Finite Group Databasebeta

← #16857561

Subgroups — #16857561

Order 3968.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521745C211yesmaximal, characteristic, complemented
2#14521403C211yesmaximal, characteristic, complemented
3#14521382C211yesmaximal, characteristic, complemented
4#14521370C211yesmaximal, characteristic, complemented
5#14521349C211yesmaximal, characteristic, complemented
6#14521283C211yesmaximal, characteristic, complemented
7#14521280C211yesmaximal, characteristic, complemented
8#14521261C211yesmaximal, characteristic, complemented
9#14521194C211yesmaximal, characteristic, complemented
10#14521183C211yesmaximal, characteristic, complemented
11C4×#92479C211yesmaximal, characteristic, complemented
12D4×C31⋊C8C211yesmaximal, characteristic, complemented
13#14521045C211yesmaximal, characteristic, complemented
14C2×#11758420C211yesmaximal, characteristic, complemented
15C31×#546C211yesmaximal, characteristic, complemented
16C2×#41×C31C2211yescharacteristic
17C22×D4×C31C2211yescharacteristic
18C31×#124C2211yescharacteristic
19C31×#123—21no—
20C31×C22⋊Q8C2211yescharacteristic
21C31×#121—21no—
22C31×#121C2211yescharacteristic
23C31×#120—21no—
24C4×D4×C31C2211yescharacteristic
25C4×D4×C31C2211yescharacteristic
26C2×C22⋊C4×C31—21no—
27C2×#92481C2211yescharacteristic, complemented
28#11758516—21no—
29C2×#92479C2211yescharacteristic
30C2×#92479C2211yescharacteristic
31#11758507C2211yescharacteristic
32#11758507C2211yescharacteristic, complemented
33#11758503C2211yescharacteristic, complemented
34C2×C4⋊Dic31C2211yescharacteristic
35C22×C31⋊C8C2211yescharacteristic
36C22×C31⋊C8C2211yescharacteristic, complemented
37#11758475—21no—
38#11758460—21no—
39(C22⋊D31)⋊C4—21no—
40C4×D124C2211yescharacteristic, complemented
41#11758447C2211yescharacteristic, 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#11758395C2211yescharacteristic, complemented
56#11758395C2211yescharacteristic, complemented
57C4⋊(C31⋊C8)C2211yescharacteristic, complemented
58C4×C31⋊C8C2211yescharacteristic, 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—
78C2×D124C2311yescharacteristic
79C2×C4×D31—21no—
80C4⋊C4×C31—21no—
81C4⋊C4×C31D411yescharacteristic
82C4⋊C4×C31C2311yescharacteristic
83C22⋊C4×C31—21no—
84C22⋊C4×C31—21no—
85C22⋊C4×C31—21no—
86C22⋊C4×C31—21no—
87C22⋊C4×C31—21no—
88C22⋊C4×C31D411yescharacteristic
89C22⋊C4×C31D411yescharacteristic
90C42×C31C2311yescharacteristic
91C22⋊Dic31—21no—
92#92481—41no—
93#92479—22no—
94#92479—41no—
95(C2×D31)⋊C4—21no—
96(C2×D31)⋊C4—21no—
97(C2×D31)⋊C4—21no—
98C4⋊Dic31—21no—
99C4⋊Dic31C2311yescharacteristic
100C4⋊Dic31C2311yescharacteristic
101C4⋊Dic31C2311yescharacteristic
102Dic31⋊C4—21no—
103Dic31⋊C4—21no—
104C4×Dic31—21no—
105C2×C31⋊C8—41no—
106C2×C31⋊C8—41no—
107C2×C31⋊C8C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110C2×C31⋊C8C2311yescharacteristic
111C23×C31—21no—
112C23×C31—21no—
113C23×C31—42no—
114C23×C31—42no—
115C23×C31—81no—
116C23×C31C2×D411yescharacteristic
117C23×C31C2×D411yescharacteristic
118C22×D31—21no—
119Q8×C31—21no—
120Q8×C31—21no—
121D4×C31—22no—
122D4×C31—21no—
123D4×C31—21no—
124D4×C31—21no—
125D4×C31—42no—
126D4×C31—42no—
127D4×C31—81no—
128D4×C31#4112yes—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—21no—
134C2×C4×C31—21no—
135C2×C4×C31—42no—
136C2×C4×C31—81no—
137C2×C4×C31C2×D411yescharacteristic
138C2×C4×C31C2×D411yescharacteristic
139C2×C4×C31C2×D411yescharacteristic
140C2×C4×C31C2×D411yescharacteristic
141C2×C4×C31C2411yescharacteristic
142C22⋊D31—42no—
143C22⋊D31—81no—
144C2×Dic31—21no—
145C2×Dic31—21no—
146C2×Dic31—21no—
147C2×Dic31—81no—
148D124—21no—
149D124—21no—
150C4×D31—81no—
151C31⋊C8—21no—
152C31⋊C8—21no—
153C31⋊C8—21no—
154C31⋊C8—21no—
155#3297—311nomaximal, Sylow
156C22×C31—21no—
157C22×C31—21no—
158C22×C31—21no—
159C22×C31—22no—
160C22×C31—21no—
161C22×C31—21no—
162C22×C31—41no—
163C22×C31—41no—
164C22×C31—41no—
165C22×C31—41no—
166C22×C31—41no—
167C22×C31—84no—
168C22×C31#13512yes—
169C22×C31C22×D411yescharacteristic
170C2×D31—41no—
171C2×D31—41no—
172C2×D31—41no—
173C4×C31—21no—
174C4×C31—21no—
175C4×C31—21no—
176C4×C31—21no—
177C4×C31—41no—
178C4×C31—41no—
179C4×C31C2×#4111yescharacteristic
180C4×C31H(5,𝔽2)11yescharacteristic
181Dic31—41no—
182Dic31—41no—
183Dic31—41no—
184#553—311no—
185#546D3111yescharacteristic, complemented
186#488—311no—
187#484—311no—
188#482—311no—
189#478—311no—
190#466—311no—
191#465—311no—
192#463—311no—
193#449—311no—
194#447—311no—
195C4×D8—311no—
196C8×D4—311no—
197#416—311no—
198C2×#102—311no—
199C2×C31—22no—
200C2×C31—41no—
201C2×C31—42no—
202C2×C31—81no—
203C2×C31#54611yescharacteristic
204C2×C31C2×#13511yescharacteristic
205C2×C31#57611yescharacteristic
206D31—81no—
207C2×#41C2×D3111yescharacteristic
208C22×D4C2×D3111yescharacteristic
209C2×SD16—311no—
210C2×D8—311no—
211C2×D8—311no—
212C22×C8—311no—
213C22×C8—311no—
214#126—621no—
215#125—311no—
216#124C2×D3111yescharacteristic
217#123—21no—
218#123—621no—
219C22⋊Q8C2×D3111yescharacteristic
220#121—21no—
221#121—311no—
222#121—311no—
223#121—621no—
224#121C2×D3111yescharacteristic
225#120—21no—
226C4×D4—311no—
227C4×D4—621no—
228C4×D4C2×D3111yescharacteristic
229C4×D4C2×D3111yescharacteristic
230#117—311no—
231C2×C4⋊C4—311no—
232C2×C22⋊C4—21no—
233#107—311no—
234#107—311no—
235#106—311no—
236C4⋊C8—311no—
237#103—311no—
238#103—311no—
239#103—311no—
240#102—311no—
241#102—311no—
242#102—311no—
243#102—311no—
244#102—311no—
245#102—311no—
246#102—311no—
247C22⋊C8—311no—
248C22⋊C8—311no—
249C4×C8—311no—
250C31#329711yescharacteristic, complemented, Sylow
251C24—21no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D3111yescharacteristic
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—41no—
260C2×D4—311no—
261C2×D4—621no—
262C2×D4—621no—
263C2×D4C22⋊D3111yescharacteristic
264C2×D4C22×D3111yescharacteristic
265C2×D4C22×D3111yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—621no—
269C22×C4—621no—
270C22×C4C22×D3111yescharacteristic
271C22×C4C22×D3111yescharacteristic
272SD16—1241no—
273D8—622no—
274D8—1241no—
275C2×C8—311no—
276C2×C8—311no—
277C2×C8—311no—
278C2×C8—311no—
279C2×C8—1241no—
280C2×C8—1241no—
281C4⋊C4—21no—
282C4⋊C4—311no—
283C4⋊C4—311no—
284C4⋊C4—311no—
285C4⋊C4—621no—
286C4⋊C4—621no—
287C4⋊C4—621no—
288C4⋊C4C22⋊D3111yescharacteristic
289C4⋊C4C22×D3111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—621no—
296C22⋊C4—621no—
297C22⋊C4—621no—
298C22⋊C4—621no—
299C22⋊C4C22⋊D3111yescharacteristic
300C22⋊C4C22⋊D3111yescharacteristic
301C42—621no—
302C42C22×D3111yescharacteristic
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—621no—
309C23C2×C22⋊D3111yescharacteristic
310C23C2×C22⋊D3111yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—22no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—42no—
318D4—42no—
319D4—81no—
320D4—621no—
321D4—621no—
322D4—1242no—
323D4—2481no—
324D4#9249712yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—81no—
333C2×C4—621no—
334C2×C4—621no—
335C2×C4—621no—
336C2×C4—2481no—
337C2×C4—2481no—
338C2×C4C2×C22⋊D3111yescharacteristic
339C2×C4C2×C22⋊D3111yescharacteristic
340C2×C4C2×C22⋊D3111yescharacteristic
341C2×C4C2×C22⋊D3111yescharacteristic
342C2×C4C23×D3111yescharacteristic
343C8—621no—
344C8—621no—
345C8—621no—
346C8—621no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—21no—
352C22—21no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—84no—
359C22—1241no—
360C22—1241no—
361C22—1241no—
362C22#1175852712yes—
363C22C22×C22⋊D3111yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—1241no—
371C4—1241no—
372C4—1241no—
373C4C2×#9249711yescharacteristic
374C4#1175856111yescharacteristic
375C2—22no—
376C2—41no—
377C2—42no—
378C2—81no—
379C2—2481no—
380C2#1452169311yescharacteristic
381C2C2×#1175852711yescharacteristic
382C2#1452185211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#546C2
socleC22×C31C22×D4
hypercenter#546D31
hypocenterC31#3297
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. #14521745C2semidirect
2. #14521403C2semidirect
3. #14521382C2semidirect
4. #14521370C2semidirect
5. #14521349C2semidirect
6. #14521283C2semidirect
7. #14521280C2semidirect
8. #14521261C2semidirect
9. #14521194C2semidirect
10. #14521183C2semidirect
11. C4×#92479C2semidirect
12. D4×C31⋊C8C2semidirect
13. #14521045C2semidirect
14. C2×#11758420C2semidirect
15. C31×#546C2semidirect
27. C2×#92481C22semidirect
32. #11758507C22semidirect
33. #11758503C22semidirect
36. C22×C31⋊C8C22semidirect
40. C4×D124C22semidirect
41. #11758447C22semidirect
42. #11758423C22semidirect
43. #11758423C22semidirect
44. #11758423C22semidirect
52. C22⋊(C31⋊C8)C22semidirect
53. #11758397C22semidirect
54. #11758396C22semidirect
55. #11758395C22semidirect
56. #11758395C22semidirect
57. C4⋊(C31⋊C8)C22semidirect
58. C4×C31⋊C8C22semidirect
185. #546D31semidirect
250. C31#3297semidirect

Maximal subgroups

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

subgroupindex
#145217452
#145214032
#145213822
#145213702
#145213492
#145212832
#145212802
#145212612
#145211942
#145211832
C4×#924792
D4×C31⋊C82
#145210452
C2×#117584202
C31×#5462
#329731