Finite Group Databasebeta

← #11876995

Subgroups — #11876995

Order 1152.

1047 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595948C211yesmaximal, characteristic, complemented
2C3×#5477C211yesmaximal, characteristic, complemented
3C3×C4×#208C211yesmaximal, characteristic, complemented
4#10591165C214yesmaximal, complemented
5#10590350C211yesmaximal, characteristic, complemented
6#10590346C214yesmaximal, complemented
7#10590303C211yesmaximal, characteristic, complemented
8#10590281C211yesmaximal, characteristic, complemented
9#10590273C211yesmaximal, characteristic, complemented
10#83295—31nomaximal
11#78535—31nomaximal
12C2×#3828—21no—
13C2×C3×#235—21no—
14C2×C32×C42C2211yescharacteristic
15#64139—21no—
16#64139C2212yes—
17#64084—21no—
18#64083C2211yescharacteristic
19C4×C4⋊(C3⋊D3)—21no—
20C4×C4⋊(C3⋊D3)C2212yes—
21#64078C2211yescharacteristic
22C3×#930—21no—
23C3×#930C2212yes—
24C2×C3×#208C2212yes—
25C3×#875—21no—
26C3×#874C2211yescharacteristic
27C3×C4×D12—21no—
28C3×C4×D12C2212yes—
29C3×#869C2211yescharacteristic
30C2×#3714C2214yes—
31C3×#803C2212yes—
32C3×C4×C3⋊C8C2211yescharacteristic
33C3×C4×C3⋊C8C2211yescharacteristic
34#63573C2214yes—
35#63564C2214yes—
36#63563C2214yes—
37C3×#532—31no—
38#5477—31no—
39#5477—31no—
40#5477—61no—
41#5477D311yescharacteristic, complemented
42C3×C4×M16—31no—
43#5135—34no—
44#5088—31no—
45#5080—31no—
46#5073—31no—
47#5070—31no—
48#5039—34no—
49#5014—34no—
50C4×#208D311yescharacteristic, complemented
51#4711—34no—
52#4695—31no—
53#4694—31no—
54#4694—31no—
55#4680—31no—
56C22×C32×C4D411yescharacteristic
57C22×C32×C4D411yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C2×#638—22no—
60#3828—44no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)—21no—
63C2×C4⋊(C3⋊D3)C2312yes—
64C2×C4×C3⋊D3—22no—
65C2×#634—21no—
66C2×C3×#67—22no—
67C3×#235—44no—
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12C2312yes—
71C2×C3×C4×D3—22no—
72C2×C3×Dic6—21no—
73C32×C42D411yescharacteristic
74C32×C42D411yescharacteristic
75C32×C42C2311yescharacteristic
76C32×C42C2311yescharacteristic
77#3752—22no—
78#3752—22no—
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)C2312yes—
81C3×(C2×D3)⋊C4—22no—
82C3×(C2×D3)⋊C4—22no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3C2312yes—
85C3×#208—24no—
86C2×C3×C3⋊C8C2312yes—
87C2×C3×C3⋊C8C2312yes—
88#3714—28no—
89#3184—91noSylow
90C2×C3×#41—61no—
91C2×#235—21no—
92C2×#235—62no—
93C2×#235—61no—
94C2×#235—61no—
95C2×C3×M16—32no—
96C3×C4⋊Q8—31no—
97C3×#127—31no—
98C3×#124—61no—
99C3×#121—32no—
100C3×#121—61no—
101C3×C4×D4—32no—
102C3×C4×D4—61no—
103C2×C3×C42—21no—
104C2×C3×C42C2×D311yescharacteristic
105C2×C3×C42C2×D311yescharacteristic
106C2×#213—34no—
107#930—21no—
108#930—32no—
109#930—32no—
110#930—62no—
111#930—62no—
112#930—61no—
113#930—61no—
114#930C2×D312yes—
115C2×#208C2×D312yes—
116C2×D24—34no—
117#875—21no—
118#875—62no—
119#875—61no—
120#875—61no—
121#874—31no—
122#874—31no—
123#874—61no—
124#874C2×D311yescharacteristic
125C4×D12—21no—
126C4×D12—32no—
127C4×D12—32no—
128C4×D12—62no—
129C4×D12—62no—
130C4×D12—61no—
131C4×D12—61no—
132C4×D12C2×D312yes—
133#869—31no—
134#869—31no—
135#869—61no—
136#869C2×D311yescharacteristic
137C3×#97—32no—
138C3×C4×C8—31no—
139C3×C4×C8—31no—
140#832—34no—
141#821—34no—
142#821—34no—
143#817—34no—
144#809—34no—
145#808—34no—
146#803C2×D312yes—
147C4×C3⋊C8C2×D311yescharacteristic
148C4×C3⋊C8C2×D311yescharacteristic
149C23×C32C2×D411yescharacteristic
150C22×C3⋊D3—22no—
151C22×C3×D3—22no—
152C2×C32×C4—22no—
153C2×C32×C4—22no—
154C2×C32×C4—22no—
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2411yescharacteristic
161#638—44no—
162C2×C3⋊Dic3—22no—
163C4⋊(C3⋊D3)—24no—
164C4⋊(C3⋊D3)—42no—
165C4⋊(C3⋊D3)—42no—
166C4×C3⋊D3—44no—
167#634—42no—
168C3×#67—44no—
169C2×C3×Dic3—22no—
170C3×D12—24no—
171C3×D12—42no—
172C3×D12—42no—
173C3×C4×D3—44no—
174C3×Dic6—42no—
175C3×C3⋊C8—22no—
176C3×C3⋊C8#4114yescomplemented
177#532—31no—
178#532—91no—
179#498—91no—
180#493—91no—
181#486—91no—
182#486—91no—
183#469—94no—
184#442—94no—
185C4×M16—31no—
186C3×#41—124no—
187C2×C3×Q8—61no—
188C2×C3×D4—32no—
189C2×C3×D4—62no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—62no—
196C22×C3×C4D1211yescharacteristic
197C22×C3×C4D1211yescharacteristic
198C22×C3×C4#6711yescharacteristic
199C22×C3×C4#6711yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C2×#67—22no—
203C2×#67—64no—
204C2×#67—62no—
205C2×#67—62no—
206#235—44no—
207#235—128no—
208#235—124no—
209#235—124no—
210C2×D12—21no—
211C2×D12—21no—
212C2×D12—32no—
213C2×D12—32no—
214C2×D12—62no—
215C2×D12—62no—
216C2×D12—62no—
217C2×D12—61no—
218C2×D12—61no—
219C2×D12—61no—
220C2×D12—61no—
221C2×D12C22×D312yes—
222C2×C4×D3—22no—
223C2×C4×D3—64no—
224C2×C4×D3—62no—
225C2×C4×D3—62no—
226C2×Dic6—21no—
227C2×Dic6—62no—
228C2×Dic6—61no—
229C2×Dic6—61no—
230C3×M16—64no—
231C2×C3×C8—32no—
232C2×C3×C8—32no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—61no—
235C3×C22⋊C4—62no—
236C3×C22⋊C4—62no—
237C3×C42—21no—
238C3×C42—21no—
239C3×C42—21no—
240C3×C42—21no—
241C3×C42D1211yescharacteristic
242C3×C42D1211yescharacteristic
243C3×C42#6711yescharacteristic
244C3×C42#6711yescharacteristic
245C3×C42C22×D311yescharacteristic
246C3×C42C22×D311yescharacteristic
247C3×C42C22×D311yescharacteristic
248C3×C42C22×D311yescharacteristic
249#213—68no—
250(C2×D3)⋊C4—22no—
251(C2×D3)⋊C4—22no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—62no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—62no—
258C4⋊Dic3—21no—
259C4⋊Dic3—32no—
260C4⋊Dic3—32no—
261C4⋊Dic3—62no—
262C4⋊Dic3—62no—
263C4⋊Dic3—61no—
264C4⋊Dic3—61no—
265C4⋊Dic3C22×D312yes—
266#208—24no—
267C2×C3⋊C8C22×D312yes—
268C2×C3⋊C8C22×D312yes—
269D24—68no—
270C22×C32—21no—
271C22×C32—21no—
272C22×C32—21no—
273C22×C32C22×D411yescharacteristic
274C2×C3⋊D3—42no—
275C2×C3⋊D3—42no—
276C2×C3⋊D3—42no—
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C32×C4—21no—
281C32×C4—21no—
282C32×C4—21no—
283C32×C4AGL(1,ℤ/8)12yes—
284C32×C4AGL(1,ℤ/8)12yes—
285C32×C4C2×#4112yes—
286C3⋊Dic3—42no—
287C3×Dic3—42no—
288C2×#41—61no—
289C2×#41—181no—
290C2×D8—94no—
291C2×M16—32no—
292C4⋊Q8—31no—
293C4⋊Q8—91no—
294#127—31no—
295#127—91no—
296#124—61no—
297#124—181no—
298#121—32no—
299#121—61no—
300#121—92no—
301#121—181no—
302C4×D4—32no—
303C4×D4—61no—
304C4×D4—92no—
305C4×D4—181no—
306C2×C42D3211yescharacteristic
307#106—94no—
308#102—94no—
309#102—94no—
310#97—32no—
311C4×C8—31no—
312C4×C8—31no—
313C23×C3—21no—
314C23×C3—62no—
315C23×C3C2×D1211yescharacteristic
316C23×C3C2×#6711yescharacteristic
317C22×D3—22no—
318C22×D3—64no—
319C22×D3—62no—
320C22×D3—62no—
321C3×Q8—122no—
322C3×D4—64no—
323C3×D4—124no—
324C3×D4—122no—
325C3×D4—122no—
326C2×C3×C4—24no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—42no—
340C2×C3×C4—42no—
341C2×C3×C4—62no—
342C2×C3×C4—124no—
343C2×C3×C4C2×D1211yescharacteristic
344C2×C3×C4C2×D1211yescharacteristic
345C2×C3×C4C2×D1211yescharacteristic
346C2×C3×C4C2×D1211yescharacteristic
347C2×C3×C4C2×D1211yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C2×#6711yescharacteristic
352C2×C3×C4C2×#6711yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355#67—44no—
356#67—128no—
357#67—124no—
358#67—124no—
359C2×Dic3—22no—
360C2×Dic3—64no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363D12—24no—
364D12—42no—
365D12—42no—
366D12—64no—
367D12—64no—
368D12—124no—
369D12—124no—
370D12—124no—
371D12—122no—
372D12—122no—
373D12—122no—
374D12—122no—
375C4×D3—44no—
376C4×D3—128no—
377C4×D3—124no—
378C4×D3—124no—
379Dic6—42no—
380Dic6—124no—
381Dic6—122no—
382Dic6—122no—
383C3×C8—34no—
384C3×C8—62no—
385C3⋊C8—22no—
386C3⋊C8#23514yescomplemented
387C2×C32—41no—
388C2×C32#53211yescharacteristic
389C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
390C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
391C3⋊D3—82no—
392C3×D3—82no—
393#41—124no—
394#41—364no—
395C2×Q8—61no—
396C2×Q8—181no—
397C2×D4—32no—
398C2×D4—62no—
399C2×D4—61no—
400C2×D4—61no—
401C2×D4—92no—
402C2×D4—182no—
403C2×D4—181no—
404C2×D4—181no—
405C22×C4—62no—
406C22×C4—182no—
407C22×C4#62611yescharacteristic
408C22×C4#62611yescharacteristic
409C22×C4C2×D3211yescharacteristic
410D8—188no—
411M16—64no—
412C2×C8—32no—
413C2×C8—32no—
414C4⋊C4—32no—
415C4⋊C4—61no—
416C4⋊C4—92no—
417C4⋊C4—181no—
418C22⋊C4—62no—
419C22⋊C4—62no—
420C22⋊C4—182no—
421C22⋊C4—182no—
422C42#62611yescharacteristic
423C42#62611yescharacteristic
424C42C2×D3211yescharacteristic
425C42C2×D3211yescharacteristic
426C22×C3—22no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—122no—
437C22×C3—122no—
438C22×C3—122no—
439C22×C3C22×D1211yescharacteristic
440C22×C3C22×#6711yescharacteristic
441C2×D3—42no—
442C2×D3—42no—
443C2×D3—42no—
444C2×D3—124no—
445C2×D3—124no—
446C2×D3—124no—
447C2×D3—122no—
448C2×D3—122no—
449C2×D3—122no—
450C2×D3—122no—
451C2×D3—122no—
452C2×D3—122no—
453C3×C4—22no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—22no—
461C3×C4—22no—
462C3×C4—22no—
463C3×C4—41no—
464C3×C4—41no—
465C3×C4—122no—
466C3×C4#90812yes—
467C3×C4#90812yes—
468C3×C4#93212yes—
469C3×C4#94912yes—
470C3×C4C2×#23512yes—
471C3×C4D3×#4112yes—
472Dic3—42no—
473Dic3—124no—
474Dic3—122no—
475Dic3—122no—
476C32#318411yescharacteristic, complemented, Sylow
477C23—62no—
478C23—182no—
479C23C2×#62611yescharacteristic
480Q8—122no—
481Q8—362no—
482D4—64no—
483D4—124no—
484D4—122no—
485D4—122no—
486D4—184no—
487D4—364no—
488D4—362no—
489D4—362no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—62no—
494C2×C4—124no—
495C2×C4—182no—
496C2×C4—364no—
497C2×C4C2×#62611yescharacteristic
498C2×C4C2×#62611yescharacteristic
499C2×C4C2×#62611yescharacteristic
500C2×C4C2×#62611yescharacteristic
501C2×C4C2×#62611yescharacteristic
502C2×C4C22×D3211yescharacteristic
503C8—34no—
504C8—62no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—42no—
509C2×C3—41no—
510C2×C3—41no—
511C2×C3—242no—
512C2×C3#547711yescharacteristic
513C2×C3C2×#90811yescharacteristic
514C2×C3C2×#90811yescharacteristic
515C2×C3C2×#93211yescharacteristic
516C2×C3C2×#94911yescharacteristic
517C2×C3#583211yescharacteristic
518D3—82no—
519D3—244no—
520D3—242no—
521D3—242no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—122no—
526C22—122no—
527C22—122no—
528C22—362no—
529C22—362no—
530C22—362no—
531C22C22×#62611yescharacteristic
532C4—21no—
533C4—21no—
534C4—21no—
535C4—122no—
536C4—362no—
537C4#6382512yes—
538C4#6383012yes—
539C4D3×#23512yes—
540C3—21no—
541C3#7853511yescharacteristic, complemented
542C3#8329511yescharacteristic, complemented
543C2—41no—
544C2—242no—
545C2—722no—
546C2C2×#6382511yescharacteristic
547C2C2×#6383011yescharacteristic
548C2#1059502911yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
hypercenterC2×C42D32
hypocenterC32#3184
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10595948C2semidirect
2. C3×#5477C2semidirect
3. C3×C4×#208C2semidirect
4. #10591165C2semidirect
5. #10590350C2semidirect
6. #10590346C2semidirect
7. #10590303C2semidirect
8. #10590281C2semidirect
9. #10590273C2semidirect
41. #5477D3semidirect
50. C4×#208D3semidirect
176. C3×C3⋊C8#41semidirect
386. C3⋊C8#235semidirect
476. C32#3184semidirect
541. C3#78535semidirect
542. C3#83295semidirect

Maximal subgroups

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

subgroupindex
#105959482
C3×#54772
C3×C4×#2082
#105911652
#105903502
#105903462
#105903032
#105902812
#105902732
#832953
#785353