Finite Group Databasebeta

← #16859328

Subgroups — #16859328

Order 3968.

1094 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521775C211yesmaximal, characteristic, complemented
2#14521771C213yesmaximal, complemented
3#14521740C213yesmaximal, complemented
4#14521734C213yesmaximal, complemented
5Q8×C22⋊D31C211yesmaximal, characteristic, complemented
6#14521711C211yesmaximal, characteristic, complemented
7#14521710C211yesmaximal, characteristic, complemented
8#14521700C213yesmaximal, complemented
9#14521603C213yesmaximal, complemented
10#14521586C213yesmaximal, complemented
11#14521583C213yesmaximal, complemented
12C4×#92499C211yesmaximal, characteristic, complemented
13C4×#92495C213yesmaximal, complemented
14C4×Q8×D31C211yesmaximal, characteristic, complemented
15C2×C4×Q8×C31C211yesmaximal, characteristic, complemented
16C22×Q8×C31C2211yescharacteristic
17C2×#92499C2211yescharacteristic
18C2×Q8×D31C2211yescharacteristic
19C2×#92495C2213yes—
20C4×Q8×C31C2213yes—
21C4×Q8×C31C2211yescharacteristic
22C4×Q8×C31C2213yes—
23C4×Q8×C31C2211yescharacteristic
24C2×C4⋊C4×C31C2213yes—
25C2×C42×C31C2213yes—
26#11758524C2213yes—
27#11758523C2213yes—
28#11758523C2213yes—
29Q8×Dic31C2211yescharacteristic
30Q8×Dic31C2211yescharacteristic
31#11758521C2213yes—
32#11758507C2213yes—
33#11758506C2216yes—
34C4×C22⋊D31C2213yes—
35C4×C22⋊D31C2213yes—
36C4×C22⋊D31C2211yescharacteristic
37C4×C22⋊D31C2213yes—
38#11758503C2213yes—
39#11758501C2213yes—
40#11758475C2216yes—
41#11758474C2213yes—
42#11758473C2216yes—
43#11758472C2213yes—
44#11758471C2216yes—
45#11758470C2213yes—
46#11758469C2213yes—
47C4⋊C4×D31C2213yes—
48#11758467C2213yes—
49#11758466C2216yes—
50#11758465C2213yes—
51#11758464C2213yes—
52#11758453C2216yes—
53#11758452C2213yes—
54C4×D124C2213yes—
55C4×D124C2213yes—
56C4×D124C2213yes—
57#11758449C2216yes—
58#11758449C2213yes—
59#11758449C2213yes—
60C42×D31C2213yes—
61C42×D31C2213yes—
62#11758447C2213yes—
63C4×Dic62C2213yes—
64C4×Dic62C2213yes—
65C4×Dic62C2213yes—
66C2×Q8×C31—24no—
67C2×Q8×C31C2313yes—
68C2×Q8×C31C2311yescharacteristic
69C22×C4×C31C2313yes—
70C22×C4×C31C2313yes—
71C22×C4×C31C2311yescharacteristic
72C2×C22⋊D31C2313yes—
73C2×C22⋊D31C2311yescharacteristic
74#92499—24no—
75Q8×D31—24no—
76#92495—212no—
77C2×D124C2313yes—
78C2×D124C2313yes—
79C2×C4×D31C2311yescharacteristic
80C2×C4×D31C2313yes—
81C2×C4×D31C2313yes—
82C2×C4×D31C2313yes—
83C2×C4×D31C2313yes—
84C2×C4×D31C2313yes—
85C2×Dic62C2313yes—
86C2×Dic62C2313yes—
87C4⋊C4×C31C2313yes—
88C4⋊C4×C31C2313yes—
89C4⋊C4×C31C2316yes—
90C42×C31C2313yes—
91C42×C31C2313yes—
92C42×C31C2313yes—
93C42×C31C2313yes—
94C22⋊Dic31C2313yes—
95C22⋊Dic31C2311yescharacteristic
96(C2×D31)⋊C4C2311yescharacteristic
97(C2×D31)⋊C4C2313yes—
98(C2×D31)⋊C4C2313yes—
99(C2×D31)⋊C4C2313yes—
100(C2×D31)⋊C4C2316yes—
101(C2×D31)⋊C4C2316yes—
102(C2×D31)⋊C4C2316yes—
103C4⋊Dic31C2313yes—
104C4⋊Dic31C2313yes—
105C4⋊Dic31C2313yes—
106C4⋊Dic31C2313yes—
107Dic31⋊C4C2311yescharacteristic
108Dic31⋊C4C2313yes—
109Dic31⋊C4C2313yes—
110Dic31⋊C4C2313yes—
111Dic31⋊C4C2316yes—
112Dic31⋊C4C2316yes—
113Dic31⋊C4C2316yes—
114C4×Dic31C2311yescharacteristic
115C4×Dic31C2313yes—
116C4×Dic31C2313yes—
117C4×Dic31C2313yes—
118C4×Dic31C2313yes—
119C4×Dic31C2313yes—
120C23×C31C2411yescharacteristic
121C22×D31C2413yes—
122C22×D31C2411yescharacteristic
123Q8×C31—26no—
124Q8×C31#4114yescomplemented
125C2×C4×C31—26no—
126C2×C4×C31—26no—
127C2×C4×C31—22no—
128C2×C4×C31C2413yes—
129C2×C4×C31C2411yescharacteristic
130C2×C4×C31C2413yes—
131C2×C4×C31C2413yes—
132C2×C4×C31C2413yes—
133C2×C4×C31C2411yescharacteristic
134C22⋊D31—26no—
135C22⋊D31#4114yescomplemented
136C2×Dic31C2411yescharacteristic
137C2×Dic31C2411yescharacteristic
138C2×Dic31C2413yes—
139C2×Dic31C2413yes—
140C2×Dic31C2413yes—
141C2×Dic31C2411yescharacteristic
142D124—26no—
143D124—26no—
144C4×D31—26no—
145C4×D31—26no—
146C4×D31—26no—
147C4×D31—22no—
148C4×D31—26no—
149C4×D31—26no—
150Dic62—26no—
151Dic62—26no—
152#3482—311nomaximal, Sylow
153C22×C31—21no—
154C22×C31—21no—
155C22×C31C2×#4112yes—
156C22×C31C2511yescharacteristic
157C2×D31—21no—
158C2×D31—21no—
159C2×D31—23no—
160C2×D31—23no—
161C2×D31—23no—
162C2×D31C2×#4112yes—
163C4×C31—23no—
164C4×C31—23no—
165C4×C31—23no—
166C4×C31—21no—
167C4×C31C2×#4116yes—
168C4×C312−1+412yes—
169Dic31—23no—
170Dic31—23no—
171Dic31—21no—
172Dic31—21no—
173Dic31—23no—
174Dic31C2×#4112yes—
175#557—311no—
176#556—313no—
177#552—313no—
178#552—313no—
179D4×Q8—311no—
180#548—311no—
181#548—311no—
182#547—313no—
183#533—313no—
184#529—313no—
185#529—313no—
186C4×#41—311no—
187C4×#41—313no—
188C2×C4×Q8—311no—
189C2×C4×Q8D3111yescharacteristic, complemented
190C2×C31—22no—
191C2×C31C22×#4111yescharacteristic
192C2×C31C22×#4111yescharacteristic
193C2×C31C2×2−1+411yescharacteristic
194D31—22no—
195D31—43no—
196C2×#41—311no—
197C2×#41—313no—
198C22×Q8—311no—
199C22×Q8C2×D3111yescharacteristic
200C4⋊Q8—313no—
201C4⋊Q8—313no—
202#126—316no—
203#126—316no—
204#125—313no—
205#125—316no—
206#125—313no—
207#124—313no—
208#124—313no—
209#123—316no—
210#123—316no—
211C22⋊Q8—313no—
212C22⋊Q8—313no—
213C22⋊Q8—313no—
214C22⋊Q8—316no—
215C22⋊Q8—313no—
216#121—313no—
217#121—313no—
218C4×Q8—311no—
219C4×Q8—311no—
220C4×Q8—313no—
221C4×Q8—313no—
222C4×Q8—313no—
223C4×Q8—313no—
224C4×Q8C2×D3111yescharacteristic
225C4×Q8C2×D3113yes—
226C4×Q8C2×D3111yescharacteristic
227C4×Q8C2×D3113yes—
228C4×D4—311no—
229C4×D4—313no—
230C4×D4—313no—
231C4×D4—313no—
232C4×D4—313no—
233C4×D4—313no—
234C4×D4—313no—
235C4×D4—313no—
236#117—313no—
237#117—313no—
238#117—313no—
239#117—313no—
240#117—316no—
241C2×C4⋊C4—313no—
242C2×C4⋊C4C2×D3113yes—
243C2×C42—313no—
244C2×C42—313no—
245C2×C42C2×D3113yes—
246C31#348211yescharacteristic, complemented, Sylow
247#41—6212no—
248#41—624no—
249C2×Q8—24no—
250C2×Q8—313no—
251C2×Q8—313no—
252C2×Q8—624no—
253C2×Q8C22×D3113yes—
254C2×Q8C22×D3111yescharacteristic
255C2×D4—311no—
256C2×D4—313no—
257C2×D4—313no—
258C2×D4—313no—
259C22×C4—313no—
260C22×C4—313no—
261C22×C4—313no—
262C22×C4—313no—
263C22×C4—311no—
264C22×C4—313no—
265C22×C4C22×D3113yes—
266C22×C4C22×D3113yes—
267C22×C4C22×D3111yescharacteristic
268C4⋊C4—316no—
269C4⋊C4—311no—
270C4⋊C4—313no—
271C4⋊C4—313no—
272C4⋊C4—313no—
273C4⋊C4—316no—
274C4⋊C4—316no—
275C4⋊C4—313no—
276C4⋊C4—313no—
277C4⋊C4—313no—
278C4⋊C4—313no—
279C4⋊C4C22×D3113yes—
280C4⋊C4C22×D3113yes—
281C4⋊C4C22×D3116yes—
282C22⋊C4—311no—
283C22⋊C4—313no—
284C22⋊C4—311no—
285C22⋊C4—313no—
286C22⋊C4—316no—
287C22⋊C4—313no—
288C22⋊C4—313no—
289C22⋊C4—316no—
290C22⋊C4—316no—
291C42—313no—
292C42—313no—
293C42—313no—
294C42—313no—
295C42—311no—
296C42—313no—
297C42C22×D3113yes—
298C42C22×D3113yes—
299C42C22×D3113yes—
300C42C22×D3113yes—
301C23—311no—
302C23—313no—
303C23C23×D3111yescharacteristic
304Q8—26no—
305Q8—626no—
306Q8—626no—
307Q8#9249514yescomplemented
308D4—314no—
309D4—626no—
310D4—626no—
311D4—626no—
312C2×C4—26no—
313C2×C4—26no—
314C2×C4—22no—
315C2×C4—311no—
316C2×C4—311no—
317C2×C4—311no—
318C2×C4—313no—
319C2×C4—313no—
320C2×C4—313no—
321C2×C4—626no—
322C2×C4—626no—
323C2×C4—626no—
324C2×C4—626no—
325C2×C4—622no—
326C2×C4—626no—
327C2×C4C23×D3113yes—
328C2×C4C23×D3111yescharacteristic
329C2×C4C23×D3113yes—
330C2×C4C23×D3113yes—
331C2×C4C23×D3113yes—
332C2×C4C23×D3111yescharacteristic
333C22—21no—
334C22—21no—
335C22—312no—
336C22—621no—
337C22—621no—
338C22—623no—
339C22—623no—
340C22—623no—
341C22#41×D3112yes—
342C22C24×D3111yescharacteristic
343C4—23no—
344C4—23no—
345C4—23no—
346C4—21no—
347C4—312no—
348C4—623no—
349C4—621no—
350C4—623no—
351C4—621no—
352C4—623no—
353C4C2×#9249516yes—
354C4#1175856412yes—
355C2—22no—
356C2—622no—
357C2—1243no—
358C2C2×#41×D3111yescharacteristic
359C2C22×#9249511yescharacteristic
360C2C2×#1175856411yescharacteristic
subgroupG/H
centerC2×C4C23×D31
commutator, socle, cosocleC22×C31C25
FrattiniC22C24×D31
FittingC2×C4×Q8×C31C2
hypercenterC2×C4×Q8D31
hypocenterC31#3482
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #14521775C2semidirect
2. #14521771C2semidirect
3. #14521740C2semidirect
4. #14521734C2semidirect
5. Q8×C22⋊D31C2semidirect
6. #14521711C2semidirect
7. #14521710C2semidirect
8. #14521700C2semidirect
9. #14521603C2semidirect
10. #14521586C2semidirect
11. #14521583C2semidirect
12. C4×#92499C2semidirect
13. C4×#92495C2semidirect
14. C4×Q8×D31C2semidirect
15. C2×C4×Q8×C31C2semidirect
124. Q8×C31#41semidirect
135. C22⋊D31#41semidirect
189. C2×C4×Q8D31semidirect
246. C31#3482semidirect
307. Q8#92495semidirect

Maximal subgroups

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

subgroupindex
#145217752
#145217712
#145217402
#145217342
Q8×C22⋊D312
#145217112
#145217102
#145217002
#145216032
#145215862
#145215832
C4×#924992
C4×#924952
C4×Q8×D312
C2×C4×Q8×C312
#348231