Finite Group Databasebeta

← #11873491

Subgroups — #11873491

Order 1152.

849 conjugacy classes of subgroups.

The subgroup lattice has 479 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593897C211yesmaximal, characteristic
2#10593859C211yesmaximal, characteristic, complemented
3#10592380C211yesmaximal, characteristic, complemented
4C3×#4694C211yesmaximal, characteristic, complemented
5C3×C4×D3×C8C211yesmaximal, characteristic, complemented
6#10590954C214yesmaximal, complemented
7#10590863C214yesmaximal, complemented
8#10590288C211yesmaximal, characteristic, complemented
9#10590273C211yesmaximal, characteristic, complemented
10#81562—31nomaximal
11#78463—31nomaximal
12C2×#3795C2212yes—
13#64078C2211yescharacteristic
14#64078C2211yescharacteristic
15C2×C3×D3×C8C2212yes—
16C3×#874C2211yescharacteristic
17C3×C42×D3C2211yescharacteristic
18C3×#869C2211yescharacteristic
19#63908—21no—
20#63908—21no—
21Dic3×D12—21no—
22Dic3×D12—21no—
23#63869C2212yes—
24#63860C2212yes—
25#63857—21no—
26#63856—21no—
27#63844—21no—
28Dic3×Dic6—21no—
29#63841C2212yes—
30C32×C4×C8C2211yescharacteristic
31#63643C2214yes—
32C3×#821C2214yes—
33C3×C8×Dic3C2212yes—
34C3×C4×C3⋊C8C2211yescharacteristic
35#63567C2214yes—
36#63563C2214yes—
37#5728—31no—
38#5716—31no—
39#5477—31no—
40#5470—31no—
41C3×#486—31no—
42C2×C3×C4×C8—31no—
43#5113—34no—
44#5093—31no—
45#5070—31no—
46#4772—34no—
47#4768—34no—
48#4697—34no—
49#4694—31no—
50#4694D311yescharacteristic, complemented
51C4×D3×C8D311yescharacteristic, complemented
52#4681—31no—
53#4681—31no—
54#4681—31no—
55#4681—61no—
56C2×#634—21no—
57C2×#634C2312yes—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12C2312yes—
61C2×C3×C4×D3D411yescharacteristic
62C2×C3×C4×D3D411yescharacteristic
63C2×C3×C4×D3C2311yescharacteristic
64C2×C3×Dic6—21no—
65C2×#625—22no—
66C2×D3×Dic3—22no—
67#3795—28no—
68C2×C32×C8C2312yes—
69C32×C42C2311yescharacteristic
70C4⋊(C3⋊Dic3)—21no—
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)—21no—
73C4⋊(C3⋊Dic3)C2312yes—
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(C2×D3)⋊Dic3—22no—
84(C2×D3)⋊Dic3—22no—
85(C2×D3)⋊Dic3—22no—
86Dic32—22no—
87#3131—91noSylow
88C2×#237—32no—
89C2×#235—32no—
90C22×C3×C8—32no—
91C3×C4⋊Q8—31no—
92C3×#127—31no—
93C2×C3×C42—31no—
94#946—61no—
95Q8×Dic3—61no—
96#938—61no—
97#938—61no—
98#936—32no—
99D4×Dic3—61no—
100D4×Dic3—61no—
101#930—61no—
102#930—61no—
103#926—32no—
104#924—61no—
105#924—61no—
106C2×D3×C8C2×D312yes—
107#897—61no—
108#892—32no—
109#890—32no—
110#887—61no—
111#875—32no—
112#874C2×D311yescharacteristic
113C4×D12—61no—
114C4×D12—61no—
115C42×D3C2×D311yescharacteristic
116#870—32no—
117#869—31no—
118#869—31no—
119#869—31no—
120#869—31no—
121#869—61no—
122#869—61no—
123#869C2×D311yescharacteristic
124C4×Dic6—61no—
125C4×Dic6—61no—
126C3×#102—34no—
127C3×C4×C8—21no—
128C3×C4×C8—32no—
129C3×C4×C8—31no—
130C3×C4×C8C2×D311yescharacteristic
131C3×C4×C8C2×D311yescharacteristic
132#832—34no—
133#821—34no—
134#821C2×D314yes—
135#816—34no—
136#816—34no—
137#816—34no—
138#816—64no—
139C8×Dic3C2×D312yes—
140#810—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—
148C2×C3⋊Dic3—22no—
149#634—24no—
150#634—42no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3C2×D411yescharacteristic
153C2×C3×Dic3C2×D411yescharacteristic
154C2×C3×Dic3C2×D411yescharacteristic
155C3×D12—24no—
156C3×D12—42no—
157C3×D12—42no—
158C3×C4×D3—22no—
159C3×C4×D3—22no—
160C3×C4×D3#4114yes—
161C3×Dic6—42no—
162#625—44no—
163D3×Dic3—44no—
164C32×C8—22no—
165C3×C3⋊C8—22no—
166#533—91no—
167#532—91no—
168#488—94no—
169#487—91no—
170#487—91no—
171#486—31no—
172#486—91no—
173#416—94no—
174C2×C4×C8—31no—
175C2×C3×Q8—61no—
176C2×C3×D4—32no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C22×C3×C4—31no—
180C22×C3×C4—31no—
181C22×C3×C4—31no—
182C2×#67—62no—
183C2×#67—62no—
184C22×Dic3—62no—
185#237—68no—
186#235—68no—
187C2×D12—21no—
188C2×D12—21no—
189C2×D12C22×D312yes—
190C2×C4×D3—62no—
191C2×C4×D3D1211yescharacteristic
192C2×C4×D3D1211yescharacteristic
193C2×C4×D3C22×D311yescharacteristic
194C2×Dic6—21no—
195C2×Dic6—32no—
196C2×Dic6—32no—
197C2×Dic6—62no—
198C2×Dic6—61no—
199C2×Dic6—61no—
200C2×Dic6—121no—
201C2×C3×C8—22no—
202C2×C3×C8—32no—
203C2×C3×C8—64no—
204C2×C3×C8C22×D312yes—
205C2×C3×C8C22×D312yes—
206C3×C4⋊C4—32no—
207C3×C4⋊C4—61no—
208C3×C42—21no—
209C3×C42—31no—
210C3×C42—31no—
211C3×C42—31no—
212C3×C42C22×D311yescharacteristic
213C3×C42C22×D311yescharacteristic
214#217—62no—
215#217—62no—
216#217—62no—
217(C2×D3)⋊C4—62no—
218(C2×D3)⋊C4—62no—
219(C2×D3)⋊C4—62no—
220C4⋊Dic3—21no—
221C4⋊Dic3—32no—
222C4⋊Dic3—32no—
223C4⋊Dic3—62no—
224C4⋊Dic3—61no—
225C4⋊Dic3—61no—
226C4⋊Dic3—61no—
227C4⋊Dic3—61no—
228C4⋊Dic3—61no—
229C4⋊Dic3—61no—
230C4⋊Dic3—62no—
231C4⋊Dic3—121no—
232C4⋊Dic3—121no—
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—21no—
247C2×C3×D3—21no—
248C2×C3×D3—42no—
249C2×C3×D3—42no—
250C2×C3×D3—42no—
251C2×C3×D3#12412yes—
252C32×C4#13512yes—
253C32×C4#13512yes—
254C32×C4C2×#4112yes—
255C3⋊Dic3—42no—
256C3⋊Dic3—42no—
257C3×Dic3—21no—
258C3×Dic3—21no—
259C3×Dic3—42no—
260C3×Dic3#12412yes—
261C2×#41—92no—
262C22×C8—32no—
263C4⋊Q8—31no—
264C4⋊Q8—91no—
265C4⋊Q8—91no—
266#127—31no—
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—94no—
280#103—94no—
281#102—34no—
282#102—94no—
283C4×C8—32no—
284C4×C8—31no—
285C4×C8D3211yescharacteristic
286C23×C3—31no—
287C23×C3—62no—
288C22×D3—22no—
289C22×D3C2×D1211yescharacteristic
290C3×Q8—122no—
291C3×D4—64no—
292C3×D4—122no—
293C3×D4—122no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—31no—
298C2×C3×C4—34no—
299C2×C3×C4—31no—
300C2×C3×C4—31no—
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—
311#67—124no—
312C2×Dic3—22no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—122no—
318C2×Dic3—122no—
319C2×Dic3—124no—
320C2×Dic3C2×D1211yescharacteristic
321C2×Dic3C2×D1211yescharacteristic
322C2×Dic3C2×D1211yescharacteristic
323D12—24no—
324D12—42no—
325D12—42no—
326C4×D3—22no—
327C4×D3—22no—
328C4×D3—124no—
329C4×D3#23514yes—
330Dic6—42no—
331Dic6—64no—
332Dic6—64no—
333Dic6—124no—
334Dic6—122no—
335Dic6—122no—
336Dic6—242no—
337C3×C8—22no—
338C3×C8—22no—
339C3×C8—42no—
340C3×C8—62no—
341C3⋊C8—22no—
342C2×C32C2×#12411yescharacteristic
343C2×C32C2×#13511yescharacteristic
344C2×C32C2×#13511yescharacteristic
345C3×D3—22no—
346C3×D3—82no—
347#41—188no—
348C2×Q8—61no—
349C2×Q8—92no—
350C2×Q8—181no—
351C2×D4—32no—
352C2×D4—61no—
353C2×D4—61no—
354C2×D4—182no—
355C22×C4—31no—
356C22×C4—31no—
357C22×C4—31no—
358C22×C4—182no—
359C2×C8—32no—
360C2×C8—64no—
361C2×C8C2×D3212yes—
362C4⋊C4—32no—
363C4⋊C4—61no—
364C4⋊C4—92no—
365C4⋊C4—182no—
366C4⋊C4—182no—
367C4⋊C4—181no—
368C4⋊C4—181no—
369C4⋊C4—181no—
370C22⋊C4—182no—
371C22⋊C4—182no—
372C22⋊C4—182no—
373C42—31no—
374C42—31no—
375C42—31no—
376C42—182no—
377C42C2×D3211yescharacteristic
378C22×C3—21no—
379C22×C3—32no—
380C22×C3—61no—
381C22×C3—61no—
382C22×C3—122no—
383C22×C3—122no—
384C22×C3—122no—
385C22×C3C22×D1211yescharacteristic
386C22×C3C2×D3×D411yescharacteristic
387C2×D3—21no—
388C2×D3—21no—
389C2×D3—42no—
390C2×D3—42no—
391C2×D3—42no—
392C2×D3#87512yes—
393C3×C4—22no—
394C3×C4—22no—
395C3×C4—22no—
396C3×C4—32no—
397C3×C4—61no—
398C3×C4—61no—
399C3×C4—122no—
400C3×C4#90412yes—
401C3×C4#90412yes—
402C3×C4#91212yes—
403C3×C4#91612yes—
404C3×C4C2×#23512yes—
405C3×C4D3×#4112yes—
406Dic3—21no—
407Dic3—21no—
408Dic3—42no—
409Dic3—122no—
410Dic3—122no—
411Dic3—122no—
412Dic3—122no—
413Dic3—242no—
414Dic3—242no—
415Dic3#87512yes—
416C32#313111yescharacteristic, complemented, Sylow
417C23—31no—
418C23—62no—
419Q8—122no—
420Q8—184no—
421Q8—362no—
422D4—64no—
423D4—122no—
424D4—122no—
425D4—364no—
426C2×C4—31no—
427C2×C4—34no—
428C2×C4—31no—
429C2×C4—31no—
430C2×C4—62no—
431C2×C4—62no—
432C2×C4—62no—
433C2×C4—182no—
434C2×C4—182no—
435C2×C4—364no—
436C2×C4D3×D1211yescharacteristic
437C2×C4D3×D1211yescharacteristic
438C2×C4C22×D3211yescharacteristic
439C8—22no—
440C8—62no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—62no—
445C2×C3—242no—
446C2×C3C2×#87511yescharacteristic
447C2×C3D3×#12411yescharacteristic
448C2×C3C2×#90411yescharacteristic
449C2×C3C2×#90411yescharacteristic
450C2×C3C2×#91211yescharacteristic
451C2×C3C2×#91611yescharacteristic
452D3—22no—
453D3—82no—
454C22—32no—
455C22—61no—
456C22—61no—
457C22—122no—
458C22—122no—
459C22—122no—
460C22C2×D3×D1211yescharacteristic
461C4—32no—
462C4—61no—
463C4—61no—
464C4—122no—
465C4—362no—
466C4—362no—
467C4#6380612yes—
468C4#6380712yes—
469C4D3×#23512yes—
470C3—21no—
471C3#7846311yescharacteristic, complemented
472C3#8156211yescharacteristic, complemented
473C2—62no—
474C2—242no—
475C2D3×#87511yescharacteristic
476C2C2×#6380611yescharacteristic
477C2C2×#6380711yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10593897C2
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. #10592380C2semidirect
4. C3×#4694C2semidirect
5. C3×C4×D3×C8C2semidirect
6. #10590954C2semidirect
7. #10590863C2semidirect
8. #10590288C2semidirect
9. #10590273C2semidirect
50. #4694D3semidirect
51. C4×D3×C8D3semidirect
416. C32#3131semidirect
471. C3#78463semidirect
472. C3#81562semidirect

Maximal subgroups

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

subgroupindex
#105938972
#105938592
#105923802
C3×#46942
C3×C4×D3×C82
#105909542
#105908632
#105902882
#105902732
#815623
#784633