Finite Group Databasebeta

← #30648936

Subgroups — #30648936

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#22550482C211yesmaximal, characteristic, complemented
2#22550358C211yesmaximal, characteristic, complemented
3#22550196C211yesmaximal, characteristic, complemented
4#22550191C211yesmaximal, characteristic, complemented
5#22550173C211yesmaximal, characteristic, complemented
6#22550076C211yesmaximal, characteristic, complemented
7#22550072C211yesmaximal, characteristic, complemented
8#22550024C211yesmaximal, characteristic, complemented
9#22550024C211yesmaximal, characteristic, complemented
10#22549987C211yesmaximal, characteristic, complemented
11#22549979C211yesmaximal, characteristic, complemented
12#22549961C211yesmaximal, characteristic, complemented
13#22549958C211yesmaximal, characteristic, complemented
14#22549936C211yesmaximal, characteristic, complemented
15#479×C127C211yesmaximal, characteristic, complemented
16C2×#14523249C2211yescharacteristic
17C2×#14523235C2211yescharacteristic
18C2×#14523235C2211yescharacteristic
19C2×D1016C2211yescharacteristic
20C2×D1016C2211yescharacteristic
21#16861206C2211yescharacteristic
22#16861194—21no—
23#16861194—21no—
24#16861184—21no—
25#16861184—21no—
26#16861184C2211yescharacteristic
27#16861184C2211yescharacteristic
28Q8×Dic127C2211yescharacteristic
29C4×D508—21no—
30C4×D508C2211yescharacteristic
31#16861171—21no—
32#16861171C2211yescharacteristic
33#16861171C2211yescharacteristic
34#16861171C2211yescharacteristic
35#16861166—21no—
36#16861166C2211yescharacteristic
37C4⋊C4×D127—21no—
38C4⋊C4×D127C2211yescharacteristic
39#16861142C2211yescharacteristic
40#16861140C2211yescharacteristic
41C4⋊(C127⋊C8)C2211yescharacteristic
42#16861131C2211yescharacteristic
43#16861131C2211yescharacteristic
44#16861129C2211yescharacteristic
45#16861129C2211yescharacteristic
46#16861129C2211yescharacteristic
47#16861129C2211yescharacteristic
48(C2×D127)⋊C8C2211yescharacteristic
49(C2×D127)⋊C8C2211yescharacteristic
50#16861119C2211yescharacteristic
51C8×Dic127C2211yescharacteristic
52#125×C127C2211yescharacteristic
53C4×Q8×C127C2211yescharacteristic
54#107×C127C2211yescharacteristic
55#106×C127C2211yescharacteristic
56C4⋊C8×C127C2211yescharacteristic
57#103×C127C2211yescharacteristic
58#103×C127C2211yescharacteristic
59#14523249—22no—
60#14523249—22no—
61C2×D508—21no—
62C2×D508—21no—
63C2×D508—21no—
64C2×D508—21no—
65C2×D508—21no—
66C2×D508C2311yescharacteristic
67C2×D508C2311yescharacteristic
68C2×D508C2311yescharacteristic
69C2×C4×D127—21no—
70C2×C4×D127—21no—
71C2×C4×D127—21no—
72C2×C4×D127—21no—
73C2×C4×D127—21no—
74C2×C4×D127—21no—
75C2×C4×D127C2311yescharacteristic
76#14523235—22no—
77#14523235—22no—
78D1016—22no—
79D1016—22no—
80C2×C127⋊C8C2311yescharacteristic
81C2×C127⋊C8C2311yescharacteristic
82C4⋊Dic127—21no—
83C4⋊Dic127C2311yescharacteristic
84Dic127⋊C4—21no—
85Dic127⋊C4D411yescharacteristic
86Dic127⋊C4D411yescharacteristic
87(C2×D127)⋊C4—21no—
88(C2×D127)⋊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)⋊C4D411yescharacteristic
94(C2×D127)⋊C4D411yescharacteristic
95C4×Dic127—21no—
96C4×Dic127C2311yescharacteristic
97C2×Q8×C127C2311yescharacteristic
98C2×C8×C127C2311yescharacteristic
99C2×C8×C127C2311yescharacteristic
100C4⋊C4×C127—21no—
101C4⋊C4×C127—21no—
102C4⋊C4×C127—21no—
103C4⋊C4×C127C2311yescharacteristic
104C4⋊C4×C127C2311yescharacteristic
105C4⋊C4×C127C2311yescharacteristic
106C42×C127—21no—
107C42×C127C2311yescharacteristic
108C22×D127—21no—
109C22×D127—21no—
110C22×D127—21no—
111C22×D127C2×D411yescharacteristic
112D508—24no—
113D508—21no—
114D508—21no—
115D508—21no—
116D508—21no—
117D508—21no—
118D508—81no—
119D508—81no—
120D508—81no—
121D508—81no—
122D508#4112yes—
123C2×Dic127—21no—
124C2×Dic127C2×D411yescharacteristic
125C2×Dic127C2×D411yescharacteristic
126C2×Dic127C2×D411yescharacteristic
127C4×D127—24no—
128C4×D127—21no—
129C4×D127—21no—
130C4×D127—81no—
131C4×D127—81no—
132C4×D127—81no—
133C4×D127—81no—
134C4×D127—81no—
135C127⋊C8—21no—
136C127⋊C8—21no—
137Q8×C127—21no—
138Q8×C127#4112yes—
139C2×C4×C127—21no—
140C2×C4×C127—21no—
141C2×C4×C127—21no—
142C2×C4×C127—21no—
143C2×C4×C127C2×D411yescharacteristic
144C2×C4×C127C2×D411yescharacteristic
145C2×C4×C127C2411yescharacteristic
146C8×C127—21no—
147C8×C127—21no—
148C22×C127C22×D411yescharacteristic
149C2×D127—21no—
150C2×D127—22no—
151C2×D127—21no—
152C2×D127—21no—
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—22no—
162C4×C127—21no—
163C4×C127—21no—
164C4×C127—41no—
165C4×C127—41no—
166C4×C127—41no—
167C4×C127C2×#4111yescharacteristic
168C4×C127C2×#4111yescharacteristic
169Dic127—21no—
170Dic127—21no—
171Dic127—21no—
172Dic127—41no—
173C2×C127#52511yescharacteristic
174C2×C127#57611yescharacteristic
175C2×C127#57711yescharacteristic
176D127—41no—
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#479D12711yescharacteristic, complemented
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#433—1271no—
197C2×#41—1271no—
198C2×SD16—1271no—
199C2×SD16—1271no—
200C2×D8—1271no—
201C2×D8—1271no—
202#127—1271no—
203#125C2×D12711yescharacteristic
204#123—2541no—
205#123—2541no—
206#121—1271no—
207#121—1271no—
208#121—2541no—
209#121—2541no—
210C4×Q8—1271no—
211C4×Q8C2×D12711yescharacteristic
212C4×D4—1271no—
213C4×D4—1271no—
214C4×D4—1271no—
215C4×D4—1271no—
216C4×D4—2541no—
217C4×D4—2541no—
218#117—1271no—
219#117—2541no—
220C2×C4⋊C4—1271no—
221C2×C4⋊C4—2541no—
222#107—1271no—
223#107C2×D12711yescharacteristic
224#106—1271no—
225#106C2×D12711yescharacteristic
226C4⋊C8—1271no—
227C4⋊C8C2×D12711yescharacteristic
228#103C2×D12711yescharacteristic
229#103C2×D12711yescharacteristic
230#102—1271no—
231#102—1271no—
232#102—1271no—
233#102—1271no—
234#102—1271no—
235#102—1271no—
236C22⋊C8—1271no—
237C22⋊C8—1271no—
238#97—1271no—
239C4×C8—1271no—
240#41—2542no—
241#41—2542no—
242C2×Q8C22×D12711yescharacteristic
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—1271no—
252C22×C4—2541no—
253C22×C4—2541no—
254C22×C4—2541no—
255C22×C4—2541no—
256C22×C4—2541no—
257C22×C4—2541no—
258SD16—2542no—
259SD16—2542no—
260D8—2542no—
261D8—2542no—
262C2×C8—1271no—
263C2×C8—1271no—
264C2×C8C22×D12711yescharacteristic
265C2×C8C22×D12711yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—1271no—
270C4⋊C4—1271no—
271C4⋊C4—1271no—
272C4⋊C4—2541no—
273C4⋊C4—2541no—
274C4⋊C4C22×D12711yescharacteristic
275C4⋊C4C22×D12711yescharacteristic
276C4⋊C4C22×D12711yescharacteristic
277C22⋊C4—1271no—
278C22⋊C4—1271no—
279C22⋊C4—2541no—
280C22⋊C4—2541no—
281C22⋊C4—2541no—
282C22⋊C4—2541no—
283C22⋊C4—2541no—
284C22⋊C4—2541no—
285C42—21no—
286C42—1271no—
287C42—2541no—
288C42C22×D12711yescharacteristic
289C23—1271no—
290C23—2541no—
291C23—2541no—
292C23—2541no—
293Q8—21no—
294Q8#1452324912yes—
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—21no—
309C2×C4—21no—
310C2×C4—1271no—
311C2×C4—1271no—
312C2×C4—1271no—
313C2×C4—10161no—
314C2×C4—10161no—
315C2×C4—10161no—
316C2×C4—10161no—
317C2×C4—10161no—
318C2×C4—2544no—
319C2×C4—2541no—
320C2×C4—2541no—
321C2×C4—2541no—
322C2×C4D4×D12711yescharacteristic
323C2×C4D4×D12711yescharacteristic
324C2×C4C23×D12711yescharacteristic
325C8—21no—
326C8—21no—
327C8—2541no—
328C8—2541no—
329C22—5081no—
330C22—5081no—
331C22—5081no—
332C22—5081no—
333C22—5081no—
334C22—5081no—
335C22—5081no—
336C22—5081no—
337C22—2542no—
338C22—2541no—
339C22—2541no—
340C22—2541no—
341C22C2×D4×D12711yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—5081no—
349C4—2541no—
350C4—2541no—
351C4—2541no—
352C4#41×D12711yescharacteristic
353C4C2×#1452324911yescharacteristic
354C2—10161no—
355C2—10161no—
356C2—5082no—
357C2—5081no—
358C2#2255038911yescharacteristic
359C2#2255067811yescharacteristic
360C2#2255068511yescharacteristic
subgroupG/H
centerC22C2×D4×D127
commutator, cosocleC2×C4×C127C24
FrattiniC2×C4C23×D127
Fitting#479×C127C2
socleC22×C127C22×D4
hypercenter#479D127
hypocenterC127#3119
LCSG ▷ C2×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #22550482C2semidirect
2. #22550358C2semidirect
3. #22550196C2semidirect
4. #22550191C2semidirect
5. #22550173C2semidirect
6. #22550076C2semidirect
7. #22550072C2semidirect
8. #22550024C2semidirect
9. #22550024C2semidirect
10. #22549987C2semidirect
11. #22549979C2semidirect
12. #22549961C2semidirect
13. #22549958C2semidirect
14. #22549936C2semidirect
15. #479×C127C2semidirect
181. C127#3119semidirect
186. #479D127semidirect

Maximal subgroups

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

subgroupindex
#225504822
#225503582
#225501962
#225501912
#225501732
#225500762
#225500722
#225500242
#225499872
#225499792
#225499612
#225499582
#225499362
#479×C1272
#3119127