Finite Group Databasebeta

← #16857617

Subgroups — #16857617

Order 3968.

398 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#14521751C211yesmaximal, characteristic, complemented
2#14521710C211yesmaximal, characteristic, complemented
3#14521405C211yesmaximal, characteristic, complemented
4#14521388C211yesmaximal, characteristic, complemented
5#14521368C211yesmaximal, characteristic, complemented
6#14521354C211yesmaximal, characteristic, complemented
7#14521283C211yesmaximal, characteristic, complemented
8#14521275C211yesmaximal, characteristic, complemented
9#14521266C211yesmaximal, characteristic, complemented
10#14521193C211yesmaximal, characteristic, complemented
11SD16×Dic31C211yesmaximal, characteristic, complemented
12(C22⋊D31)⋊C8C211yesmaximal, characteristic, complemented
13#14521044C211yesmaximal, characteristic, complemented
14C2×#11758423C211yesmaximal, characteristic, complemented
15C31×#448C211yesmaximal, characteristic, complemented
16C22×Q8×C31C2211yescharacteristic
17C2×#92499C2211yescharacteristic
18C2×SD16×C31C2211yescharacteristic
19C2×SD16×C31C2211yescharacteristic
20C31×#121C2211yescharacteristic
21#11758524—21no—
22#11758524C2211yescharacteristic
23#11758523—21no—
24#11758523C2211yescharacteristic
25Q8×Dic31C2211yescharacteristic
26#11758516—21no—
27#11758515C2211yescharacteristic
28D4×Dic31—21no—
29D4×Dic31C2211yescharacteristic
30C2×#92479C2211yescharacteristic
31#11758507—21no—
32#11758507C2211yescharacteristic
33C4×C22⋊D31—21no—
34C4×C22⋊D31C2211yescharacteristic
35C2×C4⋊Dic31C2211yescharacteristic
36C22×C31⋊C8C2211yescharacteristic
37C2×C8×D31C2211yescharacteristic
38#11758469C2211yescharacteristic
39#11758467C2211yescharacteristic
40#11758463—21no—
41#11758456—21no—
42C31×#103C2211yescharacteristic
43C31×#103C2211yescharacteristic
44C31×C22⋊C8C2211yescharacteristic
45#11758423C2211yescharacteristic
46#11758423C2211yescharacteristic
47#11758423C2211yescharacteristic
48#11758423C2211yescharacteristic
49#11758420C2211yescharacteristic
50#11758409C2211yescharacteristic
51#11758409C2211yescharacteristic
52(C2×D31)⋊C8C2211yescharacteristic
53#11758405C2211yescharacteristic
54#11758405C2211yescharacteristic
55Dic31⋊C8C2211yescharacteristic
56C8×Dic31C2211yescharacteristic
57#11758397C2211yescharacteristic
58#11758395C2211yescharacteristic
59C2×Q8×C31—21no—
60C2×Q8×C31—22no—
61C2×Q8×C31—41no—
62C2×Q8×C31C2311yescharacteristic
63C2×Q8×C31C2311yescharacteristic
64C2×D4×C31—21no—
65C2×D4×C31C2311yescharacteristic
66C22×C4×C31—21no—
67C22×C4×C31C2311yescharacteristic
68C2×C22⋊D31—21no—
69C2×C22⋊D31—21no—
70C2×C22⋊D31D411yescharacteristic
71C22×Dic31—21no—
72C22×Dic31—21no—
73#92499—22no—
74#92499—41no—
75C2×D124—21no—
76C2×D124C2311yescharacteristic
77C2×C4×D31—21no—
78C2×C4×D31C2311yescharacteristic
79SD16×C31—22no—
80SD16×C31—41no—
81C2×C8×C31C2311yescharacteristic
82C2×C8×C31C2311yescharacteristic
83C4⋊C4×C31C2311yescharacteristic
84C22⋊C4×C31—21no—
85C22⋊Dic31—21no—
86C22⋊Dic31—21no—
87C22⋊Dic31D411yescharacteristic
88#92479—41no—
89(C2×D31)⋊C4—21no—
90(C2×D31)⋊C4—21no—
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⋊Dic31—21no—
98C4⋊Dic31C2311yescharacteristic
99C4⋊Dic31C2311yescharacteristic
100C4⋊Dic31C2311yescharacteristic
101Dic31⋊C4—21no—
102Dic31⋊C4—21no—
103Dic31⋊C4D411yescharacteristic
104C4×Dic31—21no—
105C4×Dic31—21no—
106C4×Dic31C2311yescharacteristic
107C2×C31⋊C8—41no—
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110C8×D31—41no—
111C23×C31—21no—
112C23×C31C2×D411yescharacteristic
113C22×D31—21no—
114C22×D31C2×D411yescharacteristic
115Q8×C31—21no—
116Q8×C31—21no—
117Q8×C31—21no—
118Q8×C31—42no—
119Q8×C31#4112yes—
120D4×C31—21no—
121D4×C31—21no—
122D4×C31—42no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—42no—
129C2×C4×C31C2×D411yescharacteristic
130C2×C4×C31C2411yescharacteristic
131C22⋊D31—22no—
132C22⋊D31—42no—
133C22⋊D31—81no—
134C2×Dic31—21no—
135C2×Dic31—21no—
136C2×Dic31—21no—
137C2×Dic31—81no—
138C2×Dic31—81no—
139C2×Dic31C2×D411yescharacteristic
140C2×Dic31C2×D411yescharacteristic
141C2×Dic31C2×D411yescharacteristic
142D124—21no—
143D124—21no—
144D124—42no—
145C4×D31—21no—
146C4×D31—21no—
147C4×D31—42no—
148C8×C31—21no—
149C8×C31—21no—
150C31⋊C8—21no—
151C31⋊C8—21no—
152#3301—311nomaximal, Sylow
153C22×C31—21no—
154C22×C31—21no—
155C22×C31—41no—
156C22×C31—41no—
157C22×C31—41no—
158C22×C31#13512yes—
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—21no—
175Dic31—41no—
176Dic31—41no—
177Dic31—41no—
178#553—311no—
179#548—311no—
180#488—311no—
181#485—311no—
182#481—311no—
183#479—311no—
184#466—311no—
185#465—311no—
186#463—311no—
187#449—311no—
188#448D3111yescharacteristic, complemented
189C4×SD16—311no—
190C8×D4—311no—
191#416—311no—
192C2×#103—311no—
193C2×C31—22no—
194C2×C31—81no—
195C2×C31#54611yescharacteristic
196C2×C31C2×#13511yescharacteristic
197C2×C31#57711yescharacteristic
198D31—41no—
199D31—81no—
200C2×#41—311no—
201C22×Q8C2×D3111yescharacteristic
202C2×SD16C2×D3111yescharacteristic
203C2×SD16C2×D3111yescharacteristic
204C2×D8—311no—
205C22×C8—311no—
206C22×C8—311no—
207#126—621no—
208#125—311no—
209#124—311no—
210#124—621no—
211#123—621no—
212C22⋊Q8—311no—
213C22⋊Q8—621no—
214#121—311no—
215#121—311no—
216#121—621no—
217#121—621no—
218#121C2×D3111yescharacteristic
219C4×Q8—311no—
220C4×D4—311no—
221C4×D4—311no—
222C4×D4—621no—
223C4×D4—621no—
224#117—311no—
225C2×C4⋊C4—311no—
226#107—311no—
227#106—311no—
228#106—311no—
229C4⋊C8—311no—
230#103—311no—
231#103—311no—
232#103—311no—
233#103—311no—
234#103C2×D3111yescharacteristic
235#103C2×D3111yescharacteristic
236#102—311no—
237#102—311no—
238#102—311no—
239#102—311no—
240C22⋊C8—311no—
241C22⋊C8C2×D3111yescharacteristic
242C4×C8—311no—
243C31#330111yescharacteristic, complemented, Sylow
244#41—622no—
245#41—1241no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C22×D3111yescharacteristic
250C2×Q8C22×D3111yescharacteristic
251C2×D4—21no—
252C2×D4—311no—
253C2×D4—311no—
254C2×D4—621no—
255C2×D4—621no—
256C2×D4—621no—
257C2×D4C22×D3111yescharacteristic
258C22×C4—21no—
259C22×C4—311no—
260C22×C4—621no—
261C22×C4—621no—
262C22×C4—621no—
263C22×C4C22×D3111yescharacteristic
264SD16—22no—
265SD16—41no—
266D8—1241no—
267C2×C8—311no—
268C2×C8—311no—
269C2×C8—1241no—
270C2×C8—1241no—
271C2×C8C22×D3111yescharacteristic
272C2×C8C22×D3111yescharacteristic
273C4⋊C4—311no—
274C4⋊C4—311no—
275C4⋊C4—311no—
276C4⋊C4—311no—
277C4⋊C4—621no—
278C4⋊C4—621no—
279C4⋊C4—621no—
280C4⋊C4—621no—
281C4⋊C4—621no—
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—
291C22⋊C4—621no—
292C22⋊C4—621no—
293C42—311no—
294C42—621no—
295C42—621no—
296C23—21no—
297C23—311no—
298C23—621no—
299C23D4×D3111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#9249712yes—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—622no—
309D4—621no—
310D4—621no—
311D4—1242no—
312D4—1242no—
313D4—2481no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—311no—
321C2×C4—311no—
322C2×C4—311no—
323C2×C4—621no—
324C2×C4—621no—
325C2×C4—621no—
326C2×C4—621no—
327C2×C4—621no—
328C2×C4—1242no—
329C2×C4—2481no—
330C2×C4—2481no—
331C2×C4D4×D3111yescharacteristic
332C2×C4C23×D3111yescharacteristic
333C8—21no—
334C8—21no—
335C8—621no—
336C8—621no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—621no—
343C22—621no—
344C22—621no—
345C22—1241no—
346C22—1241no—
347C22—1241no—
348C22#1175849312yes—
349C22C2×D4×D3111yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—621no—
355C4—621no—
356C4—621no—
357C4—1241no—
358C4—1241no—
359C4—1241no—
360C4C2×#9249711yescharacteristic
361C4#1175856111yescharacteristic
362C2—22no—
363C2—81no—
364C2—1241no—
365C2—2481no—
366C2#1452168611yescharacteristic
367C2C2×#1175849311yescharacteristic
368C2#1452185811yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#448C2
socleC22×C31C22×D4
hypercenter#448D31
hypocenterC31#3301
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. #14521751C2semidirect
2. #14521710C2semidirect
3. #14521405C2semidirect
4. #14521388C2semidirect
5. #14521368C2semidirect
6. #14521354C2semidirect
7. #14521283C2semidirect
8. #14521275C2semidirect
9. #14521266C2semidirect
10. #14521193C2semidirect
11. SD16×Dic31C2semidirect
12. (C22⋊D31)⋊C8C2semidirect
13. #14521044C2semidirect
14. C2×#11758423C2semidirect
15. C31×#448C2semidirect
188. #448D31semidirect
243. C31#3301semidirect

Maximal subgroups

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

subgroupindex
#145217512
#145217102
#145214052
#145213882
#145213682
#145213542
#145212832
#145212752
#145212662
#145211932
SD16×Dic312
(C22⋊D31)⋊C82
#145210442
C2×#117584232
C31×#4482
#330131