Finite Group Databasebeta

← #21448968

Subgroups — #21448968

Order 7808.

512 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519759C211yesmaximal, characteristic
2#16839662C211yesmaximal, characteristic
3#16839658C211yesmaximal, characteristic, complemented
4#16839657C211yesmaximal, characteristic, complemented
5#16839655C211yesmaximal, characteristic, complemented
6#16839652C211yesmaximal, characteristic, complemented
7#16839651C211yesmaximal, characteristic, complemented
8#16839650C211yesmaximal, characteristic, complemented
9#16839649C211yesmaximal, characteristic, complemented
10#16839647C211yesmaximal, characteristic, complemented
11#16839641C211yesmaximal, characteristic
12#16839635C211yesmaximal, characteristic, complemented
13#16839621C211yesmaximal, characteristic, complemented
14#16839619C211yesmaximal, characteristic, complemented
15C61×#385C211yesmaximal, characteristic, complemented
16C22×C22⋊D61C2211yescharacteristic
17C22×C4×D61C2211yescharacteristic
18#14519759C418yescomplemented
19C2×C4⋊Dic61C2211yescharacteristic
20C2×C4⋊Dic61C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×C22⋊Dic61C2211yescharacteristic
27C2×C22⋊Dic61C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×C4×Dic61C2211yescharacteristic
35C2×C4×Dic61C2211yescharacteristic
36C2×C4×Dic61C2211yescharacteristic
37#14519684C2211yescharacteristic
38#14519684C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45C23×C4×C61C2211yescharacteristic
46C2×C4⋊C4×C61C2211yescharacteristic
47C2×C4⋊C4×C61C2211yescharacteristic
48C2×C22⋊C4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50#95×C61C2211yescharacteristic
51#95×C61C2211yescharacteristic
52C24×C61C2311yescharacteristic
53C23×D61C2311yescharacteristic
54C22×C4×C61—41no—
55C22×C4×C61—41no—
56C22×C4×C61—41no—
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61—41no—
64C2×C22⋊D61—41no—
65C2×C22⋊D61C2×C414yes—
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C22×Dic61C2311yescharacteristic
70C22×Dic61C2311yescharacteristic
71C22×Dic61C2311yescharacteristic
72C22×Dic61C2311yescharacteristic
73C2×C4×D61—41no—
74C2×C4×D61—41no—
75C2×C4×D61C2×C414yescomplemented
76C4⋊C4×C61—41no—
77C4⋊C4×C61—41no—
78C22⋊C4×C61—41no—
79C22⋊C4×C61C2×C414yes—
80C22⋊Dic61—41no—
81C22⋊Dic61—41no—
82C22⋊Dic61C2×C414yes—
83#11758198—41no—
84#11758198—41no—
85#11758198—41no—
86#11758198—41no—
87#11758198C2×C414yescomplemented
88C4⋊Dic61—41no—
89C4⋊Dic61C2×C414yescomplemented
90#11758196—41no—
91#11758196—41no—
92#11758196—41no—
93#11758196—41no—
94#11758196C2×C414yescomplemented
95C4×Dic61—41no—
96C4×Dic61—41no—
97C4×Dic61—41no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61C22×C412yes—
105C23×C61C2411yescharacteristic
106C22×D61—21no—
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—21no—
111C22×D61—21no—
112C22×D61C22×C412yes—
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×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—44no—
130C2×C4×C61C22×C412yes—
131C2×C4×C61C22×C412yes—
132C22⋊D61—44no—
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×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61C22×C412yes—
152C2×Dic61C22×C412yes—
153C2×Dic61C22×C412yes—
154C4×D61—44no—
155C22×C61—22no—
156C22×C61—22no—
157C22×C61—22no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61C23×C411yescharacteristic
163C22×C61H(5,𝔽2)11yescharacteristic
164C22×C61H(5,𝔽2)11yescharacteristic
165C22×C61H(5,𝔽2)11yescharacteristic
166C22×C61H(5,𝔽2)11yescharacteristic
167C22×C612−1+411yescharacteristic
168C22×C612−1+411yescharacteristic
169C2×D61—22no—
170C2×D61—22no—
171C2×D61—22no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—41no—
176C4×C61—22no—
177C4×C61—22no—
178C4×C61—41no—
179C4×C61—41no—
180C4×C61—41no—
181C4×C61—41no—
182Dic61—22no—
183Dic61—22no—
184Dic61—22no—
185Dic61—41no—
186Dic61—41no—
187Dic61—41no—
188Dic61—41no—
189#2376—611nomaximal, Sylow
190C2×C61—42no—
191C2×C61#51811yescharacteristic
192C2×C61#52011yescharacteristic
193C2×C61#52011yescharacteristic
194C2×C61#56011yescharacteristic
195C2×C61#56211yescharacteristic
196C2×C61#56211yescharacteristic
197C2×C61#56311yescharacteristic
198D61—42no—
199C2×#123—611no—
200#390—611no—
201#389—611no—
202#389—611no—
203#388—611no—
204#388—611no—
205#388—611no—
206#388—611no—
207#387—611no—
208#387—611no—
209#386—611no—
210#385—611no—
211#385D6111yescharacteristic, complemented
212#380—611no—
213#380—611no—
214C61#237611yescharacteristic, complemented, Sylow
215C22×D4—611no—
216C23×C4—611no—
217C23×C4C2×D6111yescharacteristic
218#123—618no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4C2×D6111yescharacteristic
227C2×C4⋊C4C2×D6111yescharacteristic
228C2×C22⋊C4—611no—
229C2×C22⋊C4—611no—
230C2×C22⋊C4—611no—
231C2×C22⋊C4—611no—
232C2×C22⋊C4—611no—
233C2×C22⋊C4—611no—
234C2×C22⋊C4—611no—
235C2×C22⋊C4—611no—
236C2×C22⋊C4C2×D6111yescharacteristic
237C2×C22⋊C4C2×D6111yescharacteristic
238C2×C42—611no—
239C2×C42—611no—
240C2×C42—611no—
241#95—611no—
242#95—611no—
243#95—611no—
244#95—611no—
245#95—611no—
246#95—611no—
247#95—611no—
248#95—611no—
249#95C2×D6111yescharacteristic
250#95C2×D6111yescharacteristic
251C24—611no—
252C24C22×D6111yescharacteristic
253C2×D4—614no—
254C2×D4—2441no—
255C2×D4—2441no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—614no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—2441no—
268C22×C4—2441no—
269C22×C4C22×D6111yescharacteristic
270C22×C4C22×D6111yescharacteristic
271C22×C4C22×D6111yescharacteristic
272C22×C4C22×D6111yescharacteristic
273C22×C4C22×D6111yescharacteristic
274C22×C4C22×D6111yescharacteristic
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—614no—
278C4⋊C4—614no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C4⋊C4—2441no—
283C4⋊C4—2441no—
284C22⋊C4—41no—
285C22⋊C4—614no—
286C22⋊C4—614no—
287C22⋊C4—2441no—
288C22⋊C4—2441no—
289C22⋊C4—2441no—
290C22⋊C4—2441no—
291C22⋊C4—2441no—
292C22⋊C4—2441no—
293C22⋊C4C4×D6114yes—
294C42—2441no—
295C42—2441no—
296C42—2441no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—612no—
304C23—1221no—
305C23—1221no—
306C23—1221no—
307C23—1221no—
308C23—1221no—
309C23—1221no—
310C23C2×C4×D6112yes—
311C23C23×D6111yescharacteristic
312D4—2444no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—44no—
330C2×C4—612no—
331C2×C4—612no—
332C2×C4—612no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—2444no—
352C2×C4C2×C4×D6112yes—
353C2×C4C2×C4×D6112yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—1222no—
362C22—1222no—
363C22—1222no—
364C22—2441no—
365C22—2441no—
366C22—2441no—
367C22—2441no—
368C22C22×C4×D6111yescharacteristic
369C22#1451982211yescharacteristic
370C22#1451982211yescharacteristic
371C22#1451982211yescharacteristic
372C22#1451982311yescharacteristic
373C22#1451982411yescharacteristic
374C22#1451982511yescharacteristic
375C4—22no—
376C4—22no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—1222no—
382C4—1222no—
383C4—1222no—
384C4—2441no—
385C4—2441no—
386C4—2441no—
387C4—2441no—
388C2—42no—
389C2—2442no—
390C2#1684023411yescharacteristic
391C2#1684024111yescharacteristic
392C2#1684024311yescharacteristic
393C2#1684050111yescharacteristic
394C2#1684050811yescharacteristic
395C2#1684050911yescharacteristic
396C2#1684051311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#385C2
socleC23×C61C24
hypercenter#385D61
hypocenterC61#2376
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. #16839658C2semidirect
4. #16839657C2semidirect
5. #16839655C2semidirect
6. #16839652C2semidirect
7. #16839651C2semidirect
8. #16839650C2semidirect
9. #16839649C2semidirect
10. #16839647C2semidirect
12. #16839635C2semidirect
13. #16839621C2semidirect
14. #16839619C2semidirect
15. C61×#385C2semidirect
18. #14519759C4semidirect
75. C2×C4×D61C2×C4semidirect
87. #11758198C2×C4semidirect
89. C4⋊Dic61C2×C4semidirect
94. #11758196C2×C4semidirect
211. #385D61semidirect
214. C61#2376semidirect