Finite Group Databasebeta

← #11878808

Subgroups — #11878808

Order 1152.

1031 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#10596196C211yesmaximal, characteristic, complemented
2#10593907C211yesmaximal, characteristic, complemented
3C3×#5085C211yesmaximal, characteristic, complemented
4C3×#5079C211yesmaximal, characteristic, complemented
5#10591593C214yesmaximal, complemented
6#10591570C214yesmaximal, complemented
7#10590350C211yesmaximal, characteristic, complemented
8#10590297C211yesmaximal, characteristic, complemented
9#10590281C211yesmaximal, characteristic, complemented
10#81765—31nomaximal
11#81603—31nomaximal
12C2×#3832C2212yes—
13C2×#3796—21no—
14C32×C4⋊Q8C2211yescharacteristic
15#64156C2212yes—
16#64104—21no—
17#64104—21no—
18#64102—21no—
19#64102—21no—
20#64083C2211yescharacteristic
21C42×C3⋊D3C2211yescharacteristic
22C2×C3×#215C2214yes—
23C3×#874C2211yescharacteristic
24C3×#869C2211yescharacteristic
25#63916—21no—
26#63916C2212yes—
27#63898—21no—
28#63898C2212yes—
29#63863—21no—
30C2×#3714C2214yes—
31C3×#835C2214yes—
32C3×C4×C3⋊C8C2211yescharacteristic
33C3×C4×C3⋊C8C2211yescharacteristic
34#63572C2212yes—
35#63564C2214yes—
36#63557C2212yes—
37#5725—31no—
38#5725—31no—
39#5725—31no—
40#5725—61no—
41#5716—31no—
42C3×#492—31no—
43C3×#487—31no—
44#5172—34no—
45#5165—34no—
46#5088—31no—
47#5085D311yescharacteristic, complemented
48#5079D311yescharacteristic, complemented
49#5073—31no—
50#4819—34no—
51#4810—34no—
52#4695—31no—
53#4694—31no—
54#4685—31no—
55#4685—31no—
56C2×C32×Q8C2312yes—
57#3832—44no—
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)C2312yes—
62C2×C4×C3⋊D3—22no—
63C2×C4×C3⋊D3D411yescharacteristic
64C2×C4×C3⋊D3D411yescharacteristic
65C2×C4×C3⋊D3C2311yescharacteristic
66C2×C3×D12—21no—
67C2×C3×D12—21no—
68C2×C3×D12C2312yes—
69C2×C3×Dic6—21no—
70C2×#626—22no—
71C2×D3×Dic3—22no—
72#3796—44no—
73C32×C4⋊C4—21no—
74C32×C4⋊C4—21no—
75C32×C42C2311yescharacteristic
76#3752—22no—
77#3752—22no—
78C4×C3⋊Dic3D411yescharacteristic
79C4×C3⋊Dic3D411yescharacteristic
80C4×C3⋊Dic3C2311yescharacteristic
81C3×#215—44no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3C2312yes—
84C2×C3×C3⋊C8C2312yes—
85C2×C3×C3⋊C8C2312yes—
86(C2×D3)⋊Dic3—22no—
87(C2×D3)⋊Dic3—22no—
88#3714—44no—
89#3207—91noSylow
90C2×#239—32no—
91C2×#239—32no—
92C2×#239—62no—
93C2×#239—61no—
94C2×#237—61no—
95C2×C3×SD16—34no—
96C3×C4⋊Q8—21no—
97C3×C4⋊Q8—31no—
98C3×C4⋊Q8C2×D311yescharacteristic
99C3×C4⋊Q8C2×D311yescharacteristic
100C3×#127—31no—
101#947—32no—
102#947—32no—
103#947—62no—
104#947—61no—
105C2×#215C2×D314yes—
106#938—32no—
107#938—61no—
108#936—61no—
109D4×Dic3—32no—
110D4×Dic3—61no—
111C2×#213—34no—
112C2×D24—34no—
113#895—32no—
114#895—61no—
115#895—61no—
116#895—61no—
117#895—61no—
118#895—62no—
119#895—62no—
120#895—61no—
121#893—32no—
122#893—61no—
123#893—61no—
124#893—61no—
125#893—61no—
126#893—61no—
127#893—62no—
128#893—62no—
129#874—31no—
130#874—31no—
131#874—61no—
132#874C2×D311yescharacteristic
133C42×D3—31no—
134C42×D3—31no—
135C42×D3—61no—
136#869C2×D311yescharacteristic
137C3×#103—34no—
138C3×C4×C8—31no—
139C3×C4×C8—31no—
140#835C2×D314yes—
141#821—34no—
142(C2×D3)⋊C8—32no—
143(C2×D3)⋊C8—32no—
144Dic3⋊C8—32no—
145Dic3⋊C8—32no—
146#809—34no—
147C4×C3⋊C8C2×D311yescharacteristic
148C4×C3⋊C8C2×D311yescharacteristic
149C22×C3⋊D3—22no—
150C22×C3⋊D3C2×D411yescharacteristic
151C22×C3×D3—22no—
152C32×Q8—24no—
153C2×C32×C4—22no—
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2411yescharacteristic
157C2×C3⋊Dic3C2×D411yescharacteristic
158C2×C3⋊Dic3C2×D411yescharacteristic
159C2×C3⋊Dic3C2×D411yescharacteristic
160C4⋊(C3⋊D3)—24no—
161C4⋊(C3⋊D3)—44no—
162C4⋊(C3⋊D3)—42no—
163C4⋊(C3⋊D3)—42no—
164C4×C3⋊D3—22no—
165C4×C3⋊D3—22no—
166C4×C3⋊D3—22no—
167C4×C3⋊D3—44no—
168C2×C3×Dic3—22no—
169C3×D12—24no—
170C3×D12—42no—
171C3×D12—42no—
172C3×Dic6—42no—
173#626—44no—
174D3×Dic3—44no—
175C3×C3⋊C8—22no—
176C3×C3⋊C8—22no—
177#532—91no—
178#532—91no—
179#493—91no—
180#492—31no—
181#487—31no—
182#486—91no—
183#463—94no—
184#449—94no—
185#431—91no—
186C2×C3×Q8—22no—
187C2×C3×Q8—61no—
188C2×C3×Q8C22×D312yes—
189C2×C3×Q8C22×D312yes—
190C2×C3×D4—32no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C2×#67—62no—
194C22×Dic3—62no—
195#239—124no—
196#239—124no—
197#239—124no—
198#239—128no—
199#237—124no—
200C2×D12—21no—
201C2×D12—21no—
202C2×D12—32no—
203C2×D12—32no—
204C2×D12—62no—
205C2×D12—62no—
206C2×D12—62no—
207C2×D12—62no—
208C2×D12—62no—
209C2×D12—64no—
210C2×D12—62no—
211C2×D12—61no—
212C2×D12—61no—
213C2×D12—61no—
214C2×D12—61no—
215C2×D12C22×D312yes—
216C2×C4×D3—31no—
217C2×C4×D3—31no—
218C2×C4×D3—31no—
219C2×C4×D3—31no—
220C2×C4×D3—31no—
221C2×C4×D3—31no—
222C2×C4×D3—61no—
223C2×C4×D3—61no—
224C2×C4×D3—61no—
225C2×C4×D3—62no—
226C2×C4×D3—62no—
227C2×C4×D3—62no—
228C2×C4×D3—64no—
229C2×Dic6—21no—
230C3×SD16—124no—
231C2×C3×C8—32no—
232C2×C3×C8—32no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—22no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—32no—
240C3×C4⋊C4—61no—
241C3×C42—21no—
242C3×C42C22×D311yescharacteristic
243C3×C42C22×D311yescharacteristic
244#217—62no—
245#217—62no—
246#215—44no—
247#213—124no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4—62no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—64no—
255(C2×D3)⋊C4—64no—
256C4⋊Dic3—21no—
257C4⋊Dic3C22×D312yes—
258C4×Dic3—31no—
259C4×Dic3—31no—
260C4×Dic3—31no—
261C4×Dic3—31no—
262C4×Dic3—31no—
263C4×Dic3—31no—
264C4×Dic3—61no—
265C4×Dic3—61no—
266C4×Dic3—61no—
267C2×C3⋊C8C22×D312yes—
268C2×C3⋊C8C22×D312yes—
269D24—124no—
270C22×C32C22×D411yescharacteristic
271C2×C3⋊D3—21no—
272C2×C3⋊D3—21no—
273C2×C3⋊D3—21no—
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—42no—
281C32×C4#13512yes—
282C32×C4AGL(1,ℤ/8)12yes—
283C32×C4H(5,𝔽2)12yes—
284C3⋊Dic3—21no—
285C3⋊Dic3—21no—
286C3⋊Dic3—21no—
287C3×Dic3—42no—
288C2×#41—92no—
289C2×#41—181no—
290C2×SD16—34no—
291C2×D8—94no—
292C4⋊Q8—31no—
293C4⋊Q8D3211yescharacteristic
294#127—31no—
295#127—91no—
296#124—92no—
297#124—181no—
298#121—92no—
299#121—181no—
300#121—181no—
301#121—181no—
302C4×D4—92no—
303C4×D4—181no—
304C4×D4—181no—
305C4×D4—181no—
306C2×C42—91no—
307C4⋊C8—92no—
308#103—34no—
309#102—94no—
310C22⋊C8—92no—
311C4×C8—31no—
312C4×C8—31no—
313C23×C3—62no—
314C22×D3—22no—
315C22×D3—31no—
316C22×D3—31no—
317C22×D3—61no—
318C22×D3—64no—
319C22×D3—62no—
320C22×D3—62no—
321C3×Q8—24no—
322C3×Q8—24no—
323C3×Q8—44no—
324C3×Q8—122no—
325C3×D4—64no—
326C3×D4—122no—
327C3×D4—122no—
328C2×C3×C4—24no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—62no—
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4C23×D311yescharacteristic
340C2×C3×C4C23×D311yescharacteristic
341#67—124no—
342C2×Dic3—22no—
343C2×Dic3—31no—
344C2×Dic3—31no—
345C2×Dic3—31no—
346C2×Dic3—31no—
347C2×Dic3—31no—
348C2×Dic3—31no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—124no—
353D12—24no—
354D12—42no—
355D12—42no—
356D12—64no—
357D12—64no—
358D12—124no—
359D12—124no—
360D12—124no—
361D12—128no—
362D12—124no—
363D12—124no—
364D12—124no—
365D12—122no—
366D12—122no—
367D12—122no—
368D12—122no—
369C4×D3—64no—
370C4×D3—62no—
371C4×D3—62no—
372C4×D3—62no—
373C4×D3—62no—
374C4×D3—62no—
375C4×D3—62no—
376C4×D3—122no—
377C4×D3—122no—
378C4×D3—128no—
379C4×D3—124no—
380C4×D3—124no—
381C4×D3—124no—
382Dic6—42no—
383C3×C8—62no—
384C3×C8—62no—
385C3⋊C8—22no—
386C3⋊C8—22no—
387C2×C32#53511yescharacteristic
388C2×C32C2×#13511yescharacteristic
389C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
390C3⋊D3—41no—
391C3⋊D3—82no—
392C3×D3—82no—
393#41—364no—
394#41—364no—
395C2×Q8—61no—
396C2×Q8C2×D3212yes—
397C2×D4—32no—
398C2×D4—61no—
399C2×D4—61no—
400C2×D4—92no—
401C2×D4—182no—
402C2×D4—182no—
403C2×D4—181no—
404C2×D4—181no—
405C22×C4—91no—
406C22×C4—91no—
407C22×C4—91no—
408C22×C4—182no—
409C22×C4—182no—
410SD16—124no—
411D8—364no—
412C2×C8—32no—
413C2×C8—32no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—32no—
417C4⋊C4—61no—
418C22⋊C4—182no—
419C22⋊C4—182no—
420C22⋊C4—182no—
421C22⋊C4—182no—
422C42—91no—
423C42—91no—
424C42—91no—
425C42C2×D3211yescharacteristic
426C22×C3—21no—
427C22×C3—122no—
428C22×C3—122no—
429C22×C3—122no—
430C22×C3C2×D3×D411yescharacteristic
431C22×C3C2×D3×D411yescharacteristic
432C2×D3—42no—
433C2×D3—42no—
434C2×D3—42no—
435C2×D3—62no—
436C2×D3—61no—
437C2×D3—61no—
438C2×D3—61no—
439C2×D3—61no—
440C2×D3—61no—
441C2×D3—61no—
442C2×D3—121no—
443C2×D3—121no—
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—22no—
455C3×C4—22no—
456C3×C4—44no—
457C3×C4—42no—
458C3×C4—42no—
459C3×C4—122no—
460C3×C4#91412yes—
461C3×C4#91412yes—
462C3×C4#91612yes—
463C3×C4#91912yes—
464C3×C4#100412yes—
465C3×C4#100912yes—
466Dic3—42no—
467Dic3—62no—
468Dic3—61no—
469Dic3—61no—
470Dic3—61no—
471Dic3—61no—
472Dic3—61no—
473Dic3—61no—
474Dic3—121no—
475Dic3—121no—
476C32#320711yescharacteristic, complemented, Sylow
477C23—62no—
478C23—91no—
479C23—182no—
480Q8—24no—
481Q8—122no—
482D4—64no—
483D4—122no—
484D4—122no—
485D4—184no—
486D4—364no—
487D4—364no—
488D4—362no—
489D4—362no—
490C2×C4—22no—
491C2×C4—62no—
492C2×C4—91no—
493C2×C4—91no—
494C2×C4—91no—
495C2×C4—182no—
496C2×C4—182no—
497C2×C4—182no—
498C2×C4—364no—
499C2×C4—364no—
500C2×C4#381111yescharacteristic
501C2×C4#381111yescharacteristic
502C2×C4C22×D3211yescharacteristic
503C8—62no—
504C8—62no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—242no—
509C2×C3#567411yescharacteristic
510C2×C3#571511yescharacteristic
511C2×C3C2×#91411yescharacteristic
512C2×C3C2×#91411yescharacteristic
513C2×C3C2×#91611yescharacteristic
514C2×C3C2×#91911yescharacteristic
515D3—82no—
516D3—122no—
517D3—121no—
518D3—121no—
519D3—244no—
520D3—242no—
521D3—242no—
522C22—122no—
523C22—122no—
524C22—122no—
525C22—181no—
526C22—181no—
527C22—181no—
528C22—362no—
529C22—362no—
530C22—362no—
531C22C2×#381111yescharacteristic
532C4—42no—
533C4—122no—
534C4—181no—
535C4—181no—
536C4—181no—
537C4#6394112yes—
538C4#6395012yes—
539C4#6431412yes—
540C3—21no—
541C3#8160311yescharacteristic, complemented
542C3#8176511yescharacteristic, complemented
543C2—242no—
544C2—361no—
545C2—722no—
546C2#1059516811yescharacteristic
547C2C2×#6394111yescharacteristic
548C2C2×#6395011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
hypercenterC4⋊Q8D32
hypocenterC32#3207
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596196C2semidirect
2. #10593907C2semidirect
3. C3×#5085C2semidirect
4. C3×#5079C2semidirect
5. #10591593C2semidirect
6. #10591570C2semidirect
7. #10590350C2semidirect
8. #10590297C2semidirect
9. #10590281C2semidirect
47. #5085D3semidirect
48. #5079D3semidirect
476. C32#3207semidirect
541. C3#81603semidirect
542. C3#81765semidirect

Maximal subgroups

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

subgroupindex
#105961962
#105939072
C3×#50852
C3×#50792
#105915932
#105915702
#105903502
#105902972
#105902812
#817653
#816033