Finite Group Databasebeta

← #16855916

Subgroups — #16855916

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#14521531C211yesmaximal, characteristic, complemented
3#14521369C211yesmaximal, characteristic, complemented
4#14521361C211yesmaximal, characteristic, complemented
5#14521358C211yesmaximal, characteristic, complemented
6#14521348C211yesmaximal, characteristic, complemented
7#14521247C211yesmaximal, characteristic, complemented
8#14521243C211yesmaximal, characteristic, complemented
9#14521197C211yesmaximal, characteristic, complemented
10#14521193C211yesmaximal, characteristic, complemented
11#14521159C211yesmaximal, characteristic, complemented
12#14521147C211yesmaximal, characteristic, complemented
13C4×D248C211yesmaximal, characteristic, complemented
14#14521108C211yesmaximal, characteristic, complemented
15C4×SD16×C31C211yesmaximal, characteristic, complemented
16C2×#92499C2211yescharacteristic
17C2×SD16×C31C2211yescharacteristic
18C4×Q8×C31C2211yescharacteristic
19C4×D4×C31C2211yescharacteristic
20Q8×Dic31C2211yescharacteristic
21C2×#92481C2211yescharacteristic
22#11758517C2211yescharacteristic
23#11758515C2211yescharacteristic
24C2×#92479C2211yescharacteristic
25#11758507—21no—
26#11758506—21no—
27C2×D248C2211yescharacteristic
28#11758472C2211yescharacteristic
29#11758470—21no—
30#11758470C2211yescharacteristic
31C4⋊C4×D31—21no—
32C4⋊C4×D31C2211yescharacteristic
33#11758467C2211yescharacteristic
34#11758461—21no—
35#11758460—21no—
36C4×D124—21no—
37C4×D124C2211yescharacteristic
38C4×D124C2211yescharacteristic
39#11758449—21no—
40#11758449C2211yescharacteristic
41C31×#106C2211yescharacteristic
42C31×#103C2211yescharacteristic
43C31×#102C2211yescharacteristic
44C4×C8×C31C2211yescharacteristic
45#11758423C2211yescharacteristic
46#11758420C2211yescharacteristic
47#11758409C2211yescharacteristic
48#11758409C2211yescharacteristic
49(C2×D31)⋊C8C2211yescharacteristic
50(C2×D31)⋊C8C2211yescharacteristic
51#11758406C2211yescharacteristic
52Dic31⋊C8C2211yescharacteristic
53Dic31⋊C8C2211yescharacteristic
54#11758397C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758396C2211yescharacteristic
57#11758395C2211yescharacteristic
58#11758391C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C2×D4×C31C2311yescharacteristic
61C22×C4×C31—21no—
62C2×C22⋊D31—21no—
63C2×C22⋊D31—21no—
64C2×C22⋊D31—21no—
65#92499—22no—
66#92499—22no—
67C2×D124—21no—
68C2×D124—21no—
69C2×D124C2311yescharacteristic
70C2×D124C2311yescharacteristic
71C2×C4×D31—21no—
72C2×C4×D31—21no—
73C2×C4×D31—21no—
74C2×C4×D31—21no—
75C2×C4×D31—21no—
76C2×C4×D31C2311yescharacteristic
77SD16×C31—22no—
78C2×C8×C31C2311yescharacteristic
79C2×C8×C31C2311yescharacteristic
80C4⋊C4×C31—21no—
81C4⋊C4×C31C2311yescharacteristic
82C4⋊C4×C31C2311yescharacteristic
83C22⋊C4×C31—21no—
84C42×C31—21no—
85C42×C31C2311yescharacteristic
86C22⋊Dic31—21no—
87#92481—22no—
88#92479—22no—
89(C2×D31)⋊C4—21no—
90(C2×D31)⋊C4—21no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4—21no—
93(C2×D31)⋊C4D411yescharacteristic
94(C2×D31)⋊C4D411yescharacteristic
95C4⋊Dic31—21no—
96C4⋊Dic31—21no—
97C4⋊Dic31C2311yescharacteristic
98C4⋊Dic31C2311yescharacteristic
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101Dic31⋊C4D411yescharacteristic
102Dic31⋊C4D411yescharacteristic
103C4×Dic31—21no—
104C4×Dic31C2311yescharacteristic
105C2×C31⋊C8C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107D248—22no—
108C23×C31—21no—
109C22×D31—21no—
110C22×D31—21no—
111C22×D31C2×D411yescharacteristic
112Q8×C31—21no—
113Q8×C31#4112yes—
114D4×C31—21no—
115D4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—81no—
120C2×C4×C31C2×D411yescharacteristic
121C2×C4×C31C2×D411yescharacteristic
122C2×C4×C31C2411yescharacteristic
123C22⋊D31—81no—
124C22⋊D31—81no—
125C22⋊D31—81no—
126C2×Dic31—21no—
127C2×Dic31—21no—
128C2×Dic31C2×D411yescharacteristic
129C2×Dic31C2×D411yescharacteristic
130C2×Dic31C2×D411yescharacteristic
131D124—24no—
132D124—21no—
133D124—21no—
134D124—21no—
135D124—81no—
136D124#4112yes—
137C4×D31—24no—
138C4×D31—21no—
139C4×D31—21no—
140C4×D31—81no—
141C4×D31—81no—
142C4×D31—81no—
143C4×D31—81no—
144C8×C31—21no—
145C8×C31—21no—
146C31⋊C8—21no—
147C31⋊C8—21no—
148#3119—311nomaximal, Sylow
149C22×C31—41no—
150C22×C31—41no—
151C22×C31—41no—
152C22×C31C22×D411yescharacteristic
153C2×D31—21no—
154C2×D31—22no—
155C2×D31—21no—
156C2×D31—21no—
157C2×D31—41no—
158C2×D31—41no—
159C2×D31—41no—
160C2×D31—41no—
161C2×D31—41no—
162C4×C31—22no—
163C4×C31—21no—
164C4×C31—21no—
165C4×C31—41no—
166C4×C31—41no—
167C4×C31C2×#4111yescharacteristic
168C4×C31C2×#4111yescharacteristic
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×SD16D3111yescharacteristic, complemented
187C4×D8—311no—
188#433—311no—
189C2×C31—81no—
190C2×C31#52511yescharacteristic
191C2×C31#57611yescharacteristic
192C2×C31#57711yescharacteristic
193D31—41no—
194D31—42no—
195D31—81no—
196C2×#41—311no—
197C2×SD16—311no—
198C2×SD16C2×D3111yescharacteristic
199C2×D8—311no—
200C2×D8—311no—
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×Q8C2×D3111yescharacteristic
211C4×D4—311no—
212C4×D4—311no—
213C4×D4—311no—
214C4×D4—621no—
215C4×D4—621no—
216C4×D4C2×D3111yescharacteristic
217#117—311no—
218#117—621no—
219C2×C4⋊C4—311no—
220C2×C4⋊C4—621no—
221#107—311no—
222#107—311no—
223#106—311no—
224#106C2×D3111yescharacteristic
225C4⋊C8—311no—
226C4⋊C8—311no—
227#103—311no—
228#103C2×D3111yescharacteristic
229#102—311no—
230#102—311no—
231#102—311no—
232#102—311no—
233#102—311no—
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×Q8C22×D3111yescharacteristic
243C2×D4—311no—
244C2×D4—311no—
245C2×D4—621no—
246C2×D4—621no—
247C2×D4—621no—
248C2×D4—621no—
249C2×D4—621no—
250C2×D4C22×D3111yescharacteristic
251C22×C4—21no—
252C22×C4—311no—
253C22×C4—621no—
254C22×C4—621no—
255C22×C4—621no—
256C22×C4—621no—
257C22×C4—621no—
258SD16—22no—
259SD16—622no—
260D8—622no—
261D8—622no—
262C2×C8—311no—
263C2×C8—311no—
264C2×C8C22×D3111yescharacteristic
265C2×C8C22×D3111yescharacteristic
266C4⋊C4—21no—
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⋊C4C22×D3111yescharacteristic
276C4⋊C4C22×D3111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—311no—
279C22⋊C4—311no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C22⋊C4—621no—
284C22⋊C4—621no—
285C42—21no—
286C42—311no—
287C42—621no—
288C42C22×D3111yescharacteristic
289C23—21no—
290C23—311no—
291C23—621no—
292C23—621no—
293Q8—21no—
294Q8#9249512yes—
295D4—21no—
296D4—21no—
297D4—312no—
298D4—624no—
299D4—621no—
300D4—621no—
301D4—621no—
302D4—2481no—
303D4—2481no—
304D4—2481no—
305D4—2481no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
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—2481no—
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—41no—
330C22—41no—
331C22—41no—
332C22—622no—
333C22—621no—
334C22—621no—
335C22—621no—
336C22—1241no—
337C22—1241no—
338C22—1241no—
339C22—1241no—
340C22—1241no—
341C22C2×D4×D3111yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—621no—
348C4—621no—
349C4—621no—
350C4—1241no—
351C4—1241no—
352C4C2×#9249511yescharacteristic
353C4#41×D3111yescharacteristic
354C2—81no—
355C2—1241no—
356C2—1242no—
357C2—2481no—
358C2#1452155811yescharacteristic
359C2#1452185111yescharacteristic
360C2#1452185511yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC4×SD16×C31C2
socleC22×C31C22×D4
hypercenterC4×SD16D31
hypocenterC31#3119
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #14521650C2semidirect
2. #14521531C2semidirect
3. #14521369C2semidirect
4. #14521361C2semidirect
5. #14521358C2semidirect
6. #14521348C2semidirect
7. #14521247C2semidirect
8. #14521243C2semidirect
9. #14521197C2semidirect
10. #14521193C2semidirect
11. #14521159C2semidirect
12. #14521147C2semidirect
13. C4×D248C2semidirect
14. #14521108C2semidirect
15. C4×SD16×C31C2semidirect
186. C4×SD16D31semidirect
239. C31#3119semidirect

Maximal subgroups

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

subgroupindex
#145216502
#145215312
#145213692
#145213612
#145213582
#145213482
#145212472
#145212432
#145211972
#145211932
#145211592
#145211472
C4×D2482
#145211082
C4×SD16×C312
#311931