Finite Group Databasebeta

← #16857637

Subgroups — #16857637

Order 3968.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521762C211yesmaximal, characteristic, complemented
2#14521701C211yesmaximal, characteristic, complemented
3#14521398C211yesmaximal, characteristic, complemented
4#14521392C211yesmaximal, characteristic, complemented
5#14521338C211yesmaximal, characteristic, complemented
6#14521280C211yesmaximal, characteristic, complemented
7#14521279C211yesmaximal, characteristic, complemented
8#14521253C211yesmaximal, characteristic, complemented
9#14521197C211yesmaximal, characteristic, complemented
10#14521196C211yesmaximal, characteristic, complemented
11#14521131C211yesmaximal, characteristic, complemented
12(C22⋊D31)⋊C8C211yesmaximal, characteristic, complemented
13#14521044C211yesmaximal, characteristic, complemented
14#14521043C211yesmaximal, characteristic, complemented
15C31×#485C211yesmaximal, characteristic, complemented
16C2×#92499C2211yescharacteristic
17C2×#92495C2211yescharacteristic
18C31×C22⋊Q8C2211yescharacteristic
19C31×#117C2211yescharacteristic
20#11758521C2211yescharacteristic
21C2×#92481C2211yescharacteristic
22#11758507C2211yescharacteristic
23C4×C22⋊D31C2211yescharacteristic
24C22×C31⋊C8C2211yescharacteristic
25C2×D248C2211yescharacteristic
26C2×#92470C2211yescharacteristic
27C2×C8×D31C2211yescharacteristic
28#11758474C2211yescharacteristic
29#11758472C2211yescharacteristic
30#11758471—21no—
31#11758470C2211yescharacteristic
32#11758470C2211yescharacteristic
33#11758469C2211yescharacteristic
34C4⋊C4×D31—21no—
35#11758465C2211yescharacteristic
36#11758462—21no—
37#11758461—21no—
38#11758461—21no—
39#11758460—21no—
40#11758452—21no—
41#11758449—21no—
42C31×#107C2211yescharacteristic
43C31×#106C2211yescharacteristic
44C31×#103C2211yescharacteristic
45C31×#103C2211yescharacteristic
46C31×C22⋊C8C2211yescharacteristic
47#11758423C2211yescharacteristic
48#11758409C2211yescharacteristic
49(C2×D31)⋊C8C2211yescharacteristic
50#11758404C2211yescharacteristic
51Dic31⋊C8C2211yescharacteristic
52C8×Dic31C2211yescharacteristic
53#11758398C2211yescharacteristic
54#11758398C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758397C2211yescharacteristic
57#11758397C2211yescharacteristic
58#11758396C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C22×C4×C31C2311yescharacteristic
61C2×C22⋊D31—21no—
62C2×C22⋊D31—21no—
63C2×C22⋊D31D411yescharacteristic
64#92499—22no—
65#92499—41no—
66#92495—22no—
67#92495—41no—
68C2×D124—21no—
69C2×D124—21no—
70C2×D124C2311yescharacteristic
71C2×D124C2311yescharacteristic
72C2×C4×D31—21no—
73C2×C4×D31—21no—
74C2×C4×D31—21no—
75C2×C4×D31—21no—
76C2×C4×D31C2311yescharacteristic
77C2×Dic62—21no—
78C2×Dic62C2311yescharacteristic
79C2×C8×C31C2311yescharacteristic
80C2×C8×C31C2311yescharacteristic
81C4⋊C4×C31—21no—
82C4⋊C4×C31C2311yescharacteristic
83C4⋊C4×C31C2311yescharacteristic
84C4⋊C4×C31C2311yescharacteristic
85C22⋊C4×C31—21no—
86C22⋊C4×C31—21no—
87C42×C31—21no—
88C22⋊Dic31D411yescharacteristic
89#92481—41no—
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—
95(C2×D31)⋊C4—21no—
96(C2×D31)⋊C4D411yescharacteristic
97C4⋊Dic31—21no—
98C4⋊Dic31C2311yescharacteristic
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101Dic31⋊C4—21no—
102Dic31⋊C4D411yescharacteristic
103C4×Dic31—21no—
104C4×Dic31C2311yescharacteristic
105C2×C31⋊C8—41no—
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108D248—22no—
109#92470—41no—
110C8×D31—41no—
111C23×C31C2×D411yescharacteristic
112C22×D31—21no—
113C22×D31—21no—
114C22×D31C2×D411yescharacteristic
115Q8×C31—21no—
116Q8×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31C2×D411yescharacteristic
124C2×C4×C31C2411yescharacteristic
125C22⋊D31—22no—
126C22⋊D31—42no—
127C22⋊D31—81no—
128C2×Dic31—21no—
129C2×Dic31—21no—
130C2×Dic31C2×D411yescharacteristic
131C2×Dic31C2×D411yescharacteristic
132C2×Dic31C2×D411yescharacteristic
133D124—21no—
134D124—21no—
135D124—21no—
136D124—42no—
137D124—81no—
138D124#4112yes—
139C4×D31—21no—
140C4×D31—21no—
141C4×D31—42no—
142C4×D31—42no—
143C4×D31—42no—
144C4×D31—42no—
145Dic62—21no—
146Dic62—21no—
147Dic62—81no—
148C8×C31—21no—
149C8×C31—21no—
150C31⋊C8—21no—
151C31⋊C8—21no—
152#3303—311nomaximal, Sylow
153C22×C31—21no—
154C22×C31—21no—
155C22×C31—21no—
156C22×C31C22×D411yescharacteristic
157C2×D31—21no—
158C2×D31—22no—
159C2×D31—21no—
160C2×D31—21no—
161C2×D31—41no—
162C2×D31—41no—
163C2×D31—41no—
164C2×D31—41no—
165C2×D31—41no—
166C4×C31—21no—
167C4×C31—41no—
168C4×C31—41no—
169C4×C31—41no—
170C4×C31—41no—
171C4×C31C2×#4111yescharacteristic
172C4×C31H(5,𝔽2)11yescharacteristic
173Dic31—21no—
174Dic31—21no—
175Dic31—41no—
176Dic31—41no—
177Dic31#13512yes—
178#555—311no—
179#547—311no—
180#487—311no—
181#485—311no—
182#485D3111yescharacteristic, complemented
183#476—311no—
184#465—311no—
185#465—311no—
186#461—311no—
187#449—311no—
188#449—311no—
189C4×D8—311no—
190C8×D4—311no—
191#416—311no—
192#416—311no—
193C2×C31—41no—
194C2×C31#54611yescharacteristic
195C2×C31C2×#13511yescharacteristic
196C2×C31#57711yescharacteristic
197D31—41no—
198D31—42no—
199D31—81no—
200C2×#41—311no—
201C2×#41—311no—
202C2×SD16—311no—
203C2×SD16—311no—
204C2×D8—311no—
205C22×C8—311no—
206C22×C8—311no—
207C4⋊Q8—311no—
208C4⋊Q8—311no—
209#124—621no—
210#124—621no—
211#123—621no—
212#123—621no—
213C22⋊Q8—311no—
214C22⋊Q8C2×D3111yescharacteristic
215#121—311no—
216#121—311no—
217#121—621no—
218#121—621no—
219C4×D4—311no—
220C4×D4—311no—
221C4×D4—311no—
222#117—311no—
223#117—621no—
224#117C2×D3111yescharacteristic
225C2×C4⋊C4—621no—
226#107C2×D3111yescharacteristic
227#106—311no—
228#106C2×D3111yescharacteristic
229C4⋊C8—311no—
230#103—311no—
231#103—311no—
232#103—311no—
233#103—311no—
234#103C2×D3111yescharacteristic
235#103C2×D3111yescharacteristic
236#102—311no—
237#102—311no—
238#102—311no—
239#102—311no—
240C22⋊C8—311no—
241C22⋊C8C2×D3111yescharacteristic
242C4×C8—311no—
243C31#330311yescharacteristic, complemented, Sylow
244#41—622no—
245#41—622no—
246#41—1241no—
247#41—1241no—
248C2×Q8—311no—
249C2×Q8—621no—
250C2×Q8C22×D3111yescharacteristic
251C2×D4—311no—
252C2×D4—311no—
253C2×D4—311no—
254C2×D4—621no—
255C2×D4—621no—
256C2×D4—621no—
257C2×D4—621no—
258C22×C4—311no—
259C22×C4—621no—
260C22×C4—621no—
261C22×C4—621no—
262C22×C4—621no—
263C22×C4C22×D3111yescharacteristic
264SD16—1241no—
265SD16—1241no—
266D8—622no—
267C2×C8—311no—
268C2×C8—311no—
269C2×C8—1241no—
270C2×C8—1241no—
271C2×C8C22×D3111yescharacteristic
272C2×C8C22×D3111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—311no—
275C4⋊C4—311no—
276C4⋊C4—621no—
277C4⋊C4—621no—
278C4⋊C4—621no—
279C4⋊C4—621no—
280C4⋊C4C22×D3111yescharacteristic
281C4⋊C4C22×D3111yescharacteristic
282C4⋊C4C22×D3111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—311no—
286C22⋊C4—311no—
287C22⋊C4—621no—
288C22⋊C4—621no—
289C22⋊C4—621no—
290C22⋊C4—621no—
291C22⋊C4—621no—
292C22⋊C4—621no—
293C42—21no—
294C42—311no—
295C42—621no—
296C23—311no—
297C23—621no—
298C23—621no—
299C23D4×D3111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—621no—
303Q8—621no—
304Q8—2481no—
305D4—312no—
306D4—622no—
307D4—621no—
308D4—621no—
309D4—621no—
310D4—1242no—
311D4—1242no—
312D4—2481no—
313D4—2481no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—311no—
321C2×C4—311no—
322C2×C4—311no—
323C2×C4—621no—
324C2×C4—621no—
325C2×C4—621no—
326C2×C4—621no—
327C2×C4—1242no—
328C2×C4—1242no—
329C2×C4—1242no—
330C2×C4—1242no—
331C2×C4D4×D3111yescharacteristic
332C2×C4C23×D3111yescharacteristic
333C8—21no—
334C8—21no—
335C8—621no—
336C8—621no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—621no—
341C22—621no—
342C22—622no—
343C22—621no—
344C22—1241no—
345C22—1241no—
346C22—1241no—
347C22—1241no—
348C22—1241no—
349C22C2×D4×D3111yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—312no—
356C4—621no—
357C4—621no—
358C4—1241no—
359C4—1241no—
360C4#41×D3111yescharacteristic
361C4#1175856611yescharacteristic
362C2—41no—
363C2—1241no—
364C2—1242no—
365C2—2481no—
366C2#1452169111yescharacteristic
367C2#135×D3111yescharacteristic
368C2#1452185811yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#485C2
socleC22×C31C22×D4
hypercenter#485D31
hypocenterC31#3303
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #14521762C2semidirect
2. #14521701C2semidirect
3. #14521398C2semidirect
4. #14521392C2semidirect
5. #14521338C2semidirect
6. #14521280C2semidirect
7. #14521279C2semidirect
8. #14521253C2semidirect
9. #14521197C2semidirect
10. #14521196C2semidirect
11. #14521131C2semidirect
12. (C22⋊D31)⋊C8C2semidirect
13. #14521044C2semidirect
14. #14521043C2semidirect
15. C31×#485C2semidirect
182. #485D31semidirect
243. C31#3303semidirect

Maximal subgroups

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

subgroupindex
#145217622
#145217012
#145213982
#145213922
#145213382
#145212802
#145212792
#145212532
#145211972
#145211962
#145211312
(C22⋊D31)⋊C82
#145210442
#145210432
C31×#4852
#330331