Finite Group Databasebeta

← #16856304

Subgroups — #16856304

Order 3968.

408 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521596C211yesmaximal, characteristic, complemented
2#14521581C211yesmaximal, characteristic, complemented
3#14521457C211yesmaximal, characteristic, complemented
4#14521437C211yesmaximal, characteristic, complemented
5#14521412C211yesmaximal, characteristic, complemented
6#14521407C211yesmaximal, characteristic, complemented
7#14521301C211yesmaximal, characteristic, complemented
8#14521299C211yesmaximal, characteristic, complemented
9#14521296C211yesmaximal, characteristic, complemented
10#14521294C211yesmaximal, characteristic, complemented
11C4×#92470C211yesmaximal, characteristic, complemented
12C4×#92480C211yesmaximal, characteristic, complemented
13C4×#92479C211yesmaximal, characteristic, complemented
14C4×#92469C211yesmaximal, characteristic, complemented
15C4×D8×C31C211yesmaximal, characteristic, complemented
16C2×#92495—21no—
17C2×D8×C31C2211yescharacteristic
18C4×D4×C31C2211yescharacteristic
19C4×D4×C31C2211yescharacteristic
20#11758517C2211yescharacteristic
21#11758515C2211yescharacteristic
22#11758515C2211yescharacteristic
23#11758513C2211yescharacteristic
24C2×#92480C2211yescharacteristic
25C2×#92479C2211yescharacteristic
26C4×C22⋊D31—21no—
27C4×C22⋊D31—21no—
28#11758503—21no—
29C2×#92470C2211yescharacteristic
30C2×#92469C2211yescharacteristic
31C2×#92469C2211yescharacteristic
32#11758474C2211yescharacteristic
33#11758472C2211yescharacteristic
34#11758467C2211yescharacteristic
35#11758465C2211yescharacteristic
36#11758462—21no—
37#11758461—21no—
38#11758460—21no—
39#11758456—21no—
40C4×D124C2211yescharacteristic
41C42×D31C2211yescharacteristic
42C4×Dic62C2211yescharacteristic
43C31×#107C2211yescharacteristic
44C31×#102C2211yescharacteristic
45C31×#102C2211yescharacteristic
46C4×C8×C31C2211yescharacteristic
47#11758420C2211yescharacteristic
48#11758420C2211yescharacteristic
49#11758409C2211yescharacteristic
50#11758405C2211yescharacteristic
51#11758404C2211yescharacteristic
52#11758403C2211yescharacteristic
53#11758403C2211yescharacteristic
54#11758398C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758396C2211yescharacteristic
57#11758395C2211yescharacteristic
58C4×C31⋊C8C2211yescharacteristic
59C2×D4×C31C2311yescharacteristic
60C2×D4×C31C2311yescharacteristic
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C2×C22⋊D31—21no—
64C2×C22⋊D31—21no—
65C2×C22⋊D31—21no—
66C2×C22⋊D31—21no—
67#92495—44no—
68C2×D124—21no—
69C2×D124C2311yescharacteristic
70C2×C4×D31—21no—
71C2×C4×D31D411yescharacteristic
72C2×C4×D31D411yescharacteristic
73C2×C4×D31C2311yescharacteristic
74C2×Dic62—21no—
75C2×Dic62C2311yescharacteristic
76D8×C31—22no—
77C2×C8×C31C2311yescharacteristic
78C2×C8×C31C2311yescharacteristic
79C4⋊C4×C31C2311yescharacteristic
80C4⋊C4×C31C2311yescharacteristic
81C22⋊C4×C31—21no—
82C22⋊C4×C31—21no—
83C42×C31C2311yescharacteristic
84C22⋊Dic31—21no—
85C22⋊Dic31—21no—
86C22⋊Dic31—21no—
87C22⋊Dic31—21no—
88#92480—22no—
89#92479—22no—
90(C2×D31)⋊C4—21no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4—21no—
93C4⋊Dic31—21no—
94C4⋊Dic31—21no—
95C4⋊Dic31C2311yescharacteristic
96C4⋊Dic31C2311yescharacteristic
97Dic31⋊C4—21no—
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100C4×Dic31—21no—
101C4×Dic31D411yescharacteristic
102C4×Dic31D411yescharacteristic
103C4×Dic31C2311yescharacteristic
104C2×C31⋊C8C2311yescharacteristic
105C2×C31⋊C8C2311yescharacteristic
106#92470—22no—
107#92469—22no—
108#92469—22no—
109C23×C31—21no—
110C23×C31—21no—
111C22×D31—21no—
112C22×D31C2×D411yescharacteristic
113D4×C31—21no—
114D4×C31—21no—
115D4×C31—21no—
116D4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—42no—
120C2×C4×C31—42no—
121C2×C4×C31C2×D411yescharacteristic
122C2×C4×C31C2×D411yescharacteristic
123C2×C4×C31C2411yescharacteristic
124C22⋊D31—42no—
125C22⋊D31—42no—
126C22⋊D31—42no—
127C22⋊D31—42no—
128C2×Dic31—21no—
129C2×Dic31—21no—
130C2×Dic31—21no—
131C2×Dic31C2×D411yescharacteristic
132C2×Dic31C2×D411yescharacteristic
133C2×Dic31C2×D411yescharacteristic
134D124—21no—
135D124—21no—
136D124—42no—
137C4×D31—22no—
138C4×D31—21no—
139C4×D31—21no—
140C4×D31—41no—
141C4×D31—42no—
142Dic62—21no—
143Dic62—21no—
144Dic62—42no—
145C8×C31—21no—
146C8×C31#4112yescomplemented
147C31⋊C8—21no—
148C31⋊C8#4112yescomplemented
149#3171—311nomaximal, Sylow
150C22×C31—41no—
151C22×C31—41no—
152C22×C31—41no—
153C22×C31—41no—
154C22×C31—41no—
155C22×C31—41no—
156C22×C31C22×D411yescharacteristic
157C2×D31—21no—
158C2×D31—21no—
159C2×D31—21no—
160C2×D31—41no—
161C2×D31—41no—
162C2×D31—41no—
163C4×C31—21no—
164C4×C31—41no—
165C4×C31—41no—
166C4×C31AGL(1,ℤ/8)12yes—
167C4×C31C2×#4111yescharacteristic
168C4×C31C2×#4111yescharacteristic
169Dic31—21no—
170Dic31—21no—
171Dic31—21no—
172Dic31—41no—
173Dic31—41no—
174Dic31—41no—
175#532—311no—
176#529—311no—
177#501—311no—
178#496—311no—
179#490—311no—
180#489—311no—
181#469—311no—
182#469—311no—
183#468—311no—
184#468—311no—
185C4×SD16—311no—
186C4×SD16—311no—
187C4×D8—311no—
188C4×D8D3111yescharacteristic, complemented
189C4×M16—311no—
190C2×C31—81no—
191C2×C31—81no—
192C2×C31#53211yescharacteristic
193C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
194C2×C31#57511yescharacteristic
195D31—41no—
196D31—81no—
197C2×#41—621no—
198C2×SD16—311no—
199C2×SD16—311no—
200C2×D8—311no—
201C2×D8C2×D3111yescharacteristic
202C2×M16—311no—
203C2×M16—311no—
204C4⋊Q8—311no—
205#127—311no—
206#126—621no—
207#125—311no—
208#124—311no—
209#124—621no—
210#123—621no—
211C22⋊Q8—311no—
212#121—311no—
213#121—311no—
214#121—311no—
215#121—621no—
216C4×Q8—311no—
217C4×D4—311no—
218C4×D4—621no—
219C4×D4—621no—
220C4×D4C2×D3111yescharacteristic
221C4×D4C2×D3111yescharacteristic
222#117—621no—
223C2×C42—311no—
224#107—311no—
225#107C2×D3111yescharacteristic
226#106—311no—
227#106—311no—
228#103—311no—
229#103—311no—
230#102—311no—
231#102—311no—
232#102—311no—
233#102—311no—
234#102C2×D3111yescharacteristic
235#102C2×D3111yescharacteristic
236#97—311no—
237#97—311no—
238C4×C8—311no—
239C4×C8C2×D3111yescharacteristic
240C31#317111yescharacteristic, complemented, Sylow
241#41—1244no—
242C2×Q8—311no—
243C2×Q8—621no—
244C2×D4—311no—
245C2×D4—621no—
246C2×D4—621no—
247C2×D4—621no—
248C2×D4—621no—
249C2×D4—621no—
250C2×D4C22×D3111yescharacteristic
251C2×D4C22×D3111yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—311no—
255C22×C4—311no—
256C22×C4—311no—
257C22×C4—621no—
258SD16—622no—
259SD16—622no—
260D8—22no—
261D8—622no—
262M16—622no—
263M16—622no—
264C2×C8—311no—
265C2×C8—311no—
266C2×C8C22×D3111yescharacteristic
267C2×C8C22×D3111yescharacteristic
268C4⋊C4—311no—
269C4⋊C4—311no—
270C4⋊C4—621no—
271C4⋊C4—621no—
272C4⋊C4—621no—
273C4⋊C4—621no—
274C4⋊C4—621no—
275C4⋊C4C22×D3111yescharacteristic
276C4⋊C4C22×D3111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C22⋊C4—621no—
284C22⋊C4—621no—
285C22⋊C4—621no—
286C42—311no—
287C42—311no—
288C42—311no—
289C42—621no—
290C42C22×D3111yescharacteristic
291C23—21no—
292C23—21no—
293C23—311no—
294C23—621no—
295Q8—621no—
296Q8—621no—
297Q8—1242no—
298D4—21no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—621no—
303D4—621no—
304D4—1242no—
305D4—1242no—
306D4—1242no—
307D4—1242no—
308D4—1242no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—311no—
314C2×C4—311no—
315C2×C4—311no—
316C2×C4—622no—
317C2×C4—621no—
318C2×C4—621no—
319C2×C4—621no—
320C2×C4—621no—
321C2×C4—621no—
322C2×C4—1241no—
323C2×C4—1242no—
324C2×C4D4×D3111yescharacteristic
325C2×C4D4×D3111yescharacteristic
326C2×C4C23×D3111yescharacteristic
327C8—21no—
328C8—312no—
329C8—621no—
330C8#9249512yescomplemented
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—621no—
338C22—621no—
339C22—621no—
340C22—1241no—
341C22—1241no—
342C22—1241no—
343C22C2×D4×D3111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—621no—
348C4—621no—
349C4—621no—
350C4—1241no—
351C4—1241no—
352C4—1241no—
353C4#1175848812yes—
354C4C2×#9249511yescharacteristic
355C4#41×D3111yescharacteristic
356C2—81no—
357C2—81no—
358C2—1241no—
359C2—2481no—
360C2#1452159611yescharacteristic
361C2C2×#1175848811yescharacteristic
362C2#1452184611yescharacteristic
subgroupG/H
centerC2×C4D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC4×D8×C31C2
socleC22×C31C22×D4
hypercenterC4×D8D31
hypocenterC31#3171
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #14521596C2semidirect
2. #14521581C2semidirect
3. #14521457C2semidirect
4. #14521437C2semidirect
5. #14521412C2semidirect
6. #14521407C2semidirect
7. #14521301C2semidirect
8. #14521299C2semidirect
9. #14521296C2semidirect
10. #14521294C2semidirect
11. C4×#92470C2semidirect
12. C4×#92480C2semidirect
13. C4×#92479C2semidirect
14. C4×#92469C2semidirect
15. C4×D8×C31C2semidirect
146. C8×C31#41semidirect
148. C31⋊C8#41semidirect
188. C4×D8D31semidirect
240. C31#3171semidirect
330. C8#92495semidirect

Maximal subgroups

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

subgroupindex
#145215962
#145215812
#145214572
#145214372
#145214122
#145214072
#145213012
#145212992
#145212962
#145212942
C4×#924702
C4×#924802
C4×#924792
C4×#924692
C4×D8×C312
#317131