Finite Group Databasebeta

← #16856265

Subgroups — #16856265

Order 3968.

412 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521601C211yesmaximal, characteristic, complemented
2#14521594C211yesmaximal, characteristic
3#14521446C211yesmaximal, characteristic, complemented
4#14521420C211yesmaximal, characteristic, complemented
5#14521398C211yesmaximal, characteristic, complemented
6#14521394C211yesmaximal, characteristic, complemented
7#14521280C211yesmaximal, characteristic, complemented
8#14521278C211yesmaximal, characteristic, complemented
9#14521276C211yesmaximal, characteristic, complemented
10#14521140C211yesmaximal, characteristic, complemented
11SD16×Dic31C211yesmaximal, characteristic, complemented
12#14521136C211yesmaximal, characteristic, complemented
13#14521134C211yesmaximal, characteristic, complemented
14C2×C8×Dic31C211yesmaximal, characteristic, complemented
15C31×#465C211yesmaximal, characteristic, complemented
16C2×#92497—21no—
17C2×SD16×C31C2211yescharacteristic
18C22×C8×C31C2211yescharacteristic
19C31×C22⋊Q8C2211yescharacteristic
20C31×#121C2211yescharacteristic
21Q8×Dic31C2211yescharacteristic
22#11758521C2211yescharacteristic
23C2×#92481C2211yescharacteristic
24#11758517C2211yescharacteristic
25#11758516—21no—
26D4×Dic31C2211yescharacteristic
27C2×#92480C2211yescharacteristic
28#11758507C2211yescharacteristic
29#11758501C2211yescharacteristic
30C2×C4×Dic31C2211yescharacteristic
31C22×C31⋊C8C2211yescharacteristic
32C2×#92470C2211yescharacteristic
33#11758470C2211yescharacteristic
34#11758466—21no—
35#11758465C2211yescharacteristic
36#11758465C2211yescharacteristic
37#11758464—21no—
38#11758464C2211yescharacteristic
39#11758462—21no—
40(C22⋊D31)⋊C4—21no—
41#11758455—21no—
42#11758454—21no—
43C31×#106C2211yescharacteristic
44C31×#103C2211yescharacteristic
45C31×#102C2211yescharacteristic
46#11758423C2211yescharacteristic
47#11758420C2211yescharacteristic
48#11758409C2211yescharacteristic
49#11758405C2211yescharacteristic
50#11758404C2211yescharacteristic
51C8×Dic31C2211yescharacteristic
52C8×Dic31C2211yescharacteristic
53C8×Dic31C2211yescharacteristic
54C8×Dic31C2211yescharacteristic
55#11758398C2211yescharacteristic
56#11758397C2211yescharacteristic
57#11758396C2211yescharacteristic
58#11758396C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C2×D4×C31—21no—
61C2×D4×C31C2311yescharacteristic
62C22×C4×C31C2311yescharacteristic
63C2×C22⋊D31—21no—
64C2×C22⋊D31—21no—
65C2×C22⋊D31—21no—
66C22×Dic31—21no—
67C22×Dic31D411yescharacteristic
68C22×Dic31D411yescharacteristic
69#92497—44no—
70C2×D124C2311yescharacteristic
71C2×C4×D31—21no—
72C2×Dic62—21no—
73C2×Dic62—21no—
74C2×Dic62C2311yescharacteristic
75SD16×C31—22no—
76C2×C8×C31—22no—
77C2×C8×C31C2311yescharacteristic
78C2×C8×C31C2311yescharacteristic
79C4⋊C4×C31—21no—
80C4⋊C4×C31C2311yescharacteristic
81C4⋊C4×C31C2311yescharacteristic
82C22⋊C4×C31—21no—
83C22⋊C4×C31—21no—
84C22⋊Dic31—21no—
85C22⋊Dic31—21no—
86#92481—22no—
87#92480—22no—
88(C2×D31)⋊C4—21no—
89(C2×D31)⋊C4—21no—
90C4⋊Dic31—21no—
91C4⋊Dic31C2311yescharacteristic
92C4⋊Dic31C2311yescharacteristic
93Dic31⋊C4—21no—
94Dic31⋊C4—21no—
95Dic31⋊C4—21no—
96Dic31⋊C4—21no—
97Dic31⋊C4—21no—
98Dic31⋊C4—21no—
99C4×Dic31—21no—
100C4×Dic31—21no—
101C4×Dic31D411yescharacteristic
102C4×Dic31D411yescharacteristic
103C4×Dic31C2311yescharacteristic
104C4×Dic31C2311yescharacteristic
105C2×C31⋊C8—22no—
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108#92470—22no—
109C23×C31—21no—
110C23×C31C2×D411yescharacteristic
111C22×D31—21no—
112Q8×C31—21no—
113Q8×C31—21no—
114D4×C31—21no—
115D4×C31—21no—
116D4×C31—42no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31C2×D411yescharacteristic
123C2×C4×C31C2411yescharacteristic
124C22⋊D31—42no—
125C22⋊D31—42no—
126C22⋊D31—42no—
127C2×Dic31—22no—
128C2×Dic31—21no—
129C2×Dic31—21no—
130C2×Dic31—21no—
131C2×Dic31—42no—
132C2×Dic31SD1614yescomplemented
133C2×Dic31C2×D411yescharacteristic
134C2×Dic31C2×D411yescharacteristic
135C2×Dic31C2×D411yescharacteristic
136C2×Dic31C2×D411yescharacteristic
137D124—21no—
138D124—21no—
139C4×D31—42no—
140Dic62—21no—
141Dic62—21no—
142Dic62—42no—
143Dic62—42no—
144C8×C31—21no—
145C8×C31#4112yescomplemented
146C31⋊C8—21no—
147C31⋊C8#4112yescomplemented
148#3167—311nomaximal, Sylow
149C22×C31—21no—
150C22×C31—21no—
151C22×C31—41no—
152C22×C31—41no—
153C22×C31—41no—
154C22×C31C2×SD1612yes—
155C22×C31C22×D411yescharacteristic
156C2×D31—41no—
157C2×D31—41no—
158C2×D31—41no—
159C4×C31—21no—
160C4×C31—41no—
161C4×C31—41no—
162C4×C31—41no—
163C4×C31C2×#4111yescharacteristic
164C4×C31C2×#4111yescharacteristic
165Dic31—21no—
166Dic31—41no—
167Dic31—41no—
168Dic31—41no—
169Dic31C2×SD1612yes—
170Dic31C2×SD1612yes—
171Dic31#13512yes—
172#533—311no—
173#532—311no—
174#498—311no—
175#492—311no—
176#487—311no—
177#486—311no—
178#465—311no—
179#465—311no—
180#465—311no—
181#465D3111yescharacteristic, complemented
182C4×SD16—311no—
183C4×SD16—311no—
184C4×SD16—311no—
185C4×SD16—311no—
186C2×C4×C8—311no—
187C2×C31—22no—
188C2×C31—81no—
189C2×C31#53211yescharacteristic
190C2×C31C22×SD1611yescharacteristic
191C2×C31C2×#13511yescharacteristic
192D31—81no—
193C2×#41—621no—
194C2×SD16—311no—
195C2×SD16—311no—
196C2×SD16—311no—
197C2×SD16C2×D3111yescharacteristic
198C22×C8—311no—
199C22×C8C2×D3111yescharacteristic
200C4⋊Q8—311no—
201C4⋊Q8—311no—
202C4⋊Q8—311no—
203#127—311no—
204#125—621no—
205#124—621no—
206C22⋊Q8—311no—
207C22⋊Q8—621no—
208C22⋊Q8C2×D3111yescharacteristic
209#121—311no—
210#121—621no—
211#121C2×D3111yescharacteristic
212C4×Q8—311no—
213C4×Q8—311no—
214C4×Q8—621no—
215C4×D4—311no—
216C4×D4—311no—
217C4×D4—621no—
218#117—621no—
219C2×C42—311no—
220#106—311no—
221#106—311no—
222#106—311no—
223#106C2×D3111yescharacteristic
224#103—311no—
225#103—311no—
226#103—311no—
227#103C2×D3111yescharacteristic
228#102—311no—
229#102—311no—
230#102—311no—
231#102C2×D3111yescharacteristic
232C4×C8—311no—
233C4×C8—311no—
234C4×C8—311no—
235C4×C8—311no—
236C31#316711yescharacteristic, complemented, Sylow
237#41—1244no—
238C2×Q8—311no—
239C2×Q8—621no—
240C2×Q8—621no—
241C2×Q8C22×D3111yescharacteristic
242C2×D4—21no—
243C2×D4—311no—
244C2×D4—621no—
245C2×D4—621no—
246C2×D4—621no—
247C2×D4C22×D3111yescharacteristic
248C22×C4—311no—
249C22×C4—311no—
250C22×C4—621no—
251C22×C4—621no—
252C22×C4C22×D3111yescharacteristic
253SD16—22no—
254SD16—622no—
255SD16—622no—
256SD16—622no—
257C2×C8—22no—
258C2×C8—311no—
259C2×C8—311no—
260C2×C8—622no—
261C2×C8C22×D3111yescharacteristic
262C2×C8C22×D3111yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—311no—
265C4⋊C4—311no—
266C4⋊C4—621no—
267C4⋊C4—621no—
268C4⋊C4—621no—
269C4⋊C4—621no—
270C4⋊C4—621no—
271C4⋊C4—621no—
272C4⋊C4—621no—
273C4⋊C4C22×D3111yescharacteristic
274C4⋊C4C22×D3111yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—621no—
278C22⋊C4—621no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C42—311no—
282C42—311no—
283C42—311no—
284C42—311no—
285C42—621no—
286C42—621no—
287C23—21no—
288C23—621no—
289C23D4×D3111yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—621no—
293Q8—621no—
294Q8—1242no—
295Q8—1242no—
296D4—21no—
297D4—21no—
298D4—42no—
299D4—621no—
300D4—621no—
301D4—1242no—
302D4—1242no—
303D4—1242no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—314no—
310C2×C4—311no—
311C2×C4—311no—
312C2×C4—311no—
313C2×C4—311no—
314C2×C4—622no—
315C2×C4—621no—
316C2×C4—621no—
317C2×C4—621no—
318C2×C4—1242no—
319C2×C4—1242no—
320C2×C4D4×D3111yescharacteristic
321C2×C4C23×D3111yescharacteristic
322C8—21no—
323C8—312no—
324C8—621no—
325C8#9249712yescomplemented
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—1241no—
332C22—1241no—
333C22—1241no—
334C22SD16×D3112yes—
335C22C2×D4×D3111yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—312no—
341C4—312no—
342C4—312no—
343C4—621no—
344C4—1241no—
345C4—1241no—
346C4—1241no—
347C4C2×#9249711yescharacteristic
348C4#41×D3111yescharacteristic
349C2—22no—
350C2—81no—
351C2—2481no—
352C2#1452159411yescharacteristic
353C2C2×SD16×D3111yescharacteristic
354C2#135×D3111yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#465C2
socleC22×C31C22×D4
prime radical#14521594C2
hypercenter#465D31
hypocenterC31#3167
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #14521601C2semidirect
3. #14521446C2semidirect
4. #14521420C2semidirect
5. #14521398C2semidirect
6. #14521394C2semidirect
7. #14521280C2semidirect
8. #14521278C2semidirect
9. #14521276C2semidirect
10. #14521140C2semidirect
11. SD16×Dic31C2semidirect
12. #14521136C2semidirect
13. #14521134C2semidirect
14. C2×C8×Dic31C2semidirect
15. C31×#465C2semidirect
132. C2×Dic31SD16semidirect
145. C8×C31#41semidirect
147. C31⋊C8#41semidirect
181. #465D31semidirect
236. C31#3167semidirect
325. C8#92497semidirect

Maximal subgroups

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

subgroupindex
#145216012
#145215942
#145214462
#145214202
#145213982
#145213942
#145212802
#145212782
#145212762
#145211402
SD16×Dic312
#145211362
#145211342
C2×C8×Dic312
C31×#4652
#316731