Finite Group Databasebeta

← #16855831

Subgroups — #16855831

Order 3968.

424 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521596C211yesmaximal, characteristic
2C4×Q8×D31C211yesmaximal, characteristic, complemented
3#14521364C211yesmaximal, characteristic, complemented
4#14521361C211yesmaximal, characteristic, complemented
5#14521343C211yesmaximal, characteristic, complemented
6#14521342C211yesmaximal, characteristic, complemented
7#14521248C211yesmaximal, characteristic, complemented
8#14521247C211yesmaximal, characteristic, complemented
9#14521189C211yesmaximal, characteristic, complemented
10#14521186C211yesmaximal, characteristic, complemented
11#14521151C211yesmaximal, characteristic, complemented
12#14521149C211yesmaximal, characteristic, complemented
13#14521147C211yesmaximal, characteristic, complemented
14#14521104C211yesmaximal, characteristic, complemented
15C31×#440C211yesmaximal, characteristic, complemented
16C2×Q8×D31C2211yescharacteristic
17C2×#92495—21no—
18C2×SD16×C31C2211yescharacteristic
19C4×Q8×C31C2211yescharacteristic
20C4×D4×C31C2211yescharacteristic
21Q8×Dic31C2211yescharacteristic
22C2×#92481C2211yescharacteristic
23#11758517C2211yescharacteristic
24#11758515C2211yescharacteristic
25C2×#92480C2211yescharacteristic
26C4×C22⋊D31—21no—
27C2×#92470C2211yescharacteristic
28#11758472C2211yescharacteristic
29C4⋊C4×D31—21no—
30C4⋊C4×D31C2211yescharacteristic
31#11758465C2211yescharacteristic
32#11758464—21no—
33#11758464C2211yescharacteristic
34#11758462—21no—
35#11758461—21no—
36C4×D124C2211yescharacteristic
37C42×D31—21no—
38C42×D31C2211yescharacteristic
39C4×Dic62—21no—
40C4×Dic62C2211yescharacteristic
41C31×#107C2211yescharacteristic
42C31×#103C2211yescharacteristic
43C31×#102C2211yescharacteristic
44C31×#97C2211yescharacteristic
45#11758423C2211yescharacteristic
46#11758420C2211yescharacteristic
47#11758409C2211yescharacteristic
48(C2×D31)⋊C8C2211yescharacteristic
49(C2×D31)⋊C8C2211yescharacteristic
50#11758406C2211yescharacteristic
51#11758404C2211yescharacteristic
52Dic31⋊C8C2211yescharacteristic
53Dic31⋊C8C2211yescharacteristic
54#11758398C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758395C2211yescharacteristic
57#11758395C2211yescharacteristic
58#11758391C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C2×D4×C31C2311yescharacteristic
61C22×C4×C31—21no—
62C2×C22⋊D31—21no—
63C2×C22⋊D31—21no—
64C2×C22⋊D31—21no—
65Q8×D31—22no—
66Q8×D31—22no—
67#92495—44no—
68C2×D124—21no—
69C2×D124C2311yescharacteristic
70C2×C4×D31—21no—
71C2×C4×D31—21no—
72C2×C4×D31—21no—
73C2×C4×D31D411yescharacteristic
74C2×C4×D31D411yescharacteristic
75C2×C4×D31C2311yescharacteristic
76C2×Dic62—21no—
77C2×Dic62—21no—
78C2×Dic62C2311yescharacteristic
79SD16×C31—22no—
80C2×C8×C31C2311yescharacteristic
81C2×C8×C31C2311yescharacteristic
82C4⋊C4×C31—21no—
83C4⋊C4×C31C2311yescharacteristic
84C4⋊C4×C31C2311yescharacteristic
85C22⋊C4×C31—21no—
86C42×C31—21no—
87C42×C31C2311yescharacteristic
88C22⋊Dic31—21no—
89#92481—22no—
90#92480—22no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4—21no—
93C4⋊Dic31—21no—
94C4⋊Dic31C2311yescharacteristic
95C4⋊Dic31C2311yescharacteristic
96Dic31⋊C4—21no—
97Dic31⋊C4—21no—
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100C4×Dic31—21no—
101C4×Dic31—21no—
102C4×Dic31—21no—
103C4×Dic31D411yescharacteristic
104C4×Dic31D411yescharacteristic
105C4×Dic31C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108#92470—22no—
109C23×C31—21no—
110C22×D31—21no—
111C22×D31C2×D411yescharacteristic
112Q8×C31—21no—
113Q8×C31#4112yescomplemented
114D4×C31—21no—
115D4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—42no—
120C2×C4×C31C2×D411yescharacteristic
121C2×C4×C31C2×D411yescharacteristic
122C2×C4×C31C2411yescharacteristic
123C22⋊D31—42no—
124C22⋊D31—42no—
125C22⋊D31—42no—
126C2×Dic31—21no—
127C2×Dic31—21no—
128C2×Dic31—21no—
129C2×Dic31C2×D411yescharacteristic
130C2×Dic31C2×D411yescharacteristic
131C2×Dic31C2×D411yescharacteristic
132D124—21no—
133D124—21no—
134D124—42no—
135C4×D31—24no—
136C4×D31—22no—
137C4×D31—21no—
138C4×D31—21no—
139C4×D31—22no—
140C4×D31—42no—
141C4×D31—42no—
142Dic62—24no—
143Dic62—21no—
144Dic62—42no—
145Dic62#4112yescomplemented
146C8×C31—21no—
147C8×C31—21no—
148C31⋊C8—21no—
149C31⋊C8—21no—
150#3112—311nomaximal, Sylow
151C22×C31—41no—
152C22×C31—41no—
153C22×C31—41no—
154C22×C31C22×D411yescharacteristic
155C2×D31—21no—
156C2×D31—21no—
157C2×D31—41no—
158C2×D31—41no—
159C2×D31—41no—
160C2×D31AGL(1,ℤ/8)12yes—
161C4×C31—22no—
162C4×C31—21no—
163C4×C31—21no—
164C4×C31—41no—
165C4×C31—41no—
166C4×C31C2×#4111yescharacteristic
167C4×C31C2×#4111yescharacteristic
168Dic31—21no—
169Dic31—22no—
170Dic31—21no—
171Dic31—41no—
172Dic31—41no—
173Dic31#13712yes—
174#532—311no—
175C2×C4×Q8—311no—
176#480—311no—
177#480—311no—
178#477—311no—
179#477—311no—
180#460—311no—
181#460—311no—
182#448—311no—
183#448—311no—
184#440—311no—
185#440—311no—
186#440—311no—
187#440D3111yescharacteristic, complemented
188#432—311no—
189C2×C31—81no—
190C2×C31#52511yescharacteristic
191C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C31C2×#13711yescharacteristic
193D31—22no—
194D31—81no—
195C2×#41—621no—
196C22×Q8—311no—
197C2×SD16—311no—
198C2×SD16—311no—
199C2×SD16—311no—
200C2×SD16C2×D3111yescharacteristic
201C4⋊Q8—311no—
202#127—311no—
203#124—621no—
204#121—311no—
205#121—311no—
206#121—621no—
207C4×Q8—311no—
208C4×Q8—311no—
209C4×Q8—311no—
210C4×Q8—621no—
211C4×Q8—621no—
212C4×Q8C2×D3111yescharacteristic
213C4×D4—311no—
214C4×D4—621no—
215C4×D4C2×D3111yescharacteristic
216C2×C4⋊C4—311no—
217C2×C4⋊C4—621no—
218C2×C42—311no—
219C2×C42—621no—
220#107—311no—
221#107—311no—
222#107—311no—
223#107C2×D3111yescharacteristic
224C4⋊C8—311no—
225C4⋊C8—311no—
226#103—311no—
227#103—311no—
228#103—311no—
229#103C2×D3111yescharacteristic
230#102—311no—
231#102—311no—
232#102—311no—
233#102C2×D3111yescharacteristic
234C22⋊C8—311no—
235C22⋊C8—311no—
236#97—311no—
237#97C2×D3111yescharacteristic
238C31#311211yescharacteristic, complemented, Sylow
239#41—1244no—
240C2×Q8—311no—
241C2×Q8—621no—
242C2×Q8—621no—
243C2×Q8—622no—
244C2×Q8—622no—
245C2×Q8C22×D3111yescharacteristic
246C2×D4—311no—
247C2×D4—621no—
248C2×D4—621no—
249C2×D4—621no—
250C2×D4—621no—
251C2×D4C22×D3111yescharacteristic
252C22×C4—21no—
253C22×C4—311no—
254C22×C4—311no—
255C22×C4—311no—
256C22×C4—621no—
257C22×C4—621no—
258C22×C4—621no—
259SD16—22no—
260SD16—622no—
261SD16—622no—
262SD16—622no—
263C2×C8—311no—
264C2×C8—311no—
265C2×C8C22×D3111yescharacteristic
266C2×C8C22×D3111yescharacteristic
267C4⋊C4—21no—
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—621no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C42—21no—
282C42—311no—
283C42—311no—
284C42—311no—
285C42—621no—
286C42—621no—
287C42—621no—
288C42C22×D3111yescharacteristic
289C23—21no—
290C23—311no—
291C23—621no—
292Q8—21no—
293Q8—312no—
294Q8—624no—
295Q8—621no—
296Q8—1242no—
297Q8#9249512yescomplemented
298D4—21no—
299D4—21no—
300D4—621no—
301D4—621no—
302D4—1242no—
303D4—1242no—
304D4—1242no—
305D4—1242no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—311no—
311C2×C4—311no—
312C2×C4—311no—
313C2×C4—622no—
314C2×C4—622no—
315C2×C4—624no—
316C2×C4—621no—
317C2×C4—621no—
318C2×C4—621no—
319C2×C4—621no—
320C2×C4—621no—
321C2×C4—1242no—
322C2×C4—1242no—
323C2×C4D4×D3111yescharacteristic
324C2×C4D4×D3111yescharacteristic
325C2×C4C23×D3111yescharacteristic
326C8—21no—
327C8—21no—
328C8—621no—
329C8—621no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—312no—
334C22—621no—
335C22—621no—
336C22—1241no—
337C22—1241no—
338C22—1241no—
339C22C2×D4×D3111yescharacteristic
340C4—22no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—312no—
346C4—621no—
347C4—622no—
348C4—621no—
349C4—1241no—
350C4—1241no—
351C4C2×#9249511yescharacteristic
352C4#41×D3111yescharacteristic
353C2—81no—
354C2—622no—
355C2—2481no—
356C2#1452155811yescharacteristic
357C2AGL(1,ℤ/8)×D3111yescharacteristic
358C2#137×D3111yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#440C2
socleC22×C31C22×D4
prime radical#14521596C2
hypercenter#440D31
hypocenterC31#3112
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D31C2semidirect
3. #14521364C2semidirect
4. #14521361C2semidirect
5. #14521343C2semidirect
6. #14521342C2semidirect
7. #14521248C2semidirect
8. #14521247C2semidirect
9. #14521189C2semidirect
10. #14521186C2semidirect
11. #14521151C2semidirect
12. #14521149C2semidirect
13. #14521147C2semidirect
14. #14521104C2semidirect
15. C31×#440C2semidirect
113. Q8×C31#41semidirect
145. Dic62#41semidirect
187. #440D31semidirect
238. C31#3112semidirect
297. Q8#92495semidirect

Maximal subgroups

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

subgroupindex
#145215962
C4×Q8×D312
#145213642
#145213612
#145213432
#145213422
#145212482
#145212472
#145211892
#145211862
#145211512
#145211492
#145211472
#145211042
C31×#4402
#311231