Finite Group Databasebeta

← #16848862

Subgroups — #16848862

Order 3968.

576 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758516C211yesmaximal, characteristic
2#14520949C211yesmaximal, characteristic, complemented
3#14520943C211yesmaximal, characteristic, complemented
4#14520940C211yesmaximal, characteristic, complemented
5#14520933C211yesmaximal, characteristic, complemented
6#14520930C211yesmaximal, characteristic, complemented
7#14520929C211yesmaximal, characteristic, complemented
8#14520926C211yesmaximal, characteristic, complemented
9#14520925C211yesmaximal, characteristic, complemented
10#14520925C211yesmaximal, characteristic, complemented
11#14520921C211yesmaximal, characteristic, complemented
12#14520920C211yesmaximal, characteristic, complemented
13#14520910C211yesmaximal, characteristic, complemented
14#14520907C211yesmaximal, characteristic, complemented
15C31×#390C211yesmaximal, characteristic, complemented
16C22×D4×C31C2211yescharacteristic
17C22×C22⋊D31C2211yescharacteristic
18C22×C22⋊D31C2211yescharacteristic
19C23×Dic31C2211yescharacteristic
20C23×Dic31C2211yescharacteristic
21C22×C4×D31C2211yescharacteristic
22C2×C4⋊C4×C31C2211yescharacteristic
23C2×C22⋊C4×C31C2211yescharacteristic
24C2×C22⋊C4×C31C2211yescharacteristic
25C2×C22⋊C4×C31C2211yescharacteristic
26C2×C22⋊C4×C31C2211yescharacteristic
27C2×C42×C31C2211yescharacteristic
28C2×C22⋊Dic31C2211yescharacteristic
29C2×C22⋊Dic31C2211yescharacteristic
30C2×C22⋊Dic31C2211yescharacteristic
31C2×C22⋊Dic31C2211yescharacteristic
32#11758516C418yescomplemented
33C2×(C2×D31)⋊C4C2211yescharacteristic
34C2×(C2×D31)⋊C4C2211yescharacteristic
35C2×(C2×D31)⋊C4C2211yescharacteristic
36C2×(C2×D31)⋊C4C2211yescharacteristic
37C2×Dic31⋊C4C2211yescharacteristic
38C2×Dic31⋊C4C2211yescharacteristic
39C2×Dic31⋊C4C2211yescharacteristic
40C2×Dic31⋊C4C2211yescharacteristic
41C2×C4×Dic31C2211yescharacteristic
42C31⋊#95C2211yescharacteristic
43C31⋊#95C2211yescharacteristic
44C31⋊#95C2211yescharacteristic
45C31⋊#95C2211yescharacteristic
46C31⋊#95C2211yescharacteristic
47C31⋊#95C2211yescharacteristic
48C31⋊#95C2211yescharacteristic
49C31⋊#95C2211yescharacteristic
50C31⋊#95C2211yescharacteristic
51C31⋊#95C2211yescharacteristic
52C24×C31C2311yescharacteristic
53C24×C31C2311yescharacteristic
54C23×D31C2311yescharacteristic
55C2×D4×C31—41no—
56C2×D4×C31—41no—
57C2×D4×C31C2×C414yescomplemented
58C22×C4×C31C2311yescharacteristic
59C22×C4×C31C2311yescharacteristic
60C22×C4×C31C2311yescharacteristic
61C22×C4×C31C2311yescharacteristic
62C22×C4×C31C2311yescharacteristic
63C2×C22⋊D31—41no—
64C2×C22⋊D31—41no—
65C2×C22⋊D31—41no—
66C2×C22⋊D31—41no—
67C2×C22⋊D31C2×C414yes—
68C2×C22⋊D31C2×C414yescomplemented
69C22×Dic31—41no—
70C22×Dic31—41no—
71C22×Dic31—41no—
72C22×Dic31—41no—
73C22×Dic31—41no—
74C22×Dic31C2×C414yescomplemented
75C22×Dic31C2311yescharacteristic
76C22×Dic31C2311yescharacteristic
77C22×Dic31C2311yescharacteristic
78C22×Dic31C2311yescharacteristic
79C22×Dic31C2311yescharacteristic
80C22×Dic31C2311yescharacteristic
81C22×Dic31C2311yescharacteristic
82C2×C4×D31—41no—
83C2×C4×D31—41no—
84C2×C4×D31—41no—
85C4⋊C4×C31—41no—
86C22⋊C4×C31—41no—
87C22⋊C4×C31—41no—
88C22⋊C4×C31—41no—
89C22⋊C4×C31—41no—
90C42×C31—41no—
91C22⋊Dic31—41no—
92C22⋊Dic31—41no—
93C22⋊Dic31—41no—
94C22⋊Dic31C2×C414yescomplemented
95(C2×D31)⋊C4—41no—
96(C2×D31)⋊C4—41no—
97(C2×D31)⋊C4—41no—
98(C2×D31)⋊C4C2×C414yescomplemented
99Dic31⋊C4—41no—
100Dic31⋊C4—41no—
101Dic31⋊C4—41no—
102Dic31⋊C4C2×C414yescomplemented
103C4×Dic31—41no—
104C23×C31—21no—
105C23×C31—21no—
106C23×C31—21no—
107C23×C31—21no—
108C23×C31—21no—
109C23×C31—21no—
110C23×C31—21no—
111C23×C31—21no—
112C23×C31—21no—
113C23×C31—21no—
114C23×C31—21no—
115C23×C31—21no—
116C23×C31C22×C412yes—
117C23×C31C22×C412yes—
118C23×C31C2411yescharacteristic
119C22×D31—21no—
120C22×D31—21no—
121C22×D31—21no—
122C22×D31—21no—
123C22×D31—21no—
124C22×D31—21no—
125C22×D31C22×C412yes—
126D4×C31—44no—
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—21no—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31C22×C412yes—
142C22⋊D31—44no—
143C22⋊D31—44no—
144C2×Dic31—21no—
145C2×Dic31—21no—
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—21no—
156C2×Dic31—21no—
157C2×Dic31—21no—
158C2×Dic31—21no—
159C2×Dic31—21no—
160C2×Dic31—21no—
161C2×Dic31—21no—
162C2×Dic31—44no—
163C2×Dic31—44no—
164C2×Dic31C22×C412yes—
165C2×Dic31C22×C412yes—
166C2×Dic31C22×C412yes—
167C4×D31—44no—
168#2377—311nomaximal, Sylow
169C22×C31—22no—
170C22×C31—22no—
171C22×C31—22no—
172C22×C31—22no—
173C22×C31—22no—
174C22×C31—22no—
175C22×C31—41no—
176C22×C31—41no—
177C22×C31—41no—
178C22×C31—41no—
179C22×C31—41no—
180C22×C31—41no—
181C22×C31—41no—
182C22×C31—41no—
183C22×C31C23×C411yescharacteristic
184C22×C31H(5,𝔽2)11yescharacteristic
185C22×C31H(5,𝔽2)11yescharacteristic
186C22×C31H(5,𝔽2)11yescharacteristic
187C22×C31H(5,𝔽2)11yescharacteristic
188C22×C31H(5,𝔽2)11yescharacteristic
189C22×C312−1+411yescharacteristic
190C2×D31—22no—
191C2×D31—22no—
192C2×D31—22no—
193C2×D31—41no—
194C2×D31—41no—
195C2×D31—41no—
196C2×D31—41no—
197C4×C31—22no—
198C4×C31—41no—
199C4×C31—41no—
200C4×C31—41no—
201C4×C31—41no—
202Dic31—22no—
203Dic31—22no—
204Dic31—22no—
205Dic31—41no—
206Dic31—41no—
207Dic31—41no—
208Dic31—41no—
209C2×#121—311no—
210#390—311no—
211#390D3111yescharacteristic, complemented
212#388—311no—
213#388—311no—
214#387—311no—
215#387—311no—
216#386—311no—
217#386—311no—
218#386—311no—
219#386—311no—
220#385—311no—
221#385—311no—
222#381—311no—
223#380—311no—
224C2×C31—42no—
225C2×C31—42no—
226C2×C31#51811yescharacteristic
227C2×C31#51811yescharacteristic
228C2×C31#52011yescharacteristic
229C2×C31#56011yescharacteristic
230C2×C31#56011yescharacteristic
231C2×C31#56211yescharacteristic
232C2×C31#56211yescharacteristic
233D31—42no—
234C22×D4—311no—
235C22×D4—311no—
236C22×D4C2×D3111yescharacteristic
237C23×C4—311no—
238C23×C4—311no—
239C23×C4—311no—
240#121—318no—
241C2×C4⋊C4—311no—
242C2×C4⋊C4—311no—
243C2×C4⋊C4—311no—
244C2×C4⋊C4—311no—
245C2×C4⋊C4C2×D3111yescharacteristic
246C2×C22⋊C4—311no—
247C2×C22⋊C4—311no—
248C2×C22⋊C4—311no—
249C2×C22⋊C4—311no—
250C2×C22⋊C4—311no—
251C2×C22⋊C4—311no—
252C2×C22⋊C4—311no—
253C2×C22⋊C4—311no—
254C2×C22⋊C4C2×D3111yescharacteristic
255C2×C22⋊C4C2×D3111yescharacteristic
256C2×C22⋊C4C2×D3111yescharacteristic
257C2×C22⋊C4C2×D3111yescharacteristic
258C2×C42—311no—
259C2×C42C2×D3111yescharacteristic
260#95—311no—
261#95—311no—
262#95—311no—
263#95—311no—
264#95—311no—
265#95—311no—
266#95—311no—
267#95—311no—
268#95—311no—
269#95—311no—
270C31#237711yescharacteristic, complemented, Sylow
271C24—311no—
272C24C22×D3111yescharacteristic
273C24C22×D3111yescharacteristic
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—314no—
277C2×D4—314no—
278C2×D4—1241no—
279C2×D4—1241no—
280C2×D4—1241no—
281C2×D4—1241no—
282C2×D4C4×D3114yescomplemented
283C22×C4—311no—
284C22×C4—311no—
285C22×C4—311no—
286C22×C4—314no—
287C22×C4—311no—
288C22×C4—311no—
289C22×C4—311no—
290C22×C4—311no—
291C22×C4—1241no—
292C22×C4—1241no—
293C22×C4—1241no—
294C22×C4—1241no—
295C22×C4—1241no—
296C22×C4—1241no—
297C22×C4—1241no—
298C22×C4—1241no—
299C22×C4C22×D3111yescharacteristic
300C22×C4C22×D3111yescharacteristic
301C22×C4C22×D3111yescharacteristic
302C22×C4C22×D3111yescharacteristic
303C22×C4C22×D3111yescharacteristic
304C4⋊C4—41no—
305C4⋊C4—314no—
306C4⋊C4—1241no—
307C4⋊C4—1241no—
308C4⋊C4—1241no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—314no—
314C22⋊C4—314no—
315C22⋊C4—1241no—
316C22⋊C4—1241no—
317C22⋊C4—1241no—
318C22⋊C4—1241no—
319C22⋊C4—1241no—
320C22⋊C4—1241no—
321C42—41no—
322C42—1241no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—312no—
336C23—621no—
337C23—621no—
338C23—621no—
339C23—621no—
340C23—621no—
341C23—621no—
342C23C2×C4×D3112yes—
343C23C2×C4×D3112yes—
344C23C23×D3111yescharacteristic
345D4—44no—
346D4—1244no—
347D4—1244no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—312no—
363C2×C4—312no—
364C2×C4—312no—
365C2×C4—621no—
366C2×C4—621no—
367C2×C4—621no—
368C2×C4—621no—
369C2×C4—621no—
370C2×C4—621no—
371C2×C4—621no—
372C2×C4—621no—
373C2×C4—621no—
374C2×C4—621no—
375C2×C4—621no—
376C2×C4—621no—
377C2×C4—621no—
378C2×C4—621no—
379C2×C4—621no—
380C2×C4—621no—
381C2×C4—621no—
382C2×C4—621no—
383C2×C4—1244no—
384C2×C4—1244no—
385C2×C4—1244no—
386C2×C4C2×C4×D3112yes—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—622no—
402C22—622no—
403C22—622no—
404C22—1241no—
405C22—1241no—
406C22—1241no—
407C22—1241no—
408C22C22×C4×D3111yescharacteristic
409C22#1175856111yescharacteristic
410C22#1175856111yescharacteristic
411C22#1175856111yescharacteristic
412C22#1175856111yescharacteristic
413C22#1175856611yescharacteristic
414C22#1175856711yescharacteristic
415C4—22no—
416C4—41no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—622no—
421C4—622no—
422C4—622no—
423C4—1241no—
424C4—1241no—
425C4—1241no—
426C4—1241no—
427C2—42no—
428C2—42no—
429C2—1242no—
430C2#1452152111yescharacteristic
431C2#1452152211yescharacteristic
432C2#1452152811yescharacteristic
433C2#1452178611yescharacteristic
434C2#1452178711yescharacteristic
435C2#1452179311yescharacteristic
436C2#1452179411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#390C2
socle, cosocleC23×C31C24
prime radicalC2×#11758516C2
hypercenter#390D31
hypocenterC31#2377
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. #14520949C2semidirect
3. #14520943C2semidirect
4. #14520940C2semidirect
5. #14520933C2semidirect
6. #14520930C2semidirect
7. #14520929C2semidirect
8. #14520926C2semidirect
9. #14520925C2semidirect
10. #14520925C2semidirect
11. #14520921C2semidirect
12. #14520920C2semidirect
13. #14520910C2semidirect
14. #14520907C2semidirect
15. C31×#390C2semidirect
32. #11758516C4semidirect
57. C2×D4×C31C2×C4semidirect
68. C2×C22⋊D31C2×C4semidirect
74. C22×Dic31C2×C4semidirect
94. C22⋊Dic31C2×C4semidirect
98. (C2×D31)⋊C4C2×C4semidirect
102. Dic31⋊C4C2×C4semidirect
211. #390D31semidirect
270. C31#2377semidirect
282. C2×D4C4×D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117585162
#145209492
#145209432
#145209402
#145209332
#145209302
#145209292
#145209262
#145209252
#145209212
#145209202
#145209102
#145209072
C31×#3902
#237731