Finite Group Databasebeta

← #16857464

Subgroups — #16857464

Order 3968.

504 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758493C211yesmaximal, characteristic, complemented
2C2×#11758527C211yesmaximal, characteristic, complemented
3#14521718C211yesmaximal, characteristic, complemented
4#14521717C211yesmaximal, characteristic, complemented
5#14521424C211yesmaximal, characteristic, complemented
6#14521284C211yesmaximal, characteristic, complemented
7#14521283C211yesmaximal, characteristic, complemented
8#14521248C211yesmaximal, characteristic, complemented
9#14521247C211yesmaximal, characteristic, complemented
10#14521197C211yesmaximal, characteristic, complemented
11#14521196C211yesmaximal, characteristic, complemented
12#14521191C211yesmaximal, characteristic, complemented
13#14521141C211yesmaximal, characteristic, complemented
14(C22⋊D31)⋊C8C211yesmaximal, characteristic, complemented
15C31×#449C211yesmaximal, characteristic, complemented
16C2×#41×C31C2211yescharacteristic
17C2×#92499C2211yescharacteristic
18C2×#92497C2211yescharacteristic
19C2×#92495C2211yescharacteristic
20C2×SD16×C31C2211yescharacteristic
21C2×D8×C31C2211yescharacteristic
22C31×#121C2211yescharacteristic
23#11758527—24no—
24Q8×Dic31C2211yescharacteristic
25C2×#92482C2211yescharacteristic
26C2×#92481C2211yescharacteristic
27#11758517—21no—
28#11758517—21no—
29#11758517C2211yescharacteristic
30#11758517C2211yescharacteristic
31#11758516—21no—
32#11758515—21no—
33#11758515C2211yescharacteristic
34C2×#92480C2211yescharacteristic
35C2×#92479C2211yescharacteristic
36C2×#92479C2211yescharacteristic
37#11758507—21no—
38#11758507C2211yescharacteristic
39C4×C22⋊D31—21no—
40C4×C22⋊D31C2211yescharacteristic
41C22×C31⋊C8C2211yescharacteristic
42#11758493—24no—
43C2×D248C2211yescharacteristic
44C2×#92470C2211yescharacteristic
45C2×C8×D31C2211yescharacteristic
46#11758472C2211yescharacteristic
47#11758464C2211yescharacteristic
48#11758461—21no—
49(C22⋊D31)⋊C4—21no—
50C31×#103C2211yescharacteristic
51C31×#102C2211yescharacteristic
52C31×C22⋊C8C2211yescharacteristic
53#11758420C2211yescharacteristic
54#11758409C2211yescharacteristic
55(C2×D31)⋊C8C2211yescharacteristic
56#11758404C2211yescharacteristic
57Dic31⋊C8C2211yescharacteristic
58C8×Dic31C2211yescharacteristic
59#11758397C2211yescharacteristic
60#11758395C2211yescharacteristic
61#41×C31—22no—
62#41×C31—41no—
63C2×Q8×C31C2311yescharacteristic
64C2×D4×C31—21no—
65C2×D4×C31—21no—
66C2×D4×C31C2311yescharacteristic
67C2×D4×C31C2311yescharacteristic
68C22×C4×C31—21no—
69C22×C4×C31C2311yescharacteristic
70C2×C22⋊D31—21no—
71C2×C22⋊D31—21no—
72C2×C22⋊D31—21no—
73C2×C22⋊D31—21no—
74C2×C22⋊D31—21no—
75C2×C22⋊D31—21no—
76C2×C22⋊D31—21no—
77C2×C22⋊D31—21no—
78C2×C22⋊D31D411yescharacteristic
79C22×Dic31—21no—
80#92499—22no—
81#92499—41no—
82#92497—22no—
83#92497—41no—
84#92495—22no—
85#92495—41no—
86C2×D124—21no—
87C2×D124—21no—
88C2×D124C2311yescharacteristic
89C2×D124C2311yescharacteristic
90C2×C4×D31—21no—
91C2×C4×D31—21no—
92C2×C4×D31C2311yescharacteristic
93C2×Dic62C2311yescharacteristic
94SD16×C31—22no—
95D8×C31—41no—
96C2×C8×C31C2311yescharacteristic
97C2×C8×C31C2311yescharacteristic
98C4⋊C4×C31C2311yescharacteristic
99C22⋊C4×C31—21no—
100C22⋊Dic31—21no—
101C22⋊Dic31D411yescharacteristic
102#92482D414yescomplemented
103#92481—22no—
104#92480—22no—
105#92479—22no—
106#92479—22no—
107(C2×D31)⋊C4—21no—
108(C2×D31)⋊C4—21no—
109(C2×D31)⋊C4D411yescharacteristic
110C4⋊Dic31—21no—
111C4⋊Dic31C2311yescharacteristic
112Dic31⋊C4—21no—
113Dic31⋊C4D411yescharacteristic
114C4×Dic31—21no—
115C4×Dic31—21no—
116C4×Dic31C2311yescharacteristic
117C2×C31⋊C8—22no—
118C2×C31⋊C8C2311yescharacteristic
119C2×C31⋊C8C2311yescharacteristic
120D248—41no—
121#92470—22no—
122C8×D31—22no—
123C23×C31—21no—
124C23×C31—21no—
125C23×C31C2×D411yescharacteristic
126C22×D31—21no—
127C22×D31—21no—
128C22×D31C2×D411yescharacteristic
129Q8×C31—21no—
130Q8×C31C2×D412yes—
131D4×C31—21no—
132D4×C31—21no—
133D4×C31—21no—
134D4×C31—21no—
135D4×C31—42no—
136D4×C31—81no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—42no—
142C2×C4×C31C2×D411yescharacteristic
143C2×C4×C31C2411yescharacteristic
144C22⋊D31—22no—
145C22⋊D31—42no—
146C22⋊D31—42no—
147C22⋊D31—42no—
148C22⋊D31—42no—
149C22⋊D31—81no—
150C22⋊D31—81no—
151C22⋊D31—81no—
152C22⋊D31—81no—
153C2×Dic31—21no—
154C2×Dic31—21no—
155C2×Dic31—42no—
156C2×Dic31C2×D411yescharacteristic
157C2×Dic31C2×D411yescharacteristic
158C2×Dic31C2×D411yescharacteristic
159D124—21no—
160D124—21no—
161D124—21no—
162D124—21no—
163D124—42no—
164D124—81no—
165C4×D31—21no—
166C4×D31—21no—
167C4×D31—42no—
168C4×D31—42no—
169Dic62—21no—
170Dic62C2×D412yes—
171C8×C31—21no—
172C8×C31—21no—
173C31⋊C8—21no—
174C31⋊C8C2×D412yes—
175#3287—311nomaximal, Sylow
176C22×C31—21no—
177C22×C31—21no—
178C22×C31—21no—
179C22×C31—41no—
180C22×C31—41no—
181C22×C31—41no—
182C22×C31—41no—
183C22×C31—41no—
184C22×C31—41no—
185C22×C31C22×D411yescharacteristic
186C2×D31—21no—
187C2×D31—21no—
188C2×D31—21no—
189C2×D31—41no—
190C2×D31—41no—
191C2×D31—41no—
192C2×D31—41no—
193C2×D31—41no—
194C2×D31—41no—
195C4×C31—21no—
196C4×C31—22no—
197C4×C31—41no—
198C4×C31C22×D411yescharacteristic
199C4×C31H(5,𝔽2)11yescharacteristic
200Dic31—22no—
201Dic31—21no—
202Dic31—21no—
203Dic31—41no—
204Dic31#13512yescomplemented
205C2×#135—311no—
206C2×#135—311no—
207#550—311no—
208#550—311no—
209#493—311no—
210#466—311no—
211#466—311no—
212#460—311no—
213#460—311no—
214#449—311no—
215#449—311no—
216#449—311no—
217#449D3111yescharacteristic, complemented
218C4×Q16—311no—
219C8×D4—311no—
220C2×C31—41no—
221C2×C31—81no—
222C2×C31—81no—
223C2×C31D4211yescharacteristic
224C2×C31C2×#13511yescharacteristic
225C2×C31#57611yescharacteristic
226D31—41no—
227D31—81no—
228D31—81no—
229C2×#41—311no—
230C2×#41—311no—
231C2×#41—311no—
232C2×#41C2×D3111yescharacteristic
233#135—624no—
234#135—624no—
235C2×Q16—311no—
236C2×SD16—311no—
237C2×SD16—311no—
238C2×SD16—311no—
239C2×SD16C2×D3111yescharacteristic
240C2×D8—311no—
241C2×D8—311no—
242C2×D8—311no—
243C2×D8C2×D3111yescharacteristic
244C22×C8—311no—
245C22×C8—311no—
246#127—311no—
247#127—311no—
248#127—621no—
249#127—621no—
250#121—311no—
251#121—311no—
252#121—311no—
253#121—621no—
254#121—621no—
255#121—621no—
256#121—621no—
257#121C2×D3111yescharacteristic
258C4×Q8—311no—
259C4×Q8—311no—
260C4×D4—311no—
261C4×D4—621no—
262C4×D4—621no—
263#107—311no—
264C4⋊C8—311no—
265#103—311no—
266#103C2×D3111yescharacteristic
267#102—311no—
268#102—311no—
269#102—311no—
270#102C2×D3111yescharacteristic
271C22⋊C8—311no—
272C22⋊C8C2×D3111yescharacteristic
273C4×C8—311no—
274C31#328711yescharacteristic, complemented, Sylow
275#41—22no—
276#41—41no—
277#41—622no—
278#41—622no—
279#41—622no—
280#41—1241no—
281#41—1241no—
282#41—1241no—
283C2×Q8—311no—
284C2×Q8C22×D3111yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—311no—
288C2×D4—311no—
289C2×D4—311no—
290C2×D4—621no—
291C2×D4—621no—
292C2×D4—621no—
293C2×D4—621no—
294C2×D4—621no—
295C2×D4—621no—
296C2×D4—621no—
297C2×D4—621no—
298C2×D4—621no—
299C2×D4—621no—
300C2×D4C22×D3111yescharacteristic
301C2×D4C22×D3111yescharacteristic
302C22×C4—21no—
303C22×C4—311no—
304C22×C4—621no—
305C22×C4—621no—
306C22×C4—621no—
307C22×C4C22×D3111yescharacteristic
308Q16—314no—
309SD16—22no—
310SD16—622no—
311SD16—622no—
312SD16—622no—
313D8—41no—
314D8—622no—
315D8—622no—
316D8—1241no—
317C2×C8—311no—
318C2×C8—311no—
319C2×C8—622no—
320C2×C8—622no—
321C2×C8C22×D3111yescharacteristic
322C2×C8C22×D3111yescharacteristic
323C4⋊C4—311no—
324C4⋊C4—311no—
325C4⋊C4—621no—
326C4⋊C4—621no—
327C4⋊C4C22×D3111yescharacteristic
328C22⋊C4—21no—
329C22⋊C4—311no—
330C22⋊C4—311no—
331C22⋊C4—621no—
332C22⋊C4—621no—
333C22⋊C4—621no—
334C42—311no—
335C42—621no—
336C42—621no—
337C23—21no—
338C23—21no—
339C23—311no—
340C23—621no—
341C23—621no—
342C23D4×D3111yescharacteristic
343Q8—21no—
344Q8—312no—
345Q8—621no—
346Q8D4×D3112yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—42no—
352D4—81no—
353D4—622no—
354D4—621no—
355D4—621no—
356D4—621no—
357D4—621no—
358D4—1242no—
359D4—1242no—
360D4—1242no—
361D4—1242no—
362D4—1242no—
363D4—2481no—
364D4—2481no—
365D4—2481no—
366D4—2481no—
367D4—2481no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—42no—
373C2×C4—311no—
374C2×C4—311no—
375C2×C4—311no—
376C2×C4—621no—
377C2×C4—621no—
378C2×C4—621no—
379C2×C4—621no—
380C2×C4—1242no—
381C2×C4—1242no—
382C2×C4—1242no—
383C2×C4D4×D3111yescharacteristic
384C2×C4C23×D3111yescharacteristic
385C8—21no—
386C8—21no—
387C8—312no—
388C8—621no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—621no—
399C22—621no—
400C22—621no—
401C22—1241no—
402C22—1241no—
403C22—1241no—
404C22—1241no—
405C22—1241no—
406C22—1241no—
407C22C2×D4×D3111yescharacteristic
408C4—21no—
409C4—22no—
410C4—41no—
411C4—312no—
412C4—621no—
413C4—622no—
414C4—621no—
415C4—1241no—
416C4C2×D4×D3111yescharacteristic
417C4#1175856111yescharacteristic
418C2—41no—
419C2—81no—
420C2—81no—
421C2—1241no—
422C2—2481no—
423C2—2481no—
424C2#1452168111yescharacteristic
425C2#135×D3111yescharacteristic
426C2#1452185311yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#449C2
socleC22×C31C22×D4
hypercenter#449D31
hypocenterC31#3287
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#11758493C2semidirect
2. C2×#11758527C2semidirect
3. #14521718C2semidirect
4. #14521717C2semidirect
5. #14521424C2semidirect
6. #14521284C2semidirect
7. #14521283C2semidirect
8. #14521248C2semidirect
9. #14521247C2semidirect
10. #14521197C2semidirect
11. #14521196C2semidirect
12. #14521191C2semidirect
13. #14521141C2semidirect
14. (C22⋊D31)⋊C8C2semidirect
15. C31×#449C2semidirect
102. #92482D4semidirect
204. Dic31#135semidirect
217. #449D31semidirect
274. C31#3287semidirect

Maximal subgroups

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

subgroupindex
C2×#117584932
C2×#117585272
#145217182
#145217172
#145214242
#145212842
#145212832
#145212482
#145212472
#145211972
#145211962
#145211912
#145211412
(C22⋊D31)⋊C82
C31×#4492
#328731