Finite Group Databasebeta

← #16857672

Subgroups — #16857672

Order 3968.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521703C211yesmaximal, characteristic, complemented
2#14521408C211yesmaximal, characteristic, complemented
3#14521377C211yesmaximal, characteristic, complemented
4#14521365C211yesmaximal, characteristic, complemented
5#14521339C211yesmaximal, characteristic, complemented
6#14521300C211yesmaximal, characteristic, complemented
7#14521280C211yesmaximal, characteristic, complemented
8#14521261C211yesmaximal, characteristic, complemented
9#14521194C211yesmaximal, characteristic, complemented
10#14521183C211yesmaximal, characteristic, complemented
11#14521159C211yesmaximal, characteristic, complemented
12#14521121C211yesmaximal, characteristic, complemented
13#14521050C211yesmaximal, characteristic, complemented
14C2×#11758420C211yesmaximal, characteristic, complemented
15C31×#546C211yesmaximal, characteristic, complemented
16C2×#41×C31C2211yescharacteristic
17C22×D4×C31C2211yescharacteristic
18C2×#92497—21no—
19C31×#124C2211yescharacteristic
20C31×#123—21no—
21C31×C22⋊Q8C2211yescharacteristic
22C31×#121—21no—
23C31×#121C2211yescharacteristic
24C31×#120—21no—
25C4×D4×C31C2211yescharacteristic
26C4×D4×C31C2211yescharacteristic
27C2×C22⋊C4×C31—21no—
28C2×#92481C2211yescharacteristic, complemented
29C2×#92479C2211yescharacteristic
30C2×#92479C2211yescharacteristic
31#11758507C2211yescharacteristic
32#11758507C2211yescharacteristic, complemented
33C2×C4⋊Dic31C2211yescharacteristic
34C2×C4⋊Dic31C2211yescharacteristic, complemented
35C2×#92474C2211yescharacteristic, complemented
36C22×C31⋊C8C2211yescharacteristic
37#11758474—21no—
38#11758463—21no—
39#11758463—21no—
40C4×D124C2211yescharacteristic, complemented
41#11758446C2211yescharacteristic, complemented
42#11758423C2211yescharacteristic, complemented
43#11758423C2211yescharacteristic, complemented
44#11758423C2211yescharacteristic, complemented
45#11758420C2211yescharacteristic
46#11758420C2211yescharacteristic
47#11758420C2211yescharacteristic
48#11758420C2211yescharacteristic
49#11758420C2211yescharacteristic
50#11758420C2211yescharacteristic
51C22⋊(C31⋊C8)C2211yescharacteristic
52C22⋊(C31⋊C8)C2211yescharacteristic, complemented
53#11758397C2211yescharacteristic, complemented
54#11758396C2211yescharacteristic, complemented
55#11758396C2211yescharacteristic, complemented
56#11758396C2211yescharacteristic, complemented
57C4⋊(C31⋊C8)C2211yescharacteristic, complemented
58#11758391C2211yescharacteristic, complemented
59C24×C31—21no—
60#41×C31—22no—
61#41×C31—41no—
62C2×Q8×C31C2311yescharacteristic
63C2×D4×C31—22no—
64C2×D4×C31—21no—
65C2×D4×C31—21no—
66C2×D4×C31—21no—
67C2×D4×C31—41no—
68C2×D4×C31D411yescharacteristic
69C2×D4×C31C2311yescharacteristic
70C2×D4×C31C2311yescharacteristic
71C22×C4×C31—21no—
72C22×C4×C31—21no—
73C22×C4×C31C2311yescharacteristic
74C22×C4×C31C2311yescharacteristic
75C2×C22⋊D31—21no—
76C2×C22⋊D31—21no—
77C22×Dic31—21no—
78C22×Dic31—21no—
79#92497—44no—
80C2×D124C2311yescharacteristic
81C2×C4×D31—21no—
82C2×Dic62—21no—
83C4⋊C4×C31—21no—
84C4⋊C4×C31D411yescharacteristic
85C4⋊C4×C31C2311yescharacteristic
86C22⋊C4×C31—21no—
87C22⋊C4×C31—21no—
88C22⋊C4×C31—21no—
89C22⋊C4×C31—21no—
90C22⋊C4×C31—21no—
91C22⋊C4×C31D411yescharacteristic
92C22⋊C4×C31D411yescharacteristic
93C42×C31C2311yescharacteristic
94#92481—41no—
95#92479—22no—
96#92479—41no—
97(C2×D31)⋊C4—21no—
98(C2×D31)⋊C4—21no—
99(C2×D31)⋊C4—21no—
100C4⋊Dic31—21no—
101C4⋊Dic31—21no—
102C4⋊Dic31—21no—
103C4⋊Dic31C2311yescharacteristic
104C4⋊Dic31C2311yescharacteristic
105C4⋊Dic31C2311yescharacteristic
106#92474—41no—
107C2×C31⋊C8—41no—
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110C2×C31⋊C8C2311yescharacteristic
111C2×C31⋊C8C2311yescharacteristic
112C23×C31—21no—
113C23×C31—21no—
114C23×C31—42no—
115C23×C31—42no—
116C23×C31—81no—
117C23×C31C2×D411yescharacteristic
118C23×C31C2×D411yescharacteristic
119C22×D31—21no—
120Q8×C31—21no—
121Q8×C31—21no—
122D4×C31—22no—
123D4×C31—21no—
124D4×C31—21no—
125D4×C31—21no—
126D4×C31—42no—
127D4×C31—42no—
128D4×C31—81no—
129D4×C31#4112yescomplemented
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—21no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31—42no—
137C2×C4×C31—81no—
138C2×C4×C31C2×D411yescharacteristic
139C2×C4×C31C2×D411yescharacteristic
140C2×C4×C31C2×D411yescharacteristic
141C2×C4×C31C2×D411yescharacteristic
142C2×C4×C31C2411yescharacteristic
143C22⋊D31—42no—
144C22⋊D31—42no—
145C2×Dic31—21no—
146C2×Dic31—21no—
147C2×Dic31—21no—
148C2×Dic31—42no—
149C2×Dic31—42no—
150D124—21no—
151D124—21no—
152C4×D31—42no—
153Dic62—42no—
154C31⋊C8—21no—
155C31⋊C8—21no—
156C31⋊C8—21no—
157C31⋊C8—21no—
158#3306—311nomaximal, Sylow
159C22×C31—21no—
160C22×C31—21no—
161C22×C31—21no—
162C22×C31—22no—
163C22×C31—21no—
164C22×C31—21no—
165C22×C31—41no—
166C22×C31—41no—
167C22×C31—41no—
168C22×C31—41no—
169C22×C31—41no—
170C22×C31—84no—
171C22×C31AGL(1,ℤ/8)12yes—
172C22×C31C22×D411yescharacteristic
173C2×D31—41no—
174C2×D31—41no—
175C2×D31—41no—
176C4×C31—21no—
177C4×C31—21no—
178C4×C31—21no—
179C4×C31—21no—
180C4×C31—41no—
181C4×C31—41no—
182C4×C31C2×#4111yescharacteristic
183C4×C31H(5,𝔽2)11yescharacteristic
184Dic31—41no—
185Dic31—41no—
186Dic31—41no—
187#547—311no—
188#546D3111yescharacteristic, complemented
189#489—311no—
190#483—311no—
191#481—311no—
192#476—311no—
193#469—311no—
194#465—311no—
195#463—311no—
196#449—311no—
197#447—311no—
198#442—311no—
199#435—311no—
200#417—311no—
201C2×#102—311no—
202C2×C31—22no—
203C2×C31—41no—
204C2×C31—42no—
205C2×C31—81no—
206C2×C31#54611yescharacteristic
207C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
208C2×C31#57711yescharacteristic
209D31—81no—
210C2×#41—621no—
211C2×#41C2×D3111yescharacteristic
212C22×D4C2×D3111yescharacteristic
213C2×SD16—311no—
214C2×D8—311no—
215C2×D8—311no—
216C2×M16—311no—
217C22×C8—311no—
218C4⋊Q8—311no—
219#124C2×D3111yescharacteristic
220#123—21no—
221#123—621no—
222#123—621no—
223C22⋊Q8—621no—
224C22⋊Q8C2×D3111yescharacteristic
225#121—21no—
226#121—311no—
227#121—311no—
228#121C2×D3111yescharacteristic
229#120—21no—
230C4×D4—311no—
231C4×D4C2×D3111yescharacteristic
232C4×D4C2×D3111yescharacteristic
233C2×C4⋊C4—311no—
234C2×C4⋊C4—311no—
235C2×C22⋊C4—21no—
236#106—311no—
237#106—311no—
238#106—311no—
239C4⋊C8—311no—
240#103—311no—
241#103—311no—
242#103—311no—
243#102—311no—
244#102—311no—
245#102—311no—
246#102—311no—
247#102—311no—
248#102—311no—
249#102—311no—
250C22⋊C8—311no—
251C22⋊C8—311no—
252#97—311no—
253C31#330611yescharacteristic, complemented, Sylow
254C24—21no—
255#41—22no—
256#41—41no—
257#41—1244no—
258C2×Q8—621no—
259C2×Q8C22×D3111yescharacteristic
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—311no—
266C2×D4—621no—
267C2×D4—621no—
268C2×D4C22⋊D3111yescharacteristic
269C2×D4C22×D3111yescharacteristic
270C2×D4C22×D3111yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—621no—
274C22×C4—621no—
275C22×C4—621no—
276C22×C4C22×D3111yescharacteristic
277C22×C4C22×D3111yescharacteristic
278SD16—1241no—
279D8—622no—
280D8—1241no—
281M16—1241no—
282C2×C8—311no—
283C2×C8—311no—
284C2×C8—311no—
285C2×C8—311no—
286C2×C8—1241no—
287C4⋊C4—21no—
288C4⋊C4—311no—
289C4⋊C4—311no—
290C4⋊C4—311no—
291C4⋊C4—621no—
292C4⋊C4—621no—
293C4⋊C4—621no—
294C4⋊C4C22⋊D3111yescharacteristic
295C4⋊C4C22×D3111yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—621no—
302C22⋊C4—621no—
303C22⋊C4—621no—
304C22⋊C4C22⋊D3111yescharacteristic
305C22⋊C4C22⋊D3111yescharacteristic
306C42C22×D3111yescharacteristic
307C23—21no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—621no—
313C23C2×C22⋊D3111yescharacteristic
314C23C2×C22⋊D3111yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—1242no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—42no—
324D4—81no—
325D4—621no—
326D4—621no—
327D4—1242no—
328D4—1242no—
329D4#9249712yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—81no—
338C2×C4—621no—
339C2×C4—621no—
340C2×C4—621no—
341C2×C4—1242no—
342C2×C4—1242no—
343C2×C4—1242no—
344C2×C4C2×C22⋊D3111yescharacteristic
345C2×C4C2×C22⋊D3111yescharacteristic
346C2×C4C2×C22⋊D3111yescharacteristic
347C2×C4C2×C22⋊D3111yescharacteristic
348C2×C4C23×D3111yescharacteristic
349C8—621no—
350C8—621no—
351C8—621no—
352C8—621no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—21no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—1241no—
366C22—1241no—
367C22—1241no—
368C22#1175852612yes—
369C22C22×C22⋊D3111yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—1241no—
377C4—1241no—
378C4—1241no—
379C4C2×#9249711yescharacteristic
380C4#1175856111yescharacteristic
381C2—22no—
382C2—41no—
383C2—42no—
384C2—81no—
385C2—2481no—
386C2#1452169311yescharacteristic
387C2C2×#1175852611yescharacteristic
388C2#1452186011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#546C2
socleC22×C31C22×D4
hypercenter#546D31
hypocenterC31#3306
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #14521703C2semidirect
2. #14521408C2semidirect
3. #14521377C2semidirect
4. #14521365C2semidirect
5. #14521339C2semidirect
6. #14521300C2semidirect
7. #14521280C2semidirect
8. #14521261C2semidirect
9. #14521194C2semidirect
10. #14521183C2semidirect
11. #14521159C2semidirect
12. #14521121C2semidirect
13. #14521050C2semidirect
14. C2×#11758420C2semidirect
15. C31×#546C2semidirect
28. C2×#92481C22semidirect
32. #11758507C22semidirect
34. C2×C4⋊Dic31C22semidirect
35. C2×#92474C22semidirect
40. C4×D124C22semidirect
41. #11758446C22semidirect
42. #11758423C22semidirect
43. #11758423C22semidirect
44. #11758423C22semidirect
52. C22⋊(C31⋊C8)C22semidirect
53. #11758397C22semidirect
54. #11758396C22semidirect
55. #11758396C22semidirect
56. #11758396C22semidirect
57. C4⋊(C31⋊C8)C22semidirect
58. #11758391C22semidirect
129. D4×C31#41semidirect
188. #546D31semidirect
253. C31#3306semidirect
329. D4#92497semidirect

Maximal subgroups

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

subgroupindex
#145217032
#145214082
#145213772
#145213652
#145213392
#145213002
#145212802
#145212612
#145211942
#145211832
#145211592
#145211212
#145210502
C2×#117584202
C31×#5462
#330631