Finite Group Databasebeta

← C4×#16861186 #30641261

Subgroups — C4×#16861186 #30641261

Order 16256.

656 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16861186C211yesmaximal, characteristic
2C2×C4×Dic254C211yesmaximal, characteristic, complemented
3C22×C4×Dic127C211yesmaximal, characteristic
4#22549780C211yesmaximal, characteristic, complemented
5#22549773C211yesmaximal, characteristic, complemented
6#22549763C211yesmaximal, characteristic, complemented
7#22549759C211yesmaximal, characteristic, complemented
8#22549751C211yesmaximal, characteristic
9#22549748C211yesmaximal, characteristic
10#22549734C211yesmaximal, characteristic
11C4×Dic127⋊C4C211yesmaximal, characteristic, complemented
12C4×Dic127⋊C4C211yesmaximal, characteristic, complemented
13C4×C4⋊Dic127C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic127C211yesmaximal, characteristic
15C4×C22⋊C4×C127C211yesmaximal, characteristic
16C22×Dic254C2211yescharacteristic
17C23×Dic127C2211yescharacteristic
18C23×Dic127C2211yescharacteristic
19#16861186C418yesdirect product factor
20C4×Dic254—24no—
21C2×C4⋊Dic127C2211yescharacteristic
22C2×C4⋊Dic127C2211yescharacteristic
23C2×C4⋊Dic127C2211yescharacteristic
24C2×Dic127⋊C4C2211yescharacteristic
25C2×Dic127⋊C4C2211yescharacteristic
26C2×Dic127⋊C4C2211yescharacteristic
27C2×Dic127⋊C4C2211yescharacteristic
28C2×Dic127⋊C4C2211yescharacteristic
29C2×Dic127⋊C4C2211yescharacteristic
30C2×C22⋊Dic127C2211yescharacteristic
31C2×C22⋊Dic127C2211yescharacteristic
32C2×C4×Dic127—24no—
33C2×C4×Dic127C2211yescharacteristic
34C2×C4×Dic127C2211yescharacteristic
35C2×C4×Dic127C2211yescharacteristic
36C2×C4×Dic127C2211yescharacteristic
37C2×C4×Dic127C2211yescharacteristic
38C2×C4×Dic127C2211yescharacteristic
39C127⋊#95C2211yescharacteristic
40C127⋊#95C2211yescharacteristic
41C127⋊#95C2211yescharacteristic
42C127⋊#95C2211yescharacteristic
43C127⋊#95C2211yescharacteristic
44C127⋊#95C2211yescharacteristic
45C127⋊#95C2211yescharacteristic
46C127⋊#95C2211yescharacteristic
47C23×C4×C127C2211yescharacteristic
48C2×C22⋊C4×C127C2211yescharacteristic
49C2×C22⋊C4×C127C2211yescharacteristic
50C2×C42×C127C2211yescharacteristic
51C2×C42×C127C2211yescharacteristic
52#95×C127C2211yescharacteristic
53#95×C127C2211yescharacteristic
54C2×Dic254—22no—
55C2×Dic254—22no—
56C2×Dic254C2×C414yescomplemented
57C22×Dic127—22no—
58C22×Dic127—22no—
59C22×Dic127—22no—
60C22×Dic127—22no—
61C22×Dic127—22no—
62C22×Dic127C2×C414yes—
63C22×Dic127C2311yescharacteristic
64C22×Dic127C2311yescharacteristic
65C22×Dic127C2311yescharacteristic
66C22×Dic127C2311yescharacteristic
67C22×Dic127C2311yescharacteristic
68C22×Dic127C2311yescharacteristic
69C22×Dic127C2311yescharacteristic
70C22×Dic127C2311yescharacteristic
71C4⋊Dic127—22no—
72C4⋊Dic127—22no—
73C4⋊Dic127C2×C414yescomplemented
74Dic127⋊C4—22no—
75Dic127⋊C4—22no—
76Dic127⋊C4—22no—
77Dic127⋊C4—22no—
78Dic127⋊C4C2×C414yescomplemented
79Dic127⋊C4C2×C414yescomplemented
80C22⋊Dic127—22no—
81C22⋊Dic127C2×C414yes—
82C4×Dic127—22no—
83C4×Dic127—22no—
84C4×Dic127—22no—
85C4×Dic127—22no—
86C4×Dic127—22no—
87C4×Dic127D414yes—
88C24×C127C2311yescharacteristic
89C22×C4×C127—22no—
90C22×C4×C127—22no—
91C22×C4×C127Q814yescomplemented
92C22×C4×C127C2311yescharacteristic
93C22×C4×C127C2311yescharacteristic
94C22×C4×C127C2311yescharacteristic
95C22×C4×C127C2311yescharacteristic
96C22×C4×C127C2311yescharacteristic
97C22×C4×C127C2311yescharacteristic
98C22⋊C4×C127—22no—
99C22⋊C4×C127C2×C414yes—
100C42×C127—22no—
101C42×C127—22no—
102Dic254—28no—
103C2×Dic127—28no—
104C2×Dic127—21no—
105C2×Dic127—21no—
106C2×Dic127—21no—
107C2×Dic127—21no—
108C2×Dic127—21no—
109C2×Dic127—21no—
110C2×Dic127—21no—
111C2×Dic127—21no—
112C2×Dic127—21no—
113C2×Dic127—21no—
114C2×Dic127—28no—
115C2×Dic127—21no—
116C2×Dic127—21no—
117C2×Dic127—21no—
118C2×Dic127—21no—
119C2×Dic127—21no—
120C2×Dic127—21no—
121C2×Dic127C22×C412yes—
122C2×Dic127C22×C412yes—
123C2×Dic127C22×C412yes—
124C2×Dic127C22×C412yes—
125C2×Dic127C2×D412yes—
126C2×Dic127C2×D412yes—
127C2×Dic127#4112yes—
128C2×Dic127#4112yes—
129C23×C127—21no—
130C23×C127—21no—
131C23×C127—21no—
132C23×C127—21no—
133C23×C127C22×C412yes—
134C23×C127C2×Q812yes—
135C23×C127#4112yes—
136C23×C127C2411yescharacteristic
137C2×C4×C127—21no—
138C2×C4×C127—21no—
139C2×C4×C127—21no—
140C2×C4×C127—21no—
141C2×C4×C127—21no—
142C2×C4×C127—21no—
143C2×C4×C127—28no—
144C2×C4×C127—21no—
145C2×C4×C127—21no—
146C2×C4×C127—21no—
147C2×C4×C127—21no—
148C2×C4×C127—21no—
149C2×C4×C127—21no—
150C2×C4×C127C22×C412yes—
151C2×C4×C127C22×C412yes—
152C2×C4×C127C2×D412yes—
153C2×C4×C127C2×Q812yes—
154C2×C4×C127C2×Q812yes—
155C2×C4×C127#4112yes—
156C22×C127—22no—
157C22×C127—22no—
158C22×C127—22no—
159C22×C127—22no—
160C22×C127—22no—
161C22×C127—22no—
162C22×C127C4×Q814yescomplemented
163C22×C127C23×C411yescharacteristic
164C22×C127C22×D411yescharacteristic
165C22×C127C22×Q811yescharacteristic
166C22×C127C2×#4111yescharacteristic
167C22×C127C2×#4111yescharacteristic
168C22×C127C2×#4111yescharacteristic
169C22×C127C2×#4111yescharacteristic
170C4×C127—22no—
171C4×C127—22no—
172C4×C127—22no—
173C4×C127—41no—
174C4×C127—41no—
175C4×C127C22⋊Q814yescomplemented
176Dic127—22no—
177Dic127—22no—
178Dic127—22no—
179Dic127—22no—
180Dic127—22no—
181Dic127—41no—
182Dic127—41no—
183Dic127C4×D414yes—
184C2×C127—24no—
185C2×C127C2×C4×D411yescharacteristic
186C2×C127C2×C4×Q811yescharacteristic
187C2×C127C4×#4111yescharacteristic
188C2×C127C2×C22⋊Q811yescharacteristic
189C2×C127#52511yescharacteristic
190C2×C127#52911yescharacteristic
191C2×C127#53311yescharacteristic
192C4×C22⋊Q8—1271nomaximal, Sylow
193C127C4×C22⋊Q811yescharacteristic, complemented, Sylow
194C2×C22⋊Q8—1271no—
195C2×C4×Q8—1271no—
196C22×C42—1271no—
197#391—1271no—
198#389—1271no—
199#387—1271no—
200#387—1271no—
201#385—1271no—
202#385—1271no—
203#380—1271no—
204C4×C4⋊C4—1271no—
205C4×C4⋊C4—1271no—
206C4×C4⋊C4—1271no—
207C4×C22⋊C4—1271no—
208C4×C22⋊C4D12711yescharacteristic
209C22×Q8—1271no—
210C23×C4—1271no—
211C23×C4—1271no—
212C23×C4C2×D12711yescharacteristic
213C22⋊Q8—1278no—
214C4×Q8—2544no—
215C2×C4⋊C4—1271no—
216C2×C4⋊C4—1271no—
217C2×C4⋊C4—1271no—
218C2×C4⋊C4—1271no—
219C2×C4⋊C4—1271no—
220C2×C4⋊C4—1271no—
221C2×C4⋊C4—1271no—
222C2×C4⋊C4—1271no—
223C2×C4⋊C4—1271no—
224C2×C22⋊C4—1271no—
225C2×C22⋊C4—1271no—
226C2×C22⋊C4C2×D12711yescharacteristic
227C2×C22⋊C4C2×D12711yescharacteristic
228C2×C42—1271no—
229C2×C42—1271no—
230C2×C42—1271no—
231C2×C42—1271no—
232C2×C42—1271no—
233C2×C42—1271no—
234C2×C42—2544no—
235C2×C42C2×D12711yescharacteristic
236C2×C42C2×D12711yescharacteristic
237#95—1271no—
238#95—1271no—
239#95—1271no—
240#95—1271no—
241#95—1271no—
242#95—1271no—
243#95—1271no—
244#95—1271no—
245#95C2×D12711yescharacteristic
246#95C2×D12711yescharacteristic
247C24C22×D12711yescharacteristic
248C2×Q8—1274no—
249C2×Q8—2542no—
250C2×Q8—2542no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—1271no—
254C22×C4—1274no—
255C22×C4—1271no—
256C22×C4—1271no—
257C22×C4—1271no—
258C22×C4—1271no—
259C22×C4—1271no—
260C22×C4—1271no—
261C22×C4—1271no—
262C22×C4—2542no—
263C22×C4—2542no—
264C22×C4—2542no—
265C22×C4—2542no—
266C22×C4—2542no—
267C22×C4Dic25414yescomplemented
268C22×C4C22×D12711yescharacteristic
269C22×C4C22×D12711yescharacteristic
270C22×C4C22×D12711yescharacteristic
271C22×C4C22×D12711yescharacteristic
272C22×C4C22×D12711yescharacteristic
273C22×C4C22×D12711yescharacteristic
274C4⋊C4—1274no—
275C4⋊C4—1274no—
276C4⋊C4—1274no—
277C4⋊C4—2542no—
278C4⋊C4—2542no—
279C4⋊C4—2542no—
280C4⋊C4—2542no—
281C4⋊C4—2542no—
282C4⋊C4—2542no—
283C22⋊C4—22no—
284C22⋊C4—1274no—
285C22⋊C4—2542no—
286C22⋊C4C4×D12714yes—
287C42—22no—
288C42—22no—
289C42—1274no—
290C42—2542no—
291C42—2542no—
292C42—2542no—
293C42—2542no—
294C42—2542no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23C2×C4×D12712yes—
300C23C2×Dic25412yes—
301C23#1452324812yes—
302C23C23×D12711yescharacteristic
303Q8—2548no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—28no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—1272no—
318C2×C4—1272no—
319C2×C4—1272no—
320C2×C4—1272no—
321C2×C4—1272no—
322C2×C4—1272no—
323C2×C4—1272no—
324C2×C4—1272no—
325C2×C4—2548no—
326C2×C4—2541no—
327C2×C4—2541no—
328C2×C4—2541no—
329C2×C4—2541no—
330C2×C4—2541no—
331C2×C4—2541no—
332C2×C4—2548no—
333C2×C4—2541no—
334C2×C4—2541no—
335C2×C4—2541no—
336C2×C4—2541no—
337C2×C4—2541no—
338C2×C4—2541no—
339C2×C4—2541no—
340C2×C4—2541no—
341C2×C4—2541no—
342C2×C4—2541no—
343C2×C4C2×C4×D12712yes—
344C2×C4C2×C4×D12712yes—
345C2×C4D4×D12712yes—
346C2×C4C2×Dic25412yes—
347C2×C4C2×Dic25412yes—
348C2×C4#1452324712yes—
349C22—22no—
350C22—22no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—22no—
355C22C4×Dic25414yescomplemented
356C22C22×C4×D12711yescharacteristic
357C22C2×D4×D12711yescharacteristic
358C22C22×Dic25411yescharacteristic
359C22#41×D12711yescharacteristic
360C22#41×D12711yescharacteristic
361C22C2×#1452324711yescharacteristic
362C22C2×#1452324811yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—41no—
367C4—41no—
368C4—1274no—
369C4—5081no—
370C4—5081no—
371C4—2542no—
372C4—2542no—
373C4—2542no—
374C4—2542no—
375C4—2542no—
376C4#1686118614yesdirect product factor
377C2—24no—
378C2C4×D4×D12711yescharacteristic
379C2C2×C4×Dic25411yescharacteristic
380C2C4×#1452324711yescharacteristic
381C2C2×#1686118611yescharacteristic
382C2#2255038511yescharacteristic
383C2#2255040611yescharacteristic
384C2#2255042911yescharacteristic
subgroupG/H
centerC22×C4C22×D127
commutatorC22×C127C23×C4
FrattiniC23C23×D127
FittingC4×C22⋊C4×C127C2
socle, cosocleC23×C127C24
prime radicalC24×C127C23
hypercenterC4×C22⋊C4D127
hypocenterC127C4×C22⋊Q8
LCSG ▷ C22×C127 ▷ C127
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic254C2semidirect
4. #22549780C2semidirect
5. #22549773C2semidirect
6. #22549763C2semidirect
7. #22549759C2semidirect
11. C4×Dic127⋊C4C2semidirect
12. C4×Dic127⋊C4C2semidirect
13. C4×C4⋊Dic127C2semidirect
19. #16861186C4direct (N × H)
56. C2×Dic254C2×C4semidirect
73. C4⋊Dic127C2×C4semidirect
78. Dic127⋊C4C2×C4semidirect
79. Dic127⋊C4C2×C4semidirect
91. C22×C4×C127Q8semidirect
162. C22×C127C4×Q8semidirect
175. C4×C127C22⋊Q8semidirect
193. C127C4×C22⋊Q8semidirect
267. C22×C4Dic254semidirect
355. C22C4×Dic254semidirect
376. C4#16861186direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168611862
C2×C4×Dic2542
C22×C4×Dic1272
#225497802
#225497732
#225497632
#225497592
#225497512
#225497482
#225497342
C4×Dic127⋊C42
C4×C4⋊Dic1272
C4×C22⋊Dic1272
C4×C22⋊C4×C1272
C4×C22⋊Q8127