Finite Group Databasebeta

← C4×#15690782 #27144245

Subgroups — C4×#15690782 #27144245

Order 12416.

824 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15690782C211yesmaximal, characteristic
2C2×C4×C22⋊D97C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D97C211yesmaximal, characteristic, complemented
4C22×C4×Dic97C211yesmaximal, characteristic, complemented
5#20260635C211yesmaximal, characteristic, complemented
6#20260630C211yesmaximal, characteristic, complemented
7#20260629C211yesmaximal, characteristic, complemented
8#20260625C211yesmaximal, characteristic, complemented
9#20260615C211yesmaximal, characteristic, complemented
10#20260612C211yesmaximal, characteristic, complemented
11#20260593C211yesmaximal, characteristic, complemented
12C4×#13095490C211yesmaximal, characteristic, complemented
13C4×#13095488C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic97C211yesmaximal, characteristic, complemented
15C2×C4×D4×C97C211yesmaximal, characteristic, complemented
16C22×C22⋊D97C2211yescharacteristic
17C22×C22⋊D97C2211yescharacteristic
18C23×Dic97C2211yescharacteristic
19C23×Dic97C2211yescharacteristic
20C22×C4×D97C2211yescharacteristic
21#15690782C418yesdirect product factor
22C4×C22⋊D97—24no—
23C4×C22⋊D97—24no—
24C2×#13095490C2211yescharacteristic
25C2×#13095490C2211yescharacteristic
26C2×#13095490C2211yescharacteristic
27C2×#13095490C2211yescharacteristic
28C2×C22⋊Dic97C2211yescharacteristic
29C2×C22⋊Dic97C2211yescharacteristic
30C2×C22⋊Dic97C2211yescharacteristic
31C2×C22⋊Dic97C2211yescharacteristic
32C2×#13095488C2211yescharacteristic
33C2×#13095488C2211yescharacteristic
34C2×#13095488C2211yescharacteristic
35C2×#13095488C2211yescharacteristic
36C2×C4×Dic97—24no—
37C2×C4×Dic97C2211yescharacteristic
38C2×C4×Dic97C2211yescharacteristic
39C2×C4×Dic97C2211yescharacteristic
40C2×C4×Dic97C2211yescharacteristic
41C2×C4×Dic97C2211yescharacteristic
42#15690717C2211yescharacteristic
43#15690717C2211yescharacteristic
44#15690717C2211yescharacteristic
45#15690717C2211yescharacteristic
46#15690717C2211yescharacteristic
47#15690717C2211yescharacteristic
48C22×D4×C97C2211yescharacteristic
49C23×C4×C97C2211yescharacteristic
50C23×C4×C97C2211yescharacteristic
51C4×D4×C97—24no—
52C2×C4⋊C4×C97C2211yescharacteristic
53C2×C22⋊C4×C97C2211yescharacteristic
54C2×C22⋊C4×C97C2211yescharacteristic
55C2×C42×C97C2211yescharacteristic
56C23×D97C2311yescharacteristic
57C2×C22⋊D97—22no—
58C2×C22⋊D97—22no—
59C2×C22⋊D97—22no—
60C2×C22⋊D97—22no—
61C2×C22⋊D97C2×C414yescomplemented
62C2×C22⋊D97C2×C414yescomplemented
63C22×Dic97—22no—
64C22×Dic97—22no—
65C22×Dic97—22no—
66C22×Dic97—22no—
67C22×Dic97—22no—
68C22×Dic97C2×C414yescomplemented
69C22×Dic97C2311yescharacteristic
70C22×Dic97C2311yescharacteristic
71C22×Dic97C2311yescharacteristic
72C22×Dic97C2311yescharacteristic
73C22×Dic97C2311yescharacteristic
74C22×Dic97C2311yescharacteristic
75C22×Dic97C2311yescharacteristic
76C2×C4×D97—22no—
77C2×C4×D97—22no—
78C2×C4×D97—22no—
79#13095490—22no—
80#13095490—22no—
81#13095490—22no—
82#13095490C2×C414yescomplemented
83C22⋊Dic97—22no—
84C22⋊Dic97—22no—
85C22⋊Dic97—22no—
86C22⋊Dic97C2×C414yescomplemented
87#13095488—22no—
88#13095488—22no—
89#13095488—22no—
90#13095488C2×C414yescomplemented
91C4×Dic97—22no—
92C4×Dic97—22no—
93C4×Dic97—22no—
94C4×Dic97—22no—
95C4×Dic97D414yescomplemented
96C24×C97C2311yescharacteristic
97C24×C97C2311yescharacteristic
98C2×D4×C97—22no—
99C2×D4×C97—22no—
100C2×D4×C97C2×C414yescomplemented
101C22×C4×C97—22no—
102C22×C4×C97—22no—
103C22×C4×C97—22no—
104C22×C4×C97—22no—
105C22×C4×C97—22no—
106C22×C4×C97D414yescomplemented
107C22×C4×C97C2311yescharacteristic
108C22×C4×C97C2311yescharacteristic
109C22×C4×C97C2311yescharacteristic
110C22×C4×C97C2311yescharacteristic
111C22×C4×C97C2311yescharacteristic
112C4⋊C4×C97—22no—
113C22⋊C4×C97—22no—
114C22⋊C4×C97—22no—
115C42×C97—22no—
116C23×C97—21no—
117C23×C97—21no—
118C23×C97—21no—
119C23×C97—21no—
120C23×C97—21no—
121C23×C97—21no—
122C23×C97—21no—
123C23×C97—21no—
124C23×C97—21no—
125C23×C97—21no—
126C23×C97C22×C412yes—
127C23×C97C22×C412yes—
128C23×C97C2×D412yes—
129C23×C97#4112yes—
130C23×C97C2411yescharacteristic
131C22×D97—21no—
132C22×D97—21no—
133C22×D97—21no—
134C22×D97—21no—
135C22×D97—21no—
136C22×D97—21no—
137C22×D97C22×C412yes—
138D4×C97—28no—
139C2×C4×C97—21no—
140C2×C4×C97—21no—
141C2×C4×C97—21no—
142C2×C4×C97—21no—
143C2×C4×C97—28no—
144C2×C4×C97—21no—
145C2×C4×C97—21no—
146C2×C4×C97—21no—
147C2×C4×C97—21no—
148C2×C4×C97—21no—
149C2×C4×C97—21no—
150C2×C4×C97—44no—
151C2×C4×C97C22×C412yes—
152C2×C4×C97C2×D412yes—
153C2×C4×C97C2×D412yes—
154C2×C4×C97C2×D412yes—
155C2×C4×C97#4112yes—
156C22⋊D97—28no—
157C22⋊D97—28no—
158C2×Dic97—28no—
159C2×Dic97—21no—
160C2×Dic97—21no—
161C2×Dic97—21no—
162C2×Dic97—21no—
163C2×Dic97—21no—
164C2×Dic97—21no—
165C2×Dic97—21no—
166C2×Dic97—21no—
167C2×Dic97—28no—
168C2×Dic97—21no—
169C2×Dic97—21no—
170C2×Dic97—21no—
171C2×Dic97—21no—
172C2×Dic97—21no—
173C2×Dic97—21no—
174C2×Dic97C22×C412yes—
175C2×Dic97C22×C412yes—
176C2×Dic97C22×C412yes—
177C2×Dic97C2×D412yes—
178C2×Dic97C2×D412yes—
179C2×Dic97#4112yes—
180C2×Dic97#4112yes—
181C4×D97—44no—
182C22×C97—22no—
183C22×C97—22no—
184C22×C97—22no—
185C22×C97—22no—
186C22×C97—22no—
187C22×C97—22no—
188C22×C97—22no—
189C22×C97—22no—
190C22×C97—22no—
191C22×C97—41no—
192C22×C97—41no—
193C22×C97—41no—
194C22×C97—41no—
195C22×C97C4×D414yescomplemented
196C22×C97C23×C411yescharacteristic
197C22×C97C22×D411yescharacteristic
198C22×C97C22×D411yescharacteristic
199C22×C97C2×#4111yescharacteristic
200C22×C97C2×#4111yescharacteristic
201C22×C97C2×#4111yescharacteristic
202C22×C97C2×#4111yescharacteristic
203C2×D97—22no—
204C2×D97—22no—
205C2×D97—22no—
206C2×D97—41no—
207C2×D97—41no—
208C2×D97—41no—
209C2×D97—41no—
210C4×C97—22no—
211C4×C97—22no—
212C4×C97—41no—
213C4×C97—41no—
214C4×C97#12114yescomplemented
215Dic97—22no—
216Dic97—22no—
217Dic97—22no—
218Dic97—22no—
219Dic97—41no—
220Dic97—41no—
221Dic97C4×D414yescomplemented
222C2×C97—24no—
223C2×C97—42no—
224C2×C97C2×C4×D411yescharacteristic
225C2×C97C2×C4×D411yescharacteristic
226C2×C97C4×#4111yescharacteristic
227C2×C97C2×#12111yescharacteristic
228C2×C97#52511yescharacteristic
229C2×C97#52911yescharacteristic
230C2×C97#53211yescharacteristic
231D97—42no—
232C4×#121—971nomaximal, Sylow
233C97C4×#12111yescharacteristic, complemented, Sylow
234C2×#121—971no—
235C2×C4×D4—971no—
236C2×C4×D4—971no—
237C2×C4×D4D9711yescharacteristic, complemented
238C22×C42—971no—
239#390—971no—
240#389—971no—
241#388—971no—
242#388—971no—
243#386—971no—
244#386—971no—
245#380—971no—
246C4×C4⋊C4—971no—
247C4×C22⋊C4—971no—
248C4×C22⋊C4—971no—
249C22×D4—971no—
250C22×D4—971no—
251C22×D4C2×D9711yescharacteristic
252C23×C4—971no—
253C23×C4—971no—
254C23×C4—971no—
255C23×C4C2×D9711yescharacteristic
256C23×C4C2×D9711yescharacteristic
257#121—978no—
258C4×D4—24no—
259C4×D4—1944no—
260C4×D4—1944no—
261C2×C4⋊C4—971no—
262C2×C4⋊C4—971no—
263C2×C4⋊C4—971no—
264C2×C4⋊C4—971no—
265C2×C4⋊C4C2×D9711yescharacteristic
266C2×C22⋊C4—971no—
267C2×C22⋊C4—971no—
268C2×C22⋊C4—971no—
269C2×C22⋊C4—971no—
270C2×C22⋊C4—971no—
271C2×C22⋊C4—971no—
272C2×C22⋊C4—971no—
273C2×C22⋊C4—971no—
274C2×C22⋊C4C2×D9711yescharacteristic
275C2×C22⋊C4C2×D9711yescharacteristic
276C2×C42—971no—
277C2×C42—971no—
278C2×C42—971no—
279C2×C42—971no—
280C2×C42—971no—
281C2×C42—1944no—
282C2×C42C2×D9711yescharacteristic
283#95—971no—
284#95—971no—
285#95—971no—
286#95—971no—
287#95—971no—
288#95—971no—
289C24—971no—
290C24C22×D9711yescharacteristic
291C24C22×D9711yescharacteristic
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—974no—
295C2×D4—974no—
296C2×D4—1942no—
297C2×D4—1942no—
298C2×D4—1942no—
299C2×D4—1942no—
300C2×D4C4×D9714yescomplemented
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—971no—
307C22×C4—974no—
308C22×C4—971no—
309C22×C4—971no—
310C22×C4—971no—
311C22×C4—971no—
312C22×C4—971no—
313C22×C4—971no—
314C22×C4—1942no—
315C22×C4—1942no—
316C22×C4—1942no—
317C22×C4—1942no—
318C22×C4—1942no—
319C22×C4—1942no—
320C22×C4—1942no—
321C22×C4—1942no—
322C22×C4C22⋊D9714yescomplemented
323C22×C4C22×D9711yescharacteristic
324C22×C4C22×D9711yescharacteristic
325C22×C4C22×D9711yescharacteristic
326C22×C4C22×D9711yescharacteristic
327C22×C4C22×D9711yescharacteristic
328C4⋊C4—22no—
329C4⋊C4—974no—
330C4⋊C4—1942no—
331C4⋊C4—1942no—
332C4⋊C4—1942no—
333C22⋊C4—22no—
334C22⋊C4—22no—
335C22⋊C4—974no—
336C22⋊C4—974no—
337C22⋊C4—1942no—
338C22⋊C4—1942no—
339C22⋊C4—1942no—
340C22⋊C4—1942no—
341C22⋊C4—1942no—
342C22⋊C4—1942no—
343C42—22no—
344C42—974no—
345C42—1942no—
346C42—1942no—
347C42—1942no—
348C42—1942no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—972no—
360C23—1941no—
361C23—1941no—
362C23—1941no—
363C23—1941no—
364C23—1941no—
365C23—1941no—
366C23C2×C4×D9712yes—
367C23C2×C4×D9712yes—
368C23C2×C22⋊D9712yes—
369C23#1309551112yes—
370C23C23×D9711yescharacteristic
371D4—28no—
372D4—1948no—
373D4—1948no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—28no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—44no—
386C2×C4—972no—
387C2×C4—972no—
388C2×C4—972no—
389C2×C4—972no—
390C2×C4—972no—
391C2×C4—972no—
392C2×C4—972no—
393C2×C4—3884no—
394C2×C4—1948no—
395C2×C4—1941no—
396C2×C4—1941no—
397C2×C4—1941no—
398C2×C4—1941no—
399C2×C4—1941no—
400C2×C4—1941no—
401C2×C4—1948no—
402C2×C4—1941no—
403C2×C4—1941no—
404C2×C4—1941no—
405C2×C4—1941no—
406C2×C4—1941no—
407C2×C4—1941no—
408C2×C4—1941no—
409C2×C4—1941no—
410C2×C4C2×C4×D9712yes—
411C2×C4D4×D9712yes—
412C2×C4C2×C22⋊D9712yes—
413C2×C4C2×C22⋊D9712yes—
414C2×C4#1309551012yes—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—3881no—
429C22—3881no—
430C22—3881no—
431C22—3881no—
432C22—1942no—
433C22—1942no—
434C22—1942no—
435C22C4×C22⋊D9714yescomplemented
436C22C22×C4×D9711yescharacteristic
437C22C2×D4×D9711yescharacteristic
438C22C22×C22⋊D9711yescharacteristic
439C22#41×D9711yescharacteristic
440C22#41×D9711yescharacteristic
441C22C2×#1309551011yescharacteristic
442C22C2×#1309551111yescharacteristic
443C4—22no—
444C4—22no—
445C4—41no—
446C4—41no—
447C4—974no—
448C4—3881no—
449C4—3881no—
450C4—1942no—
451C4—1942no—
452C4—1942no—
453C4—1942no—
454C4#1569078214yesdirect product factor
455C2—24no—
456C2—42no—
457C2—3882no—
458C2C4×D4×D9711yescharacteristic
459C2C2×C4×C22⋊D9711yescharacteristic
460C2C4×#1309551011yescharacteristic
461C2C2×#1569078211yescharacteristic
462C2#2026124411yescharacteristic
463C2#2026126511yescharacteristic
464C2#2026128111yescharacteristic
subgroupG/H
centerC22×C4C22×D97
commutatorC22×C97C23×C4
FrattiniC23C23×D97
FittingC2×C4×D4×C97C2
socle, cosocleC23×C97C24
prime radicalC2×#15690782C2
hypercenterC2×C4×D4D97
hypocenterC97C4×#121
LCSG ▷ C22×C97 ▷ C97
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D97C2semidirect
3. C2×C4×C22⋊D97C2semidirect
4. C22×C4×Dic97C2semidirect
5. #20260635C2semidirect
6. #20260630C2semidirect
7. #20260629C2semidirect
8. #20260625C2semidirect
9. #20260615C2semidirect
10. #20260612C2semidirect
11. #20260593C2semidirect
12. C4×#13095490C2semidirect
13. C4×#13095488C2semidirect
14. C4×C22⋊Dic97C2semidirect
15. C2×C4×D4×C97C2semidirect
21. #15690782C4direct (N × H)
61. C2×C22⋊D97C2×C4semidirect
62. C2×C22⋊D97C2×C4semidirect
68. C22×Dic97C2×C4semidirect
82. #13095490C2×C4semidirect
86. C22⋊Dic97C2×C4semidirect
90. #13095488C2×C4semidirect
95. C4×Dic97D4semidirect
100. C2×D4×C97C2×C4semidirect
106. C22×C4×C97D4semidirect
195. C22×C97C4×D4semidirect
214. C4×C97#121semidirect
221. Dic97C4×D4semidirect
233. C97C4×#121semidirect
237. C2×C4×D4D97semidirect
300. C2×D4C4×D97semidirect
322. C22×C4C22⋊D97semidirect
435. C22C4×C22⋊D97semidirect
454. C4#15690782direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156907822
C2×C4×C22⋊D972
C22×C4×Dic972
#202606352
#202606302
#202606292
#202606252
#202606152
#202606122
#202605932
C4×#130954902
C4×#130954882
C4×C22⋊Dic972
C2×C4×D4×C972
C4×#12197