Finite Group Databasebeta

← #16855816

Subgroups — #16855816

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#14521581C211yesmaximal, characteristic, complemented
2C4×#92497C211yesmaximal, characteristic, complemented
3#14521393C211yesmaximal, characteristic, complemented
4#14521372C211yesmaximal, characteristic, complemented
5#14521359C211yesmaximal, characteristic, complemented
6#14521351C211yesmaximal, characteristic, complemented
7#14521270C211yesmaximal, characteristic, complemented
8#14521262C211yesmaximal, characteristic, complemented
9#14521212C211yesmaximal, characteristic, complemented
10#14521191C211yesmaximal, characteristic
11#14521157C211yesmaximal, characteristic, complemented
12#14521149C211yesmaximal, characteristic, complemented
13#14521149C211yesmaximal, characteristic, complemented
14#14521104C211yesmaximal, characteristic, complemented
15C31×#442C211yesmaximal, characteristic, complemented
16C2×#92497C2211yescharacteristic
17C2×D8×C31C2211yescharacteristic
18C4×D4×C31C2211yescharacteristic
19C4×D4×C31C2211yescharacteristic
20#11758515C2211yescharacteristic
21#11758513C2211yescharacteristic
22D4×Dic31C2211yescharacteristic
23C2×#92480C2211yescharacteristic
24C2×#92480C2211yescharacteristic
25C4×C22⋊D31—21no—
26C4×C22⋊D31—21no—
27#11758503—21no—
28C2×C4×Dic31—21no—
29C2×Dic124C2211yescharacteristic
30#11758474C2211yescharacteristic
31#11758469C2211yescharacteristic
32#11758467C2211yescharacteristic
33#11758464C2211yescharacteristic
34#11758460—21no—
35(C22⋊D31)⋊C4—21no—
36#11758456—21no—
37#11758454—21no—
38C42×D31C2211yescharacteristic
39C4×Dic62C2211yescharacteristic
40C4×Dic62C2211yescharacteristic
41C31×#106C2211yescharacteristic
42C31×#102C2211yescharacteristic
43C31×#102C2211yescharacteristic
44C31×#97C2211yescharacteristic
45#11758420C2211yescharacteristic
46#11758420C2211yescharacteristic
47(C2×D31)⋊C8C2211yescharacteristic
48(C2×D31)⋊C8C2211yescharacteristic
49#11758405C2211yescharacteristic
50#11758404C2211yescharacteristic
51#11758404C2211yescharacteristic
52Dic31⋊C8C2211yescharacteristic
53Dic31⋊C8C2211yescharacteristic
54#11758398C2211yescharacteristic
55#11758398C2211yescharacteristic
56#11758395C2211yescharacteristic
57#11758395C2211yescharacteristic
58#11758391C2211yescharacteristic
59C2×D4×C31C2311yescharacteristic
60C2×D4×C31C2311yescharacteristic
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C2×C22⋊D31—21no—
64C2×C22⋊D31—21no—
65C22×Dic31—21no—
66C22×Dic31—21no—
67#92497—22no—
68#92497—22no—
69C2×C4×D31D411yescharacteristic
70C2×C4×D31D411yescharacteristic
71C2×C4×D31C2311yescharacteristic
72C2×Dic62C2311yescharacteristic
73C2×Dic62C2311yescharacteristic
74D8×C31—22no—
75C2×C8×C31C2311yescharacteristic
76C2×C8×C31C2311yescharacteristic
77C4⋊C4×C31C2311yescharacteristic
78C4⋊C4×C31C2311yescharacteristic
79C22⋊C4×C31—21no—
80C22⋊C4×C31—21no—
81C42×C31C2311yescharacteristic
82C22⋊Dic31—21no—
83C22⋊Dic31—21no—
84C22⋊Dic31—21no—
85C22⋊Dic31—21no—
86#92480—22no—
87#92480—22no—
88(C2×D31)⋊C4—21no—
89(C2×D31)⋊C4—21no—
90C4⋊Dic31—21no—
91C4⋊Dic31—21no—
92C4⋊Dic31C2311yescharacteristic
93C4⋊Dic31C2311yescharacteristic
94Dic31⋊C4—21no—
95Dic31⋊C4—21no—
96Dic31⋊C4—21no—
97Dic31⋊C4—21no—
98C4×Dic31—21no—
99C4×Dic31—21no—
100C4×Dic31—21no—
101C4×Dic31—21no—
102C4×Dic31D411yescharacteristic
103C4×Dic31D411yescharacteristic
104C4×Dic31C2311yescharacteristic
105C2×C31⋊C8C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107Dic124—22no—
108C23×C31—21no—
109C23×C31—21no—
110C22×D31C2×D411yescharacteristic
111D4×C31—21no—
112D4×C31—21no—
113D4×C31—21no—
114D4×C31#4112yes—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—42no—
118C2×C4×C31—42no—
119C2×C4×C31C2×D411yescharacteristic
120C2×C4×C31C2×D411yescharacteristic
121C2×C4×C31C2411yescharacteristic
122C22⋊D31—24no—
123C22⋊D31—42no—
124C2×Dic31—24no—
125C2×Dic31—21no—
126C2×Dic31—21no—
127C2×Dic31—21no—
128C2×Dic31—21no—
129C2×Dic31—42no—
130C2×Dic31C2×D411yescharacteristic
131C2×Dic31C2×D411yescharacteristic
132C2×Dic31C2×D411yescharacteristic
133C4×D31—21no—
134C4×D31—21no—
135C4×D31—41no—
136C4×D31—41no—
137Dic62—21no—
138Dic62—21no—
139Dic62—21no—
140Dic62#4112yes—
141C8×C31—21no—
142C8×C31—21no—
143C31⋊C8—21no—
144C31⋊C8—21no—
145#3111—311nomaximal, Sylow
146C22×C31—22no—
147C22×C31—41no—
148C22×C31—41no—
149C22×C31—41no—
150C22×C31—41no—
151C22×C31—41no—
152C22×C31C22×D411yescharacteristic
153C2×D31—21no—
154C2×D31—21no—
155C2×D31—21no—
156C4×C31—21no—
157C4×C31—21no—
158C4×C31—41no—
159C4×C31—41no—
160C4×C31C2×#4111yescharacteristic
161C4×C31C2×#4111yescharacteristic
162Dic31—22no—
163Dic31—21no—
164Dic31—21no—
165Dic31—21no—
166Dic31—41no—
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#442D3111yescharacteristic, complemented
180#441—311no—
181#440—311no—
182#440—311no—
183#432—311no—
184C2×C31—42no—
185C2×C31—81no—
186C2×C31#52511yescharacteristic
187C2×C31#57511yescharacteristic
188C2×C31#57511yescharacteristic
189D31—41no—
190C2×#41—311no—
191C2×Q16—311no—
192C2×SD16—311no—
193C2×SD16—311no—
194C2×D8C2×D3111yescharacteristic
195#126—621no—
196#125—311no—
197#124—311no—
198#123—621no—
199C22⋊Q8—311no—
200#121—311no—
201C4×Q8—311no—
202C4×Q8—311no—
203C4×Q8—311no—
204C4×D4—311no—
205C4×D4—621no—
206C4×D4—621no—
207C4×D4—621no—
208C4×D4C2×D3111yescharacteristic
209C4×D4C2×D3111yescharacteristic
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#103—311no—
224#103—311no—
225#102—311no—
226#102—311no—
227#102C2×D3111yescharacteristic
228#102C2×D3111yescharacteristic
229C22⋊C8—311no—
230C22⋊C8—311no—
231#97—311no—
232#97C2×D3111yescharacteristic
233C31#311111yescharacteristic, complemented, Sylow
234#41—622no—
235#41—622no—
236C2×Q8—311no—
237C2×Q8—311no—
238C2×D4—621no—
239C2×D4—621no—
240C2×D4C22×D3111yescharacteristic
241C2×D4C22×D3111yescharacteristic
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—311no—
245C22×C4—311no—
246C22×C4—311no—
247C22×C4—621no—
248C22×C4—621no—
249Q16—622no—
250SD16—622no—
251SD16—622no—
252D8—22no—
253C2×C8—311no—
254C2×C8—311no—
255C2×C8C22×D3111yescharacteristic
256C2×C8C22×D3111yescharacteristic
257C4⋊C4—311no—
258C4⋊C4—311no—
259C4⋊C4—621no—
260C4⋊C4—621no—
261C4⋊C4—621no—
262C4⋊C4—621no—
263C4⋊C4—621no—
264C4⋊C4—621no—
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—311no—
276C42—311no—
277C42—311no—
278C42—621no—
279C42—621no—
280C42—621no—
281C42—621no—
282C42C22×D3111yescharacteristic
283C23—21no—
284C23—21no—
285C23—311no—
286Q8—312no—
287Q8—621no—
288Q8—621no—
289Q8—621no—
290D4—21no—
291D4—21no—
292D4—21no—
293D4—624no—
294D4—1242no—
295D4#9249512yes—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—42no—
299C2×C4—42no—
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—621no—
309C2×C4—621no—
310C2×C4—1241no—
311C2×C4—1241no—
312C2×C4—1242no—
313C2×C4D4×D3111yescharacteristic
314C2×C4D4×D3111yescharacteristic
315C2×C4C23×D3111yescharacteristic
316C8—21no—
317C8—21no—
318C8—621no—
319C8—621no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—621no—
327C22—621no—
328C22—621no—
329C22C2×D4×D3111yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—621no—
335C4—622no—
336C4—621no—
337C4—621no—
338C4—1241no—
339C4—1241no—
340C4—1241no—
341C4C2×#9249511yescharacteristic
342C4#41×D3111yescharacteristic
343C2—42no—
344C2—81no—
345C2—1241no—
346C2#1452155811yescharacteristic
347C2#1452184511yescharacteristic
348C2#1452184511yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#442C2
socleC22×C31C22×D4
prime radical#14521191C2
hypercenter#442D31
hypocenterC31#3111
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #14521581C2semidirect
2. C4×#92497C2semidirect
3. #14521393C2semidirect
4. #14521372C2semidirect
5. #14521359C2semidirect
6. #14521351C2semidirect
7. #14521270C2semidirect
8. #14521262C2semidirect
9. #14521212C2semidirect
11. #14521157C2semidirect
12. #14521149C2semidirect
13. #14521149C2semidirect
14. #14521104C2semidirect
15. C31×#442C2semidirect
179. #442D31semidirect
233. C31#3111semidirect

Maximal subgroups

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

subgroupindex
#145215812
C4×#924972
#145213932
#145213722
#145213592
#145213512
#145212702
#145212622
#145212122
#145211912
#145211572
#145211492
#145211042
C31×#4422
#311131