Finite Group Databasebeta

← #16858301

Subgroups — #16858301

Order 3968.

386 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521763C211yesmaximal, characteristic, complemented
2#14521699C211yesmaximal, characteristic, complemented
3#14521446C211yesmaximal, characteristic, complemented
4#14521371C211yesmaximal, characteristic, complemented
5#14521370C211yesmaximal, characteristic, complemented
6#14521366C211yesmaximal, characteristic, complemented
7#14521365C211yesmaximal, characteristic, complemented
8#14521337C211yesmaximal, characteristic, complemented
9#14521327C211yesmaximal, characteristic, complemented
10#14521299C211yesmaximal, characteristic, complemented
11D8×Dic31C211yesmaximal, characteristic, complemented
12#14521125C211yesmaximal, characteristic, complemented
13#14521091C211yesmaximal, characteristic, complemented
14#14521088C211yesmaximal, characteristic, complemented
15C31×#469C211yesmaximal, characteristic, complemented
16C2×#92497—21no—
17C2×D8×C31C2211yescharacteristic
18C2×M16×C31C2211yescharacteristic
19C31×#121C2211yescharacteristic
20C31×#121C2211yescharacteristic
21#11758516—21no—
22#11758515C2211yescharacteristic
23#11758515C2211yescharacteristic
24#11758513—21no—
25#11758512—21no—
26D4×Dic31C2211yescharacteristic
27D4×Dic31C2211yescharacteristic
28C4×C22⋊D31C2211yescharacteristic
29#11758503C2211yescharacteristic
30C2×C4⋊Dic31C2211yescharacteristic
31C2×#92469C2211yescharacteristic
32#11758469C2211yescharacteristic
33C4⋊C4×D31C2211yescharacteristic
34#11758465C2211yescharacteristic
35#11758465C2211yescharacteristic
36#11758462—21no—
37#11758460—21no—
38#11758455—21no—
39#11758454—21no—
40C31×#106C2211yescharacteristic
41C31×#102C2211yescharacteristic
42C31×#102C2211yescharacteristic
43#11758420C2211yescharacteristic
44#11758420C2211yescharacteristic
45#11758420C2211yescharacteristic
46#11758420C2211yescharacteristic
47C22⋊(C31⋊C8)C2211yescharacteristic
48(C2×D31)⋊C8C2211yescharacteristic
49#11758406C2211yescharacteristic
50#11758406C2211yescharacteristic
51#11758405C2211yescharacteristic
52#11758405C2211yescharacteristic
53Dic31⋊C8C2211yescharacteristic
54C8×Dic31C2211yescharacteristic
55#11758396C2211yescharacteristic
56#11758396C2211yescharacteristic
57#11758396C2211yescharacteristic
58#11758395C2211yescharacteristic
59C2×D4×C31—21no—
60C2×D4×C31—21no—
61C2×D4×C31C2311yescharacteristic
62C2×D4×C31C2311yescharacteristic
63C22×C4×C31C2311yescharacteristic
64C2×C22⋊D31—21no—
65C2×C22⋊D31—21no—
66C2×C22⋊D31D411yescharacteristic
67C22×Dic31—21no—
68C22×Dic31—21no—
69C22×Dic31—21no—
70#92497—44no—
71C2×C4×D31—21no—
72C2×C4×D31C2311yescharacteristic
73C2×Dic62—21no—
74C2×Dic62—21no—
75D8×C31—22no—
76M16×C31—22no—
77C2×C8×C31C2311yescharacteristic
78C2×C8×C31C2311yescharacteristic
79C4⋊C4×C31C2311yescharacteristic
80C4⋊C4×C31C2311yescharacteristic
81C22⋊C4×C31—21no—
82C22⋊C4×C31—21no—
83C22⋊Dic31—21no—
84C22⋊Dic31—21no—
85C22⋊Dic31—21no—
86C22⋊Dic31—21no—
87C22⋊Dic31—21no—
88C22⋊Dic31D411yescharacteristic
89(C2×D31)⋊C4—21no—
90(C2×D31)⋊C4D411yescharacteristic
91C4⋊Dic31—21no—
92C4⋊Dic31C2311yescharacteristic
93C4⋊Dic31C2311yescharacteristic
94C4⋊Dic31C2311yescharacteristic
95C4⋊Dic31C2311yescharacteristic
96Dic31⋊C4—21no—
97Dic31⋊C4—21no—
98Dic31⋊C4—21no—
99Dic31⋊C4D411yescharacteristic
100C4×Dic31—21no—
101C4×Dic31—21no—
102C4×Dic31C2311yescharacteristic
103C2×C31⋊C8C2311yescharacteristic
104C2×C31⋊C8C2311yescharacteristic
105#92469—22no—
106C23×C31—21no—
107C23×C31—21no—
108C23×C31C2×D411yescharacteristic
109C22×D31C2×D411yescharacteristic
110D4×C31—21no—
111D4×C31—21no—
112D4×C31—21no—
113D4×C31—21no—
114D4×C31—42no—
115D4×C31—81no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31C2×D411yescharacteristic
121C2×C4×C31C2411yescharacteristic
122C22⋊D31—22no—
123C22⋊D31—42no—
124C22⋊D31—81no—
125C2×Dic31—21no—
126C2×Dic31—21no—
127C2×Dic31—21no—
128C2×Dic31—21no—
129C2×Dic31—42no—
130C2×Dic31—42no—
131C2×Dic31—42no—
132C2×Dic31C2×D411yescharacteristic
133C2×Dic31C2×D411yescharacteristic
134C2×Dic31C2×D411yescharacteristic
135C4×D31—21no—
136C4×D31—21no—
137C4×D31—42no—
138Dic62—42no—
139Dic62—81no—
140C8×C31—21no—
141C8×C31#4112yescomplemented
142C31⋊C8—21no—
143C31⋊C8—21no—
144#3354—311nomaximal, Sylow
145C22×C31—21no—
146C22×C31—21no—
147C22×C31—21no—
148C22×C31—41no—
149C22×C31—41no—
150C22×C31—41no—
151C22×C31—41no—
152C22×C31—41no—
153C22×C31—41no—
154C22×C31C22×D411yescharacteristic
155C2×D31—21no—
156C2×D31—21no—
157C2×D31—21no—
158C4×C31—21no—
159C4×C31—41no—
160C4×C31—41no—
161C4×C31C2×#4111yescharacteristic
162C4×C312−1+411yescharacteristic
163Dic31—21no—
164Dic31—21no—
165Dic31—41no—
166Dic31—41no—
167Dic31—41no—
168Dic31—41no—
169Dic31AGL(1,ℤ/8)12yes—
170#555—311no—
171#547—311no—
172#498—311no—
173#482—311no—
174#482—311no—
175#481—311no—
176#481—311no—
177#476—311no—
178#474—311no—
179#469—311no—
180#469D3111yescharacteristic, complemented
181C4×D8—311no—
182#436—311no—
183#428—311no—
184#428—311no—
185C2×C31—41no—
186C2×C31—81no—
187C2×C31—81no—
188C2×C31#54711yescharacteristic
189C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C31#57711yescharacteristic
191D31—41no—
192C2×#41—621no—
193C2×D8C2×D3111yescharacteristic
194C2×M16—311no—
195C2×M16C2×D3111yescharacteristic
196C4⋊Q8—311no—
197C4⋊Q8—311no—
198#124—621no—
199#124—621no—
200#123—621no—
201#123—621no—
202C22⋊Q8—621no—
203#121—311no—
204#121—311no—
205#121—621no—
206#121C2×D3111yescharacteristic
207#121C2×D3111yescharacteristic
208C4×D4—311no—
209C4×D4—311no—
210C4×D4—311no—
211#117—311no—
212#117—311no—
213#117—621no—
214C2×C4⋊C4—311no—
215C2×C4⋊C4—311no—
216#107—311no—
217#107—311no—
218#107—311no—
219#106—311no—
220#106—311no—
221#106—311no—
222#106—311no—
223#106—311no—
224#106C2×D3111yescharacteristic
225C4⋊C8—311no—
226#102—311no—
227#102—311no—
228#102—311no—
229#102—311no—
230#102C2×D3111yescharacteristic
231#102C2×D3111yescharacteristic
232C22⋊C8—311no—
233C22⋊C8—311no—
234C4×C8—311no—
235C31#335411yescharacteristic, complemented, Sylow
236#41—1244no—
237C2×Q8—621no—
238C2×Q8—621no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—311no—
242C2×D4—621no—
243C2×D4—621no—
244C2×D4C22×D3111yescharacteristic
245C2×D4C22×D3111yescharacteristic
246C22×C4—311no—
247C22×C4—621no—
248C22×C4—621no—
249C22×C4—621no—
250C22×C4—621no—
251C22×C4C22×D3111yescharacteristic
252D8—22no—
253M16—22no—
254M16—622no—
255C2×C8—311no—
256C2×C8—311no—
257C2×C8C22×D3111yescharacteristic
258C2×C8C22×D3111yescharacteristic
259C4⋊C4—311no—
260C4⋊C4—311no—
261C4⋊C4—311no—
262C4⋊C4—311no—
263C4⋊C4—311no—
264C4⋊C4—621no—
265C4⋊C4—621no—
266C4⋊C4—621no—
267C4⋊C4—621no—
268C4⋊C4C22×D3111yescharacteristic
269C4⋊C4C22×D3111yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—311no—
273C22⋊C4—311no—
274C22⋊C4—621no—
275C22⋊C4—621no—
276C22⋊C4—621no—
277C22⋊C4—621no—
278C22⋊C4—621no—
279C22⋊C4—621no—
280C42—311no—
281C42—621no—
282C42—621no—
283C23—21no—
284C23—21no—
285C23—311no—
286C23D4×D3111yescharacteristic
287Q8—1242no—
288Q8—2481no—
289D4—21no—
290D4—21no—
291D4—21no—
292D4—21no—
293D4—42no—
294D4—81no—
295D4—622no—
296D4—1242no—
297D4—2481no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—311no—
303C2×C4—311no—
304C2×C4—311no—
305C2×C4—621no—
306C2×C4—621no—
307C2×C4—621no—
308C2×C4—621no—
309C2×C4—621no—
310C2×C4—621no—
311C2×C4—1242no—
312C2×C4—1242no—
313C2×C4—1242no—
314C2×C4—1242no—
315C2×C4D4×D3111yescharacteristic
316C2×C4C23×D3111yescharacteristic
317C8—21no—
318C8—621no—
319C8—621no—
320C8#9249712yescomplemented
321C22—21no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—621no—
331C22—621no—
332C22—621no—
333C22C2×D4×D3111yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—312no—
338C4—621no—
339C4—621no—
340C4—1241no—
341C4—1241no—
342C4—1241no—
343C4—1241no—
344C4C2×#9249711yescharacteristic
345C4#1175856711yescharacteristic
346C2—41no—
347C2—81no—
348C2—81no—
349C2—1241no—
350C2#1452169911yescharacteristic
351C2AGL(1,ℤ/8)×D3111yescharacteristic
352C2#1452185911yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#469C2
socleC22×C31C22×D4
hypercenter#469D31
hypocenterC31#3354
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #14521763C2semidirect
2. #14521699C2semidirect
3. #14521446C2semidirect
4. #14521371C2semidirect
5. #14521370C2semidirect
6. #14521366C2semidirect
7. #14521365C2semidirect
8. #14521337C2semidirect
9. #14521327C2semidirect
10. #14521299C2semidirect
11. D8×Dic31C2semidirect
12. #14521125C2semidirect
13. #14521091C2semidirect
14. #14521088C2semidirect
15. C31×#469C2semidirect
141. C8×C31#41semidirect
180. #469D31semidirect
235. C31#3354semidirect
320. C8#92497semidirect

Maximal subgroups

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

subgroupindex
#145217632
#145216992
#145214462
#145213712
#145213702
#145213662
#145213652
#145213372
#145213272
#145212992
D8×Dic312
#145211252
#145210912
#145210882
C31×#4692
#335431