Finite Group Databasebeta

← #16855906

Subgroups — #16855906

Order 3968.

396 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#14521650C211yesmaximal, characteristic, complemented
2#14521528C211yesmaximal, characteristic, complemented
3#14521366C211yesmaximal, characteristic, complemented
4#14521364C211yesmaximal, characteristic, complemented
5#14521355C211yesmaximal, characteristic, complemented
6#14521351C211yesmaximal, characteristic, complemented
7#14521248C211yesmaximal, characteristic, complemented
8#14521242C211yesmaximal, characteristic, complemented
9#14521195C211yesmaximal, characteristic, complemented
10#14521191C211yesmaximal, characteristic, complemented
11#14521159C211yesmaximal, characteristic, complemented
12#14521149C211yesmaximal, characteristic, complemented
13C4×#92470C211yesmaximal, characteristic, complemented
14#14521108C211yesmaximal, characteristic, complemented
15C4×D8×C31C211yesmaximal, characteristic, complemented
16C2×#92497C2211yescharacteristic
17C2×D8×C31C2211yescharacteristic
18C4×D4×C31C2211yescharacteristic
19C4×D4×C31C2211yescharacteristic
20#11758517C2211yescharacteristic
21#11758515C2211yescharacteristic
22D4×Dic31C2211yescharacteristic
23C2×#92480C2211yescharacteristic
24C2×#92479C2211yescharacteristic
25#11758507—21no—
26#11758506—21no—
27C4×C22⋊D31—21no—
28C2×Dic31⋊C4—21no—
29C2×#92470C2211yescharacteristic
30#11758472C2211yescharacteristic
31C4⋊C4×D31C2211yescharacteristic
32#11758467C2211yescharacteristic
33#11758464C2211yescharacteristic
34#11758461—21no—
35#11758460—21no—
36(C22⋊D31)⋊C4—21no—
37#11758454—21no—
38C4×D124C2211yescharacteristic
39#11758449C2211yescharacteristic
40C4×Dic62C2211yescharacteristic
41C31×#107C2211yescharacteristic
42C31×#102C2211yescharacteristic
43C31×#102C2211yescharacteristic
44C4×C8×C31C2211yescharacteristic
45#11758420C2211yescharacteristic
46#11758420C2211yescharacteristic
47#11758409C2211yescharacteristic
48(C2×D31)⋊C8C2211yescharacteristic
49(C2×D31)⋊C8C2211yescharacteristic
50#11758405C2211yescharacteristic
51#11758404C2211yescharacteristic
52Dic31⋊C8C2211yescharacteristic
53Dic31⋊C8C2211yescharacteristic
54#11758398C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758396C2211yescharacteristic
57#11758395C2211yescharacteristic
58#11758391C2211yescharacteristic
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#92497—22no—
70#92497—22no—
71C2×D124—21no—
72C2×D124C2311yescharacteristic
73C2×C4×D31—21no—
74C2×C4×D31—21no—
75C2×C4×D31C2311yescharacteristic
76C2×Dic62C2311yescharacteristic
77D8×C31—22no—
78C2×C8×C31C2311yescharacteristic
79C2×C8×C31C2311yescharacteristic
80C4⋊C4×C31C2311yescharacteristic
81C4⋊C4×C31C2311yescharacteristic
82C22⋊C4×C31—21no—
83C22⋊C4×C31—21no—
84C42×C31C2311yescharacteristic
85C22⋊Dic31—21no—
86C22⋊Dic31—21no—
87#92480—22no—
88#92479—22no—
89(C2×D31)⋊C4—21no—
90(C2×D31)⋊C4—21no—
91(C2×D31)⋊C4D411yescharacteristic
92(C2×D31)⋊C4D411yescharacteristic
93C4⋊Dic31—21no—
94C4⋊Dic31C2311yescharacteristic
95C4⋊Dic31C2311yescharacteristic
96Dic31⋊C4—21no—
97Dic31⋊C4—21no—
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100Dic31⋊C4D411yescharacteristic
101Dic31⋊C4D411yescharacteristic
102C4×Dic31—21no—
103C4×Dic31—21no—
104C4×Dic31C2311yescharacteristic
105C2×C31⋊C8C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107#92470—22no—
108C23×C31—21no—
109C23×C31—21no—
110C22×D31—21no—
111C22×D31C2×D411yescharacteristic
112D4×C31—21no—
113D4×C31—21no—
114D4×C31—21no—
115D4×C31#4112yes—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—81no—
119C2×C4×C31—81no—
120C2×C4×C31C2×D411yescharacteristic
121C2×C4×C31C2×D411yescharacteristic
122C2×C4×C31C2411yescharacteristic
123C22⋊D31—24no—
124C22⋊D31—81no—
125C22⋊D31—81no—
126C22⋊D31—81no—
127C2×Dic31—24no—
128C2×Dic31—21no—
129C2×Dic31—21no—
130C2×Dic31—21no—
131C2×Dic31—81no—
132C2×Dic31C2×D411yescharacteristic
133C2×Dic31C2×D411yescharacteristic
134C2×Dic31C2×D411yescharacteristic
135D124—21no—
136D124—21no—
137D124—81no—
138C4×D31—21no—
139C4×D31—21no—
140C4×D31—81no—
141C4×D31—81no—
142Dic62—21no—
143Dic62#4112yes—
144C8×C31—21no—
145C8×C31—21no—
146C31⋊C8—21no—
147C31⋊C8—21no—
148#3119—311nomaximal, Sylow
149C22×C31—22no—
150C22×C31—41no—
151C22×C31—41no—
152C22×C31—41no—
153C22×C31—41no—
154C22×C31—41no—
155C22×C31C22×D411yescharacteristic
156C2×D31—21no—
157C2×D31—21no—
158C2×D31—21no—
159C2×D31—41no—
160C2×D31—41no—
161C2×D31—41no—
162C4×C31—21no—
163C4×C31—21no—
164C4×C31—41no—
165C4×C31—41no—
166C4×C31C2×#4111yescharacteristic
167C4×C31C2×#4111yescharacteristic
168Dic31—22no—
169Dic31—21no—
170Dic31—21no—
171Dic31—21no—
172Dic31—41no—
173Dic31—41no—
174#540—311no—
175#520—311no—
176#481—311no—
177#480—311no—
178#479—311no—
179#478—311no—
180#460—311no—
181#459—311no—
182#449—311no—
183#449—311no—
184#442—311no—
185#440—311no—
186C4×SD16—311no—
187C4×D8D3111yescharacteristic, complemented
188#433—311no—
189C2×C31—42no—
190C2×C31—81no—
191C2×C31#52511yescharacteristic
192C2×C31#57611yescharacteristic
193C2×C31#57711yescharacteristic
194D31—41no—
195D31—81no—
196C2×#41—311no—
197C2×SD16—311no—
198C2×SD16—311no—
199C2×D8—311no—
200C2×D8C2×D3111yescharacteristic
201#127—311no—
202#125—311no—
203#123—621no—
204#123—621no—
205#121—311no—
206#121—311no—
207#121—621no—
208#121—621no—
209C4×Q8—311no—
210C4×Q8—311no—
211C4×D4—311no—
212C4×D4—311no—
213C4×D4—621no—
214C4×D4—621no—
215C4×D4C2×D3111yescharacteristic
216C4×D4C2×D3111yescharacteristic
217#117—311no—
218#117—621no—
219C2×C4⋊C4—311no—
220C2×C4⋊C4—621no—
221#107—311no—
222#107C2×D3111yescharacteristic
223#106—311no—
224#106—311no—
225C4⋊C8—311no—
226C4⋊C8—311no—
227#103—311no—
228#103—311no—
229#102—311no—
230#102—311no—
231#102—311no—
232#102—311no—
233#102C2×D3111yescharacteristic
234#102C2×D3111yescharacteristic
235C22⋊C8—311no—
236C22⋊C8—311no—
237#97—311no—
238C4×C8C2×D3111yescharacteristic
239C31#311911yescharacteristic, complemented, Sylow
240#41—622no—
241#41—622no—
242C2×Q8—311no—
243C2×D4—311no—
244C2×D4—621no—
245C2×D4—621no—
246C2×D4—621no—
247C2×D4—621no—
248C2×D4—621no—
249C2×D4C22×D3111yescharacteristic
250C2×D4C22×D3111yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—311no—
254C22×C4—621no—
255C22×C4—621no—
256C22×C4—621no—
257C22×C4—621no—
258SD16—622no—
259SD16—622no—
260D8—22no—
261D8—622no—
262C2×C8—311no—
263C2×C8—311no—
264C2×C8C22×D3111yescharacteristic
265C2×C8C22×D3111yescharacteristic
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—311no—
280C22⋊C4—311no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C22⋊C4—621no—
284C22⋊C4—621no—
285C42—311no—
286C42—621no—
287C42—621no—
288C42C22×D3111yescharacteristic
289C23—21no—
290C23—21no—
291C23—311no—
292C23—621no—
293Q8—312no—
294Q8—621no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—624no—
299D4—621no—
300D4—621no—
301D4—2481no—
302D4—2481no—
303D4—2481no—
304D4—2481no—
305D4#9249512yes—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—311no—
311C2×C4—311no—
312C2×C4—311no—
313C2×C4—624no—
314C2×C4—621no—
315C2×C4—621no—
316C2×C4—621no—
317C2×C4—621no—
318C2×C4—621no—
319C2×C4—2481no—
320C2×C4—2481no—
321C2×C4—2481no—
322C2×C4D4×D3111yescharacteristic
323C2×C4D4×D3111yescharacteristic
324C2×C4C23×D3111yescharacteristic
325C8—21no—
326C8—21no—
327C8—621no—
328C8—621no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—621no—
336C22—621no—
337C22—621no—
338C22—1241no—
339C22—1241no—
340C22—1241no—
341C22C2×D4×D3111yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—621no—
347C4—621no—
348C4—622no—
349C4—621no—
350C4—1241no—
351C4—1241no—
352C4C2×#9249511yescharacteristic
353C4#41×D3111yescharacteristic
354C2—42no—
355C2—81no—
356C2—1241no—
357C2—2481no—
358C2#1452155811yescharacteristic
359C2#1452185011yescharacteristic
360C2#1452185611yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC4×D8×C31C2
socleC22×C31C22×D4
hypercenterC4×D8D31
hypocenterC31#3119
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #14521650C2semidirect
2. #14521528C2semidirect
3. #14521366C2semidirect
4. #14521364C2semidirect
5. #14521355C2semidirect
6. #14521351C2semidirect
7. #14521248C2semidirect
8. #14521242C2semidirect
9. #14521195C2semidirect
10. #14521191C2semidirect
11. #14521159C2semidirect
12. #14521149C2semidirect
13. C4×#92470C2semidirect
14. #14521108C2semidirect
15. C4×D8×C31C2semidirect
187. C4×D8D31semidirect
239. C31#3119semidirect

Maximal subgroups

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

subgroupindex
#145216502
#145215282
#145213662
#145213642
#145213552
#145213512
#145212482
#145212422
#145211952
#145211912
#145211592
#145211492
C4×#924702
#145211082
C4×D8×C312
#311931