Finite Group Databasebeta

← #16855823

Subgroups — #16855823

Order 3968.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521585C211yesmaximal, characteristic, complemented
2#14521517C211yesmaximal, characteristic, complemented
3#14521373C211yesmaximal, characteristic, complemented
4#14521359C211yesmaximal, characteristic, complemented
5#14521352C211yesmaximal, characteristic, complemented
6#14521274C211yesmaximal, characteristic, complemented
7#14521267C211yesmaximal, characteristic, complemented
8#14521209C211yesmaximal, characteristic, complemented
9#14521196C211yesmaximal, characteristic
10#14521160C211yesmaximal, characteristic, complemented
11#14521153C211yesmaximal, characteristic, complemented
12#14521152C211yesmaximal, characteristic, complemented
13#14521148C211yesmaximal, characteristic, complemented
14#14521103C211yesmaximal, characteristic, complemented
15C31×#485C211yesmaximal, characteristic, complemented
16C2×#92495C2211yescharacteristic
17C31×C22⋊Q8C2211yescharacteristic
18C31×#117C2211yescharacteristic
19#11758524C2211yescharacteristic
20Q8×Dic31C2211yescharacteristic
21C2×#92482C2211yescharacteristic
22C2×#92481C2211yescharacteristic
23#11758507C2211yescharacteristic
24C2×C4×Dic31C2211yescharacteristic
25C2×D248C2211yescharacteristic
26C2×#92470C2211yescharacteristic
27#11758475—21no—
28#11758470C2211yescharacteristic
29#11758470C2211yescharacteristic
30#11758470C2211yescharacteristic
31#11758469—21no—
32#11758467C2211yescharacteristic
33#11758464C2211yescharacteristic
34#11758464C2211yescharacteristic
35#11758463—21no—
36(C22⋊D31)⋊C4—21no—
37(C22⋊D31)⋊C4—21no—
38(C22⋊D31)⋊C4—21no—
39#11758449—21no—
40C42×D31—21no—
41C31×#107C2211yescharacteristic
42C31×#106C2211yescharacteristic
43C31×#103C2211yescharacteristic
44C31×#103C2211yescharacteristic
45C31×C22⋊C8C2211yescharacteristic
46C22⋊(C31⋊C8)C2211yescharacteristic
47#11758409C2211yescharacteristic
48#11758404C2211yescharacteristic
49#11758403C2211yescharacteristic
50#11758403C2211yescharacteristic
51Dic31⋊C8C2211yescharacteristic
52Dic31⋊C8C2211yescharacteristic
53#11758398C2211yescharacteristic
54#11758397C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758397C2211yescharacteristic
57#11758396C2211yescharacteristic
58#11758395C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C22×C4×C31C2311yescharacteristic
61C2×C22⋊D31—21no—
62C2×C22⋊D31—21no—
63C22×Dic31D411yescharacteristic
64C22×Dic31D411yescharacteristic
65#92495—22no—
66#92495—22no—
67C2×D124C2311yescharacteristic
68C2×D124C2311yescharacteristic
69C2×C4×D31—21no—
70C2×C4×D31—21no—
71C2×C4×D31—21no—
72C2×C4×D31—21no—
73C2×Dic62C2311yescharacteristic
74C2×C8×C31C2311yescharacteristic
75C2×C8×C31C2311yescharacteristic
76C4⋊C4×C31—21no—
77C4⋊C4×C31C2311yescharacteristic
78C4⋊C4×C31C2311yescharacteristic
79C4⋊C4×C31C2311yescharacteristic
80C22⋊C4×C31—21no—
81C22⋊C4×C31—21no—
82C42×C31—21no—
83#92482—22no—
84#92481—22no—
85(C2×D31)⋊C4—21no—
86(C2×D31)⋊C4—21no—
87(C2×D31)⋊C4—21no—
88(C2×D31)⋊C4—21no—
89(C2×D31)⋊C4—21no—
90(C2×D31)⋊C4—21no—
91C4⋊Dic31—21no—
92C4⋊Dic31—21no—
93C4⋊Dic31C2311yescharacteristic
94Dic31⋊C4—21no—
95Dic31⋊C4—21no—
96Dic31⋊C4—21no—
97C4×Dic31—21no—
98C4×Dic31—21no—
99C4×Dic31—21no—
100C4×Dic31D411yescharacteristic
101C4×Dic31D411yescharacteristic
102C4×Dic31C2311yescharacteristic
103C4×Dic31C2311yescharacteristic
104C2×C31⋊C8C2311yescharacteristic
105C2×C31⋊C8C2311yescharacteristic
106D248—22no—
107#92470—22no—
108C23×C31C2×D411yescharacteristic
109C22×D31—21no—
110C22×D31—21no—
111Q8×C31—21no—
112Q8×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31C2×D411yescharacteristic
120C2×C4×C31C2411yescharacteristic
121C22⋊D31—24no—
122C22⋊D31—42no—
123C2×Dic31—21no—
124C2×Dic31—21no—
125C2×Dic31—41no—
126C2×Dic31—41no—
127C2×Dic31C2×D411yescharacteristic
128C2×Dic31C2×D411yescharacteristic
129C2×Dic31C2×D411yescharacteristic
130C2×Dic31C2×D411yescharacteristic
131D124—21no—
132D124—21no—
133D124—21no—
134D124#4112yes—
135C4×D31—24no—
136C4×D31—42no—
137C4×D31—42no—
138C4×D31—42no—
139Dic62—21no—
140Dic62#4112yes—
141C8×C31—21no—
142C8×C31—21no—
143C31⋊C8—21no—
144C31⋊C8—21no—
145#3111—311nomaximal, Sylow
146C22×C31—21no—
147C22×C31—21no—
148C22×C31—21no—
149C22×C31C22×D411yescharacteristic
150C2×D31—22no—
151C2×D31—41no—
152C2×D31—41no—
153C2×D31—41no—
154C2×D31—41no—
155C2×D31—41no—
156C4×C31—21no—
157C4×C31—41no—
158C4×C31—41no—
159C4×C31—41no—
160C4×C31—41no—
161C4×C31C2×#4111yescharacteristic
162C4×C31C2×#4111yescharacteristic
163Dic31—22no—
164Dic31—21no—
165Dic31—21no—
166Dic31—21no—
167Dic31—21no—
168Dic31—41no—
169#529—311no—
170C4×#41—311no—
171#485D3111yescharacteristic, complemented
172#482—311no—
173#479—311no—
174#478—311no—
175#464—311no—
176#463—311no—
177#452—311no—
178#449—311no—
179#442—311no—
180#441—311no—
181#440—311no—
182#440—311no—
183#432—311no—
184C2×C31—41no—
185C2×C31#52511yescharacteristic
186C2×C31#57511yescharacteristic
187C2×C31#57511yescharacteristic
188D31—42no—
189D31—81no—
190C2×#41—311no—
191C2×Q16—311no—
192C2×SD16—311no—
193C2×SD16—311no—
194C2×D8—311no—
195#126—621no—
196#125—311no—
197#124—311no—
198#123—621no—
199C22⋊Q8C2×D3111yescharacteristic
200#121—311no—
201C4×Q8—311no—
202C4×Q8—311no—
203C4×Q8—311no—
204C4×D4—311no—
205C4×D4—311no—
206C4×D4—311no—
207C4×D4—621no—
208C4×D4—621no—
209C4×D4—621no—
210#117—621no—
211#117—621no—
212#117C2×D3111yescharacteristic
213C2×C42—311no—
214C2×C42—621no—
215#107—311no—
216#107C2×D3111yescharacteristic
217#106—311no—
218#106C2×D3111yescharacteristic
219C4⋊C8—311no—
220C4⋊C8—311no—
221#103—311no—
222#103—311no—
223#103C2×D3111yescharacteristic
224#103C2×D3111yescharacteristic
225#102—311no—
226#102—311no—
227#102—311no—
228#102—311no—
229C22⋊C8—311no—
230C22⋊C8C2×D3111yescharacteristic
231#97—311no—
232#97—311no—
233C31#311111yescharacteristic, complemented, Sylow
234#41—622no—
235#41—622no—
236C2×Q8—311no—
237C2×Q8C22×D3111yescharacteristic
238C2×D4—311no—
239C2×D4—311no—
240C2×D4—621no—
241C2×D4—621no—
242C22×C4—311no—
243C22×C4—311no—
244C22×C4—621no—
245C22×C4—621no—
246C22×C4—621no—
247C22×C4—621no—
248C22×C4C22×D3111yescharacteristic
249Q16—622no—
250SD16—622no—
251SD16—622no—
252D8—622no—
253C2×C8—311no—
254C2×C8—311no—
255C2×C8C22×D3111yescharacteristic
256C2×C8C22×D3111yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—311no—
259C4⋊C4—621no—
260C4⋊C4—621no—
261C4⋊C4—621no—
262C4⋊C4—621no—
263C4⋊C4—621no—
264C4⋊C4C22×D3111yescharacteristic
265C4⋊C4C22×D3111yescharacteristic
266C4⋊C4C22×D3111yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—621no—
270C22⋊C4—621no—
271C22⋊C4—621no—
272C22⋊C4—621no—
273C22⋊C4—621no—
274C22⋊C4—621no—
275C42—21no—
276C42—311no—
277C42—311no—
278C42—311no—
279C42—311no—
280C42—621no—
281C42—621no—
282C42—621no—
283C23—621no—
284C23—621no—
285C23D4×D3111yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—312no—
289Q8—621no—
290D4—312no—
291D4—624no—
292D4—621no—
293D4—621no—
294D4—621no—
295D4—1242no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—311no—
303C2×C4—311no—
304C2×C4—311no—
305C2×C4—311no—
306C2×C4—624no—
307C2×C4—621no—
308C2×C4—621no—
309C2×C4—1242no—
310C2×C4—1242no—
311C2×C4—1242no—
312C2×C4—1241no—
313C2×C4—1241no—
314C2×C4D4×D3111yescharacteristic
315C2×C4C23×D3111yescharacteristic
316C8—21no—
317C8—21no—
318C8—621no—
319C8—621no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—622no—
324C22—1241no—
325C22—1241no—
326C22—1241no—
327C22—1241no—
328C22—1241no—
329C22C2×D4×D3111yescharacteristic
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—622no—
336C4—621no—
337C4—621no—
338C4—621no—
339C4—621no—
340C4—1241no—
341C4#41×D3111yescharacteristic
342C4#41×D3111yescharacteristic
343C2—41no—
344C2—1242no—
345C2—2481no—
346C2#1452155711yescharacteristic
347C2#1452184611yescharacteristic
348C2#1452184811yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#485C2
socleC22×C31C22×D4
prime radical#14521196C2
hypercenter#485D31
hypocenterC31#3111
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #14521585C2semidirect
2. #14521517C2semidirect
3. #14521373C2semidirect
4. #14521359C2semidirect
5. #14521352C2semidirect
6. #14521274C2semidirect
7. #14521267C2semidirect
8. #14521209C2semidirect
10. #14521160C2semidirect
11. #14521153C2semidirect
12. #14521152C2semidirect
13. #14521148C2semidirect
14. #14521103C2semidirect
15. C31×#485C2semidirect
171. #485D31semidirect
233. C31#3111semidirect

Maximal subgroups

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

subgroupindex
#145215852
#145215172
#145213732
#145213592
#145213522
#145212742
#145212672
#145212092
#145211962
#145211602
#145211532
#145211522
#145211482
#145211032
C31×#4852
#311131