Finite Group Databasebeta

← #16855826

Subgroups — #16855826

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#14521586C211yesmaximal, characteristic, complemented
2C4×#92499C211yesmaximal, characteristic, complemented
3#14521388C211yesmaximal, characteristic, complemented
4#14521375C211yesmaximal, characteristic, complemented
5#14521354C211yesmaximal, characteristic, complemented
6#14521348C211yesmaximal, characteristic, complemented
7#14521273C211yesmaximal, characteristic, complemented
8#14521267C211yesmaximal, characteristic, complemented
9#14521210C211yesmaximal, characteristic, complemented
10#14521197C211yesmaximal, characteristic
11#14521162C211yesmaximal, characteristic, complemented
12#14521147C211yesmaximal, characteristic, complemented
13#14521147C211yesmaximal, characteristic, complemented
14#14521104C211yesmaximal, characteristic, complemented
15C31×#441C211yesmaximal, characteristic, complemented
16C2×#92499C2211yescharacteristic
17C2×Q16×C31C2211yescharacteristic
18C4×Q8×C31C2211yescharacteristic
19C4×Q8×C31C2211yescharacteristic
20#11758524C2211yescharacteristic
21#11758523C2211yescharacteristic
22Q8×Dic31C2211yescharacteristic
23C2×#92481C2211yescharacteristic
24C2×#92481C2211yescharacteristic
25C2×D248C2211yescharacteristic
26#11758475—21no—
27#11758472C2211yescharacteristic
28#11758471—21no—
29#11758470—21no—
30#11758470C2211yescharacteristic
31#11758469—21no—
32#11758469C2211yescharacteristic
33#11758467C2211yescharacteristic
34C4×D124—21no—
35C4×D124—21no—
36C4×D124C2211yescharacteristic
37C4×D124C2211yescharacteristic
38#11758449—21no—
39C42×D31—21no—
40C42×D31C2211yescharacteristic
41C31×#106C2211yescharacteristic
42C31×#103C2211yescharacteristic
43C31×#103C2211yescharacteristic
44C31×#97C2211yescharacteristic
45#11758423C2211yescharacteristic
46#11758423C2211yescharacteristic
47#11758409C2211yescharacteristic
48#11758409C2211yescharacteristic
49(C2×D31)⋊C8C2211yescharacteristic
50(C2×D31)⋊C8C2211yescharacteristic
51#11758405C2211yescharacteristic
52Dic31⋊C8C2211yescharacteristic
53Dic31⋊C8C2211yescharacteristic
54#11758397C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758395C2211yescharacteristic
57#11758395C2211yescharacteristic
58#11758391C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C2×Q8×C31C2311yescharacteristic
61#92499—22no—
62#92499—22no—
63C2×D124—21no—
64C2×D124—21no—
65C2×D124C2311yescharacteristic
66C2×D124C2311yescharacteristic
67C2×C4×D31—21no—
68C2×C4×D31—21no—
69C2×C4×D31—21no—
70C2×C4×D31—21no—
71C2×C4×D31D411yescharacteristic
72C2×C4×D31D411yescharacteristic
73C2×C4×D31C2311yescharacteristic
74Q16×C31—22no—
75C2×C8×C31C2311yescharacteristic
76C2×C8×C31C2311yescharacteristic
77C4⋊C4×C31—21no—
78C4⋊C4×C31—21no—
79C4⋊C4×C31C2311yescharacteristic
80C4⋊C4×C31C2311yescharacteristic
81C42×C31—21no—
82C42×C31—21no—
83C42×C31C2311yescharacteristic
84#92481—22no—
85#92481—22no—
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—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4—21no—
93(C2×D31)⋊C4—21no—
94C4⋊Dic31—21no—
95C4⋊Dic31—21no—
96C4⋊Dic31C2311yescharacteristic
97C4⋊Dic31C2311yescharacteristic
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100C4×Dic31—21no—
101C4×Dic31—21no—
102C4×Dic31D411yescharacteristic
103C4×Dic31D411yescharacteristic
104C4×Dic31C2311yescharacteristic
105C2×C31⋊C8C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107D248—22no—
108C22×D31—21no—
109C22×D31—21no—
110C22×D31C2×D411yescharacteristic
111Q8×C31—21no—
112Q8×C31—21no—
113Q8×C31—21no—
114Q8×C31#4112yes—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31C2×D411yescharacteristic
120C2×C4×C31C2×D411yescharacteristic
121C2×C4×C31C2411yescharacteristic
122C2×Dic31—21no—
123C2×Dic31—21no—
124C2×Dic31C2×D411yescharacteristic
125C2×Dic31C2×D411yescharacteristic
126C2×Dic31C2×D411yescharacteristic
127D124—24no—
128D124—21no—
129D124—21no—
130D124—21no—
131D124—42no—
132D124#4112yes—
133C4×D31—24no—
134C4×D31—21no—
135C4×D31—21no—
136C4×D31—41no—
137C4×D31—41no—
138C4×D31—42no—
139C4×D31—42no—
140C4×D31—42no—
141C8×C31—21no—
142C8×C31—21no—
143C31⋊C8—21no—
144C31⋊C8—21no—
145#3111—311nomaximal, Sylow
146C22×C31C22×D411yescharacteristic
147C2×D31—21no—
148C2×D31—22no—
149C2×D31—21no—
150C2×D31—21no—
151C2×D31—41no—
152C2×D31—41no—
153C2×D31—41no—
154C2×D31—41no—
155C2×D31—41no—
156C4×C31—22no—
157C4×C31—21no—
158C4×C31—21no—
159C4×C31—41no—
160C4×C31—41no—
161C4×C31—41no—
162C4×C31C2×#4111yescharacteristic
163C4×C31C2×#4111yescharacteristic
164Dic31—21no—
165Dic31—21no—
166Dic31—21no—
167Dic31—41no—
168Dic31—41no—
169#529—311no—
170C4×#41—311no—
171#485—311no—
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#441D3111yescharacteristic, complemented
181#440—311no—
182#440—311no—
183#432—311no—
184C2×C31#52511yescharacteristic
185C2×C31#57511yescharacteristic
186C2×C31#57511yescharacteristic
187D31—41no—
188D31—42no—
189D31—81no—
190C2×#41—311no—
191C2×Q16C2×D3111yescharacteristic
192C2×SD16—311no—
193C2×SD16—311no—
194C2×D8—311no—
195#126—621no—
196#125—311no—
197#124—311no—
198#123—621no—
199C22⋊Q8—311no—
200#121—311no—
201C4×Q8—311no—
202C4×Q8C2×D3111yescharacteristic
203C4×Q8C2×D3111yescharacteristic
204C4×D4—311no—
205C4×D4—311no—
206C4×D4—311no—
207C4×D4—621no—
208C4×D4—621no—
209C4×D4—621no—
210#117—311no—
211#117—621no—
212#117—621no—
213C2×C42—311no—
214C2×C42—621no—
215#107—311no—
216#107—311no—
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⋊C8—311no—
231#97—311no—
232#97C2×D3111yescharacteristic
233C31#311111yescharacteristic, complemented, Sylow
234#41—622no—
235#41—622no—
236C2×Q8C22×D3111yescharacteristic
237C2×Q8C22×D3111yescharacteristic
238C2×D4—311no—
239C2×D4—311no—
240C2×D4—621no—
241C2×D4—621no—
242C22×C4—311no—
243C22×C4—311no—
244C22×C4—311no—
245C22×C4—621no—
246C22×C4—621no—
247C22×C4—621no—
248C22×C4—621no—
249Q16—22no—
250SD16—622no—
251SD16—622no—
252D8—622no—
253C2×C8—311no—
254C2×C8—311no—
255C2×C8C22×D3111yescharacteristic
256C2×C8C22×D3111yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—311no—
260C4⋊C4—311no—
261C4⋊C4—621no—
262C4⋊C4—621no—
263C4⋊C4—621no—
264C4⋊C4—621no—
265C4⋊C4C22×D3111yescharacteristic
266C4⋊C4C22×D3111yescharacteristic
267C22⋊C4—621no—
268C22⋊C4—621no—
269C22⋊C4—621no—
270C22⋊C4—621no—
271C22⋊C4—621no—
272C22⋊C4—621no—
273C22⋊C4—621no—
274C22⋊C4—621no—
275C42—21no—
276C42—21no—
277C42—311no—
278C42—311no—
279C42—311no—
280C42—621no—
281C42—621no—
282C42C22×D3111yescharacteristic
283C23—311no—
284C23—621no—
285C23—621no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8#9249512yes—
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—311no—
301C2×C4—311no—
302C2×C4—311no—
303C2×C4—624no—
304C2×C4—621no—
305C2×C4—621no—
306C2×C4—621no—
307C2×C4—621no—
308C2×C4—1241no—
309C2×C4—1241no—
310C2×C4—1242no—
311C2×C4—1242no—
312C2×C4—1242no—
313C2×C4D4×D3111yescharacteristic
314C2×C4D4×D3111yescharacteristic
315C2×C4C23×D3111yescharacteristic
316C8—21no—
317C8—21no—
318C8—621no—
319C8—621no—
320C22—622no—
321C22—621no—
322C22—621no—
323C22—621no—
324C22—1241no—
325C22—1241no—
326C22—1241no—
327C22—1241no—
328C22—1241no—
329C22C2×D4×D3111yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—621no—
337C4—621no—
338C4—621no—
339C4—1241no—
340C4—1241no—
341C4C2×#9249511yescharacteristic
342C4#41×D3111yescharacteristic
343C2—1241no—
344C2—1242no—
345C2—2481no—
346C2#1452155811yescharacteristic
347C2#1452184811yescharacteristic
348C2#1452184811yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#441C2
socleC22×C31C22×D4
prime radical#14521197C2
hypercenter#441D31
hypocenterC31#3111
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #14521586C2semidirect
2. C4×#92499C2semidirect
3. #14521388C2semidirect
4. #14521375C2semidirect
5. #14521354C2semidirect
6. #14521348C2semidirect
7. #14521273C2semidirect
8. #14521267C2semidirect
9. #14521210C2semidirect
11. #14521162C2semidirect
12. #14521147C2semidirect
13. #14521147C2semidirect
14. #14521104C2semidirect
15. C31×#441C2semidirect
180. #441D31semidirect
233. C31#3111semidirect

Maximal subgroups

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

subgroupindex
#145215862
C4×#924992
#145213882
#145213752
#145213542
#145213482
#145212732
#145212672
#145212102
#145211972
#145211622
#145211472
#145211042
C31×#4412
#311131