Finite Group Databasebeta

← #21448662

Subgroups — #21448662

Order 7808.

792 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519734C211yesmaximal, characteristic, complemented
2C22×#11758198C211yesmaximal, characteristic
3C2×C22⋊C4×D61C211yesmaximal, characteristic
4#16839653C211yesmaximal, characteristic, complemented
5#16839653C211yesmaximal, characteristic, complemented
6#16839651C211yesmaximal, characteristic, complemented
7#16839651C211yesmaximal, characteristic, complemented
8#16839635C211yesmaximal, characteristic, complemented
9#16839634C211yesmaximal, characteristic, complemented
10#16839624C211yesmaximal, characteristic, complemented
11#16839621C211yesmaximal, characteristic, complemented
12#16839617C211yesmaximal, characteristic
13C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
14C4×#11758198C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C23×Dic61C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19C22×C4×D61C2211yescharacteristic
20#14519734—24no—
21C2×#11758196C2211yescharacteristic, complemented
22C2×#11758196C2211yescharacteristic, complemented
23C2×#11758196C2211yescharacteristic, complemented
24C2×#11758196C2211yescharacteristic, complemented
25C2×C22⋊Dic61C2211yescharacteristic
26C2×C22⋊Dic61C2211yescharacteristic
27C2×#11758198—24no—
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C22⋊C4×D61C418yescomplemented
39C2×C4×Dic61C2211yescharacteristic, complemented
40C2×C4×Dic61C2211yescharacteristic, complemented
41#14519684C2211yescharacteristic, complemented
42#14519684C2211yescharacteristic, complemented
43#14519684C2211yescharacteristic, complemented
44#14519684C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46#14519684C2211yescharacteristic, complemented
47C23×C4×C61C2211yescharacteristic
48C2×C22⋊C4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C42×C61C2211yescharacteristic, complemented
51C2×C42×C61C2211yescharacteristic, complemented
52#95×C61C2211yescharacteristic, complemented
53#95×C61C2211yescharacteristic, complemented
54C24×C61C2311yescharacteristic
55C23×D61—22no—
56C23×D61—22no—
57C23×D61—22no—
58C23×D61—22no—
59C23×D61—41no—
60C23×D61—41no—
61C23×D61C2×C414yes—
62C23×D61C2311yescharacteristic
63C23×D61C2311yescharacteristic
64C22×C4×C61—22no—
65C22×C4×C61—22no—
66C22×C4×C61—41no—
67C22×C4×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
69C22×C4×C61C2311yescharacteristic
70C22×C4×C61C2311yescharacteristic
71C22×C4×C61C2311yescharacteristic
72C22×C4×C61C2311yescharacteristic
73C22×Dic61—22no—
74C22×Dic61—22no—
75C22×Dic61—41no—
76C22×Dic61C2311yescharacteristic
77C22×Dic61C2311yescharacteristic
78C22×Dic61C2311yescharacteristic
79C22×Dic61C2311yescharacteristic
80C22×Dic61C2311yescharacteristic
81C22×Dic61C2311yescharacteristic
82C2×C4×D61—22no—
83C2×C4×D61—22no—
84C2×C4×D61—41no—
85C2×C4×D61—41no—
86C2×C4×D61C2×C414yescomplemented
87C2×C4×D61C2×C414yescomplemented
88C22⋊C4×C61—22no—
89C22⋊C4×C61C2×C414yes—
90C42×C61—22no—
91C42×C61—41no—
92C22⋊Dic61—22no—
93C22⋊Dic61C2×C414yes—
94#11758198—22no—
95#11758198—22no—
96#11758198—22no—
97#11758198—22no—
98#11758198—22no—
99#11758198—41no—
100#11758198—41no—
101#11758198C2×C414yescomplemented
102#11758198C2×C414yescomplemented
103#11758198D414yes—
104#11758196—22no—
105#11758196—22no—
106#11758196—41no—
107#11758196—41no—
108C4×Dic61—22no—
109C4×Dic61—41no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61C22×C412yes—
115C23×C61#4112yes—
116C23×C61#4112yes—
117C23×C61C2411yescharacteristic
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—28no—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—28no—
130C22×D61—44no—
131C22×D61—44no—
132C22×D61—44no—
133C22×D61—44no—
134C22×D61—44no—
135C22×D61C22×C412yes—
136C22×D61C22×C412yes—
137C22×D61C2×D412yes—
138C22×D61#4112yes—
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—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—44no—
155C2×C4×C61C22×C412yes—
156C2×C4×C61C22×C412yes—
157C2×C4×C61C2×D412yes—
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—21no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—44no—
174C2×Dic61C22×C412yes—
175C2×Dic61C22×C412yes—
176C2×Dic61C2×D412yes—
177C4×D61—28no—
178C4×D61—44no—
179C22×C61—22no—
180C22×C61—22no—
181C22×C61—22no—
182C22×C61—22no—
183C22×C61—22no—
184C22×C61—22no—
185C22×C61#11714yescomplemented
186C22×C61C23×C411yescharacteristic
187C22×C61C22×D411yescharacteristic
188C22×C61C2×#4111yescharacteristic
189C22×C61C2×#4111yescharacteristic
190C22×C61C2×#4111yescharacteristic
191C22×C61H(5,𝔽2)11yescharacteristic
192C22×C61H(5,𝔽2)11yescharacteristic
193C2×D61—22no—
194C2×D61—22no—
195C2×D61—22no—
196C2×D61—22no—
197C2×D61—22no—
198C2×D61—22no—
199C2×D61—22no—
200C2×D61—22no—
201C2×D61—22no—
202C2×D61—416no—
203C2×D61—41no—
204C2×D61—41no—
205C2×D61—41no—
206C2×D61—41no—
207C2×D61C4×D414yes—
208C4×C61—22no—
209C4×C61—22no—
210C4×C61—22no—
211C4×C61—41no—
212C4×C61—41no—
213C4×C61—41no—
214Dic61—22no—
215Dic61—22no—
216Dic61—22no—
217Dic61—41no—
218Dic61—41no—
219Dic61—41no—
220#2342—611nomaximal, Sylow
221C2×C61—24no—
222C2×C61C2×#11711yescharacteristic
223C2×C61C2×C4×D411yescharacteristic
224C2×C61#51811yescharacteristic
225C2×C61#54611yescharacteristic
226C2×C61#54611yescharacteristic
227C2×C61#55111yescharacteristic
228C2×C61#55111yescharacteristic
229D61—24no—
230D61—42no—
231C2×#117—611no—
232C22×C22⋊C4—611no—
233C22×C22⋊C4—611no—
234#388—611no—
235#388—611no—
236#388—611no—
237#388—611no—
238#385—611no—
239#385—611no—
240#381—611no—
241#380—611no—
242#379—611no—
243C4×C22⋊C4—611no—
244C4×C22⋊C4—611no—
245C4×C22⋊C4D6111yescharacteristic, complemented
246C61#234211yescharacteristic, complemented, Sylow
247C25—611no—
248C23×C4—611no—
249C23×C4—611no—
250C23×C4—611no—
251C23×C4C2×D6111yescharacteristic
252#117—1224no—
253C2×C4⋊C4—611no—
254C2×C4⋊C4—611no—
255C2×C4⋊C4—611no—
256C2×C4⋊C4—611no—
257C2×C22⋊C4—611no—
258C2×C22⋊C4—611no—
259C2×C22⋊C4—611no—
260C2×C22⋊C4—611no—
261C2×C22⋊C4—618no—
262C2×C22⋊C4—611no—
263C2×C22⋊C4—611no—
264C2×C22⋊C4—611no—
265C2×C22⋊C4—611no—
266C2×C22⋊C4—611no—
267C2×C22⋊C4—611no—
268C2×C22⋊C4—611no—
269C2×C22⋊C4—611no—
270C2×C22⋊C4—1224no—
271C2×C22⋊C4C2×D6111yescharacteristic
272C2×C22⋊C4C2×D6111yescharacteristic
273C2×C42—611no—
274C2×C42—611no—
275C2×C42C2×D6111yescharacteristic, complemented
276C2×C42C2×D6111yescharacteristic, complemented
277#95—611no—
278#95—611no—
279#95—611no—
280#95—611no—
281#95—611no—
282#95—611no—
283#95C2×D6111yescharacteristic, complemented
284#95C2×D6111yescharacteristic, complemented
285C24—611no—
286C24—611no—
287C24—614no—
288C24—1222no—
289C24—1222no—
290C24—1222no—
291C24—1222no—
292C24—2441no—
293C24—2441no—
294C24C22×D6111yescharacteristic
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—41no—
298C22×C4—611no—
299C22×C4—611no—
300C22×C4—611no—
301C22×C4—614no—
302C22×C4—614no—
303C22×C4—611no—
304C22×C4—611no—
305C22×C4—611no—
306C22×C4—1222no—
307C22×C4—1222no—
308C22×C4—1222no—
309C22×C4—1222no—
310C22×C4—2441no—
311C22×C4—2441no—
312C22×C4—2441no—
313C22×C4C22×D6111yescharacteristic
314C22×C4C22×D6111yescharacteristic
315C22×C4C22×D6111yescharacteristic
316C22×C4C22×D6111yescharacteristic
317C22×C4C22×D6111yescharacteristic
318C22×C4C22×D6111yescharacteristic
319C4⋊C4—1222no—
320C4⋊C4—1222no—
321C4⋊C4—2441no—
322C4⋊C4—2441no—
323C22⋊C4—22no—
324C22⋊C4—614no—
325C22⋊C4—614no—
326C22⋊C4—614no—
327C22⋊C4—614no—
328C22⋊C4—1222no—
329C22⋊C4—1222no—
330C22⋊C4—1222no—
331C22⋊C4—1222no—
332C22⋊C4—1222no—
333C22⋊C4—1222no—
334C22⋊C4—2441no—
335C22⋊C4—2441no—
336C22⋊C4C4×D6114yes—
337C42—22no—
338C42—41no—
339C42—1222no—
340C42—2441no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—612no—
346C23—612no—
347C23—612no—
348C23—612no—
349C23—1228no—
350C23—1221no—
351C23—1221no—
352C23—1221no—
353C23—1221no—
354C23—1221no—
355C23—1221no—
356C23—1221no—
357C23—1221no—
358C23—1221no—
359C23—1221no—
360C23—1228no—
361C23—2444no—
362C23—2444no—
363C23—2444no—
364C23—2444no—
365C23—2444no—
366C23C2×C4×D6112yes—
367C23#1175822212yes—
368C23#1175822212yes—
369C23C23×D6111yescharacteristic
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—44no—
386C2×C4—612no—
387C2×C4—612no—
388C2×C4—612no—
389C2×C4—1228no—
390C2×C4—1221no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—1221no—
402C2×C4—1221no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—2444no—
406C2×C4—2444no—
407C2×C4C2×C4×D6112yes—
408C2×C4C2×C4×D6112yes—
409C2×C4D4×D6112yes—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—22no—
416C22—614no—
417C22—1222no—
418C22—1222no—
419C22—1222no—
420C22—1222no—
421C22—1222no—
422C22—1222no—
423C22—1222no—
424C22—1222no—
425C22—1222no—
426C22—24416no—
427C22—2441no—
428C22—2441no—
429C22—2441no—
430C22—2441no—
431C22#1451973414yescomplemented
432C22C22×C4×D6111yescharacteristic
433C22C2×D4×D6111yescharacteristic
434C22#41×D6111yescharacteristic
435C22C2×#1175822211yescharacteristic
436C22C2×#1175822211yescharacteristic
437C22#1451982211yescharacteristic
438C22#1451982311yescharacteristic
439C4—22no—
440C4—22no—
441C4—22no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—1222no—
446C4—1222no—
447C4—1222no—
448C4—2441no—
449C4—2441no—
450C4—2441no—
451C2—24no—
452C2—1224no—
453C2—2442no—
454C2C2×#1451973411yescharacteristic
455C2C4×D4×D6111yescharacteristic
456C2#1684023411yescharacteristic
457C2#1684040211yescharacteristic
458C2#1684040811yescharacteristic
459C2#1684043611yescharacteristic
460C2#1684044111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC4×C22⋊C4×C61C2
socleC23×C61C24
hypercenterC4×C22⋊C4D61
hypocenterC61#2342
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14519734C2semidirect
4. #16839653C2semidirect
5. #16839653C2semidirect
6. #16839651C2semidirect
7. #16839651C2semidirect
8. #16839635C2semidirect
9. #16839634C2semidirect
10. #16839624C2semidirect
11. #16839621C2semidirect
13. C22⋊C4×Dic61C2semidirect
14. C4×#11758198C2semidirect
15. C4×C22⋊C4×C61C2semidirect
21. C2×#11758196C22semidirect
22. C2×#11758196C22semidirect
23. C2×#11758196C22semidirect
24. C2×#11758196C22semidirect
38. C22⋊C4×D61C4semidirect
39. C2×C4×Dic61C22semidirect
40. C2×C4×Dic61C22semidirect
41. #14519684C22semidirect
42. #14519684C22semidirect
43. #14519684C22semidirect
44. #14519684C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
50. C2×C42×C61C22semidirect
51. C2×C42×C61C22semidirect
52. #95×C61C22semidirect
53. #95×C61C22semidirect
86. C2×C4×D61C2×C4semidirect
87. C2×C4×D61C2×C4semidirect
101. #11758198C2×C4semidirect
102. #11758198C2×C4semidirect
185. C22×C61#117semidirect
245. C4×C22⋊C4D61semidirect
246. C61#2342semidirect
275. C2×C42C2×D61semidirect
276. C2×C42C2×D61semidirect
283. #95C2×D61semidirect
284. #95C2×D61semidirect
431. C22#14519734semidirect