Finite Group Databasebeta

← #16858783

Subgroups — #16858783

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#14521768C211yesmaximal, characteristic, complemented
3#14521442C211yesmaximal, characteristic, complemented
4#14521437C211yesmaximal, characteristic
5#14521269C211yesmaximal, characteristic, complemented
6#14521268C211yesmaximal, characteristic, complemented
7#14521266C211yesmaximal, characteristic, complemented
8#14521261C211yesmaximal, characteristic, complemented
9#14521252C211yesmaximal, characteristic, complemented
10#14521247C211yesmaximal, characteristic, complemented
11#14521179C211yesmaximal, characteristic, complemented
12#14521161C211yesmaximal, characteristic, complemented
13#14521156C211yesmaximal, characteristic, complemented
14C4×#92470C211yesmaximal, characteristic, complemented
15C31×#495C211yesmaximal, characteristic, complemented
16C2×Q16×C31C2211yescharacteristic
17C2×SD16×C31C2211yescharacteristic
18C2×SD16×C31C2211yescharacteristic
19C2×D8×C31C2211yescharacteristic
20C31×#124C2211yescharacteristic
21C31×#124C2211yescharacteristic
22#11758524C2211yescharacteristic
23Q8×Dic31C2211yescharacteristic
24Q8×Dic31C2211yescharacteristic
25#11758521C2211yescharacteristic
26C2×#92482C2211yescharacteristic
27C2×#92481C2211yescharacteristic
28#11758517C2211yescharacteristic
29#11758513C2211yescharacteristic
30D4×Dic31C2211yescharacteristic
31D4×Dic31C2211yescharacteristic
32C2×#92480C2211yescharacteristic
33C2×#92479C2211yescharacteristic
34C2×#92470C2211yescharacteristic
35#11758463—21no—
36#11758462—21no—
37#11758460—21no—
38(C22⋊D31)⋊C4—21no—
39#11758456—21no—
40#11758456—21no—
41#11758455—21no—
42#11758454—21no—
43C4×D124C2211yescharacteristic
44C4×Dic62C2211yescharacteristic
45C4×Dic62C2211yescharacteristic
46C4×C8×C31C2211yescharacteristic
47#11758423C2211yescharacteristic
48#11758423C2211yescharacteristic
49#11758420C2211yescharacteristic
50#11758420C2211yescharacteristic
51#11758409C2211yescharacteristic
52#11758405C2211yescharacteristic
53#11758404C2211yescharacteristic
54#11758403C2211yescharacteristic
55#11758403C2211yescharacteristic
56Dic31⋊C8C2211yescharacteristic
57Dic31⋊C8C2211yescharacteristic
58C4⋊(C31⋊C8)C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C2×Q8×C31C2311yescharacteristic
61C2×D4×C31C2311yescharacteristic
62C2×D4×C31C2311yescharacteristic
63C2×C22⋊D31—21no—
64C2×C22⋊D31—21no—
65C22×Dic31—21no—
66C22×Dic31—21no—
67C2×D124C2311yescharacteristic
68C2×C4×D31—21no—
69C2×Dic62D411yescharacteristic
70C2×Dic62C2311yescharacteristic
71Q16×C31—22no—
72SD16×C31—41no—
73SD16×C31—41no—
74D8×C31—22no—
75C2×C8×C31C2311yescharacteristic
76C2×C8×C31C2311yescharacteristic
77C22⋊C4×C31—21no—
78C22⋊C4×C31—21no—
79C22⋊C4×C31—21no—
80C22⋊C4×C31—21no—
81C42×C31C2311yescharacteristic
82C22⋊Dic31—21no—
83C22⋊Dic31—21no—
84C22⋊Dic31—21no—
85C22⋊Dic31—21no—
86#92482—41no—
87#92481—41no—
88#92480—41no—
89#92479—41no—
90(C2×D31)⋊C4—21no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4—21no—
93C4⋊Dic31—21no—
94C4⋊Dic31—21no—
95C4⋊Dic31D411yescharacteristic
96C4⋊Dic31C2311yescharacteristic
97C4⋊Dic31C2311yescharacteristic
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101Dic31⋊C4D411yescharacteristic
102Dic31⋊C4D411yescharacteristic
103C4×Dic31—21no—
104C4×Dic31—21no—
105C4×Dic31—21no—
106C4×Dic31C2311yescharacteristic
107C4×Dic31C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110#92470—22no—
111C23×C31—21no—
112C23×C31—21no—
113C22×D31—21no—
114Q8×C31—21no—
115Q8×C31—21no—
116Q8×C31—21no—
117Q8×C31—21no—
118D4×C31—21no—
119D4×C31—21no—
120D4×C31—21no—
121D4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31C2×D411yescharacteristic
126C2×C4×C31C2411yescharacteristic
127C22⋊D31—42no—
128C22⋊D31—81no—
129C2×Dic31—21no—
130C2×Dic31—21no—
131C2×Dic31—21no—
132C2×Dic31—42no—
133C2×Dic31—81no—
134C2×Dic31C2×D411yescharacteristic
135C2×Dic31C2×D411yescharacteristic
136C2×Dic31C2×D411yescharacteristic
137C2×Dic31C2×D411yescharacteristic
138D124—21no—
139D124—21no—
140C4×D31—81no—
141Dic62—21no—
142Dic62—21no—
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×C31—41no—
153C22×C31—41no—
154C22×C31—41no—
155C22×C31C22×D411yescharacteristic
156C2×D31—41no—
157C2×D31—41no—
158C2×D31—41no—
159C4×C31—21no—
160C4×C31—21no—
161C4×C31—41no—
162C4×C31—41no—
163C4×C31C2×#4111yescharacteristic
164C4×C31H(5,𝔽2)11yescharacteristic
165Dic31—21no—
166Dic31—21no—
167Dic31—21no—
168Dic31—21no—
169Dic31—41no—
170Dic31—41no—
171Dic31—41no—
172#559—311no—
173#556—311no—
174#497—311no—
175#496—311no—
176#495D3111yescharacteristic, complemented
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—81no—
189C2×C31#55011yescharacteristic
190C2×C31#57511yescharacteristic
191C2×C31#57711yescharacteristic
192D31—81no—
193C2×Q16—311no—
194C2×Q16C2×D3111yescharacteristic
195C2×SD16—311no—
196C2×SD16—311no—
197C2×SD16—311no—
198C2×SD16C2×D3111yescharacteristic
199C2×SD16C2×D3111yescharacteristic
200C2×D8—311no—
201C2×D8C2×D3111yescharacteristic
202C4⋊Q8—311no—
203#127—311no—
204#126—621no—
205#126—621no—
206#124—311no—
207#124—311no—
208#124—621no—
209#124C2×D3111yescharacteristic
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#97—311no—
235C4×C8C2×D3111yescharacteristic
236C31#340111yescharacteristic, complemented, Sylow
237C2×Q8—311no—
238C2×Q8—311no—
239C2×Q8C22×D3111yescharacteristic
240C2×Q8C22×D3111yescharacteristic
241C2×D4—311no—
242C2×D4—621no—
243C2×D4—621no—
244C2×D4C22×D3111yescharacteristic
245C2×D4C22×D3111yescharacteristic
246C22×C4—621no—
247C22×C4—621no—
248C22×C4—621no—
249Q16—22no—
250Q16—1241no—
251SD16—41no—
252SD16—41no—
253SD16—622no—
254SD16—1241no—
255SD16—1241no—
256D8—22no—
257D8—1241no—
258C2×C8—311no—
259C2×C8—311no—
260C2×C8C22×D3111yescharacteristic
261C2×C8C22×D3111yescharacteristic
262C4⋊C4—311no—
263C4⋊C4—311no—
264C4⋊C4—311no—
265C4⋊C4—311no—
266C4⋊C4—311no—
267C4⋊C4—621no—
268C4⋊C4—621no—
269C4⋊C4—621no—
270C4⋊C4—621no—
271C4⋊C4—621no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
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—21no—
291C23—621no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—621no—
297Q8—621no—
298Q8—1241no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—621no—
304D4—621no—
305D4—1242no—
306D4—2481no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—311no—
310C2×C4—311no—
311C2×C4—311no—
312C2×C4—311no—
313C2×C4—621no—
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—41no—
330C22—41no—
331C22—41no—
332C22—1241no—
333C22—1241no—
334C22—1241no—
335C22C2×D4×D3111yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—621no—
341C4—621no—
342C4—621no—
343C4—621no—
344C4—1241no—
345C4—1241no—
346C4—1241no—
347C4C2×#9249711yescharacteristic
348C4#1175856111yescharacteristic
349C2—81no—
350C2—81no—
351C2—2481no—
352C2#1452171911yescharacteristic
353C2#1452184611yescharacteristic
354C2#1452185611yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#495C2
socleC22×C31C22×D4
prime radical#14521437C2
hypercenter#495D31
hypocenterC31#3401
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #14521781C2semidirect
2. #14521768C2semidirect
3. #14521442C2semidirect
5. #14521269C2semidirect
6. #14521268C2semidirect
7. #14521266C2semidirect
8. #14521261C2semidirect
9. #14521252C2semidirect
10. #14521247C2semidirect
11. #14521179C2semidirect
12. #14521161C2semidirect
13. #14521156C2semidirect
14. C4×#92470C2semidirect
15. C31×#495C2semidirect
176. #495D31semidirect
236. C31#3401semidirect

Maximal subgroups

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

subgroupindex
#145217812
#145217682
#145214422
#145214372
#145212692
#145212682
#145212662
#145212612
#145212522
#145212472
#145211792
#145211612
#145211562
C4×#924702
C31×#4952
#340131