Finite Group Databasebeta

← #21448901

Subgroups — #21448901

Order 7808.

548 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519757C211yesmaximal, characteristic
2#16839666C211yesmaximal, characteristic, complemented
3#16839666C211yesmaximal, characteristic, complemented
4#16839648C211yesmaximal, characteristic, complemented
5#16839647C211yesmaximal, characteristic, complemented
6#16839645C211yesmaximal, characteristic, complemented
7#16839636C211yesmaximal, characteristic
8#16839633C211yesmaximal, characteristic
9C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
10C4×C4⋊Dic61C211yesmaximal, characteristic, complemented
11C4×#11758198C211yesmaximal, characteristic
12#16839609C211yesmaximal, characteristic
13#16839609C211yesmaximal, characteristic
14#95×D61C211yesmaximal, characteristic
15C61×#387C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C22×C4×D61C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19C22×C4×D61C2211yescharacteristic
20#14519757C418yescomplemented
21C2×C4⋊Dic61C2211yescharacteristic
22C2×C4⋊Dic61C2211yescharacteristic
23C2×C4⋊Dic61C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758198C2211yescharacteristic
27C2×#11758198C2211yescharacteristic
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×C4×Dic61C2211yescharacteristic
31C2×C4×Dic61C2211yescharacteristic
32C2×C4×Dic61C2211yescharacteristic
33C2×C4×Dic61C2211yescharacteristic
34C2×C4×Dic61C2211yescharacteristic
35#14519684C2211yescharacteristic
36#14519684C2211yescharacteristic
37#14519684C2211yescharacteristic
38#14519684C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45C2×C4⋊C4×C61C2211yescharacteristic
46C2×C4⋊C4×C61C2211yescharacteristic
47C2×C42×C61C2211yescharacteristic
48#95×C61C2211yescharacteristic
49#95×C61C2211yescharacteristic
50#95×C61C2211yescharacteristic
51#95×C61C2211yescharacteristic
52C23×D61C2311yescharacteristic
53C22×C4×C61C2311yescharacteristic
54C22×C4×C61C2311yescharacteristic
55C22×C4×C61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×Dic61C2311yescharacteristic
61C22×Dic61C2311yescharacteristic
62C22×Dic61C2311yescharacteristic
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C2×C4×D61—22no—
68C2×C4×D61—22no—
69C2×C4×D61—22no—
70C2×C4×D61—22no—
71C2×C4×D61—41no—
72C2×C4×D61—41no—
73C2×C4×D61—41no—
74C2×C4×D61—41no—
75C2×C4×D61C2×C414yes—
76C2×Dic122—41no—
77C2×Dic122—41no—
78C2×Dic122C2×C414yescomplemented
79C4⋊C4×C61—22no—
80C4⋊C4×C61C2×C414yescomplemented
81C42×C61—22no—
82#11758198—22no—
83#11758198C2×C414yes—
84#11758198C2×C414yes—
85#11758198Q814yescomplemented
86C4⋊Dic61—22no—
87C4⋊Dic61C2×C414yescomplemented
88C4⋊Dic61C2×C414yescomplemented
89#11758196—41no—
90#11758196—41no—
91C4×Dic61—22no—
92C4×Dic61—41no—
93C4×Dic61—41no—
94C4×Dic61—41no—
95C4×Dic61—41no—
96C23×C61C2411yescharacteristic
97C22×D61—21no—
98C22×D61—21no—
99C22×D61—21no—
100C22×D61—21no—
101C22×D61C22×C412yes—
102C22×D61C2×Q812yes—
103C22×D61#4112yes—
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—21no—
119C2×C4×C61—21no—
120C2×C4×C61C22×C412yes—
121C2×C4×C61C22×C412yes—
122C2×C4×C61C22×C412yes—
123C2×C4×C61C2×Q812yes—
124C2×C4×C61#4112yes—
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×Dic61C22×C412yes—
142C2×Dic61C22×C412yes—
143C2×Dic61C22×C412yes—
144C2×Dic61C2×Q812yes—
145C2×Dic61#4112yes—
146C4×D61—44no—
147C4×D61—44no—
148C4×D61—44no—
149Dic122—44no—
150C22×C61C23×C411yescharacteristic
151C22×C61C22×Q811yescharacteristic
152C22×C61C2×#4111yescharacteristic
153C22×C61C2×#4111yescharacteristic
154C22×C61C2×#4111yescharacteristic
155C22×C61H(5,𝔽2)11yescharacteristic
156C22×C61H(5,𝔽2)11yescharacteristic
157C2×D61—22no—
158C2×D61—22no—
159C2×D61—22no—
160C2×D61—22no—
161C2×D61—22no—
162C2×D61—22no—
163C2×D61C4×Q814yes—
164C4×C61—22no—
165C4×C61—22no—
166C4×C61—22no—
167C4×C61—22no—
168C4×C61—22no—
169C4×C61—41no—
170C4×C61—41no—
171Dic61—22no—
172Dic61—22no—
173Dic61—22no—
174Dic61—22no—
175Dic61—22no—
176Dic61—41no—
177Dic61—41no—
178#2368—611nomaximal, Sylow
179C2×C61C2×C4×Q811yescharacteristic
180C2×C61C4×#4111yescharacteristic
181C2×C61#51811yescharacteristic
182C2×C61#55111yescharacteristic
183C2×C61#55111yescharacteristic
184C2×C61#55411yescharacteristic
185C2×C61#55411yescharacteristic
186D61—24no—
187C2×C22⋊Q8—611no—
188#391—611no—
189#391—611no—
190#387—611no—
191#387—611no—
192#387—611no—
193#387D6111yescharacteristic, complemented
194#385—611no—
195#385—611no—
196C4×C4⋊C4—611no—
197C4×C4⋊C4—611no—
198C4×C22⋊C4—611no—
199C4×C22⋊C4—611no—
200C4×C22⋊C4—611no—
201C2×#95—611no—
202C61#236811yescharacteristic, complemented, Sylow
203C22×Q8—611no—
204C23×C4—611no—
205C23×C4—611no—
206C23×C4—611no—
207C22⋊Q8—618no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4C2×D6111yescharacteristic
214C2×C4⋊C4C2×D6111yescharacteristic
215C2×C22⋊C4—611no—
216C2×C22⋊C4—611no—
217C2×C22⋊C4—611no—
218C2×C22⋊C4—611no—
219C2×C42—611no—
220C2×C42—611no—
221C2×C42—611no—
222C2×C42—611no—
223C2×C42—611no—
224C2×C42C2×D6111yescharacteristic
225#95—611no—
226#95—611no—
227#95—611no—
228#95—611no—
229#95—611no—
230#95—611no—
231#95—611no—
232#95—611no—
233#95—611no—
234#95—611no—
235#95C2×D6111yescharacteristic
236#95C2×D6111yescharacteristic
237#95C2×D6111yescharacteristic
238#95C2×D6111yescharacteristic
239C24—611no—
240C2×Q8—614no—
241C2×Q8—2441no—
242C2×Q8—2441no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—614no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—1222no—
252C22×C4—1222no—
253C22×C4—1222no—
254C22×C4—1222no—
255C22×C4—2441no—
256C22×C4—2441no—
257C22×C4—2441no—
258C22×C4—2441no—
259C22×C4C22×D6111yescharacteristic
260C22×C4C22×D6111yescharacteristic
261C22×C4C22×D6111yescharacteristic
262C22×C4C22×D6111yescharacteristic
263C22×C4C22×D6111yescharacteristic
264C22×C4C22×D6111yescharacteristic
265C22×C4C22×D6111yescharacteristic
266C4⋊C4—22no—
267C4⋊C4—614no—
268C4⋊C4—614no—
269C4⋊C4—1222no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C4⋊C4C4×D6114yescomplemented
273C22⋊C4—614no—
274C22⋊C4—614no—
275C22⋊C4—614no—
276C22⋊C4—1222no—
277C42—22no—
278C42—1222no—
279C42—2441no—
280C42—2441no—
281C42—2441no—
282C42—2441no—
283C23—612no—
284C23—612no—
285C23—612no—
286C23—1221no—
287C23—1221no—
288C23—1221no—
289C23—1221no—
290C23C23×D6111yescharacteristic
291Q8—2444no—
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—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—612no—
309C2×C4—612no—
310C2×C4—612no—
311C2×C4—612no—
312C2×C4—612no—
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—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—2444no—
330C2×C4—2444no—
331C2×C4—2444no—
332C2×C4C2×C4×D6112yes—
333C2×C4C2×C4×D6112yes—
334C2×C4C2×C4×D6112yes—
335C2×C4#1175822412yes—
336C2×C4Q8×D6112yes—
337C22—614no—
338C22—1222no—
339C22—1222no—
340C22—1222no—
341C22—1222no—
342C22—1222no—
343C22—1222no—
344C22C22×C4×D6111yescharacteristic
345C22C2×Q8×D6111yescharacteristic
346C22#41×D6111yescharacteristic
347C22#41×D6111yescharacteristic
348C22C2×#1175822411yescharacteristic
349C22#1451982311yescharacteristic
350C22#1451982311yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—22no—
356C4—41no—
357C4—41no—
358C4—1222no—
359C4—1222no—
360C4—1222no—
361C4—1222no—
362C4—1222no—
363C4—2441no—
364C4—2441no—
365C2—1224no—
366C2C4×Q8×D6111yescharacteristic
367C2C4×#1175822411yescharacteristic
368C2#1684023611yescharacteristic
369C2#1684043511yescharacteristic
370C2#1684043711yescharacteristic
371C2#1684046811yescharacteristic
372C2#1684047011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#387C2
socleC23×C61C24
hypercenter#387D61
hypocenterC61#2368
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #16839666C2semidirect
3. #16839666C2semidirect
4. #16839648C2semidirect
5. #16839647C2semidirect
6. #16839645C2semidirect
9. C4⋊C4×Dic61C2semidirect
10. C4×C4⋊Dic61C2semidirect
15. C61×#387C2semidirect
20. #14519757C4semidirect
78. C2×Dic122C2×C4semidirect
80. C4⋊C4×C61C2×C4semidirect
85. #11758198Q8semidirect
87. C4⋊Dic61C2×C4semidirect
88. C4⋊Dic61C2×C4semidirect
193. #387D61semidirect
202. C61#2368semidirect
272. C4⋊C4C4×D61semidirect