Finite Group Databasebeta

← #16858419

Subgroups — #16858419

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#14521720C211yesmaximal, characteristic, complemented
3#14521414C211yesmaximal, characteristic, complemented
4#14521412C211yesmaximal, characteristic, complemented
5#14521394C211yesmaximal, characteristic, complemented
6#14521349C211yesmaximal, characteristic, complemented
7#14521348C211yesmaximal, characteristic, complemented
8#14521338C211yesmaximal, characteristic, complemented
9#14521244C211yesmaximal, characteristic, complemented
10#14521242C211yesmaximal, characteristic, complemented
11#14521242C211yesmaximal, characteristic, complemented
12#14521177C211yesmaximal, characteristic, complemented
13#14521158C211yesmaximal, characteristic, complemented
14#14521129C211yesmaximal, characteristic, complemented
15C31×#442C211yesmaximal, characteristic, complemented
16C2×#92495—21no—
17C2×D8×C31C2211yescharacteristic
18C4×D4×C31C2211yescharacteristic
19C4×D4×C31C2211yescharacteristic
20#11758517C2211yescharacteristic
21#11758517C2211yescharacteristic
22D4×Dic31C2211yescharacteristic
23D4×Dic31C2211yescharacteristic
24C2×#92479C2211yescharacteristic
25C2×#92479C2211yescharacteristic
26#11758507—21no—
27#11758501—21no—
28C2×Dic31⋊C4—21no—
29#11758470C2211yescharacteristic
30#11758470C2211yescharacteristic
31#11758467C2211yescharacteristic
32#11758465C2211yescharacteristic
33#11758461—21no—
34#11758461—21no—
35#11758455—21no—
36#11758455—21no—
37#11758451C2211yescharacteristic
38#11758447C2211yescharacteristic
39C4×Dic62C2211yescharacteristic
40C31×#106C2211yescharacteristic
41C31×#102C2211yescharacteristic
42C31×#102C2211yescharacteristic
43C31×#97C2211yescharacteristic
44#11758420C2211yescharacteristic
45#11758420C2211yescharacteristic
46#11758409C2211yescharacteristic
47#11758409C2211yescharacteristic
48#11758409C2211yescharacteristic
49#11758409C2211yescharacteristic
50#11758403C2211yescharacteristic
51Dic31⋊C8C2211yescharacteristic
52Dic31⋊C8C2211yescharacteristic
53C8×Dic31C2211yescharacteristic
54#11758397C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758396C2211yescharacteristic
57#11758395C2211yescharacteristic
58C4⋊(C31⋊C8)C2211yescharacteristic
59C2×D4×C31C2311yescharacteristic
60C2×D4×C31C2311yescharacteristic
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C2×C22⋊D31—21no—
64C2×C22⋊D31—21no—
65C2×C22⋊D31—21no—
66C2×C22⋊D31—21no—
67C22×Dic31—21no—
68C22×Dic31—21no—
69#92495—44no—
70C2×D124—21no—
71C2×D124—21no—
72C2×D124C2311yescharacteristic
73C2×D124C2311yescharacteristic
74C2×C4×D31—21no—
75C2×C4×D31—21no—
76C2×Dic62—21no—
77C2×Dic62D411yescharacteristic
78D8×C31—22no—
79C2×C8×C31C2311yescharacteristic
80C2×C8×C31C2311yescharacteristic
81C4⋊C4×C31C2311yescharacteristic
82C4⋊C4×C31C2311yescharacteristic
83C22⋊C4×C31—21no—
84C22⋊C4×C31—21no—
85C42×C31C2311yescharacteristic
86C22⋊Dic31—21no—
87C22⋊Dic31—21no—
88#92479—22no—
89#92479—22no—
90(C2×D31)⋊C4—21no—
91(C2×D31)⋊C4—21no—
92C4⋊Dic31—21no—
93C4⋊Dic31D411yescharacteristic
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—
108C22×D31—21no—
109C22×D31—21no—
110D4×C31—21no—
111D4×C31—21no—
112D4×C31—21no—
113D4×C31#4112yescomplemented
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—42no—
117C2×C4×C31—81no—
118C2×C4×C31C2×D411yescharacteristic
119C2×C4×C31C2×D411yescharacteristic
120C2×C4×C31C2411yescharacteristic
121C22⋊D31—42no—
122C22⋊D31—42no—
123C22⋊D31—81no—
124C22⋊D31—81no—
125C2×Dic31—21no—
126C2×Dic31—21no—
127C2×Dic31—42no—
128C2×Dic31—81no—
129C2×Dic31C2×D411yescharacteristic
130C2×Dic31C2×D411yescharacteristic
131C2×Dic31C2×D411yescharacteristic
132C2×Dic31C2×D411yescharacteristic
133D124—21no—
134D124—21no—
135D124—21no—
136D124—21no—
137D124—42no—
138D124—81no—
139C4×D31—42no—
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×C31C22×D411yescharacteristic
155C2×D31—41no—
156C2×D31—41no—
157C2×D31—41no—
158C2×D31—41no—
159C2×D31—41no—
160C2×D31—41no—
161C4×C31—21no—
162C4×C31—21no—
163C4×C31—41no—
164C4×C31—41no—
165C4×C31C2×#4111yescharacteristic
166C4×C312−1+411yescharacteristic
167Dic31—21no—
168Dic31—21no—
169Dic31—21no—
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#459—311no—
184#446—311no—
185#442—311no—
186#442D3111yescharacteristic, complemented
187C4×D8—311no—
188C2×C31—42no—
189C2×C31—81no—
190C2×C31#54811yescharacteristic
191C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C31#57611yescharacteristic
193D31—81no—
194D31—81no—
195C2×#41—621no—
196C2×D8—311no—
197C2×D8—311no—
198C2×D8C2×D3111yescharacteristic
199C4⋊Q8—311no—
200#127—311no—
201#127—311no—
202#127—311no—
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×D4C2×D3111yescharacteristic
217C4×D4C2×D3111yescharacteristic
218C2×C4⋊C4—621no—
219#107—311no—
220#106—311no—
221#106C2×D3111yescharacteristic
222C4⋊C8—311no—
223C4⋊C8—311no—
224C4⋊C8—311no—
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#97C2×D3111yescharacteristic
237C4×C8—311no—
238C31#336611yescharacteristic, complemented, Sylow
239#41—1244no—
240C2×Q8—311no—
241C2×Q8—621no—
242C2×D4—311no—
243C2×D4—311no—
244C2×D4—621no—
245C2×D4—621no—
246C2×D4—621no—
247C2×D4—621no—
248C2×D4—621no—
249C2×D4—621no—
250C2×D4C22×D3111yescharacteristic
251C2×D4C22×D3111yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—621no—
255C22×C4—621no—
256C22×C4—621no—
257C22×C4—621no—
258D8—22no—
259D8—622no—
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—621no—
271C4⋊C4—621no—
272C4⋊C4—621no—
273C4⋊C4—621no—
274C4⋊C4—621no—
275C4⋊C4C22×D3111yescharacteristic
276C4⋊C4C22×D3111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C42—311no—
284C42—311no—
285C42C22×D3111yescharacteristic
286C23—21no—
287C23—21no—
288C23—621no—
289C23—621no—
290Q8—622no—
291Q8—2481no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—621no—
296D4—621no—
297D4—621no—
298D4—621no—
299D4—1242no—
300D4—1242no—
301D4—1242no—
302D4—2481no—
303D4—2481no—
304D4—2481no—
305D4#9249512yescomplemented
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—81no—
310C2×C4—311no—
311C2×C4—311no—
312C2×C4—311no—
313C2×C4—311no—
314C2×C4—621no—
315C2×C4—621no—
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—1241no—
334C22—1241no—
335C22—1241no—
336C22—1241no—
337C22—1241no—
338C22—1241no—
339C22C2×D4×D3111yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—312no—
345C4—621no—
346C4—621no—
347C4—621no—
348C4—1241no—
349C4—1241no—
350C4C2×#9249511yescharacteristic
351C4#1175856711yescharacteristic
352C2—42no—
353C2—81no—
354C2—2481no—
355C2—2481no—
356C2#1452170811yescharacteristic
357C2AGL(1,ℤ/8)×D3111yescharacteristic
358C2#1452185311yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#442C2
socleC22×C31C22×D4
hypercenter#442D31
hypocenterC31#3366
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #14521758C2semidirect
2. #14521720C2semidirect
3. #14521414C2semidirect
4. #14521412C2semidirect
5. #14521394C2semidirect
6. #14521349C2semidirect
7. #14521348C2semidirect
8. #14521338C2semidirect
9. #14521244C2semidirect
10. #14521242C2semidirect
11. #14521242C2semidirect
12. #14521177C2semidirect
13. #14521158C2semidirect
14. #14521129C2semidirect
15. C31×#442C2semidirect
113. D4×C31#41semidirect
186. #442D31semidirect
238. C31#3366semidirect
305. D4#92495semidirect

Maximal subgroups

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

subgroupindex
#145217582
#145217202
#145214142
#145214122
#145213942
#145213492
#145213482
#145213382
#145212442
#145212422
#145211772
#145211582
#145211292
C31×#4422
#336631