Finite Group Databasebeta

← #21448667

Subgroups — #21448667

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×#14519735C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D61C211yesmaximal, characteristic
3C2×C22⋊C4×D61C211yesmaximal, characteristic
4#16839656C211yesmaximal, characteristic, complemented
5#16839655C211yesmaximal, characteristic, complemented
6#16839650C211yesmaximal, characteristic, complemented
7#16839636C211yesmaximal, characteristic, complemented
8#16839633C211yesmaximal, characteristic, complemented
9#16839624C211yesmaximal, characteristic, complemented
10#16839621C211yesmaximal, characteristic, complemented
11#16839617C211yesmaximal, characteristic
12C4×#11758198C211yesmaximal, characteristic, complemented
13C4×#11758198C211yesmaximal, characteristic, complemented
14#16839609C211yesmaximal, characteristic, complemented
15C61×#388C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×C4×D61C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19C22×C4×D61C2211yescharacteristic
20C22×C4×D61C2211yescharacteristic
21#14519735—24no—
22C2×C4⋊Dic61C2211yescharacteristic, complemented
23C2×#11758196C2211yescharacteristic, complemented
24C2×#11758196C2211yescharacteristic, complemented
25C2×C22⋊Dic61C2211yescharacteristic
26C2×C22⋊Dic61C2211yescharacteristic
27C2×C22⋊Dic61C2211yescharacteristic
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C22⋊C4×D61—24no—
37C22⋊C4×D61C418yescomplemented
38C2×C4×Dic61C2211yescharacteristic, complemented
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
47C2×C4⋊C4×C61C2211yescharacteristic, complemented
48C2×C22⋊C4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
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×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
69C22×C4×C61C2311yescharacteristic
70C22×Dic61C2311yescharacteristic
71C22×Dic61C2311yescharacteristic
72C22×Dic61C2311yescharacteristic
73C22×Dic61C2311yescharacteristic
74C22×Dic61C2311yescharacteristic
75C22×Dic61C2311yescharacteristic
76C2×C4×D61—22no—
77C2×C4×D61—22no—
78C2×C4×D61—22no—
79C2×C4×D61—22no—
80C2×C4×D61—22no—
81C2×C4×D61—22no—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×C4×D61—41no—
86C2×C4×D61C2×C414yescomplemented
87C2×C4×D61C2×C414yescomplemented
88C4⋊C4×C61—22no—
89C22⋊C4×C61—22no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61C2×C414yescomplemented
92C42×C61—41no—
93C22⋊Dic61—22no—
94C22⋊Dic61—41no—
95C22⋊Dic61C2×C414yescomplemented
96#11758198—22no—
97#11758198—22no—
98#11758198—22no—
99#11758198—22no—
100#11758198—22no—
101#11758198C2×C414yes—
102#11758198C2×C414yes—
103#11758198D414yes—
104C4⋊Dic61—22no—
105#11758196—41no—
106#11758196—41no—
107C4×Dic61—22no—
108C4×Dic61—22no—
109C4×Dic61—41no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61C22×C412yes—
117C23×C61C2411yescharacteristic
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—28no—
127C22×D61—28no—
128C22×D61—44no—
129C22×D61—44no—
130C22×D61—44no—
131C22×D61—44no—
132C22×D61—44no—
133C22×D61C22×C412yes—
134C22×D61C22×C412yes—
135C22×D61C2×D412yes—
136C22×D61#4112yes—
137C22×D61#4112yes—
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×C61C22×C412yes—
155C2×C4×C61C22×C412yes—
156C2×C4×C61C2×D412yes—
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—21no—
171C2×Dic61—21no—
172C2×Dic61C22×C412yes—
173C2×Dic61C22×C412yes—
174C2×Dic61C2×D412yes—
175C4×D61—28no—
176C4×D61—44no—
177C4×D61—44no—
178C4×D61—44no—
179C22×C61—22no—
180C22×C61—22no—
181C22×C61—22no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—41no—
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—22no—
203C2×D61—22no—
204C2×D61—22no—
205C2×D61—416no—
206C2×D61#11714yescomplemented
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—42no—
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—24no—
231C2×#117—611no—
232C22×C22⋊C4—611no—
233C22×C22⋊C4—611no—
234#388—611no—
235#388—611no—
236#388—611no—
237#388D6111yescharacteristic, complemented
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⋊C4—611no—
246C61#234211yescharacteristic, complemented, Sylow
247C25—611no—
248C23×C4—611no—
249C23×C4—611no—
250C23×C4—611no—
251C23×C4—611no—
252#117—1224no—
253C2×C4⋊C4—611no—
254C2×C4⋊C4—611no—
255C2×C4⋊C4—611no—
256C2×C4⋊C4C2×D6111yescharacteristic, complemented
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—1224no—
270C2×C22⋊C4C2×D6111yescharacteristic
271C2×C22⋊C4C2×D6111yescharacteristic
272C2×C22⋊C4C2×D6111yescharacteristic
273C2×C42—611no—
274C2×C42—611no—
275C2×C42—611no—
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—611no—
296C22×C4—611no—
297C22×C4—611no—
298C22×C4—614no—
299C22×C4—614no—
300C22×C4—611no—
301C22×C4—611no—
302C22×C4—611no—
303C22×C4—1222no—
304C22×C4—1222no—
305C22×C4—1222no—
306C22×C4—1222no—
307C22×C4—1222no—
308C22×C4—1222no—
309C22×C4—2441no—
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—22no—
320C4⋊C4—1222no—
321C4⋊C4—2441no—
322C4⋊C4—2441no—
323C22⋊C4—22no—
324C22⋊C4—41no—
325C22⋊C4—614no—
326C22⋊C4—614no—
327C22⋊C4—614no—
328C22⋊C4—614no—
329C22⋊C4—1222no—
330C22⋊C4—1222no—
331C22⋊C4—1222no—
332C22⋊C4—1222no—
333C22⋊C4—1222no—
334C22⋊C4—1222no—
335C22⋊C4—2441no—
336C22⋊C4C4×D6114yescomplemented
337C42—41no—
338C42—1222no—
339C42—1222no—
340C42—2441no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—612no—
348C23—612no—
349C23—612no—
350C23—612no—
351C23—612no—
352C23—612no—
353C23—1228no—
354C23—1228no—
355C23—1221no—
356C23—1221no—
357C23—1221no—
358C23—1221no—
359C23—1221no—
360C23—1221no—
361C23—1221no—
362C23—1221no—
363C23—2444no—
364C23—2444no—
365C23—2444no—
366C23—2444no—
367C23—2444no—
368C23C2×C4×D6112yes—
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—612no—
386C2×C4—612no—
387C2×C4—612no—
388C2×C4—1228no—
389C2×C4—1221no—
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—2444no—
405C2×C4—2444no—
406C2×C4—2444no—
407C2×C4C2×C4×D6112yes—
408C2×C4C2×C4×D6112yes—
409C2×C4D4×D6112yes—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—614no—
418C22—614no—
419C22—1222no—
420C22—1222no—
421C22—1222no—
422C22—1222no—
423C22—1222no—
424C22—1222no—
425C22—1222no—
426C22—1222no—
427C22—1222no—
428C22—1222no—
429C22—1222no—
430C22—1222no—
431C22—24416no—
432C22C22×C4×D6111yescharacteristic
433C22C2×D4×D6111yescharacteristic
434C22#41×D6111yescharacteristic
435C22#41×D6111yescharacteristic
436C22#41×D6111yescharacteristic
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—42no—
452C2—1224no—
453C2—1224no—
454C2#117×D6111yescharacteristic
455C2C4×D4×D6111yescharacteristic
456C2#1684023411yescharacteristic
457C2#1684040111yescharacteristic
458C2#1684040511yescharacteristic
459C2#1684043711yescharacteristic
460C2#1684044011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#388C2
socleC23×C61C24
hypercenter#388D61
hypocenterC61#2342
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#14519735C2semidirect
4. #16839656C2semidirect
5. #16839655C2semidirect
6. #16839650C2semidirect
7. #16839636C2semidirect
8. #16839633C2semidirect
9. #16839624C2semidirect
10. #16839621C2semidirect
12. C4×#11758198C2semidirect
13. C4×#11758198C2semidirect
14. #16839609C2semidirect
15. C61×#388C2semidirect
22. C2×C4⋊Dic61C22semidirect
23. C2×#11758196C22semidirect
24. C2×#11758196C22semidirect
37. C22⋊C4×D61C4semidirect
38. C2×C4×Dic61C22semidirect
39. C2×C4×Dic61C22semidirect
40. C2×C4×Dic61C22semidirect
41. #14519684C22semidirect
42. #14519684C22semidirect
43. #14519684C22semidirect
44. #14519684C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
47. C2×C4⋊C4×C61C22semidirect
51. C2×C42×C61C22semidirect
52. #95×C61C22semidirect
53. #95×C61C22semidirect
86. C2×C4×D61C2×C4semidirect
87. C2×C4×D61C2×C4semidirect
91. C22⋊C4×C61C2×C4semidirect
95. C22⋊Dic61C2×C4semidirect
206. C2×D61#117semidirect
237. #388D61semidirect
246. C61#2342semidirect
256. C2×C4⋊C4C2×D61semidirect
276. C2×C42C2×D61semidirect
283. #95C2×D61semidirect
284. #95C2×D61semidirect
336. C22⋊C4C4×D61semidirect