Finite Group Databasebeta

← #21457365

Subgroups — #21457365

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×#14519801C211yesmaximal, characteristic, complemented
2C2×#14519796C211yesmaximal, characteristic, complemented
3#16840432C211yesmaximal, characteristic, complemented
4#16840407C211yesmaximal, characteristic, complemented
5#16840149C211yesmaximal, characteristic, complemented
6#16840007C211yesmaximal, characteristic, complemented
7#16839997C211yesmaximal, characteristic, complemented
8#16839985C211yesmaximal, characteristic, complemented
9#16839925C211yesmaximal, characteristic, complemented
10#16839908C211yesmaximal, characteristic, complemented
11#16839904C211yesmaximal, characteristic, complemented
12#16839894C211yesmaximal, characteristic, complemented
13#16839862C211yesmaximal, characteristic, complemented
14#16839832C211yesmaximal, characteristic, complemented
15C61×#459C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×#11758224C2211yescharacteristic, complemented
19C2×D4×D61C2211yescharacteristic
20#14519801—24no—
21#14519796—24no—
22C2×Dic244C2211yescharacteristic, complemented
23C2×#11758190C2211yescharacteristic
24C2×#11758200C2211yescharacteristic
25C2×#11758200C2211yescharacteristic, complemented
26C2×#11758200C2211yescharacteristic, complemented
27C2×#11758199C2211yescharacteristic
28C2×#11758199C2211yescharacteristic
29C2×#11758189C2211yescharacteristic
30C2×C8×D61C2211yescharacteristic, complemented
31#14519773—21no—
32#14519765C2211yescharacteristic
33#14519761—21no—
34#14519757C2211yescharacteristic
35#14519752C2211yescharacteristic
36#14519751—21no—
37#14519749—21no—
38#14519749—21no—
39#14519748C2211yescharacteristic
40#14519748C2211yescharacteristic, complemented
41#14519747—21no—
42C4×Dic122C2211yescharacteristic, complemented
43C4×D244C2211yescharacteristic
44D4×Dic61—21no—
45C2×#11758198—21no—
46#14519710C2211yescharacteristic, complemented
47#14519702C2211yescharacteristic, complemented
48#14519700C2211yescharacteristic, complemented
49#14519699C2211yescharacteristic
50#14519698C2211yescharacteristic
51#14519689C2211yescharacteristic
52#14519689C2211yescharacteristic, complemented
53#14519688C2211yescharacteristic, complemented
54C2×D8×C61C2211yescharacteristic
55C2×D8×C61C2211yescharacteristic
56#127×C61C2211yescharacteristic, complemented
57C4×D4×C61C2211yescharacteristic
58C4⋊C8×C61C2211yescharacteristic, complemented
59#102×C61C2211yescharacteristic, complemented
60#102×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C2×D4×C61—21no—
63C2×D4×C61—21no—
64C2×D4×C61C2311yescharacteristic
65C2×D4×C61C2311yescharacteristic
66C2×D4×C61C2311yescharacteristic
67C22×C4×C61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—21no—
73C2×C22⋊D61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77#11758224—22no—
78#11758224—22no—
79#11758224—22no—
80#11758224—41no—
81#11758224—41no—
82#11758224—41no—
83D4×D61—22no—
84D4×D61—41no—
85C2×D244—21no—
86C2×D244D411yescharacteristic
87C2×D244C2311yescharacteristic
88C2×C4×D61C2311yescharacteristic
89C2×C4×D61C2311yescharacteristic
90C2×Dic122C2311yescharacteristic
91C2×Dic122C2311yescharacteristic
92D8×C61—22no—
93D8×C61—22no—
94C2×C8×C61C2311yescharacteristic
95C2×C8×C61C2311yescharacteristic
96C4⋊C4×C61C2311yescharacteristic
97C22⋊C4×C61—21no—
98C42×C61C2311yescharacteristic
99C22⋊Dic61—21no—
100C22⋊Dic61—21no—
101#11758200—22no—
102#11758200—41no—
103#11758200D414yescomplemented
104#11758199—22no—
105#11758199—41no—
106#11758198—21no—
107#11758198—21no—
108#11758198—21no—
109#11758198—21no—
110#11758198D411yescharacteristic
111#11758198D411yescharacteristic
112C4⋊Dic61—21no—
113C4⋊Dic61D411yescharacteristic
114C4⋊Dic61C2311yescharacteristic
115#11758196—21no—
116C4×Dic61—21no—
117C2×#92418C2311yescharacteristic
118C2×#92418C2311yescharacteristic
119Dic244—22no—
120#11758190—22no—
121#11758189—22no—
122C8×D61—22no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C22×D61—21no—
127C22×D61—42no—
128C22×D61—42no—
129C22×D61—81no—
130C22×D61C2×D411yescharacteristic
131C22×D61C2×D411yescharacteristic
132D4×C61—21no—
133D4×C61—21no—
134D4×C61—21no—
135D4×C61—21no—
136D4×C61—21no—
137D4×C61—42no—
138D4×C61—81no—
139D4×C61C2×D412yes—
140C2×C4×C61—21no—
141C2×C4×C61—81no—
142C2×C4×C61C2×D411yescharacteristic
143C2×C4×C61C2×D411yescharacteristic
144C2×C4×C61C2411yescharacteristic
145C22⋊D61—42no—
146C22⋊D61—42no—
147C22⋊D61—42no—
148C22⋊D61—42no—
149C22⋊D61—81no—
150C22⋊D61—81no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—42no—
155C2×Dic61—42no—
156C2×Dic61—42no—
157C2×Dic61C2×D411yescharacteristic
158C2×Dic61C2×D411yescharacteristic
159D244—21no—
160D244—21no—
161D244—41no—
162D244—81no—
163C4×D61—21no—
164C4×D61—21no—
165C4×D61—21no—
166C4×D61—21no—
167Dic122—21no—
168Dic122—21no—
169Dic122—21no—
170Dic122C2×D412yes—
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×C61—41no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61C22×D411yescharacteristic
185C2×D61—21no—
186C2×D61—21no—
187C2×D61—21no—
188C2×D61—21no—
189C2×D61—21no—
190C2×D61—21no—
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—84no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—41no—
198C4×C61C22×D411yescharacteristic
199C4×C61H(5,𝔽2)11yescharacteristic
200Dic61—22no—
201Dic61—21no—
202Dic61—21no—
203Dic61—41no—
204Dic61—41no—
205#3268—611nomaximal, Sylow
206C2×C61—42no—
207C2×C61—81no—
208C2×C61—81no—
209C2×C61D4211yescharacteristic
210C2×C61#57511yescharacteristic
211C2×C61#57611yescharacteristic
212D61—41no—
213D61—41no—
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#464—611no—
223#459D6111yescharacteristic, complemented
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×Q16—611no—
238C2×SD16—611no—
239C2×SD16—611no—
240C2×SD16—611no—
241C2×SD16—611no—
242C2×D8—611no—
243C2×D8—611no—
244C2×D8C2×D6111yescharacteristic
245C2×D8C2×D6111yescharacteristic
246C2×M16—611no—
247C22×C8—611no—
248#127—1221no—
249#127C2×D6111yescharacteristic, complemented
250#124—611no—
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×Q8—611no—
261C4×D4—611no—
262C4×D4—1221no—
263C4×D4C2×D6111yescharacteristic
264C2×C22⋊C4—1221no—
265#107—611no—
266C4⋊C8C2×D6111yescharacteristic, complemented
267#103—611no—
268#103—611no—
269#102—611no—
270#102—611no—
271#102C2×D6111yescharacteristic, complemented
272#102C2×D6111yescharacteristic, complemented
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×Q8—611no—
284C2×Q8—611no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—611no—
288C2×D4—611no—
289C2×D4—1221no—
290C2×D4—1221no—
291C2×D4—1222no—
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—1221no—
295C2×D4—1221no—
296C2×D4—1221no—
297C2×D4—2441no—
298C2×D4C22×D6111yescharacteristic
299C2×D4C22×D6111yescharacteristic
300C2×D4C22×D6111yescharacteristic
301C22×C4—21no—
302C22×C4—611no—
303C22×C4—611no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—1221no—
307Q16—1222no—
308SD16—614no—
309SD16—1222no—
310SD16—1222no—
311SD16—2441no—
312D8—22no—
313D8—22no—
314D8—1222no—
315D8—2441no—
316M16—1222no—
317C2×C8—611no—
318C2×C8—611no—
319C2×C8—1222no—
320C2×C8C22×D6111yescharacteristic
321C2×C8C22×D6111yescharacteristic
322C4⋊C4—611no—
323C4⋊C4—611no—
324C4⋊C4—1221no—
325C4⋊C4—1221no—
326C4⋊C4C22×D6111yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—611no—
329C22⋊C4—611no—
330C22⋊C4—1221no—
331C22⋊C4—1221no—
332C22⋊C4—1221no—
333C22⋊C4—1221no—
334C22⋊C4—1221no—
335C22⋊C4—1221no—
336C42—1221no—
337C42C22×D6111yescharacteristic
338C23—21no—
339C23—21no—
340C23—21no—
341C23—611no—
342C23—611no—
343C23—1221no—
344C23—4881no—
345C23—2442no—
346C23—2442no—
347Q8—612no—
348Q8—1221no—
349Q8—1221no—
350Q8—1221no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—42no—
357D4—81no—
358D4—1221no—
359D4—1221no—
360D4—4881no—
361D4—4881no—
362D4—4881no—
363D4—2441no—
364D4—2442no—
365D4—2442no—
366D4—2442no—
367D4—2442no—
368D4D4×D6112yes—
369C2×C4—21no—
370C2×C4—81no—
371C2×C4—611no—
372C2×C4—611no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—1221no—
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—22no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—1221no—
400C22—1221no—
401C22—1221no—
402C22—1221no—
403C22—1221no—
404C22—1221no—
405C22—4884no—
406C22—2441no—
407C22—2441no—
408C22—2441no—
409C22C2×D4×D6111yescharacteristic
410C4—21no—
411C4—21no—
412C4—41no—
413C4—1221no—
414C4—1221no—
415C4—1222no—
416C4—2441no—
417C4—2441no—
418C4C2×D4×D6111yescharacteristic
419C4#1451982311yescharacteristic
420C2—42no—
421C2—81no—
422C2—81no—
423C2—4881no—
424C2—2441no—
425C2—2441no—
426C2#1684039611yescharacteristic
427C2#1684055811yescharacteristic
428C2#1684056311yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#459C2
socleC22×C61C22×D4
hypercenter#459D61
hypocenterC61#3268
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#14519801C2semidirect
2. C2×#14519796C2semidirect
3. #16840432C2semidirect
4. #16840407C2semidirect
5. #16840149C2semidirect
6. #16840007C2semidirect
7. #16839997C2semidirect
8. #16839985C2semidirect
9. #16839925C2semidirect
10. #16839908C2semidirect
11. #16839904C2semidirect
12. #16839894C2semidirect
13. #16839862C2semidirect
14. #16839832C2semidirect
15. C61×#459C2semidirect
18. C2×#11758224C22semidirect
22. C2×Dic244C22semidirect
25. C2×#11758200C22semidirect
26. C2×#11758200C22semidirect
30. C2×C8×D61C22semidirect
40. #14519748C22semidirect
42. C4×Dic122C22semidirect
46. #14519710C22semidirect
47. #14519702C22semidirect
48. #14519700C22semidirect
52. #14519689C22semidirect
53. #14519688C22semidirect
56. #127×C61C22semidirect
58. C4⋊C8×C61C22semidirect
59. #102×C61C22semidirect
60. #102×C61C22semidirect
103. #11758200D4semidirect
223. #459D61semidirect
230. C61#3268semidirect
249. #127C2×D61semidirect
266. C4⋊C8C2×D61semidirect
271. #102C2×D61semidirect
272. #102C2×D61semidirect