Finite Group Databasebeta

← #16855860

Subgroups — #16855860

Order 3968.

430 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521596C211yesmaximal, characteristic, complemented
2C4×#92499C211yesmaximal, characteristic, complemented
3#14521376C211yesmaximal, characteristic, complemented
4#14521372C211yesmaximal, characteristic, complemented
5#14521332C211yesmaximal, characteristic, complemented
6#14521328C211yesmaximal, characteristic, complemented
7#14521247C211yesmaximal, characteristic, complemented
8#14521243C211yesmaximal, characteristic, complemented
9#14521197C211yesmaximal, characteristic, complemented
10#14521193C211yesmaximal, characteristic, complemented
11#14521162C211yesmaximal, characteristic, complemented
12#14521159C211yesmaximal, characteristic, complemented
13#14521147C211yesmaximal, characteristic, complemented
14#14521104C211yesmaximal, characteristic, complemented
15C31×#440C211yesmaximal, characteristic, complemented
16C2×#92499C2211yescharacteristic
17C2×#92495—21no—
18C2×SD16×C31C2211yescharacteristic
19C4×Q8×C31C2211yescharacteristic
20C4×D4×C31C2211yescharacteristic
21Q8×Dic31C2211yescharacteristic
22C2×#92481C2211yescharacteristic
23#11758517C2211yescharacteristic
24#11758515C2211yescharacteristic
25C2×#92479C2211yescharacteristic
26C4×C22⋊D31—21no—
27C2×D248C2211yescharacteristic
28#11758472C2211yescharacteristic
29#11758470—21no—
30#11758470C2211yescharacteristic
31#11758469—21no—
32#11758469C2211yescharacteristic
33#11758465C2211yescharacteristic
34#11758462—21no—
35#11758461—21no—
36C4×D124—21no—
37C4×D124C2211yescharacteristic
38C4×D124C2211yescharacteristic
39C42×D31—21no—
40C42×D31C2211yescharacteristic
41C31×#107C2211yescharacteristic
42C31×#103C2211yescharacteristic
43C31×#102C2211yescharacteristic
44C31×#97C2211yescharacteristic
45#11758423C2211yescharacteristic
46#11758420C2211yescharacteristic
47#11758409C2211yescharacteristic
48#11758409C2211yescharacteristic
49(C2×D31)⋊C8C2211yescharacteristic
50(C2×D31)⋊C8C2211yescharacteristic
51#11758405C2211yescharacteristic
52Dic31⋊C8C2211yescharacteristic
53Dic31⋊C8C2211yescharacteristic
54#11758397C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758396C2211yescharacteristic
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—
65#92499—22no—
66#92499—22no—
67#92495—44no—
68C2×D124—21no—
69C2×D124—21no—
70C2×D124C2311yescharacteristic
71C2×D124C2311yescharacteristic
72C2×C4×D31—21no—
73C2×C4×D31—21no—
74C2×C4×D31—21no—
75C2×C4×D31—21no—
76C2×C4×D31D411yescharacteristic
77C2×C4×D31D411yescharacteristic
78C2×C4×D31C2311yescharacteristic
79C2×Dic62—21no—
80SD16×C31—22no—
81C2×C8×C31C2311yescharacteristic
82C2×C8×C31C2311yescharacteristic
83C4⋊C4×C31—21no—
84C4⋊C4×C31C2311yescharacteristic
85C4⋊C4×C31C2311yescharacteristic
86C22⋊C4×C31—21no—
87C42×C31—21no—
88C42×C31C2311yescharacteristic
89C22⋊Dic31—21no—
90#92481—22no—
91#92479—22no—
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—
97C4⋊Dic31—21no—
98C4⋊Dic31C2311yescharacteristic
99C4⋊Dic31C2311yescharacteristic
100Dic31⋊C4—21no—
101C4×Dic31—21no—
102C4×Dic31—21no—
103C4×Dic31D411yescharacteristic
104C4×Dic31D411yescharacteristic
105C4×Dic31C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108D248—22no—
109C23×C31—21no—
110C22×D31—21no—
111C22×D31—21no—
112C22×D31C2×D411yescharacteristic
113Q8×C31—21no—
114Q8×C31#4112yescomplemented
115D4×C31—21no—
116D4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—42no—
121C2×C4×C31C2×D411yescharacteristic
122C2×C4×C31C2×D411yescharacteristic
123C2×C4×C31C2411yescharacteristic
124C22⋊D31—42no—
125C22⋊D31—42no—
126C22⋊D31—42no—
127C2×Dic31—21no—
128C2×Dic31—21no—
129C2×Dic31C2×D411yescharacteristic
130C2×Dic31C2×D411yescharacteristic
131C2×Dic31C2×D411yescharacteristic
132D124—24no—
133D124—21no—
134D124—21no—
135D124—21no—
136D124—42no—
137D124#4112yescomplemented
138C4×D31—24no—
139C4×D31—21no—
140C4×D31—21no—
141C4×D31—22no—
142C4×D31—41no—
143C4×D31—42no—
144C4×D31—42no—
145C4×D31—42no—
146Dic62—42no—
147C8×C31—21no—
148C8×C31—21no—
149C31⋊C8—21no—
150C31⋊C8—21no—
151#3115—311nomaximal, Sylow
152C22×C31—41no—
153C22×C31—41no—
154C22×C31—41no—
155C22×C31C22×D411yescharacteristic
156C2×D31—21no—
157C2×D31—22no—
158C2×D31—21no—
159C2×D31—21no—
160C2×D31—41no—
161C2×D31—41no—
162C2×D31—41no—
163C2×D31—41no—
164C2×D31—41no—
165C4×C31—22no—
166C4×C31—21no—
167C4×C31—21no—
168C4×C31—41no—
169C4×C31—41no—
170C4×C31C2×#4111yescharacteristic
171C4×C31C2×#4111yescharacteristic
172Dic31—21no—
173Dic31—21no—
174Dic31—41no—
175Dic31—41no—
176Dic31AGL(1,ℤ/8)12yes—
177#532—311no—
178C4×#41—311no—
179#482—311no—
180#482—311no—
181#475—311no—
182#474—311no—
183#460—311no—
184#459—311no—
185#449—311no—
186#449—311no—
187#442—311no—
188#442—311no—
189#440—311no—
190#440D3111yescharacteristic, complemented
191#432—311no—
192C2×C31—81no—
193C2×C31#52511yescharacteristic
194C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
195C2×C31#57511yescharacteristic
196D31—41no—
197D31—42no—
198D31—81no—
199C2×#41—311no—
200C2×#41—621no—
201C2×SD16—311no—
202C2×SD16C2×D3111yescharacteristic
203C2×D8—311no—
204C2×D8—311no—
205C4⋊Q8—311no—
206#127—311no—
207#124—621no—
208#121—311no—
209#121—311no—
210#121—621no—
211C4×Q8—311no—
212C4×Q8C2×D3111yescharacteristic
213C4×D4—311no—
214C4×D4—311no—
215C4×D4—311no—
216C4×D4—621no—
217C4×D4—621no—
218C4×D4—621no—
219C4×D4C2×D3111yescharacteristic
220#117—311no—
221#117—621no—
222C2×C42—311no—
223C2×C42—621no—
224#107—311no—
225#107C2×D3111yescharacteristic
226#106—311no—
227#106—311no—
228C4⋊C8—311no—
229C4⋊C8—311no—
230#103—311no—
231#103C2×D3111yescharacteristic
232#102—311no—
233#102—311no—
234#102—311no—
235#102—311no—
236#102—311no—
237#102C2×D3111yescharacteristic
238C22⋊C8—311no—
239C22⋊C8—311no—
240#97—311no—
241#97C2×D3111yescharacteristic
242C31#311511yescharacteristic, complemented, Sylow
243#41—622no—
244#41—622no—
245#41—1244no—
246C2×Q8—621no—
247C2×Q8C22×D3111yescharacteristic
248C2×D4—311no—
249C2×D4—311no—
250C2×D4—621no—
251C2×D4—621no—
252C2×D4—621no—
253C2×D4—621no—
254C2×D4—621no—
255C2×D4C22×D3111yescharacteristic
256C22×C4—21no—
257C22×C4—311no—
258C22×C4—311no—
259C22×C4—311no—
260C22×C4—621no—
261C22×C4—621no—
262C22×C4—621no—
263C22×C4—621no—
264SD16—22no—
265SD16—622no—
266D8—622no—
267D8—622no—
268C2×C8—311no—
269C2×C8—311no—
270C2×C8C22×D3111yescharacteristic
271C2×C8C22×D3111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—311no—
274C4⋊C4—311no—
275C4⋊C4—621no—
276C4⋊C4—621no—
277C4⋊C4C22×D3111yescharacteristic
278C4⋊C4C22×D3111yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C22⋊C4—621no—
284C22⋊C4—621no—
285C22⋊C4—621no—
286C42—21no—
287C42—311no—
288C42—311no—
289C42—311no—
290C42—621no—
291C42—621no—
292C42C22×D3111yescharacteristic
293C23—21no—
294C23—311no—
295C23—621no—
296C23—621no—
297Q8—21no—
298Q8—1242no—
299Q8#9249512yescomplemented
300D4—21no—
301D4—21no—
302D4—312no—
303D4—624no—
304D4—621no—
305D4—621no—
306D4—621no—
307D4—1242no—
308D4—1242no—
309D4—1242no—
310D4—1242no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—311no—
316C2×C4—311no—
317C2×C4—311no—
318C2×C4—622no—
319C2×C4—624no—
320C2×C4—621no—
321C2×C4—621no—
322C2×C4—621no—
323C2×C4—621no—
324C2×C4—1241no—
325C2×C4—1242no—
326C2×C4—1242no—
327C2×C4—1242no—
328C2×C4D4×D3111yescharacteristic
329C2×C4D4×D3111yescharacteristic
330C2×C4C23×D3111yescharacteristic
331C8—21no—
332C8—21no—
333C8—621no—
334C8—621no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—622no—
339C22—621no—
340C22—621no—
341C22—621no—
342C22—1241no—
343C22—1241no—
344C22—1241no—
345C22—1241no—
346C22—1241no—
347C22C2×D4×D3111yescharacteristic
348C4—22no—
349C4—21no—
350C4—21no—
351C4—41no—
352C4—41no—
353C4—312no—
354C4—621no—
355C4—621no—
356C4—1241no—
357C4—1241no—
358C4C2×#9249511yescharacteristic
359C4#41×D3111yescharacteristic
360C2—81no—
361C2—1241no—
362C2—1242no—
363C2—2481no—
364C2#1452155811yescharacteristic
365C2AGL(1,ℤ/8)×D3111yescharacteristic
366C2#1452184811yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#440C2
socleC22×C31C22×D4
hypercenter#440D31
hypocenterC31#3115
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
1. #14521596C2semidirect
2. C4×#92499C2semidirect
3. #14521376C2semidirect
4. #14521372C2semidirect
5. #14521332C2semidirect
6. #14521328C2semidirect
7. #14521247C2semidirect
8. #14521243C2semidirect
9. #14521197C2semidirect
10. #14521193C2semidirect
11. #14521162C2semidirect
12. #14521159C2semidirect
13. #14521147C2semidirect
14. #14521104C2semidirect
15. C31×#440C2semidirect
114. Q8×C31#41semidirect
137. D124#41semidirect
190. #440D31semidirect
242. C31#3115semidirect
299. Q8#92495semidirect

Maximal subgroups

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

subgroupindex
#145215962
C4×#924992
#145213762
#145213722
#145213322
#145213282
#145212472
#145212432
#145211972
#145211932
#145211622
#145211592
#145211472
#145211042
C31×#4402
#311531