Finite Group Databasebeta

← #21450070

Subgroups — #21450070

Order 7808.

664 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519772C211yesmaximal, characteristic, complemented
2C22×#11758198C211yesmaximal, characteristic
3#16839691C211yesmaximal, characteristic, complemented
4#16839689C211yesmaximal, characteristic, complemented
5#16839688C211yesmaximal, characteristic, complemented
6#16839684C211yesmaximal, characteristic, complemented
7#16839654C211yesmaximal, characteristic, complemented
8#16839652C211yesmaximal, characteristic, complemented
9#16839651C211yesmaximal, characteristic, complemented
10#16839637C211yesmaximal, characteristic, complemented
11#16839635C211yesmaximal, characteristic, complemented
12#16839617C211yesmaximal, characteristic
13#16839617C211yesmaximal, characteristic
14C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
15C61×#380C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C23×Dic61C2211yescharacteristic
18#14519772—24no—
19C2×C4⋊Dic61C2211yescharacteristic, complemented
20C2×C4⋊Dic61C2211yescharacteristic, complemented
21C2×#11758196C2211yescharacteristic, complemented
22C2×#11758196C2211yescharacteristic, complemented
23C2×C22⋊Dic61C2211yescharacteristic
24C2×C22⋊Dic61C2211yescharacteristic
25C2×#11758198—24no—
26C2×#11758198C2211yescharacteristic
27C2×#11758198C2211yescharacteristic
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×C4×Dic61C2211yescharacteristic, complemented
39C2×C4×Dic61C2211yescharacteristic, complemented
40#14519684C2211yescharacteristic, complemented
41#14519684C2211yescharacteristic, complemented
42#14519684C2211yescharacteristic, complemented
43#14519684C2211yescharacteristic, complemented
44#14519684C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46C23×C4×C61C2211yescharacteristic
47C2×C4⋊C4×C61C2211yescharacteristic, complemented
48C2×C4⋊C4×C61C2211yescharacteristic, complemented
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51#95×C61C2211yescharacteristic, complemented
52#95×C61C2211yescharacteristic, complemented
53C24×C61C2311yescharacteristic
54C23×D61—22no—
55C23×D61—22no—
56C23×D61—22no—
57C23×D61—22no—
58C23×D61—22no—
59C23×D61—41no—
60C23×D61—41no—
61C23×D61C2311yescharacteristic
62C23×D61C2311yescharacteristic
63C22×C4×C61—22no—
64C22×C4×C61—22no—
65C22×C4×C61—41no—
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
69C22×C4×C61C2311yescharacteristic
70C22×C4×C61C2311yescharacteristic
71C22×C4×C61C2311yescharacteristic
72C22×Dic61—22no—
73C22×Dic61—22no—
74C22×Dic61—41no—
75C22×Dic61C2311yescharacteristic
76C22×Dic61C2311yescharacteristic
77C22×Dic61C2311yescharacteristic
78C22×Dic61C2311yescharacteristic
79C22×Dic61C2311yescharacteristic
80C22×Dic61C2311yescharacteristic
81C4⋊C4×C61—22no—
82C4⋊C4×C61—41no—
83C22⋊C4×C61—22no—
84C22⋊C4×C61—22no—
85C22⋊Dic61—22no—
86C22⋊Dic61—22no—
87#11758198—22no—
88#11758198—22no—
89#11758198—22no—
90#11758198—22no—
91#11758198—22no—
92#11758198—22no—
93#11758198—22no—
94#11758198—41no—
95#11758198—41no—
96#11758198—41no—
97#11758198—41no—
98#11758198D414yes—
99C4⋊Dic61—22no—
100C4⋊Dic61—41no—
101#11758196—22no—
102#11758196—41no—
103C4×Dic61—22no—
104C4×Dic61—41no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61#4112yes—
110C23×C61#4112yes—
111C23×C61#4112yes—
112C23×C61C2411yescharacteristic
113C22×D61—28no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—44no—
127C22×D61—44no—
128C22×D61—44no—
129C22×D61—44no—
130C22×D61—44no—
131C22×D61—44no—
132C22×D61C2×D412yes—
133C22×D61#4112yes—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—44no—
152C2×C4×C61C2×D412yes—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—44no—
171C2×Dic61C2×D412yes—
172C22×C61—22no—
173C22×C61—22no—
174C22×C61—22no—
175C22×C61—22no—
176C22×C61—22no—
177C22×C61—22no—
178C22×C61#12614yescomplemented
179C22×C61C22×D411yescharacteristic
180C22×C61C2×#4111yescharacteristic
181C22×C61C2×#4111yescharacteristic
182C22×C61C2×#4111yescharacteristic
183C22×C61C2×#4111yescharacteristic
184C22×C61H(5,𝔽2)11yescharacteristic
185C22×C61H(5,𝔽2)11yescharacteristic
186C2×D61—22no—
187C2×D61—22no—
188C2×D61—22no—
189C2×D61—22no—
190C2×D61—22no—
191C2×D61—22no—
192C2×D61—416no—
193C2×D61—41no—
194C2×D61—41no—
195C2×D61—41no—
196C2×D61—41no—
197C2×D61—41no—
198C2×D61—41no—
199C2×D61—41no—
200C2×D61—41no—
201C4×C61—22no—
202C4×C61—41no—
203C4×C61—41no—
204C4×C61—41no—
205C4×C61—41no—
206C4×C61—41no—
207Dic61—22no—
208Dic61—41no—
209Dic61—41no—
210Dic61—41no—
211Dic61—41no—
212Dic61—41no—
213#2480—611nomaximal, Sylow
214C2×C61—24no—
215C2×C61#52511yescharacteristic
216C2×C61C2×#12611yescharacteristic
217C2×C61#53811yescharacteristic
218C2×C61#54611yescharacteristic
219C2×C61#54611yescharacteristic
220C2×C61#55111yescharacteristic
221C2×C61#55111yescharacteristic
222D61—42no—
223D61—42no—
224C2×#126—611no—
225C22×C22⋊C4—611no—
226#397—611no—
227#397—611no—
228#397—611no—
229#396—611no—
230#388—611no—
231#388—611no—
232#388—611no—
233#385—611no—
234#385—611no—
235#380D6111yescharacteristic, complemented
236#379—611no—
237#379—611no—
238C4×C22⋊C4—611no—
239C61#248011yescharacteristic, complemented, Sylow
240C25—611no—
241C23×C4—611no—
242C23×C4C2×D6111yescharacteristic
243#126—1224no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4—611no—
246C2×C4⋊C4—611no—
247C2×C4⋊C4—611no—
248C2×C4⋊C4C2×D6111yescharacteristic, complemented
249C2×C4⋊C4C2×D6111yescharacteristic, complemented
250C2×C22⋊C4—611no—
251C2×C22⋊C4—611no—
252C2×C22⋊C4—611no—
253C2×C22⋊C4—611no—
254C2×C22⋊C4—611no—
255C2×C22⋊C4—611no—
256C2×C22⋊C4—611no—
257C2×C22⋊C4—611no—
258C2×C22⋊C4—611no—
259C2×C22⋊C4—611no—
260C2×C22⋊C4—611no—
261C2×C22⋊C4—611no—
262C2×C22⋊C4—611no—
263C2×C22⋊C4—611no—
264C2×C22⋊C4—1224no—
265C2×C22⋊C4C2×D6111yescharacteristic
266C2×C22⋊C4C2×D6111yescharacteristic
267C2×C42—611no—
268C2×C42—611no—
269#95—611no—
270#95—611no—
271#95—611no—
272#95—611no—
273#95—611no—
274#95—611no—
275#95C2×D6111yescharacteristic, complemented
276#95C2×D6111yescharacteristic, complemented
277C24—611no—
278C24—611no—
279C24—1222no—
280C24—1222no—
281C24—1222no—
282C24—1222no—
283C24—1222no—
284C24—2441no—
285C24—2441no—
286C24C22×D6111yescharacteristic
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—41no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—611no—
293C22×C4—611no—
294C22×C4—611no—
295C22×C4—611no—
296C22×C4—1222no—
297C22×C4—1222no—
298C22×C4—2441no—
299C22×C4C22×D6111yescharacteristic
300C22×C4C22×D6111yescharacteristic
301C22×C4C22×D6111yescharacteristic
302C22×C4C22×D6111yescharacteristic
303C22×C4C22×D6111yescharacteristic
304C22×C4C22×D6111yescharacteristic
305C4⋊C4—22no—
306C4⋊C4—41no—
307C4⋊C4—1222no—
308C4⋊C4—1222no—
309C4⋊C4—2441no—
310C4⋊C4—2441no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—614no—
314C22⋊C4—1222no—
315C22⋊C4—1222no—
316C22⋊C4—1222no—
317C22⋊C4—1222no—
318C22⋊C4—1222no—
319C22⋊C4—1222no—
320C22⋊C4—1222no—
321C22⋊C4—1222no—
322C22⋊C4—1222no—
323C22⋊C4—2441no—
324C22⋊C4—2441no—
325C22⋊C4—2441no—
326C22⋊C4—2441no—
327C42—1222no—
328C42—2441no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—612no—
334C23—612no—
335C23—1228no—
336C23—1221no—
337C23—1221no—
338C23—1221no—
339C23—1221no—
340C23—1221no—
341C23—1221no—
342C23—1221no—
343C23—1221no—
344C23—1221no—
345C23—1221no—
346C23—1221no—
347C23—1221no—
348C23—2444no—
349C23—2444no—
350C23—2444no—
351C23—2444no—
352C23—2444no—
353C23—2444no—
354C23#1175822212yes—
355C23#1175822412yes—
356C23#1175822612yes—
357C23C23×D6111yescharacteristic
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—44no—
376C2×C4—612no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—1221no—
382C2×C4—1221no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—1221no—
386C2×C4—1221no—
387C2×C4—1221no—
388C2×C4—1221no—
389C2×C4—1221no—
390C2×C4—1221no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—2444no—
395C2×C4D4×D6112yes—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—1222no—
403C22—1222no—
404C22—1222no—
405C22—1222no—
406C22—1222no—
407C22—1222no—
408C22—24416no—
409C22—2441no—
410C22—2441no—
411C22—2441no—
412C22—2441no—
413C22—2441no—
414C22—2441no—
415C22—2441no—
416C22—2441no—
417C22#1451977214yescomplemented
418C22C2×D4×D6111yescharacteristic
419C22#41×D6111yescharacteristic
420C22C2×#1175822411yescharacteristic
421C22C2×#1175822211yescharacteristic
422C22C2×#1175822611yescharacteristic
423C22#1451982211yescharacteristic
424C22#1451982311yescharacteristic
425C4—22no—
426C4—41no—
427C4—41no—
428C4—41no—
429C4—41no—
430C4—41no—
431C4—1222no—
432C4—2441no—
433C4—2441no—
434C4—2441no—
435C4—2441no—
436C4—2441no—
437C2—24no—
438C2—2442no—
439C2—2442no—
440C2#1684027211yescharacteristic
441C2C2×#1451977211yescharacteristic
442C2#1684034911yescharacteristic
443C2#1684040211yescharacteristic
444C2#1684040311yescharacteristic
445C2#1684043611yescharacteristic
446C2#1684043911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#380C2
hypercenter#380D61
hypocenterC61#2480
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C2×#14519772C2semidirect
3. #16839691C2semidirect
4. #16839689C2semidirect
5. #16839688C2semidirect
6. #16839684C2semidirect
7. #16839654C2semidirect
8. #16839652C2semidirect
9. #16839651C2semidirect
10. #16839637C2semidirect
11. #16839635C2semidirect
14. C22⋊C4×Dic61C2semidirect
15. C61×#380C2semidirect
19. C2×C4⋊Dic61C22semidirect
20. C2×C4⋊Dic61C22semidirect
21. C2×#11758196C22semidirect
22. C2×#11758196C22semidirect
38. C2×C4×Dic61C22semidirect
39. C2×C4×Dic61C22semidirect
40. #14519684C22semidirect
41. #14519684C22semidirect
42. #14519684C22semidirect
43. #14519684C22semidirect
44. #14519684C22semidirect
45. #14519684C22semidirect
47. C2×C4⋊C4×C61C22semidirect
48. C2×C4⋊C4×C61C22semidirect
51. #95×C61C22semidirect
52. #95×C61C22semidirect
178. C22×C61#126semidirect
235. #380D61semidirect
239. C61#2480semidirect
248. C2×C4⋊C4C2×D61semidirect
249. C2×C4⋊C4C2×D61semidirect
275. #95C2×D61semidirect
276. #95C2×D61semidirect
417. C22#14519772semidirect