Finite Group Databasebeta

← #21457425

Subgroups — #21457425

Order 7808.

520 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519804C211yesmaximal, characteristic, complemented
2C2×#14519801C211yesmaximal, characteristic, complemented
3#16840407C211yesmaximal, characteristic, complemented
4#16840405C211yesmaximal, characteristic, complemented
5#16840144C211yesmaximal, characteristic, complemented
6#16840011C211yesmaximal, characteristic, complemented
7#16840007C211yesmaximal, characteristic, complemented
8#16839978C211yesmaximal, characteristic, complemented
9#16839927C211yesmaximal, characteristic, complemented
10#16839921C211yesmaximal, characteristic, complemented
11#16839897C211yesmaximal, characteristic, complemented
12#16839894C211yesmaximal, characteristic, complemented
13C4×#11758199C211yesmaximal, characteristic, complemented
14#16839839C211yesmaximal, characteristic, complemented
15C61×#463C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×D4×D61C2211yescharacteristic, complemented
19C2×D4×D61C2211yescharacteristic, complemented
20#14519804—24no—
21#14519801—24no—
22C2×#11758202C2211yescharacteristic, complemented
23C2×#11758190C2211yescharacteristic, complemented
24C2×#11758200C2211yescharacteristic, complemented
25C2×#11758201C2211yescharacteristic, complemented
26C2×D488C2211yescharacteristic
27C2×#11758199C2211yescharacteristic
28C2×#11758199C2211yescharacteristic
29C2×#11758189C2211yescharacteristic, complemented
30C2×#11758189C2211yescharacteristic, complemented
31#14519765C2211yescharacteristic, complemented
32#14519761—21no—
33#14519759—21no—
34#14519757C2211yescharacteristic, complemented
35#14519753C2211yescharacteristic, complemented
36#14519752C2211yescharacteristic
37#14519751—21no—
38#14519750—21no—
39#14519748C2211yescharacteristic
40#14519747—21no—
41#14519747—21no—
42C4×D244C2211yescharacteristic
43C4×D244C2211yescharacteristic, complemented
44C2×#11758198—21no—
45C22⋊C4×D61—21no—
46#14519710C2211yescharacteristic, complemented
47#14519702C2211yescharacteristic, complemented
48#14519699C2211yescharacteristic, complemented
49#14519698C2211yescharacteristic, complemented
50#14519697C2211yescharacteristic, complemented
51#14519689C2211yescharacteristic, complemented
52#14519689C2211yescharacteristic, complemented
53C4×#92418C2211yescharacteristic, complemented
54C2×SD16×C61C2211yescharacteristic, complemented
55C2×D8×C61C2211yescharacteristic
56#124×C61C2211yescharacteristic, complemented
57C4×D4×C61C2211yescharacteristic, complemented
58C4⋊C8×C61C2211yescharacteristic, complemented
59#103×C61C2211yescharacteristic, complemented
60#102×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C23×D61—21no—
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C22×Dic61—21no—
72#11758226—22no—
73#11758226—41no—
74#11758224—22no—
75#11758224—41no—
76D4×D61—22no—
77D4×D61—22no—
78D4×D61—41no—
79D4×D61—41no—
80C2×D244—21no—
81C2×D244—21no—
82C2×D244D411yescharacteristic
83C2×D244C2311yescharacteristic
84C2×D244C2311yescharacteristic
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61C2311yescharacteristic
88C2×C4×D61C2311yescharacteristic
89C2×Dic122C2311yescharacteristic
90SD16×C61—22no—
91D8×C61—22no—
92C2×C8×C61C2311yescharacteristic
93C2×C8×C61C2311yescharacteristic
94C4⋊C4×C61C2311yescharacteristic
95C22⋊C4×C61—21no—
96C22⋊C4×C61—21no—
97C22⋊C4×C61—21no—
98C42×C61C2311yescharacteristic
99C22⋊Dic61—21no—
100#11758202—41no—
101#11758201—22no—
102#11758200—22no—
103#11758199—41no—
104#11758199D414yescomplemented
105#11758198—21no—
106#11758198—21no—
107#11758198—21no—
108#11758198—21no—
109#11758198—21no—
110#11758198—21no—
111#11758198D411yescharacteristic
112#11758198D411yescharacteristic
113C4⋊Dic61—21no—
114C4⋊Dic61D411yescharacteristic
115C4⋊Dic61C2311yescharacteristic
116#11758196—21no—
117C2×#92418C2311yescharacteristic
118C2×#92418C2311yescharacteristic
119D488—22no—
120#11758190—22no—
121#11758189—22no—
122#11758189—22no—
123C23×C61—21no—
124C23×C61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—42no—
128C22×D61—42no—
129C22×D61—42no—
130C22×D61—42no—
131C22×D61—81no—
132C22×D61—81no—
133C22×D61C2×D411yescharacteristic
134C22×D61C2×D411yescharacteristic
135Q8×C61—21no—
136Q8×C61—21no—
137D4×C61—21no—
138D4×C61—21no—
139D4×C61—21no—
140D4×C61C2×D412yes—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—81no—
144C2×C4×C61C2×D411yescharacteristic
145C2×C4×C61C2×D411yescharacteristic
146C2×C4×C61C2411yescharacteristic
147C22⋊D61—42no—
148C22⋊D61—42no—
149C22⋊D61—42no—
150C22⋊D61—81no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—42no—
154C2×Dic61C2×D411yescharacteristic
155C2×Dic61C2×D411yescharacteristic
156D244—21no—
157D244—21no—
158D244—21no—
159D244—41no—
160D244—42no—
161D244—81no—
162D244C2×D412yes—
163C4×D61—21no—
164C4×D61—21no—
165C4×D61—21no—
166C4×D61—21no—
167C4×D61—42no—
168C4×D61—81no—
169Dic122—21no—
170Dic122—21no—
171C8×C61—21no—
172C8×C61—21no—
173#92418—21no—
174#92418C2×D412yes—
175C22×C61—22no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61C22×D411yescharacteristic
182C2×D61—21no—
183C2×D61—21no—
184C2×D61—22no—
185C2×D61—21no—
186C2×D61—21no—
187C2×D61—21no—
188C2×D61—21no—
189C2×D61—41no—
190C2×D61—41no—
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—84no—
195C2×D61—84no—
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—41no—
199C4×C61—41no—
200C4×C61C22×D411yescharacteristic
201C4×C61H(5,𝔽2)11yescharacteristic
202Dic61—21no—
203Dic61—21no—
204Dic61—41no—
205Dic61—41no—
206#3273—611nomaximal, Sylow
207C2×C61—42no—
208C2×C61—81no—
209C2×C61D4211yescharacteristic
210C2×C61#57511yescharacteristic
211C2×C61#57611yescharacteristic
212D61—41no—
213D61—41no—
214D61—42no—
215D61—81no—
216C2×AGL(1,ℤ/8)—611no—
217C2×AGL(1,ℤ/8)—611no—
218#546—611no—
219#546—611no—
220#495—611no—
221#468—611no—
222#468—611no—
223#463—611no—
224#463D6111yescharacteristic, complemented
225#452—611no—
226#452—611no—
227#447—611no—
228#447—611no—
229C4×D8—611no—
230#436—611no—
231C61#327311yescharacteristic, complemented, Sylow
232C2×#41—611no—
233C2×#41—611no—
234C22×D4—611no—
235C22×D4—611no—
236AGL(1,ℤ/8)—1224no—
237AGL(1,ℤ/8)—1224no—
238C2×Q16—611no—
239C2×SD16—611no—
240C2×SD16—611no—
241C2×SD16—611no—
242C2×SD16C2×D6111yescharacteristic, complemented
243C2×D8—611no—
244C2×D8—611no—
245C2×D8—611no—
246C2×D8C2×D6111yescharacteristic
247C2×M16—611no—
248C2×M16—611no—
249#124—611no—
250#124C2×D6111yescharacteristic, complemented
251#123—1221no—
252#123—1221no—
253C22⋊Q8—611no—
254C22⋊Q8—611no—
255#121—611no—
256#121—611no—
257#121—1221no—
258#121—1221no—
259#120—1221no—
260#120—1221no—
261C4×D4—611no—
262C4×D4—611no—
263C4×D4C2×D6111yescharacteristic, complemented
264C2×C22⋊C4—1221no—
265C2×C22⋊C4—1221no—
266#107—611no—
267C4⋊C8C2×D6111yescharacteristic, complemented
268#103—611no—
269#103C2×D6111yescharacteristic, complemented
270#102—611no—
271#102—611no—
272#102—611no—
273#102C2×D6111yescharacteristic, complemented
274C22⋊C8—611no—
275C22⋊C8—611no—
276C4×C8—611no—
277C24—1221no—
278C24—1221no—
279#41—1222no—
280#41—1222no—
281#41—2441no—
282#41—2441no—
283C2×Q8—611no—
284C2×Q8C22×D6111yescharacteristic
285C2×D4—611no—
286C2×D4—611no—
287C2×D4—611no—
288C2×D4—1221no—
289C2×D4—1221no—
290C2×D4—1221no—
291C2×D4—1221no—
292C2×D4—1222no—
293C2×D4—1222no—
294C2×D4—1221no—
295C2×D4—1221no—
296C2×D4—2441no—
297C2×D4—2441no—
298C2×D4C22×D6111yescharacteristic
299C2×D4C22×D6111yescharacteristic
300C22×C4—21no—
301C22×C4—611no—
302C22×C4—611no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—1221no—
306Q16—2441no—
307SD16—22no—
308SD16—1222no—
309SD16—1222no—
310SD16—1222no—
311D8—22no—
312D8—614no—
313D8—1222no—
314D8—2441no—
315M16—1222no—
316M16—1222no—
317C2×C8—611no—
318C2×C8—611no—
319C2×C8C22×D6111yescharacteristic
320C2×C8C22×D6111yescharacteristic
321C4⋊C4—611no—
322C4⋊C4—611no—
323C4⋊C4—1221no—
324C4⋊C4—1221no—
325C4⋊C4C22×D6111yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—611no—
330C22⋊C4—611no—
331C22⋊C4—1221no—
332C22⋊C4—1221no—
333C22⋊C4—1221no—
334C22⋊C4—1221no—
335C22⋊C4—1221no—
336C22⋊C4—1221no—
337C22⋊C4—1221no—
338C42C22×D6111yescharacteristic
339C23—21no—
340C23—21no—
341C23—611no—
342C23—611no—
343C23—1221no—
344C23—1221no—
345C23—4881no—
346C23—4881no—
347C23—2442no—
348C23—2442no—
349C23—2442no—
350C23—2442no—
351Q8—21no—
352Q8—21no—
353Q8—1221no—
354Q8—1221no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—612no—
359D4—1221no—
360D4—1221no—
361D4—1221no—
362D4—4881no—
363D4—4881no—
364D4—2441no—
365D4—2442no—
366D4—2442no—
367D4—2442no—
368D4—2442no—
369D4D4×D6112yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—611no—
374C2×C4—611no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—4881no—
382C2×C4—2442no—
383C2×C4—2442no—
384C2×C4D4×D6111yescharacteristic
385C2×C4D4×D6111yescharacteristic
386C2×C4C23×D6111yescharacteristic
387C8—21no—
388C8—21no—
389C8—612no—
390C8—1221no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—1221no—
398C22—1221no—
399C22—1221no—
400C22—1221no—
401C22—1221no—
402C22—1221no—
403C22—1222no—
404C22—4884no—
405C22—4884no—
406C22—2441no—
407C22—2441no—
408C22—2441no—
409C22—2441no—
410C22—2441no—
411C22C2×D4×D6111yescharacteristic
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—1221no—
417C4—1221no—
418C4—2441no—
419C4—2441no—
420C4C2×D4×D6111yescharacteristic
421C4#1451982311yescharacteristic
422C2—42no—
423C2—81no—
424C2—4881no—
425C2—2441no—
426C2—2441no—
427C2—2442no—
428C2#1684039611yescharacteristic
429C2#1684055911yescharacteristic
430C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#463C2
socleC22×C61C22×D4
hypercenter#463D61
hypocenterC61#3273
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#14519804C2semidirect
2. C2×#14519801C2semidirect
3. #16840407C2semidirect
4. #16840405C2semidirect
5. #16840144C2semidirect
6. #16840011C2semidirect
7. #16840007C2semidirect
8. #16839978C2semidirect
9. #16839927C2semidirect
10. #16839921C2semidirect
11. #16839897C2semidirect
12. #16839894C2semidirect
13. C4×#11758199C2semidirect
14. #16839839C2semidirect
15. C61×#463C2semidirect
18. C2×D4×D61C22semidirect
19. C2×D4×D61C22semidirect
22. C2×#11758202C22semidirect
23. C2×#11758190C22semidirect
24. C2×#11758200C22semidirect
25. C2×#11758201C22semidirect
29. C2×#11758189C22semidirect
30. C2×#11758189C22semidirect
31. #14519765C22semidirect
34. #14519757C22semidirect
35. #14519753C22semidirect
43. C4×D244C22semidirect
46. #14519710C22semidirect
47. #14519702C22semidirect
48. #14519699C22semidirect
49. #14519698C22semidirect
50. #14519697C22semidirect
51. #14519689C22semidirect
52. #14519689C22semidirect
53. C4×#92418C22semidirect
54. C2×SD16×C61C22semidirect
56. #124×C61C22semidirect
57. C4×D4×C61C22semidirect
58. C4⋊C8×C61C22semidirect
59. #103×C61C22semidirect
60. #102×C61C22semidirect
104. #11758199D4semidirect
224. #463D61semidirect
231. C61#3273semidirect
242. C2×SD16C2×D61semidirect
250. #124C2×D61semidirect
263. C4×D4C2×D61semidirect
267. C4⋊C8C2×D61semidirect
269. #103C2×D61semidirect
273. #102C2×D61semidirect