Finite Group Databasebeta

← #16857646

Subgroups — #16857646

Order 3968.

396 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#14521767C211yesmaximal, characteristic, complemented
2#14521718C211yesmaximal, characteristic
3#14521394C211yesmaximal, characteristic, complemented
4#14521373C211yesmaximal, characteristic, complemented
5#14521372C211yesmaximal, characteristic, complemented
6#14521332C211yesmaximal, characteristic, complemented
7#14521278C211yesmaximal, characteristic, complemented
8#14521277C211yesmaximal, characteristic, complemented
9#14521248C211yesmaximal, characteristic, complemented
10#14521214C211yesmaximal, characteristic, complemented
11#14521211C211yesmaximal, characteristic, complemented
12#14521141C211yesmaximal, characteristic, complemented
13C8×C22⋊D31C211yesmaximal, characteristic, complemented
14#14521044C211yesmaximal, characteristic, complemented
15C31×#416C211yesmaximal, characteristic, complemented
16C2×#41×C31C2211yescharacteristic
17C2×#92499C2211yescharacteristic
18C22×C8×C31C2211yescharacteristic
19C31×#117C2211yescharacteristic
20Q8×Dic31C2211yescharacteristic
21C2×#92482C2211yescharacteristic
22#11758517—21no—
23#11758517C2211yescharacteristic
24#11758515—21no—
25#11758515C2211yescharacteristic
26C2×#92480C2211yescharacteristic
27#11758507—21no—
28#11758507C2211yescharacteristic
29C4×C22⋊D31—21no—
30C4×C22⋊D31C2211yescharacteristic
31#11758501C2211yescharacteristic
32C2×#92470C2211yescharacteristic
33C2×C8×D31C2211yescharacteristic
34#11758474C2211yescharacteristic
35#11758469C2211yescharacteristic
36#11758465C2211yescharacteristic
37#11758464C2211yescharacteristic
38#11758462—21no—
39#11758456—21no—
40#11758453—21no—
41C4×Dic62—21no—
42C31×#103C2211yescharacteristic
43C31×#103C2211yescharacteristic
44C31×#102C2211yescharacteristic
45C31×#102C2211yescharacteristic
46#11758423C2211yescharacteristic
47#11758420C2211yescharacteristic
48C22⋊(C31⋊C8)C2211yescharacteristic
49#11758409C2211yescharacteristic
50(C2×D31)⋊C8C2211yescharacteristic
51#11758405C2211yescharacteristic
52#11758404C2211yescharacteristic
53Dic31⋊C8C2211yescharacteristic
54C8×Dic31C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758397C2211yescharacteristic
57#11758396C2211yescharacteristic
58#11758395C2211yescharacteristic
59#41×C31—22no—
60#41×C31—41no—
61C2×Q8×C31C2311yescharacteristic
62C2×D4×C31—21no—
63C2×D4×C31C2311yescharacteristic
64C22×C4×C31—21no—
65C22×C4×C31C2311yescharacteristic
66C2×C22⋊D31—21no—
67C2×C22⋊D31—21no—
68C2×C22⋊D31—21no—
69C2×C22⋊D31—21no—
70C2×C22⋊D31D411yescharacteristic
71#92499—22no—
72#92499—41no—
73C2×D124—21no—
74C2×D124C2311yescharacteristic
75C2×C4×D31—21no—
76C2×C4×D31C2311yescharacteristic
77C2×Dic62—21no—
78C2×Dic62C2311yescharacteristic
79C2×C8×C31—41no—
80C2×C8×C31C2311yescharacteristic
81C2×C8×C31C2311yescharacteristic
82C4⋊C4×C31C2311yescharacteristic
83C4⋊C4×C31C2311yescharacteristic
84C22⋊C4×C31—21no—
85C42×C31—21no—
86C22⋊Dic31—21no—
87C22⋊Dic31—21no—
88C22⋊Dic31D411yescharacteristic
89#92482—22no—
90#92480—41no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4—21no—
93(C2×D31)⋊C4—21no—
94(C2×D31)⋊C4D411yescharacteristic
95C4⋊Dic31—21no—
96C4⋊Dic31—21no—
97C4⋊Dic31C2311yescharacteristic
98C4⋊Dic31C2311yescharacteristic
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101Dic31⋊C4—21no—
102Dic31⋊C4D411yescharacteristic
103C4×Dic31—21no—
104C4×Dic31—21no—
105C4×Dic31—21no—
106C4×Dic31C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109#92470—41no—
110C8×D31—41no—
111C23×C31—21no—
112C23×C31C2×D411yescharacteristic
113C22×D31—21no—
114C22×D31C2×D411yescharacteristic
115Q8×C31—21no—
116Q8×C31#4112yes—
117D4×C31—21no—
118D4×C31—21no—
119D4×C31—42no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—42no—
126C2×C4×C31C2×D411yescharacteristic
127C2×C4×C31C2411yescharacteristic
128C22⋊D31—22no—
129C22⋊D31—42no—
130C22⋊D31—81no—
131C22⋊D31—81no—
132C22⋊D31—81no—
133C2×Dic31—21no—
134C2×Dic31—21no—
135C2×Dic31—21no—
136C2×Dic31C2×D411yescharacteristic
137C2×Dic31C2×D411yescharacteristic
138C2×Dic31C2×D411yescharacteristic
139D124—21no—
140D124—21no—
141D124—42no—
142C4×D31—21no—
143C4×D31—21no—
144C4×D31—42no—
145Dic62—21no—
146Dic62—21no—
147Dic62—42no—
148C8×C31—21no—
149C8×C31—21no—
150C31⋊C8—21no—
151C31⋊C8—21no—
152#3304—311nomaximal, Sylow
153C22×C31—21no—
154C22×C31—21no—
155C22×C31—21no—
156C22×C31—41no—
157C22×C31—41no—
158C22×C31—41no—
159C22×C31C22×D411yescharacteristic
160C2×D31—21no—
161C2×D31—21no—
162C2×D31—21no—
163C2×D31—41no—
164C2×D31—41no—
165C2×D31—41no—
166C4×C31—22no—
167C4×C31—21no—
168C4×C31—41no—
169C4×C31—41no—
170C4×C31C2×#4111yescharacteristic
171C4×C31H(5,𝔽2)11yescharacteristic
172Dic31—21no—
173Dic31—21no—
174Dic31—41no—
175Dic31—41no—
176Dic31—41no—
177Dic31#13512yes—
178#556—311no—
179#550—311no—
180#486—311no—
181#482—311no—
182#482—311no—
183#475—311no—
184#465—311no—
185#465—311no—
186#460—311no—
187#452—311no—
188#452—311no—
189C4×Q16—311no—
190C8×D4—311no—
191#416—311no—
192#416D3111yescharacteristic, complemented
193C2×C31—41no—
194C2×C31—81no—
195C2×C31#54611yescharacteristic
196C2×C31C2×#13511yescharacteristic
197C2×C31#57711yescharacteristic
198D31—41no—
199D31—81no—
200C2×#41—311no—
201C2×#41C2×D3111yescharacteristic
202C2×Q16—311no—
203C2×SD16—311no—
204C2×SD16—311no—
205C22×C8—311no—
206C22×C8C2×D3111yescharacteristic
207C4⋊Q8—311no—
208#127—311no—
209#127—621no—
210#126—621no—
211#126—621no—
212#124—621no—
213C22⋊Q8—311no—
214C22⋊Q8—311no—
215#121—311no—
216#121—311no—
217#121—621no—
218#121—621no—
219C4×Q8—311no—
220C4×Q8—311no—
221C4×Q8—621no—
222C4×D4—311no—
223C4×D4—621no—
224#117—311no—
225#117C2×D3111yescharacteristic
226#107—311no—
227#106—311no—
228#106—311no—
229C4⋊C8—311no—
230#103—311no—
231#103—311no—
232#103C2×D3111yescharacteristic
233#103C2×D3111yescharacteristic
234#102—311no—
235#102—311no—
236#102—311no—
237#102—311no—
238#102C2×D3111yescharacteristic
239#102C2×D3111yescharacteristic
240C22⋊C8—311no—
241C22⋊C8—311no—
242C4×C8—311no—
243C31#330411yescharacteristic, complemented, Sylow
244#41—22no—
245#41—41no—
246#41—622no—
247#41—1241no—
248C2×Q8—311no—
249C2×Q8—621no—
250C2×Q8C22×D3111yescharacteristic
251C2×D4—21no—
252C2×D4—311no—
253C2×D4—311no—
254C2×D4—621no—
255C2×D4—621no—
256C2×D4—621no—
257C2×D4—621no—
258C2×D4—621no—
259C2×D4C22×D3111yescharacteristic
260C22×C4—21no—
261C22×C4—311no—
262C22×C4—621no—
263C22×C4C22×D3111yescharacteristic
264Q16—622no—
265SD16—1241no—
266SD16—1241no—
267C2×C8—41no—
268C2×C8—311no—
269C2×C8—311no—
270C2×C8—1241no—
271C2×C8C22×D3111yescharacteristic
272C2×C8C22×D3111yescharacteristic
273C4⋊C4—311no—
274C4⋊C4—311no—
275C4⋊C4—311no—
276C4⋊C4—621no—
277C4⋊C4—621no—
278C4⋊C4—621no—
279C4⋊C4—621no—
280C4⋊C4—621no—
281C4⋊C4C22×D3111yescharacteristic
282C4⋊C4C22×D3111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—311no—
285C22⋊C4—311no—
286C22⋊C4—621no—
287C22⋊C4—621no—
288C22⋊C4—621no—
289C22⋊C4—621no—
290C22⋊C4—621no—
291C42—21no—
292C42—311no—
293C42—621no—
294C42—621no—
295C42—621no—
296C23—21no—
297C23—311no—
298C23—621no—
299C23D4×D3111yescharacteristic
300Q8—21no—
301Q8—621no—
302Q8—621no—
303Q8—1242no—
304Q8#9249512yes—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—622no—
309D4—621no—
310D4—621no—
311D4—1242no—
312D4—1242no—
313D4—2481no—
314D4—2481no—
315D4—2481no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—311no—
323C2×C4—311no—
324C2×C4—311no—
325C2×C4—621no—
326C2×C4—621no—
327C2×C4—621no—
328C2×C4—621no—
329C2×C4—621no—
330C2×C4—1242no—
331C2×C4D4×D3111yescharacteristic
332C2×C4C23×D3111yescharacteristic
333C8—21no—
334C8—21no—
335C8—621no—
336C8—621no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—621no—
344C22—621no—
345C22—621no—
346C22—1241no—
347C22—1241no—
348C22—1241no—
349C22C2×D4×D3111yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—312no—
355C4—621no—
356C4—621no—
357C4—1241no—
358C4—1241no—
359C4—1241no—
360C4C2×#9249511yescharacteristic
361C4#1175856111yescharacteristic
362C2—41no—
363C2—81no—
364C2—1241no—
365C2—2481no—
366C2#1452168911yescharacteristic
367C2#135×D3111yescharacteristic
368C2#1452185611yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#416C2
socleC22×C31C22×D4
prime radical#14521718C2
hypercenter#416D31
hypocenterC31#3304
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #14521767C2semidirect
3. #14521394C2semidirect
4. #14521373C2semidirect
5. #14521372C2semidirect
6. #14521332C2semidirect
7. #14521278C2semidirect
8. #14521277C2semidirect
9. #14521248C2semidirect
10. #14521214C2semidirect
11. #14521211C2semidirect
12. #14521141C2semidirect
13. C8×C22⋊D31C2semidirect
14. #14521044C2semidirect
15. C31×#416C2semidirect
192. #416D31semidirect
243. C31#3304semidirect

Maximal subgroups

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

subgroupindex
#145217672
#145217182
#145213942
#145213732
#145213722
#145213322
#145212782
#145212772
#145212482
#145212142
#145212112
#145211412
C8×C22⋊D312
#145210442
C31×#4162
#330431