Finite Group Databasebeta

← C4×#15690787 #27144267

Subgroups — C4×#15690787 #27144267

Order 12416.

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×#15690787C211yesmaximal, characteristic
2C2×C4×Dic194C211yesmaximal, characteristic, complemented
3C22×C4×Dic97C211yesmaximal, characteristic
4#20260639C211yesmaximal, characteristic, complemented
5#20260632C211yesmaximal, characteristic, complemented
6#20260622C211yesmaximal, characteristic, complemented
7#20260618C211yesmaximal, characteristic, complemented
8#20260610C211yesmaximal, characteristic
9#20260607C211yesmaximal, characteristic
10#20260593C211yesmaximal, characteristic
11C4×#13095490C211yesmaximal, characteristic, complemented
12C4×#13095490C211yesmaximal, characteristic, complemented
13C4×C4⋊Dic97C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic97C211yesmaximal, characteristic
15C4×C22⋊C4×C97C211yesmaximal, characteristic
16C22×Dic194C2211yescharacteristic
17C23×Dic97C2211yescharacteristic
18C23×Dic97C2211yescharacteristic
19#15690787C418yesdirect product factor
20C4×Dic194—24no—
21C2×C4⋊Dic97C2211yescharacteristic
22C2×C4⋊Dic97C2211yescharacteristic
23C2×C4⋊Dic97C2211yescharacteristic
24C2×#13095490C2211yescharacteristic
25C2×#13095490C2211yescharacteristic
26C2×#13095490C2211yescharacteristic
27C2×#13095490C2211yescharacteristic
28C2×#13095490C2211yescharacteristic
29C2×#13095490C2211yescharacteristic
30C2×C22⋊Dic97C2211yescharacteristic
31C2×C22⋊Dic97C2211yescharacteristic
32C2×C4×Dic97—24no—
33C2×C4×Dic97C2211yescharacteristic
34C2×C4×Dic97C2211yescharacteristic
35C2×C4×Dic97C2211yescharacteristic
36C2×C4×Dic97C2211yescharacteristic
37C2×C4×Dic97C2211yescharacteristic
38C2×C4×Dic97C2211yescharacteristic
39#15690717C2211yescharacteristic
40#15690717C2211yescharacteristic
41#15690717C2211yescharacteristic
42#15690717C2211yescharacteristic
43#15690717C2211yescharacteristic
44#15690717C2211yescharacteristic
45#15690717C2211yescharacteristic
46#15690717C2211yescharacteristic
47C23×C4×C97C2211yescharacteristic
48C2×C22⋊C4×C97C2211yescharacteristic
49C2×C22⋊C4×C97C2211yescharacteristic
50C2×C42×C97C2211yescharacteristic
51C2×C42×C97C2211yescharacteristic
52#95×C97C2211yescharacteristic
53#95×C97C2211yescharacteristic
54C2×Dic194—22no—
55C2×Dic194—22no—
56C2×Dic194C2×C414yescomplemented
57C22×Dic97—22no—
58C22×Dic97—22no—
59C22×Dic97—22no—
60C22×Dic97—22no—
61C22×Dic97—22no—
62C22×Dic97C2×C414yes—
63C22×Dic97C2311yescharacteristic
64C22×Dic97C2311yescharacteristic
65C22×Dic97C2311yescharacteristic
66C22×Dic97C2311yescharacteristic
67C22×Dic97C2311yescharacteristic
68C22×Dic97C2311yescharacteristic
69C22×Dic97C2311yescharacteristic
70C22×Dic97C2311yescharacteristic
71C4⋊Dic97—22no—
72C4⋊Dic97—22no—
73C4⋊Dic97C2×C414yescomplemented
74#13095490—22no—
75#13095490—22no—
76#13095490—22no—
77#13095490—22no—
78#13095490C2×C414yescomplemented
79#13095490C2×C414yescomplemented
80C22⋊Dic97—22no—
81C22⋊Dic97C2×C414yes—
82C4×Dic97—22no—
83C4×Dic97—22no—
84C4×Dic97—22no—
85C4×Dic97—22no—
86C4×Dic97—22no—
87C4×Dic97D414yes—
88C24×C97C2311yescharacteristic
89C22×C4×C97—22no—
90C22×C4×C97—22no—
91C22×C4×C97Q814yescomplemented
92C22×C4×C97C2311yescharacteristic
93C22×C4×C97C2311yescharacteristic
94C22×C4×C97C2311yescharacteristic
95C22×C4×C97C2311yescharacteristic
96C22×C4×C97C2311yescharacteristic
97C22×C4×C97C2311yescharacteristic
98C22⋊C4×C97—22no—
99C22⋊C4×C97C2×C414yes—
100C42×C97—22no—
101C42×C97—22no—
102C23×C97—21no—
103C23×C97—21no—
104C23×C97—21no—
105C23×C97—21no—
106C23×C97C22×C412yes—
107C23×C97C2×Q812yes—
108C23×C97#4112yes—
109C23×C97C2411yescharacteristic
110C2×C4×C97—21no—
111C2×C4×C97—21no—
112C2×C4×C97—21no—
113C2×C4×C97—21no—
114C2×C4×C97—21no—
115C2×C4×C97—21no—
116C2×C4×C97—28no—
117C2×C4×C97—21no—
118C2×C4×C97—21no—
119C2×C4×C97—21no—
120C2×C4×C97—21no—
121C2×C4×C97—21no—
122C2×C4×C97—21no—
123C2×C4×C97C22×C412yes—
124C2×C4×C97C22×C412yes—
125C2×C4×C97C2×D412yes—
126C2×C4×C97C2×Q812yes—
127C2×C4×C97C2×Q812yes—
128C2×C4×C97#4112yes—
129C2×Dic97—28no—
130C2×Dic97—21no—
131C2×Dic97—21no—
132C2×Dic97—21no—
133C2×Dic97—21no—
134C2×Dic97—21no—
135C2×Dic97—21no—
136C2×Dic97—21no—
137C2×Dic97—21no—
138C2×Dic97—21no—
139C2×Dic97—21no—
140C2×Dic97—28no—
141C2×Dic97—21no—
142C2×Dic97—21no—
143C2×Dic97—21no—
144C2×Dic97—21no—
145C2×Dic97—21no—
146C2×Dic97—21no—
147C2×Dic97C22×C412yes—
148C2×Dic97C22×C412yes—
149C2×Dic97C22×C412yes—
150C2×Dic97C22×C412yes—
151C2×Dic97C2×D412yes—
152C2×Dic97C2×D412yes—
153C2×Dic97#4112yes—
154C2×Dic97#4112yes—
155Dic194—28no—
156C22×C97—22no—
157C22×C97—22no—
158C22×C97—22no—
159C22×C97—22no—
160C22×C97—22no—
161C22×C97—22no—
162C22×C97C4×Q814yescomplemented
163C22×C97C23×C411yescharacteristic
164C22×C97C22×D411yescharacteristic
165C22×C97C22×Q811yescharacteristic
166C22×C97C2×#4111yescharacteristic
167C22×C97C2×#4111yescharacteristic
168C22×C97C2×#4111yescharacteristic
169C22×C97C2×#4111yescharacteristic
170C4×C97—22no—
171C4×C97—22no—
172C4×C97—22no—
173C4×C97—41no—
174C4×C97—41no—
175C4×C97C22⋊Q814yescomplemented
176Dic97—22no—
177Dic97—22no—
178Dic97—22no—
179Dic97—22no—
180Dic97—22no—
181Dic97—41no—
182Dic97—41no—
183Dic97C4×D414yes—
184C2×C97—24no—
185C2×C97C2×C4×D411yescharacteristic
186C2×C97C2×C4×Q811yescharacteristic
187C2×C97C4×#4111yescharacteristic
188C2×C97C2×C22⋊Q811yescharacteristic
189C2×C97#52511yescharacteristic
190C2×C97#52911yescharacteristic
191C2×C97#53311yescharacteristic
192C4×C22⋊Q8—971nomaximal, Sylow
193C97C4×C22⋊Q811yescharacteristic, complemented, Sylow
194C2×C22⋊Q8—971no—
195C2×C4×Q8—971no—
196C22×C42—971no—
197#391—971no—
198#389—971no—
199#387—971no—
200#387—971no—
201#385—971no—
202#385—971no—
203#380—971no—
204C4×C4⋊C4—971no—
205C4×C4⋊C4—971no—
206C4×C4⋊C4—971no—
207C4×C22⋊C4—971no—
208C4×C22⋊C4D9711yescharacteristic
209C22×Q8—971no—
210C23×C4—971no—
211C23×C4—971no—
212C23×C4C2×D9711yescharacteristic
213C22⋊Q8—978no—
214C4×Q8—1944no—
215C2×C4⋊C4—971no—
216C2×C4⋊C4—971no—
217C2×C4⋊C4—971no—
218C2×C4⋊C4—971no—
219C2×C4⋊C4—971no—
220C2×C4⋊C4—971no—
221C2×C4⋊C4—971no—
222C2×C4⋊C4—971no—
223C2×C4⋊C4—971no—
224C2×C22⋊C4—971no—
225C2×C22⋊C4—971no—
226C2×C22⋊C4C2×D9711yescharacteristic
227C2×C22⋊C4C2×D9711yescharacteristic
228C2×C42—971no—
229C2×C42—971no—
230C2×C42—971no—
231C2×C42—971no—
232C2×C42—971no—
233C2×C42—971no—
234C2×C42—1944no—
235C2×C42C2×D9711yescharacteristic
236C2×C42C2×D9711yescharacteristic
237#95—971no—
238#95—971no—
239#95—971no—
240#95—971no—
241#95—971no—
242#95—971no—
243#95—971no—
244#95—971no—
245#95C2×D9711yescharacteristic
246#95C2×D9711yescharacteristic
247C24C22×D9711yescharacteristic
248C2×Q8—974no—
249C2×Q8—1942no—
250C2×Q8—1942no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—971no—
254C22×C4—974no—
255C22×C4—971no—
256C22×C4—971no—
257C22×C4—971no—
258C22×C4—971no—
259C22×C4—971no—
260C22×C4—971no—
261C22×C4—971no—
262C22×C4—1942no—
263C22×C4—1942no—
264C22×C4—1942no—
265C22×C4—1942no—
266C22×C4—1942no—
267C22×C4Dic19414yescomplemented
268C22×C4C22×D9711yescharacteristic
269C22×C4C22×D9711yescharacteristic
270C22×C4C22×D9711yescharacteristic
271C22×C4C22×D9711yescharacteristic
272C22×C4C22×D9711yescharacteristic
273C22×C4C22×D9711yescharacteristic
274C4⋊C4—974no—
275C4⋊C4—974no—
276C4⋊C4—974no—
277C4⋊C4—1942no—
278C4⋊C4—1942no—
279C4⋊C4—1942no—
280C4⋊C4—1942no—
281C4⋊C4—1942no—
282C4⋊C4—1942no—
283C22⋊C4—22no—
284C22⋊C4—974no—
285C22⋊C4—1942no—
286C22⋊C4C4×D9714yes—
287C42—22no—
288C42—22no—
289C42—974no—
290C42—1942no—
291C42—1942no—
292C42—1942no—
293C42—1942no—
294C42—1942no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23C2×C4×D9712yes—
300C23C2×Dic19412yes—
301C23#1309551112yes—
302C23C23×D9711yescharacteristic
303Q8—1948no—
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—972no—
318C2×C4—972no—
319C2×C4—972no—
320C2×C4—972no—
321C2×C4—972no—
322C2×C4—972no—
323C2×C4—972no—
324C2×C4—972no—
325C2×C4—1948no—
326C2×C4—1941no—
327C2×C4—1941no—
328C2×C4—1941no—
329C2×C4—1941no—
330C2×C4—1941no—
331C2×C4—1941no—
332C2×C4—1948no—
333C2×C4—1941no—
334C2×C4—1941no—
335C2×C4—1941no—
336C2×C4—1941no—
337C2×C4—1941no—
338C2×C4—1941no—
339C2×C4—1941no—
340C2×C4—1941no—
341C2×C4—1941no—
342C2×C4—1941no—
343C2×C4C2×C4×D9712yes—
344C2×C4C2×C4×D9712yes—
345C2×C4D4×D9712yes—
346C2×C4C2×Dic19412yes—
347C2×C4C2×Dic19412yes—
348C2×C4#1309551012yes—
349C22—22no—
350C22—22no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—22no—
355C22C4×Dic19414yescomplemented
356C22C22×C4×D9711yescharacteristic
357C22C2×D4×D9711yescharacteristic
358C22C22×Dic19411yescharacteristic
359C22#41×D9711yescharacteristic
360C22#41×D9711yescharacteristic
361C22C2×#1309551011yescharacteristic
362C22C2×#1309551111yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—41no—
367C4—41no—
368C4—974no—
369C4—3881no—
370C4—3881no—
371C4—1942no—
372C4—1942no—
373C4—1942no—
374C4—1942no—
375C4—1942no—
376C4#1569078714yesdirect product factor
377C2—24no—
378C2C4×D4×D9711yescharacteristic
379C2C2×C4×Dic19411yescharacteristic
380C2C4×#1309551011yescharacteristic
381C2C2×#1569078711yescharacteristic
382C2#2026124411yescharacteristic
383C2#2026126511yescharacteristic
384C2#2026128811yescharacteristic
subgroupG/H
centerC22×C4C22×D97
commutatorC22×C97C23×C4
FrattiniC23C23×D97
FittingC4×C22⋊C4×C97C2
socle, cosocleC23×C97C24
prime radicalC24×C97C23
hypercenterC4×C22⋊C4D97
hypocenterC97C4×C22⋊Q8
LCSG ▷ C22×C97 ▷ C97
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic194C2semidirect
4. #20260639C2semidirect
5. #20260632C2semidirect
6. #20260622C2semidirect
7. #20260618C2semidirect
11. C4×#13095490C2semidirect
12. C4×#13095490C2semidirect
13. C4×C4⋊Dic97C2semidirect
19. #15690787C4direct (N × H)
56. C2×Dic194C2×C4semidirect
73. C4⋊Dic97C2×C4semidirect
78. #13095490C2×C4semidirect
79. #13095490C2×C4semidirect
91. C22×C4×C97Q8semidirect
162. C22×C97C4×Q8semidirect
175. C4×C97C22⋊Q8semidirect
193. C97C4×C22⋊Q8semidirect
267. C22×C4Dic194semidirect
355. C22C4×Dic194semidirect
376. C4#15690787direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156907872
C2×C4×Dic1942
C22×C4×Dic972
#202606392
#202606322
#202606222
#202606182
#202606102
#202606072
#202605932
C4×#130954902
C4×C4⋊Dic972
C4×C22⋊Dic972
C4×C22⋊C4×C972
C4×C22⋊Q897