Finite Group Databasebeta

← #16857610

Subgroups — #16857610

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#14521752C211yesmaximal, characteristic, complemented
2#14521711C211yesmaximal, characteristic, complemented
3#14521406C211yesmaximal, characteristic, complemented
4#14521392C211yesmaximal, characteristic, complemented
5#14521369C211yesmaximal, characteristic, complemented
6#14521286C211yesmaximal, characteristic, complemented
7#14521279C211yesmaximal, characteristic, complemented
8#14521265C211yesmaximal, characteristic, complemented
9#14521197C211yesmaximal, characteristic, complemented
10#14521189C211yesmaximal, characteristic, complemented
11C4×#92481C211yesmaximal, characteristic, complemented
12#14521114C211yesmaximal, characteristic, complemented
13#14521044C211yesmaximal, characteristic, complemented
14#103×D31C211yesmaximal, characteristic, complemented
15C31×#479C211yesmaximal, characteristic, complemented
16C2×#92499C2211yescharacteristic
17C2×Q8×D31C2211yescharacteristic
18C31×#125C2211yescharacteristic
19C4×Q8×C31C2211yescharacteristic
20C2×#92481C2211yescharacteristic
21C2×D248C2211yescharacteristic
22C2×#92470C2211yescharacteristic
23C2×C8×D31C2211yescharacteristic
24C2×C8×D31C2211yescharacteristic
25#11758475—21no—
26#11758474—21no—
27#11758474C2211yescharacteristic
28#11758472—21no—
29#11758472—21no—
30#11758472C2211yescharacteristic
31#11758472C2211yescharacteristic
32#11758472C2211yescharacteristic
33#11758471—21no—
34#11758470—21no—
35#11758469C2211yescharacteristic
36C4⋊C4×D31C2211yescharacteristic
37#11758452—21no—
38#11758452C2211yescharacteristic
39C4×D124—21no—
40C4×D124C2211yescharacteristic
41C4×D124C2211yescharacteristic
42C31×#107C2211yescharacteristic
43C31×#106C2211yescharacteristic
44C31×C4⋊C8C2211yescharacteristic
45C31×#103C2211yescharacteristic
46C31×#103C2211yescharacteristic
47#11758423C2211yescharacteristic
48#11758409C2211yescharacteristic
49(C2×D31)⋊C8C2211yescharacteristic
50(C2×D31)⋊C8C2211yescharacteristic
51#11758404C2211yescharacteristic
52#11758398C2211yescharacteristic
53#11758398C2211yescharacteristic
54#11758397C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758397C2211yescharacteristic
57#11758396C2211yescharacteristic
58C4×C31⋊C8C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60#92499—22no—
61#92499—41no—
62Q8×D31—22no—
63Q8×D31—41no—
64C2×D124—21no—
65C2×D124—21no—
66C2×D124—21no—
67C2×D124—21no—
68C2×D124D411yescharacteristic
69C2×D124C2311yescharacteristic
70C2×D124C2311yescharacteristic
71C2×C4×D31—21no—
72C2×C4×D31—21no—
73C2×C4×D31—21no—
74C2×C4×D31—21no—
75C2×C4×D31C2311yescharacteristic
76C2×C4×D31C2311yescharacteristic
77C2×Dic62—21no—
78C2×Dic62C2311yescharacteristic
79C2×C8×C31C2311yescharacteristic
80C2×C8×C31C2311yescharacteristic
81C4⋊C4×C31—21no—
82C4⋊C4×C31—21no—
83C4⋊C4×C31—21no—
84C4⋊C4×C31C2311yescharacteristic
85C4⋊C4×C31C2311yescharacteristic
86C4⋊C4×C31C2311yescharacteristic
87C42×C31—21no—
88C42×C31C2311yescharacteristic
89#92481—22no—
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)⋊C4—21no—
97(C2×D31)⋊C4—21no—
98(C2×D31)⋊C4D411yescharacteristic
99(C2×D31)⋊C4D411yescharacteristic
100C4⋊Dic31—21no—
101C4⋊Dic31D411yescharacteristic
102C4⋊Dic31C2311yescharacteristic
103Dic31⋊C4—21no—
104C4×Dic31—21no—
105C2×C31⋊C8C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107D248—41no—
108#92470—41no—
109C8×D31—41no—
110C8×D31—41no—
111C22×D31—21no—
112C22×D31—21no—
113C22×D31C2×D411yescharacteristic
114C22×D31C2×D411yescharacteristic
115Q8×C31—21no—
116Q8×C31#4112yes—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31C2×D411yescharacteristic
122C2×C4×C31C2×D411yescharacteristic
123C2×C4×C31C2411yescharacteristic
124C2×Dic31—21no—
125C2×Dic31—21no—
126C2×Dic31C2×D411yescharacteristic
127C2×Dic31C2×D411yescharacteristic
128D124—22no—
129D124—21no—
130D124—21no—
131D124—21no—
132D124—21no—
133D124—42no—
134D124—42no—
135D124—42no—
136D124—81no—
137C4×D31—21no—
138C4×D31—21no—
139C4×D31—21no—
140C4×D31—21no—
141C4×D31—42no—
142C4×D31—42no—
143C4×D31—81no—
144C4×D31—81no—
145Dic62—21no—
146Dic62—21no—
147Dic62—42no—
148C8×C31—21no—
149C8×C31—21no—
150C31⋊C8—21no—
151C31⋊C8—21no—
152#3301—311nomaximal, Sylow
153C22×C31C22×D411yescharacteristic
154C2×D31—21no—
155C2×D31—21no—
156C2×D31—21no—
157C2×D31—21no—
158C2×D31—21no—
159C2×D31—41no—
160C2×D31—41no—
161C2×D31—41no—
162C2×D31—41no—
163C2×D31—41no—
164C2×D31—41no—
165C2×D31#13512yes—
166C4×C31—22no—
167C4×C31—21no—
168C4×C31—21no—
169C4×C31—41no—
170C4×C31—41no—
171C4×C31—41no—
172C4×C31C2×#4111yescharacteristic
173C4×C31H(5,𝔽2)11yescharacteristic
174Dic31—21no—
175Dic31—21no—
176Dic31—41no—
177Dic31—41no—
178#553—311no—
179#548—311no—
180#488—311no—
181#485—311no—
182#481—311no—
183#479D3111yescharacteristic, complemented
184#466—311no—
185#465—311no—
186#463—311no—
187#449—311no—
188#448—311no—
189C4×SD16—311no—
190C8×D4—311no—
191#416—311no—
192C2×#103—311no—
193C2×C31#54611yescharacteristic
194C2×C31C2×#13511yescharacteristic
195C2×C31#57711yescharacteristic
196D31—22no—
197D31—41no—
198D31—81no—
199D31—81no—
200C2×#41—311no—
201C22×Q8—311no—
202C2×SD16—311no—
203C2×SD16—311no—
204C2×D8—311no—
205C22×C8—311no—
206C22×C8—311no—
207#126—621no—
208#125C2×D3111yescharacteristic
209#124—311no—
210#124—621no—
211#123—621no—
212C22⋊Q8—311no—
213C22⋊Q8—621no—
214#121—311no—
215#121—311no—
216#121—311no—
217#121—621no—
218#121—621no—
219C4×Q8C2×D3111yescharacteristic
220C4×D4—311no—
221C4×D4—311no—
222C4×D4—621no—
223C4×D4—621no—
224#117—311no—
225C2×C4⋊C4—311no—
226#107C2×D3111yescharacteristic
227#106—311no—
228#106C2×D3111yescharacteristic
229C4⋊C8C2×D3111yescharacteristic
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⋊C8—311no—
242C4×C8—311no—
243C31#330111yescharacteristic, complemented, Sylow
244#41—622no—
245#41—1241no—
246C2×Q8—311no—
247C2×Q8—621no—
248C2×Q8—622no—
249C2×Q8—1241no—
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—311no—
260C22×C4—621no—
261C22×C4—621no—
262C22×C4—621no—
263C22×C4—621no—
264SD16—622no—
265SD16—1241no—
266D8—1241no—
267C2×C8—311no—
268C2×C8—311no—
269C2×C8—1241no—
270C2×C8—1241no—
271C2×C8C22×D3111yescharacteristic
272C2×C8C22×D3111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—311no—
277C4⋊C4—311no—
278C4⋊C4—621no—
279C4⋊C4—621no—
280C4⋊C4C22×D3111yescharacteristic
281C4⋊C4C22×D3111yescharacteristic
282C4⋊C4C22×D3111yescharacteristic
283C22⋊C4—311no—
284C22⋊C4—311no—
285C22⋊C4—621no—
286C22⋊C4—621no—
287C22⋊C4—621no—
288C22⋊C4—621no—
289C22⋊C4—621no—
290C22⋊C4—621no—
291C22⋊C4—621no—
292C22⋊C4—621no—
293C42—21no—
294C42—621no—
295C42C22×D3111yescharacteristic
296C23—311no—
297C23—311no—
298C23—621no—
299C23—621no—
300Q8—21no—
301Q8—621no—
302Q8—621no—
303Q8—1242no—
304Q8#9249912yes—
305D4—622no—
306D4—621no—
307D4—621no—
308D4—621no—
309D4—621no—
310D4—1242no—
311D4—1242no—
312D4—1242no—
313D4—2481no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—311no—
319C2×C4—311no—
320C2×C4—621no—
321C2×C4—621no—
322C2×C4—621no—
323C2×C4—621no—
324C2×C4—621no—
325C2×C4—621no—
326C2×C4—1242no—
327C2×C4—1242no—
328C2×C4—2481no—
329C2×C4—2481no—
330C2×C4D4×D3111yescharacteristic
331C2×C4D4×D3111yescharacteristic
332C2×C4C23×D3111yescharacteristic
333C8—21no—
334C8—21no—
335C8—621no—
336C8—621no—
337C22—312no—
338C22—621no—
339C22—621no—
340C22—621no—
341C22—621no—
342C22—621no—
343C22—1241no—
344C22—1241no—
345C22—1241no—
346C22—1241no—
347C22—1241no—
348C22—1241no—
349C22C2×D4×D3111yescharacteristic
350C4—21no—
351C4—22no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—621no—
357C4—621no—
358C4—1241no—
359C4—1241no—
360C4C2×#9249911yescharacteristic
361C4#1175856611yescharacteristic
362C2—622no—
363C2—1241no—
364C2—2481no—
365C2—2481no—
366C2#1452169011yescharacteristic
367C2#135×D3111yescharacteristic
368C2#1452185811yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#479C2
socleC22×C31C22×D4
hypercenter#479D31
hypocenterC31#3301
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #14521752C2semidirect
2. #14521711C2semidirect
3. #14521406C2semidirect
4. #14521392C2semidirect
5. #14521369C2semidirect
6. #14521286C2semidirect
7. #14521279C2semidirect
8. #14521265C2semidirect
9. #14521197C2semidirect
10. #14521189C2semidirect
11. C4×#92481C2semidirect
12. #14521114C2semidirect
13. #14521044C2semidirect
14. #103×D31C2semidirect
15. C31×#479C2semidirect
183. #479D31semidirect
243. C31#3301semidirect

Maximal subgroups

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

subgroupindex
#145217522
#145217112
#145214062
#145213922
#145213692
#145212862
#145212792
#145212652
#145211972
#145211892
C4×#924812
#145211142
#145210442
#103×D312
C31×#4792
#330131