Finite Group Databasebeta

← #16858413

Subgroups — #16858413

Order 3968.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521758C211yesmaximal, characteristic, complemented
2#14521719C211yesmaximal, characteristic, complemented
3#14521413C211yesmaximal, characteristic, complemented
4#14521412C211yesmaximal, characteristic, complemented
5#14521394C211yesmaximal, characteristic, complemented
6#14521350C211yesmaximal, characteristic, complemented
7#14521347C211yesmaximal, characteristic, complemented
8#14521337C211yesmaximal, characteristic, complemented
9#14521242C211yesmaximal, characteristic, complemented
10#14521242C211yesmaximal, characteristic, complemented
11#14521178C211yesmaximal, characteristic, complemented
12#14521161C211yesmaximal, characteristic, complemented
13#14521159C211yesmaximal, characteristic, complemented
14D8×Dic31C211yesmaximal, characteristic, complemented
15C31×#459C211yesmaximal, characteristic, complemented
16C2×#92497—21no—
17C2×D8×C31C2211yescharacteristic
18C2×D8×C31C2211yescharacteristic
19C31×#127C2211yescharacteristic
20C4×D4×C31C2211yescharacteristic
21#11758517C2211yescharacteristic
22#11758517C2211yescharacteristic
23#11758516—21no—
24#11758516—21no—
25#11758515—21no—
26D4×Dic31C2211yescharacteristic
27D4×Dic31C2211yescharacteristic
28D4×Dic31C2211yescharacteristic
29D4×Dic31C2211yescharacteristic
30C2×#92479C2211yescharacteristic
31#11758501—21no—
32C2×Dic31⋊C4—21no—
33#11758467C2211yescharacteristic
34#11758465C2211yescharacteristic
35#11758455—21no—
36#11758455—21no—
37C4×D124C2211yescharacteristic
38#11758447C2211yescharacteristic
39C4×Dic62C2211yescharacteristic
40C31×C4⋊C8C2211yescharacteristic
41C31×#102C2211yescharacteristic
42C31×#102C2211yescharacteristic
43#11758420C2211yescharacteristic
44#11758420C2211yescharacteristic
45#11758420C2211yescharacteristic
46#11758420C2211yescharacteristic
47#11758420C2211yescharacteristic
48#11758409C2211yescharacteristic
49#11758409C2211yescharacteristic
50#11758406C2211yescharacteristic
51#11758405C2211yescharacteristic
52#11758403C2211yescharacteristic
53Dic31⋊C8C2211yescharacteristic
54Dic31⋊C8C2211yescharacteristic
55C8×Dic31C2211yescharacteristic
56#11758397C2211yescharacteristic
57#11758396C2211yescharacteristic
58#11758391C2211yescharacteristic
59C2×D4×C31—21no—
60C2×D4×C31—21no—
61C2×D4×C31C2311yescharacteristic
62C2×D4×C31C2311yescharacteristic
63C2×D4×C31C2311yescharacteristic
64C22×C4×C31—21no—
65C2×C22⋊D31—21no—
66C2×C22⋊D31—21no—
67C2×C22⋊D31—21no—
68C2×C22⋊D31—21no—
69C22×Dic31—21no—
70C22×Dic31—21no—
71C22×Dic31—21no—
72C22×Dic31—21no—
73#92497—44no—
74C2×D124C2311yescharacteristic
75C2×C4×D31—21no—
76C2×Dic62—21no—
77C2×Dic62D411yescharacteristic
78D8×C31—22no—
79D8×C31—22no—
80C2×C8×C31C2311yescharacteristic
81C2×C8×C31C2311yescharacteristic
82C4⋊C4×C31C2311yescharacteristic
83C22⋊C4×C31—21no—
84C42×C31C2311yescharacteristic
85C22⋊Dic31—21no—
86C22⋊Dic31—21no—
87C22⋊Dic31—21no—
88C22⋊Dic31—21no—
89#92479—22no—
90(C2×D31)⋊C4—21no—
91C4⋊Dic31—21no—
92C4⋊Dic31D411yescharacteristic
93C4⋊Dic31C2311yescharacteristic
94C4⋊Dic31C2311yescharacteristic
95C4⋊Dic31C2311yescharacteristic
96Dic31⋊C4—21no—
97Dic31⋊C4—21no—
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100Dic31⋊C4D411yescharacteristic
101Dic31⋊C4D411yescharacteristic
102C4×Dic31C2311yescharacteristic
103C4×Dic31C2311yescharacteristic
104C2×C31⋊C8C2311yescharacteristic
105C2×C31⋊C8C2311yescharacteristic
106C23×C31—21no—
107C23×C31—21no—
108C23×C31—21no—
109C22×D31—21no—
110D4×C31—21no—
111D4×C31—21no—
112D4×C31—21no—
113D4×C31—21no—
114D4×C31—21no—
115D4×C31—42no—
116D4×C31—81no—
117D4×C31#4112yescomplemented
118C2×C4×C31—21no—
119C2×C4×C31—81no—
120C2×C4×C31C2×D411yescharacteristic
121C2×C4×C31C2×D411yescharacteristic
122C2×C4×C31C2411yescharacteristic
123C22⋊D31—42no—
124C22⋊D31—42no—
125C22⋊D31—81no—
126C22⋊D31—81no—
127C2×Dic31—21no—
128C2×Dic31—21no—
129C2×Dic31—21no—
130C2×Dic31—42no—
131C2×Dic31—42no—
132C2×Dic31—42no—
133C2×Dic31—81no—
134C2×Dic31C2×D411yescharacteristic
135C2×Dic31C2×D411yescharacteristic
136C2×Dic31C2×D411yescharacteristic
137C2×Dic31C2×D411yescharacteristic
138D124—21no—
139D124—21no—
140C4×D31—42no—
141Dic62—22no—
142Dic62—81no—
143C8×C31—21no—
144C8×C31—21no—
145C31⋊C8—21no—
146C31⋊C8—21no—
147#3366—311nomaximal, Sylow
148C22×C31—22no—
149C22×C31—41no—
150C22×C31—41no—
151C22×C31—41no—
152C22×C31—41no—
153C22×C31—41no—
154C22×C31—41no—
155C22×C31—41no—
156C22×C31—41no—
157C22×C31C22×D411yescharacteristic
158C2×D31—41no—
159C2×D31—41no—
160C2×D31—41no—
161C4×C31—21no—
162C4×C31—21no—
163C4×C31—41no—
164C4×C31C2×#4111yescharacteristic
165C4×C312−1+411yescharacteristic
166Dic31—21no—
167Dic31—21no—
168Dic31—21no—
169Dic31—41no—
170Dic31—41no—
171Dic31—41no—
172Dic31AGL(1,ℤ/8)12yes—
173#554—311no—
174#550—311no—
175#490—311no—
176#490—311no—
177#486—311no—
178#478—311no—
179#478—311no—
180#476—311no—
181#459—311no—
182#459—311no—
183#459D3111yescharacteristic, complemented
184#446—311no—
185#442—311no—
186#442—311no—
187C4×D8—311no—
188C2×C31—42no—
189C2×C31—81no—
190C2×C31—81no—
191C2×C31#54811yescharacteristic
192C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
193C2×C31#57611yescharacteristic
194D31—81no—
195C2×#41—621no—
196C2×D8—311no—
197C2×D8C2×D3111yescharacteristic
198C2×D8C2×D3111yescharacteristic
199C4⋊Q8—311no—
200#127—311no—
201#127—311no—
202#127C2×D3111yescharacteristic
203#125—311no—
204#125—311no—
205C22⋊Q8—621no—
206C22⋊Q8—621no—
207C22⋊Q8—621no—
208#121—621no—
209#121—621no—
210#121—621no—
211C4×Q8—311no—
212C4×D4—311no—
213C4×D4—311no—
214C4×D4—311no—
215C4×D4—311no—
216C4×D4—311no—
217C4×D4C2×D3111yescharacteristic
218C2×C4⋊C4—621no—
219#107—311no—
220#106—311no—
221#106—311no—
222C4⋊C8—311no—
223C4⋊C8—311no—
224C4⋊C8C2×D3111yescharacteristic
225#102—311no—
226#102—311no—
227#102—311no—
228#102—311no—
229#102—311no—
230#102—311no—
231#102—311no—
232#102—311no—
233#102C2×D3111yescharacteristic
234#102C2×D3111yescharacteristic
235#97—311no—
236#97—311no—
237C4×C8—311no—
238C31#336611yescharacteristic, complemented, Sylow
239#41—1244no—
240C2×Q8—311no—
241C2×Q8—621no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—311no—
245C2×D4—621no—
246C2×D4—621no—
247C2×D4—621no—
248C2×D4—621no—
249C2×D4C22×D3111yescharacteristic
250C2×D4C22×D3111yescharacteristic
251C2×D4C22×D3111yescharacteristic
252C22×C4—21no—
253C22×C4—621no—
254C22×C4—621no—
255C22×C4—621no—
256C22×C4—621no—
257C22×C4—621no—
258D8—22no—
259D8—22no—
260D8—622no—
261C2×C8—311no—
262C2×C8—311no—
263C2×C8C22×D3111yescharacteristic
264C2×C8C22×D3111yescharacteristic
265C4⋊C4—311no—
266C4⋊C4—311no—
267C4⋊C4—311no—
268C4⋊C4—311no—
269C4⋊C4—311no—
270C4⋊C4—311no—
271C4⋊C4—621no—
272C4⋊C4—621no—
273C4⋊C4—621no—
274C4⋊C4—621no—
275C4⋊C4—621no—
276C4⋊C4C22×D3111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—621no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C42—311no—
284C42—311no—
285C42C22×D3111yescharacteristic
286C23—21no—
287C23—21no—
288C23—21no—
289C23—621no—
290Q8—622no—
291Q8—2481no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—42no—
298D4—81no—
299D4—621no—
300D4—621no—
301D4—1242no—
302D4—1242no—
303D4—2481no—
304D4—2481no—
305D4#9249712yescomplemented
306C2×C4—21no—
307C2×C4—81no—
308C2×C4—311no—
309C2×C4—311no—
310C2×C4—311no—
311C2×C4—311no—
312C2×C4—621no—
313C2×C4—621no—
314C2×C4—621no—
315C2×C4—1242no—
316C2×C4—1242no—
317C2×C4—1242no—
318C2×C4—1242no—
319C2×C4—2481no—
320C2×C4D4×D3111yescharacteristic
321C2×C4D4×D3111yescharacteristic
322C2×C4C23×D3111yescharacteristic
323C8—21no—
324C8—21no—
325C8—621no—
326C8—621no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—1241no—
337C22—1241no—
338C22—1241no—
339C22C2×D4×D3111yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—312no—
344C4—621no—
345C4—621no—
346C4—621no—
347C4—1241no—
348C4—1241no—
349C4—1241no—
350C4C2×#9249711yescharacteristic
351C4#1175856711yescharacteristic
352C2—42no—
353C2—81no—
354C2—81no—
355C2—2481no—
356C2#1452170511yescharacteristic
357C2AGL(1,ℤ/8)×D3111yescharacteristic
358C2#1452185011yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#459C2
socleC22×C31C22×D4
hypercenter#459D31
hypocenterC31#3366
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #14521758C2semidirect
2. #14521719C2semidirect
3. #14521413C2semidirect
4. #14521412C2semidirect
5. #14521394C2semidirect
6. #14521350C2semidirect
7. #14521347C2semidirect
8. #14521337C2semidirect
9. #14521242C2semidirect
10. #14521242C2semidirect
11. #14521178C2semidirect
12. #14521161C2semidirect
13. #14521159C2semidirect
14. D8×Dic31C2semidirect
15. C31×#459C2semidirect
117. D4×C31#41semidirect
183. #459D31semidirect
238. C31#3366semidirect
305. D4#92497semidirect

Maximal subgroups

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

subgroupindex
#145217582
#145217192
#145214132
#145214122
#145213942
#145213502
#145213472
#145213372
#145212422
#145211782
#145211612
#145211592
D8×Dic312
C31×#4592
#336631