Finite Group Databasebeta

← #21457513

Subgroups — #21457513

Order 7808.

546 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
1C22×#11758200C211yesmaximal, characteristic, complemented
2C2×SD16×D61C211yesmaximal, characteristic, complemented
3#16840425C211yesmaximal, characteristic, complemented
4D4×C22⋊D61C211yesmaximal, characteristic
5#16840133C211yesmaximal, characteristic, complemented
6#16839993C211yesmaximal, characteristic, complemented
7#16839990C211yesmaximal, characteristic, complemented
8#16839965C211yesmaximal, characteristic, complemented
9#16839961C211yesmaximal, characteristic, complemented
10#16839914C211yesmaximal, characteristic, complemented
11#16839903C211yesmaximal, characteristic, complemented
12#16839899C211yesmaximal, characteristic, complemented
13#16839853C211yesmaximal, characteristic, complemented
14#16839825C211yesmaximal, characteristic, complemented
15C61×#450C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic, complemented
17C2×Q8×D61C2211yescharacteristic, complemented
18C22×C22⋊D61—21no—
19C2×D4×D61C2211yescharacteristic
20C2×#11758190C2211yescharacteristic, complemented
21C2×#11758190C2211yescharacteristic, complemented
22C2×#11758200—24no—
23C2×#11758200C2211yescharacteristic
24C2×#11758200C2211yescharacteristic
25C2×#11758200C2211yescharacteristic, complemented
26C2×#11758200C2211yescharacteristic, complemented
27C2×#11758201C2211yescharacteristic, complemented
28SD16×D61—24no—
29C22×#92418C2211yescharacteristic, complemented
30C2×C8×D61C2211yescharacteristic, complemented
31#14519776—21no—
32#14519775C2211yescharacteristic, complemented
33#14519773C2211yescharacteristic
34#14519757C2211yescharacteristic, complemented
35#14519755—21no—
36#14519754—21no—
37#14519751C2211yescharacteristic
38#14519749—21no—
39#14519748C2211yescharacteristic
40#14519746—21no—
41#14519745—21no—
42#14519742C2211yescharacteristic, complemented
43D4×Dic61C2211yescharacteristic
44C4×C22⋊D61C2211yescharacteristic
45#14519737—21no—
46#14519708C2211yescharacteristic, complemented
47#14519706C2211yescharacteristic, complemented
48#14519702C2211yescharacteristic, complemented
49#14519702C2211yescharacteristic, complemented
50#14519701C2211yescharacteristic, complemented
51#14519697C2211yescharacteristic, complemented
52#14519689C2211yescharacteristic, complemented
53C8×Dic61C2211yescharacteristic, complemented
54C22×D4×C61C2211yescharacteristic
55C2×SD16×C61C2211yescharacteristic
56C2×SD16×C61C2211yescharacteristic, complemented
57C22⋊Q8×C61C2211yescharacteristic, complemented
58#102×C61C2211yescharacteristic
59#102×C61C2211yescharacteristic, complemented
60C22⋊C8×C61C2211yescharacteristic, complemented
61C24×C61—21no—
62C23×D61—21no—
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61—22no—
65C2×D4×C61—21no—
66C2×D4×C61—41no—
67C2×D4×C61C2311yescharacteristic
68C2×D4×C61C2311yescharacteristic
69C22×C4×C61C2311yescharacteristic
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—21no—
73C2×C22⋊D61—21no—
74C2×C22⋊D61—21no—
75C2×C22⋊D61—44no—
76C2×C22⋊D61D411yescharacteristic
77C22×Dic61—21no—
78C22×Dic61—21no—
79Q8×D61—22no—
80Q8×D61—41no—
81D4×D61—22no—
82D4×D61—41no—
83C2×D244C2311yescharacteristic
84C2×C4×D61—21no—
85C2×C4×D61C2311yescharacteristic
86C2×Dic122—22no—
87C2×Dic122—21no—
88C2×Dic122—21no—
89C2×Dic122—41no—
90C2×Dic122C2311yescharacteristic
91C2×Dic122C2311yescharacteristic
92SD16×C61—22no—
93SD16×C61—41no—
94C2×C8×C61C2311yescharacteristic
95C2×C8×C61C2311yescharacteristic
96C4⋊C4×C61—21no—
97C4⋊C4×C61C2311yescharacteristic
98C22⋊C4×C61—21no—
99C22⋊Dic61—21no—
100C22⋊Dic61—21no—
101C22⋊Dic61D411yescharacteristic
102#11758201—22no—
103#11758200—22no—
104#11758200—22no—
105#11758200—22no—
106#11758200D414yescomplemented
107#11758198—21no—
108#11758198—21no—
109#11758198D411yescharacteristic
110C4⋊Dic61—21no—
111C4⋊Dic61C2311yescharacteristic
112#11758196—21no—
113#11758196—21no—
114#11758196—21no—
115#11758196D411yescharacteristic
116C4×Dic61—21no—
117C4×Dic61C2311yescharacteristic
118C2×#92418—22no—
119C2×#92418C2311yescharacteristic
120C2×#92418C2311yescharacteristic
121#11758190—22no—
122#11758190—41no—
123C8×D61—22no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—42no—
127C23×C61—42no—
128C23×C61—81no—
129C23×C61C2×D411yescharacteristic
130C22×D61—21no—
131C22×D61—42no—
132C22×D61—42no—
133C22×D61—81no—
134C22×D61C2×D411yescharacteristic
135Q8×C61—21no—
136Q8×C61—21no—
137D4×C61—21no—
138D4×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×C61C2×D411yescharacteristic
147C2×C4×C61C2411yescharacteristic
148C22⋊D61—42no—
149C22⋊D61—42no—
150C22⋊D61—42no—
151C22⋊D61—42no—
152C22⋊D61—81no—
153C22⋊D61SD1614yescomplemented
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—42no—
158C2×Dic61—42no—
159C2×Dic61C2×D411yescharacteristic
160C2×Dic61C2×D411yescharacteristic
161C2×Dic61C2×D411yescharacteristic
162D244—21no—
163D244—21no—
164C4×D61—21no—
165C4×D61—21no—
166C4×D61—42no—
167Dic122—21no—
168Dic122—21no—
169Dic122—21no—
170Dic122—42no—
171Dic122—42no—
172Dic122C2×D412yescomplemented
173C8×C61—21no—
174C8×C61—21no—
175#92418—21no—
176#92418C2×D412yescomplemented
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—22no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—84no—
186C22×C61C2×SD1612yescomplemented
187C22×C61C22×D411yescharacteristic
188C2×D61—21no—
189C2×D61—21no—
190C2×D61—41no—
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—84no—
194C2×D61C2×SD1612yescomplemented
195C4×C61—21no—
196C4×C61—41no—
197C4×C61—41no—
198C4×C61C22×D411yescharacteristic
199C4×C61H(5,𝔽2)11yescharacteristic
200Dic61—22no—
201Dic61—21no—
202Dic61—21no—
203Dic61—41no—
204Dic61—41no—
205Dic61C2×SD1612yescomplemented
206D4×SD16—611nomaximal, Sylow
207C2×C61—22no—
208C2×C61—42no—
209C2×C61—81no—
210C2×C61D4211yescharacteristic
211C2×C61C22×SD1611yescharacteristic
212C2×C61#57711yescharacteristic
213D61—22no—
214D61—81no—
215C22×SD16—611no—
216C22×SD16—611no—
217D4×Q8—611no—
218D42—611no—
219#492—611no—
220#465—611no—
221#465—611no—
222#461—611no—
223#460—611no—
224#450—611no—
225#450D6111yescharacteristic, complemented
226#448—611no—
227#448—611no—
228C4×SD16—611no—
229C8×D4—611no—
230C61D4×SD1611yescharacteristic, complemented, Sylow
231C22×Q8—611no—
232C22×Q8—611no—
233C22×D4—611no—
234C22×D4—1221no—
235C22×D4C2×D6111yescharacteristic
236C2×SD16—611no—
237C2×SD16—611no—
238C2×SD16—611no—
239C2×SD16—611no—
240C2×SD16—611no—
241C2×SD16—611no—
242C2×SD16—611no—
243C2×SD16—1224no—
244C2×SD16—1224no—
245C2×SD16C2×D6111yescharacteristic
246C2×SD16C2×D6111yescharacteristic, complemented
247C22×C8—611no—
248C22×C8—611no—
249C4⋊Q8—611no—
250C4⋊Q8—1221no—
251#127—611no—
252C22⋊Q8—611no—
253C22⋊Q8—1221no—
254C22⋊Q8—1221no—
255C22⋊Q8C2×D6111yescharacteristic, complemented
256#121—611no—
257#121—611no—
258#121—1221no—
259#120—1221no—
260#120—1221no—
261C4×Q8—611no—
262C4×D4—611no—
263C4×D4—611no—
264C4×D4—1221no—
265#106—611no—
266C4⋊C8—611no—
267#103—611no—
268#103—611no—
269#103—611no—
270#102—611no—
271#102C2×D6111yescharacteristic
272#102C2×D6111yescharacteristic, complemented
273C22⋊C8—611no—
274C22⋊C8C2×D6111yescharacteristic, complemented
275C4×C8—611no—
276C24—21no—
277C24—1221no—
278C2×Q8—611no—
279C2×Q8—611no—
280C2×Q8—1221no—
281C2×Q8—1222no—
282C2×Q8—1221no—
283C2×Q8—1222no—
284C2×Q8—2441no—
285C2×Q8—2441no—
286C2×Q8C22×D6111yescharacteristic
287C2×D4—22no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—611no—
291C2×D4—611no—
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—1221no—
295C2×D4—1222no—
296C2×D4—1221no—
297C2×D4—1221no—
298C2×D4—2441no—
299C2×D4—2444no—
300C2×D4C22×D6111yescharacteristic
301C2×D4C22×D6111yescharacteristic
302C22×C4—611no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4C22×D6111yescharacteristic
307SD16—22no—
308SD16—41no—
309SD16—614no—
310SD16—1222no—
311SD16—1222no—
312SD16—1222no—
313SD16—1222no—
314SD16—1222no—
315SD16—2441no—
316C2×C8—611no—
317C2×C8—611no—
318C2×C8—1222no—
319C2×C8—1222no—
320C2×C8C22×D6111yescharacteristic
321C2×C8C22×D6111yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—611no—
324C4⋊C4—611no—
325C4⋊C4—1221no—
326C4⋊C4—1221no—
327C4⋊C4—1221no—
328C4⋊C4—1221no—
329C4⋊C4C22×D6111yescharacteristic
330C22⋊C4—21no—
331C22⋊C4—611no—
332C22⋊C4—611no—
333C22⋊C4—1221no—
334C22⋊C4—1221no—
335C22⋊C4—1221no—
336C22⋊C4—1221no—
337C42—611no—
338C42—1221no—
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—611no—
345C23—1221no—
346C23—4881no—
347C23—2442no—
348C23—2442no—
349C23D4×D6111yescharacteristic
350Q8—21no—
351Q8—21no—
352Q8—612no—
353Q8—1221no—
354Q8—1221no—
355Q8—1221no—
356Q8—2442no—
357Q8—2442no—
358D4—21no—
359D4—21no—
360D4—21no—
361D4—42no—
362D4—614no—
363D4—1221no—
364D4—1221no—
365D4—4881no—
366D4—2442no—
367D4—2442no—
368D4—2442no—
369D4—2442no—
370D4D4×D6112yes—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—611no—
376C2×C4—611no—
377C2×C4—611no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—1221no—
382C2×C4—1221no—
383C2×C4—2442no—
384C2×C4—2442no—
385C2×C4—2442no—
386C2×C4D4×D6111yescharacteristic
387C2×C4C23×D6111yescharacteristic
388C8—21no—
389C8—21no—
390C8—612no—
391C8—1221no—
392C22—21no—
393C22—21no—
394C22—22no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—84no—
401C22—612no—
402C22—1221no—
403C22—1221no—
404C22—4884no—
405C22—2441no—
406C22—2441no—
407C22—2441no—
408C22SD16×D6112yescomplemented
409C22C2×D4×D6111yescharacteristic
410C4—21no—
411C4—41no—
412C4—41no—
413C4—612no—
414C4—1221no—
415C4—1221no—
416C4—1222no—
417C4—2441no—
418C4—2441no—
419C4C2×D4×D6111yescharacteristic
420C4#1451982211yescharacteristic
421C2—22no—
422C2—42no—
423C2—81no—
424C2—1222no—
425C2—4881no—
426C2#1684039411yescharacteristic
427C2C2×SD16×D6111yescharacteristic
428C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#450C2
socleC22×C61C22×D4
hypercenter#450D61
hypocenterC61D4×SD16
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C22×#11758200C2semidirect
2. C2×SD16×D61C2semidirect
3. #16840425C2semidirect
5. #16840133C2semidirect
6. #16839993C2semidirect
7. #16839990C2semidirect
8. #16839965C2semidirect
9. #16839961C2semidirect
10. #16839914C2semidirect
11. #16839903C2semidirect
12. #16839899C2semidirect
13. #16839853C2semidirect
14. #16839825C2semidirect
15. C61×#450C2semidirect
16. C22×Dic122C22semidirect
17. C2×Q8×D61C22semidirect
20. C2×#11758190C22semidirect
21. C2×#11758190C22semidirect
25. C2×#11758200C22semidirect
26. C2×#11758200C22semidirect
27. C2×#11758201C22semidirect
29. C22×#92418C22semidirect
30. C2×C8×D61C22semidirect
32. #14519775C22semidirect
34. #14519757C22semidirect
42. #14519742C22semidirect
46. #14519708C22semidirect
47. #14519706C22semidirect
48. #14519702C22semidirect
49. #14519702C22semidirect
50. #14519701C22semidirect
51. #14519697C22semidirect
52. #14519689C22semidirect
53. C8×Dic61C22semidirect
56. C2×SD16×C61C22semidirect
57. C22⋊Q8×C61C22semidirect
59. #102×C61C22semidirect
60. C22⋊C8×C61C22semidirect
106. #11758200D4semidirect
153. C22⋊D61SD16semidirect
172. Dic122C2×D4semidirect
176. #92418C2×D4semidirect
186. C22×C61C2×SD16semidirect
194. C2×D61C2×SD16semidirect
205. Dic61C2×SD16semidirect
225. #450D61semidirect
230. C61D4×SD16semidirect
246. C2×SD16C2×D61semidirect
255. C22⋊Q8C2×D61semidirect
272. #102C2×D61semidirect
274. C22⋊C8C2×D61semidirect
408. C22SD16×D61semidirect