Finite Group Databasebeta

← #21452697

Subgroups — #21452697

Order 7808.

472 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519767C211yesmaximal, characteristic, complemented
2C2×#14519757C211yesmaximal, characteristic
3#16839702C211yesmaximal, characteristic, complemented
4#16839699C211yesmaximal, characteristic
5#16839694C211yesmaximal, characteristic, complemented
6#16839684C211yesmaximal, characteristic
7#16839683C211yesmaximal, characteristic, complemented
8#16839683C211yesmaximal, characteristic, complemented
9#16839661C211yesmaximal, characteristic, complemented
10#16839654C211yesmaximal, characteristic
11#16839653C211yesmaximal, characteristic
12#16839636C211yesmaximal, characteristic
13#16839636C211yesmaximal, characteristic
14#16839632C211yesmaximal, characteristic, complemented
15C61×#387C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C22×C4×D61C2211yescharacteristic
18#14519767—24no—
19#14519757—24no—
20C2×C4⋊Dic61C2211yescharacteristic
21C2×C4⋊Dic61C2211yescharacteristic
22C2×C4⋊Dic61C2211yescharacteristic
23C2×C4⋊Dic61C2211yescharacteristic
24C2×C4⋊Dic61C2211yescharacteristic
25C2×C4⋊Dic61C2211yescharacteristic
26C2×C4⋊Dic61C2211yescharacteristic
27C2×C4⋊Dic61C2211yescharacteristic
28C2×C4⋊Dic61C2211yescharacteristic
29C2×#11758196C2211yescharacteristic
30C2×#11758196C2211yescharacteristic
31C2×#11758196C2211yescharacteristic
32C2×#11758196C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×C4×Dic61C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46C2×C4⋊C4×C61C2211yescharacteristic
47C2×C4⋊C4×C61C2211yescharacteristic
48C2×C42×C61C2211yescharacteristic
49#95×C61C2211yescharacteristic
50#95×C61C2211yescharacteristic
51#95×C61C2211yescharacteristic
52#95×C61C2211yescharacteristic
53C23×D61C2311yescharacteristic
54C22×C4×C61C2311yescharacteristic
55C22×C4×C61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×Dic61C2311yescharacteristic
62C22×Dic61C2311yescharacteristic
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C2×C4×D61—22no—
69C2×C4×D61—41no—
70C2×C4×D61—41no—
71C2×Dic122—22no—
72C2×Dic122—41no—
73C2×Dic122—41no—
74C4⋊C4×C61—22no—
75C4⋊C4×C61D414yes—
76C42×C61—22no—
77#11758198—22no—
78#11758198—22no—
79#11758198—22no—
80#11758198—41no—
81#11758198—41no—
82#11758198Q814yescomplemented
83C4⋊Dic61—22no—
84C4⋊Dic61—22no—
85C4⋊Dic61—22no—
86C4⋊Dic61—41no—
87C4⋊Dic61—41no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92#11758196—22no—
93#11758196—22no—
94#11758196—22no—
95#11758196—22no—
96C4×Dic61—22no—
97C23×C61C2411yescharacteristic
98C22×D61—21no—
99C22×D61—21no—
100C22×D61—21no—
101C22×D61—21no—
102C22×D61—21no—
103C22×D61—21no—
104C22×D61C2×Q812yes—
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×C61—21no—
121C2×C4×C61C2×D412yes—
122C2×C4×C61C2×D412yes—
123C2×C4×C61C2×D412yes—
124C2×C4×C61C2×Q812yes—
125C2×C4×C61#4112yes—
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—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61C2×Q812yes—
147C4×D61—44no—
148Dic122—44no—
149C22×C61C22×D411yescharacteristic
150C22×C61C22×Q811yescharacteristic
151C22×C61C2×#4111yescharacteristic
152C22×C61H(5,𝔽2)11yescharacteristic
153C22×C61H(5,𝔽2)11yescharacteristic
154C22×C612−1+411yescharacteristic
155C22×C612−1+411yescharacteristic
156C2×D61—22no—
157C2×D61—22no—
158C2×D61—22no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—41no—
163C4×C61—22no—
164C4×C61—22no—
165C4×C61—22no—
166C4×C61—22no—
167C4×C61—22no—
168C4×C61—41no—
169C4×C61—41no—
170Dic61—22no—
171Dic61—41no—
172Dic61—41no—
173Dic61—41no—
174Dic61—41no—
175Dic61—41no—
176Dic61—41no—
177#2720—611nomaximal, Sylow
178C2×C61#53511yescharacteristic
179C2×C61#53911yescharacteristic
180C2×C61#54411yescharacteristic
181C2×C61#54711yescharacteristic
182C2×C61D4×Q811yescharacteristic
183C2×C61#55411yescharacteristic
184C2×C61#56311yescharacteristic
185D61—42no—
186C2×#125—611no—
187C2×C22⋊Q8—611no—
188#400—611no—
189#399—611no—
190#398—611no—
191#396—611no—
192#395—611no—
193#395—611no—
194#389—611no—
195#388—611no—
196#388—611no—
197#387D6111yescharacteristic, complemented
198#385—611no—
199#385—611no—
200#384—611no—
201C61#272011yescharacteristic, complemented, Sylow
202C22×Q8—611no—
203C23×C4—611no—
204#125—1224no—
205C22⋊Q8—1224no—
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×C4⋊C4—611no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4C2×D6111yescharacteristic
220C2×C4⋊C4C2×D6111yescharacteristic
221C2×C22⋊C4—611no—
222C2×C22⋊C4—611no—
223C2×C22⋊C4—611no—
224C2×C22⋊C4—611no—
225C2×C22⋊C4—611no—
226C2×C22⋊C4—611no—
227C2×C42—611no—
228C2×C42C2×D6111yescharacteristic
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—1222no—
241C2×Q8—2441no—
242C2×Q8—2441no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—1222no—
251C22×C4—2441no—
252C22×C4—2441no—
253C22×C4C22×D6111yescharacteristic
254C22×C4C22×D6111yescharacteristic
255C22×C4C22×D6111yescharacteristic
256C22×C4C22×D6111yescharacteristic
257C22×C4C22×D6111yescharacteristic
258C22×C4C22×D6111yescharacteristic
259C22×C4C22×D6111yescharacteristic
260C4⋊C4—22no—
261C4⋊C4—1222no—
262C4⋊C4—1222no—
263C4⋊C4—1222no—
264C4⋊C4—1222no—
265C4⋊C4—1222no—
266C4⋊C4—1222no—
267C4⋊C4—1222no—
268C4⋊C4—2441no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C4⋊C4D24414yes—
275C22⋊C4—614no—
276C22⋊C4—1222no—
277C22⋊C4—1222no—
278C22⋊C4—1222no—
279C22⋊C4—2441no—
280C22⋊C4—2441no—
281C42—22no—
282C42—1222no—
283C23—612no—
284C23—1221no—
285C23—1221no—
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—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—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—2444no—
330C2×C4C2×D24412yes—
331C2×C4C2×D24412yes—
332C2×C4C2×D24412yes—
333C2×C4#1175822412yes—
334C2×C4Q8×D6112yes—
335C22—1222no—
336C22—1222no—
337C22—1222no—
338C22—2441no—
339C22—2441no—
340C22—2441no—
341C22—2441no—
342C22C22×D24411yescharacteristic
343C22C2×Q8×D6111yescharacteristic
344C22C2×#1175822411yescharacteristic
345C22#1451982311yescharacteristic
346C22#1451982311yescharacteristic
347C22#1451982411yescharacteristic
348C22#1451982411yescharacteristic
349C4—22no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—41no—
355C4—41no—
356C4—1222no—
357C4—2441no—
358C4—2441no—
359C4—2441no—
360C4—2441no—
361C4—2441no—
362C4—2441no—
363C2—2442no—
364C2#1684033111yescharacteristic
365C2#1684035611yescharacteristic
366C2#1684039211yescharacteristic
367C2#1684041611yescharacteristic
368C2Q8×D24411yescharacteristic
369C2#1684047011yescharacteristic
370C2#1684051411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#387C2
hypercenter#387D61
hypocenterC61#2720
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. C2×#14519767C2semidirect
3. #16839702C2semidirect
5. #16839694C2semidirect
7. #16839683C2semidirect
8. #16839683C2semidirect
9. #16839661C2semidirect
14. #16839632C2semidirect
15. C61×#387C2semidirect
82. #11758198Q8semidirect
197. #387D61semidirect
201. C61#2720semidirect