Finite Group Databasebeta

← #16855965

Subgroups — #16855965

Order 3968.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521662C211yesmaximal, characteristic, complemented
2#14521521C211yesmaximal, characteristic
3#14521393C211yesmaximal, characteristic, complemented
4#14521392C211yesmaximal, characteristic, complemented
5#14521346C211yesmaximal, characteristic, complemented
6#14521255C211yesmaximal, characteristic, complemented
7#14521254C211yesmaximal, characteristic, complemented
8#14521201C211yesmaximal, characteristic
9#14521201C211yesmaximal, characteristic
10#14521148C211yesmaximal, characteristic, complemented
11#14521146C211yesmaximal, characteristic, complemented
12#14521140C211yesmaximal, characteristic, complemented
13#14521136C211yesmaximal, characteristic, complemented
14#14521109C211yesmaximal, characteristic, complemented
15C31×#478C211yesmaximal, characteristic, complemented
16C2×D4×D31C2211yescharacteristic
17C31×#125C2211yescharacteristic, complemented
18C4×D4×C31C2211yescharacteristic
19D4×Dic31C2211yescharacteristic
20C2×#92480C2211yescharacteristic
21C2×#92480C2211yescharacteristic
22C4×C22⋊D31—21no—
23C2×(C2×D31)⋊C4—21no—
24C2×#92470C2211yescharacteristic
25C2×#92470C2211yescharacteristic
26#11758475—21no—
27#11758475—21no—
28#11758474C2211yescharacteristic
29#11758474C2211yescharacteristic
30#11758470C2211yescharacteristic
31#11758469C2211yescharacteristic
32#11758467—21no—
33#11758467—21no—
34#11758464C2211yescharacteristic, complemented
35#11758464C2211yescharacteristic, complemented
36(C22⋊D31)⋊C4—21no—
37C22⋊C4×D31—21no—
38C4×D124C2211yescharacteristic
39#11758449C2211yescharacteristic
40#11758446C2211yescharacteristic, complemented
41C31×#107C2211yescharacteristic, complemented
42C31×#106C2211yescharacteristic, complemented
43C31×C4⋊C8C2211yescharacteristic, complemented
44C31×#102C2211yescharacteristic
45C31×#102C2211yescharacteristic
46(C2×D31)⋊C8C2211yescharacteristic
47(C2×D31)⋊C8C2211yescharacteristic
48#11758404C2211yescharacteristic, complemented
49#11758404C2211yescharacteristic, complemented
50#11758403C2211yescharacteristic, complemented
51C8×Dic31C2211yescharacteristic, complemented
52#11758398C2211yescharacteristic, complemented
53#11758398C2211yescharacteristic, complemented
54#11758397C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758396C2211yescharacteristic, complemented
57#11758395C2211yescharacteristic, complemented
58C4⋊(C31⋊C8)C2211yescharacteristic, complemented
59C23×D31—21no—
60C2×D4×C31C2311yescharacteristic
61C22×C4×C31—21no—
62C2×C22⋊D31—21no—
63C22×Dic31—21no—
64D4×D31—22no—
65D4×D31—22no—
66C2×D124C2311yescharacteristic
67C2×C4×D31—21no—
68C2×C4×D31—21no—
69C2×C4×D31C2311yescharacteristic
70C2×Dic62C2311yescharacteristic
71C2×Dic62C2311yescharacteristic
72C2×C8×C31C2311yescharacteristic
73C2×C8×C31C2311yescharacteristic
74C4⋊C4×C31—21no—
75C4⋊C4×C31—21no—
76C4⋊C4×C31C2311yescharacteristic
77C4⋊C4×C31C2311yescharacteristic
78C4⋊C4×C31C2311yescharacteristic
79C22⋊C4×C31—21no—
80C42×C31C2311yescharacteristic
81C22⋊Dic31—21no—
82#92480—22no—
83#92480—22no—
84(C2×D31)⋊C4—21no—
85(C2×D31)⋊C4—21no—
86(C2×D31)⋊C4—21no—
87(C2×D31)⋊C4—21no—
88(C2×D31)⋊C4—21no—
89(C2×D31)⋊C4D411yescharacteristic
90(C2×D31)⋊C4D411yescharacteristic
91C4⋊Dic31—21no—
92C4⋊Dic31—21no—
93C4⋊Dic31—21no—
94C4⋊Dic31—21no—
95C4⋊Dic31C2311yescharacteristic
96Dic31⋊C4—21no—
97Dic31⋊C4—21no—
98Dic31⋊C4D411yescharacteristic
99Dic31⋊C4D411yescharacteristic
100C4×Dic31—21no—
101C4×Dic31—21no—
102C4×Dic31—21no—
103C4×Dic31C2311yescharacteristic
104C2×C31⋊C8C2311yescharacteristic
105C2×C31⋊C8C2311yescharacteristic
106#92470—22no—
107#92470—22no—
108C23×C31—21no—
109C22×D31—21no—
110C22×D31—24no—
111C22×D31—81no—
112C22×D31—81no—
113C22×D31C2×D411yescharacteristic
114D4×C31—21no—
115D4×C31#4112yes—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—81no—
120C2×C4×C31C2×D411yescharacteristic
121C2×C4×C31C2×D411yescharacteristic
122C2×C4×C31C2411yescharacteristic
123C22⋊D31—24no—
124C2×Dic31—21no—
125C2×Dic31—21no—
126C2×Dic31—21no—
127C2×Dic31—81no—
128C2×Dic31C2×D411yescharacteristic
129C2×Dic31C2×D411yescharacteristic
130C2×Dic31C2×D411yescharacteristic
131D124—21no—
132D124#4112yes—
133C4×D31—21no—
134C4×D31—21no—
135C4×D31—81no—
136C4×D31—81no—
137Dic62—21no—
138Dic62—21no—
139Dic62—21no—
140Dic62—21no—
141C8×C31—21no—
142C8×C31—21no—
143C31⋊C8—21no—
144C31⋊C8—21no—
145#3123—311nomaximal, Sylow
146C22×C31—22no—
147C22×C31—41no—
148C22×C31—41no—
149C22×C31C22×D411yescharacteristic
150C2×D31—21no—
151C2×D31—22no—
152C2×D31—21no—
153C2×D31—21no—
154C2×D31—41no—
155C2×D31—41no—
156C2×D31—84no—
157C4×C31—21no—
158C4×C31—21no—
159C4×C31—41no—
160C4×C31—41no—
161C4×C31—41no—
162C4×C31C2×#4111yescharacteristic
163C4×C31C2×#4111yescharacteristic
164Dic31—21no—
165Dic31—21no—
166Dic31—21no—
167Dic31—41no—
168Dic31—41no—
169Dic31—41no—
170#541—311no—
171#518—311no—
172#485—311no—
173#485—311no—
174#478—311no—
175#478D3111yescharacteristic, complemented
176#461—311no—
177#461—311no—
178#450—311no—
179#450—311no—
180#440—311no—
181#440—311no—
182C4×SD16—311no—
183C4×SD16—311no—
184#433—311no—
185C2×C31—42no—
186C2×C31#52511yescharacteristic
187C2×C31#57711yescharacteristic
188C2×C31#57711yescharacteristic
189D31—41no—
190D31—42no—
191C22×D4—311no—
192C2×SD16—311no—
193C2×SD16—311no—
194C2×SD16—311no—
195C2×SD16—311no—
196C4⋊Q8—311no—
197#126—621no—
198#126—621no—
199#125—621no—
200#125—621no—
201#125C2×D3111yescharacteristic, complemented
202C22⋊Q8—311no—
203C22⋊Q8—311no—
204C4×Q8—311no—
205C4×Q8—311no—
206C4×D4—311no—
207C4×D4—311no—
208C4×D4—311no—
209C4×D4—621no—
210C4×D4—621no—
211C4×D4C2×D3111yescharacteristic
212#117—311no—
213#117—311no—
214C2×C22⋊C4—621no—
215C2×C22⋊C4—621no—
216#107—311no—
217#107C2×D3111yescharacteristic, complemented
218#106—311no—
219#106C2×D3111yescharacteristic, complemented
220C4⋊C8—311no—
221C4⋊C8C2×D3111yescharacteristic, complemented
222#103—311no—
223#103—311no—
224#103—311no—
225#103—311no—
226#102—311no—
227#102—311no—
228#102C2×D3111yescharacteristic
229#102C2×D3111yescharacteristic
230C22⋊C8—311no—
231C22⋊C8—311no—
232#97—311no—
233C4×C8—311no—
234C31#312311yescharacteristic, complemented, Sylow
235C24—621no—
236C2×Q8—311no—
237C2×Q8—311no—
238C2×D4—311no—
239C2×D4—621no—
240C2×D4—622no—
241C2×D4—622no—
242C2×D4C22×D3111yescharacteristic
243C22×C4—21no—
244C22×C4—311no—
245C22×C4—621no—
246C22×C4—621no—
247C22×C4—621no—
248SD16—622no—
249SD16—622no—
250SD16—622no—
251SD16—622no—
252C2×C8—311no—
253C2×C8—311no—
254C2×C8C22×D3111yescharacteristic
255C2×C8C22×D3111yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—311no—
259C4⋊C4—311no—
260C4⋊C4—311no—
261C4⋊C4—621no—
262C4⋊C4—621no—
263C4⋊C4—621no—
264C4⋊C4—621no—
265C4⋊C4—621no—
266C4⋊C4—621no—
267C4⋊C4C22×D3111yescharacteristic
268C4⋊C4C22×D3111yescharacteristic
269C4⋊C4C22×D3111yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—311no—
272C22⋊C4—311no—
273C22⋊C4—621no—
274C22⋊C4—621no—
275C22⋊C4—621no—
276C22⋊C4—621no—
277C22⋊C4—621no—
278C22⋊C4—621no—
279C42—311no—
280C42—621no—
281C42—621no—
282C42—621no—
283C42C22×D3111yescharacteristic
284C23—21no—
285C23—311no—
286C23—624no—
287C23—621no—
288C23—2481no—
289C23—2481no—
290Q8—621no—
291Q8—621no—
292Q8—621no—
293Q8—621no—
294D4—21no—
295D4—312no—
296D4—624no—
297D4—621no—
298D4#9249912yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—311no—
304C2×C4—311no—
305C2×C4—311no—
306C2×C4—621no—
307C2×C4—621no—
308C2×C4—621no—
309C2×C4—621no—
310C2×C4—621no—
311C2×C4—2481no—
312C2×C4—2481no—
313C2×C4—2481no—
314C2×C4D4×D3111yescharacteristic
315C2×C4D4×D3111yescharacteristic
316C2×C4C23×D3111yescharacteristic
317C8—21no—
318C8—21no—
319C8—621no—
320C8—621no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—621no—
325C22—621no—
326C22—621no—
327C22—622no—
328C22—1241no—
329C22—1241no—
330C22—2484no—
331C22C2×D4×D3111yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—621no—
338C4—621no—
339C4—621no—
340C4—1241no—
341C4—1241no—
342C4—1241no—
343C4C2×#9249911yescharacteristic
344C4#41×D3111yescharacteristic
345C2—42no—
346C2—1241no—
347C2—1242no—
348C2#1452156211yescharacteristic
349C2#1452185611yescharacteristic
350C2#1452185911yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#478C2
socleC22×C31C22×D4
prime radicalC2×D4×D31C22
hypercenter#478D31
hypocenterC31#3123
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #14521662C2semidirect
3. #14521393C2semidirect
4. #14521392C2semidirect
5. #14521346C2semidirect
6. #14521255C2semidirect
7. #14521254C2semidirect
10. #14521148C2semidirect
11. #14521146C2semidirect
12. #14521140C2semidirect
13. #14521136C2semidirect
14. #14521109C2semidirect
15. C31×#478C2semidirect
17. C31×#125C22semidirect
34. #11758464C22semidirect
35. #11758464C22semidirect
40. #11758446C22semidirect
41. C31×#107C22semidirect
42. C31×#106C22semidirect
43. C31×C4⋊C8C22semidirect
48. #11758404C22semidirect
49. #11758404C22semidirect
50. #11758403C22semidirect
51. C8×Dic31C22semidirect
52. #11758398C22semidirect
53. #11758398C22semidirect
56. #11758396C22semidirect
57. #11758395C22semidirect
58. C4⋊(C31⋊C8)C22semidirect
175. #478D31semidirect
201. #125C2×D31semidirect
217. #107C2×D31semidirect
219. #106C2×D31semidirect
221. C4⋊C8C2×D31semidirect
234. C31#3123semidirect

Maximal subgroups

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

subgroupindex
#145216622
#145215212
#145213932
#145213922
#145213462
#145212552
#145212542
#145212012
#145211482
#145211462
#145211402
#145211362
#145211092
C31×#4782
#312331