Finite Group Databasebeta

← #16848634

Subgroups — #16848634

Order 3968.

660 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×(C22⋊D31)⋊C4C211yesmaximal, characteristic
2C2×#11758449C211yesmaximal, characteristic, complemented
3C22×Dic31⋊C4C211yesmaximal, characteristic, complemented
4#14520940C211yesmaximal, characteristic, complemented
5#14520938C211yesmaximal, characteristic, complemented
6#14520933C211yesmaximal, characteristic, complemented
7#14520931C211yesmaximal, characteristic, complemented
8#14520928C211yesmaximal, characteristic
9#14520926C211yesmaximal, characteristic
10#14520913C211yesmaximal, characteristic, complemented
11#14520908C211yesmaximal, characteristic, complemented
12#14520907C211yesmaximal, characteristic, complemented
13C4×Dic31⋊C4C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic31C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
16C23×C4×C31C2211yescharacteristic
17C22×C22⋊D31C2211yescharacteristic
18C23×Dic31C2211yescharacteristic
19C23×Dic31C2211yescharacteristic
20C22×C4×D31C2211yescharacteristic
21C2×C22⋊C4×C31C2211yescharacteristic
22C2×C22⋊C4×C31C2211yescharacteristic
23C2×C42×C31C2211yescharacteristic
24C2×C42×C31C2211yescharacteristic
25C2×C22⋊Dic31C2211yescharacteristic
26C2×(C2×D31)⋊C4C2211yescharacteristic
27C2×(C2×D31)⋊C4C2211yescharacteristic
28C2×(C2×D31)⋊C4C2211yescharacteristic
29C2×(C2×D31)⋊C4C2211yescharacteristic
30C2×(C2×D31)⋊C4C2211yescharacteristic
31C2×Dic31⋊C4—24no—
32C2×Dic31⋊C4C2211yescharacteristic
33C2×Dic31⋊C4C2211yescharacteristic
34C2×Dic31⋊C4C2211yescharacteristic
35C2×Dic31⋊C4C2211yescharacteristic
36C2×Dic31⋊C4C2211yescharacteristic
37C2×Dic31⋊C4C2211yescharacteristic
38C2×Dic31⋊C4C2211yescharacteristic
39C2×C4×Dic31C2211yescharacteristic
40C2×C4×Dic31C2211yescharacteristic
41C2×C4×Dic31C2211yescharacteristic
42(C22⋊D31)⋊C4C418yescomplemented
43#11758449—24no—
44C31×#95C2211yescharacteristic
45C31×#95C2211yescharacteristic
46C31⋊#95C2211yescharacteristic
47C31⋊#95C2211yescharacteristic
48C31⋊#95C2211yescharacteristic
49C31⋊#95C2211yescharacteristic
50C31⋊#95C2211yescharacteristic
51C31⋊#95C2211yescharacteristic
52C31⋊#95C2211yescharacteristic
53C31⋊#95C2211yescharacteristic
54C24×C31C2311yescharacteristic
55C23×D31C2311yescharacteristic
56C22×C4×C31—22no—
57C22×C4×C31—22no—
58C22×C4×C31—41no—
59C22×C4×C31C2311yescharacteristic
60C22×C4×C31C2311yescharacteristic
61C22×C4×C31C2311yescharacteristic
62C22×C4×C31C2311yescharacteristic
63C22×C4×C31C2311yescharacteristic
64C22×C4×C31C2311yescharacteristic
65C2×C22⋊D31—22no—
66C2×C22⋊D31—22no—
67C2×C22⋊D31C2×C414yes—
68C22×Dic31—22no—
69C22×Dic31—22no—
70C22×Dic31—22no—
71C22×Dic31—22no—
72C22×Dic31—41no—
73C22×Dic31C2×C414yes—
74C22×Dic31C2311yescharacteristic
75C22×Dic31C2311yescharacteristic
76C22×Dic31C2311yescharacteristic
77C22×Dic31C2311yescharacteristic
78C22×Dic31C2311yescharacteristic
79C22×Dic31C2311yescharacteristic
80C22×Dic31C2311yescharacteristic
81C2×C4×D31—22no—
82C2×C4×D31—22no—
83C2×C4×D31C2×C414yescomplemented
84C22⋊C4×C31—22no—
85C22⋊C4×C31C2×C414yes—
86C42×C31—22no—
87C42×C31—41no—
88C22⋊Dic31—22no—
89(C2×D31)⋊C4—22no—
90(C2×D31)⋊C4—22no—
91(C2×D31)⋊C4—41no—
92(C2×D31)⋊C4—41no—
93(C2×D31)⋊C4C2×C414yescomplemented
94Dic31⋊C4—22no—
95Dic31⋊C4—22no—
96Dic31⋊C4—22no—
97Dic31⋊C4—22no—
98Dic31⋊C4—22no—
99Dic31⋊C4C2×C414yescomplemented
100Dic31⋊C4D414yescomplemented
101C4×Dic31—22no—
102C4×Dic31—41no—
103C4×Dic31C2×C414yescomplemented
104C23×C31—21no—
105C23×C31—21no—
106C23×C31—21no—
107C23×C31—21no—
108C23×C31C22×C412yes—
109C23×C31#4112yes—
110C23×C31#4112yes—
111C23×C31C2411yescharacteristic
112C22×D31—21no—
113C22×D31—21no—
114C22×D31—21no—
115C22×D31—21no—
116C22×D31—21no—
117C22×D31—21no—
118C22×D31C22×C412yes—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—21no—
134C2×C4×C31—44no—
135C2×C4×C31C22×C412yes—
136C2×C4×C31C22×C412yes—
137C2×C4×C31C2×D412yes—
138C22⋊D31—28no—
139C2×Dic31—21no—
140C2×Dic31—21no—
141C2×Dic31—21no—
142C2×Dic31—21no—
143C2×Dic31—21no—
144C2×Dic31—21no—
145C2×Dic31—28no—
146C2×Dic31—21no—
147C2×Dic31—21no—
148C2×Dic31—21no—
149C2×Dic31—21no—
150C2×Dic31—21no—
151C2×Dic31—21no—
152C2×Dic31—21no—
153C2×Dic31—21no—
154C2×Dic31—21no—
155C2×Dic31—44no—
156C2×Dic31C22×C412yes—
157C2×Dic31C22×C412yes—
158C2×Dic31C22×C412yes—
159C2×Dic31C2×D412yes—
160C2×Dic31C2×D412yes—
161C2×Dic31#4112yes—
162C4×D31—28no—
163#2352—311nomaximal, Sylow
164C22×C31—22no—
165C22×C31—22no—
166C22×C31—22no—
167C22×C31—22no—
168C22×C31—22no—
169C22×C31—22no—
170C22×C31#11714yescomplemented
171C22×C31C23×C411yescharacteristic
172C22×C31C22×D411yescharacteristic
173C22×C31C2×#4111yescharacteristic
174C22×C31C2×#4111yescharacteristic
175C22×C31C2×#4111yescharacteristic
176C22×C31H(5,𝔽2)11yescharacteristic
177C22×C312−1+411yescharacteristic
178C2×D31—22no—
179C2×D31—22no—
180C2×D31—22no—
181C2×D31—41no—
182C2×D31—41no—
183C2×D31—41no—
184C2×D31—41no—
185C4×C31—22no—
186C4×C31—22no—
187C4×C31—22no—
188C4×C31—41no—
189C4×C31—41no—
190C4×C31—41no—
191Dic31—22no—
192Dic31—22no—
193Dic31—22no—
194Dic31—41no—
195Dic31—41no—
196Dic31—41no—
197Dic31C4×D414yes—
198C2×C4×D4—311no—
199C2×#117—311no—
200C22×C4⋊C4—311no—
201#388—311no—
202#388—311no—
203#387—311no—
204#387—311no—
205#386—311no—
206#386—311no—
207#382—311no—
208#380—311no—
209#380—311no—
210C4×C4⋊C4—311no—
211C4×C22⋊C4—311no—
212C4×C22⋊C4D3111yescharacteristic, complemented
213C2×C31—24no—
214C2×C31C2×#11711yescharacteristic
215C2×C31C2×C4×D411yescharacteristic
216C2×C31#52011yescharacteristic
217C2×C31#54611yescharacteristic
218C2×C31#54811yescharacteristic
219C2×C31#55211yescharacteristic
220C2×C31#55311yescharacteristic
221D31—42no—
222C22×D4—311no—
223C23×C4—311no—
224C23×C4—311no—
225C23×C4—311no—
226C23×C4C2×D3111yescharacteristic
227C4×D4—318no—
228#117—624no—
229C2×C4⋊C4—311no—
230C2×C4⋊C4—311no—
231C2×C4⋊C4—311no—
232C2×C4⋊C4—311no—
233C2×C4⋊C4—311no—
234C2×C4⋊C4—311no—
235C2×C4⋊C4—311no—
236C2×C4⋊C4—624no—
237C2×C22⋊C4—311no—
238C2×C22⋊C4—311no—
239C2×C22⋊C4—311no—
240C2×C22⋊C4—311no—
241C2×C22⋊C4—311no—
242C2×C22⋊C4—311no—
243C2×C22⋊C4C2×D3111yescharacteristic
244C2×C22⋊C4C2×D3111yescharacteristic
245C2×C42—311no—
246C2×C42—311no—
247C2×C42—311no—
248C2×C42C2×D3111yescharacteristic
249C2×C42C2×D3111yescharacteristic
250#95—311no—
251#95—311no—
252#95—311no—
253#95—311no—
254#95—311no—
255#95—311no—
256#95—311no—
257#95—311no—
258#95C2×D3111yescharacteristic
259#95C2×D3111yescharacteristic
260C31#235211yescharacteristic, complemented, Sylow
261C24—311no—
262C24C22×D3111yescharacteristic
263C2×D4—314no—
264C2×D4—622no—
265C2×D4—622no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—41no—
269C22×C4—311no—
270C22×C4—314no—
271C22×C4—311no—
272C22×C4—311no—
273C22×C4—311no—
274C22×C4—314no—
275C22×C4—311no—
276C22×C4—311no—
277C22×C4—311no—
278C22×C4—622no—
279C22×C4—622no—
280C22×C4—622no—
281C22×C4—622no—
282C22×C4—622no—
283C22×C4—622no—
284C22×C4—1241no—
285C22×C4C22×D3111yescharacteristic
286C22×C4C22×D3111yescharacteristic
287C22×C4C22×D3111yescharacteristic
288C22×C4C22×D3111yescharacteristic
289C22×C4C22×D3111yescharacteristic
290C22×C4C22×D3111yescharacteristic
291C4⋊C4—314no—
292C4⋊C4—314no—
293C4⋊C4—622no—
294C4⋊C4—622no—
295C4⋊C4—622no—
296C4⋊C4—622no—
297C4⋊C4—622no—
298C22⋊C4—22no—
299C22⋊C4—314no—
300C22⋊C4—622no—
301C22⋊C4—622no—
302C22⋊C4—622no—
303C22⋊C4—1241no—
304C22⋊C4—1241no—
305C22⋊C4C4×D3114yes—
306C42—22no—
307C42—41no—
308C42—314no—
309C42—622no—
310C42—1241no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—312no—
316C23—621no—
317C23—621no—
318C23—621no—
319C23—621no—
320C23—621no—
321C23—621no—
322C23C2×C4×D3112yes—
323C23#9249512yes—
324C23#9249512yes—
325C23C23×D3111yescharacteristic
326D4—628no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—44no—
343C2×C4—312no—
344C2×C4—312no—
345C2×C4—312no—
346C2×C4—312no—
347C2×C4—312no—
348C2×C4—312no—
349C2×C4—628no—
350C2×C4—628no—
351C2×C4—621no—
352C2×C4—621no—
353C2×C4—621no—
354C2×C4—621no—
355C2×C4—621no—
356C2×C4—621no—
357C2×C4—621no—
358C2×C4—621no—
359C2×C4—621no—
360C2×C4—621no—
361C2×C4—621no—
362C2×C4—621no—
363C2×C4—621no—
364C2×C4—621no—
365C2×C4—621no—
366C2×C4—1244no—
367C2×C4C2×C4×D3112yes—
368C2×C4C2×C4×D3112yes—
369C2×C4D4×D3112yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—622no—
377C22—622no—
378C22—622no—
379C22—1241no—
380C22—1241no—
381C22—1241no—
382C22—1241no—
383C22#1175844914yescomplemented
384C22C22×C4×D3111yescharacteristic
385C22C2×#9249511yescharacteristic
386C22C2×#9249511yescharacteristic
387C22C2×D4×D3111yescharacteristic
388C22#1175856111yescharacteristic
389C22#41×D3111yescharacteristic
390C22#1175856711yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—314no—
398C4—622no—
399C4—622no—
400C4—622no—
401C4—1241no—
402C4—1241no—
403C4—1241no—
404C2—24no—
405C2—1242no—
406C2C2×#1175844911yescharacteristic
407C2C4×D4×D3111yescharacteristic
408C2#1452152811yescharacteristic
409C2#1452168911yescharacteristic
410C2#1452170811yescharacteristic
411C2#1452173211yescharacteristic
412C2#1452174811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC4×C22⋊C4×C31C2
socle, cosocleC23×C31C24
prime radicalC22×C22⋊D31C22
hypercenterC4×C22⋊C4D31
hypocenterC31#2352
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11758449C2semidirect
3. C22×Dic31⋊C4C2semidirect
4. #14520940C2semidirect
5. #14520938C2semidirect
6. #14520933C2semidirect
7. #14520931C2semidirect
10. #14520913C2semidirect
11. #14520908C2semidirect
12. #14520907C2semidirect
13. C4×Dic31⋊C4C2semidirect
14. C22⋊C4×Dic31C2semidirect
15. C4×C22⋊C4×C31C2semidirect
42. (C22⋊D31)⋊C4C4semidirect
83. C2×C4×D31C2×C4semidirect
93. (C2×D31)⋊C4C2×C4semidirect
99. Dic31⋊C4C2×C4semidirect
100. Dic31⋊C4D4semidirect
103. C4×Dic31C2×C4semidirect
170. C22×C31#117semidirect
212. C4×C22⋊C4D31semidirect
260. C31#2352semidirect
383. C22#11758449semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D31)⋊C42
C2×#117584492
C22×Dic31⋊C42
#145209402
#145209382
#145209332
#145209312
#145209282
#145209262
#145209132
#145209082
#145209072
C4×Dic31⋊C42
C22⋊C4×Dic312
C4×C22⋊C4×C312
#235231