Finite Group Databasebeta

← #16855909

Subgroups — #16855909

Order 3968.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521653C211yesmaximal, characteristic, complemented
2#14521531C211yesmaximal, characteristic, complemented
3#14521366C211yesmaximal, characteristic, complemented
4#14521361C211yesmaximal, characteristic, complemented
5#14521356C211yesmaximal, characteristic, complemented
6#14521350C211yesmaximal, characteristic, complemented
7#14521241C211yesmaximal, characteristic, complemented
8#14521193C211yesmaximal, characteristic, complemented
9#14521193C211yesmaximal, characteristic, complemented
10#14521158C211yesmaximal, characteristic, complemented
11#14521150C211yesmaximal, characteristic, complemented
12SD16×Dic31C211yesmaximal, characteristic, complemented
13#14521129C211yesmaximal, characteristic, complemented
14#14521109C211yesmaximal, characteristic, complemented
15C31×#460C211yesmaximal, characteristic, complemented
16C2×#92499C2211yescharacteristic
17C2×SD16×C31C2211yescharacteristic
18C2×SD16×C31C2211yescharacteristic
19C31×#127C2211yescharacteristic
20C4×Q8×C31C2211yescharacteristic
21Q8×Dic31C2211yescharacteristic
22#11758516—21no—
23#11758516—21no—
24#11758515C2211yescharacteristic
25#11758515C2211yescharacteristic
26#11758512—21no—
27#11758512—21no—
28D4×Dic31C2211yescharacteristic
29D4×Dic31C2211yescharacteristic
30C2×#92479C2211yescharacteristic
31C2×#92479C2211yescharacteristic
32#11758470—21no—
33#11758470C2211yescharacteristic
34C4⋊C4×D31—21no—
35C4⋊C4×D31C2211yescharacteristic
36C4×D124—21no—
37C4×D124C2211yescharacteristic
38#11758449—21no—
39#11758449C2211yescharacteristic
40#11758447C2211yescharacteristic
41C31×C4⋊C8C2211yescharacteristic
42C31×#102C2211yescharacteristic
43C31×#102C2211yescharacteristic
44#11758423C2211yescharacteristic
45#11758423C2211yescharacteristic
46#11758420C2211yescharacteristic
47#11758420C2211yescharacteristic
48#11758409C2211yescharacteristic
49#11758409C2211yescharacteristic
50(C2×D31)⋊C8C2211yescharacteristic
51(C2×D31)⋊C8C2211yescharacteristic
52#11758406C2211yescharacteristic
53#11758405C2211yescharacteristic
54#11758403C2211yescharacteristic
55C8×Dic31C2211yescharacteristic
56#11758396C2211yescharacteristic
57#11758395C2211yescharacteristic
58C4⋊(C31⋊C8)C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C2×D4×C31—21no—
61C2×D4×C31—21no—
62C2×D4×C31C2311yescharacteristic
63C2×D4×C31C2311yescharacteristic
64C2×C22⋊D31—21no—
65C2×C22⋊D31—21no—
66C22×Dic31—21no—
67C22×Dic31—21no—
68#92499—22no—
69#92499—22no—
70C2×D124—21no—
71C2×D124C2311yescharacteristic
72C2×C4×D31—21no—
73C2×C4×D31—21no—
74C2×C4×D31—21no—
75C2×C4×D31—21no—
76C2×C4×D31C2311yescharacteristic
77SD16×C31—22no—
78SD16×C31—22no—
79C2×C8×C31C2311yescharacteristic
80C2×C8×C31C2311yescharacteristic
81C4⋊C4×C31—21no—
82C4⋊C4×C31C2311yescharacteristic
83C42×C31—21no—
84C42×C31C2311yescharacteristic
85C22⋊Dic31—21no—
86C22⋊Dic31—21no—
87C22⋊Dic31—21no—
88C22⋊Dic31—21no—
89#92479—22no—
90#92479—22no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4—21no—
93(C2×D31)⋊C4D411yescharacteristic
94(C2×D31)⋊C4D411yescharacteristic
95C4⋊Dic31—21no—
96C4⋊Dic31C2311yescharacteristic
97C4⋊Dic31C2311yescharacteristic
98C4⋊Dic31C2311yescharacteristic
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101Dic31⋊C4—21no—
102Dic31⋊C4D411yescharacteristic
103Dic31⋊C4D411yescharacteristic
104C4×Dic31—21no—
105C4×Dic31C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108C23×C31—21no—
109C23×C31—21no—
110C22×D31—21no—
111C22×D31C2×D411yescharacteristic
112Q8×C31—21no—
113Q8×C31#4112yes—
114D4×C31—21no—
115D4×C31—21no—
116D4×C31—21no—
117D4×C31—21no—
118D4×C31—81no—
119D4×C31—81no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31C2×D411yescharacteristic
123C2×C4×C31C2×D411yescharacteristic
124C2×C4×C31C2411yescharacteristic
125C22⋊D31—81no—
126C22⋊D31—81no—
127C2×Dic31—21no—
128C2×Dic31—21no—
129C2×Dic31—21no—
130C2×Dic31—81no—
131C2×Dic31—81no—
132C2×Dic31C2×D411yescharacteristic
133C2×Dic31C2×D411yescharacteristic
134C2×Dic31C2×D411yescharacteristic
135D124—24no—
136D124—21no—
137D124#4112yes—
138C4×D31—24no—
139C4×D31—21no—
140C4×D31—21no—
141C4×D31—81no—
142C4×D31—81no—
143C4×D31—81no—
144C8×C31—21no—
145C8×C31—21no—
146C31⋊C8—21no—
147C31⋊C8—21no—
148#3119—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—21no—
157C2×D31—22no—
158C2×D31—21no—
159C2×D31—21no—
160C2×D31—41no—
161C2×D31—41no—
162C4×C31—22no—
163C4×C31—21no—
164C4×C31—21no—
165C4×C31—41no—
166C4×C31C2×#4111yescharacteristic
167C4×C31C2×#4111yescharacteristic
168Dic31—21no—
169Dic31—21no—
170Dic31—21no—
171Dic31—41no—
172Dic31—41no—
173Dic31—41no—
174#540—311no—
175#520—311no—
176#481—311no—
177#480—311no—
178#479—311no—
179#478—311no—
180#460D3111yescharacteristic, complemented
181#459—311no—
182#449—311no—
183#449—311no—
184#442—311no—
185#440—311no—
186C4×SD16—311no—
187C4×D8—311no—
188#433—311no—
189C2×C31—81no—
190C2×C31—81no—
191C2×C31#52511yescharacteristic
192C2×C31#57611yescharacteristic
193C2×C31#57711yescharacteristic
194D31—41no—
195D31—42no—
196C2×#41—311no—
197C2×SD16C2×D3111yescharacteristic
198C2×SD16C2×D3111yescharacteristic
199C2×D8—311no—
200C2×D8—311no—
201#127C2×D3111yescharacteristic
202#125—311no—
203#123—621no—
204#123—621no—
205#121—311no—
206#121—311no—
207#121—621no—
208#121—621no—
209C4×Q8—311no—
210C4×Q8C2×D3111yescharacteristic
211C4×D4—311no—
212C4×D4—311no—
213C4×D4—311no—
214C4×D4—311no—
215C4×D4—621no—
216C4×D4—621no—
217#117—311no—
218#117—621no—
219C2×C4⋊C4—311no—
220C2×C4⋊C4—621no—
221#107—311no—
222#107—311no—
223#106—311no—
224#106—311no—
225C4⋊C8—311no—
226C4⋊C8C2×D3111yescharacteristic
227#103—311no—
228#103—311no—
229#102—311no—
230#102—311no—
231#102—311no—
232#102—311no—
233#102C2×D3111yescharacteristic
234#102C2×D3111yescharacteristic
235C22⋊C8—311no—
236C22⋊C8—311no—
237#97—311no—
238C4×C8—311no—
239C31#311911yescharacteristic, complemented, Sylow
240#41—622no—
241#41—622no—
242C2×Q8C22×D3111yescharacteristic
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—311no—
246C2×D4—621no—
247C2×D4—621no—
248C2×D4—621no—
249C2×D4C22×D3111yescharacteristic
250C2×D4C22×D3111yescharacteristic
251C22×C4—311no—
252C22×C4—621no—
253C22×C4—621no—
254C22×C4—621no—
255C22×C4—621no—
256C22×C4—621no—
257C22×C4—621no—
258SD16—22no—
259SD16—22no—
260D8—622no—
261D8—622no—
262C2×C8—311no—
263C2×C8—311no—
264C2×C8C22×D3111yescharacteristic
265C2×C8C22×D3111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—311no—
268C4⋊C4—311no—
269C4⋊C4—311no—
270C4⋊C4—311no—
271C4⋊C4—311no—
272C4⋊C4—621no—
273C4⋊C4—621no—
274C4⋊C4—621no—
275C4⋊C4—621no—
276C4⋊C4C22×D3111yescharacteristic
277C22⋊C4—311no—
278C22⋊C4—311no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C22⋊C4—621no—
284C22⋊C4—621no—
285C42—21no—
286C42—311no—
287C42—621no—
288C42C22×D3111yescharacteristic
289C23—21no—
290C23—21no—
291C23—311no—
292C23—621no—
293Q8—21no—
294Q8#9249712yes—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—81no—
301D4—312no—
302D4—624no—
303D4—621no—
304D4—2481no—
305D4—2481no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—311no—
309C2×C4—311no—
310C2×C4—311no—
311C2×C4—624no—
312C2×C4—621no—
313C2×C4—621no—
314C2×C4—621no—
315C2×C4—621no—
316C2×C4—621no—
317C2×C4—2481no—
318C2×C4—2481no—
319C2×C4—2481no—
320C2×C4—2481no—
321C2×C4—2481no—
322C2×C4D4×D3111yescharacteristic
323C2×C4D4×D3111yescharacteristic
324C2×C4C23×D3111yescharacteristic
325C8—21no—
326C8—21no—
327C8—621no—
328C8—621no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—622no—
336C22—621no—
337C22—621no—
338C22—621no—
339C22—1241no—
340C22—1241no—
341C22C2×D4×D3111yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—621no—
347C4—621no—
348C4—621no—
349C4—1241no—
350C4—1241no—
351C4—1241no—
352C4C2×#9249711yescharacteristic
353C4#41×D3111yescharacteristic
354C2—81no—
355C2—81no—
356C2—1241no—
357C2—1242no—
358C2#1452155911yescharacteristic
359C2#1452185311yescharacteristic
360C2#1452185511yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#460C2
socleC22×C31C22×D4
hypercenter#460D31
hypocenterC31#3119
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #14521653C2semidirect
2. #14521531C2semidirect
3. #14521366C2semidirect
4. #14521361C2semidirect
5. #14521356C2semidirect
6. #14521350C2semidirect
7. #14521241C2semidirect
8. #14521193C2semidirect
9. #14521193C2semidirect
10. #14521158C2semidirect
11. #14521150C2semidirect
12. SD16×Dic31C2semidirect
13. #14521129C2semidirect
14. #14521109C2semidirect
15. C31×#460C2semidirect
180. #460D31semidirect
239. C31#3119semidirect

Maximal subgroups

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

subgroupindex
#145216532
#145215312
#145213662
#145213612
#145213562
#145213502
#145212412
#145211932
#145211582
#145211502
SD16×Dic312
#145211292
#145211092
C31×#4602
#311931