Finite Group Databasebeta

← #21457354

Subgroups — #21457354

Order 7808.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519804C211yesmaximal, characteristic, complemented
2C2×#14519800C211yesmaximal, characteristic, complemented
3#16840434C211yesmaximal, characteristic, complemented
4#16840405C211yesmaximal, characteristic, complemented
5#16840152C211yesmaximal, characteristic, complemented
6#16840011C211yesmaximal, characteristic, complemented
7#16839997C211yesmaximal, characteristic, complemented
8#16839958C211yesmaximal, characteristic, complemented
9#16839923C211yesmaximal, characteristic, complemented
10#16839910C211yesmaximal, characteristic, complemented
11#16839906C211yesmaximal, characteristic, complemented
12#16839897C211yesmaximal, characteristic, complemented
13#16839860C211yesmaximal, characteristic, complemented
14#16839832C211yesmaximal, characteristic, complemented
15C61×#464C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758226C2211yescharacteristic
18C2×#11758226C2211yescharacteristic, complemented
19C2×D4×D61C2211yescharacteristic
20#14519804—24no—
21#14519800—24no—
22C2×#11758201C2211yescharacteristic
23C2×#11758201C2211yescharacteristic, complemented
24C2×#11758201C2211yescharacteristic, complemented
25C2×D488C2211yescharacteristic
26C2×D488C2211yescharacteristic
27C2×#11758199C2211yescharacteristic
28C2×#11758199C2211yescharacteristic
29C2×#11758189C2211yescharacteristic
30C2×C8×D61C2211yescharacteristic, complemented
31#14519774—21no—
32#14519774C2211yescharacteristic, complemented
33#14519759—21no—
34#14519753C2211yescharacteristic
35#14519752—21no—
36#14519752—21no—
37#14519752C2211yescharacteristic
38#14519752C2211yescharacteristic, complemented
39#14519750—21no—
40#14519748C2211yescharacteristic
41#14519747—21no—
42C4×D244—21no—
43C4×D244C2211yescharacteristic
44C4×D244C2211yescharacteristic
45C22⋊C4×D61—21no—
46#14519710C2211yescharacteristic, complemented
47#14519701C2211yescharacteristic, complemented
48#14519699C2211yescharacteristic, complemented
49#14519699C2211yescharacteristic, complemented
50#14519697C2211yescharacteristic
51#14519689C2211yescharacteristic
52#14519689C2211yescharacteristic, complemented
53#14519688C2211yescharacteristic, complemented
54C2×Q16×C61C2211yescharacteristic, complemented
55C2×SD16×C61C2211yescharacteristic
56#124×C61C2211yescharacteristic
57C4×Q8×C61C2211yescharacteristic, complemented
58C4⋊C8×C61C2211yescharacteristic, complemented
59#103×C61C2211yescharacteristic, complemented
60#102×C61C2211yescharacteristic
61C23×D61—21no—
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67#11758226—22no—
68#11758226—22no—
69#11758226—22no—
70#11758226—41no—
71#11758226—41no—
72#11758226—41no—
73D4×D61—22no—
74D4×D61—41no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244—21no—
82C2×D244D411yescharacteristic
83C2×D244C2311yescharacteristic
84C2×D244C2311yescharacteristic
85C2×D244C2311yescharacteristic
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61C2311yescharacteristic
91C2×C4×D61C2311yescharacteristic
92Q16×C61—22no—
93SD16×C61—22no—
94C2×C8×C61C2311yescharacteristic
95C2×C8×C61C2311yescharacteristic
96C4⋊C4×C61—21no—
97C4⋊C4×C61C2311yescharacteristic
98C22⋊C4×C61—21no—
99C22⋊C4×C61—21no—
100C42×C61—21no—
101C42×C61C2311yescharacteristic
102C22⋊Dic61—21no—
103#11758201—22no—
104#11758201—41no—
105#11758201D414yescomplemented
106#11758199—22no—
107#11758199—41no—
108#11758198—21no—
109#11758198—21no—
110#11758198—21no—
111#11758198—21no—
112#11758198D411yescharacteristic
113#11758198D411yescharacteristic
114C4⋊Dic61D411yescharacteristic
115C4⋊Dic61C2311yescharacteristic
116#11758196—21no—
117C2×#92418C2311yescharacteristic
118C2×#92418C2311yescharacteristic
119D488—22no—
120D488—22no—
121#11758189—22no—
122C8×D61—22no—
123C23×C61—21no—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—42no—
128C22×D61—42no—
129C22×D61—81no—
130C22×D61C2×D411yescharacteristic
131C22×D61C2×D411yescharacteristic
132Q8×C61—21no—
133Q8×C61—21no—
134Q8×C61—21no—
135Q8×C61C2×D412yes—
136D4×C61—21no—
137D4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61C2×D411yescharacteristic
142C2×C4×C61C2×D411yescharacteristic
143C2×C4×C61C2411yescharacteristic
144C22⋊D61—42no—
145C22⋊D61—81no—
146C2×Dic61—21no—
147C2×Dic61C2×D411yescharacteristic
148C2×Dic61C2×D411yescharacteristic
149D244—21no—
150D244—21no—
151D244—21no—
152D244—21no—
153D244—21no—
154D244—41no—
155D244—42no—
156D244—42no—
157D244—42no—
158D244—42no—
159D244—81no—
160D244—81no—
161D244—81no—
162D244C2×D412yes—
163C4×D61—21no—
164C4×D61—21no—
165C4×D61—21no—
166C4×D61—21no—
167C4×D61—42no—
168C4×D61—42no—
169C4×D61—42no—
170C4×D61—81no—
171C8×C61—21no—
172C8×C61—21no—
173#92418—21no—
174#92418C2×D412yes—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61C22×D411yescharacteristic
179C2×D61—21no—
180C2×D61—21no—
181C2×D61—22no—
182C2×D61—21no—
183C2×D61—21no—
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—
195C4×C61—22no—
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—
205#3268—611nomaximal, Sylow
206C2×C61—81no—
207C2×C61D4211yescharacteristic
208C2×C61#57511yescharacteristic
209C2×C61#57611yescharacteristic
210D61—41no—
211D61—41no—
212D61—42no—
213D61—81no—
214D61—81no—
215C2×AGL(1,ℤ/8)—611no—
216C2×#135—611no—
217#550—611no—
218#546—611no—
219#496—611no—
220#468—611no—
221#466—611no—
222#464D6111yescharacteristic, complemented
223#459—611no—
224#452—611no—
225#449—611no—
226#449—611no—
227#447—611no—
228#440—611no—
229#435—611no—
230C61#326811yescharacteristic, complemented, Sylow
231C2×#41—611no—
232C2×#41—611no—
233C2×#41—611no—
234C22×D4—611no—
235AGL(1,ℤ/8)—1224no—
236#135—1224no—
237C2×Q16C2×D6111yescharacteristic, complemented
238C2×SD16—611no—
239C2×SD16—611no—
240C2×SD16—611no—
241C2×SD16C2×D6111yescharacteristic
242C2×D8—611no—
243C2×D8—611no—
244C2×D8—611no—
245C2×D8—611no—
246C2×M16—611no—
247C22×C8—611no—
248#127—611no—
249#127—1221no—
250#124C2×D6111yescharacteristic
251#123—1221no—
252C22⋊Q8—611no—
253#121—611no—
254#121—611no—
255#121—611no—
256#121—1221no—
257#121—1221no—
258#121—1221no—
259#120—1221no—
260C4×Q8C2×D6111yescharacteristic, complemented
261C4×D4—611no—
262C4×D4—611no—
263C4×D4—1221no—
264C2×C22⋊C4—1221no—
265#107—611no—
266C4⋊C8C2×D6111yescharacteristic, complemented
267#103—611no—
268#103C2×D6111yescharacteristic, complemented
269#102—611no—
270#102—611no—
271#102—611no—
272#102C2×D6111yescharacteristic
273C22⋊C8—611no—
274C22⋊C8—611no—
275#97—611no—
276C24—1221no—
277#41—1222no—
278#41—1222no—
279#41—1222no—
280#41—2441no—
281#41—2441no—
282#41—2441no—
283C2×Q8C22×D6111yescharacteristic
284C2×Q8C22×D6111yescharacteristic
285C2×D4—611no—
286C2×D4—611no—
287C2×D4—611no—
288C2×D4—611no—
289C2×D4—1221no—
290C2×D4—1221no—
291C2×D4—1221no—
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—1221no—
295C2×D4—1222no—
296C2×D4—1221no—
297C2×D4—1221no—
298C2×D4—1221no—
299C2×D4—2441no—
300C2×D4C22×D6111yescharacteristic
301C22×C4—611no—
302C22×C4—611no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—1221no—
307Q16—22no—
308SD16—22no—
309SD16—614no—
310SD16—1222no—
311SD16—2441no—
312D8—1222no—
313D8—1222no—
314D8—1222no—
315D8—2441no—
316M16—1222no—
317C2×C8—611no—
318C2×C8—611no—
319C2×C8—1222no—
320C2×C8C22×D6111yescharacteristic
321C2×C8C22×D6111yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—611no—
324C4⋊C4—611no—
325C4⋊C4—1221no—
326C4⋊C4C22×D6111yescharacteristic
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—
336C42—21no—
337C42C22×D6111yescharacteristic
338C23—21no—
339C23—611no—
340C23—611no—
341C23—1221no—
342C23—1221no—
343C23—1221no—
344C23—4881no—
345C23—2442no—
346C23—2442no—
347Q8—21no—
348Q8—21no—
349Q8—21no—
350Q8D4×D6112yes—
351D4—21no—
352D4—21no—
353D4—612no—
354D4—1221no—
355D4—1221no—
356D4—1221no—
357D4—1221no—
358D4—1221no—
359D4—4881no—
360D4—4881no—
361D4—4881no—
362D4—4881no—
363D4—2441no—
364D4—2442no—
365D4—2442no—
366D4—2442no—
367D4—2442no—
368D4—2442no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—611no—
373C2×C4—611no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—4881no—
380C2×C4—2442no—
381C2×C4—2442no—
382C2×C4—2442no—
383C2×C4D4×D6111yescharacteristic
384C2×C4D4×D6111yescharacteristic
385C2×C4C23×D6111yescharacteristic
386C8—21no—
387C8—21no—
388C8—612no—
389C8—1221no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—1221no—
394C22—1221no—
395C22—1221no—
396C22—1221no—
397C22—1221no—
398C22—1221no—
399C22—1222no—
400C22—4884no—
401C22—2441no—
402C22—2441no—
403C22—2441no—
404C22—2441no—
405C22—2441no—
406C22—2441no—
407C22—2441no—
408C22—2441no—
409C22C2×D4×D6111yescharacteristic
410C4—21no—
411C4—21no—
412C4—22no—
413C4—41no—
414C4—41no—
415C4—1221no—
416C4—1221no—
417C4—2441no—
418C4C2×D4×D6111yescharacteristic
419C4#1451982311yescharacteristic
420C2—81no—
421C2—4881no—
422C2—4881no—
423C2—2441no—
424C2—2441no—
425C2—2442no—
426C2#1684039611yescharacteristic
427C2#1684056111yescharacteristic
428C2#1684056411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#464C2
socleC22×C61C22×D4
hypercenter#464D61
hypocenterC61#3268
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#14519804C2semidirect
2. C2×#14519800C2semidirect
3. #16840434C2semidirect
4. #16840405C2semidirect
5. #16840152C2semidirect
6. #16840011C2semidirect
7. #16839997C2semidirect
8. #16839958C2semidirect
9. #16839923C2semidirect
10. #16839910C2semidirect
11. #16839906C2semidirect
12. #16839897C2semidirect
13. #16839860C2semidirect
14. #16839832C2semidirect
15. C61×#464C2semidirect
18. C2×#11758226C22semidirect
23. C2×#11758201C22semidirect
24. C2×#11758201C22semidirect
30. C2×C8×D61C22semidirect
32. #14519774C22semidirect
38. #14519752C22semidirect
46. #14519710C22semidirect
47. #14519701C22semidirect
48. #14519699C22semidirect
49. #14519699C22semidirect
52. #14519689C22semidirect
53. #14519688C22semidirect
54. C2×Q16×C61C22semidirect
57. C4×Q8×C61C22semidirect
58. C4⋊C8×C61C22semidirect
59. #103×C61C22semidirect
105. #11758201D4semidirect
222. #464D61semidirect
230. C61#3268semidirect
237. C2×Q16C2×D61semidirect
260. C4×Q8C2×D61semidirect
266. C4⋊C8C2×D61semidirect
268. #103C2×D61semidirect