Finite Group Databasebeta

← #21457423

Subgroups — #21457423

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×#14519802C211yesmaximal, characteristic, complemented
3#16840403C211yesmaximal, characteristic, complemented
4#16840400C211yesmaximal, characteristic, complemented
5#16840147C211yesmaximal, characteristic, complemented
6#16840011C211yesmaximal, characteristic, complemented
7#16840010C211yesmaximal, characteristic, complemented
8#16839980C211yesmaximal, characteristic, complemented
9#16839979C211yesmaximal, characteristic, complemented
10#16839923C211yesmaximal, characteristic, complemented
11#16839898C211yesmaximal, characteristic, complemented
12#16839897C211yesmaximal, characteristic, complemented
13#16839842C211yesmaximal, characteristic, complemented
14#16839837C211yesmaximal, characteristic, complemented
15C61×#452C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C22×D244C2211yescharacteristic, complemented
18C2×D4×D61C2211yescharacteristic, complemented
19#14519804—24no—
20#14519802—24no—
21C2×#11758201C2211yescharacteristic, complemented
22C2×#11758201C2211yescharacteristic, complemented
23C2×#11758201C2211yescharacteristic, complemented
24C2×D488C2211yescharacteristic
25C2×D488C2211yescharacteristic
26C2×#11758199C2211yescharacteristic
27C2×#11758199C2211yescharacteristic
28C2×#11758194C2211yescharacteristic, complemented
29C2×#11758189C2211yescharacteristic, complemented
30#14519766C2211yescharacteristic, complemented
31#14519766C2211yescharacteristic, complemented
32#14519762—21no—
33#14519760—21no—
34#14519753C2211yescharacteristic, complemented
35#14519752—21no—
36#14519752C2211yescharacteristic
37#14519751C2211yescharacteristic
38#14519749—21no—
39#14519747—21no—
40#14519745—21no—
41D4×Dic61C2211yescharacteristic, complemented
42#14519739C2211yescharacteristic, complemented
43C4×C22⋊D61C2211yescharacteristic
44C2×#11758198—21no—
45C22⋊C4×D61—21no—
46#14519710C2211yescharacteristic, complemented
47#14519706C2211yescharacteristic, complemented
48#14519701C2211yescharacteristic, complemented
49#14519699C2211yescharacteristic, complemented
50#14519699C2211yescharacteristic, complemented
51#14519697C2211yescharacteristic, complemented
52#14519689C2211yescharacteristic, complemented
53C8×Dic61C2211yescharacteristic, complemented
54C2×#41×C61C2211yescharacteristic
55C2×Q16×C61C2211yescharacteristic, complemented
56C2×SD16×C61C2211yescharacteristic, complemented
57C22⋊Q8×C61C2211yescharacteristic, complemented
58#103×C61C2211yescharacteristic, complemented
59#102×C61C2211yescharacteristic, complemented
60C22⋊C8×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C23×D61—21no—
63#41×C61—22no—
64#41×C61—41no—
65C2×Q8×C61C2311yescharacteristic
66C2×Q8×C61C2311yescharacteristic
67C2×D4×C61—21no—
68C2×D4×C61C2311yescharacteristic
69C22×C4×C61—21no—
70C22×C4×C61C2311yescharacteristic
71C2×C22⋊D61—21no—
72C2×C22⋊D61—21no—
73C2×C22⋊D61D411yescharacteristic
74C22×Dic61—21no—
75#11758226—22no—
76#11758226—41no—
77D4×D61—22no—
78D4×D61—41no—
79C2×D244—22no—
80C2×D244—21no—
81C2×D244—21no—
82C2×D244—21no—
83C2×D244—41no—
84C2×D244C2311yescharacteristic
85C2×D244C2311yescharacteristic
86C2×D244C2311yescharacteristic
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61C2311yescharacteristic
90Q16×C61—41no—
91SD16×C61—22no—
92C2×C8×C61C2311yescharacteristic
93C2×C8×C61C2311yescharacteristic
94C4⋊C4×C61—21no—
95C4⋊C4×C61C2311yescharacteristic
96C22⋊C4×C61—21no—
97C22⋊Dic61—21no—
98C22⋊Dic61D411yescharacteristic
99#11758201—22no—
100#11758201—22no—
101#11758201—22no—
102#11758199—22no—
103#11758199D414yescomplemented
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107#11758198—21no—
108#11758198—21no—
109#11758198—21no—
110#11758198—21no—
111#11758198—21no—
112#11758198D411yescharacteristic
113C4⋊Dic61C2311yescharacteristic
114#11758196—21no—
115#11758196D411yescharacteristic
116C4×Dic61C2311yescharacteristic
117#11758194—22no—
118C2×#92418C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120D488—22no—
121D488—41no—
122#11758189—22no—
123C23×C61—21no—
124C23×C61C2×D411yescharacteristic
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—42no—
129C22×D61—42no—
130C22×D61—42no—
131C22×D61—42no—
132C22×D61—81no—
133C22×D61—81no—
134C22×D61C2×D411yescharacteristic
135Q8×C61—21no—
136Q8×C61—21no—
137Q8×C61—21no—
138Q8×C61—21no—
139D4×C61—21no—
140D4×C61—42no—
141D4×C61C2×D412yes—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—42no—
148C2×C4×C61C2×D411yescharacteristic
149C2×C4×C61C2411yescharacteristic
150C22⋊D61—41no—
151C22⋊D61—42no—
152C22⋊D61—81no—
153C2×Dic61—21no—
154C2×Dic61—81no—
155C2×Dic61C2×D411yescharacteristic
156C2×Dic61C2×D411yescharacteristic
157C2×Dic61C2×D411yescharacteristic
158D244—21no—
159D244—21no—
160D244—21no—
161D244—21no—
162D244—21no—
163D244—42no—
164D244—42no—
165D244—81no—
166D244C2×D412yes—
167C4×D61—21no—
168C4×D61—21no—
169C4×D61—42no—
170C4×D61—81no—
171C8×C61—21no—
172C8×C61—21no—
173#92418—21no—
174#92418C2×D412yes—
175C22×C61—22no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61C22×D411yescharacteristic
182C2×D61—21no—
183C2×D61—22no—
184C2×D61—21no—
185C2×D61—21no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—41no—
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—41no—
198C4×C61—41no—
199C4×C61—41no—
200C4×C61C22×D411yescharacteristic
201C4×C61H(5,𝔽2)11yescharacteristic
202Dic61—21no—
203Dic61—21no—
204Dic61—21no—
205Dic61—41no—
206#3273—611nomaximal, Sylow
207C2×C61—41no—
208C2×C61—42no—
209C2×C61D4211yescharacteristic
210C2×C61#57511yescharacteristic
211C2×C61#57611yescharacteristic
212D61—41no—
213D61—42no—
214D61—81no—
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#463—611no—
225#452—611no—
226#452D6111yescharacteristic, complemented
227#447—611no—
228#447—611no—
229C4×D8—611no—
230#436—611no—
231C61#327311yescharacteristic, complemented, Sylow
232C2×#41—611no—
233C2×#41C2×D6111yescharacteristic
234C22×D4—611no—
235C22×D4—611no—
236AGL(1,ℤ/8)—1224no—
237AGL(1,ℤ/8)—1224no—
238C2×Q16C2×D6111yescharacteristic, complemented
239C2×SD16—611no—
240C2×SD16—611no—
241C2×SD16—611no—
242C2×SD16C2×D6111yescharacteristic, complemented
243C2×D8—611no—
244C2×D8—611no—
245C2×D8—611no—
246C2×D8—611no—
247C2×M16—611no—
248C2×M16—611no—
249#124—611no—
250#124—611no—
251#123—1221no—
252#123—1221no—
253C22⋊Q8—611no—
254C22⋊Q8C2×D6111yescharacteristic, complemented
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×D4—611no—
264C2×C22⋊C4—1221no—
265C2×C22⋊C4—1221no—
266#107—611no—
267C4⋊C8—611no—
268#103—611no—
269#103C2×D6111yescharacteristic, complemented
270#102—611no—
271#102—611no—
272#102—611no—
273#102C2×D6111yescharacteristic, complemented
274C22⋊C8—611no—
275C22⋊C8C2×D6111yescharacteristic, complemented
276C4×C8—611no—
277C24—1221no—
278C24—1221no—
279#41—22no—
280#41—41no—
281#41—1222no—
282#41—2441no—
283C2×Q8C22×D6111yescharacteristic
284C2×Q8C22×D6111yescharacteristic
285C2×D4—21no—
286C2×D4—611no—
287C2×D4—611no—
288C2×D4—611no—
289C2×D4—611no—
290C2×D4—1222no—
291C2×D4—1221no—
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—1222no—
295C2×D4—1221no—
296C2×D4—1221no—
297C2×D4—2441no—
298C2×D4—2441no—
299C2×D4C22×D6111yescharacteristic
300C22×C4—21no—
301C22×C4—611no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4C22×D6111yescharacteristic
306Q16—41no—
307SD16—22no—
308SD16—1222no—
309SD16—1222no—
310SD16—1222no—
311D8—614no—
312D8—1222no—
313D8—1222no—
314D8—2441no—
315M16—1222no—
316M16—1222no—
317C2×C8—611no—
318C2×C8—611no—
319C2×C8C22×D6111yescharacteristic
320C2×C8C22×D6111yescharacteristic
321C4⋊C4—21no—
322C4⋊C4—611no—
323C4⋊C4—611no—
324C4⋊C4—1221no—
325C4⋊C4C22×D6111yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—611no—
328C22⋊C4—611no—
329C22⋊C4—1221no—
330C22⋊C4—1221no—
331C22⋊C4—1221no—
332C22⋊C4—1221no—
333C22⋊C4—1221no—
334C22⋊C4—1221no—
335C22⋊C4—1221no—
336C22⋊C4—1221no—
337C22⋊C4—1221no—
338C42—611no—
339C23—21no—
340C23—611no—
341C23—1221no—
342C23—1221no—
343C23—1221no—
344C23—4881no—
345C23—4881no—
346C23—2442no—
347C23—2442no—
348C23—2442no—
349C23—2442no—
350C23D4×D6111yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—21no—
354Q8—21no—
355D4—21no—
356D4—42no—
357D4—612no—
358D4—1221no—
359D4—1221no—
360D4—1221no—
361D4—1221no—
362D4—1221no—
363D4—4881no—
364D4—4881no—
365D4—2442no—
366D4—2442no—
367D4—2441no—
368D4—2442no—
369D4D4×D6112yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—611no—
377C2×C4—611no—
378C2×C4—611no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—1221no—
382C2×C4—4881no—
383C2×C4—4881no—
384C2×C4—2442no—
385C2×C4D4×D6111yescharacteristic
386C2×C4C23×D6111yescharacteristic
387C8—21no—
388C8—21no—
389C8—612no—
390C8—1221no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—22no—
395C22—41no—
396C22—41no—
397C22—1221no—
398C22—1221no—
399C22—1221no—
400C22—1222no—
401C22—4884no—
402C22—4884no—
403C22—2441no—
404C22—2441no—
405C22—2441no—
406C22—2441no—
407C22—2441no—
408C22—2441no—
409C22—2441no—
410C22—2441no—
411C22C2×D4×D6111yescharacteristic
412C4—21no—
413C4—41no—
414C4—41no—
415C4—41no—
416C4—1221no—
417C4—1221no—
418C4—1221no—
419C4—2441no—
420C4C2×D4×D6111yescharacteristic
421C4#1451982211yescharacteristic
422C2—41no—
423C2—42no—
424C2—4881no—
425C2—4881no—
426C2—2441no—
427C2—2442no—
428C2#1684039411yescharacteristic
429C2#1684056111yescharacteristic
430C2#1684056411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#452C2
socleC22×C61C22×D4
hypercenter#452D61
hypocenterC61#3273
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#14519804C2semidirect
2. C2×#14519802C2semidirect
3. #16840403C2semidirect
4. #16840400C2semidirect
5. #16840147C2semidirect
6. #16840011C2semidirect
7. #16840010C2semidirect
8. #16839980C2semidirect
9. #16839979C2semidirect
10. #16839923C2semidirect
11. #16839898C2semidirect
12. #16839897C2semidirect
13. #16839842C2semidirect
14. #16839837C2semidirect
15. C61×#452C2semidirect
17. C22×D244C22semidirect
18. C2×D4×D61C22semidirect
21. C2×#11758201C22semidirect
22. C2×#11758201C22semidirect
23. C2×#11758201C22semidirect
28. C2×#11758194C22semidirect
29. C2×#11758189C22semidirect
30. #14519766C22semidirect
31. #14519766C22semidirect
34. #14519753C22semidirect
41. D4×Dic61C22semidirect
42. #14519739C22semidirect
46. #14519710C22semidirect
47. #14519706C22semidirect
48. #14519701C22semidirect
49. #14519699C22semidirect
50. #14519699C22semidirect
51. #14519697C22semidirect
52. #14519689C22semidirect
53. C8×Dic61C22semidirect
55. C2×Q16×C61C22semidirect
56. C2×SD16×C61C22semidirect
57. C22⋊Q8×C61C22semidirect
58. #103×C61C22semidirect
59. #102×C61C22semidirect
60. C22⋊C8×C61C22semidirect
103. #11758199D4semidirect
226. #452D61semidirect
231. C61#3273semidirect
238. C2×Q16C2×D61semidirect
242. C2×SD16C2×D61semidirect
254. C22⋊Q8C2×D61semidirect
269. #103C2×D61semidirect
273. #102C2×D61semidirect
275. C22⋊C8C2×D61semidirect