Finite Group Databasebeta

← #21451629

Subgroups — #21451629

Order 7808.

668 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519755C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D61C211yesmaximal, characteristic
3#16839698C211yesmaximal, characteristic, complemented
4#16839697C211yesmaximal, characteristic, complemented
5#16839685C211yesmaximal, characteristic, complemented
6#16839684C211yesmaximal, characteristic, complemented
7#16839684C211yesmaximal, characteristic, complemented
8#16839675C211yesmaximal, characteristic, complemented
9#16839674C211yesmaximal, characteristic, complemented
10#16839636C211yesmaximal, characteristic, complemented
11#16839633C211yesmaximal, characteristic, complemented
12#16839619C211yesmaximal, characteristic, complemented
13#16839617C211yesmaximal, characteristic
14#16839617C211yesmaximal, characteristic
15C61×#396C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×Dic122C2211yescharacteristic, complemented
18C22×C4×D61C2211yescharacteristic
19C22×C4×D61C2211yescharacteristic
20#14519755—24no—
21C2×C4⋊Dic61C2211yescharacteristic, complemented
22C2×C4⋊Dic61C2211yescharacteristic, complemented
23C2×#11758196C2211yescharacteristic, complemented
24C2×#11758196C2211yescharacteristic, complemented
25C2×#11758196C2211yescharacteristic, complemented
26C2×#11758196C2211yescharacteristic, complemented
27C2×C22⋊Dic61C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×C22⋊Dic61C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C22⋊C4×D61—24no—
41#14519684C2211yescharacteristic, complemented
42#14519684C2211yescharacteristic, complemented
43#14519684C2211yescharacteristic, complemented
44#14519684C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46C2×C4⋊C4×C61C2211yescharacteristic, complemented
47C2×C4⋊C4×C61C2211yescharacteristic, complemented
48C2×C4⋊C4×C61C2211yescharacteristic, complemented
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52#95×C61C2211yescharacteristic, complemented
53C24×C61C2311yescharacteristic
54C23×D61—22no—
55C23×D61—22no—
56C23×D61—41no—
57C23×D61—41no—
58C23×D61—41no—
59C23×D61—41no—
60C23×D61Q814yescomplemented
61C23×D61C2311yescharacteristic
62C23×D61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
69C22×Dic61C2311yescharacteristic
70C22×Dic61C2311yescharacteristic
71C22×Dic61C2311yescharacteristic
72C22×Dic61C2311yescharacteristic
73C22×Dic61C2311yescharacteristic
74C22×Dic61C2311yescharacteristic
75C2×C4×D61—22no—
76C2×C4×D61—41no—
77C2×C4×D61—41no—
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C2×C4×D61D414yes—
81C2×Dic122—22no—
82C2×Dic122—41no—
83C2×Dic122—41no—
84C4⋊C4×C61—22no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C22⋊C4×C61—22no—
88C22⋊C4×C61—41no—
89C22⋊C4×C61—41no—
90C22⋊Dic61—22no—
91C22⋊Dic61—41no—
92C22⋊Dic61—41no—
93#11758198—22no—
94#11758198—22no—
95#11758198—22no—
96#11758198—22no—
97#11758198—22no—
98#11758198—22no—
99#11758198—41no—
100#11758198—41no—
101#11758198—41no—
102#11758198—41no—
103C4⋊Dic61—41no—
104C4⋊Dic61—41no—
105#11758196—22no—
106#11758196—22no—
107#11758196—41no—
108#11758196—41no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61C2×Q812yes—
116C23×C61C2411yescharacteristic
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—21no—
127C22×D61—28no—
128C22×D61—44no—
129C22×D61—44no—
130C22×D61—44no—
131C22×D61—44no—
132C22×D61—44no—
133C22×D61—44no—
134C22×D61C2×D412yes—
135C22×D61C2×Q812yes—
136C22×D61C2×Q812yes—
137C22×D61#4112yes—
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—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61C2×D412yes—
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—21no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61C2×D412yes—
174C4×D61—44no—
175C4×D61—44no—
176Dic122—44no—
177C22×C61—22no—
178C22×C61—22no—
179C22×C61—22no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61C22×D411yescharacteristic
185C22×C61C22×Q811yescharacteristic
186C22×C61C2×#4111yescharacteristic
187C22×C61H(5,𝔽2)11yescharacteristic
188C22×C61H(5,𝔽2)11yescharacteristic
189C22×C61H(5,𝔽2)11yescharacteristic
190C22×C61H(5,𝔽2)11yescharacteristic
191C2×D61—22no—
192C2×D61—22no—
193C2×D61—22no—
194C2×D61—22no—
195C2×D61—22no—
196C2×D61—22no—
197C2×D61—22no—
198C2×D61—22no—
199C2×D61—22no—
200C2×D61—416no—
201C2×D61—41no—
202C2×D61—41no—
203C2×D61—41no—
204C2×D61—41no—
205C2×D61C22⋊Q814yes—
206C4×C61—22no—
207C4×C61—41no—
208C4×C61—41no—
209C4×C61—41no—
210C4×C61—41no—
211C4×C61—41no—
212Dic61—22no—
213Dic61—41no—
214Dic61—41no—
215Dic61—41no—
216Dic61—41no—
217Dic61—41no—
218#2626—611nomaximal, Sylow
219C2×C61—42no—
220C2×C61C2×C22⋊Q811yescharacteristic
221C2×C61#53411yescharacteristic
222C2×C61#53511yescharacteristic
223C2×C61#53811yescharacteristic
224C2×C61#53811yescharacteristic
225C2×C61#54311yescharacteristic
226C2×C61#54311yescharacteristic
227D61—24no—
228D61—42no—
229C2×C22⋊Q8—611no—
230C22×C22⋊C4—611no—
231#399—611no—
232#399—611no—
233#396—611no—
234#396—611no—
235#396—611no—
236#396D6111yescharacteristic, complemented
237#393—611no—
238#393—611no—
239#385—611no—
240#385—611no—
241#380—611no—
242#379—611no—
243#379—611no—
244C61#262611yescharacteristic, complemented, Sylow
245C25—611no—
246C22×Q8—611no—
247C23×C4—611no—
248C23×C4—611no—
249C22⋊Q8—1224no—
250C2×C4⋊C4—611no—
251C2×C4⋊C4—611no—
252C2×C4⋊C4—611no—
253C2×C4⋊C4—611no—
254C2×C4⋊C4—611no—
255C2×C4⋊C4—611no—
256C2×C4⋊C4C2×D6111yescharacteristic, complemented
257C2×C4⋊C4C2×D6111yescharacteristic, complemented
258C2×C4⋊C4C2×D6111yescharacteristic, complemented
259C2×C22⋊C4—611no—
260C2×C22⋊C4—611no—
261C2×C22⋊C4—611no—
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—611no—
271C2×C22⋊C4—611no—
272C2×C22⋊C4—1224no—
273C2×C22⋊C4C2×D6111yescharacteristic
274C2×C22⋊C4C2×D6111yescharacteristic
275C2×C22⋊C4C2×D6111yescharacteristic
276#95—611no—
277#95—611no—
278#95—611no—
279#95—611no—
280#95—611no—
281#95C2×D6111yescharacteristic, complemented
282C24—611no—
283C24—611no—
284C24—614no—
285C24—1222no—
286C24—1222no—
287C24—2441no—
288C24—2441no—
289C24—2441no—
290C24—2441no—
291C24C22×D6111yescharacteristic
292C2×Q8—1222no—
293C2×Q8—2441no—
294C2×Q8—2441no—
295C22×C4—611no—
296C22×C4—614no—
297C22×C4—611no—
298C22×C4—611no—
299C22×C4—611no—
300C22×C4—611no—
301C22×C4—611no—
302C22×C4—1222no—
303C22×C4—2441no—
304C22×C4—2441no—
305C22×C4—2441no—
306C22×C4—2441no—
307C22×C4C22×D6111yescharacteristic
308C22×C4C22×D6111yescharacteristic
309C22×C4C22×D6111yescharacteristic
310C22×C4C22×D6111yescharacteristic
311C22×C4C22×D6111yescharacteristic
312C22×C4C22×D6111yescharacteristic
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—1222no—
317C4⋊C4—1222no—
318C4⋊C4—2441no—
319C4⋊C4—2441no—
320C4⋊C4—2441no—
321C4⋊C4—2441no—
322C22⋊C4—22no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—1222no—
326C22⋊C4—1222no—
327C22⋊C4—1222no—
328C22⋊C4—1222no—
329C22⋊C4—1222no—
330C22⋊C4—1222no—
331C22⋊C4—1222no—
332C22⋊C4—2441no—
333C22⋊C4—2441no—
334C22⋊C4—2441no—
335C22⋊C4—2441no—
336C22⋊C4—2441no—
337C22⋊C4—2441no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—612no—
345C23—612no—
346C23—612no—
347C23—612no—
348C23—1228no—
349C23—1221no—
350C23—1221no—
351C23—1221no—
352C23—1221no—
353C23—1221no—
354C23—1221no—
355C23—1221no—
356C23—1221no—
357C23—1221no—
358C23—1221no—
359C23—2444no—
360C23—2444no—
361C23—2444no—
362C23—2444no—
363C23—2444no—
364C23—2444no—
365C23Q8×D6112yes—
366C23C23×D6111yescharacteristic
367Q8—2444no—
368C2×C4—21no—
369C2×C4—21no—
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—1221no—
387C2×C4—1221no—
388C2×C4—1221no—
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—2444no—
404C2×C4—2444no—
405C2×C4D4×D6112yes—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—614no—
414C22—1222no—
415C22—1222no—
416C22—1222no—
417C22—1222no—
418C22—1222no—
419C22—1222no—
420C22—1222no—
421C22—1222no—
422C22—1222no—
423C22—24416no—
424C22—2441no—
425C22—2441no—
426C22—2441no—
427C22—2441no—
428C22C2×D4×D6111yescharacteristic
429C22C2×Q8×D6111yescharacteristic
430C22#41×D6111yescharacteristic
431C22#1451982211yescharacteristic
432C22#1451982211yescharacteristic
433C22#1451982311yescharacteristic
434C22#1451982311yescharacteristic
435C4—22no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—41no—
440C4—41no—
441C4—1222no—
442C4—2441no—
443C4—2441no—
444C4—2441no—
445C4—2441no—
446C4—2441no—
447C2—42no—
448C2—1224no—
449C2—2442no—
450C2C22⋊Q8×D6111yescharacteristic
451C2#1684032011yescharacteristic
452C2#1684032811yescharacteristic
453C2#1684034411yescharacteristic
454C2#1684035111yescharacteristic
455C2#1684038711yescharacteristic
456C2#1684038711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#396C2
hypercenter#396D61
hypocenterC61#2626
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#14519755C2semidirect
3. #16839698C2semidirect
4. #16839697C2semidirect
5. #16839685C2semidirect
6. #16839684C2semidirect
7. #16839684C2semidirect
8. #16839675C2semidirect
9. #16839674C2semidirect
10. #16839636C2semidirect
11. #16839633C2semidirect
12. #16839619C2semidirect
15. C61×#396C2semidirect
17. C22×Dic122C22semidirect
21. C2×C4⋊Dic61C22semidirect
22. C2×C4⋊Dic61C22semidirect
23. C2×#11758196C22semidirect
24. C2×#11758196C22semidirect
25. C2×#11758196C22semidirect
26. C2×#11758196C22semidirect
41. #14519684C22semidirect
42. #14519684C22semidirect
43. #14519684C22semidirect
44. #14519684C22semidirect
45. #14519684C22semidirect
46. C2×C4⋊C4×C61C22semidirect
47. C2×C4⋊C4×C61C22semidirect
48. C2×C4⋊C4×C61C22semidirect
52. #95×C61C22semidirect
60. C23×D61Q8semidirect
236. #396D61semidirect
244. C61#2626semidirect
256. C2×C4⋊C4C2×D61semidirect
257. C2×C4⋊C4C2×D61semidirect
258. C2×C4⋊C4C2×D61semidirect
281. #95C2×D61semidirect