Finite Group Databasebeta

← #16857605

Subgroups — #16857605

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#14521740C211yesmaximal, characteristic, complemented
2#14521707C211yesmaximal, characteristic
3#14521403C211yesmaximal, characteristic, complemented
4#14521388C211yesmaximal, characteristic, complemented
5#14521361C211yesmaximal, characteristic, complemented
6#14521357C211yesmaximal, characteristic, complemented
7#14521287C211yesmaximal, characteristic, complemented
8#14521275C211yesmaximal, characteristic, complemented
9#14521208C211yesmaximal, characteristic, complemented
10#14521203C211yesmaximal, characteristic, complemented
11C4×#92482C211yesmaximal, characteristic, complemented
12#14521114C211yesmaximal, characteristic, complemented
13#14521042C211yesmaximal, characteristic, complemented
14#103×D31C211yesmaximal, characteristic, complemented
15C31×#464C211yesmaximal, characteristic, complemented
16C2×Q8×D31C2211yescharacteristic
17C2×#92497C2211yescharacteristic
18C2×Q16×C31C2211yescharacteristic
19C2×SD16×C31C2211yescharacteristic
20C31×#124C2211yescharacteristic
21C4×Q8×C31C2211yescharacteristic
22#11758523C2211yescharacteristic
23#11758523C2211yescharacteristic
24#11758523C2211yescharacteristic
25C2×#92482C2211yescharacteristic
26#11758515C2211yescharacteristic
27C2×C8×D31C2211yescharacteristic
28C2×C8×D31C2211yescharacteristic
29#11758471—21no—
30#11758469C2211yescharacteristic
31C4⋊C4×D31C2211yescharacteristic
32#11758466—21no—
33#11758462—21no—
34#11758461—21no—
35(C22⋊D31)⋊C4—21no—
36#11758455—21no—
37#11758453—21no—
38C4×D124C2211yescharacteristic
39#11758449—21no—
40#11758447C2211yescharacteristic
41C4×Dic62C2211yescharacteristic
42C31×C4⋊C8C2211yescharacteristic
43C31×#103C2211yescharacteristic
44C31×#102C2211yescharacteristic
45#11758423C2211yescharacteristic
46#11758423C2211yescharacteristic
47#11758423C2211yescharacteristic
48#11758420C2211yescharacteristic
49#11758420C2211yescharacteristic
50(C2×D31)⋊C8C2211yescharacteristic
51(C2×D31)⋊C8C2211yescharacteristic
52#11758406C2211yescharacteristic
53#11758405C2211yescharacteristic
54#11758404C2211yescharacteristic
55#11758404C2211yescharacteristic
56#11758398C2211yescharacteristic
57#11758395C2211yescharacteristic
58C4×C31⋊C8C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C2×Q8×C31C2311yescharacteristic
61C2×D4×C31C2311yescharacteristic
62C2×C22⋊D31—21no—
63C2×C22⋊D31—21no—
64C22×Dic31—21no—
65Q8×D31—22no—
66Q8×D31—41no—
67#92497—22no—
68#92497—41no—
69C2×D124D411yescharacteristic
70C2×C4×D31—21no—
71C2×C4×D31—21no—
72C2×C4×D31C2311yescharacteristic
73C2×C4×D31C2311yescharacteristic
74C2×Dic62—21no—
75C2×Dic62C2311yescharacteristic
76Q16×C31—41no—
77SD16×C31—41no—
78C2×C8×C31C2311yescharacteristic
79C2×C8×C31C2311yescharacteristic
80C4⋊C4×C31—21no—
81C4⋊C4×C31C2311yescharacteristic
82C22⋊C4×C31—21no—
83C22⋊C4×C31—21no—
84C42×C31—21no—
85C42×C31C2311yescharacteristic
86C22⋊Dic31—21no—
87#92482—22no—
88(C2×D31)⋊C4—21no—
89(C2×D31)⋊C4—21no—
90(C2×D31)⋊C4—21no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4D411yescharacteristic
93(C2×D31)⋊C4D411yescharacteristic
94C4⋊Dic31D411yescharacteristic
95C4⋊Dic31C2311yescharacteristic
96C4⋊Dic31C2311yescharacteristic
97C4⋊Dic31C2311yescharacteristic
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101Dic31⋊C4—21no—
102Dic31⋊C4—21no—
103Dic31⋊C4—21no—
104Dic31⋊C4—21no—
105C4×Dic31—21no—
106C4×Dic31—21no—
107C2×C31⋊C8C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109C8×D31—41no—
110C8×D31—41no—
111C23×C31—21no—
112C22×D31C2×D411yescharacteristic
113C22×D31C2×D411yescharacteristic
114Q8×C31—21no—
115Q8×C31—21no—
116Q8×C31—21no—
117Q8×C31—21no—
118D4×C31—21no—
119D4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31C2×D411yescharacteristic
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31C2411yescharacteristic
126C22⋊D31—42no—
127C22⋊D31—42no—
128C2×Dic31—21no—
129C2×Dic31—21no—
130C2×Dic31—21no—
131C2×Dic31—21no—
132C2×Dic31—42no—
133C2×Dic31C2×D411yescharacteristic
134C2×Dic31C2×D411yescharacteristic
135D124—22no—
136C4×D31—21no—
137C4×D31—21no—
138C4×D31—21no—
139C4×D31—21no—
140C4×D31—42no—
141C4×D31—42no—
142Dic62—21no—
143Dic62—42no—
144Dic62#4112yes—
145C8×C31—21no—
146C8×C31—21no—
147C31⋊C8—21no—
148C31⋊C8—21no—
149#3300—311nomaximal, Sylow
150C22×C31—41no—
151C22×C31—41no—
152C22×C31—41no—
153C22×C31C22×D411yescharacteristic
154C2×D31—21no—
155C2×D31—21no—
156C2×D31—21no—
157C2×D31—21no—
158C2×D31—21no—
159C2×D31#13512yes—
160C4×C31—21no—
161C4×C31—21no—
162C4×C31—41no—
163C4×C31—41no—
164C4×C31—41no—
165C4×C31C2×#4111yescharacteristic
166C4×C31H(5,𝔽2)11yescharacteristic
167Dic31—22no—
168Dic31—21no—
169Dic31—21no—
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#464D3111yescharacteristic, complemented
182#452—311no—
183#451—311no—
184C4×Q16—311no—
185C8×D4—311no—
186#416—311no—
187C2×#103—311no—
188C2×C31—81no—
189C2×C31#54611yescharacteristic
190C2×C31C2×#13511yescharacteristic
191C2×C31#57811yescharacteristic
192D31—22no—
193D31—41no—
194C2×#41—311no—
195C22×Q8—311no—
196C2×Q16—311no—
197C2×Q16C2×D3111yescharacteristic
198C2×SD16C2×D3111yescharacteristic
199C22×C8—311no—
200C22×C8—311no—
201#126—621no—
202#125—311no—
203#125—621no—
204#124—621no—
205#124C2×D3111yescharacteristic
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×Q8C2×D3111yescharacteristic
215C4×D4—311no—
216C4×D4—621no—
217#117—311no—
218#117—621no—
219C2×C4⋊C4—311no—
220#107—311no—
221#107—311no—
222#106—311no—
223C4⋊C8C2×D3111yescharacteristic
224#103—311no—
225#103—311no—
226#103—311no—
227#103—311no—
228#103—311no—
229#103—311no—
230#103C2×D3111yescharacteristic
231#102—311no—
232#102—311no—
233#102C2×D3111yescharacteristic
234C22⋊C8—311no—
235C22⋊C8—311no—
236C4×C8—311no—
237C31#330011yescharacteristic, complemented, Sylow
238#41—622no—
239#41—1241no—
240C2×Q8—311no—
241C2×Q8—621no—
242C2×Q8—622no—
243C2×Q8—1241no—
244C2×Q8C22×D3111yescharacteristic
245C2×Q8C22×D3111yescharacteristic
246C2×D4—311no—
247C2×D4—621no—
248C2×D4—621no—
249C2×D4C22×D3111yescharacteristic
250C22×C4—311no—
251C22×C4—311no—
252C22×C4—621no—
253C22×C4—621no—
254C22×C4—621no—
255Q16—41no—
256Q16—622no—
257SD16—41no—
258C2×C8—311no—
259C2×C8—311no—
260C2×C8—1241no—
261C2×C8—1241no—
262C2×C8C22×D3111yescharacteristic
263C2×C8C22×D3111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—311no—
266C4⋊C4—311no—
267C4⋊C4—311no—
268C4⋊C4—311no—
269C4⋊C4—621no—
270C4⋊C4—621no—
271C4⋊C4—621no—
272C4⋊C4—621no—
273C4⋊C4—621no—
274C4⋊C4—621no—
275C4⋊C4—621no—
276C4⋊C4C22×D3111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—311no—
280C22⋊C4—311no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C22⋊C4—621no—
284C22⋊C4—621no—
285C22⋊C4—621no—
286C42—21no—
287C42—621no—
288C42—621no—
289C42C22×D3111yescharacteristic
290C23—21no—
291C23—311no—
292C23—311no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—312no—
298Q8—621no—
299Q8—1242no—
300D4—21no—
301D4—21no—
302D4—622no—
303D4—1242no—
304D4—1242no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—311no—
309C2×C4—311no—
310C2×C4—621no—
311C2×C4—621no—
312C2×C4—621no—
313C2×C4—621no—
314C2×C4—621no—
315C2×C4—621no—
316C2×C4—621no—
317C2×C4—621no—
318C2×C4—1242no—
319C2×C4—1242no—
320C2×C4—1242no—
321C2×C4D4×D3111yescharacteristic
322C2×C4D4×D3111yescharacteristic
323C2×C4C23×D3111yescharacteristic
324C8—21no—
325C8—21no—
326C8—621no—
327C8—621no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—312no—
332C22—621no—
333C22—621no—
334C22—621no—
335C22—621no—
336C22—621no—
337C22C2×D4×D3111yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—621no—
344C4—621no—
345C4—622no—
346C4—1241no—
347C4—1241no—
348C4—1241no—
349C4#1175856111yescharacteristic
350C4#41×D3111yescharacteristic
351C2—81no—
352C2—622no—
353C2—1241no—
354C2#1452169611yescharacteristic
355C2#135×D3111yescharacteristic
356C2#1452186511yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#464C2
socleC22×C31C22×D4
prime radical#14521707C2
hypercenter#464D31
hypocenterC31#3300
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #14521740C2semidirect
3. #14521403C2semidirect
4. #14521388C2semidirect
5. #14521361C2semidirect
6. #14521357C2semidirect
7. #14521287C2semidirect
8. #14521275C2semidirect
9. #14521208C2semidirect
10. #14521203C2semidirect
11. C4×#92482C2semidirect
12. #14521114C2semidirect
13. #14521042C2semidirect
14. #103×D31C2semidirect
15. C31×#464C2semidirect
181. #464D31semidirect
237. C31#3300semidirect

Maximal subgroups

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

subgroupindex
#145217402
#145217072
#145214032
#145213882
#145213612
#145213572
#145212872
#145212752
#145212082
#145212032
C4×#924822
#145211142
#145210422
#103×D312
C31×#4642
#330031