Finite Group Databasebeta

← #16857686

Subgroups — #16857686

Order 3968.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521752C211yesmaximal, characteristic, complemented
2#14521702C211yesmaximal, characteristic, complemented
3#14521388C211yesmaximal, characteristic, complemented
4#14521378C211yesmaximal, characteristic, complemented
5#14521346C211yesmaximal, characteristic, complemented
6#14521298C211yesmaximal, characteristic, complemented
7#14521281C211yesmaximal, characteristic, complemented
8#14521251C211yesmaximal, characteristic, complemented
9#14521197C211yesmaximal, characteristic, complemented
10#14521197C211yesmaximal, characteristic, complemented
11#14521162C211yesmaximal, characteristic, complemented
12#14521122C211yesmaximal, characteristic, complemented
13#14521049C211yesmaximal, characteristic, complemented
14#14521044C211yesmaximal, characteristic, complemented
15C31×#491C211yesmaximal, characteristic, complemented
16C2×#92499C2211yescharacteristic
17C2×#92499C2211yescharacteristic
18C31×C4⋊Q8C2211yescharacteristic
19C31×#125C2211yescharacteristic
20#11758523C2211yescharacteristic
21#11758523C2211yescharacteristic
22C2×#92481C2211yescharacteristic
23C2×#92481C2211yescharacteristic
24C2×D248C2211yescharacteristic
25C2×#92469C2211yescharacteristic
26C2×C8×D31C2211yescharacteristic
27#11758475—21no—
28#11758472—21no—
29#11758472—21no—
30#11758472C2211yescharacteristic
31#11758472C2211yescharacteristic
32#11758471—21no—
33#11758471—21no—
34#11758471—21no—
35#11758470—21no—
36#11758469C2211yescharacteristic
37C4⋊C4×D31—21no—
38C4⋊C4×D31C2211yescharacteristic
39C4×D124C2211yescharacteristic
40C4×D124C2211yescharacteristic
41C4×D124C2211yescharacteristic
42C31×#103C2211yescharacteristic
43C31×#103C2211yescharacteristic
44C31×#103C2211yescharacteristic
45C31×#103C2211yescharacteristic
46C31×#97C2211yescharacteristic
47#11758423C2211yescharacteristic
48#11758423C2211yescharacteristic
49#11758409C2211yescharacteristic
50#11758409C2211yescharacteristic
51(C2×D31)⋊C8C2211yescharacteristic
52(C2×D31)⋊C8C2211yescharacteristic
53#11758405C2211yescharacteristic
54#11758397C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758396C2211yescharacteristic
57#11758395C2211yescharacteristic
58C4⋊(C31⋊C8)C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C2×Q8×C31C2311yescharacteristic
61#92499—22no—
62#92499—22no—
63#92499—41no—
64#92499—41no—
65C2×D124—21no—
66C2×D124—21no—
67C2×D124—21no—
68C2×D124—21no—
69C2×D124D411yescharacteristic
70C2×D124C2311yescharacteristic
71C2×D124C2311yescharacteristic
72C2×C4×D31—21no—
73C2×C4×D31—21no—
74C2×C4×D31—21no—
75C2×C4×D31—21no—
76C2×C4×D31—21no—
77C2×C4×D31C2311yescharacteristic
78C2×C4×D31C2311yescharacteristic
79C2×C8×C31C2311yescharacteristic
80C2×C8×C31C2311yescharacteristic
81C4⋊C4×C31—21no—
82C4⋊C4×C31—21no—
83C4⋊C4×C31—21no—
84C4⋊C4×C31—21no—
85C4⋊C4×C31C2311yescharacteristic
86C4⋊C4×C31C2311yescharacteristic
87C42×C31C2311yescharacteristic
88#92481—41no—
89#92481—41no—
90(C2×D31)⋊C4—21no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4—21no—
93(C2×D31)⋊C4—21no—
94(C2×D31)⋊C4—21no—
95(C2×D31)⋊C4—21no—
96(C2×D31)⋊C4—21no—
97(C2×D31)⋊C4D411yescharacteristic
98(C2×D31)⋊C4D411yescharacteristic
99C4⋊Dic31D411yescharacteristic
100C4⋊Dic31C2311yescharacteristic
101C4⋊Dic31C2311yescharacteristic
102Dic31⋊C4—21no—
103Dic31⋊C4—21no—
104Dic31⋊C4—21no—
105C4×Dic31—21no—
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108D248—22no—
109#92469—41no—
110C8×D31—41no—
111C22×D31—21no—
112C22×D31—21no—
113C22×D31C2×D411yescharacteristic
114C22×D31C2×D411yescharacteristic
115Q8×C31—21no—
116Q8×C31—21no—
117Q8×C31—21no—
118Q8×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31C2×D411yescharacteristic
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31C2411yescharacteristic
126C2×Dic31—21no—
127C2×Dic31—21no—
128C2×Dic31C2×D411yescharacteristic
129C2×Dic31C2×D411yescharacteristic
130D124—21no—
131D124—21no—
132D124—21no—
133D124—41no—
134D124—42no—
135D124—42no—
136D124—42no—
137D124—81no—
138D124#4112yes—
139C4×D31—21no—
140C4×D31—21no—
141C4×D31—21no—
142C4×D31—21no—
143C4×D31—42no—
144C4×D31—42no—
145C4×D31—42no—
146C4×D31—81no—
147C4×D31—81no—
148C8×C31—21no—
149C8×C31—21no—
150C31⋊C8—21no—
151C31⋊C8—21no—
152#3307—311nomaximal, Sylow
153C22×C31C22×D411yescharacteristic
154C2×D31—21no—
155C2×D31—21no—
156C2×D31—22no—
157C2×D31—21no—
158C2×D31—21no—
159C2×D31—21no—
160C2×D31—21no—
161C2×D31—41no—
162C2×D31—41no—
163C2×D31—41no—
164C2×D31—41no—
165C2×D31—41no—
166C4×C31—21no—
167C4×C31—21no—
168C4×C31—41no—
169C4×C31—41no—
170C4×C31—41no—
171C4×C31—41no—
172C4×C31C2×#4111yescharacteristic
173C4×C31H(5,𝔽2)11yescharacteristic
174Dic31—21no—
175Dic31—21no—
176Dic31—41no—
177Dic31—41no—
178#553—311no—
179#547—311no—
180#491D3111yescharacteristic, complemented
181#485—311no—
182#483—311no—
183#478—311no—
184#468—311no—
185#465—311no—
186#461—311no—
187#449—311no—
188#449—311no—
189#442—311no—
190#435—311no—
191#417—311no—
192#416—311no—
193C2×C31#54611yescharacteristic
194C2×C31#57511yescharacteristic
195C2×C31#57711yescharacteristic
196D31—41no—
197D31—41no—
198D31—42no—
199D31—81no—
200C2×#41—311no—
201C2×#41—311no—
202C2×SD16—311no—
203C2×SD16—311no—
204C2×D8—311no—
205C2×M16—311no—
206C22×C8—311no—
207C4⋊Q8C2×D3111yescharacteristic
208#126—621no—
209#125C2×D3111yescharacteristic
210#123—621no—
211#123—621no—
212#123—621no—
213C22⋊Q8—311no—
214C22⋊Q8—311no—
215#121—311no—
216#121—311no—
217#121—621no—
218#121—621no—
219C4×D4—311no—
220C4×D4—311no—
221C4×D4—311no—
222C4×D4—621no—
223#117—311no—
224C2×C4⋊C4—311no—
225C2×C4⋊C4—621no—
226#107—311no—
227#106—311no—
228#106—311no—
229C4⋊C8—311no—
230#103—311no—
231#103—311no—
232#103C2×D3111yescharacteristic
233#103C2×D3111yescharacteristic
234#103C2×D3111yescharacteristic
235#103C2×D3111yescharacteristic
236#102—311no—
237#102—311no—
238#102—311no—
239#102—311no—
240C22⋊C8—311no—
241C22⋊C8—311no—
242#97C2×D3111yescharacteristic
243C31#330711yescharacteristic, complemented, Sylow
244#41—622no—
245#41—622no—
246#41—1241no—
247#41—1241no—
248C2×Q8C22×D3111yescharacteristic
249C2×Q8C22×D3111yescharacteristic
250C2×D4—311no—
251C2×D4—311no—
252C2×D4—311no—
253C2×D4—621no—
254C2×D4—621no—
255C2×D4—621no—
256C2×D4—621no—
257C22×C4—311no—
258C22×C4—311no—
259C22×C4—621no—
260C22×C4—621no—
261C22×C4—621no—
262C22×C4—621no—
263C22×C4—621no—
264SD16—1241no—
265SD16—1241no—
266D8—622no—
267M16—1241no—
268C2×C8—311no—
269C2×C8—311no—
270C2×C8—1241no—
271C2×C8C22×D3111yescharacteristic
272C2×C8C22×D3111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—311no—
278C4⋊C4—311no—
279C4⋊C4—311no—
280C4⋊C4—621no—
281C4⋊C4—621no—
282C4⋊C4—621no—
283C4⋊C4C22×D3111yescharacteristic
284C4⋊C4C22×D3111yescharacteristic
285C22⋊C4—311no—
286C22⋊C4—311no—
287C22⋊C4—621no—
288C22⋊C4—621no—
289C22⋊C4—621no—
290C22⋊C4—621no—
291C22⋊C4—621no—
292C22⋊C4—621no—
293C22⋊C4—621no—
294C42—621no—
295C42C22×D3111yescharacteristic
296C23—311no—
297C23—311no—
298C23—621no—
299C23—621no—
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—21no—
304D4—312no—
305D4—621no—
306D4—621no—
307D4—621no—
308D4—1241no—
309D4—1242no—
310D4—1242no—
311D4—1242no—
312D4—2481no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—311no—
318C2×C4—311no—
319C2×C4—621no—
320C2×C4—621no—
321C2×C4—621no—
322C2×C4—621no—
323C2×C4—621no—
324C2×C4—621no—
325C2×C4—1242no—
326C2×C4—1242no—
327C2×C4—1242no—
328C2×C4—2481no—
329C2×C4—2481no—
330C2×C4D4×D3111yescharacteristic
331C2×C4D4×D3111yescharacteristic
332C2×C4C23×D3111yescharacteristic
333C8—21no—
334C8—21no—
335C8—621no—
336C8—621no—
337C22—621no—
338C22—621no—
339C22—621no—
340C22—621no—
341C22—622no—
342C22—621no—
343C22—621no—
344C22—1241no—
345C22—1241no—
346C22—1241no—
347C22—1241no—
348C22—1241no—
349C22C2×D4×D3111yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—621no—
357C4—621no—
358C4—1241no—
359C4—1241no—
360C4#41×D3111yescharacteristic
361C4#1175856611yescharacteristic
362C2—1241no—
363C2—1241no—
364C2—1242no—
365C2—2481no—
366C2#1452169211yescharacteristic
367C2#1452184811yescharacteristic
368C2#1452185811yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#491C2
socleC22×C31C22×D4
hypercenter#491D31
hypocenterC31#3307
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #14521752C2semidirect
2. #14521702C2semidirect
3. #14521388C2semidirect
4. #14521378C2semidirect
5. #14521346C2semidirect
6. #14521298C2semidirect
7. #14521281C2semidirect
8. #14521251C2semidirect
9. #14521197C2semidirect
10. #14521197C2semidirect
11. #14521162C2semidirect
12. #14521122C2semidirect
13. #14521049C2semidirect
14. #14521044C2semidirect
15. C31×#491C2semidirect
180. #491D31semidirect
243. C31#3307semidirect

Maximal subgroups

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

subgroupindex
#145217522
#145217022
#145213882
#145213782
#145213462
#145212982
#145212812
#145212512
#145211972
#145211622
#145211222
#145210492
#145210442
C31×#4912
#330731