Finite Group Databasebeta

← #16855822

Subgroups — #16855822

Order 3968.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521583C211yesmaximal, characteristic, complemented
2C4×#92495C211yesmaximal, characteristic, complemented
3#14521391C211yesmaximal, characteristic, complemented
4#14521374C211yesmaximal, characteristic, complemented
5#14521357C211yesmaximal, characteristic, complemented
6#14521350C211yesmaximal, characteristic, complemented
7#14521272C211yesmaximal, characteristic, complemented
8#14521265C211yesmaximal, characteristic, complemented
9#14521213C211yesmaximal, characteristic, complemented
10#14521196C211yesmaximal, characteristic
11#14521162C211yesmaximal, characteristic, complemented
12#14521157C211yesmaximal, characteristic, complemented
13#14521151C211yesmaximal, characteristic, complemented
14#14521151C211yesmaximal, characteristic, complemented
15C31×#432C211yesmaximal, characteristic, complemented
16C2×#92495C2211yescharacteristic
17C2×C42×C31C2211yescharacteristic
18#11758507C2211yescharacteristic
19#11758506—21no—
20C4×C22⋊D31—21no—
21C4×C22⋊D31—21no—
22C4×C22⋊D31—21no—
23#11758503C2211yescharacteristic
24#11758501C2211yescharacteristic
25C2×Dic124C2211yescharacteristic
26C2×D248C2211yescharacteristic
27C2×#92470C2211yescharacteristic
28C2×#92470C2211yescharacteristic
29#11758453—21no—
30#11758452C2211yescharacteristic
31C4×D124C2211yescharacteristic
32C4×D124C2211yescharacteristic
33C4×D124C2211yescharacteristic
34#11758449—21no—
35#11758449—21no—
36C42×D31—21no—
37#11758447C2211yescharacteristic
38C4×Dic62C2211yescharacteristic
39C4×Dic62C2211yescharacteristic
40C4×Dic62C2211yescharacteristic
41C31×C4⋊C8C2211yescharacteristic
42C31×C4⋊C8C2211yescharacteristic
43C31×C22⋊C8C2211yescharacteristic
44C31×C22⋊C8C2211yescharacteristic
45C31×#97C2211yescharacteristic
46C31×#97C2211yescharacteristic
47#11758409C2211yescharacteristic
48#11758409C2211yescharacteristic
49#11758409C2211yescharacteristic
50#11758409C2211yescharacteristic
51#11758406C2211yescharacteristic
52#11758406C2211yescharacteristic
53#11758405C2211yescharacteristic
54#11758405C2211yescharacteristic
55#11758404C2211yescharacteristic
56#11758404C2211yescharacteristic
57#11758404C2211yescharacteristic
58#11758404C2211yescharacteristic
59C22×C4×C31D411yescharacteristic
60C22×C4×C31D411yescharacteristic
61C22×C4×C31C2311yescharacteristic
62C2×C22⋊D31—21no—
63C2×C22⋊D31—21no—
64#92495—22no—
65#92495—22no—
66C2×D124C2311yescharacteristic
67C2×D124C2311yescharacteristic
68C2×C4×D31—21no—
69C2×C4×D31—21no—
70C2×C4×D31—21no—
71C2×C4×D31—21no—
72C2×Dic62C2311yescharacteristic
73C2×Dic62C2311yescharacteristic
74C2×C8×C31C2311yescharacteristic
75C2×C8×C31C2311yescharacteristic
76C2×C8×C31C2311yescharacteristic
77C2×C8×C31C2311yescharacteristic
78C42×C31D411yescharacteristic
79C42×C31D411yescharacteristic
80C42×C31C2311yescharacteristic
81C42×C31C2311yescharacteristic
82C22⋊Dic31—21no—
83C22⋊Dic31—21no—
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)⋊C4—21no—
90C4⋊Dic31C2311yescharacteristic
91C4⋊Dic31C2311yescharacteristic
92C4⋊Dic31C2311yescharacteristic
93C4⋊Dic31C2311yescharacteristic
94Dic31⋊C4—21no—
95Dic31⋊C4—21no—
96Dic31⋊C4—21no—
97Dic31⋊C4—21no—
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100C4×Dic31—21no—
101C4×Dic31—21no—
102C4×Dic31—21no—
103C4×Dic31—21no—
104Dic124—22no—
105D248—22no—
106#92470—22no—
107#92470—22no—
108C23×C31C2×D411yescharacteristic
109C22×D31—21no—
110C22×D31—21no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—41no—
114C2×C4×C31—41no—
115C2×C4×C31C2×D411yescharacteristic
116C2×C4×C31C2×D411yescharacteristic
117C2×C4×C31C2×D411yescharacteristic
118C2×C4×C31C2×D411yescharacteristic
119C2×C4×C31C2×D411yescharacteristic
120C2×C4×C31C2411yescharacteristic
121C22⋊D31—24no—
122C22⋊D31—42no—
123C2×Dic31—21no—
124C2×Dic31—21no—
125C2×Dic31—21no—
126C2×Dic31—21no—
127C2×Dic31—21no—
128C2×Dic31—21no—
129D124—21no—
130D124—21no—
131D124—21no—
132D124#4112yes—
133C4×D31—24no—
134C4×D31—42no—
135C4×D31—42no—
136C4×D31—42no—
137Dic62—21no—
138Dic62—21no—
139Dic62—21no—
140Dic62#4112yes—
141C8×C31—21no—
142C8×C31—21no—
143C8×C31—21no—
144C8×C31—21no—
145#3111—311nomaximal, Sylow
146C22×C31—21no—
147C22×C31—21no—
148C22×C31—21no—
149C22×C31C22×D411yescharacteristic
150C2×D31—22no—
151C2×D31—41no—
152C2×D31—41no—
153C2×D31—41no—
154C2×D31—41no—
155C2×D31—41no—
156C4×C31—21no—
157C4×C31—21no—
158C4×C31—21no—
159C4×C31—21no—
160C4×C31—21no—
161C4×C31C2×#4111yescharacteristic
162C4×C31C2×#4111yescharacteristic
163Dic31—22no—
164Dic31—41no—
165Dic31—41no—
166Dic31—41no—
167Dic31—41no—
168Dic31—41no—
169#529—311no—
170C4×#41—311no—
171#485—311no—
172#482—311no—
173#479—311no—
174#478—311no—
175#464—311no—
176#463—311no—
177#452—311no—
178#449—311no—
179#442—311no—
180#441—311no—
181#440—311no—
182#440—311no—
183#432D3111yescharacteristic, complemented
184C2×C31—41no—
185C2×C31#52511yescharacteristic
186C2×C31#57511yescharacteristic
187C2×C31#57511yescharacteristic
188D31—42no—
189D31—81no—
190C2×#41—311no—
191C2×Q16—311no—
192C2×SD16—311no—
193C2×SD16—311no—
194C2×D8—311no—
195#126—621no—
196#125—311no—
197#124—311no—
198#123—621no—
199C22⋊Q8—311no—
200#121—311no—
201C4×Q8—311no—
202C4×Q8—311no—
203C4×Q8—311no—
204C4×D4—311no—
205C4×D4—311no—
206C4×D4—311no—
207C4×D4—621no—
208C4×D4—621no—
209C4×D4—621no—
210#117—311no—
211#117—621no—
212#117—621no—
213C2×C42—621no—
214C2×C42C2×D3111yescharacteristic
215#107—311no—
216#107—311no—
217#106—311no—
218#106—311no—
219C4⋊C8C2×D3111yescharacteristic
220C4⋊C8C2×D3111yescharacteristic
221#103—311no—
222#103—311no—
223#103—311no—
224#103—311no—
225#102—311no—
226#102—311no—
227#102—311no—
228#102—311no—
229C22⋊C8C2×D3111yescharacteristic
230C22⋊C8C2×D3111yescharacteristic
231#97C2×D3111yescharacteristic
232#97C2×D3111yescharacteristic
233C31#311111yescharacteristic, complemented, Sylow
234#41—622no—
235#41—622no—
236C2×Q8—311no—
237C2×Q8—311no—
238C2×D4—311no—
239C2×D4—311no—
240C2×D4—621no—
241C2×D4—621no—
242C22×C4—621no—
243C22×C4—621no—
244C22×C4—621no—
245C22×C4—621no—
246C22×C4D12411yescharacteristic
247C22×C4D12411yescharacteristic
248C22×C4C22×D3111yescharacteristic
249Q16—622no—
250SD16—622no—
251SD16—622no—
252D8—622no—
253C2×C8C22×D3111yescharacteristic
254C2×C8C22×D3111yescharacteristic
255C2×C8C22×D3111yescharacteristic
256C2×C8C22×D3111yescharacteristic
257C4⋊C4—311no—
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—
267C22⋊C4—621no—
268C22⋊C4—621no—
269C22⋊C4—621no—
270C22⋊C4—621no—
271C22⋊C4—621no—
272C22⋊C4—621no—
273C22⋊C4—621no—
274C22⋊C4—621no—
275C42—621no—
276C42—621no—
277C42—621no—
278C42—621no—
279C42D12411yescharacteristic
280C42D12411yescharacteristic
281C42C22×D3111yescharacteristic
282C42C22×D3111yescharacteristic
283C23—621no—
284C23—621no—
285C23C2×D12411yescharacteristic
286Q8—312no—
287Q8—621no—
288Q8—621no—
289Q8—621no—
290D4—312no—
291D4—624no—
292D4—621no—
293D4—621no—
294D4—621no—
295D4—1242no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—624no—
301C2×C4—621no—
302C2×C4—621no—
303C2×C4—621no—
304C2×C4—621no—
305C2×C4—621no—
306C2×C4—621no—
307C2×C4—1242no—
308C2×C4—1242no—
309C2×C4—1242no—
310C2×C4C2×D12411yescharacteristic
311C2×C4C2×D12411yescharacteristic
312C2×C4C2×D12411yescharacteristic
313C2×C4C2×D12411yescharacteristic
314C2×C4C2×D12411yescharacteristic
315C2×C4C23×D3111yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—622no—
324C22—1241no—
325C22—1241no—
326C22—1241no—
327C22—1241no—
328C22—1241no—
329C22C22×D12411yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—622no—
336C4—1241no—
337C4—1241no—
338C4—1241no—
339C4—1241no—
340C4—1241no—
341C4#41×D3111yescharacteristic
342C4#41×D3111yescharacteristic
343C2—41no—
344C2—1242no—
345C2—2481no—
346C2#1452156111yescharacteristic
347C2#1452184911yescharacteristic
348C2#1452184911yescharacteristic
subgroupG/H
centerC22C22×D124
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#432C2
socleC22×C31C22×D4
prime radical#14521196C2
hypercenter#432D31
hypocenterC31#3111
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #14521583C2semidirect
2. C4×#92495C2semidirect
3. #14521391C2semidirect
4. #14521374C2semidirect
5. #14521357C2semidirect
6. #14521350C2semidirect
7. #14521272C2semidirect
8. #14521265C2semidirect
9. #14521213C2semidirect
11. #14521162C2semidirect
12. #14521157C2semidirect
13. #14521151C2semidirect
14. #14521151C2semidirect
15. C31×#432C2semidirect
183. #432D31semidirect
233. C31#3111semidirect

Maximal subgroups

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

subgroupindex
#145215832
C4×#924952
#145213912
#145213742
#145213572
#145213502
#145212722
#145212652
#145212132
#145211962
#145211622
#145211572
#145211512
C31×#4322
#311131