Finite Group Databasebeta

← #16857599

Subgroups — #16857599

Order 3968.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521738C211yesmaximal, characteristic, complemented
2#14521706C211yesmaximal, characteristic
3#14521402C211yesmaximal, characteristic, complemented
4#14521390C211yesmaximal, characteristic, complemented
5#14521361C211yesmaximal, characteristic, complemented
6#14521358C211yesmaximal, characteristic, complemented
7#14521290C211yesmaximal, characteristic, complemented
8#14521277C211yesmaximal, characteristic, complemented
9#14521270C211yesmaximal, characteristic, complemented
10#14521211C211yesmaximal, characteristic, complemented
11#14521206C211yesmaximal, characteristic, complemented
12#14521141C211yesmaximal, 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×#92482C2211yescharacteristic
22#11758515—21no—
23#11758515C2211yescharacteristic
24#11758513—21no—
25#11758513C2211yescharacteristic
26C2×#92480C2211yescharacteristic
27C4×C22⋊D31—21no—
28C4×C22⋊D31C2211yescharacteristic
29#11758501—21no—
30#11758501C2211yescharacteristic
31#11758501C2211yescharacteristic
32C2×Dic124C2211yescharacteristic
33C2×C8×D31C2211yescharacteristic
34#11758474C2211yescharacteristic
35C4⋊C4×D31C2211yescharacteristic
36#11758467C2211yescharacteristic
37#11758464C2211yescharacteristic
38#11758460—21no—
39#11758456—21no—
40#11758449—21no—
41#11758447—21no—
42C31×#103C2211yescharacteristic
43C31×#103C2211yescharacteristic
44C31×#102C2211yescharacteristic
45C31×#102C2211yescharacteristic
46#11758423C2211yescharacteristic
47#11758420C2211yescharacteristic
48C22⋊(C31⋊C8)C2211yescharacteristic
49(C2×D31)⋊C8C2211yescharacteristic
50#11758406C2211yescharacteristic
51#11758404C2211yescharacteristic
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⋊D31D411yescharacteristic
68Q8×D31—22no—
69Q8×D31—41no—
70C2×C4×D31—21no—
71C2×C4×D31—21no—
72C2×C4×D31C2311yescharacteristic
73C2×Dic62—21no—
74C2×Dic62C2311yescharacteristic
75C2×Dic62C2311yescharacteristic
76C2×C8×C31—41no—
77C2×C8×C31C2311yescharacteristic
78C2×C8×C31C2311yescharacteristic
79C4⋊C4×C31C2311yescharacteristic
80C4⋊C4×C31C2311yescharacteristic
81C22⋊C4×C31—21no—
82C42×C31—21no—
83C22⋊Dic31—21no—
84C22⋊Dic31—21no—
85C22⋊Dic31—21no—
86C22⋊Dic31—21no—
87C22⋊Dic31—21no—
88C22⋊Dic31D411yescharacteristic
89#92482—22no—
90#92480—41no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4D411yescharacteristic
93C4⋊Dic31—21no—
94C4⋊Dic31—21no—
95C4⋊Dic31—21no—
96C4⋊Dic31C2311yescharacteristic
97C4⋊Dic31C2311yescharacteristic
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101Dic31⋊C4—21no—
102Dic31⋊C4—21no—
103Dic31⋊C4D411yescharacteristic
104C4×Dic31—21no—
105C4×Dic31—21no—
106C4×Dic31C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109Dic124—41no—
110C8×D31—41no—
111C23×C31—21no—
112C23×C31C2×D411yescharacteristic
113C22×D31C2×D411yescharacteristic
114Q8×C31—21no—
115Q8×C31#4112yes—
116D4×C31—21no—
117D4×C31—21no—
118D4×C31—42no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—42no—
125C2×C4×C31C2×D411yescharacteristic
126C2×C4×C31C2411yescharacteristic
127C22⋊D31—22no—
128C22⋊D31—42no—
129C2×Dic31—21no—
130C2×Dic31—21no—
131C2×Dic31—21no—
132C2×Dic31—21no—
133C2×Dic31C2×D411yescharacteristic
134C2×Dic31C2×D411yescharacteristic
135C2×Dic31C2×D411yescharacteristic
136C4×D31—21no—
137C4×D31—21no—
138C4×D31—42no—
139C4×D31—42no—
140Dic62—21no—
141Dic62—21no—
142Dic62—21no—
143Dic62—21no—
144Dic62—42no—
145C8×C31—21no—
146C8×C31—21no—
147C31⋊C8—21no—
148C31⋊C8—21no—
149#3300—311nomaximal, Sylow
150C22×C31—21no—
151C22×C31—21no—
152C22×C31—21no—
153C22×C31—41no—
154C22×C31—41no—
155C22×C31—41no—
156C22×C31C22×D411yescharacteristic
157C2×D31—21no—
158C2×D31—21no—
159C2×D31#13512yes—
160C4×C31—22no—
161C4×C31—21no—
162C4×C31—41no—
163C4×C31—41no—
164C4×C31C2×#4111yescharacteristic
165C4×C31H(5,𝔽2)11yescharacteristic
166Dic31—21no—
167Dic31—21no—
168Dic31—21no—
169Dic31—41no—
170Dic31—41no—
171Dic31—41no—
172Dic31—41no—
173#552—311no—
174#548—311no—
175#488—311no—
176#485—311no—
177#480—311no—
178#479—311no—
179#467—311no—
180#465—311no—
181#464—311no—
182#452—311no—
183#451—311no—
184C4×Q16—311no—
185C8×D4—311no—
186#416D3111yescharacteristic, complemented
187C2×#103—311no—
188C2×C31—41no—
189C2×C31—81no—
190C2×C31#54611yescharacteristic
191C2×C31C2×#13511yescharacteristic
192C2×C31#57811yescharacteristic
193D31—22no—
194C2×#41C2×D3111yescharacteristic
195C22×Q8—311no—
196C2×Q16—311no—
197C2×Q16—311no—
198C2×SD16—311no—
199C22×C8—311no—
200C22×C8C2×D3111yescharacteristic
201#126—621no—
202#125—311no—
203#125—621no—
204#124—311no—
205#124—621no—
206#123—621no—
207C22⋊Q8—311no—
208C22⋊Q8—311no—
209C22⋊Q8—311no—
210C22⋊Q8—621no—
211#121—311no—
212#121—621no—
213C4×Q8—311no—
214C4×Q8—311no—
215C4×D4—311no—
216C4×D4—621no—
217#117—621no—
218#117C2×D3111yescharacteristic
219C2×C4⋊C4—311no—
220#107—311no—
221#107—311no—
222#106—311no—
223C4⋊C8—311no—
224#103—311no—
225#103—311no—
226#103—311no—
227#103—311no—
228#103—311no—
229#103C2×D3111yescharacteristic
230#103C2×D3111yescharacteristic
231#102—311no—
232#102C2×D3111yescharacteristic
233#102C2×D3111yescharacteristic
234C22⋊C8—311no—
235C22⋊C8—311no—
236C4×C8—311no—
237C31#330011yescharacteristic, complemented, Sylow
238#41—22no—
239#41—41no—
240C2×Q8—311no—
241C2×Q8—311no—
242C2×Q8—621no—
243C2×Q8—622no—
244C2×Q8—1241no—
245C2×Q8C22×D3111yescharacteristic
246C2×D4—21no—
247C2×D4—311no—
248C2×D4—621no—
249C2×D4C22×D3111yescharacteristic
250C22×C4—21no—
251C22×C4—311no—
252C22×C4—621no—
253C22×C4—621no—
254C22×C4C22×D3111yescharacteristic
255Q16—622no—
256Q16—1241no—
257SD16—1241no—
258C2×C8—41no—
259C2×C8—311no—
260C2×C8—311no—
261C2×C8—1241no—
262C2×C8C22×D3111yescharacteristic
263C2×C8C22×D3111yescharacteristic
264C4⋊C4—311no—
265C4⋊C4—311no—
266C4⋊C4—311no—
267C4⋊C4—621no—
268C4⋊C4—621no—
269C4⋊C4—621no—
270C4⋊C4—621no—
271C4⋊C4—621no—
272C4⋊C4—621no—
273C4⋊C4—621no—
274C4⋊C4—621no—
275C4⋊C4C22×D3111yescharacteristic
276C4⋊C4C22×D3111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—311no—
279C22⋊C4—311no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C22⋊C4—621no—
284C22⋊C4—621no—
285C22⋊C4—621no—
286C42—21no—
287C42—311no—
288C42—621no—
289C42—621no—
290C23—21no—
291C23—311no—
292C23D4×D3111yescharacteristic
293Q8—21no—
294Q8—621no—
295Q8—621no—
296Q8—621no—
297Q8—621no—
298Q8—1242no—
299Q8#9249512yes—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—622no—
304D4—1242no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—311no—
312C2×C4—311no—
313C2×C4—311no—
314C2×C4—621no—
315C2×C4—621no—
316C2×C4—621no—
317C2×C4—621no—
318C2×C4—621no—
319C2×C4—621no—
320C2×C4—1242no—
321C2×C4—1242no—
322C2×C4D4×D3111yescharacteristic
323C2×C4C23×D3111yescharacteristic
324C8—21no—
325C8—21no—
326C8—621no—
327C8—621no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—312no—
335C22—621no—
336C22—621no—
337C22C2×D4×D3111yescharacteristic
338C4—21no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—621no—
343C4—621no—
344C4—621no—
345C4—1241no—
346C4—1241no—
347C4—1241no—
348C4—1241no—
349C4C2×#9249511yescharacteristic
350C4#1175856111yescharacteristic
351C2—41no—
352C2—81no—
353C2—622no—
354C2#1452168911yescharacteristic
355C2#135×D3111yescharacteristic
356C2#1452186311yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#416C2
socleC22×C31C22×D4
prime radical#14521706C2
hypercenter#416D31
hypocenterC31#3300
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. #14521738C2semidirect
3. #14521402C2semidirect
4. #14521390C2semidirect
5. #14521361C2semidirect
6. #14521358C2semidirect
7. #14521290C2semidirect
8. #14521277C2semidirect
9. #14521270C2semidirect
10. #14521211C2semidirect
11. #14521206C2semidirect
12. #14521141C2semidirect
13. C8×C22⋊D31C2semidirect
14. #103×D31C2semidirect
15. C31×#416C2semidirect
186. #416D31semidirect
237. C31#3300semidirect

Maximal subgroups

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

subgroupindex
#145217382
#145217062
#145214022
#145213902
#145213612
#145213582
#145212902
#145212772
#145212702
#145212112
#145212062
#145211412
C8×C22⋊D312
#103×D312
C31×#4162
#330031