Finite Group Databasebeta

← #16857614

Subgroups — #16857614

Order 3968.

398 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#14521743C211yesmaximal, characteristic, complemented
2#14521706C211yesmaximal, characteristic, complemented
3#14521402C211yesmaximal, characteristic, complemented
4#14521390C211yesmaximal, characteristic, complemented
5#14521366C211yesmaximal, characteristic, complemented
6#14521354C211yesmaximal, characteristic, complemented
7#14521284C211yesmaximal, characteristic, complemented
8#14521278C211yesmaximal, characteristic, complemented
9#14521263C211yesmaximal, characteristic, complemented
10#14521194C211yesmaximal, characteristic, complemented
11#14521189C211yesmaximal, characteristic, complemented
12#14521134C211yesmaximal, characteristic, complemented
13C8×C22⋊D31C211yesmaximal, characteristic, complemented
14#103×D31C211yesmaximal, characteristic, complemented
15C31×#416C211yesmaximal, characteristic, complemented
16C2×#41×C31C2211yescharacteristic
17C2×Q8×D31C2211yescharacteristic
18C22×C8×C31C2211yescharacteristic
19C31×#117C2211yescharacteristic
20Q8×Dic31C2211yescharacteristic
21C2×#92481C2211yescharacteristic
22#11758515—21no—
23#11758515C2211yescharacteristic
24#11758513—21no—
25#11758513C2211yescharacteristic
26C2×#92479C2211yescharacteristic
27#11758507C2211yescharacteristic
28C4×C22⋊D31—21no—
29C4×C22⋊D31C2211yescharacteristic
30#11758501—21no—
31#11758501C2211yescharacteristic
32C2×#92470C2211yescharacteristic
33C2×C8×D31C2211yescharacteristic
34#11758472C2211yescharacteristic
35#11758470C2211yescharacteristic
36C4⋊C4×D31C2211yescharacteristic
37#11758467C2211yescharacteristic
38#11758461—21no—
39#11758460—21no—
40#11758453—21no—
41C4×D124—21no—
42C31×#103C2211yescharacteristic
43C31×#103C2211yescharacteristic
44C31×#102C2211yescharacteristic
45C31×#102C2211yescharacteristic
46#11758423C2211yescharacteristic
47#11758420C2211yescharacteristic
48C22⋊(C31⋊C8)C2211yescharacteristic
49#11758409C2211yescharacteristic
50(C2×D31)⋊C8C2211yescharacteristic
51#11758405C2211yescharacteristic
52#11758404C2211yescharacteristic
53Dic31⋊C8C2211yescharacteristic
54C8×Dic31C2211yescharacteristic
55#11758398C2211yescharacteristic
56#11758398C2211yescharacteristic
57#11758396C2211yescharacteristic
58#11758395C2211yescharacteristic
59#41×C31—22no—
60#41×C31—41no—
61C2×Q8×C31C2311yescharacteristic
62C2×D4×C31—21no—
63C2×D4×C31C2311yescharacteristic
64C22×C4×C31—21no—
65C22×C4×C31C2311yescharacteristic
66C2×C22⋊D31—21no—
67C2×C22⋊D31—21no—
68C2×C22⋊D31D411yescharacteristic
69Q8×D31—22no—
70Q8×D31—41no—
71C2×D124—21no—
72C2×D124C2311yescharacteristic
73C2×C4×D31—21no—
74C2×C4×D31—21no—
75C2×C4×D31—21no—
76C2×C4×D31C2311yescharacteristic
77C2×Dic62—21no—
78C2×Dic62C2311yescharacteristic
79C2×C8×C31—41no—
80C2×C8×C31C2311yescharacteristic
81C2×C8×C31C2311yescharacteristic
82C4⋊C4×C31C2311yescharacteristic
83C4⋊C4×C31C2311yescharacteristic
84C22⋊C4×C31—21no—
85C42×C31—21no—
86C22⋊Dic31—21no—
87C22⋊Dic31—21no—
88C22⋊Dic31—21no—
89C22⋊Dic31—21no—
90C22⋊Dic31D411yescharacteristic
91#92481—22no—
92#92479—41no—
93(C2×D31)⋊C4—21no—
94(C2×D31)⋊C4—21no—
95(C2×D31)⋊C4—21no—
96(C2×D31)⋊C4D411yescharacteristic
97C4⋊Dic31—21no—
98C4⋊Dic31—21no—
99C4⋊Dic31C2311yescharacteristic
100C4⋊Dic31C2311yescharacteristic
101Dic31⋊C4—21no—
102Dic31⋊C4—21no—
103Dic31⋊C4—21no—
104Dic31⋊C4D411yescharacteristic
105C4×Dic31—21no—
106C4×Dic31C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109#92470—41no—
110C8×D31—41no—
111C23×C31—21no—
112C23×C31C2×D411yescharacteristic
113C22×D31—21no—
114C22×D31C2×D411yescharacteristic
115Q8×C31—21no—
116Q8×C31#4112yes—
117D4×C31—21no—
118D4×C31—21no—
119D4×C31—42no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—42no—
126C2×C4×C31C2×D411yescharacteristic
127C2×C4×C31C2411yescharacteristic
128C22⋊D31—22no—
129C22⋊D31—42no—
130C22⋊D31—81no—
131C2×Dic31—21no—
132C2×Dic31—21no—
133C2×Dic31—21no—
134C2×Dic31C2×D411yescharacteristic
135C2×Dic31C2×D411yescharacteristic
136C2×Dic31C2×D411yescharacteristic
137D124—21no—
138D124—21no—
139D124—42no—
140C4×D31—21no—
141C4×D31—21no—
142C4×D31—42no—
143C4×D31—81no—
144C4×D31—81no—
145Dic62—21no—
146Dic62—21no—
147Dic62—42no—
148C8×C31—21no—
149C8×C31—21no—
150C31⋊C8—21no—
151C31⋊C8—21no—
152#3301—311nomaximal, Sylow
153C22×C31—21no—
154C22×C31—21no—
155C22×C31—21no—
156C22×C31—41no—
157C22×C31—41no—
158C22×C31—41no—
159C22×C31C22×D411yescharacteristic
160C2×D31—21no—
161C2×D31—21no—
162C2×D31—41no—
163C2×D31—41no—
164C2×D31—41no—
165C2×D31#13512yes—
166C4×C31—22no—
167C4×C31—21no—
168C4×C31—41no—
169C4×C31—41no—
170C4×C31C2×#4111yescharacteristic
171C4×C31H(5,𝔽2)11yescharacteristic
172Dic31—21no—
173Dic31—21no—
174Dic31—21no—
175Dic31—41no—
176Dic31—41no—
177Dic31—41no—
178#553—311no—
179#548—311no—
180#488—311no—
181#485—311no—
182#481—311no—
183#479—311no—
184#466—311no—
185#465—311no—
186#463—311no—
187#449—311no—
188#448—311no—
189C4×SD16—311no—
190C8×D4—311no—
191#416D3111yescharacteristic, complemented
192C2×#103—311no—
193C2×C31—41no—
194C2×C31—81no—
195C2×C31#54611yescharacteristic
196C2×C31C2×#13511yescharacteristic
197C2×C31#57711yescharacteristic
198D31—22no—
199D31—81no—
200C2×#41C2×D3111yescharacteristic
201C22×Q8—311no—
202C2×SD16—311no—
203C2×SD16—311no—
204C2×D8—311no—
205C22×C8—311no—
206C22×C8C2×D3111yescharacteristic
207#126—621no—
208#125—311no—
209#124—311no—
210#124—621no—
211#123—621no—
212C22⋊Q8—311no—
213C22⋊Q8—621no—
214#121—311no—
215#121—311no—
216#121—311no—
217#121—621no—
218#121—621no—
219C4×Q8—311no—
220C4×D4—311no—
221C4×D4—311no—
222C4×D4—621no—
223C4×D4—621no—
224#117C2×D3111yescharacteristic
225C2×C4⋊C4—311no—
226#107—311no—
227#106—311no—
228#106—311no—
229C4⋊C8—311no—
230#103—311no—
231#103—311no—
232#103—311no—
233#103—311no—
234#103C2×D3111yescharacteristic
235#103C2×D3111yescharacteristic
236#102—311no—
237#102—311no—
238#102C2×D3111yescharacteristic
239#102C2×D3111yescharacteristic
240C22⋊C8—311no—
241C22⋊C8—311no—
242C4×C8—311no—
243C31#330111yescharacteristic, complemented, Sylow
244#41—22no—
245#41—41no—
246C2×Q8—311no—
247C2×Q8—621no—
248C2×Q8—622no—
249C2×Q8—1241no—
250C2×Q8C22×D3111yescharacteristic
251C2×D4—21no—
252C2×D4—311no—
253C2×D4—311no—
254C2×D4—621no—
255C2×D4—621no—
256C2×D4—621no—
257C2×D4C22×D3111yescharacteristic
258C22×C4—21no—
259C22×C4—311no—
260C22×C4—621no—
261C22×C4—621no—
262C22×C4—621no—
263C22×C4C22×D3111yescharacteristic
264SD16—622no—
265SD16—1241no—
266D8—1241no—
267C2×C8—41no—
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⋊C4C22×D3111yescharacteristic
282C4⋊C4C22×D3111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—311no—
285C22⋊C4—311no—
286C22⋊C4—621no—
287C22⋊C4—621no—
288C22⋊C4—621no—
289C22⋊C4—621no—
290C22⋊C4—621no—
291C22⋊C4—621no—
292C22⋊C4—621no—
293C42—21no—
294C42—311no—
295C42—621no—
296C23—21no—
297C23—311no—
298C23—621no—
299C23D4×D3111yescharacteristic
300Q8—21no—
301Q8—621no—
302Q8—621no—
303Q8—1242no—
304Q8#9249512yes—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—622no—
309D4—621no—
310D4—621no—
311D4—1242no—
312D4—1242no—
313D4—2481no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—311no—
321C2×C4—311no—
322C2×C4—311no—
323C2×C4—621no—
324C2×C4—621no—
325C2×C4—621no—
326C2×C4—621no—
327C2×C4—621no—
328C2×C4—1242no—
329C2×C4—2481no—
330C2×C4—2481no—
331C2×C4D4×D3111yescharacteristic
332C2×C4C23×D3111yescharacteristic
333C8—21no—
334C8—21no—
335C8—621no—
336C8—621no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—312no—
344C22—621no—
345C22—621no—
346C22—1241no—
347C22—1241no—
348C22—1241no—
349C22C2×D4×D3111yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—621no—
355C4—621no—
356C4—621no—
357C4—1241no—
358C4—1241no—
359C4—1241no—
360C4C2×#9249511yescharacteristic
361C4#1175856111yescharacteristic
362C2—41no—
363C2—81no—
364C2—622no—
365C2—2481no—
366C2#1452168911yescharacteristic
367C2#135×D3111yescharacteristic
368C2#1452185611yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#416C2
socleC22×C31C22×D4
hypercenter#416D31
hypocenterC31#3301
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #14521743C2semidirect
2. #14521706C2semidirect
3. #14521402C2semidirect
4. #14521390C2semidirect
5. #14521366C2semidirect
6. #14521354C2semidirect
7. #14521284C2semidirect
8. #14521278C2semidirect
9. #14521263C2semidirect
10. #14521194C2semidirect
11. #14521189C2semidirect
12. #14521134C2semidirect
13. C8×C22⋊D31C2semidirect
14. #103×D31C2semidirect
15. C31×#416C2semidirect
191. #416D31semidirect
243. C31#3301semidirect

Maximal subgroups

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

subgroupindex
#145217432
#145217062
#145214022
#145213902
#145213662
#145213542
#145212842
#145212782
#145212632
#145211942
#145211892
#145211342
C8×C22⋊D312
#103×D312
C31×#4162
#330131