Finite Group Databasebeta

← #21449845

Subgroups — #21449845

Order 7808.

508 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×#14519754C211yesmaximal, characteristic
2C2×C4×Dic122C211yesmaximal, characteristic, complemented
3#16839685C211yesmaximal, characteristic
4#16839683C211yesmaximal, characteristic, complemented
5#16839682C211yesmaximal, characteristic, complemented
6#16839674C211yesmaximal, characteristic
7#16839668C211yesmaximal, characteristic, complemented
8#16839661C211yesmaximal, characteristic, complemented
9#16839655C211yesmaximal, characteristic
10#16839649C211yesmaximal, characteristic, complemented
11#16839649C211yesmaximal, characteristic, complemented
12#16839645C211yesmaximal, characteristic, complemented
13#16839637C211yesmaximal, characteristic
14C22⋊C4×Dic61C211yesmaximal, characteristic
15C61×#388C211yesmaximal, characteristic
16C22×Dic122C2211yescharacteristic
17C22×Dic122C2211yescharacteristic
18C23×Dic61C2211yescharacteristic
19#14519754—24no—
20C4×Dic122—24no—
21C2×C4⋊Dic61C2211yescharacteristic
22C2×C4⋊Dic61C2211yescharacteristic
23C2×C4⋊Dic61C2211yescharacteristic
24C2×C4⋊Dic61C2211yescharacteristic
25C2×C4⋊Dic61C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×#11758196C2211yescharacteristic
29C2×#11758196C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic
32C2×C22⋊Dic61C2211yescharacteristic
33C2×C4×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
46C2×C4⋊C4×C61C2211yescharacteristic
47C2×C22⋊C4×C61C2211yescharacteristic
48C2×C22⋊C4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C42×C61C2211yescharacteristic
51#95×C61C2211yescharacteristic
52#95×C61C2211yescharacteristic
53C24×C61C2311yescharacteristic
54C22×C4×C61C2311yescharacteristic
55C22×C4×C61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×Dic61—22no—
61C22×Dic61—22no—
62C22×Dic61—41no—
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C22×Dic61C2311yescharacteristic
70C22×Dic61C2311yescharacteristic
71C2×Dic122—22no—
72C2×Dic122—22no—
73C2×Dic122—22no—
74C2×Dic122—22no—
75C2×Dic122—22no—
76C2×Dic122—41no—
77C4⋊C4×C61—22no—
78C22⋊C4×C61—22no—
79C22⋊C4×C61—22no—
80C22⋊C4×C61Q814yescomplemented
81C42×C61—22no—
82C22⋊Dic61—22no—
83C22⋊Dic61—22no—
84C22⋊Dic61—41no—
85C4⋊Dic61—22no—
86C4⋊Dic61—22no—
87C4⋊Dic61—22no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90#11758196—22no—
91#11758196—22no—
92#11758196—22no—
93#11758196D414yes—
94C4×Dic61—22no—
95C4×Dic61—22no—
96C4×Dic61—41no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61C2×Q812yes—
104C23×C61C2411yescharacteristic
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×C61C2×D412yes—
120C2×C4×C61C2×Q812yes—
121C2×C4×C61C2×Q812yes—
122C2×C4×C61#4112yes—
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×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—44no—
144C2×Dic61C2×D412yes—
145C2×Dic61C2×D412yes—
146C2×Dic61#4112yes—
147C2×Dic61#4112yes—
148Dic122—28no—
149Dic122—44no—
150C22×C61—22no—
151C22×C61—22no—
152C22×C61—22no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61C22×D411yescharacteristic
158C22×C61C22×Q811yescharacteristic
159C22×C61C2×#4111yescharacteristic
160C22×C61C2×#4111yescharacteristic
161C22×C61C2×#4111yescharacteristic
162C22×C61H(5,𝔽2)11yescharacteristic
163C22×C612−1+411yescharacteristic
164C4×C61—22no—
165C4×C61—22no—
166C4×C61—22no—
167C4×C61—22no—
168C4×C61—41no—
169C4×C61—41no—
170Dic61—22no—
171Dic61—22no—
172Dic61—22no—
173Dic61—22no—
174Dic61—41no—
175Dic61—41no—
176Dic61—41no—
177Dic61—41no—
178#2465—611nomaximal, Sylow
179C2×C61—42no—
180C2×C61#52511yescharacteristic
181C2×C61#53311yescharacteristic
182C2×C61#54211yescharacteristic
183C2×C61#54611yescharacteristic
184C2×C61D4×Q811yescharacteristic
185C2×C61#55411yescharacteristic
186C2×C61#55611yescharacteristic
187C2×C22⋊Q8—611no—
188C2×C4×Q8—611no—
189#396—611no—
190#395—611no—
191#395—611no—
192#393—611no—
193#391—611no—
194#389—611no—
195#388—611no—
196#388D6111yescharacteristic
197#387—611no—
198#387—611no—
199#387—611no—
200#385—611no—
201C4×C22⋊C4—611no—
202C61#246511yescharacteristic, complemented, Sylow
203C22×Q8—611no—
204C22×Q8—611no—
205C23×C4—611no—
206C22⋊Q8—1224no—
207C4×Q8—1224no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4C2×D6111yescharacteristic
218C2×C22⋊C4—611no—
219C2×C22⋊C4—611no—
220C2×C22⋊C4—611no—
221C2×C22⋊C4C2×D6111yescharacteristic
222C2×C22⋊C4C2×D6111yescharacteristic
223C2×C22⋊C4C2×D6111yescharacteristic
224C2×C42—611no—
225C2×C42—611no—
226C2×C42—611no—
227C2×C42C2×D6111yescharacteristic
228#95—611no—
229#95—611no—
230#95—611no—
231#95—611no—
232#95—611no—
233#95—611no—
234#95—611no—
235#95—611no—
236#95—611no—
237#95—611no—
238#95C2×D6111yescharacteristic
239#95C2×D6111yescharacteristic
240C24C22×D6111yescharacteristic
241C2×Q8—1222no—
242C2×Q8—1222no—
243C2×Q8—1222no—
244C2×Q8—1222no—
245C2×Q8—1222no—
246C2×Q8—2441no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—1222no—
256C22×C4—1222no—
257C22×C4—2441no—
258C22×C4C22×D6111yescharacteristic
259C22×C4C22×D6111yescharacteristic
260C22×C4C22×D6111yescharacteristic
261C22×C4C22×D6111yescharacteristic
262C22×C4C22×D6111yescharacteristic
263C22×C4C22×D6111yescharacteristic
264C4⋊C4—22no—
265C4⋊C4—614no—
266C4⋊C4—1222no—
267C4⋊C4—1222no—
268C4⋊C4—1222no—
269C4⋊C4—1222no—
270C4⋊C4—1222no—
271C4⋊C4—1222no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C22⋊C4—1222no—
277C22⋊C4—1222no—
278C22⋊C4—2441no—
279C22⋊C4Dic12214yescomplemented
280C42—22no—
281C42—1222no—
282C42—1222no—
283C42—2441no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23C2×Dic12212yes—
291C23C23×D6111yescharacteristic
292Q8—1228no—
293Q8—2444no—
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—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—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—2444no—
333C2×C4C2×Dic12212yes—
334C2×C4C2×Dic12212yes—
335C2×C4D4×D6112yes—
336C2×C4#1175822412yes—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22C2×D4×D6111yescharacteristic
345C22C22×Dic12211yescharacteristic
346C22#41×D6111yescharacteristic
347C22#41×D6111yescharacteristic
348C22C2×#1175822411yescharacteristic
349C22#1451982311yescharacteristic
350C22#1451982411yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—1222no—
358C4—1222no—
359C4—1222no—
360C4—1222no—
361C4—2441no—
362C4—2441no—
363C4—2441no—
364C4—2441no—
365C2—42no—
366C2#1684027211yescharacteristic
367C2#1684031511yescharacteristic
368C2#1684037811yescharacteristic
369C2#1684040411yescharacteristic
370C2D4×Dic12211yescharacteristic
371C2#1684046911yescharacteristic
372C2#1684048111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#388C2
hypercenter#388D61
hypocenterC61#2465
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic122C2semidirect
4. #16839683C2semidirect
5. #16839682C2semidirect
7. #16839668C2semidirect
8. #16839661C2semidirect
10. #16839649C2semidirect
11. #16839649C2semidirect
12. #16839645C2semidirect
80. C22⋊C4×C61Q8semidirect
202. C61#2465semidirect
279. C22⋊C4Dic122semidirect