Finite Group Databasebeta

← #16857696

Subgroups — #16857696

Order 3968.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521708C211yesmaximal, characteristic, complemented
2#14521411C211yesmaximal, characteristic, complemented
3#14521384C211yesmaximal, characteristic, complemented
4#14521362C211yesmaximal, characteristic, complemented
5#14521341C211yesmaximal, characteristic, complemented
6#14521293C211yesmaximal, characteristic, complemented
7#14521283C211yesmaximal, characteristic, complemented
8#14521264C211yesmaximal, characteristic, complemented
9#14521192C211yesmaximal, characteristic, complemented
10#14521187C211yesmaximal, characteristic, complemented
11#14521149C211yesmaximal, characteristic, complemented
12#14521121C211yesmaximal, characteristic, complemented
13#14521048C211yesmaximal, characteristic, complemented
14C2×#11758398C211yesmaximal, characteristic, complemented
15C31×#547C211yesmaximal, characteristic, complemented
16C2×#41×C31—21no—
17C2×#92495C2211yescharacteristic
18C22×Dic62C2211yescharacteristic
19C31×C4⋊Q8C2211yescharacteristic
20C31×#123—21no—
21C31×#123—21no—
22C31×C22⋊Q8—21no—
23C31×#121C2211yescharacteristic
24C31×#121C2211yescharacteristic
25C4×D4×C31C2211yescharacteristic
26C4×D4×C31C2211yescharacteristic
27C2×C4⋊C4×C31C2211yescharacteristic
28C2×C4⋊C4×C31C2211yescharacteristic
29#11758516—21no—
30C2×#92480C2211yescharacteristic
31C2×#92480C2211yescharacteristic
32C2×#92479C2211yescharacteristic
33#11758507C2211yescharacteristic
34#11758501C2211yescharacteristic
35C2×#92474C2211yescharacteristic
36C22×C31⋊C8C2211yescharacteristic
37#11758473—21no—
38#11758462—21no—
39(C22⋊D31)⋊C4—21no—
40#11758452C2211yescharacteristic
41C4×Dic62C2211yescharacteristic
42#11758420C2211yescharacteristic
43C22⋊(C31⋊C8)C2211yescharacteristic
44C22⋊(C31⋊C8)C2211yescharacteristic
45#11758398C2211yescharacteristic
46#11758398C2211yescharacteristic
47#11758398C2211yescharacteristic
48#11758398C2211yescharacteristic
49#11758398C2211yescharacteristic
50#11758398C2211yescharacteristic
51#11758397C2211yescharacteristic
52#11758397C2211yescharacteristic
53#11758397C2211yescharacteristic
54#11758395C2211yescharacteristic
55#11758395C2211yescharacteristic
56#11758395C2211yescharacteristic
57C4⋊(C31⋊C8)C2211yescharacteristic
58#11758391C2211yescharacteristic
59#41×C31—44no—
60C2×Q8×C31—21no—
61C2×D4×C31—21no—
62C2×D4×C31—21no—
63C2×D4×C31D411yescharacteristic
64C2×D4×C31C2311yescharacteristic
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31C2311yescharacteristic
69C22×C4×C31C2311yescharacteristic
70C2×C22⋊D31—21no—
71C2×C22⋊D31—21no—
72C22×Dic31—21no—
73#92495—22no—
74#92495—41no—
75C2×D124C2311yescharacteristic
76C2×C4×D31—21no—
77C2×Dic62—22no—
78C2×Dic62—21no—
79C2×Dic62—41no—
80C2×Dic62C2311yescharacteristic
81C2×Dic62C2311yescharacteristic
82C4⋊C4×C31—21no—
83C4⋊C4×C31—21no—
84C4⋊C4×C31—21no—
85C4⋊C4×C31D411yescharacteristic
86C4⋊C4×C31C2311yescharacteristic
87C4⋊C4×C31C2311yescharacteristic
88C4⋊C4×C31C2311yescharacteristic
89C22⋊C4×C31—21no—
90C22⋊C4×C31—21no—
91C22⋊C4×C31—21no—
92C22⋊C4×C31D411yescharacteristic
93C22⋊C4×C31D411yescharacteristic
94C42×C31C2311yescharacteristic
95C22⋊Dic31—21no—
96#92480—22no—
97#92480—41no—
98#92479—41no—
99(C2×D31)⋊C4—21no—
100(C2×D31)⋊C4—21no—
101(C2×D31)⋊C4—21no—
102C4⋊Dic31C2311yescharacteristic
103Dic31⋊C4—21no—
104Dic31⋊C4—21no—
105C4×Dic31—21no—
106#92474—41no—
107C2×C31⋊C8—41no—
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110C2×C31⋊C8C2311yescharacteristic
111C2×C31⋊C8C2311yescharacteristic
112C23×C31—21no—
113C23×C31C2×D411yescharacteristic
114C23×C31C2×D411yescharacteristic
115C22×D31—21no—
116Q8×C31—42no—
117D4×C31—22no—
118D4×C31—21no—
119D4×C31—21no—
120D4×C31—42no—
121D4×C31—42no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—42no—
130C2×C4×C31—42no—
131C2×C4×C31—42no—
132C2×C4×C31C2×D411yescharacteristic
133C2×C4×C31C2×D411yescharacteristic
134C2×C4×C31C2×D411yescharacteristic
135C2×C4×C31C2×D411yescharacteristic
136C2×C4×C31C2411yescharacteristic
137C22⋊D31—42no—
138C22⋊D31—42no—
139C2×Dic31—21no—
140C2×Dic31—21no—
141C2×Dic31—21no—
142C2×Dic31—42no—
143D124—21no—
144D124—21no—
145C4×D31—42no—
146Dic62—21no—
147Dic62—21no—
148Dic62—21no—
149Dic62—42no—
150Dic62#4112yescomplemented
151C31⋊C8—21no—
152C31⋊C8—21no—
153C31⋊C8—21no—
154C31⋊C8—21no—
155#3308—311nomaximal, Sylow
156C22×C31—21no—
157C22×C31—21no—
158C22×C31—21no—
159C22×C31—21no—
160C22×C31—21no—
161C22×C31—41no—
162C22×C31—41no—
163C22×C31—41no—
164C22×C31AGL(1,ℤ/8)12yes—
165C22×C31C22×D411yescharacteristic
166C2×D31—41no—
167C2×D31—41no—
168C2×D31—41no—
169C4×C31—21no—
170C4×C31—21no—
171C4×C31—21no—
172C4×C31—21no—
173C4×C31—41no—
174C4×C31—41no—
175C4×C31—41no—
176C4×C31C2×#4111yescharacteristic
177C4×C31H(5,𝔽2)11yescharacteristic
178Dic31—22no—
179Dic31—41no—
180Dic31—41no—
181#548—311no—
182#547D3111yescharacteristic, complemented
183#489—311no—
184#484—311no—
185#480—311no—
186#477—311no—
187#468—311no—
188#466—311no—
189#463—311no—
190#449—311no—
191#448—311no—
192#440—311no—
193#435—311no—
194#417—311no—
195C2×#103—311no—
196C2×C31—22no—
197C2×C31—41no—
198C2×C31—81no—
199C2×C31#54611yescharacteristic
200C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
201C2×C31#57811yescharacteristic
202D31—81no—
203C2×#41—21no—
204C2×#41—311no—
205C22×Q8—311no—
206C2×SD16—311no—
207C2×SD16—311no—
208C2×D8—311no—
209C2×M16—311no—
210C22×C8—311no—
211C4⋊Q8C2×D3111yescharacteristic
212#124—311no—
213#124—621no—
214#123—21no—
215#123—21no—
216C22⋊Q8—21no—
217C22⋊Q8—311no—
218C22⋊Q8—621no—
219#121—311no—
220#121—621no—
221#121C2×D3111yescharacteristic
222#121C2×D3111yescharacteristic
223C4×Q8—311no—
224C4×D4—621no—
225C4×D4C2×D3111yescharacteristic
226C4×D4C2×D3111yescharacteristic
227C2×C4⋊C4C2×D3111yescharacteristic
228C2×C4⋊C4C2×D3111yescharacteristic
229#107—311no—
230#107—311no—
231#107—311no—
232C4⋊C8—311no—
233#103—311no—
234#103—311no—
235#103—311no—
236#103—311no—
237#103—311no—
238#103—311no—
239#102—311no—
240#102—311no—
241#102—311no—
242#102—311no—
243C22⋊C8—311no—
244C22⋊C8—311no—
245#97—311no—
246C31#330811yescharacteristic, complemented, Sylow
247#41—44no—
248#41—622no—
249#41—1241no—
250C2×Q8—21no—
251C2×Q8—311no—
252C2×Q8—311no—
253C2×Q8—622no—
254C2×Q8—621no—
255C2×Q8—1241no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—311no—
259C2×D4—621no—
260C2×D4—621no—
261C2×D4C22⋊D3111yescharacteristic
262C2×D4C22×D3111yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—621no—
267C22×C4—621no—
268C22×C4C22×D3111yescharacteristic
269C22×C4C22×D3111yescharacteristic
270SD16—622no—
271SD16—1241no—
272D8—1241no—
273M16—1241no—
274C2×C8—311no—
275C2×C8—311no—
276C2×C8—311no—
277C2×C8—311no—
278C2×C8—1241no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—311no—
283C4⋊C4—621no—
284C4⋊C4—621no—
285C4⋊C4C22⋊D3111yescharacteristic
286C4⋊C4C22×D3111yescharacteristic
287C4⋊C4C22×D3111yescharacteristic
288C4⋊C4C22×D3111yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—621no—
293C22⋊C4—621no—
294C22⋊C4—621no—
295C22⋊C4—621no—
296C22⋊C4C22⋊D3111yescharacteristic
297C22⋊C4C22⋊D3111yescharacteristic
298C42—621no—
299C42C22×D3111yescharacteristic
300C23—21no—
301C23—621no—
302C23C2×C22⋊D3111yescharacteristic
303C23C2×C22⋊D3111yescharacteristic
304Q8—42no—
305Q8—312no—
306Q8—621no—
307Q8—621no—
308Q8—621no—
309Q8—1242no—
310D4—22no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—42no—
315D4—621no—
316D4—621no—
317D4—1242no—
318D4—1242no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—621no—
330C2×C4—621no—
331C2×C4—621no—
332C2×C4—1242no—
333C2×C4—1242no—
334C2×C4C2×C22⋊D3111yescharacteristic
335C2×C4C2×C22⋊D3111yescharacteristic
336C2×C4C2×C22⋊D3111yescharacteristic
337C2×C4C2×C22⋊D3111yescharacteristic
338C2×C4C23×D3111yescharacteristic
339C8—621no—
340C8—621no—
341C8—621no—
342C8—621no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—1241no—
352C22—1241no—
353C22—1241no—
354C22#1175850912yes—
355C22C22×C22⋊D3111yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—622no—
364C4—1241no—
365C4—1241no—
366C4#41×D3111yescharacteristic
367C4#1175856611yescharacteristic
368C2—22no—
369C2—41no—
370C2—81no—
371C2—2481no—
372C2#1452168711yescharacteristic
373C2C2×#1175850911yescharacteristic
374C2#1452186411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#547C2
socleC22×C31C22×D4
hypercenter#547D31
hypocenterC31#3308
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #14521708C2semidirect
2. #14521411C2semidirect
3. #14521384C2semidirect
4. #14521362C2semidirect
5. #14521341C2semidirect
6. #14521293C2semidirect
7. #14521283C2semidirect
8. #14521264C2semidirect
9. #14521192C2semidirect
10. #14521187C2semidirect
11. #14521149C2semidirect
12. #14521121C2semidirect
13. #14521048C2semidirect
14. C2×#11758398C2semidirect
15. C31×#547C2semidirect
150. Dic62#41semidirect
182. #547D31semidirect
246. C31#3308semidirect

Maximal subgroups

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

subgroupindex
#145217082
#145214112
#145213842
#145213622
#145213412
#145212932
#145212832
#145212642
#145211922
#145211872
#145211492
#145211212
#145210482
C2×#117583982
C31×#5472
#330831