Finite Group Databasebeta

← #16858771

Subgroups — #16858771

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#14521772C211yesmaximal, characteristic, complemented
2#14521444C211yesmaximal, characteristic, complemented
3#14521436C211yesmaximal, characteristic
4#14521431C211yesmaximal, characteristic, complemented
5#14521271C211yesmaximal, characteristic, complemented
6#14521268C211yesmaximal, characteristic, complemented
7#14521264C211yesmaximal, characteristic, complemented
8#14521261C211yesmaximal, characteristic, complemented
9#14521254C211yesmaximal, characteristic, complemented
10#14521246C211yesmaximal, characteristic, complemented
11#14521180C211yesmaximal, characteristic, complemented
12#14521159C211yesmaximal, characteristic, complemented
13#14521154C211yesmaximal, characteristic, complemented
14C4×#92480C211yesmaximal, characteristic, complemented
15C31×#559C211yesmaximal, characteristic, complemented
16C31×#127C2211yescharacteristic
17C31×#124—21no—
18C31×#124C2211yescharacteristic
19C31×#124C2211yescharacteristic
20C31×#123—21no—
21C31×#123—21no—
22C4×Q8×C31C2211yescharacteristic
23C4×Q8×C31C2211yescharacteristic
24C4×D4×C31—21no—
25C4×D4×C31C2211yescharacteristic
26C4×D4×C31C2211yescharacteristic
27#11758523—21no—
28C2×#92482C2211yescharacteristic
29C2×#92482C2211yescharacteristic
30C2×#92481C2211yescharacteristic
31C2×#92480C2211yescharacteristic
32C2×#92480C2211yescharacteristic
33C2×#92480C2211yescharacteristic
34C2×#92480C2211yescharacteristic
35C2×#92479C2211yescharacteristic
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#11758420C2211yescharacteristic
48#11758420C2211yescharacteristic
49#11758398C2211yescharacteristic
50#11758398C2211yescharacteristic
51#11758397C2211yescharacteristic
52#11758396C2211yescharacteristic
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×D4×C31—21no—
62C2×D4×C31—21no—
63C2×D4×C31C2311yescharacteristic
64C2×D4×C31C2311yescharacteristic
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C2×D124C2311yescharacteristic
68C2×C4×D31—21no—
69C2×Dic62C2311yescharacteristic
70C2×Dic62C2311yescharacteristic
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—
81C22⋊C4×C31—21no—
82C42×C31—21no—
83C42×C31C2311yescharacteristic
84C42×C31C2311yescharacteristic
85C42×C31C2311yescharacteristic
86#92482—22no—
87#92482—41no—
88#92481—41no—
89#92480—22no—
90#92480—41no—
91#92480—41no—
92#92480—41no—
93#92479—22no—
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—
112C23×C31—21no—
113C22×D31—21no—
114Q8×C31—21no—
115Q8×C31—21no—
116Q8×C31—41no—
117D4×C31—21no—
118D4×C31—21no—
119D4×C31—21no—
120D4×C31—21no—
121D4×C31—42no—
122D4×C31—81no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—81no—
126C2×C4×C31—81no—
127C2×C4×C31C2×D411yescharacteristic
128C2×C4×C31C2×D411yescharacteristic
129C2×C4×C31C2×D411yescharacteristic
130C2×C4×C31C2×D411yescharacteristic
131C2×C4×C31C2×D411yescharacteristic
132C2×C4×C31C2×D411yescharacteristic
133C2×C4×C31C2411yescharacteristic
134C2×Dic31—21no—
135C2×Dic31—21no—
136C2×Dic31—21no—
137D124—21no—
138D124—21no—
139C4×D31—42no—
140Dic62—21no—
141Dic62—21no—
142Dic62—21no—
143Dic62—21no—
144C31⋊C8—21no—
145C31⋊C8—21no—
146C31⋊C8—21no—
147C31⋊C8#4112yes—
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—21no—
162C4×C31—21no—
163C4×C31—21no—
164C4×C31—21no—
165C4×C31—41no—
166C4×C31—41no—
167C4×C31C2×#4111yescharacteristic
168C4×C31H(5,𝔽2)11yescharacteristic
169Dic31—41no—
170Dic31—41no—
171Dic31—41no—
172#559D3111yescharacteristic, complemented
173#556—311no—
174#497—311no—
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—81no—
189C2×C31#55011yescharacteristic
190C2×C31#57511yescharacteristic
191C2×C31#57711yescharacteristic
192D31—81no—
193C2×Q16—311no—
194C2×Q16—311no—
195C2×SD16—311no—
196C2×SD16—311no—
197C2×SD16—311no—
198C2×SD16—311no—
199C2×SD16—311no—
200C2×D8—311no—
201C2×D8—311no—
202C4⋊Q8—311no—
203#127C2×D3111yescharacteristic
204#126—621no—
205#126—621no—
206#124—21no—
207#124—311no—
208#124—311no—
209#124C2×D3111yescharacteristic
210#124C2×D3111yescharacteristic
211#123—21no—
212#123—21no—
213C22⋊Q8—621no—
214C4×Q8—311no—
215C4×Q8—311no—
216C4×Q8C2×D3111yescharacteristic
217C4×Q8C2×D3111yescharacteristic
218C4×D4—21no—
219C4×D4—311no—
220C4×D4C2×D3111yescharacteristic
221C4×D4C2×D3111yescharacteristic
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×C8—311no—
236C31#340111yescharacteristic, complemented, Sylow
237C2×Q8—311no—
238C2×Q8—311no—
239C2×Q8C22⋊D3111yescharacteristic
240C2×Q8C22×D3111yescharacteristic
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—311no—
244C2×D4C22×D3111yescharacteristic
245C2×D4C22×D3111yescharacteristic
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—621no—
249Q16—622no—
250Q16—1241no—
251SD16—622no—
252SD16—1241no—
253SD16—1241no—
254SD16—1241no—
255SD16—1241no—
256D8—622no—
257D8—1241no—
258C2×C8—311no—
259C2×C8—311no—
260C2×C8—311no—
261C2×C8—311no—
262C4⋊C4—21no—
263C4⋊C4—311no—
264C4⋊C4—621no—
265C4⋊C4—621no—
266C4⋊C4—621no—
267C4⋊C4—621no—
268C4⋊C4C22⋊D3111yescharacteristic
269C4⋊C4C22⋊D3111yescharacteristic
270C4⋊C4C22⋊D3111yescharacteristic
271C4⋊C4C22×D3111yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—621no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C42—21no—
284C42—621no—
285C42—621no—
286C42C22×D3111yescharacteristic
287C42C22×D3111yescharacteristic
288C42C22×D3111yescharacteristic
289C23—21no—
290C23—21no—
291C23—621no—
292Q8—21no—
293Q8—21no—
294Q8—41no—
295Q8—621no—
296Q8—621no—
297Q8—621no—
298Q8—621no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—42no—
304D4—81no—
305D4—621no—
306D4—621no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—621no—
312C2×C4—621no—
313C2×C4—621no—
314C2×C4—1242no—
315C2×C4C2×C22⋊D3111yescharacteristic
316C2×C4C2×C22⋊D3111yescharacteristic
317C2×C4C2×C22⋊D3111yescharacteristic
318C2×C4C2×C22⋊D3111yescharacteristic
319C2×C4C2×C22⋊D3111yescharacteristic
320C2×C4C2×C22⋊D3111yescharacteristic
321C2×C4C23×D3111yescharacteristic
322C8—312no—
323C8—621no—
324C8—621no—
325C8—621no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—1241no—
333C22—1241no—
334C22—1241no—
335C22C22×C22⋊D3111yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—1241no—
345C4—1241no—
346C4—1241no—
347C4#41×D3111yescharacteristic
348C4#1175856611yescharacteristic
349C2—81no—
350C2—81no—
351C2—2481no—
352C2#1452171811yescharacteristic
353C2#1452184711yescharacteristic
354C2#1452186011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#559C2
socleC22×C31C22×D4
prime radical#14521436C2
hypercenter#559D31
hypocenterC31#3401
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #14521772C2semidirect
2. #14521444C2semidirect
4. #14521431C2semidirect
5. #14521271C2semidirect
6. #14521268C2semidirect
7. #14521264C2semidirect
8. #14521261C2semidirect
9. #14521254C2semidirect
10. #14521246C2semidirect
11. #14521180C2semidirect
12. #14521159C2semidirect
13. #14521154C2semidirect
14. C4×#92480C2semidirect
15. C31×#559C2semidirect
172. #559D31semidirect
236. C31#3401semidirect

Maximal subgroups

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

subgroupindex
#145217722
#145214442
#145214362
#145214312
#145212712
#145212682
#145212642
#145212612
#145212542
#145212462
#145211802
#145211592
#145211542
C4×#924802
C31×#5592
#340131