Finite Group Databasebeta

← #21457364

Subgroups — #21457364

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×#14519805C211yesmaximal, characteristic, complemented
2C2×#14519799C211yesmaximal, characteristic, complemented
3#16840433C211yesmaximal, characteristic, complemented
4#16840408C211yesmaximal, characteristic, complemented
5#16840151C211yesmaximal, characteristic, complemented
6#16840008C211yesmaximal, characteristic, complemented
7#16839998C211yesmaximal, characteristic, complemented
8#16839985C211yesmaximal, characteristic, complemented
9#16839958C211yesmaximal, characteristic, complemented
10#16839926C211yesmaximal, characteristic, complemented
11#16839909C211yesmaximal, characteristic, complemented
12#16839909C211yesmaximal, characteristic, complemented
13#16839898C211yesmaximal, characteristic, complemented
14#16839864C211yesmaximal, characteristic, complemented
15C61×#435C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758222C2211yescharacteristic
18C2×#11758222C2211yescharacteristic, complemented
19C22×D244C2211yescharacteristic
20#14519805—24no—
21#14519799—24no—
22C2×Dic244C2211yescharacteristic, complemented
23C2×#11758190C2211yescharacteristic
24C2×#11758190C2211yescharacteristic
25C2×#11758190C2211yescharacteristic, complemented
26C2×#11758190C2211yescharacteristic, complemented
27C2×D488C2211yescharacteristic
28C2×D488C2211yescharacteristic
29C2×D488C2211yescharacteristic
30C2×D488C2211yescharacteristic
31#14519774C2211yescharacteristic, complemented
32#14519773—21no—
33#14519765C2211yescharacteristic
34#14519762—21no—
35#14519756C2211yescharacteristic
36#14519751C2211yescharacteristic
37#14519751C2211yescharacteristic
38#14519751C2211yescharacteristic, complemented
39#14519750—21no—
40#14519750—21no—
41#14519750—21no—
42#14519745—21no—
43C4×Dic122C2211yescharacteristic, complemented
44C4×D244C2211yescharacteristic
45#14519739—21no—
46C22⋊C4×D61—21no—
47#14519711C2211yescharacteristic, complemented
48#14519702C2211yescharacteristic, complemented
49#14519702C2211yescharacteristic, complemented
50#14519699C2211yescharacteristic
51#14519699C2211yescharacteristic
52#14519699C2211yescharacteristic, complemented
53#14519699C2211yescharacteristic, complemented
54C2×M16×C61C2211yescharacteristic
55C22×C8×C61C2211yescharacteristic, complemented
56C4×D4×C61C2211yescharacteristic
57C4⋊C8×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic
59C22⋊C8×C61C2211yescharacteristic, complemented
60#97×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C2×D4×C61D411yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71#11758222—22no—
72#11758222—22no—
73#11758222—22no—
74#11758222—41no—
75#11758222—41no—
76#11758222—41no—
77C2×D244—22no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244—41no—
82C2×D244C2311yescharacteristic
83C2×D244C2311yescharacteristic
84C2×D244C2311yescharacteristic
85C2×D244C2311yescharacteristic
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×Dic122C2311yescharacteristic
91C2×Dic122C2311yescharacteristic
92M16×C61—22no—
93C2×C8×C61—22no—
94C2×C8×C61C2311yescharacteristic
95C2×C8×C61C2311yescharacteristic
96C2×C8×C61C2311yescharacteristic
97C2×C8×C61C2311yescharacteristic
98C4⋊C4×C61D411yescharacteristic
99C22⋊C4×C61D411yescharacteristic
100C22⋊C4×C61D411yescharacteristic
101C42×C61C2311yescharacteristic
102C22⋊Dic61—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107#11758198—21no—
108#11758198—21no—
109C4⋊Dic61C2311yescharacteristic
110C4⋊Dic61C2311yescharacteristic
111#11758196—21no—
112#11758196—21no—
113C4×Dic61—21no—
114Dic244—22no—
115D488—22no—
116D488—22no—
117D488—22no—
118D488—41no—
119#11758190—22no—
120#11758190—22no—
121#11758190—41no—
122#11758190D414yescomplemented
123C23×C61C2×D411yescharacteristic
124C23×C61C2×D411yescharacteristic
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—42no—
130C22×D61—42no—
131C22×D61—81no—
132D4×C61—41no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61C2×D411yescharacteristic
138C2×C4×C61C2×D411yescharacteristic
139C2×C4×C61C2×D411yescharacteristic
140C2×C4×C61C2×D411yescharacteristic
141C2×C4×C61C2411yescharacteristic
142C22⋊D61—42no—
143C22⋊D61—42no—
144C22⋊D61—42no—
145C22⋊D61—81no—
146C22⋊D61—81no—
147C22⋊D61—81no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152D244—21no—
153D244—21no—
154D244—21no—
155D244—21no—
156D244—21no—
157D244—21no—
158D244—21no—
159D244—42no—
160D244—42no—
161D244—81no—
162D244C2×D412yes—
163C4×D61—42no—
164C4×D61—42no—
165C4×D61—42no—
166C4×D61—81no—
167Dic122—21no—
168Dic122—21no—
169Dic122—21no—
170Dic122C2×D412yes—
171C8×C61—21no—
172C8×C61—21no—
173C8×C61—21no—
174C8×C61C2×D412yes—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61C22×D411yescharacteristic
182C2×D61—22no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
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—21no—
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61C22×D411yescharacteristic
200C4×C61H(5,𝔽2)11yescharacteristic
201Dic61—22no—
202Dic61—41no—
203Dic61—41no—
204Dic61—41no—
205#3268—611nomaximal, Sylow
206C2×C61—41no—
207C2×C61—41no—
208C2×C61D4211yescharacteristic
209C2×C61#57511yescharacteristic
210C2×C61#57611yescharacteristic
211D61—42no—
212D61—81no—
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#464—611no—
223#459—611no—
224#452—611no—
225#449—611no—
226#449—611no—
227#447—611no—
228#440—611no—
229#435D6111yescharacteristic, complemented
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×D8—611no—
245C2×D8—611no—
246C2×M16C2×D6111yescharacteristic
247C22×C8C2×D6111yescharacteristic, complemented
248#127—611no—
249#127—1221no—
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#102—611no—
272#102—611no—
273C22⋊C8C2×D6111yescharacteristic
274C22⋊C8C2×D6111yescharacteristic, complemented
275#97C2×D6111yescharacteristic, complemented
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—611no—
286C2×D4—611no—
287C2×D4—611no—
288C2×D4—611no—
289C2×D4—1222no—
290C2×D4—1221no—
291C2×D4—1221no—
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—1221no—
295C2×D4—1221no—
296C2×D4—1221no—
297C2×D4—1221no—
298C2×D4—1221no—
299C2×D4—2441no—
300C2×D4D24411yescharacteristic
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4C22×D6111yescharacteristic
306C22×C4C22×D6111yescharacteristic
307Q16—1222no—
308SD16—614no—
309SD16—1222no—
310SD16—1222no—
311SD16—2441no—
312D8—1222no—
313D8—1222no—
314D8—1222no—
315D8—2441no—
316M16—22no—
317C2×C8—22no—
318C2×C8C22×D6111yescharacteristic
319C2×C8C22×D6111yescharacteristic
320C2×C8C22×D6111yescharacteristic
321C2×C8C22×D6111yescharacteristic
322C4⋊C4—611no—
323C4⋊C4—611no—
324C4⋊C4—1221no—
325C4⋊C4—1221no—
326C4⋊C4D24411yescharacteristic
327C22⋊C4—1221no—
328C22⋊C4—1221no—
329C22⋊C4—1221no—
330C22⋊C4—1221no—
331C22⋊C4—1221no—
332C22⋊C4—1221no—
333C22⋊C4—1221no—
334C22⋊C4D24411yescharacteristic
335C22⋊C4D24411yescharacteristic
336C42—1221no—
337C42C22×D6111yescharacteristic
338C23—1221no—
339C23—1221no—
340C23—1221no—
341C23—1221no—
342C23—4881no—
343C23—2442no—
344C23—2442no—
345C23C2×D24411yescharacteristic
346C23C2×D24411yescharacteristic
347Q8—612no—
348Q8—1221no—
349Q8—1221no—
350Q8—1221no—
351D4—41no—
352D4—612no—
353D4—1221no—
354D4—1221no—
355D4—1221no—
356D4—1221no—
357D4—1221no—
358D4—1221no—
359D4—1221no—
360D4—4881no—
361D4—4881no—
362D4—4881no—
363D4—4881no—
364D4—2442no—
365D4—2442no—
366D4—2442no—
367D4—2442no—
368D4—2442no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—4881no—
378C2×C4—2442no—
379C2×C4—2442no—
380C2×C4—2442no—
381C2×C4C2×D24411yescharacteristic
382C2×C4C2×D24411yescharacteristic
383C2×C4C2×D24411yescharacteristic
384C2×C4C2×D24411yescharacteristic
385C2×C4C23×D6111yescharacteristic
386C8—21no—
387C8—21no—
388C8—21no—
389C8D4×D6112yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—1222no—
397C22—4884no—
398C22—2441no—
399C22—2441no—
400C22—2441no—
401C22—2441no—
402C22—2441no—
403C22—2441no—
404C22—2441no—
405C22—2441no—
406C22—2441no—
407C22—2441no—
408C22—2441no—
409C22C22×D24411yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—1222no—
415C4—2441no—
416C4—2441no—
417C4—2441no—
418C4C2×D4×D6111yescharacteristic
419C4#1451982311yescharacteristic
420C2—41no—
421C2—41no—
422C2—4881no—
423C2—4881no—
424C2—4881no—
425C2—2442no—
426C2D4×D24411yescharacteristic
427C2#1684056211yescharacteristic
428C2#1684056711yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#435C2
socleC22×C61C22×D4
hypercenter#435D61
hypocenterC61#3268
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#14519805C2semidirect
2. C2×#14519799C2semidirect
3. #16840433C2semidirect
4. #16840408C2semidirect
5. #16840151C2semidirect
6. #16840008C2semidirect
7. #16839998C2semidirect
8. #16839985C2semidirect
9. #16839958C2semidirect
10. #16839926C2semidirect
11. #16839909C2semidirect
12. #16839909C2semidirect
13. #16839898C2semidirect
14. #16839864C2semidirect
15. C61×#435C2semidirect
18. C2×#11758222C22semidirect
22. C2×Dic244C22semidirect
25. C2×#11758190C22semidirect
26. C2×#11758190C22semidirect
31. #14519774C22semidirect
38. #14519751C22semidirect
43. C4×Dic122C22semidirect
47. #14519711C22semidirect
48. #14519702C22semidirect
49. #14519702C22semidirect
52. #14519699C22semidirect
53. #14519699C22semidirect
55. C22×C8×C61C22semidirect
57. C4⋊C8×C61C22semidirect
59. C22⋊C8×C61C22semidirect
60. #97×C61C22semidirect
122. #11758190D4semidirect
229. #435D61semidirect
230. C61#3268semidirect
247. C22×C8C2×D61semidirect
266. C4⋊C8C2×D61semidirect
274. C22⋊C8C2×D61semidirect
275. #97C2×D61semidirect