Finite Group Databasebeta

← #11873489

Subgroups — #11873489

Order 1152.

859 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593970C211yesmaximal, characteristic
2#10593859C211yesmaximal, characteristic, complemented
3#10592393C211yesmaximal, characteristic, complemented
4C3×C4×D3×C8C211yesmaximal, characteristic, complemented
5C3×#4681C211yesmaximal, characteristic, complemented
6#10590872C214yesmaximal, complemented
7#10590690C214yesmaximal, complemented
8#10590287C211yesmaximal, characteristic, complemented
9#10590281C211yesmaximal, characteristic, complemented
10#81598—31nomaximal
11#78463—31nomaximal
12C2×#3799C2212yes—
13#64083C2211yescharacteristic
14#64078C2211yescharacteristic
15C2×C3×D3×C8C2212yes—
16C3×C42×D3C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×#869C2211yescharacteristic
19#63909—21no—
20#63909—21no—
21#63894—21no—
22#63894—21no—
23#63869C2212yes—
24#63864C2212yes—
25#63857—21no—
26#63856—21no—
27#63844—21no—
28Dic3×Dic6—21no—
29#63841C2212yes—
30C32×C4×C8C2211yescharacteristic
31#63648C2214yes—
32C3×#816C2214yes—
33C3×C8×Dic3C2212yes—
34C3×C4×C3⋊C8C2211yescharacteristic
35#63566C2214yes—
36#63564C2214yes—
37#5728—31no—
38#5725—31no—
39#5477—31no—
40#5470—31no—
41C3×#487—31no—
42C2×C3×C4×C8—31no—
43#5113—34no—
44#5088—31no—
45#5079—31no—
46#4804—34no—
47#4800—34no—
48#4697—34no—
49#4694—31no—
50#4694—31no—
51#4694—31no—
52#4694—61no—
53C4×D3×C8D311yescharacteristic, complemented
54#4681—31no—
55#4681D311yescharacteristic, complemented
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)C2312yes—
59C2×#634—21no—
60C2×C3×C4×D3D411yescharacteristic
61C2×C3×C4×D3D411yescharacteristic
62C2×C3×C4×D3C2311yescharacteristic
63C2×C3×Dic6—21no—
64C2×C3×Dic6C2312yes—
65C2×#626—22no—
66C2×#624—22no—
67#3799—28no—
68C2×C32×C8C2312yes—
69C32×C42C2311yescharacteristic
70C4⋊(C3⋊Dic3)—21no—
71C4⋊(C3⋊Dic3)C2312yes—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3C2312yes—
76C3×C4×Dic3D411yescharacteristic
77C3×C4×Dic3D411yescharacteristic
78C3×C4×Dic3C2311yescharacteristic
79C2×C3×C3⋊C8C2312yes—
80C3×D3×C8—24no—
81#3724—22no—
82Dic3⋊Dic3—22no—
83#3722—22no—
84#3722—22no—
85(C2×D3)⋊Dic3—22no—
86Dic32—22no—
87#3131—91noSylow
88C2×#239—32no—
89C2×#235—32no—
90C22×C3×C8—32no—
91C3×C4⋊Q8—31no—
92C3×C4⋊Q8—31no—
93C2×C3×C42—31no—
94#947—32no—
95#946—61no—
96Q8×Dic3—61no—
97#930—61no—
98#930—61no—
99#926—32no—
100#924—61no—
101#924—61no—
102C2×D3×C8C2×D312yes—
103#897—61no—
104#895—61no—
105#895—61no—
106#893—61no—
107#893—61no—
108#892—32no—
109#890—32no—
110#887—61no—
111#875—32no—
112#874—31no—
113#874—31no—
114#874—61no—
115C4×D12—61no—
116C4×D12—61no—
117C42×D3C2×D311yescharacteristic
118#870—32no—
119#869—31no—
120#869—31no—
121#869—61no—
122#869C2×D311yescharacteristic
123#869C2×D311yescharacteristic
124C4×Dic6—61no—
125C4×Dic6—61no—
126C3×#103—34no—
127C3×C4×C8—21no—
128C3×C4×C8—32no—
129C3×C4×C8—31no—
130C3×C4×C8C2×D311yescharacteristic
131C3×C4×C8C2×D311yescharacteristic
132#835—34no—
133#821—34no—
134#821—34no—
135#821—34no—
136#821—64no—
137#816—34no—
138#816C2×D314yes—
139C8×Dic3C2×D312yes—
140#809—34no—
141C4×C3⋊C8C2×D311yescharacteristic
142C22×C3⋊D3—22no—
143C22×C3×D3C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2411yescharacteristic
147C2×C3⋊Dic3—22no—
148C4⋊(C3⋊D3)—24no—
149C4⋊(C3⋊D3)—42no—
150C4⋊(C3⋊D3)—42no—
151#634—42no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3C2×D411yescharacteristic
155C2×C3×Dic3C2×D411yescharacteristic
156C2×C3×Dic3C2×D411yescharacteristic
157C3×C4×D3—22no—
158C3×C4×D3—22no—
159C3×C4×D3#4114yes—
160C3×Dic6—24no—
161C3×Dic6—42no—
162#626—44no—
163#624—44no—
164C32×C8—22no—
165C3×C3⋊C8—22no—
166#533—91no—
167#532—91no—
168#488—94no—
169#487—31no—
170#487—91no—
171#486—91no—
172#486—91no—
173#416—94no—
174C2×C4×C8—31no—
175C2×C3×Q8—32no—
176C2×C3×Q8—61no—
177C22×C3×C4—31no—
178C22×C3×C4—31no—
179C22×C3×C4—31no—
180C2×#67—62no—
181#239—68no—
182#235—68no—
183C2×D12—32no—
184C2×D12—32no—
185C2×D12—62no—
186C2×D12—62no—
187C2×D12—61no—
188C2×D12—61no—
189C2×D12—61no—
190C2×D12—61no—
191C2×D12—121no—
192C2×D12—121no—
193C2×C4×D3—62no—
194C2×C4×D3—62no—
195C2×C4×D3D1211yescharacteristic
196C2×C4×D3D1211yescharacteristic
197C2×C4×D3C22×D311yescharacteristic
198C2×Dic6—21no—
199C2×Dic6—61no—
200C2×Dic6—61no—
201C2×Dic6—121no—
202C2×Dic6C22×D312yes—
203C2×C3×C8—22no—
204C2×C3×C8—32no—
205C2×C3×C8—64no—
206C2×C3×C8C22×D312yes—
207C2×C3×C8C22×D312yes—
208C3×C4⋊C4—32no—
209C3×C4⋊C4—61no—
210C3×C4⋊C4—61no—
211C3×C4⋊C4—61no—
212C3×C42—21no—
213C3×C42—31no—
214C3×C42—31no—
215C3×C42—31no—
216C3×C42C22×D311yescharacteristic
217C3×C42C22×D311yescharacteristic
218#217—62no—
219(C2×D3)⋊C4—62no—
220(C2×D3)⋊C4—62no—
221(C2×D3)⋊C4—62no—
222(C2×D3)⋊C4—62no—
223(C2×D3)⋊C4—62no—
224C4⋊Dic3—21no—
225C4⋊Dic3—21no—
226C4⋊Dic3—21no—
227C4⋊Dic3—32no—
228C4⋊Dic3—32no—
229C4⋊Dic3—62no—
230C4⋊Dic3—61no—
231C4⋊Dic3—61no—
232C4⋊Dic3—62no—
233C4⋊Dic3—121no—
234C4⋊Dic3C22×D312yes—
235Dic3⋊C4—62no—
236Dic3⋊C4—62no—
237Dic3⋊C4—62no—
238C4×Dic3—62no—
239C4×Dic3—62no—
240C4×Dic3D1211yescharacteristic
241C4×Dic3D1211yescharacteristic
242C4×Dic3C22×D311yescharacteristic
243C2×C3⋊C8C22×D312yes—
244D3×C8—24no—
245C22×C32C22×D411yescharacteristic
246C2×C3⋊D3—42no—
247C2×C3⋊D3—42no—
248C2×C3⋊D3—42no—
249C2×C3×D3—21no—
250C2×C3×D3—21no—
251C2×C3×D3#12412yes—
252C32×C4#13512yes—
253C32×C4#13512yes—
254C32×C4C2×#4112yes—
255C3⋊Dic3—42no—
256C3×Dic3—21no—
257C3×Dic3—21no—
258C3×Dic3—42no—
259C3×Dic3—42no—
260C3×Dic3#12412yes—
261C2×#41—92no—
262C22×C8—32no—
263C4⋊Q8—31no—
264C4⋊Q8—31no—
265C4⋊Q8—91no—
266#127—91no—
267#125—92no—
268#124—92no—
269C22⋊Q8—181no—
270C22⋊Q8—181no—
271#121—181no—
272#121—181no—
273C4×Q8—181no—
274C4×Q8—181no—
275C4×D4—181no—
276C4×D4—181no—
277#117—92no—
278C2×C42—31no—
279#103—34no—
280#103—94no—
281#102—94no—
282#102—94no—
283C4×C8—32no—
284C4×C8—31no—
285C4×C8D3211yescharacteristic
286C23×C3—31no—
287C22×D3—62no—
288C22×D3—62no—
289C22×D3—122no—
290C22×D3C2×D1211yescharacteristic
291C3×Q8—64no—
292C3×Q8—122no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—31no—
297C2×C3×C4—34no—
298C2×C3×C4—31no—
299C2×C3×C4—31no—
300C2×C3×C4—62no—
301C2×C3×C4—62no—
302C2×C3×C4—62no—
303C2×C3×C4—62no—
304C2×C3×C4C2×D1211yescharacteristic
305C2×C3×C4C2×D1211yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4C23×D311yescharacteristic
309C2×C3×C4C23×D311yescharacteristic
310#67—124no—
311C2×Dic3—22no—
312C2×Dic3—22no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—122no—
316C2×Dic3C2×D1211yescharacteristic
317C2×Dic3C2×D1211yescharacteristic
318C2×Dic3C2×D1211yescharacteristic
319D12—64no—
320D12—64no—
321D12—124no—
322D12—124no—
323D12—122no—
324D12—122no—
325D12—122no—
326D12—122no—
327D12—242no—
328D12—242no—
329C4×D3—22no—
330C4×D3—22no—
331C4×D3—124no—
332C4×D3—124no—
333C4×D3#23514yes—
334Dic6—24no—
335Dic6—42no—
336Dic6—122no—
337Dic6—122no—
338Dic6—242no—
339C3×C8—22no—
340C3×C8—22no—
341C3×C8—42no—
342C3×C8—62no—
343C3⋊C8—22no—
344C2×C32C2×#12411yescharacteristic
345C2×C32C2×#13511yescharacteristic
346C2×C32C2×#13511yescharacteristic
347C3⋊D3—82no—
348C3×D3—22no—
349#41—188no—
350C2×Q8—32no—
351C2×Q8—61no—
352C2×Q8—181no—
353C2×D4—92no—
354C2×D4—182no—
355C2×D4—181no—
356C2×D4—181no—
357C22×C4—31no—
358C22×C4—31no—
359C22×C4—31no—
360C22×C4—182no—
361C2×C8—32no—
362C2×C8—64no—
363C2×C8C2×D3212yes—
364C4⋊C4—32no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C4⋊C4—92no—
369C4⋊C4—182no—
370C4⋊C4—182no—
371C4⋊C4—181no—
372C22⋊C4—182no—
373C22⋊C4—182no—
374C22⋊C4—182no—
375C42—31no—
376C42—31no—
377C42—31no—
378C42—182no—
379C42C2×D3211yescharacteristic
380C22×C3—21no—
381C22×C3—32no—
382C22×C3—61no—
383C22×C3—61no—
384C22×C3C22×D1211yescharacteristic
385C22×C3C2×D3×D411yescharacteristic
386C2×D3—21no—
387C2×D3—21no—
388C2×D3—122no—
389C2×D3—122no—
390C2×D3—122no—
391C2×D3—122no—
392C2×D3—122no—
393C2×D3—122no—
394C2×D3—242no—
395C2×D3—242no—
396C2×D3—242no—
397C2×D3#87512yes—
398C3×C4—22no—
399C3×C4—22no—
400C3×C4—22no—
401C3×C4—32no—
402C3×C4—61no—
403C3×C4—61no—
404C3×C4—122no—
405C3×C4—122no—
406C3×C4#90412yes—
407C3×C4#90412yes—
408C3×C4#91612yes—
409C3×C4#91912yes—
410C3×C4C2×#23512yes—
411C3×C4D3×#4112yes—
412Dic3—21no—
413Dic3—21no—
414Dic3—42no—
415Dic3—42no—
416Dic3—122no—
417Dic3—122no—
418Dic3—242no—
419Dic3#87512yes—
420C32#313111yescharacteristic, complemented, Sylow
421C23—31no—
422C23—182no—
423Q8—64no—
424Q8—122no—
425Q8—362no—
426D4—184no—
427D4—364no—
428D4—362no—
429D4—362no—
430C2×C4—31no—
431C2×C4—34no—
432C2×C4—31no—
433C2×C4—31no—
434C2×C4—62no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—182no—
439C2×C4—364no—
440C2×C4D3×D1211yescharacteristic
441C2×C4D3×D1211yescharacteristic
442C2×C4C22×D3211yescharacteristic
443C8—22no—
444C8—62no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—62no—
449C2×C3C2×#87511yescharacteristic
450C2×C3D3×#12411yescharacteristic
451C2×C3C2×#90411yescharacteristic
452C2×C3C2×#90411yescharacteristic
453C2×C3C2×#91611yescharacteristic
454C2×C3C2×#91911yescharacteristic
455D3—22no—
456D3—242no—
457D3—242no—
458D3—482no—
459C22—32no—
460C22—61no—
461C22—61no—
462C22—362no—
463C22—362no—
464C22—362no—
465C22C2×D3×D1211yescharacteristic
466C4—32no—
467C4—61no—
468C4—61no—
469C4—122no—
470C4—122no—
471C4—362no—
472C4#6380612yes—
473C4#6380812yes—
474C4D3×#23512yes—
475C3—21no—
476C3#7846311yescharacteristic, complemented
477C3#8159811yescharacteristic, complemented
478C2—62no—
479C2—722no—
480C2D3×#87511yescharacteristic
481C2C2×#6380611yescharacteristic
482C2C2×#6380811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10593970C2
hypercenterC4×C8D32
hypocenterC32#3131
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10593859C2semidirect
3. #10592393C2semidirect
4. C3×C4×D3×C8C2semidirect
5. C3×#4681C2semidirect
6. #10590872C2semidirect
7. #10590690C2semidirect
8. #10590287C2semidirect
9. #10590281C2semidirect
53. C4×D3×C8D3semidirect
55. #4681D3semidirect
420. C32#3131semidirect
476. C3#78463semidirect
477. C3#81598semidirect

Maximal subgroups

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

subgroupindex
#105939702
#105938592
#105923932
C3×C4×D3×C82
C3×#46812
#105908722
#105906902
#105902872
#105902812
#815983
#784633