Finite Group Databasebeta

← #11895982

Subgroups — #11895982

Order 1152.

828 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593902C211yesmaximal, characteristic
2#10593864C211yesmaximal, characteristic, complemented
3#10592547C211yesmaximal, characteristic, complemented
4C3×#4846C211yesmaximal, characteristic, complemented
5C3×#4831C211yesmaximal, characteristic, complemented
6#10590882C212yesmaximal, complemented
7#10590879C212yesmaximal, complemented
8#10590774C212yesmaximal, complemented
9#10590773C212yesmaximal, complemented
10C4×#3716C211yesmaximal, characteristic, complemented
11#10590281C211yesmaximal, characteristic, complemented
12#80995—31nomaximal
13#79980—31nomaximal
14C2×#3799—21no—
15C2×#3744C2212yes—
16#64083C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21#63911C2212yes—
22#63910—22no—
23#63909—21no—
24#63894C2212yes—
25#63873—21no—
26#63869C2212yes—
27#63847—22no—
28#63844C2212yes—
29#63843—21no—
30C2×#3716C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32#63648C2212yes—
33C3×#821C2212yes—
34C3×#818C2212yes—
35C3×#815C2212yes—
36C3×Dic3⋊C8C2212yes—
37C3×C4×C3⋊C8C2211yescharacteristic
38#63573C2211yescharacteristic
39#63567C2211yescharacteristic
40#63564C2212yes—
41#63564C2212yes—
42#63563C2211yescharacteristic
43#5721—31no—
44#5577—31no—
45#5567—31no—
46#5553—31no—
47C3×#474—31no—
48C3×#446—31no—
49#5088—31no—
50C4×#214—31no—
51#4891—32no—
52#4889—32no—
53#4848—31no—
54#4848—31no—
55#4848—32no—
56#4848—61no—
57#4847—32no—
58#4846D311yescharacteristic, complemented
59#4831D311yescharacteristic, complemented
60#4764—32no—
61#4762—32no—
62#4713—32no—
63#4710—32no—
64#4694—31no—
65C4×#204—31no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)C2312yes—
69C2×#634C2311yescharacteristic
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6D411yescharacteristic
74C2×#626—22no—
75C2×#626—22no—
76C2×#624—22no—
77#3799—44no—
78C2×C32×C8C2312yes—
79C32×C42C2311yescharacteristic
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3750—21no—
82C4×C3⋊Dic3—21no—
83#3744—24no—
84C3×(C2×D3)⋊C4—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3D411yescharacteristic
87C3×C4⋊Dic3C2312yes—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4D412yes—
90C3×C4×Dic3C2312yes—
91C2×C3×C3⋊C8C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93#3724—22no—
94#3724—22no—
95Dic3⋊Dic3—22no—
96#3722—22no—
97Dic32—22no—
98#3716—22no—
99#3368—91noSylow
100C2×#239—61no—
101C2×#235—61no—
102C3×C4⋊Q8—31no—
103C3×C4×Q8—31no—
104C3×C4×D4—31no—
105Q8×Dic3—61no—
106#944—61no—
107#944—61no—
108#940—32no—
109C2×#214—31no—
110#930—61no—
111C2×#204—31no—
112C2×#204—32no—
113C2×#204—32no—
114C2×#204—62no—
115#895—62no—
116#895—61no—
117#893—32no—
118#890—32no—
119#889—62no—
120#889—62no—
121#887—32no—
122#887—61no—
123#884—62no—
124#874—32no—
125#874—31no—
126#874—31no—
127#874—61no—
128C4×D12—32no—
129C4×D12C2×D311yescharacteristic
130#870—32no—
131#869C2×D311yescharacteristic
132C4×Dic6—31no—
133C4×Dic6—31no—
134C4×Dic6—32no—
135C4×Dic6—61no—
136C4×Dic6C2×D311yescharacteristic
137C3×#107—32no—
138C3×C4⋊C8—21no—
139C3×C4⋊C8—32no—
140C3×C4⋊C8C2×D311yescharacteristic
141C3×C4⋊C8C2×D311yescharacteristic
142C3×#102—32no—
143C3×#97—32no—
144C3×C4×C8—31no—
145#832—31no—
146#821—31no—
147#821—32no—
148#821—32no—
149#821—32no—
150#821—32no—
151#821—62no—
152#821C2×D312yes—
153#818C2×D312yes—
154#817—31no—
155#816—31no—
156#815C2×D312yes—
157Dic3⋊C8C2×D312yes—
158#810—31no—
159#809—32no—
160#809—32no—
161#808—31no—
162C4×C3⋊C8C2×D311yescharacteristic
163C22×C3⋊D3—22no—
164C22×C3×D3—21no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C4⋊(C3⋊D3)—22no—
171C4⋊(C3⋊D3)—22no—
172C4⋊(C3⋊D3)—42no—
173C4⋊(C3⋊D3)—81no—
174#634—21no—
175#634#4112yescomplemented
176C2×C3×Dic3—22no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×D12—21no—
181C3×D12—21no—
182C3×C4×D3—42no—
183C3×Dic6—22no—
184C3×Dic6—42no—
185#626—44no—
186#626—82no—
187#624—44no—
188C32×C8—22no—
189C3×C3⋊C8—21no—
190C3×C3⋊C8—21no—
191#557—91no—
192#550—91no—
193#490—92no—
194#486—91no—
195#478—92no—
196#474—31no—
197#460—92no—
198#460—91no—
199#446—31no—
200#440—92no—
201C4×SD16—91no—
202C2×C3×Q8—31no—
203C2×C3×Q8—61no—
204C2×C3×D4—31no—
205C22×C3×C4—61no—
206C2×#67—62no—
207C2×#67—62no—
208#239—124no—
209#235—124no—
210C2×D12—32no—
211C2×D12—32no—
212C2×D12—62no—
213C2×D12—62no—
214C2×D12—61no—
215C2×D12—61no—
216C2×D12—62no—
217C2×D12—61no—
218C2×D12—61no—
219C2×D12—121no—
220C2×D12—121no—
221C2×D12C22×D311yescharacteristic
222C2×C4×D3—21no—
223C2×C4×D3—62no—
224C2×C4×D3—62no—
225C2×Dic6—21no—
226C2×Dic6—31no—
227C2×Dic6—31no—
228C2×Dic6—61no—
229C2×Dic6D1211yescharacteristic
230C2×C3×C8—22no—
231C2×C3×C8—31no—
232C2×C3×C8—31no—
233C2×C3×C8C22×D312yes—
234C2×C3×C8C22×D312yes—
235C3×C4⋊C4—31no—
236C3×C4⋊C4—32no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—61no—
240C3×C22⋊C4—61no—
241C3×C42—21no—
242C3×C42—32no—
243C3×C42C22×D311yescharacteristic
244C3×C42C22×D311yescharacteristic
245#214—62no—
246(C2×D3)⋊C4—21no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—62no—
249C4⋊Dic3—21no—
250C4⋊Dic3—31no—
251C4⋊Dic3—31no—
252C4⋊Dic3—61no—
253C4⋊Dic3—62no—
254C4⋊Dic3D1211yescharacteristic
255C4⋊Dic3C22×D311yescharacteristic
256C4⋊Dic3C22×D312yes—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4—61no—
261Dic3⋊C4—61no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—121no—
265Dic3⋊C4D1212yes—
266C4×Dic3—62no—
267C4×Dic3—61no—
268C4×Dic3—61no—
269C4×Dic3—62no—
270C4×Dic3—121no—
271C4×Dic3C22×D312yes—
272C2×C3⋊C8C22×D311yescharacteristic
273C2×C3⋊C8C22×D311yescharacteristic
274#204—64no—
275#204—64no—
276#204—62no—
277#204—124no—
278C22×C32C22×D411yescharacteristic
279C2×C3⋊D3—42no—
280C2×C3⋊D3—42no—
281C2×C3⋊D3—42no—
282C2×C3×D3—41no—
283C2×C3×D3—41no—
284C2×C3×D3—41no—
285C32×C4—21no—
286C32×C4AGL(1,ℤ/8)12yes—
287C32×C4C2×#4111yescharacteristic
288C32×C42−1+411yescharacteristic
289C3⋊Dic3—22no—
290C3⋊Dic3—41no—
291C3×Dic3—22no—
292C3×Dic3—22no—
293C3×Dic3—41no—
294C3×Dic3—42no—
295C2×#41—181no—
296C2×SD16—91no—
297C2×SD16—92no—
298C4⋊Q8—31no—
299C4⋊Q8—181no—
300#127—92no—
301#127—91no—
302#125—92no—
303#125—182no—
304#121—182no—
305#121—181no—
306C4×Q8—31no—
307C4×Q8—92no—
308C4×Q8—91no—
309C4×Q8—181no—
310C4×D4—31no—
311C4×D4—92no—
312#107—32no—
313#106—91no—
314C4⋊C8—32no—
315C4⋊C8D3211yescharacteristic
316#103—91no—
317#102—32no—
318#102—92no—
319#102—92no—
320#102—91no—
321#102—92no—
322#97—32no—
323C4×C8—31no—
324C23×C3—61no—
325C22×D3—21no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—122no—
329C3×Q8—62no—
330C3×Q8—122no—
331C3×D4—61no—
332C3×D4—61no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—32no—
337C2×C3×C4—32no—
338C2×C3×C4—62no—
339C2×C3×C4—61no—
340C2×C3×C4—122no—
341C2×C3×C4C2×D1211yescharacteristic
342C2×C3×C4C2×D1211yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4C23×D311yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347#67—124no—
348#67—242no—
349C2×Dic3—22no—
350C2×Dic3—21no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3C2×D1212yes—
358C2×Dic3C2×D1212yes—
359D12—21no—
360D12—21no—
361D12—62no—
362D12—62no—
363D12—62no—
364D12—62no—
365D12—122no—
366D12—122no—
367D12—124no—
368D12—122no—
369D12—122no—
370D12—242no—
371D12—241no—
372D12—241no—
373D12—242no—
374D12—242no—
375C4×D3—42no—
376C4×D3—124no—
377C4×D3—124no—
378Dic6—22no—
379Dic6—32no—
380Dic6—32no—
381Dic6—42no—
382Dic6—62no—
383Dic6—61no—
384Dic6—61no—
385Dic6—121no—
386C3×C8—22no—
387C3×C8—22no—
388C3×C8—42no—
389C3×C8—61no—
390C3×C8—61no—
391C3⋊C8—21no—
392C3⋊C8—21no—
393C2×C32#54811yescharacteristic
394C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
395C2×C32#57711yescharacteristic
396C3⋊D3—82no—
397C3×D3—81no—
398#41—364no—
399C2×Q8—31no—
400C2×Q8—61no—
401C2×Q8—91no—
402C2×D4—31no—
403C2×D4—92no—
404C2×D4—182no—
405C2×D4—182no—
406C2×D4—181no—
407C2×D4—181no—
408C22×C4—61no—
409C22×C4—182no—
410SD16—184no—
411SD16—182no—
412C2×C8—31no—
413C2×C8—31no—
414C2×C8C2×D3212yes—
415C4⋊C4—31no—
416C4⋊C4—32no—
417C4⋊C4—32no—
418C4⋊C4—31no—
419C4⋊C4—61no—
420C4⋊C4—91no—
421C4⋊C4—182no—
422C4⋊C4—182no—
423C4⋊C4—182no—
424C4⋊C4—181no—
425C22⋊C4—61no—
426C22⋊C4—182no—
427C42—32no—
428C42—182no—
429C42—181no—
430C42C2×D3211yescharacteristic
431C22×C3—21no—
432C22×C3—121no—
433C22×C3—121no—
434C22×C3—121no—
435C22×C3C22×D1211yescharacteristic
436C22×C3C2×D3×D411yescharacteristic
437C2×D3—41no—
438C2×D3—41no—
439C2×D3—41no—
440C2×D3—122no—
441C2×D3—122no—
442C2×D3—122no—
443C2×D3—122no—
444C2×D3—122no—
445C2×D3—122no—
446C2×D3—242no—
447C2×D3—242no—
448C2×D3—242no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—22no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—41no—
455C3×C4—62no—
456C3×C4—62no—
457C3×C4—121no—
458C3×C4—122no—
459C3×C4#90812yes—
460C3×C4#91112yes—
461C3×C4#100711yescharacteristic
462C3×C4#100711yescharacteristic
463C3×C4D3×#4111yescharacteristic
464C3×C4D3×#4111yescharacteristic
465Dic3—22no—
466Dic3—22no—
467Dic3—42no—
468Dic3—41no—
469Dic3—62no—
470Dic3—62no—
471Dic3—122no—
472Dic3—121no—
473Dic3—121no—
474Dic3—241no—
475C32#336811yescharacteristic, complemented, Sylow
476C23—61no—
477C23—182no—
478Q8—62no—
479Q8—92no—
480Q8—122no—
481Q8—181no—
482D4—61no—
483D4—61no—
484D4—182no—
485D4—182no—
486D4—364no—
487D4—362no—
488D4—721no—
489D4—722no—
490C2×C4—32no—
491C2×C4—32no—
492C2×C4—62no—
493C2×C4—61no—
494C2×C4—122no—
495C2×C4—181no—
496C2×C4—181no—
497C2×C4—364no—
498C2×C4D3×D1211yescharacteristic
499C2×C4D3×D1211yescharacteristic
500C2×C4C22×D3211yescharacteristic
501C8—22no—
502C8—61no—
503C8—61no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—241no—
508C2×C3#557611yescharacteristic
509C2×C3#563311yescharacteristic
510C2×C3C2×#90811yescharacteristic
511C2×C3#575111yescharacteristic
512C2×C3C2×#91111yescharacteristic
513C2×C3#577811yescharacteristic
514D3—81no—
515D3—242no—
516D3—242no—
517D3—482no—
518C22—121no—
519C22—121no—
520C22—121no—
521C22—362no—
522C22—362no—
523C22—362no—
524C22C2×D3×D1211yescharacteristic
525C4—21no—
526C4—62no—
527C4—62no—
528C4—121no—
529C4—122no—
530C4—182no—
531C4—361no—
532C4#6379512yes—
533C4#6431211yescharacteristic
534C4#6431611yescharacteristic
535C3—21no—
536C3#7998011yescharacteristic, complemented
537C3#8099511yescharacteristic, complemented
538C2—241no—
539C2—722no—
540C2#1059432911yescharacteristic
541C2C2×#6379511yescharacteristic
542C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10593902C2
hypercenterC4⋊C8D32
hypocenterC32#3368
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. #10593864C2semidirect
3. #10592547C2semidirect
4. C3×#4846C2semidirect
5. C3×#4831C2semidirect
6. #10590882C2semidirect
7. #10590879C2semidirect
8. #10590774C2semidirect
9. #10590773C2semidirect
10. C4×#3716C2semidirect
11. #10590281C2semidirect
58. #4846D3semidirect
59. #4831D3semidirect
175. #634#41semidirect
475. C32#3368semidirect
536. C3#79980semidirect
537. C3#80995semidirect

Maximal subgroups

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

subgroupindex
#105939022
#105938642
#105925472
C3×#48462
C3×#48312
#105908822
#105908792
#105907742
#105907732
C4×#37162
#105902812
#809953
#799803