Finite Group Databasebeta

← #16857692

Subgroups — #16857692

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#14521749C211yesmaximal, characteristic, complemented
2#14521703C211yesmaximal, characteristic, complemented
3#14521418C211yesmaximal, characteristic, complemented
4#14521393C211yesmaximal, characteristic, complemented
5#14521381C211yesmaximal, characteristic, complemented
6#14521349C211yesmaximal, characteristic, complemented
7#14521294C211yesmaximal, characteristic, complemented
8#14521277C211yesmaximal, characteristic, complemented
9#14521254C211yesmaximal, characteristic, complemented
10#14521191C211yesmaximal, characteristic, complemented
11#14521191C211yesmaximal, characteristic, complemented
12#14521122C211yesmaximal, characteristic, complemented
13#14521047C211yesmaximal, characteristic, complemented
14#14521042C211yesmaximal, characteristic, complemented
15C31×#442C211yesmaximal, characteristic, complemented
16C2×#92497C2211yescharacteristic
17C2×#92497C2211yescharacteristic
18C2×D8×C31C2211yescharacteristic
19C4×D4×C31C2211yescharacteristic
20C4×D4×C31C2211yescharacteristic
21#11758515C2211yescharacteristic
22#11758515C2211yescharacteristic
23C2×#92480C2211yescharacteristic
24C2×#92480C2211yescharacteristic
25#11758507—21no—
26#11758506—21no—
27C4×C22⋊D31—21no—
28C2×C4⋊Dic31—21no—
29C2×#92469C2211yescharacteristic
30C2×C8×D31C2211yescharacteristic
31#11758474C2211yescharacteristic
32#11758474C2211yescharacteristic
33#11758469C2211yescharacteristic
34C4⋊C4×D31C2211yescharacteristic
35#11758463—21no—
36#11758463—21no—
37#11758461—21no—
38#11758456—21no—
39C4×D124C2211yescharacteristic
40#11758447C2211yescharacteristic
41#11758446C2211yescharacteristic
42C31×#106C2211yescharacteristic
43C31×#102C2211yescharacteristic
44C31×#102C2211yescharacteristic
45C31×#97C2211yescharacteristic
46#11758420C2211yescharacteristic
47#11758420C2211yescharacteristic
48(C2×D31)⋊C8C2211yescharacteristic
49(C2×D31)⋊C8C2211yescharacteristic
50#11758404C2211yescharacteristic
51#11758404C2211yescharacteristic
52#11758404C2211yescharacteristic
53#11758404C2211yescharacteristic
54#11758398C2211yescharacteristic
55#11758398C2211yescharacteristic
56#11758396C2211yescharacteristic
57#11758395C2211yescharacteristic
58C4⋊(C31⋊C8)C2211yescharacteristic
59C2×D4×C31C2311yescharacteristic
60C2×D4×C31C2311yescharacteristic
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C2×C22⋊D31—21no—
64C2×C22⋊D31—21no—
65C2×C22⋊D31—21no—
66C2×C22⋊D31—21no—
67C22×Dic31—21no—
68C22×Dic31—21no—
69#92497—22no—
70#92497—22no—
71#92497—41no—
72#92497—41no—
73C2×D124D411yescharacteristic
74C2×C4×D31—21no—
75C2×C4×D31C2311yescharacteristic
76C2×C4×D31C2311yescharacteristic
77C2×Dic62C2311yescharacteristic
78C2×Dic62C2311yescharacteristic
79D8×C31—22no—
80C2×C8×C31C2311yescharacteristic
81C2×C8×C31C2311yescharacteristic
82C4⋊C4×C31C2311yescharacteristic
83C4⋊C4×C31C2311yescharacteristic
84C22⋊C4×C31—21no—
85C22⋊C4×C31—21no—
86C42×C31C2311yescharacteristic
87C22⋊Dic31—21no—
88C22⋊Dic31—21no—
89#92480—41no—
90#92480—41no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4—21no—
93(C2×D31)⋊C4—21no—
94(C2×D31)⋊C4D411yescharacteristic
95(C2×D31)⋊C4D411yescharacteristic
96C4⋊Dic31—21no—
97C4⋊Dic31—21no—
98C4⋊Dic31—21no—
99C4⋊Dic31—21no—
100C4⋊Dic31D411yescharacteristic
101C4⋊Dic31C2311yescharacteristic
102C4⋊Dic31C2311yescharacteristic
103Dic31⋊C4—21no—
104Dic31⋊C4—21no—
105Dic31⋊C4—21no—
106C4×Dic31—21no—
107C2×C31⋊C8C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109#92469—41no—
110C8×D31—41no—
111C23×C31—21no—
112C23×C31—21no—
113C22×D31C2×D411yescharacteristic
114C22×D31C2×D411yescharacteristic
115D4×C31—21no—
116D4×C31—21no—
117D4×C31—21no—
118D4×C31#4112yes—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—42no—
122C2×C4×C31—81no—
123C2×C4×C31C2×D411yescharacteristic
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31C2411yescharacteristic
126C22⋊D31—42no—
127C22⋊D31—42no—
128C22⋊D31—42no—
129C22⋊D31—81no—
130C2×Dic31—21no—
131C2×Dic31—21no—
132C2×Dic31—21no—
133C2×Dic31—21no—
134C2×Dic31—42no—
135C2×Dic31—42no—
136C2×Dic31C2×D411yescharacteristic
137C2×Dic31C2×D411yescharacteristic
138D124—41no—
139C4×D31—21no—
140C4×D31—21no—
141C4×D31—21no—
142C4×D31—21no—
143C4×D31—81no—
144Dic62—21no—
145Dic62—21no—
146Dic62—21no—
147Dic62—21no—
148C8×C31—21no—
149C8×C31—21no—
150C31⋊C8—21no—
151C31⋊C8—21no—
152#3307—311nomaximal, Sylow
153C22×C31—22no—
154C22×C31—41no—
155C22×C31—41no—
156C22×C31—41no—
157C22×C31—41no—
158C22×C31—41no—
159C22×C31C22×D411yescharacteristic
160C2×D31—21no—
161C2×D31—21no—
162C2×D31—21no—
163C2×D31—21no—
164C2×D31—21no—
165C2×D31—21no—
166C4×C31—21no—
167C4×C31—21no—
168C4×C31—41no—
169C4×C31—41no—
170C4×C31C2×#4111yescharacteristic
171C4×C31H(5,𝔽2)11yescharacteristic
172Dic31—21no—
173Dic31—21no—
174Dic31—41no—
175Dic31—41no—
176Dic31—41no—
177Dic31—41no—
178#553—311no—
179#547—311no—
180#491—311no—
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#442D3111yescharacteristic, complemented
190#435—311no—
191#417—311no—
192#416—311no—
193C2×C31—42no—
194C2×C31—81no—
195C2×C31#54611yescharacteristic
196C2×C31#57511yescharacteristic
197C2×C31#57711yescharacteristic
198D31—41no—
199D31—41no—
200C2×#41—311no—
201C2×#41—311no—
202C2×SD16—311no—
203C2×SD16—311no—
204C2×D8C2×D3111yescharacteristic
205C2×M16—311no—
206C22×C8—311no—
207C4⋊Q8—311no—
208#126—621no—
209#125—311no—
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—621no—
221C4×D4C2×D3111yescharacteristic
222C4×D4C2×D3111yescharacteristic
223#117—311no—
224C2×C4⋊C4—311no—
225C2×C4⋊C4—621no—
226#107—311no—
227#106—311no—
228#106C2×D3111yescharacteristic
229C4⋊C8—311no—
230#103—311no—
231#103—311no—
232#103—311no—
233#103—311no—
234#103—311no—
235#103—311no—
236#102—311no—
237#102—311no—
238#102C2×D3111yescharacteristic
239#102C2×D3111yescharacteristic
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×Q8—311no—
249C2×Q8—311no—
250C2×D4—311no—
251C2×D4—621no—
252C2×D4—621no—
253C2×D4—621no—
254C2×D4—621no—
255C2×D4C22×D3111yescharacteristic
256C2×D4C22×D3111yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—311no—
260C22×C4—311no—
261C22×C4—621no—
262C22×C4—621no—
263C22×C4—621no—
264SD16—1241no—
265SD16—1241no—
266D8—22no—
267M16—1241no—
268C2×C8—311no—
269C2×C8—311no—
270C2×C8—1241no—
271C2×C8C22×D3111yescharacteristic
272C2×C8C22×D3111yescharacteristic
273C4⋊C4—311no—
274C4⋊C4—311no—
275C4⋊C4—311no—
276C4⋊C4—621no—
277C4⋊C4—621no—
278C4⋊C4—621no—
279C4⋊C4—621no—
280C4⋊C4—621no—
281C4⋊C4—621no—
282C4⋊C4—621no—
283C4⋊C4C22×D3111yescharacteristic
284C4⋊C4C22×D3111yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—311no—
288C22⋊C4—311no—
289C22⋊C4—621no—
290C22⋊C4—621no—
291C22⋊C4—621no—
292C22⋊C4—621no—
293C22⋊C4—621no—
294C42—621no—
295C42C22×D3111yescharacteristic
296C23—21no—
297C23—21no—
298C23—311no—
299C23—311no—
300Q8—621no—
301Q8—621no—
302Q8—621no—
303Q8—621no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—1241no—
308D4—1242no—
309D4—1242no—
310D4—1242no—
311D4—2481no—
312D4#9249512yes—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—42no—
316C2×C4—81no—
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—621no—
326C2×C4—621no—
327C2×C4—1242no—
328C2×C4—1242no—
329C2×C4—2481no—
330C2×C4D4×D3111yescharacteristic
331C2×C4D4×D3111yescharacteristic
332C2×C4C23×D3111yescharacteristic
333C8—21no—
334C8—21no—
335C8—621no—
336C8—621no—
337C22—22no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—621no—
344C22—621no—
345C22—621no—
346C22—621no—
347C22—621no—
348C22—621no—
349C22C2×D4×D3111yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—621no—
355C4—621no—
356C4—1241no—
357C4—1241no—
358C4—1241no—
359C4—1241no—
360C4C2×#9249511yescharacteristic
361C4#1175856611yescharacteristic
362C2—42no—
363C2—81no—
364C2—1241no—
365C2—1241no—
366C2#1452169511yescharacteristic
367C2#1452184511yescharacteristic
368C2#1452185911yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#442C2
socleC22×C31C22×D4
hypercenter#442D31
hypocenterC31#3307
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. #14521749C2semidirect
2. #14521703C2semidirect
3. #14521418C2semidirect
4. #14521393C2semidirect
5. #14521381C2semidirect
6. #14521349C2semidirect
7. #14521294C2semidirect
8. #14521277C2semidirect
9. #14521254C2semidirect
10. #14521191C2semidirect
11. #14521191C2semidirect
12. #14521122C2semidirect
13. #14521047C2semidirect
14. #14521042C2semidirect
15. C31×#442C2semidirect
189. #442D31semidirect
243. C31#3307semidirect

Maximal subgroups

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

subgroupindex
#145217492
#145217032
#145214182
#145213932
#145213812
#145213492
#145212942
#145212772
#145212542
#145211912
#145211222
#145210472
#145210422
C31×#4422
#330731