Finite Group Databasebeta

← #21448413

Subgroups — #21448413

Order 7808.

672 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×D61C211yesmaximal, characteristic
2#16839656C211yesmaximal, characteristic, complemented
3#16839655C211yesmaximal, characteristic, complemented
4#16839654C211yesmaximal, characteristic, complemented
5#16839653C211yesmaximal, characteristic, complemented
6#16839652C211yesmaximal, characteristic, complemented
7#16839651C211yesmaximal, characteristic, complemented
8#16839650C211yesmaximal, characteristic, complemented
9#16839621C211yesmaximal, characteristic, complemented
10#16839619C211yesmaximal, characteristic, complemented
11#16839617C211yesmaximal, characteristic
12#16839617C211yesmaximal, characteristic
13C4×#11758198C211yesmaximal, characteristic, complemented
14#16839609C211yesmaximal, characteristic, complemented
15C61×#388C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×C4×D61C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19C2×C4⋊Dic61C2211yescharacteristic, complemented
20C2×#11758196C2211yescharacteristic, complemented
21C2×#11758196C2211yescharacteristic, complemented
22C2×C22⋊Dic61C2211yescharacteristic
23C2×C22⋊Dic61C2211yescharacteristic
24C2×C22⋊Dic61C2211yescharacteristic
25C2×#11758198C2211yescharacteristic
26C2×#11758198C2211yescharacteristic
27C2×#11758198C2211yescharacteristic
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C22⋊C4×D61C418yescomplemented
36C2×C4×Dic61C2211yescharacteristic, complemented
37C2×C4×Dic61C2211yescharacteristic, complemented
38C2×C4×Dic61C2211yescharacteristic, complemented
39#14519684C2211yescharacteristic, complemented
40#14519684C2211yescharacteristic, complemented
41#14519684C2211yescharacteristic, complemented
42#14519684C2211yescharacteristic, complemented
43#14519684C2211yescharacteristic, complemented
44#14519684C2211yescharacteristic, complemented
45C2×C4⋊C4×C61C2211yescharacteristic, complemented
46C2×C22⋊C4×C61C2211yescharacteristic
47C2×C22⋊C4×C61C2211yescharacteristic
48C2×C22⋊C4×C61C2211yescharacteristic
49C2×C42×C61C2211yescharacteristic, complemented
50#95×C61C2211yescharacteristic, complemented
51#95×C61C2211yescharacteristic, complemented
52C24×C61C2311yescharacteristic
53C23×D61—22no—
54C23×D61—22no—
55C23×D61—41no—
56C23×D61—41no—
57C23×D61—41no—
58C23×D61—41no—
59C23×D61C2×C414yes—
60C23×D61C2311yescharacteristic
61C23×D61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C22×Dic61C2311yescharacteristic
70C22×Dic61C2311yescharacteristic
71C22×Dic61C2311yescharacteristic
72C22×Dic61C2311yescharacteristic
73C22×Dic61C2311yescharacteristic
74C2×C4×D61—41no—
75C2×C4×D61—41no—
76C2×C4×D61—41no—
77C2×C4×D61—41no—
78C2×C4×D61C2×C414yes—
79C2×C4×D61C2×C414yes—
80C4⋊C4×C61—41no—
81C22⋊C4×C61—41no—
82C22⋊C4×C61—41no—
83C22⋊C4×C61C2×C414yes—
84C42×C61—41no—
85C22⋊Dic61—41no—
86C22⋊Dic61—41no—
87C22⋊Dic61C2×C414yes—
88#11758198—22no—
89#11758198—22no—
90#11758198—22no—
91#11758198—22no—
92#11758198—41no—
93#11758198—41no—
94#11758198—41no—
95#11758198—41no—
96#11758198C2×C414yes—
97#11758198C2×C414yes—
98C4⋊Dic61—41no—
99#11758196—41no—
100#11758196—41no—
101C4×Dic61—41no—
102C4×Dic61—41no—
103C4×Dic61—41no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61C22×C412yes—
111C23×C61C2411yescharacteristic
112C22×D61—21no—
113C22×D61—21no—
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—28no—
123C22×D61—44no—
124C22×D61—44no—
125C22×D61—44no—
126C22×D61—44no—
127C22×D61—44no—
128C22×D61—44no—
129C22×D61C22×C412yes—
130C22×D61C22×C412yes—
131C22×D61#4112yes—
132C22×D61#4112yes—
133C2×C4×C61—21no—
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×C61C22×C412yes—
150C2×C4×C61C22×C412yes—
151C2×Dic61—21no—
152C2×Dic61—21no—
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×Dic61C22×C412yes—
168C2×Dic61C22×C412yes—
169C4×D61—44no—
170C4×D61—44no—
171C22×C61—22no—
172C22×C61—22no—
173C22×C61—22no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61C23×C411yescharacteristic
179C22×C61C2×#4111yescharacteristic
180C22×C61C2×#4111yescharacteristic
181C22×C61H(5,𝔽2)11yescharacteristic
182C22×C61H(5,𝔽2)11yescharacteristic
183C22×C61H(5,𝔽2)11yescharacteristic
184C22×C61H(5,𝔽2)11yescharacteristic
185C2×D61—22no—
186C2×D61—22no—
187C2×D61—22no—
188C2×D61—22no—
189C2×D61—22no—
190C2×D61—22no—
191C2×D61—22no—
192C2×D61—22no—
193C2×D61—22no—
194C2×D61—416no—
195C2×D61—41no—
196C2×D61—41no—
197C2×D61—41no—
198C2×D61—41no—
199C2×D61#11714yes—
200C4×C61—22no—
201C4×C61—22no—
202C4×C61—41no—
203C4×C61—41no—
204C4×C61—41no—
205C4×C61—41no—
206Dic61—22no—
207Dic61—22no—
208Dic61—41no—
209Dic61—41no—
210Dic61—41no—
211Dic61—41no—
212#2312—611nomaximal, Sylow
213C2×C61—42no—
214C2×C61C2×#11711yescharacteristic
215C2×C61#51811yescharacteristic
216C2×C61#51811yescharacteristic
217C2×C61#53811yescharacteristic
218C2×C61#53811yescharacteristic
219C2×C61#53811yescharacteristic
220C2×C61#53811yescharacteristic
221D61—24no—
222D61—42no—
223C22×C22⋊C4—611no—
224#388—611no—
225#388—611no—
226#388—611no—
227#388—611no—
228#388—611no—
229#388—611no—
230#388—611no—
231#388D6111yescharacteristic, complemented
232#380—611no—
233#380—611no—
234#379—611no—
235#379—611no—
236C4×C22⋊C4—611no—
237C4×C22⋊C4—611no—
238C61#231211yescharacteristic, complemented, Sylow
239C25—611no—
240C23×C4—611no—
241C23×C4—611no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4C2×D6111yescharacteristic, complemented
246C2×C22⋊C4—611no—
247C2×C22⋊C4—611no—
248C2×C22⋊C4—611no—
249C2×C22⋊C4—618no—
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⋊C4C2×D6111yescharacteristic
261C2×C22⋊C4C2×D6111yescharacteristic
262C2×C22⋊C4C2×D6111yescharacteristic
263C2×C42—611no—
264C2×C42—611no—
265C2×C42—611no—
266C2×C42C2×D6111yescharacteristic, complemented
267#95—611no—
268#95—611no—
269#95—611no—
270#95—611no—
271#95—611no—
272#95—611no—
273#95C2×D6111yescharacteristic, complemented
274#95C2×D6111yescharacteristic, complemented
275C24—611no—
276C24—611no—
277C24—614no—
278C24—1222no—
279C24—1222no—
280C24—2441no—
281C24—2441no—
282C24—2441no—
283C24—2441no—
284C24C22×D6111yescharacteristic
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—614no—
288C22×C4—614no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—611no—
293C22×C4—2441no—
294C22×C4—2441no—
295C22×C4—2441no—
296C22×C4—2441no—
297C22×C4C22×D6111yescharacteristic
298C22×C4C22×D6111yescharacteristic
299C22×C4C22×D6111yescharacteristic
300C22×C4C22×D6111yescharacteristic
301C22×C4C22×D6111yescharacteristic
302C22×C4C22×D6111yescharacteristic
303C4⋊C4—41no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C4⋊C4—2441no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—614no—
310C22⋊C4—614no—
311C22⋊C4—614no—
312C22⋊C4—1222no—
313C22⋊C4—1222no—
314C22⋊C4—1222no—
315C22⋊C4—1222no—
316C22⋊C4—2441no—
317C22⋊C4—2441no—
318C22⋊C4—2441no—
319C22⋊C4—2441no—
320C22⋊C4—2441no—
321C22⋊C4—2441no—
322C22⋊C4C4×D6114yes—
323C42—41no—
324C42—2441no—
325C42—2441no—
326C42—2441no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—612no—
334C23—612no—
335C23—612no—
336C23—612no—
337C23—1228no—
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—
354C23C2×C4×D6112yes—
355C23C23×D6111yescharacteristic
356C2×C4—21no—
357C2×C4—21no—
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—612no—
373C2×C4—612no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1221no—
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—2444no—
391C2×C4—2444no—
392C2×C4C2×C4×D6112yes—
393C2×C4C2×C4×D6112yes—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—614no—
402C22—1222no—
403C22—1222no—
404C22—1222no—
405C22—1222no—
406C22—1222no—
407C22—1222no—
408C22—1222no—
409C22—1222no—
410C22—1222no—
411C22—24416no—
412C22—2441no—
413C22—2441no—
414C22—2441no—
415C22—2441no—
416C22C22×C4×D6111yescharacteristic
417C22#41×D6111yescharacteristic
418C22#41×D6111yescharacteristic
419C22#1451982211yescharacteristic
420C22#1451982211yescharacteristic
421C22#1451982311yescharacteristic
422C22#1451982311yescharacteristic
423C4—22no—
424C4—22no—
425C4—41no—
426C4—41no—
427C4—41no—
428C4—41no—
429C4—1222no—
430C4—1222no—
431C4—2441no—
432C4—2441no—
433C4—2441no—
434C4—2441no—
435C2—42no—
436C2—1224no—
437C2—2442no—
438C2#117×D6111yescharacteristic
439C2#1684023411yescharacteristic
440C2#1684023411yescharacteristic
441C2#1684034411yescharacteristic
442C2#1684034611yescharacteristic
443C2#1684034811yescharacteristic
444C2#1684035111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#388C2
socleC23×C61C24
hypercenter#388D61
hypocenterC61#2312
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #16839656C2semidirect
3. #16839655C2semidirect
4. #16839654C2semidirect
5. #16839653C2semidirect
6. #16839652C2semidirect
7. #16839651C2semidirect
8. #16839650C2semidirect
9. #16839621C2semidirect
10. #16839619C2semidirect
13. C4×#11758198C2semidirect
14. #16839609C2semidirect
15. C61×#388C2semidirect
19. C2×C4⋊Dic61C22semidirect
20. C2×#11758196C22semidirect
21. C2×#11758196C22semidirect
35. C22⋊C4×D61C4semidirect
36. C2×C4×Dic61C22semidirect
37. C2×C4×Dic61C22semidirect
38. C2×C4×Dic61C22semidirect
39. #14519684C22semidirect
40. #14519684C22semidirect
41. #14519684C22semidirect
42. #14519684C22semidirect
43. #14519684C22semidirect
44. #14519684C22semidirect
45. C2×C4⋊C4×C61C22semidirect
49. C2×C42×C61C22semidirect
50. #95×C61C22semidirect
51. #95×C61C22semidirect
231. #388D61semidirect
238. C61#2312semidirect
245. C2×C4⋊C4C2×D61semidirect
266. C2×C42C2×D61semidirect
273. #95C2×D61semidirect
274. #95C2×D61semidirect