Finite Group Databasebeta

← #21457512

Subgroups — #21457512

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×#11758190C211yesmaximal, characteristic, complemented
2C2×SD16×D61C211yesmaximal, characteristic, complemented
3#16840425C211yesmaximal, characteristic, complemented
4#16840396C211yesmaximal, characteristic
5#16840133C211yesmaximal, characteristic, complemented
6#16839992C211yesmaximal, characteristic, complemented
7#16839966C211yesmaximal, characteristic, complemented
8#16839961C211yesmaximal, characteristic, complemented
9#16839914C211yesmaximal, characteristic, complemented
10#16839912C211yesmaximal, characteristic, complemented
11#16839902C211yesmaximal, characteristic, complemented
12#16839900C211yesmaximal, characteristic, complemented
13#16839849C211yesmaximal, characteristic, complemented
14C8×C22⋊D61C211yesmaximal, characteristic, complemented
15C61×#465C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic, complemented
17C2×Q8×D61C2211yescharacteristic, complemented
18C22×D244C2211yescharacteristic
19C2×D4×D61—21no—
20C2×D4×D61C2211yescharacteristic
21C2×#11758190—24no—
22C2×#11758190C2211yescharacteristic
23C2×#11758190C2211yescharacteristic
24C2×#11758190C2211yescharacteristic, complemented
25C2×#11758190C2211yescharacteristic, complemented
26C2×#11758200C2211yescharacteristic, complemented
27C2×#11758200C2211yescharacteristic, complemented
28C2×#11758201C2211yescharacteristic
29C2×#11758201C2211yescharacteristic, complemented
30SD16×D61—24no—
31C2×C8×D61C2211yescharacteristic, complemented
32#14519776—21no—
33#14519775C2211yescharacteristic, complemented
34#14519773C2211yescharacteristic
35#14519757C2211yescharacteristic, complemented
36#14519755—21no—
37#14519754—21no—
38#14519752C2211yescharacteristic
39#14519750—21no—
40#14519747—21no—
41#14519745—21no—
42#14519742C2211yescharacteristic, complemented
43#14519739C2211yescharacteristic
44C4×C22⋊D61C2211yescharacteristic
45#14519737—21no—
46#14519706C2211yescharacteristic, complemented
47#14519700C2211yescharacteristic, complemented
48#14519700C2211yescharacteristic, complemented
49#14519697C2211yescharacteristic
50#14519697C2211yescharacteristic, complemented
51C22⋊#92418C2211yescharacteristic, complemented
52#14519689C2211yescharacteristic, complemented
53C8×Dic61C2211yescharacteristic, complemented
54C2×SD16×C61C2211yescharacteristic, complemented
55C22×C8×C61C2211yescharacteristic, complemented
56C22⋊Q8×C61C2211yescharacteristic, complemented
57#121×C61C2211yescharacteristic
58#106×C61C2211yescharacteristic, complemented
59#103×C61C2211yescharacteristic, complemented
60#102×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C23×D61—21no—
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61—21no—
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61D411yescharacteristic
71C22×Dic61—21no—
72Q8×D61—22no—
73Q8×D61—41no—
74D4×D61—22no—
75D4×D61—41no—
76D4×D61—44no—
77C2×D244—22no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244—41no—
81C2×D244C2311yescharacteristic
82C2×D244C2311yescharacteristic
83C2×C4×D61—21no—
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—
93C2×C8×C61—22no—
94C2×C8×C61C2311yescharacteristic
95C2×C8×C61C2311yescharacteristic
96C4⋊C4×C61—21no—
97C4⋊C4×C61C2311yescharacteristic
98C4⋊C4×C61C2311yescharacteristic
99C22⋊C4×C61—21no—
100C22⋊C4×C61—21no—
101C22⋊Dic61D411yescharacteristic
102#11758201—22no—
103#11758201—41no—
104#11758200—22no—
105#11758200—41no—
106#11758198—21no—
107#11758198—21no—
108#11758198—21no—
109#11758198D411yescharacteristic
110C4⋊Dic61—21no—
111#11758196—21no—
112#11758196—21no—
113#11758196—21no—
114#11758196D411yescharacteristic
115C4×Dic61—21no—
116C4×Dic61C2311yescharacteristic
117C2×#92418C2311yescharacteristic
118C2×#92418C2311yescharacteristic
119#11758190—22no—
120#11758190—22no—
121#11758190—22no—
122#11758190D414yescomplemented
123C8×D61—22no—
124C23×C61—21no—
125C23×C61C2×D411yescharacteristic
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—
137D4×C61—21no—
138D4×C61—21no—
139D4×C61—42no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61C2×D411yescharacteristic
146C2×C4×C61C2411yescharacteristic
147C22⋊D61—42no—
148C22⋊D61—42no—
149C22⋊D61—81no—
150C22⋊D61SD1614yescomplemented
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—42no—
154C2×Dic61C2×D411yescharacteristic
155C2×Dic61C2×D411yescharacteristic
156C2×Dic61C2×D411yescharacteristic
157D244—21no—
158D244—21no—
159D244—21no—
160D244—42no—
161D244—42no—
162D244C2×D412yes—
163C4×D61—21no—
164C4×D61—21no—
165C4×D61—42no—
166C4×D61—42no—
167Dic122—21no—
168Dic122—21no—
169Dic122—21no—
170Dic122—42no—
171Dic122—42no—
172Dic122C2×D412yescomplemented
173C8×C61—21no—
174C8×C61C2×D412yescomplemented
175#92418—21no—
176#92418—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61C2×SD1612yescomplemented
183C22×C61C22×D411yescharacteristic
184C2×D61—21no—
185C2×D61—21no—
186C2×D61—22no—
187C2×D61—41no—
188C2×D61—41no—
189C2×D61—41no—
190C2×D61—41no—
191C2×D61—41no—
192C2×D61—84no—
193C2×D61—84no—
194C2×D61C2×SD1612yescomplemented
195C4×C61—21no—
196C4×C61—41no—
197C4×C61—41no—
198C4×C61—41no—
199C4×C61C22×D411yescharacteristic
200C4×C61H(5,𝔽2)11yescharacteristic
201Dic61—22no—
202Dic61—21no—
203Dic61—21no—
204Dic61—41no—
205Dic61C2×SD1612yescomplemented
206D4×SD16—611nomaximal, Sylow
207C2×C61—22no—
208C2×C61—81no—
209C2×C61D4211yescharacteristic
210C2×C61C22×SD1611yescharacteristic
211C2×C61#57711yescharacteristic
212D61—22no—
213D61—42no—
214D61—81no—
215C22×SD16—611no—
216C22×SD16—611no—
217D4×Q8—611no—
218D42—611no—
219#492—611no—
220#465—611no—
221#465D6111yescharacteristic, complemented
222#461—611no—
223#460—611no—
224#450—611no—
225#450—611no—
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—611no—
235C22×D4—1221no—
236C2×SD16—611no—
237C2×SD16—611no—
238C2×SD16—611no—
239C2×SD16—611no—
240C2×SD16—611no—
241C2×SD16—611no—
242C2×SD16—611no—
243C2×SD16—611no—
244C2×SD16—1224no—
245C2×SD16—1224no—
246C2×SD16C2×D6111yescharacteristic, complemented
247C22×C8—611no—
248C22×C8C2×D6111yescharacteristic, complemented
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—1221no—
258#121C2×D6111yescharacteristic
259#120—1221no—
260#120—1221no—
261C4×Q8—611no—
262C4×D4—611no—
263C4×D4—611no—
264C4×D4—1221no—
265#106C2×D6111yescharacteristic, complemented
266C4⋊C8—611no—
267#103—611no—
268#103—611no—
269#103C2×D6111yescharacteristic, complemented
270#102—611no—
271#102—611no—
272#102C2×D6111yescharacteristic, complemented
273C22⋊C8—611no—
274C22⋊C8—611no—
275C4×C8—611no—
276C24—1221no—
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—21no—
288C2×D4—611no—
289C2×D4—611no—
290C2×D4—611no—
291C2×D4—1222no—
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—1221no—
295C2×D4—1221no—
296C2×D4—1222no—
297C2×D4—1221no—
298C2×D4—2441no—
299C2×D4—2441no—
300C2×D4—2444no—
301C2×D4C22×D6111yescharacteristic
302C22×C4—611no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4C22×D6111yescharacteristic
307SD16—22no—
308SD16—614no—
309SD16—1222no—
310SD16—1222no—
311SD16—1222no—
312SD16—1222no—
313SD16—1222no—
314SD16—2441no—
315SD16—2441no—
316C2×C8—22no—
317C2×C8—611no—
318C2×C8—611no—
319C2×C8—1222no—
320C2×C8C22×D6111yescharacteristic
321C2×C8C22×D6111yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—611no—
324C4⋊C4—1221no—
325C4⋊C4—1221no—
326C4⋊C4—1221no—
327C4⋊C4—1221no—
328C4⋊C4C22×D6111yescharacteristic
329C4⋊C4C22×D6111yescharacteristic
330C22⋊C4—21no—
331C22⋊C4—21no—
332C22⋊C4—611no—
333C22⋊C4—611no—
334C22⋊C4—1221no—
335C22⋊C4—1221no—
336C22⋊C4—1221no—
337C42—611no—
338C42—1221no—
339C23—21no—
340C23—611no—
341C23—1221no—
342C23—1221no—
343C23—4881no—
344C23—4881no—
345C23—2442no—
346C23—2442no—
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—42no—
361D4—614no—
362D4—612no—
363D4—1221no—
364D4—1221no—
365D4—1221no—
366D4—4881no—
367D4—2442no—
368D4—2442no—
369D4—2442no—
370D4—2442no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—611no—
377C2×C4—611no—
378C2×C4—611no—
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—1221no—
390C8—1221no—
391C8D4×D6112yescomplemented
392C22—21no—
393C22—21no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—612no—
398C22—1221no—
399C22—1221no—
400C22—1222no—
401C22—4884no—
402C22—4884no—
403C22—2441no—
404C22—2441no—
405C22—2441no—
406C22—2441no—
407C22—2441no—
408C22SD16×D6112yescomplemented
409C22C2×D4×D6111yescharacteristic
410C4—21no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—612no—
415C4—1221no—
416C4—1221no—
417C4—1222no—
418C4—2441no—
419C4C2×D4×D6111yescharacteristic
420C4#1451982311yescharacteristic
421C2—22no—
422C2—81no—
423C2—1222no—
424C2—4881no—
425C2—2442no—
426C2#1684039611yescharacteristic
427C2C2×SD16×D6111yescharacteristic
428C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#465C2
socleC22×C61C22×D4
hypercenter#465D61
hypocenterC61D4×SD16
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C22×#11758190C2semidirect
2. C2×SD16×D61C2semidirect
3. #16840425C2semidirect
5. #16840133C2semidirect
6. #16839992C2semidirect
7. #16839966C2semidirect
8. #16839961C2semidirect
9. #16839914C2semidirect
10. #16839912C2semidirect
11. #16839902C2semidirect
12. #16839900C2semidirect
13. #16839849C2semidirect
14. C8×C22⋊D61C2semidirect
15. C61×#465C2semidirect
16. C22×Dic122C22semidirect
17. C2×Q8×D61C22semidirect
24. C2×#11758190C22semidirect
25. C2×#11758190C22semidirect
26. C2×#11758200C22semidirect
27. C2×#11758200C22semidirect
29. C2×#11758201C22semidirect
31. C2×C8×D61C22semidirect
33. #14519775C22semidirect
35. #14519757C22semidirect
42. #14519742C22semidirect
46. #14519706C22semidirect
47. #14519700C22semidirect
48. #14519700C22semidirect
50. #14519697C22semidirect
51. C22⋊#92418C22semidirect
52. #14519689C22semidirect
53. C8×Dic61C22semidirect
54. C2×SD16×C61C22semidirect
55. C22×C8×C61C22semidirect
56. C22⋊Q8×C61C22semidirect
58. #106×C61C22semidirect
59. #103×C61C22semidirect
60. #102×C61C22semidirect
122. #11758190D4semidirect
150. C22⋊D61SD16semidirect
172. Dic122C2×D4semidirect
174. C8×C61C2×D4semidirect
182. C22×C61C2×SD16semidirect
194. C2×D61C2×SD16semidirect
205. Dic61C2×SD16semidirect
221. #465D61semidirect
230. C61D4×SD16semidirect
246. C2×SD16C2×D61semidirect
248. C22×C8C2×D61semidirect
255. C22⋊Q8C2×D61semidirect
265. #106C2×D61semidirect
269. #103C2×D61semidirect
272. #102C2×D61semidirect
391. C8D4×D61semidirect
408. C22SD16×D61semidirect