Finite Group Databasebeta

← #21453518

Subgroups — #21453518

Order 7808.

472 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
1#16839703C211yesmaximal, characteristic, complemented
2#16839685C211yesmaximal, characteristic, complemented
3#16839684C211yesmaximal, characteristic, complemented
4#16839683C211yesmaximal, characteristic, complemented
5#16839675C211yesmaximal, characteristic, complemented
6#16839674C211yesmaximal, characteristic, complemented
7#16839662C211yesmaximal, characteristic
8#16839648C211yesmaximal, characteristic, complemented
9#16839643C211yesmaximal, characteristic, complemented
10#16839641C211yesmaximal, characteristic
11#16839638C211yesmaximal, characteristic
12#16839636C211yesmaximal, characteristic, complemented
13#16839622C211yesmaximal, characteristic, complemented
14#16839619C211yesmaximal, characteristic, complemented
15C61×#385C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19C2×C4⋊Dic61C2211yescharacteristic
20C2×C4⋊Dic61C2211yescharacteristic
21C2×C4⋊Dic61C2211yescharacteristic
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×C22⋊Dic61C2211yescharacteristic
26C2×C22⋊Dic61C2211yescharacteristic
27C2×C22⋊Dic61C2211yescharacteristic
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×C4×Dic61C2211yescharacteristic
34#14519684C2211yescharacteristic
35#14519684C2211yescharacteristic
36#14519684C2211yescharacteristic
37#14519684C2211yescharacteristic
38#14519684C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44C23×C4×C61C2211yescharacteristic
45C2×C4⋊C4×C61C2211yescharacteristic
46C2×C4⋊C4×C61C2211yescharacteristic
47C2×C22⋊C4×C61C2211yescharacteristic
48C2×C22⋊C4×C61C2211yescharacteristic
49#95×C61C2211yescharacteristic
50#95×C61C2211yescharacteristic
51C24×C61C2311yescharacteristic
52C23×D61C2311yescharacteristic
53C22×C4×C61—22no—
54C22×C4×C61—41no—
55C22×C4×C61—41no—
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C2×C22⋊D61—41no—
63C2×C22⋊D61—41no—
64C2×C22⋊D61Q814yescomplemented
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C22×Dic61C2311yescharacteristic
70C22×Dic61C2311yescharacteristic
71C22×Dic61C2311yescharacteristic
72C2×C4×D61—22no—
73C2×C4×D61—41no—
74C2×C4×D61—41no—
75C2×Dic122—41no—
76C2×Dic122—41no—
77C2×Dic122—41no—
78C4⋊C4×C61—22no—
79C4⋊C4×C61—41no—
80C22⋊C4×C61—22no—
81C22⋊C4×C61—41no—
82C22⋊Dic61—41no—
83C22⋊Dic61—41no—
84C22⋊Dic61—41no—
85#11758198—22no—
86#11758198—41no—
87#11758198—41no—
88#11758198—41no—
89#11758198—41no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93#11758196—22no—
94#11758196—41no—
95#11758196—41no—
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
105C22×D61—21no—
106C22×D61—21no—
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—21no—
111C22×D61C2×Q812yes—
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×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—44no—
129C2×C4×C61#4112yes—
130C2×C4×C61#4112yes—
131C22⋊D61—44no—
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×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61C2×Q812yes—
153C4×D61—44no—
154Dic122—44no—
155C22×C61—22no—
156C22×C61—22no—
157C22×C61—22no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61C22×Q811yescharacteristic
163C22×C61C2×#4111yescharacteristic
164C22×C61C2×#4111yescharacteristic
165C22×C61H(5,𝔽2)11yescharacteristic
166C22×C61H(5,𝔽2)11yescharacteristic
167C22×C61H(5,𝔽2)11yescharacteristic
168C22×C61H(5,𝔽2)11yescharacteristic
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—41no—
184Dic61—41no—
185Dic61—41no—
186Dic61—41no—
187Dic61—41no—
188Dic61—41no—
189#2784—611nomaximal, Sylow
190C2×C61—42no—
191C2×C61#53811yescharacteristic
192C2×C61#53811yescharacteristic
193C2×C61#54311yescharacteristic
194C2×C61#55411yescharacteristic
195C2×C61#55411yescharacteristic
196C2×C61#55511yescharacteristic
197C2×C61#56011yescharacteristic
198D61—42no—
199#400—611no—
200#396—611no—
201#396—611no—
202#395—611no—
203#393—611no—
204#393—611no—
205#390—611no—
206#387—611no—
207#387—611no—
208#386—611no—
209#386—611no—
210#385—611no—
211#385D6111yescharacteristic, complemented
212#380—611no—
213#380—611no—
214C61#278411yescharacteristic, complemented, Sylow
215C22×Q8—611no—
216C22×D4—611no—
217C23×C4—611no—
218C23×C4C2×D6111yescharacteristic
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⋊C4C2×D6111yescharacteristic
226C2×C4⋊C4C2×D6111yescharacteristic
227C2×C22⋊C4—611no—
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⋊C4C2×D6111yescharacteristic
236C2×C22⋊C4C2×D6111yescharacteristic
237C2×C42—611no—
238#95—611no—
239#95—611no—
240#95—611no—
241#95—611no—
242#95—611no—
243#95—611no—
244#95—611no—
245#95—611no—
246#95—611no—
247#95—611no—
248#95C2×D6111yescharacteristic
249#95C2×D6111yescharacteristic
250C24—611no—
251C24C22×D6111yescharacteristic
252C2×Q8—2441no—
253C2×Q8—2441no—
254C2×Q8—2441no—
255C2×D4—614no—
256C2×D4—2441no—
257C2×D4—2441no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—1222no—
269C22×C4—2441no—
270C22×C4—2441no—
271C22×C4C22×D6111yescharacteristic
272C22×C4C22×D6111yescharacteristic
273C22×C4C22×D6111yescharacteristic
274C22×C4C22×D6111yescharacteristic
275C22×C4C22×D6111yescharacteristic
276C22×C4C22×D6111yescharacteristic
277C4⋊C4—22no—
278C4⋊C4—41no—
279C4⋊C4—1222no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C4⋊C4—2441no—
283C4⋊C4—2441no—
284C4⋊C4—2441no—
285C22⋊C4—22no—
286C22⋊C4—41no—
287C22⋊C4—1222no—
288C22⋊C4—2441no—
289C22⋊C4—2441no—
290C22⋊C4—2441no—
291C22⋊C4—2441no—
292C22⋊C4—2441no—
293C22⋊C4—2441no—
294C22⋊C4—2441no—
295C42—2441no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—612no—
303C23—1221no—
304C23—1221no—
305C23—1221no—
306C23—1221no—
307C23—1221no—
308C23—1221no—
309C23Q8×D6112yes—
310C23C23×D6111yescharacteristic
311Q8—2444no—
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—1221no—
332C2×C4—1221no—
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×C4#1175822212yes—
353C2×C4#1175822412yes—
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—
368C22C2×Q8×D6111yescharacteristic
369C22C2×#1175822411yescharacteristic
370C22C2×#1175822211yescharacteristic
371C22#1451982211yescharacteristic
372C22#1451982211yescharacteristic
373C22#1451982311yescharacteristic
374C22#1451982311yescharacteristic
375C4—22no—
376C4—22no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—1222no—
382C4—2441no—
383C4—2441no—
384C4—2441no—
385C4—2441no—
386C4—2441no—
387C4—2441no—
388C2—42no—
389C2—2442no—
390C2#1684034511yescharacteristic
391C2#1684034711yescharacteristic
392C2#1684038711yescharacteristic
393C2#1684046711yescharacteristic
394C2#1684047011yescharacteristic
395C2#1684047711yescharacteristic
396C2#1684050211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#385C2
hypercenter#385D61
hypocenterC61#2784
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. #16839703C2semidirect
2. #16839685C2semidirect
3. #16839684C2semidirect
4. #16839683C2semidirect
5. #16839675C2semidirect
6. #16839674C2semidirect
8. #16839648C2semidirect
9. #16839643C2semidirect
12. #16839636C2semidirect
13. #16839622C2semidirect
14. #16839619C2semidirect
15. C61×#385C2semidirect
64. C2×C22⋊D61Q8semidirect
211. #385D61semidirect
214. C61#2784semidirect