Finite Group Databasebeta

← #16858776

Subgroups — #16858776

Order 3968.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521781C211yesmaximal, characteristic, complemented
2#14521773C211yesmaximal, characteristic, complemented
3#14521435C211yesmaximal, characteristic
4#14521434C211yesmaximal, characteristic, complemented
5#14521273C211yesmaximal, characteristic, complemented
6#14521273C211yesmaximal, characteristic, complemented
7#14521266C211yesmaximal, characteristic, complemented
8#14521261C211yesmaximal, characteristic, complemented
9#14521251C211yesmaximal, characteristic, complemented
10#14521247C211yesmaximal, characteristic, complemented
11#14521177C211yesmaximal, characteristic, complemented
12#14521162C211yesmaximal, characteristic, complemented
13#14521156C211yesmaximal, characteristic, complemented
14SD16×Dic31C211yesmaximal, characteristic, complemented
15C31×#497C211yesmaximal, characteristic, complemented
16C2×Q16×C31C2211yescharacteristic
17C2×Q16×C31C2211yescharacteristic
18C2×SD16×C31C2211yescharacteristic
19C2×SD16×C31C2211yescharacteristic
20C31×C4⋊Q8C2211yescharacteristic
21C31×#124C2211yescharacteristic
22#11758524C2211yescharacteristic
23#11758524C2211yescharacteristic
24#11758524C2211yescharacteristic
25Q8×Dic31C2211yescharacteristic
26Q8×Dic31C2211yescharacteristic
27Q8×Dic31C2211yescharacteristic
28C2×#92481C2211yescharacteristic
29C2×#92481C2211yescharacteristic
30C2×#92481C2211yescharacteristic
31#11758517C2211yescharacteristic
32D4×Dic31C2211yescharacteristic
33C2×#92479C2211yescharacteristic
34C2×D248C2211yescharacteristic
35#11758475—21no—
36#11758475—21no—
37#11758474—21no—
38#11758469—21no—
39#11758463—21no—
40#11758462—21no—
41#11758460—21no—
42(C22⋊D31)⋊C4—21no—
43C4×D124C2211yescharacteristic
44C4×D124C2211yescharacteristic
45C4×Dic62C2211yescharacteristic
46C31×#97C2211yescharacteristic
47#11758423C2211yescharacteristic
48#11758423C2211yescharacteristic
49#11758423C2211yescharacteristic
50#11758420C2211yescharacteristic
51#11758409C2211yescharacteristic
52#11758409C2211yescharacteristic
53#11758405C2211yescharacteristic
54#11758403C2211yescharacteristic
55Dic31⋊C8C2211yescharacteristic
56Dic31⋊C8C2211yescharacteristic
57C8×Dic31C2211yescharacteristic
58C4⋊(C31⋊C8)C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C2×Q8×C31C2311yescharacteristic
61C2×Q8×C31C2311yescharacteristic
62C2×D4×C31C2311yescharacteristic
63C2×C22⋊D31—21no—
64C2×C22⋊D31—21no—
65C22×Dic31—21no—
66C2×D124C2311yescharacteristic
67C2×D124C2311yescharacteristic
68C2×C4×D31—21no—
69C2×C4×D31—21no—
70C2×Dic62D411yescharacteristic
71Q16×C31—22no—
72Q16×C31—41no—
73SD16×C31—22no—
74SD16×C31—41no—
75C2×C8×C31C2311yescharacteristic
76C2×C8×C31C2311yescharacteristic
77C4⋊C4×C31—21no—
78C4⋊C4×C31—21no—
79C22⋊C4×C31—21no—
80C22⋊C4×C31—21no—
81C42×C31C2311yescharacteristic
82C22⋊Dic31—21no—
83#92481—41no—
84#92481—41no—
85#92481—41no—
86#92479—41no—
87(C2×D31)⋊C4—21no—
88(C2×D31)⋊C4—21no—
89(C2×D31)⋊C4—21no—
90(C2×D31)⋊C4—21no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4—21no—
93(C2×D31)⋊C4—21no—
94(C2×D31)⋊C4—21no—
95C4⋊Dic31—21no—
96C4⋊Dic31—21no—
97C4⋊Dic31—21no—
98C4⋊Dic31D411yescharacteristic
99C4⋊Dic31C2311yescharacteristic
100C4⋊Dic31C2311yescharacteristic
101Dic31⋊C4D411yescharacteristic
102Dic31⋊C4D411yescharacteristic
103C4×Dic31—21no—
104C4×Dic31—21no—
105C4×Dic31—21no—
106C4×Dic31C2311yescharacteristic
107C4×Dic31C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110D248—22no—
111C23×C31—21no—
112C22×D31—21no—
113C22×D31—21no—
114Q8×C31—21no—
115Q8×C31—21no—
116Q8×C31—21no—
117Q8×C31—21no—
118Q8×C31—21no—
119Q8×C31—21no—
120D4×C31—21no—
121D4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31C2×D411yescharacteristic
126C2×C4×C31C2×D411yescharacteristic
127C2×C4×C31C2411yescharacteristic
128C22⋊D31—42no—
129C22⋊D31—81no—
130C2×Dic31—21no—
131C2×Dic31—21no—
132C2×Dic31—81no—
133C2×Dic31C2×D411yescharacteristic
134C2×Dic31C2×D411yescharacteristic
135C2×Dic31C2×D411yescharacteristic
136C2×Dic31C2×D411yescharacteristic
137D124—21no—
138D124—21no—
139D124—21no—
140D124—21no—
141C4×D31—42no—
142C4×D31—81no—
143Dic62—41no—
144C8×C31—21no—
145C8×C31#4112yes—
146C31⋊C8—21no—
147C31⋊C8—21no—
148#3401—311nomaximal, Sylow
149C22×C31—41no—
150C22×C31—41no—
151C22×C31—41no—
152C22×C31C22×D411yescharacteristic
153C2×D31—41no—
154C2×D31—41no—
155C2×D31—41no—
156C2×D31—41no—
157C2×D31—41no—
158C2×D31—41no—
159C4×C31—21no—
160C4×C31—21no—
161C4×C31—41no—
162C4×C31—41no—
163C4×C31—41no—
164C4×C31C2×#4111yescharacteristic
165C4×C31H(5,𝔽2)11yescharacteristic
166Dic31—21no—
167Dic31—21no—
168Dic31—21no—
169Dic31—21no—
170Dic31—41no—
171Dic31—41no—
172#559—311no—
173#556—311no—
174#497D3111yescharacteristic, complemented
175#496—311no—
176#495—311no—
177#464—311no—
178#464—311no—
179#463—311no—
180#463—311no—
181#461—311no—
182#460—311no—
183#446—311no—
184#442—311no—
185#441—311no—
186C4×SD16—311no—
187C2×C31—81no—
188C2×C31#55011yescharacteristic
189C2×C31#57511yescharacteristic
190C2×C31#57711yescharacteristic
191D31—81no—
192D31—81no—
193C2×Q16C2×D3111yescharacteristic
194C2×Q16C2×D3111yescharacteristic
195C2×SD16—311no—
196C2×SD16—311no—
197C2×SD16—311no—
198C2×SD16C2×D3111yescharacteristic
199C2×SD16C2×D3111yescharacteristic
200C2×D8—311no—
201C2×D8—311no—
202C4⋊Q8C2×D3111yescharacteristic
203#127—311no—
204#126—621no—
205#126—621no—
206#124—311no—
207#124—311no—
208#124—311no—
209#124—621no—
210#124C2×D3111yescharacteristic
211#123—621no—
212#123—621no—
213C22⋊Q8—621no—
214C4×Q8—311no—
215C4×Q8—311no—
216C4×Q8—311no—
217C4×Q8—311no—
218C4×D4—311no—
219C4×D4—311no—
220C4×D4—311no—
221C4×D4—621no—
222#117—621no—
223#106—311no—
224C4⋊C8—311no—
225C4⋊C8—311no—
226C4⋊C8—311no—
227#103—311no—
228#103—311no—
229#103—311no—
230#102—311no—
231#102—311no—
232#102—311no—
233#97—311no—
234#97C2×D3111yescharacteristic
235C4×C8—311no—
236C31#340111yescharacteristic, complemented, Sylow
237C2×Q8—311no—
238C2×Q8C22×D3111yescharacteristic
239C2×Q8C22×D3111yescharacteristic
240C2×Q8C22×D3111yescharacteristic
241C2×D4—311no—
242C2×D4—311no—
243C2×D4—621no—
244C2×D4—621no—
245C2×D4C22×D3111yescharacteristic
246C22×C4—621no—
247C22×C4—621no—
248C22×C4—621no—
249Q16—22no—
250Q16—41no—
251SD16—22no—
252SD16—41no—
253SD16—1241no—
254SD16—1241no—
255SD16—1241no—
256D8—622no—
257D8—1241no—
258C2×C8—311no—
259C2×C8—311no—
260C2×C8C22×D3111yescharacteristic
261C2×C8C22×D3111yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—311no—
265C4⋊C4—311no—
266C4⋊C4—311no—
267C4⋊C4—311no—
268C4⋊C4—311no—
269C4⋊C4—621no—
270C4⋊C4—621no—
271C4⋊C4—621no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—621no—
275C22⋊C4—621no—
276C22⋊C4—621no—
277C22⋊C4—621no—
278C22⋊C4—621no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C42—311no—
284C42—311no—
285C42—621no—
286C42—621no—
287C42—621no—
288C42C22×D3111yescharacteristic
289C23—21no—
290C23—621no—
291C23—621no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—1241no—
299D4—21no—
300D4—21no—
301D4—621no—
302D4—621no—
303D4—621no—
304D4—621no—
305D4—1242no—
306D4—2481no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—311no—
311C2×C4—311no—
312C2×C4—311no—
313C2×C4—311no—
314C2×C4—621no—
315C2×C4—621no—
316C2×C4—1242no—
317C2×C4—2481no—
318C2×C4—2481no—
319C2×C4D4×D3111yescharacteristic
320C2×C4D4×D3111yescharacteristic
321C2×C4C23×D3111yescharacteristic
322C8—21no—
323C8—621no—
324C8—621no—
325C8#9249712yes—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—1241no—
330C22—1241no—
331C22—1241no—
332C22—1241no—
333C22—1241no—
334C22—1241no—
335C22C2×D4×D3111yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—621no—
342C4—621no—
343C4—621no—
344C4—621no—
345C4—1241no—
346C4—1241no—
347C4C2×#9249711yescharacteristic
348C4#1175856111yescharacteristic
349C2—81no—
350C2—2481no—
351C2—2481no—
352C2#1452171911yescharacteristic
353C2#1452184811yescharacteristic
354C2#1452185811yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#497C2
socleC22×C31C22×D4
prime radical#14521435C2
hypercenter#497D31
hypocenterC31#3401
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #14521781C2semidirect
2. #14521773C2semidirect
4. #14521434C2semidirect
5. #14521273C2semidirect
6. #14521273C2semidirect
7. #14521266C2semidirect
8. #14521261C2semidirect
9. #14521251C2semidirect
10. #14521247C2semidirect
11. #14521177C2semidirect
12. #14521162C2semidirect
13. #14521156C2semidirect
14. SD16×Dic31C2semidirect
15. C31×#497C2semidirect
174. #497D31semidirect
236. C31#3401semidirect

Maximal subgroups

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

subgroupindex
#145217812
#145217732
#145214352
#145214342
#145212732
#145212662
#145212612
#145212512
#145212472
#145211772
#145211622
#145211562
SD16×Dic312
C31×#4972
#340131