Finite Group Databasebeta

← #16855821

Subgroups — #16855821

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#14521585C211yesmaximal, characteristic, complemented
2#41×Dic31C211yesmaximal, characteristic, complemented
3#14521387C211yesmaximal, characteristic, complemented
4#14521374C211yesmaximal, characteristic, complemented
5#14521358C211yesmaximal, characteristic, complemented
6#14521351C211yesmaximal, characteristic, complemented
7#14521273C211yesmaximal, characteristic, complemented
8#14521266C211yesmaximal, characteristic, complemented
9#14521194C211yesmaximal, characteristic
10#14521158C211yesmaximal, characteristic, complemented
11#14521156C211yesmaximal, characteristic, complemented
12#14521152C211yesmaximal, characteristic, complemented
13#14521150C211yesmaximal, characteristic, complemented
14#14521103C211yesmaximal, characteristic, complemented
15C31×#452C211yesmaximal, characteristic, complemented
16C2×#41×C31C2211yescharacteristic
17C2×Q16×C31C2211yescharacteristic
18C2×SD16×C31C2211yescharacteristic
19C31×C22⋊Q8C2211yescharacteristic
20#11758524C2211yescharacteristic
21Q8×Dic31C2211yescharacteristic
22Q8×Dic31C2211yescharacteristic
23Q8×Dic31C2211yescharacteristic
24C2×#92481C2211yescharacteristic
25D4×Dic31—21no—
26D4×Dic31—21no—
27D4×Dic31C2211yescharacteristic
28D4×Dic31C2211yescharacteristic
29C2×#92479C2211yescharacteristic
30#11758507C2211yescharacteristic
31#11758503—21no—
32#11758503C2211yescharacteristic
33C2×C4×Dic31—21no—
34C2×C4×Dic31C2211yescharacteristic
35#11758475—21no—
36#11758470C2211yescharacteristic
37#11758469—21no—
38#11758467C2211yescharacteristic
39#11758463—21no—
40(C22⋊D31)⋊C4—21no—
41C31×#103C2211yescharacteristic
42C31×#102C2211yescharacteristic
43C31×C22⋊C8C2211yescharacteristic
44#11758423C2211yescharacteristic
45#11758423C2211yescharacteristic
46#11758423C2211yescharacteristic
47#11758420C2211yescharacteristic
48C22⋊(C31⋊C8)C2211yescharacteristic
49#11758409C2211yescharacteristic
50#11758409C2211yescharacteristic
51#11758406C2211yescharacteristic
52#11758405C2211yescharacteristic
53#11758403C2211yescharacteristic
54#11758403C2211yescharacteristic
55Dic31⋊C8C2211yescharacteristic
56Dic31⋊C8C2211yescharacteristic
57#11758396C2211yescharacteristic
58#11758395C2211yescharacteristic
59#41×C31—22no—
60#41×C31—22no—
61C2×Q8×C31C2311yescharacteristic
62C2×Q8×C31C2311yescharacteristic
63C2×D4×C31—21no—
64C2×D4×C31C2311yescharacteristic
65C22×C4×C31—21no—
66C22×C4×C31C2311yescharacteristic
67C2×C22⋊D31—21no—
68C22×Dic31—21no—
69C22×Dic31—21no—
70C22×Dic31D411yescharacteristic
71C22×Dic31D411yescharacteristic
72C2×D124C2311yescharacteristic
73C2×C4×D31—21no—
74Q16×C31—22no—
75SD16×C31—22no—
76C2×C8×C31C2311yescharacteristic
77C2×C8×C31C2311yescharacteristic
78C4⋊C4×C31—21no—
79C4⋊C4×C31C2311yescharacteristic
80C22⋊C4×C31—21no—
81C22⋊Dic31—21no—
82C22⋊Dic31—21no—
83C22⋊Dic31—21no—
84#92481—22no—
85#92479—22no—
86(C2×D31)⋊C4—21no—
87(C2×D31)⋊C4—21no—
88(C2×D31)⋊C4—21no—
89(C2×D31)⋊C4—21no—
90C4⋊Dic31—21no—
91C4⋊Dic31—21no—
92C4⋊Dic31—21no—
93C4⋊Dic31—21no—
94C4⋊Dic31C2311yescharacteristic
95C4⋊Dic31C2311yescharacteristic
96C4⋊Dic31C2311yescharacteristic
97Dic31⋊C4—21no—
98C4×Dic31—21no—
99C4×Dic31—21no—
100C4×Dic31—21no—
101C4×Dic31—21no—
102C4×Dic31D411yescharacteristic
103C4×Dic31D411yescharacteristic
104C4×Dic31C2311yescharacteristic
105C4×Dic31C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108C23×C31—21no—
109C23×C31C2×D411yescharacteristic
110C22×D31—21no—
111Q8×C31—21no—
112Q8×C31—21no—
113Q8×C31—21no—
114Q8×C31#4112yes—
115D4×C31—24no—
116D4×C31—21no—
117D4×C31#4112yes—
118C2×C4×C31—24no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31C2411yescharacteristic
126C22⋊D31—42no—
127C2×Dic31—21no—
128C2×Dic31—21no—
129C2×Dic31—21no—
130C2×Dic31—41no—
131C2×Dic31—41no—
132C2×Dic31—42no—
133C2×Dic31—42no—
134C2×Dic31C2×D411yescharacteristic
135C2×Dic31C2×D411yescharacteristic
136C2×Dic31C2×D411yescharacteristic
137C2×Dic31C2×D411yescharacteristic
138D124—21no—
139D124—21no—
140C4×D31—42no—
141C8×C31—21no—
142C8×C31—21no—
143C31⋊C8—21no—
144C31⋊C8—21no—
145#3111—311nomaximal, Sylow
146C22×C31—21no—
147C22×C31—22no—
148C22×C31—21no—
149C22×C31—21no—
150C22×C31—41no—
151C22×C31—41no—
152C22×C31C22×D411yescharacteristic
153C2×D31—41no—
154C2×D31—41no—
155C2×D31—41no—
156C4×C31—21no—
157C4×C31—22no—
158C4×C31—41no—
159C4×C31—41no—
160C4×C31C2×#4111yescharacteristic
161C4×C31C2×#4111yescharacteristic
162Dic31—21no—
163Dic31—21no—
164Dic31—21no—
165Dic31—21no—
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#452D3111yescharacteristic, complemented
178#449—311no—
179#442—311no—
180#441—311no—
181#440—311no—
182#440—311no—
183#432—311no—
184C2×C31—41no—
185C2×C31—42no—
186C2×C31#52511yescharacteristic
187C2×C31#57511yescharacteristic
188C2×C31#57511yescharacteristic
189D31—81no—
190C2×#41C2×D3111yescharacteristic
191C2×Q16C2×D3111yescharacteristic
192C2×SD16—311no—
193C2×SD16C2×D3111yescharacteristic
194C2×D8—311no—
195#126—621no—
196#125—311no—
197#124—311no—
198#123—621no—
199C22⋊Q8C2×D3111yescharacteristic
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—311no—
214C2×C42—621no—
215#107—311no—
216#107—311no—
217#106—311no—
218#106—311no—
219C4⋊C8—311no—
220C4⋊C8—311no—
221#103—311no—
222#103—311no—
223#103—311no—
224#103C2×D3111yescharacteristic
225#102—311no—
226#102—311no—
227#102—311no—
228#102C2×D3111yescharacteristic
229C22⋊C8—311no—
230C22⋊C8C2×D3111yescharacteristic
231#97—311no—
232#97—311no—
233C31#311111yescharacteristic, complemented, Sylow
234#41—22no—
235#41—22no—
236C2×Q8C22×D3111yescharacteristic
237C2×Q8C22×D3111yescharacteristic
238C2×D4—21no—
239C2×D4—311no—
240C2×D4—621no—
241C2×D4C22×D3111yescharacteristic
242C22×C4—21no—
243C22×C4—311no—
244C22×C4—311no—
245C22×C4—621no—
246C22×C4—621no—
247C22×C4—621no—
248C22×C4C22×D3111yescharacteristic
249Q16—22no—
250SD16—22no—
251SD16—622no—
252D8—622no—
253C2×C8—311no—
254C2×C8—311no—
255C2×C8C22×D3111yescharacteristic
256C2×C8C22×D3111yescharacteristic
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⋊C4C22×D3111yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—621no—
269C22⋊C4—621no—
270C22⋊C4—621no—
271C22⋊C4—621no—
272C22⋊C4—621no—
273C22⋊C4—621no—
274C22⋊C4—621no—
275C42—311no—
276C42—311no—
277C42—311no—
278C42—311no—
279C42—621no—
280C42—621no—
281C42—621no—
282C42—621no—
283C23—21no—
284C23—621no—
285C23D4×D3111yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8#9249712yes—
290D4—24no—
291D4—21no—
292D4—621no—
293D4—621no—
294D4—1242no—
295D4#9249712yes—
296C2×C4—24no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—311no—
303C2×C4—311no—
304C2×C4—311no—
305C2×C4—311no—
306C2×C4—621no—
307C2×C4—621no—
308C2×C4—621no—
309C2×C4—1242no—
310C2×C4—1241no—
311C2×C4—1241no—
312C2×C4—1242no—
313C2×C4—1242no—
314C2×C4D4×D3111yescharacteristic
315C2×C4C23×D3111yescharacteristic
316C8—21no—
317C8—21no—
318C8—621no—
319C8—621no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—1241no—
327C22—1241no—
328C22—1241no—
329C22C2×D4×D3111yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—621no—
335C4—621no—
336C4—621no—
337C4—621no—
338C4—1241no—
339C4—1241no—
340C4—1241no—
341C4C2×#9249711yescharacteristic
342C4C2×#9249711yescharacteristic
343C2—41no—
344C2—42no—
345C2—2481no—
346C2#1452155511yescharacteristic
347C2#1452184611yescharacteristic
348C2#1452184811yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#452C2
socleC22×C31C22×D4
prime radical#14521194C2
hypercenter#452D31
hypocenterC31#3111
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #14521585C2semidirect
2. #41×Dic31C2semidirect
3. #14521387C2semidirect
4. #14521374C2semidirect
5. #14521358C2semidirect
6. #14521351C2semidirect
7. #14521273C2semidirect
8. #14521266C2semidirect
10. #14521158C2semidirect
11. #14521156C2semidirect
12. #14521152C2semidirect
13. #14521150C2semidirect
14. #14521103C2semidirect
15. C31×#452C2semidirect
177. #452D31semidirect
233. C31#3111semidirect

Maximal subgroups

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

subgroupindex
#145215852
#41×Dic312
#145213872
#145213742
#145213582
#145213512
#145212732
#145212662
#145211942
#145211582
#145211562
#145211522
#145211502
#145211032
C31×#4522
#311131