22×D6111yescharacteristic
255C22×C4C22×D6111yescharacteristic
256C4⋊C4—1222no—
257C4⋊C4—1222no—
258C4⋊C4—1222no—
259C4⋊C4—1222no—
260C4⋊C4—1222no—
261C4⋊C4—1222no—
262C4⋊C4—1222no—
263C4⋊C4—1222no—
264C4⋊C4—1222no—
265C4⋊C4—2441no—
266C4⋊C4—2441no—
267C22⋊C4—22no—
268C22⋊C4—41no—
269C22⋊C4—614no—
270C22⋊C4—1222no—
271C22⋊C4—1222no—
272C22⋊C4—1222no—
273C42—1222no—
274C42—2441no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23D4×D6112yes—
282C23C23×D6111yescharacteristic
283Q8—2444no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—44no—
302C2×C4—612no—
303C2×C4—612no—
304C2×C4—612no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4#1175822212yes—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22C2×D4×D6111yescharacteristic
335C22#41×D6111yescharacteristic
336C22C2×#1175822211yescharacteristic
337C22#1451982211yescharacteristic
338C22#1451982411yescharacteristic
339C22#1451982411yescharacteristic
340C22#1451982411yescharacteristic
341C4—22no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—1222no—
348C4—1222no—
349C4—1222no—
350C4—2441no—
351C4—2441no—
352C4—2441no—
353C4—2441no—
354C4—2441no—
355C2—42no—
356C2#1684033411yescharacteristic
357C2#1684035511yescharacteristic
358C2#1684037411yescharacteristic
359C2#1684040211yescharacteristic
360C2#1684041011yescharacteristic
361C2#1684048011yescharacteristic
362C2#1684051511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#381C2
hypercenter#381D61
hypocenterC61#2689
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
3. #16839703C2semidirect
4. #16839703C2semidirect
5. #16839696C2semidirect
8. #16839683C2semidirect
9. #16839666C2semidirect
10. #16839659C2semidirect
11. #16839659C2semidirect
13. #16839649C2semidirect
197. C61#2689semidirect