Finite Group Databasebeta

← #386×D97 #27144150

Subgroups — #386×D97 #27144150

Order 12416.

1576 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D97C211yesmaximal, characteristic
2C23×C4×D97C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×D97C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D97C212yesmaximal, complemented
5#20260615C211yesmaximal, characteristic, complemented
6#20260614C211yesmaximal, characteristic, complemented
7#20260613C212yesmaximal, complemented
8#20260612C211yesmaximal, characteristic, complemented
9#20260611C212yesmaximal, complemented
10#95×D97C212yesmaximal, complemented
11#386×C97C211yesmaximal, characteristic, complemented
12C24×D97C2211yescharacteristic
13C24×D97C2211yescharacteristic
14C22×D388C2211yescharacteristic
15C22×C22⋊D97C2211yescharacteristic
16C22×C22⋊D97C2211yescharacteristic
17C2×D4×D97—24no—
18C2×D4×D97—24no—
19C2×D4×D97C418yescomplemented
20C23×Dic97C2211yescharacteristic, complemented
21C22×C4×D97—24no—
22C22×C4×D97—28no—
23C22×C4×D97C2212yes—
24C22×C4×D97C2211yescharacteristic
25C22×C4×D97C2212yes—
26C22×C4×D97C2212yescomplemented
27C2×C22⋊Dic97C2212yescomplemented
28C2×C22⋊Dic97C2211yescharacteristic, complemented
29C2×#13095488C2212yescomplemented
30C2×#13095488C2212yescomplemented
31C2×#13095488C2212yescomplemented
32C22⋊C4×D97—24no—
33C22⋊C4×D97—28no—
34#15690717C2212yescomplemented
35#15690717C2212yescomplemented
36#15690717C2212yescomplemented
37C22×D4×C97C2211yescharacteristic
38C23×C4×C97C2211yescharacteristic, complemented
39C2×C22⋊C4×C97C2212yescomplemented
40C2×C22⋊C4×C97C2211yescharacteristic, complemented
41#95×C97C2212yescomplemented
42C23×D97—24no—
43C23×D97—24no—
44C23×D97—24no—
45C23×D97—22no—
46C23×D97—22no—
47C23×D97—24no—
48C23×D97C2×C414yes—
49C23×D97C2×C414yescomplemented
50C23×D97D414yes—
51C23×D97D414yes—
52C23×D97C2311yescharacteristic
53C23×D97C2311yescharacteristic
54C23×D97C2311yescharacteristic
55C2×D388—22no—
56C2×D388—22no—
57C2×D388C2×C414yescomplemented
58C2×C22⋊D97—22no—
59C2×C22⋊D97—22no—
60C2×C22⋊D97—22no—
61C2×C22⋊D97—22no—
62C2×C22⋊D97C2×C414yescomplemented
63C2×C22⋊D97C2×C414yescomplemented
64D4×D97—232no—
65C22×Dic97—22no—
66C22×Dic97—24no—
67C22×Dic97C2312yes—
68C22×Dic97C2311yescharacteristic
69C22×Dic97C2312yes—
70C2×C4×D97—232no—
71C2×C4×D97—24no—
72C2×C4×D97—24no—
73C2×C4×D97—24no—
74C2×C4×D97—22no—
75C2×C4×D97—22no—
76C2×C4×D97—24no—
77C2×C4×D97—24no—
78C2×C4×D97—24no—
79C2×C4×D97—24no—
80C2×C4×D97—24no—
81C2×C4×D97C2×C414yescomplemented
82C2×C4×D97D418yescomplemented
83C22⋊Dic97—22no—
84C22⋊Dic97—24no—
85#13095488—24no—
86#13095488—24no—
87#13095488—24no—
88C24×C97C2311yescharacteristic
89C24×C97C2311yescharacteristic
90C2×D4×C97—22no—
91C2×D4×C97—22no—
92C2×D4×C97C2×C414yescomplemented
93C22×C4×C97—22no—
94C22×C4×C97—24no—
95C22×C4×C97C2312yes—
96C22×C4×C97C2311yescharacteristic
97C22×C4×C97C2312yes—
98C22⋊C4×C97—22no—
99C22⋊C4×C97—24no—
100C23×C97—22no—
101C23×C97—22no—
102C23×C97—22no—
103C23×C97—21no—
104C23×C97—21no—
105C23×C97—22no—
106C23×C97C22×C412yes—
107C23×C97C22×C412yescomplemented
108C23×C97C2×D412yes—
109C23×C97C2×D412yes—
110C23×C97C2411yescharacteristic
111C22×D97—22no—
112C22×D97—22no—
113C22×D97—216no—
114C22×D97—28no—
115C22×D97—216no—
116C22×D97—28no—
117C22×D97—22no—
118C22×D97—21no—
119C22×D97—21no—
120C22×D97—22no—
121C22×D97—28no—
122C22×D97—216no—
123C22×D97—44no—
124C22×D97—48no—
125C22×D97—44no—
126C22×D97C22⋊C4116yescomplemented
127C22×D97C22×C412yes—
128C22×D97C22×C412yes—
129C22×D97C22×C412yescomplemented
130C22×D97C2×D412yes—
131C22×D97C2×D412yes—
132C22×D97C2×D412yes—
133C22×D97C2×D412yes—
134C22×D97C2×D414yes—
135C22×D97#4114yes—
136D4×C97—28no—
137C2×C4×C97—28no—
138C2×C4×C97—22no—
139C2×C4×C97—22no—
140C2×C4×C97—21no—
141C2×C4×C97—21no—
142C2×C4×C97—22no—
143C2×C4×C97—22no—
144C2×C4×C97—22no—
145C2×C4×C97C22×C412yescomplemented
146C2×C4×C97C2×D414yescomplemented
147C22⋊D97—28no—
148C22⋊D97—28no—
149C2×Dic97—28no—
150C2×Dic97—22no—
151C2×Dic97—22no—
152C2×Dic97—21no—
153C2×Dic97—21no—
154C2×Dic97—22no—
155C2×Dic97—22no—
156C2×Dic97—22no—
157C2×Dic97C22×C412yescomplemented
158C2×Dic97C2×D414yescomplemented
159D388—28no—
160C4×D97—216no—
161C4×D97—28no—
162C4×D97—216no—
163C4×D97—48no—
164C22×C97—24no—
165C22×C97—22no—
166C22×C97—24no—
167C22×C97—22no—
168C22×C97—22no—
169C22×C97—24no—
170C22×C97—41no—
171C22×C97—42no—
172C22×C97—41no—
173C22×C97C2×C22⋊C414yescomplemented
174C22×C97C23×C411yescharacteristic
175C22×C97C22×D411yescharacteristic
176C22×C97C22×D411yescharacteristic
177C22×C97C22×D412yes—
178C22×C97C2×#4112yes—
179C2×D97—24no—
180C2×D97—22no—
181C2×D97—24no—
182C2×D97—22no—
183C2×D97—232no—
184C2×D97—22no—
185C2×D97—24no—
186C2×D97—41no—
187C2×D97—42no—
188C2×D97—41no—
189C2×D97—416no—
190C2×D97C2×C22⋊C414yes—
191C2×D97C2×C22⋊C414yescomplemented
192C2×D97C4×D418yes—
193C2×D97#12014yes—
194C2×D97#12118yes—
195C2×D97#12314yes—
196C4×C97—22no—
197C4×C97—24no—
198C4×C97—42no—
199Dic97—22no—
200Dic97—24no—
201Dic97—42no—
202C2×C97—24no—
203C2×C97—42no—
204C2×C97C22×C22⋊C411yescharacteristic
205C2×C97C2×C4×D412yes—
206C2×C97C2×#12011yescharacteristic
207C2×C97C2×#12112yes—
208C2×C97C2×#12311yescharacteristic
209D97—24no—
210D97—42no—
211D97#38618yesdirect product factor
212C2×#386—971nomaximal, Sylow
213C97C2×#38611yescharacteristic, complemented, Sylow
214C23×D4—971no—
215C24×C4—971no—
216C22×C22⋊C4—972no—
217C22×C22⋊C4—971no—
218#386—971no—
219#386—971no—
220#386—972no—
221#386—971no—
222#386—972no—
223#386D9711yescharacteristic, direct product factor
224C2×#95—972no—
225C25—971no—
226C25—971no—
227C22×D4—971no—
228C22×D4—971no—
229C22×D4—978no—
230C22×D4—971no—
231C22×D4—1944no—
232C22×D4—1944no—
233C22×D4C2×D9711yescharacteristic
234C23×C4—972no—
235C23×C4—971no—
236C23×C4—971no—
237C23×C4—972no—
238C23×C4—972no—
239C23×C4—1948no—
240C23×C4—1944no—
241C23×C4C2×D9711yescharacteristic, complemented
242C2×C22⋊C4—972no—
243C2×C22⋊C4—971no—
244C2×C22⋊C4—972no—
245C2×C22⋊C4—972no—
246C2×C22⋊C4—972no—
247C2×C22⋊C4—1948no—
248C2×C22⋊C4—1944no—
249C2×C22⋊C4C2×D9711yescharacteristic, complemented
250C2×C22⋊C4C2×D9712yescomplemented
251#95—972no—
252#95—972no—
253#95—972no—
254#95C2×D9712yescomplemented
255C24—971no—
256C24—974no—
257C24—974no—
258C24—974no—
259C24—971no—
260C24—974no—
261C24—971no—
262C24—1944no—
263C24—1942no—
264C24—1942no—
265C24—1944no—
266C24—1944no—
267C24—1944no—
268C24C22×D9711yescharacteristic
269C24C22×D9711yescharacteristic
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—974no—
273C2×D4—974no—
274C2×D4—974no—
275C2×D4—1942no—
276C2×D4—1942no—
277C2×D4—19432no—
278C2×D4—1942no—
279C2×D4—1942no—
280C2×D4—1942no—
281C2×D4—1942no—
282C2×D4C4×D9714yescomplemented
283C22×C4—22no—
284C22×C4—24no—
285C22×C4—971no—
286C22×C4—972no—
287C22×C4—974no—
288C22×C4—978no—
289C22×C4—972no—
290C22×C4—1944no—
291C22×C4—1944no—
292C22×C4—1944no—
293C22×C4—1944no—
294C22×C4—1944no—
295C22×C4—1944no—
296C22×C4—1944no—
297C22×C4—1942no—
298C22×C4—1942no—
299C22×C4—19432no—
300C22×C4—1944no—
301C22×C4—1942no—
302C22×C4—1944no—
303C22×C4C22×D9712yes—
304C22×C4C22×D9711yescharacteristic
305C22×C4C22×D9712yes—
306C22⋊C4—22no—
307C22⋊C4—24no—
308C22⋊C4—1944no—
309C22⋊C4—1944no—
310C22⋊C4—1944no—
311C22⋊C4—1942no—
312C22⋊C4—1944no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—21no—
317C23—21no—
318C23—22no—
319C23—972no—
320C23—974no—
321C23—972no—
322C23—972no—
323C23—974no—
324C23—9716no—
325C23—972no—
326C23—972no—
327C23—972no—
328C23—972no—
329C23—3884no—
330C23—3888no—
331C23—3884no—
332C23—1948no—
333C23—19416no—
334C23—1948no—
335C23—19416no—
336C23—19416no—
337C23—1948no—
338C23—1942no—
339C23—1941no—
340C23—1941no—
341C23—1942no—
342C23—1942no—
343C23—1942no—
344C23C2×C4×D9712yes—
345C23C2×C4×D9712yescomplemented
346C23D4×D9712yes—
347C23D4×D9712yes—
348C23C23×D9711yescharacteristic
349D4—28no—
350D4—1948no—
351D4—1948no—
352D4—1948no—
353C2×C4—28no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—972no—
362C2×C4—974no—
363C2×C4—3888no—
364C2×C4—19416no—
365C2×C4—1948no—
366C2×C4—19416no—
367C2×C4—1942no—
368C2×C4—1942no—
369C2×C4—1942no—
370C2×C4—1948no—
371C2×C4—1942no—
372C2×C4—1942no—
373C2×C4—1941no—
374C2×C4—1941no—
375C2×C4C2×C4×D9712yescomplemented
376C2×C4D4×D9714yescomplemented
377C22—24no—
378C22—22no—
379C22—24no—
380C22—22no—
381C22—22no—
382C22—24no—
383C22—41no—
384C22—42no—
385C22—41no—
386C22—974no—
387C22—978no—
388C22—974no—
389C22—978no—
390C22—974no—
391C22—974no—
392C22—38816no—
393C22—3881no—
394C22—3882no—
395C22—3881no—
396C22—19432no—
397C22—1942no—
398C22—1944no—
399C22—1944no—
400C22—1942no—
401C22—1944no—
402C22—1942no—
403C22C22⋊C4×D9714yescomplemented
404C22C22×C4×D9711yescharacteristic
405C22C2×D4×D9711yescharacteristic
406C22C2×D4×D9711yescharacteristic
407C22C2×D4×D9712yes—
408C22#41×D9712yes—
409C4—22no—
410C4—24no—
411C4—42no—
412C4—3882no—
413C4—1942no—
414C4—1944no—
415C2—24no—
416C2—42no—
417C2—978no—
418C2—3882no—
419C2—1944no—
420C2C2×C22⋊C4×D9711yescharacteristic
421C2C4×D4×D9712yes—
422C2#120×D9711yescharacteristic
423C2#121×D9712yes—
424C2#123×D9711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D97
commutatorC22×C97C23×C4
Fitting#386×C97C2
socle, cosocleC23×C97C24
prime radicalC22×D4×D97C2
hypercenter#386D97
hypocenterC97C2×#386
LCSG ▷ C22×C97 ▷ C97
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C23×C4×D97C2semidirect
3. C2×C22⋊C4×D97C2semidirect
4. C2×C22⋊C4×D97C2semidirect
5. #20260615C2semidirect
6. #20260614C2semidirect
7. #20260613C2semidirect
8. #20260612C2semidirect
9. #20260611C2semidirect
10. #95×D97C2semidirect
11. #386×C97C2semidirect
19. C2×D4×D97C4semidirect
20. C23×Dic97C22semidirect
26. C22×C4×D97C22semidirect
27. C2×C22⋊Dic97C22semidirect
28. C2×C22⋊Dic97C22semidirect
29. C2×#13095488C22semidirect
30. C2×#13095488C22semidirect
31. C2×#13095488C22semidirect
34. #15690717C22semidirect
35. #15690717C22semidirect
36. #15690717C22semidirect
38. C23×C4×C97C22semidirect
39. C2×C22⋊C4×C97C22semidirect
40. C2×C22⋊C4×C97C22semidirect
41. #95×C97C22semidirect
49. C23×D97C2×C4semidirect
57. C2×D388C2×C4semidirect
62. C2×C22⋊D97C2×C4semidirect
63. C2×C22⋊D97C2×C4semidirect
81. C2×C4×D97C2×C4semidirect
82. C2×C4×D97D4semidirect
92. C2×D4×C97C2×C4semidirect
107. C23×C97C22×C4semidirect
126. C22×D97C22⋊C4semidirect
129. C22×D97C22×C4semidirect
145. C2×C4×C97C22×C4semidirect
146. C2×C4×C97C2×D4semidirect
157. C2×Dic97C22×C4semidirect
158. C2×Dic97C2×D4semidirect
173. C22×C97C2×C22⋊C4semidirect
191. C2×D97C2×C22⋊C4semidirect
211. D97#386direct (N × H)
213. C97C2×#386semidirect
223. #386D97direct (N × H)
241. C23×C4C2×D97semidirect
249. C2×C22⋊C4C2×D97semidirect
250. C2×C22⋊C4C2×D97semidirect
254. #95C2×D97semidirect
282. C2×D4C4×D97semidirect
345. C23C2×C4×D97semidirect
375. C2×C4C2×C4×D97semidirect
376. C2×C4D4×D97semidirect
403. C22C22⋊C4×D97semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D972
C23×C4×D972
C2×C22⋊C4×D972
#202606152
#202606142
#202606132
#202606122
#202606112
#95×D972
#386×C972
C2×#38697