Finite Group Databasebeta

← #16855162

Subgroups — #16855162

Order 3968.

496 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758527C211yesmaximal, characteristic, complemented
2#14521595C211yesmaximal, characteristic, complemented
3#41×Dic31C211yesmaximal, characteristic, complemented
4#14521273C211yesmaximal, characteristic, complemented
5#14521269C211yesmaximal, characteristic, complemented
6#14521266C211yesmaximal, characteristic, complemented
7#14521262C211yesmaximal, characteristic, complemented
8#14521257C211yesmaximal, characteristic, complemented
9#14521252C211yesmaximal, characteristic, complemented
10#14521247C211yesmaximal, characteristic, complemented
11#14521242C211yesmaximal, characteristic, complemented
12C2×Dic31⋊C8C211yesmaximal, characteristic, complemented
13#14521046C211yesmaximal, characteristic, complemented
14#14521045C211yesmaximal, characteristic, complemented
15C2×C31×#135C211yesmaximal, characteristic, complemented
16C2×#41×C31C2211yescharacteristic
17C2×#41×C31C2211yescharacteristic
18C2×#92495C2211yescharacteristic
19C31×#135—24no—
20C2×Q16×C31C2211yescharacteristic
21C2×SD16×C31C2211yescharacteristic
22C2×SD16×C31C2211yescharacteristic
23C2×D8×C31C2211yescharacteristic
24C22×C8×C31C2211yescharacteristic
25#11758527—24no—
26#11758524C2211yescharacteristic
27Q8×Dic31C2211yescharacteristic
28Q8×Dic31C2211yescharacteristic
29#11758521C2211yescharacteristic
30C2×#92482C2211yescharacteristic
31C2×#92481C2211yescharacteristic
32#11758517C2211yescharacteristic
33#11758516—21no—
34#11758516—21no—
35#11758513C2211yescharacteristic
36D4×Dic31—21no—
37D4×Dic31—21no—
38D4×Dic31C2211yescharacteristic
39D4×Dic31C2211yescharacteristic
40C2×#92480C2211yescharacteristic
41C2×#92479C2211yescharacteristic
42C4×C22⋊D31—21no—
43C4×C22⋊D31—21no—
44#11758503—21no—
45#11758503C2211yescharacteristic
46C2×C4×Dic31—21no—
47C2×C4×Dic31C2211yescharacteristic
48C22×C31⋊C8C2211yescharacteristic
49#11758423C2211yescharacteristic
50#11758423C2211yescharacteristic
51#11758420C2211yescharacteristic
52#11758420C2211yescharacteristic
53#11758409C2211yescharacteristic
54#11758409C2211yescharacteristic
55#11758404C2211yescharacteristic
56#11758404C2211yescharacteristic
57Dic31⋊C8C2211yescharacteristic
58Dic31⋊C8C2211yescharacteristic
59Dic31⋊C8C2211yescharacteristic
60Dic31⋊C8C2211yescharacteristic
61#41×C31—22no—
62#41×C31—22no—
63#41×C31—22no—
64#41×C31D414yescomplemented
65C2×Q8×C31C2311yescharacteristic
66C2×Q8×C31C2311yescharacteristic
67C2×D4×C31—21no—
68C2×D4×C31—21no—
69C2×D4×C31C2311yescharacteristic
70C2×D4×C31C2311yescharacteristic
71C22×C4×C31—21no—
72C22×C4×C31—21no—
73C22×C4×C31C2311yescharacteristic
74C2×C22⋊D31—21no—
75C2×C22⋊D31—21no—
76C2×C22⋊D31—21no—
77C22×Dic31—21no—
78C22×Dic31—21no—
79C22×Dic31D411yescharacteristic
80C22×Dic31D411yescharacteristic
81#92495—22no—
82#92495—22no—
83C2×D124C2311yescharacteristic
84C2×C4×D31—21no—
85C2×Dic62C2311yescharacteristic
86Q16×C31—22no—
87SD16×C31—22no—
88SD16×C31—22no—
89D8×C31—22no—
90C2×C8×C31—22no—
91C2×C8×C31C2311yescharacteristic
92C2×C8×C31C2311yescharacteristic
93C22⋊Dic31—21no—
94C22⋊Dic31—21no—
95C22⋊Dic31—21no—
96C22⋊Dic31—21no—
97C22⋊Dic31—21no—
98#92482—22no—
99#92481—22no—
100#92480—22no—
101#92479—22no—
102(C2×D31)⋊C4—21no—
103(C2×D31)⋊C4—21no—
104C4⋊Dic31—21no—
105C4⋊Dic31—21no—
106C4⋊Dic31C2311yescharacteristic
107C4⋊Dic31C2311yescharacteristic
108Dic31⋊C4—21no—
109Dic31⋊C4—21no—
110C4×Dic31—21no—
111C4×Dic31—21no—
112C4×Dic31—21no—
113C4×Dic31D411yescharacteristic
114C4×Dic31D411yescharacteristic
115C4×Dic31C2311yescharacteristic
116C4×Dic31C2311yescharacteristic
117C2×C31⋊C8—22no—
118C2×C31⋊C8C2311yescharacteristic
119C2×C31⋊C8C2311yescharacteristic
120C23×C31—21no—
121C23×C31—21no—
122C23×C31C2×D411yescharacteristic
123C22×D31—21no—
124Q8×C31—21no—
125Q8×C31—21no—
126Q8×C31—21no—
127Q8×C31C2×D412yes—
128D4×C31—24no—
129D4×C31—21no—
130D4×C31—21no—
131D4×C31—21no—
132D4×C31—42no—
133D4×C31C2×D412yes—
134C2×C4×C31—21no—
135C2×C4×C31—24no—
136C2×C4×C31—21no—
137C2×C4×C31—42no—
138C2×C4×C31C2×D411yescharacteristic
139C2×C4×C31C2×D412yes—
140C2×C4×C31#4112yes—
141C2×C4×C31C2411yescharacteristic
142C22⋊D31—42no—
143C22⋊D31—42no—
144C22⋊D31—42no—
145C2×Dic31—22no—
146C2×Dic31—21no—
147C2×Dic31—21no—
148C2×Dic31—21no—
149C2×Dic31—41no—
150C2×Dic31—42no—
151C2×Dic31—42no—
152C2×Dic31C2×D411yescharacteristic
153C2×Dic31C2×D411yescharacteristic
154C2×Dic31C2×D411yescharacteristic
155C2×Dic31C2×D411yescharacteristic
156D124—21no—
157D124—21no—
158C4×D31—42no—
159Dic62—21no—
160Dic62—21no—
161C8×C31—21no—
162C8×C31—21no—
163C31⋊C8—21no—
164C31⋊C8—21no—
165#3035—311nomaximal, Sylow
166C22×C31—21no—
167C22×C31—21no—
168C22×C31—22no—
169C22×C31—41no—
170C22×C31—41no—
171C22×C31—41no—
172C22×C31—41no—
173C22×C31—41no—
174C22×C31#12112yes—
175C22×C31C22×D411yescharacteristic
176C2×D31—41no—
177C2×D31—41no—
178C2×D31—41no—
179C4×C31—22no—
180C4×C31—41no—
181C4×C31#12112yes—
182C4×C31C22×D411yescharacteristic
183C4×C31C2×#4111yescharacteristic
184Dic31—21no—
185Dic31—21no—
186Dic31—21no—
187Dic31—41no—
188Dic31—41no—
189Dic31—41no—
190Dic31#13512yescomplemented
191C2×#135—311no—
192C2×#135D3111yescharacteristic, complemented
193#532—311no—
194C4×#41—311no—
195#464—311no—
196#464—311no—
197#463—311no—
198#463—311no—
199#462—311no—
200#461—311no—
201#460—311no—
202#459—311no—
203C2×C4⋊C8—311no—
204#416—311no—
205#416—311no—
206C2×C31—22no—
207C2×C31—42no—
208C2×C31—81no—
209C2×C31C2×#12111yescharacteristic
210C2×C31C2×#13511yescharacteristic
211C2×C31#57511yescharacteristic
212D31—81no—
213C2×#41—311no—
214C2×#41C2×D3111yescharacteristic
215C2×#41C2×D3111yescharacteristic
216#135—24no—
217#135—624no—
218C2×Q16—311no—
219C2×Q16C2×D3111yescharacteristic
220C2×SD16—311no—
221C2×SD16—311no—
222C2×SD16C2×D3111yescharacteristic
223C2×SD16C2×D3111yescharacteristic
224C2×D8—311no—
225C2×D8C2×D3111yescharacteristic
226C22×C8—311no—
227C22×C8C2×D3111yescharacteristic
228C4⋊Q8—311no—
229#127—311no—
230#124—311no—
231#124—311no—
232#121—621no—
233#121—621no—
234C4×Q8—311no—
235C4×Q8—311no—
236C4×D4—311no—
237C4×D4—311no—
238C4×D4—621no—
239C4×D4—621no—
240C4×D4—621no—
241C4×D4—621no—
242#117—311no—
243#117—621no—
244C2×C42—311no—
245C2×C42—621no—
246C4⋊C8—311no—
247C4⋊C8—311no—
248C4⋊C8—311no—
249C4⋊C8—311no—
250#103—311no—
251#103—311no—
252#103—311no—
253#103—311no—
254#102—311no—
255#102—311no—
256#102—311no—
257#102—311no—
258C31#303511yescharacteristic, complemented, Sylow
259#41—22no—
260#41—22no—
261#41—22no—
262#41—622no—
263#41—622no—
264#41C22⋊D3114yescomplemented
265C2×Q8—311no—
266C2×Q8C22×D3111yescharacteristic
267C2×Q8C22×D3111yescharacteristic
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—311no—
271C2×D4—621no—
272C2×D4—621no—
273C2×D4—621no—
274C2×D4C22×D3111yescharacteristic
275C2×D4C22×D3111yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—311no—
279C22×C4—311no—
280C22×C4—621no—
281C22×C4—621no—
282C22×C4—621no—
283C22×C4C22×D3111yescharacteristic
284Q16—22no—
285Q16—622no—
286SD16—22no—
287SD16—22no—
288SD16—622no—
289SD16—622no—
290D8—22no—
291D8—622no—
292C2×C8—22no—
293C2×C8—311no—
294C2×C8—311no—
295C2×C8—622no—
296C2×C8C22×D3111yescharacteristic
297C2×C8C22×D3111yescharacteristic
298C4⋊C4—311no—
299C4⋊C4—311no—
300C4⋊C4—621no—
301C4⋊C4—621no—
302C4⋊C4—621no—
303C4⋊C4—621no—
304C22⋊C4—621no—
305C22⋊C4—621no—
306C22⋊C4—621no—
307C22⋊C4—621no—
308C22⋊C4—621no—
309C22⋊C4—621no—
310C22⋊C4—621no—
311C42—311no—
312C42—311no—
313C42—311no—
314C42—311no—
315C42—621no—
316C42—621no—
317C42—621no—
318C23—21no—
319C23—21no—
320C23—621no—
321C23D4×D3111yescharacteristic
322Q8—21no—
323Q8—21no—
324Q8—21no—
325Q8—621no—
326Q8—621no—
327Q8C2×C22⋊D3112yes—
328D4—24no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—621no—
334D4—621no—
335D4—1242no—
336D4—1242no—
337D4—1242no—
338D4C2×C22⋊D3112yes—
339C2×C4—21no—
340C2×C4—24no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—311no—
344C2×C4—311no—
345C2×C4—311no—
346C2×C4—311no—
347C2×C4—622no—
348C2×C4—621no—
349C2×C4—621no—
350C2×C4—621no—
351C2×C4—1242no—
352C2×C4—1241no—
353C2×C4—1242no—
354C2×C4—1242no—
355C2×C4D4×D3111yescharacteristic
356C2×C4#9249712yes—
357C2×C4C2×C22⋊D3112yes—
358C2×C4C23×D3111yescharacteristic
359C8—21no—
360C8—21no—
361C8—621no—
362C8—621no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—1241no—
372C22—1241no—
373C22—1241no—
374C22#1175851612yes—
375C22C2×D4×D3111yescharacteristic
376C4—22no—
377C4—41no—
378C4—312no—
379C4—621no—
380C4—621no—
381C4—621no—
382C4—1241no—
383C4—1241no—
384C4—1241no—
385C4#1175851612yes—
386C4C2×#9249711yescharacteristic
387C4C22×C22⋊D3111yescharacteristic
388C2—22no—
389C2—42no—
390C2—81no—
391C2—2481no—
392C2C2×#1175851611yescharacteristic
393C2#135×D3111yescharacteristic
394C2#1452184611yescharacteristic
subgroupG/H
centerC2×C4D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#135C2
socleC22×C31C22×D4
hypercenterC2×#135D31
hypocenterC31#3035
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#11758527C2semidirect
2. #14521595C2semidirect
3. #41×Dic31C2semidirect
4. #14521273C2semidirect
5. #14521269C2semidirect
6. #14521266C2semidirect
7. #14521262C2semidirect
8. #14521257C2semidirect
9. #14521252C2semidirect
10. #14521247C2semidirect
11. #14521242C2semidirect
12. C2×Dic31⋊C8C2semidirect
13. #14521046C2semidirect
14. #14521045C2semidirect
15. C2×C31×#135C2semidirect
64. #41×C31D4semidirect
190. Dic31#135semidirect
192. C2×#135D31semidirect
258. C31#3035semidirect
264. #41C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117585272
#145215952
#41×Dic312
#145212732
#145212692
#145212662
#145212622
#145212572
#145212522
#145212472
#145212422
C2×Dic31⋊C82
#145210462
#145210452
C2×C31×#1352
#303531