Finite Group Databasebeta

← #30648931

Subgroups — #30648931

Order 16256.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22550481C211yesmaximal, characteristic, complemented
2#22550356C211yesmaximal, characteristic, complemented
3#22550195C211yesmaximal, characteristic, complemented
4#22550190C211yesmaximal, characteristic, complemented
5#22550184C211yesmaximal, characteristic, complemented
6#22550177C211yesmaximal, characteristic, complemented
7#22550077C211yesmaximal, characteristic, complemented
8#22550072C211yesmaximal, characteristic, complemented
9#22550023C211yesmaximal, characteristic, complemented
10#22550023C211yesmaximal, characteristic, complemented
11#22549989C211yesmaximal, characteristic, complemented
12#22549978C211yesmaximal, characteristic, complemented
13C4×#14523237C211yesmaximal, characteristic, complemented
14C4×D1016C211yesmaximal, characteristic, complemented
15#433×C127C211yesmaximal, characteristic, complemented
16C2×#14523248C2211yescharacteristic
17C2×#14523237C2211yescharacteristic
18C2×#14523237C2211yescharacteristic
19C2×D1016C2211yescharacteristic
20C2×D1016C2211yescharacteristic
21#16861206C2211yescharacteristic
22#16861201C2211yescharacteristic
23#16861194—21no—
24#16861194—21no—
25#16861183C2211yescharacteristic
26#16861183C2211yescharacteristic
27#16861182—21no—
28#16861182—21no—
29C4×Dic254C2211yescharacteristic
30C4×Dic254C2211yescharacteristic
31C4×D508C2211yescharacteristic
32C4×D508C2211yescharacteristic
33C4×D508C2211yescharacteristic
34C4×D508C2211yescharacteristic
35(C22⋊D127)⋊C4—21no—
36(C22⋊D127)⋊C4—21no—
37#16861167—21no—
38C2×C4⋊Dic127C2211yescharacteristic
39C4⋊C4×D127—21no—
40#16861143C2211yescharacteristic
41#16861143C2211yescharacteristic
42#16861141C2211yescharacteristic
43#16861141C2211yescharacteristic
44#16861134C2211yescharacteristic
45#16861134C2211yescharacteristic
46#16861131C2211yescharacteristic
47#16861131C2211yescharacteristic
48#16861131C2211yescharacteristic
49#16861131C2211yescharacteristic
50#16861131C2211yescharacteristic
51#16861131C2211yescharacteristic
52#117×C127C2211yescharacteristic
53C4⋊C8×C127C2211yescharacteristic
54C4⋊C8×C127C2211yescharacteristic
55C22⋊C8×C127C2211yescharacteristic
56C22⋊C8×C127C2211yescharacteristic
57#97×C127C2211yescharacteristic
58C4×C8×C127C2211yescharacteristic
59#14523248—22no—
60#14523248—22no—
61C2×Dic254C2311yescharacteristic
62C2×D508—21no—
63C2×D508—21no—
64C2×D508C2311yescharacteristic
65C2×D508C2311yescharacteristic
66C2×D508C2311yescharacteristic
67C2×C22⋊D127—21no—
68C2×C22⋊D127—21no—
69C2×C22⋊D127—21no—
70C22×Dic127—21no—
71C2×C4×D127—21no—
72C2×C4×D127—21no—
73C2×C4×D127—21no—
74C2×C4×D127—21no—
75C2×C4×D127—21no—
76#14523237—22no—
77#14523237—22no—
78D1016—22no—
79D1016—22no—
80C4⋊Dic127—21no—
81C4⋊Dic127C2311yescharacteristic
82C4⋊Dic127C2311yescharacteristic
83C4⋊Dic127C2311yescharacteristic
84C4⋊Dic127C2311yescharacteristic
85Dic127⋊C4—21no—
86Dic127⋊C4—21no—
87Dic127⋊C4—21no—
88Dic127⋊C4—21no—
89(C2×D127)⋊C4—21no—
90(C2×D127)⋊C4—21no—
91(C2×D127)⋊C4—21no—
92(C2×D127)⋊C4—21no—
93(C2×D127)⋊C4—21no—
94(C2×D127)⋊C4—21no—
95C4×Dic127—21no—
96C4×Dic127—21no—
97C22×C4×C127C2311yescharacteristic
98C2×C8×C127C2311yescharacteristic
99C2×C8×C127C2311yescharacteristic
100C2×C8×C127C2311yescharacteristic
101C2×C8×C127C2311yescharacteristic
102C4⋊C4×C127D411yescharacteristic
103C4⋊C4×C127D411yescharacteristic
104C22⋊C4×C127D411yescharacteristic
105C22⋊C4×C127D411yescharacteristic
106C42×C127C2311yescharacteristic
107C42×C127C2311yescharacteristic
108C22×D127—21no—
109C22×D127—21no—
110C22×D127—21no—
111Dic254—21no—
112Dic254#4112yes—
113D508—21no—
114D508—21no—
115D508—21no—
116D508—21no—
117D508—21no—
118D508—81no—
119D508—81no—
120D508#4112yes—
121C22⋊D127—24no—
122C22⋊D127—81no—
123C22⋊D127—81no—
124C2×Dic127—21no—
125C2×Dic127—21no—
126C2×Dic127—21no—
127C2×Dic127—21no—
128C2×Dic127—21no—
129C2×Dic127—81no—
130C4×D127—24no—
131C4×D127—81no—
132C4×D127—81no—
133C4×D127—81no—
134C4×D127—81no—
135C23×C127C2×D411yescharacteristic
136C2×C4×C127—21no—
137C2×C4×C127—21no—
138C2×C4×C127C2×D411yescharacteristic
139C2×C4×C127C2×D411yescharacteristic
140C2×C4×C127C2×D411yescharacteristic
141C2×C4×C127C2×D411yescharacteristic
142C2×C4×C127C2×D411yescharacteristic
143C2×C4×C127C2411yescharacteristic
144C8×C127—21no—
145C8×C127—21no—
146C8×C127—21no—
147C8×C127—21no—
148C22×C127—21no—
149C22×C127—21no—
150C22×C127—21no—
151C22×C127C22×D411yescharacteristic
152C2×D127—22no—
153C2×D127—41no—
154C2×D127—41no—
155C2×D127—41no—
156C2×D127—41no—
157C2×D127—41no—
158C2×D127—41no—
159C2×D127—41no—
160C2×D127—41no—
161C4×C127—21no—
162C4×C127—21no—
163C4×C127—21no—
164C4×C127—21no—
165C4×C127—21no—
166C4×C127C2×#4111yescharacteristic
167C4×C127C2×#4111yescharacteristic
168Dic127—22no—
169Dic127—41no—
170Dic127—41no—
171Dic127—41no—
172Dic127—41no—
173C2×C127—41no—
174C2×C127#52511yescharacteristic
175C2×C127#57611yescharacteristic
176C2×C127#57711yescharacteristic
177D127—42no—
178D127—81no—
179D127—81no—
180#3119—1271nomaximal, Sylow
181C127#311911yescharacteristic, complemented, Sylow
182#540—1271no—
183#520—1271no—
184#481—1271no—
185#480—1271no—
186#479—1271no—
187#478—1271no—
188#460—1271no—
189#459—1271no—
190#449—1271no—
191#449—1271no—
192#442—1271no—
193#440—1271no—
194C4×SD16—1271no—
195C4×D8—1271no—
196#433D12711yescharacteristic, complemented
197C2×#41—1271no—
198C2×SD16—1271no—
199C2×SD16—1271no—
200C2×D8—1271no—
201C2×D8—1271no—
202#127—1271no—
203#125—1271no—
204#123—2541no—
205#123—2541no—
206#121—1271no—
207#121—1271no—
208#121—2541no—
209#121—2541no—
210C4×Q8—1271no—
211C4×Q8—1271no—
212C4×D4—1271no—
213C4×D4—1271no—
214C4×D4—1271no—
215C4×D4—1271no—
216C4×D4—2541no—
217C4×D4—2541no—
218#117—2541no—
219#117C2×D12711yescharacteristic
220C2×C4⋊C4—1271no—
221C2×C4⋊C4—2541no—
222#107—1271no—
223#107—1271no—
224#106—1271no—
225#106—1271no—
226C4⋊C8C2×D12711yescharacteristic
227C4⋊C8C2×D12711yescharacteristic
228#103—1271no—
229#103—1271no—
230#102—1271no—
231#102—1271no—
232#102—1271no—
233#102—1271no—
234#102—1271no—
235#102—1271no—
236C22⋊C8C2×D12711yescharacteristic
237C22⋊C8C2×D12711yescharacteristic
238#97C2×D12711yescharacteristic
239C4×C8C2×D12711yescharacteristic
240#41—2542no—
241#41—2542no—
242C2×Q8—1271no—
243C2×D4—1271no—
244C2×D4—1271no—
245C2×D4—1271no—
246C2×D4—2541no—
247C2×D4—2541no—
248C2×D4—2541no—
249C2×D4—2541no—
250C2×D4—2541no—
251C22×C4—2541no—
252C22×C4—2541no—
253C22×C4—2541no—
254C22×C4—2541no—
255C22×C4—2541no—
256C22×C4—2541no—
257C22×C4C22×D12711yescharacteristic
258SD16—2542no—
259SD16—2542no—
260D8—2542no—
261D8—2542no—
262C2×C8C22×D12711yescharacteristic
263C2×C8C22×D12711yescharacteristic
264C2×C8C22×D12711yescharacteristic
265C2×C8C22×D12711yescharacteristic
266C4⋊C4—1271no—
267C4⋊C4—1271no—
268C4⋊C4—1271no—
269C4⋊C4—1271no—
270C4⋊C4—2541no—
271C4⋊C4—2541no—
272C4⋊C4—2541no—
273C4⋊C4—2541no—
274C4⋊C4—2541no—
275C4⋊C4D50811yescharacteristic
276C4⋊C4D50811yescharacteristic
277C22⋊C4—2541no—
278C22⋊C4—2541no—
279C22⋊C4—2541no—
280C22⋊C4—2541no—
281C22⋊C4—2541no—
282C22⋊C4—2541no—
283C22⋊C4D50811yescharacteristic
284C22⋊C4D50811yescharacteristic
285C42—2541no—
286C42—2541no—
287C42C22×D12711yescharacteristic
288C42C22×D12711yescharacteristic
289C23—2541no—
290C23—2541no—
291C23—2541no—
292C23C2×D50811yescharacteristic
293Q8—1272no—
294Q8—2541no—
295D4—1272no—
296D4—10161no—
297D4—10161no—
298D4—10161no—
299D4—10161no—
300D4—2544no—
301D4—2541no—
302D4—2541no—
303D4—2541no—
304D4—2541no—
305D4—2541no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—10161no—
309C2×C4—10161no—
310C2×C4—10161no—
311C2×C4—10161no—
312C2×C4—10161no—
313C2×C4—2544no—
314C2×C4—2541no—
315C2×C4—2541no—
316C2×C4—2541no—
317C2×C4—2541no—
318C2×C4—2541no—
319C2×C4C2×D50811yescharacteristic
320C2×C4C2×D50811yescharacteristic
321C2×C4C2×D50811yescharacteristic
322C2×C4C2×D50811yescharacteristic
323C2×C4C2×D50811yescharacteristic
324C2×C4C23×D12711yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—5081no—
333C22—5081no—
334C22—5081no—
335C22—5081no—
336C22—5081no—
337C22—5081no—
338C22—5081no—
339C22—5081no—
340C22—2542no—
341C22C22×D50811yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—5081no—
348C4—5081no—
349C4—5081no—
350C4—5081no—
351C4—2542no—
352C4#41×D12711yescharacteristic
353C4#41×D12711yescharacteristic
354C2—41no—
355C2—10161no—
356C2—10161no—
357C2—5082no—
358C2#2255038811yescharacteristic
359C2#2255068111yescharacteristic
360C2#2255068811yescharacteristic
subgroupG/H
centerC22C22×D508
commutator, cosocleC2×C4×C127C24
FrattiniC2×C4C23×D127
Fitting#433×C127C2
socleC22×C127C22×D4
hypercenter#433D127
hypocenterC127#3119
LCSG ▷ C2×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #22550481C2semidirect
2. #22550356C2semidirect
3. #22550195C2semidirect
4. #22550190C2semidirect
5. #22550184C2semidirect
6. #22550177C2semidirect
7. #22550077C2semidirect
8. #22550072C2semidirect
9. #22550023C2semidirect
10. #22550023C2semidirect
11. #22549989C2semidirect
12. #22549978C2semidirect
13. C4×#14523237C2semidirect
14. C4×D1016C2semidirect
15. #433×C127C2semidirect
181. C127#3119semidirect
196. #433D127semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#225504812
#225503562
#225501952
#225501902
#225501842
#225501772
#225500772
#225500722
#225500232
#225499892
#225499782
C4×#145232372
C4×D10162
#433×C1272
#3119127