Finite Group Databasebeta

← #16858786

Subgroups — #16858786

Order 3968.

356 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521772C211yesmaximal, characteristic, complemented
2#14521444C211yesmaximal, characteristic, complemented
3#14521441C211yesmaximal, characteristic, complemented
4#14521431C211yesmaximal, characteristic
5#14521271C211yesmaximal, characteristic, complemented
6#14521268C211yesmaximal, characteristic, complemented
7#14521264C211yesmaximal, characteristic
8#14521261C211yesmaximal, characteristic
9#14521259C211yesmaximal, characteristic, complemented
10#14521256C211yesmaximal, characteristic, complemented
11#14521180C211yesmaximal, characteristic, complemented
12#14521149C211yesmaximal, characteristic, complemented
13#14521147C211yesmaximal, characteristic, complemented
14C4×#92482C211yesmaximal, characteristic, complemented
15C31×#556C211yesmaximal, characteristic, complemented
16C31×C4⋊Q8C2211yescharacteristic
17C31×#126—21no—
18C31×#126—21no—
19C31×#124C2211yescharacteristic
20C31×#124C2211yescharacteristic
21C31×C22⋊Q8—21no—
22C4×Q8×C31C2211yescharacteristic
23C4×Q8×C31C2211yescharacteristic
24C4×Q8×C31C2211yescharacteristic
25C4×D4×C31C2211yescharacteristic
26C31×#117—21no—
27#11758523—21no—
28C2×#92482C2211yescharacteristic
29C2×#92482C2211yescharacteristic
30C2×#92482C2211yescharacteristic
31C2×#92482C2211yescharacteristic
32C2×#92481C2211yescharacteristic
33C2×#92481C2211yescharacteristic
34C2×#92480C2211yescharacteristic
35C2×#92480C2211yescharacteristic
36C2×#92479C2211yescharacteristic
37#11758475—21no—
38#11758475—21no—
39#11758469—21no—
40#11758452C2211yescharacteristic
41#11758452C2211yescharacteristic
42C4×D124C2211yescharacteristic
43#11758446C2211yescharacteristic
44C4×Dic62C2211yescharacteristic
45C4×Dic62C2211yescharacteristic
46#11758423C2211yescharacteristic
47#11758423C2211yescharacteristic
48#11758420C2211yescharacteristic
49#11758398C2211yescharacteristic
50#11758398C2211yescharacteristic
51#11758397C2211yescharacteristic
52#11758395C2211yescharacteristic
53C4⋊(C31⋊C8)C2211yescharacteristic
54C4⋊(C31⋊C8)C2211yescharacteristic
55C4⋊(C31⋊C8)C2211yescharacteristic
56#11758391C2211yescharacteristic
57#11758391C2211yescharacteristic
58C4×C31⋊C8C2211yescharacteristic
59C2×Q8×C31D411yescharacteristic
60C2×Q8×C31C2311yescharacteristic
61C2×Q8×C31C2311yescharacteristic
62C2×D4×C31C2311yescharacteristic
63C22×C4×C31—21no—
64C2×D124C2311yescharacteristic
65C2×C4×D31—21no—
66C2×Dic62C2311yescharacteristic
67C2×Dic62C2311yescharacteristic
68C4⋊C4×C31—21no—
69C4⋊C4×C31—21no—
70C4⋊C4×C31—21no—
71C4⋊C4×C31—21no—
72C4⋊C4×C31D411yescharacteristic
73C4⋊C4×C31D411yescharacteristic
74C4⋊C4×C31D411yescharacteristic
75C4⋊C4×C31C2311yescharacteristic
76C22⋊C4×C31—21no—
77C22⋊C4×C31—21no—
78C22⋊C4×C31—21no—
79C22⋊C4×C31—21no—
80C22⋊C4×C31—21no—
81C42×C31—21no—
82C42×C31—21no—
83C42×C31C2311yescharacteristic
84C42×C31C2311yescharacteristic
85C42×C31C2311yescharacteristic
86#92482—22no—
87#92482—41no—
88#92482—41no—
89#92482—41no—
90#92481—22no—
91#92481—41no—
92#92480—22no—
93#92480—41no—
94#92479—41no—
95(C2×D31)⋊C4—21no—
96(C2×D31)⋊C4—21no—
97(C2×D31)⋊C4—21no—
98(C2×D31)⋊C4—21no—
99(C2×D31)⋊C4—21no—
100C4⋊Dic31—21no—
101C4⋊Dic31—21no—
102C4⋊Dic31C2311yescharacteristic
103Dic31⋊C4—21no—
104Dic31⋊C4—21no—
105C4×Dic31—21no—
106C4×Dic31—21no—
107C2×C31⋊C8C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110C2×C31⋊C8C2311yescharacteristic
111C23×C31—21no—
112C22×D31—21no—
113Q8×C31—21no—
114Q8×C31—21no—
115Q8×C31—21no—
116Q8×C31—21no—
117Q8×C31—41no—
118D4×C31—21no—
119D4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—42no—
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31C2×D411yescharacteristic
126C2×C4×C31C2×D411yescharacteristic
127C2×C4×C31C2×D411yescharacteristic
128C2×C4×C31C2×D411yescharacteristic
129C2×C4×C31C2×D411yescharacteristic
130C2×C4×C31C2411yescharacteristic
131C2×Dic31—21no—
132C2×Dic31—21no—
133C2×Dic31—21no—
134D124—21no—
135D124—21no—
136C4×D31—42no—
137Dic62—21no—
138Dic62—21no—
139Dic62—21no—
140Dic62—21no—
141C31⋊C8—21no—
142C31⋊C8—21no—
143C31⋊C8—21no—
144C31⋊C8#4112yes—
145#3402—311nomaximal, Sylow
146C22×C31—41no—
147C22×C31—41no—
148C22×C31—41no—
149C22×C31C22×D411yescharacteristic
150C2×D31—41no—
151C2×D31—41no—
152C2×D31—41no—
153C4×C31—21no—
154C4×C31—21no—
155C4×C31—21no—
156C4×C31—21no—
157C4×C31—21no—
158C4×C31—21no—
159C4×C31—41no—
160C4×C31—41no—
161C4×C31—41no—
162C4×C31C2×#4111yescharacteristic
163C4×C31H(5,𝔽2)11yescharacteristic
164Dic31—41no—
165Dic31—41no—
166Dic31—41no—
167#556—311no—
168#556D3111yescharacteristic, complemented
169#497—311no—
170#497—311no—
171#495—311no—
172#464—311no—
173#464—311no—
174#463—311no—
175#463—311no—
176#462—311no—
177#462—311no—
178#446—311no—
179#440—311no—
180#440—311no—
181C4×Q16—311no—
182C2×C31—81no—
183C2×C31#55011yescharacteristic
184C2×C31#57511yescharacteristic
185C2×C31#57811yescharacteristic
186D31—81no—
187C2×Q16—311no—
188C2×Q16—311no—
189C2×Q16—311no—
190C2×Q16—311no—
191C2×SD16—311no—
192C2×SD16—311no—
193C2×SD16—311no—
194C2×SD16—311no—
195C2×D8—311no—
196C4⋊Q8—311no—
197C4⋊Q8C2×D3111yescharacteristic
198#126—21no—
199#126—21no—
200#126—621no—
201#126—621no—
202#124—311no—
203#124—311no—
204#124C2×D3111yescharacteristic
205#124C2×D3111yescharacteristic
206C22⋊Q8—21no—
207C22⋊Q8—621no—
208C4×Q8—311no—
209C4×Q8—311no—
210C4×Q8C2×D3111yescharacteristic
211C4×Q8C2×D3111yescharacteristic
212C4×Q8C2×D3111yescharacteristic
213C4×D4—311no—
214C4×D4C2×D3111yescharacteristic
215#117—21no—
216#117—621no—
217#107—311no—
218C4⋊C8—311no—
219C4⋊C8—311no—
220C4⋊C8—311no—
221#103—311no—
222#103—311no—
223#103—311no—
224#103—311no—
225#102—311no—
226#102—311no—
227#97—311no—
228#97—311no—
229C4×C8—311no—
230C31#340211yescharacteristic, complemented, Sylow
231C2×Q8—311no—
232C2×Q8—311no—
233C2×Q8C22⋊D3111yescharacteristic
234C2×Q8C22×D3111yescharacteristic
235C2×Q8C22×D3111yescharacteristic
236C2×D4—311no—
237C2×D4C22×D3111yescharacteristic
238C22×C4—21no—
239C22×C4—621no—
240Q16—622no—
241Q16—1241no—
242Q16—1241no—
243Q16—1241no—
244SD16—622no—
245SD16—622no—
246SD16—1241no—
247SD16—1241no—
248D8—1241no—
249C2×C8—311no—
250C2×C8—311no—
251C2×C8—311no—
252C2×C8—311no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—311no—
258C4⋊C4—621no—
259C4⋊C4—621no—
260C4⋊C4—621no—
261C4⋊C4—621no—
262C4⋊C4C22⋊D3111yescharacteristic
263C4⋊C4C22⋊D3111yescharacteristic
264C4⋊C4C22⋊D3111yescharacteristic
265C4⋊C4C22×D3111yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—621no—
272C22⋊C4—621no—
273C22⋊C4—621no—
274C22⋊C4—621no—
275C22⋊C4—621no—
276C42—21no—
277C42—21no—
278C42—621no—
279C42—621no—
280C42C22×D3111yescharacteristic
281C42C22×D3111yescharacteristic
282C42C22×D3111yescharacteristic
283C23—21no—
284C23—621no—
285Q8—21no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—41no—
290Q8—621no—
291Q8—621no—
292Q8—621no—
293Q8—621no—
294D4—21no—
295D4—21no—
296D4—621no—
297D4—621no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—621no—
303C2×C4—621no—
304C2×C4—621no—
305C2×C4—1242no—
306C2×C4C2×C22⋊D3111yescharacteristic
307C2×C4C2×C22⋊D3111yescharacteristic
308C2×C4C2×C22⋊D3111yescharacteristic
309C2×C4C2×C22⋊D3111yescharacteristic
310C2×C4C2×C22⋊D3111yescharacteristic
311C2×C4C2×C22⋊D3111yescharacteristic
312C2×C4C23×D3111yescharacteristic
313C8—312no—
314C8—621no—
315C8—621no—
316C8—621no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—1241no—
321C22—1241no—
322C22—1241no—
323C22C22×C22⋊D3111yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—1241no—
334C4—1241no—
335C4—1241no—
336C4#41×D3111yescharacteristic
337C4#1175856611yescharacteristic
338C2—81no—
339C2—2481no—
340C2#1452171811yescharacteristic
341C2#1452184711yescharacteristic
342C2#1452186411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#556C2
socleC22×C31C22×D4
prime radicalC2×#92479C22
hypercenter#556D31
hypocenterC31#3402
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
1. #14521772C2semidirect
2. #14521444C2semidirect
3. #14521441C2semidirect
5. #14521271C2semidirect
6. #14521268C2semidirect
9. #14521259C2semidirect
10. #14521256C2semidirect
11. #14521180C2semidirect
12. #14521149C2semidirect
13. #14521147C2semidirect
14. C4×#92482C2semidirect
15. C31×#556C2semidirect
168. #556D31semidirect
230. C31#3402semidirect

Maximal subgroups

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

subgroupindex
#145217722
#145214442
#145214412
#145214312
#145212712
#145212682
#145212642
#145212612
#145212592
#145212562
#145211802
#145211492
#145211472
C4×#924822
C31×#5562
#340231