Finite Group Databasebeta

← #16858421

Subgroups — #16858421

Order 3968.

396 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#14521755C211yesmaximal, characteristic, complemented
2#14521720C211yesmaximal, characteristic, complemented
3#14521415C211yesmaximal, characteristic, complemented
4#14521412C211yesmaximal, characteristic, complemented
5#14521394C211yesmaximal, characteristic, complemented
6#14521352C211yesmaximal, characteristic, complemented
7#14521338C211yesmaximal, characteristic, complemented
8#14521245C211yesmaximal, characteristic, complemented
9#14521243C211yesmaximal, characteristic, complemented
10#14521243C211yesmaximal, characteristic, complemented
11#14521178C211yesmaximal, characteristic, complemented
12#14521160C211yesmaximal, characteristic, complemented
13#14521159C211yesmaximal, characteristic, complemented
14#14521131C211yesmaximal, characteristic, complemented
15C31×#478C211yesmaximal, characteristic, complemented
16C2×#92495—21no—
17C31×#125C2211yescharacteristic
18C4×D4×C31C2211yescharacteristic
19#11758517C2211yescharacteristic
20#11758517C2211yescharacteristic
21C2×#92479C2211yescharacteristic
22#11758507—21no—
23C2×D248C2211yescharacteristic
24C2×D248C2211yescharacteristic
25#11758474—21no—
26#11758473—21no—
27#11758473—21no—
28#11758470C2211yescharacteristic
29#11758470C2211yescharacteristic
30#11758470C2211yescharacteristic
31#11758470C2211yescharacteristic
32C4⋊C4×D31—21no—
33#11758467C2211yescharacteristic
34#11758465C2211yescharacteristic
35#11758461—21no—
36#11758461—21no—
37#11758451C2211yescharacteristic
38C4×D124C2211yescharacteristic
39C4×Dic62C2211yescharacteristic
40C31×#107C2211yescharacteristic
41C31×#106C2211yescharacteristic
42C31×C4⋊C8C2211yescharacteristic
43C31×#102C2211yescharacteristic
44C31×#102C2211yescharacteristic
45#11758420C2211yescharacteristic
46#11758409C2211yescharacteristic
47#11758409C2211yescharacteristic
48#11758403C2211yescharacteristic
49Dic31⋊C8C2211yescharacteristic
50Dic31⋊C8C2211yescharacteristic
51C8×Dic31C2211yescharacteristic
52#11758397C2211yescharacteristic
53#11758397C2211yescharacteristic
54#11758397C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758397C2211yescharacteristic
57#11758396C2211yescharacteristic
58#11758391C2211yescharacteristic
59C2×D4×C31C2311yescharacteristic
60C22×C4×C31—21no—
61C2×C22⋊D31—21no—
62C2×C22⋊D31—21no—
63C2×C22⋊D31—21no—
64C2×C22⋊D31—21no—
65#92495—44no—
66C2×D124—21no—
67C2×D124—21no—
68C2×D124C2311yescharacteristic
69C2×D124C2311yescharacteristic
70C2×D124C2311yescharacteristic
71C2×C4×D31—21no—
72C2×C4×D31—21no—
73C2×C4×D31—21no—
74C2×C4×D31—21no—
75C2×C4×D31—21no—
76C2×Dic62—21no—
77C2×Dic62D411yescharacteristic
78C2×C8×C31C2311yescharacteristic
79C2×C8×C31C2311yescharacteristic
80C4⋊C4×C31—21no—
81C4⋊C4×C31—21no—
82C4⋊C4×C31C2311yescharacteristic
83C4⋊C4×C31C2311yescharacteristic
84C4⋊C4×C31C2311yescharacteristic
85C22⋊C4×C31—21no—
86C42×C31C2311yescharacteristic
87#92479—22no—
88(C2×D31)⋊C4—21no—
89(C2×D31)⋊C4—21no—
90(C2×D31)⋊C4—21no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4—21no—
93C4⋊Dic31—21no—
94C4⋊Dic31D411yescharacteristic
95C4⋊Dic31C2311yescharacteristic
96Dic31⋊C4—21no—
97Dic31⋊C4—21no—
98Dic31⋊C4D411yescharacteristic
99Dic31⋊C4D411yescharacteristic
100C4×Dic31C2311yescharacteristic
101C4×Dic31C2311yescharacteristic
102C2×C31⋊C8C2311yescharacteristic
103C2×C31⋊C8C2311yescharacteristic
104D248—22no—
105D248—22no—
106C23×C31—21no—
107C22×D31—21no—
108C22×D31—21no—
109C22×D31—21no—
110D4×C31—21no—
111D4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—21no—
115C2×C4×C31—42no—
116C2×C4×C31C2×D411yescharacteristic
117C2×C4×C31C2×D411yescharacteristic
118C2×C4×C31C2411yescharacteristic
119C22⋊D31—42no—
120C22⋊D31—42no—
121C22⋊D31—81no—
122C22⋊D31—81no—
123C2×Dic31—21no—
124C2×Dic31C2×D411yescharacteristic
125C2×Dic31C2×D411yescharacteristic
126C2×Dic31C2×D411yescharacteristic
127C2×Dic31C2×D411yescharacteristic
128D124—21no—
129D124—21no—
130D124—21no—
131D124—21no—
132D124—21no—
133D124—42no—
134D124—81no—
135D124#4112yescomplemented
136C4×D31—42no—
137C4×D31—42no—
138C4×D31—42no—
139C4×D31—81no—
140C4×D31—81no—
141Dic62—22no—
142Dic62—81no—
143C8×C31—21no—
144C8×C31—21no—
145C31⋊C8—21no—
146C31⋊C8—21no—
147#3366—311nomaximal, Sylow
148C22×C31—41no—
149C22×C31—41no—
150C22×C31—41no—
151C22×C31C22×D411yescharacteristic
152C2×D31—22no—
153C2×D31—41no—
154C2×D31—41no—
155C2×D31—41no—
156C2×D31—41no—
157C2×D31—41no—
158C2×D31—41no—
159C2×D31—41no—
160C2×D31—41no—
161C4×C31—21no—
162C4×C31—21no—
163C4×C31—41no—
164C4×C31—41no—
165C4×C31—41no—
166C4×C31C2×#4111yescharacteristic
167C4×C312−1+411yescharacteristic
168Dic31—21no—
169Dic31—21no—
170Dic31—21no—
171Dic31—41no—
172Dic31AGL(1,ℤ/8)12yes—
173#554—311no—
174#550—311no—
175#490—311no—
176#490—311no—
177#486—311no—
178#478—311no—
179#478D3111yescharacteristic, complemented
180#476—311no—
181#459—311no—
182#459—311no—
183#459—311no—
184#446—311no—
185#442—311no—
186#442—311no—
187C4×D8—311no—
188C2×C31—81no—
189C2×C31#54811yescharacteristic
190C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C31#57611yescharacteristic
192D31—42no—
193D31—81no—
194D31—81no—
195C2×#41—621no—
196C2×D8—311no—
197C2×D8—311no—
198C2×D8—311no—
199C4⋊Q8—311no—
200#127—311no—
201#127—311no—
202#127—311no—
203#125—311no—
204#125C2×D3111yescharacteristic
205C22⋊Q8—621no—
206C22⋊Q8—621no—
207C22⋊Q8—621no—
208#121—621no—
209#121—621no—
210#121—621no—
211C4×Q8—311no—
212C4×D4—311no—
213C4×D4—311no—
214C4×D4—311no—
215C4×D4—311no—
216C4×D4—311no—
217C4×D4C2×D3111yescharacteristic
218C2×C4⋊C4—621no—
219#107C2×D3111yescharacteristic
220#106—311no—
221#106C2×D3111yescharacteristic
222C4⋊C8—311no—
223C4⋊C8—311no—
224C4⋊C8C2×D3111yescharacteristic
225#102—311no—
226#102—311no—
227#102—311no—
228#102—311no—
229#102—311no—
230#102—311no—
231#102—311no—
232#102—311no—
233#102C2×D3111yescharacteristic
234#102C2×D3111yescharacteristic
235#97—311no—
236#97—311no—
237C4×C8—311no—
238C31#336611yescharacteristic, complemented, Sylow
239#41—1244no—
240C2×Q8—311no—
241C2×Q8—621no—
242C2×D4—311no—
243C2×D4—311no—
244C2×D4—311no—
245C2×D4—621no—
246C2×D4—621no—
247C2×D4—621no—
248C2×D4—621no—
249C2×D4—621no—
250C2×D4—621no—
251C2×D4C22×D3111yescharacteristic
252C22×C4—21no—
253C22×C4—621no—
254C22×C4—621no—
255C22×C4—621no—
256C22×C4—621no—
257C22×C4—621no—
258D8—622no—
259D8—622no—
260D8—622no—
261C2×C8—311no—
262C2×C8—311no—
263C2×C8C22×D3111yescharacteristic
264C2×C8C22×D3111yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—311no—
268C4⋊C4—311no—
269C4⋊C4—311no—
270C4⋊C4—311no—
271C4⋊C4—621no—
272C4⋊C4—621no—
273C4⋊C4—621no—
274C4⋊C4C22×D3111yescharacteristic
275C4⋊C4C22×D3111yescharacteristic
276C4⋊C4C22×D3111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—621no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C42—311no—
284C42—311no—
285C42C22×D3111yescharacteristic
286C23—21no—
287C23—621no—
288C23—621no—
289C23—621no—
290Q8—622no—
291Q8—2481no—
292D4—21no—
293D4—21no—
294D4—312no—
295D4—621no—
296D4—621no—
297D4—621no—
298D4—621no—
299D4—621no—
300D4—1242no—
301D4—1242no—
302D4—1242no—
303D4—2481no—
304D4—2481no—
305D4—2481no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—311no—
311C2×C4—311no—
312C2×C4—311no—
313C2×C4—311no—
314C2×C4—621no—
315C2×C4—1242no—
316C2×C4—1242no—
317C2×C4—1242no—
318C2×C4—2481no—
319C2×C4—2481no—
320C2×C4D4×D3111yescharacteristic
321C2×C4D4×D3111yescharacteristic
322C2×C4C23×D3111yescharacteristic
323C8—21no—
324C8—21no—
325C8—621no—
326C8—621no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—622no—
331C22—1241no—
332C22—1241no—
333C22—1241no—
334C22—1241no—
335C22—1241no—
336C22—1241no—
337C22—1241no—
338C22—1241no—
339C22C2×D4×D3111yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—312no—
346C4—621no—
347C4—621no—
348C4—621no—
349C4—1241no—
350C4#1175856411yescharacteristic
351C4#41×D3111yescharacteristic
352C2—81no—
353C2—1242no—
354C2—2481no—
355C2—2481no—
356C2#1452170911yescharacteristic
357C2AGL(1,ℤ/8)×D3111yescharacteristic
358C2#1452185111yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#478C2
socleC22×C31C22×D4
hypercenter#478D31
hypocenterC31#3366
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #14521755C2semidirect
2. #14521720C2semidirect
3. #14521415C2semidirect
4. #14521412C2semidirect
5. #14521394C2semidirect
6. #14521352C2semidirect
7. #14521338C2semidirect
8. #14521245C2semidirect
9. #14521243C2semidirect
10. #14521243C2semidirect
11. #14521178C2semidirect
12. #14521160C2semidirect
13. #14521159C2semidirect
14. #14521131C2semidirect
15. C31×#478C2semidirect
135. D124#41semidirect
179. #478D31semidirect
238. C31#3366semidirect

Maximal subgroups

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

subgroupindex
#145217552
#145217202
#145214152
#145214122
#145213942
#145213522
#145213382
#145212452
#145212432
#145211782
#145211602
#145211592
#145211312
C31×#4782
#336631