Finite Group Databasebeta

← #11895875

Subgroups — #11895875

Order 1152.

811 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593903C211yesmaximal, characteristic, complemented
2#10593865C211yesmaximal, characteristic, complemented
3C4×#3745C211yesmaximal, characteristic
4C3×#4681C211yesmaximal, characteristic, complemented
5C3×#4679C211yesmaximal, characteristic, complemented
6#10590893C212yesmaximal, complemented
7#10590804C212yesmaximal, complemented
8#10590795C212yesmaximal, complemented
9#10590770C212yesmaximal
10#10590379C211yesmaximal, characteristic, complemented
11#10590313C211yesmaximal, characteristic, complemented
12#81622—31nomaximal
13#79970—31nomaximal
14C2×#3797—21no—
15C2×#3745C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21#63918C2212yes—
22#63895—22no—
23#63894C2212yes—
24#63871—21no—
25#63871—21no—
26#63864C2212yes—
27#63849—21no—
28#63848—22no—
29Dic3×Dic6C2212yes—
30C2×#3717C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63648C2211yescharacteristic
33#63648C2211yescharacteristic
34#63645C2211yescharacteristic
35C3×#816C2212yes—
36C3×#816C2212yes—
37C3×#815C2212yes—
38C3×Dic3⋊C8C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63575C2212yes—
41#63566C2212yes—
42#63564C2212yes—
43#5732—31no—
44#5727—31no—
45#5584—31no—
46Q8×D12—31no—
47C3×#487—31no—
48C3×#446—31no—
49#5087—31no—
50#5083—31no—
51#4850—32no—
52#4846—31no—
53#4844—32no—
54#4841—31no—
55#4819—32no—
56#4817—32no—
57#4794—32no—
58#4793—32no—
59#4714—32no—
60#4710—32no—
61C4×D24—31no—
62C4×D24—31no—
63C4×D24—61no—
64#4681D311yescharacteristic, complemented
65#4679D311yescharacteristic, complemented
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C4×C3⋊D3—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6D411yescharacteristic
72C2×C3×Dic6C2312yes—
73C2×#627—22no—
74C2×#624—22no—
75#3797—44no—
76C2×C32×C8C2311yescharacteristic
77C2×C32×C8C2311yescharacteristic
78C32×C42C2311yescharacteristic
79#3752—21no—
80#3752—21no—
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83#3745—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2312yes—
89C3×Dic3⋊C4D412yes—
90C3×C4×Dic3C2312yes—
91C2×C3×C3⋊C8C2312yes—
92Dic3⋊Dic3—22no—
93Dic3⋊Dic3—22no—
94#3722—22no—
95#3722—22no—
96#3722—22no—
97Dic32—22no—
98#3717—24no—
99#3367—91noSylow
100C2×D3×Q8—61no—
101C2×D3×Q8—61no—
102C3×C4⋊Q8—31no—
103C3×C4⋊Q8—31no—
104C3×C4×Q8—31no—
105#947—32no—
106#946—61no—
107#946—61no—
108Q8×Dic3—32no—
109C2×#215—32no—
110C2×D24—31no—
111C2×D24—31no—
112C2×D24—61no—
113C2×#204—32no—
114#898—62no—
115#898—62no—
116#897—62no—
117#897—61no—
118#897—61no—
119#896—62no—
120#893—32no—
121#892—61no—
122#892—61no—
123#888—32no—
124#875—32no—
125C4×D12—31no—
126C4×D12—31no—
127C4×D12—31no—
128C4×D12—31no—
129C4×D12—32no—
130C4×D12—61no—
131C4×D12—61no—
132#869—32no—
133#869C2×D311yescharacteristic
134#869C2×D311yescharacteristic
135C4×Dic6—32no—
136C4×Dic6C2×D311yescharacteristic
137C3×C4⋊C8—32no—
138C3×C4⋊C8—31no—
139C3×#103—32no—
140C3×#103—32no—
141C3×#97—32no—
142C3×C4×C8—21no—
143C3×C4×C8C2×D311yescharacteristic
144C3×C4×C8C2×D311yescharacteristic
145#835—32no—
146#821—31no—
147#821—31no—
148#821—31no—
149#821—31no—
150#821—32no—
151#821—61no—
152#821—61no—
153#818—31no—
154#818—31no—
155#818—32no—
156#818—61no—
157#816—32no—
158#816C2×D312yes—
159#816C2×D312yes—
160#815C2×D312yes—
161Dic3⋊C8C2×D312yes—
162#809—32no—
163#807—32no—
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C22×C3⋊D3—21no—
166C22×C3⋊D3—21no—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172C4⋊(C3⋊D3)—21no—
173C4⋊(C3⋊D3)—21no—
174C4⋊(C3⋊D3)—21no—
175C4⋊(C3⋊D3)#4112yes—
176C4×C3⋊D3—42no—
177C4×C3⋊D3—42no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3C2×D412yes—
181C2×C3×Dic3C2×D412yes—
182C3×Dic6—22no—
183C3×Dic6—22no—
184C3×Dic6—22no—
185C3×Dic6—42no—
186#627—44no—
187#624—44no—
188C32×C8—21no—
189C32×C8—21no—
190C3×C3⋊C8—22no—
191#556—91no—
192D4×Q8—91no—
193#489—92no—
194#487—31no—
195#477—92no—
196#474—91no—
197#463—92no—
198#461—91no—
199#446—31no—
200#440—92no—
201C4×D8—91no—
202C2×C3×Q8—31no—
203C2×C3×Q8—32no—
204C2×C3×Q8—61no—
205D3×Q8—124no—
206D3×Q8—124no—
207C2×D12—31no—
208C2×D12—31no—
209C2×D12—31no—
210C2×D12—31no—
211C2×D12—61no—
212C2×D12—61no—
213C2×C4×D3—62no—
214C2×C4×D3—61no—
215C2×C4×D3—61no—
216C2×C4×D3—61no—
217C2×C4×D3—61no—
218C2×C4×D3—62no—
219C2×C4×D3—121no—
220C2×C4×D3—121no—
221C2×Dic6—21no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C2×Dic6D1211yescharacteristic
225C2×Dic6C22×D312yes—
226C2×C3×C8—21no—
227C2×C3×C8—21no—
228C2×C3×C8—32no—
229C2×C3×C8C22×D311yescharacteristic
230C2×C3×C8C22×D311yescharacteristic
231C2×C3×C8C22×D311yescharacteristic
232C2×C3×C8C22×D311yescharacteristic
233C3×C4⋊C4—31no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—61no—
237C3×C4⋊C4—61no—
238C3×C4⋊C4—61no—
239C3×C42—21no—
240C3×C42—32no—
241C3×C42C22×D311yescharacteristic
242C3×C42C22×D311yescharacteristic
243#215—64no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—61no—
248(C2×D3)⋊C4—61no—
249(C2×D3)⋊C4—61no—
250(C2×D3)⋊C4—61no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—121no—
255(C2×D3)⋊C4—121no—
256C4⋊Dic3—21no—
257C4⋊Dic3—21no—
258C4⋊Dic3—21no—
259C4⋊Dic3—31no—
260C4⋊Dic3—31no—
261C4⋊Dic3—31no—
262C4⋊Dic3—31no—
263C4⋊Dic3—61no—
264C4⋊Dic3—61no—
265C4⋊Dic3—62no—
266C4⋊Dic3—62no—
267C4⋊Dic3D1211yescharacteristic
268C4⋊Dic3C22×D312yes—
269Dic3⋊C4—62no—
270Dic3⋊C4—62no—
271Dic3⋊C4D1212yes—
272C4×Dic3—62no—
273C4×Dic3—62no—
274C4×Dic3C22×D312yes—
275C2×C3⋊C8C22×D312yes—
276D24—62no—
277D24—62no—
278D24—64no—
279#204—64no—
280C22×C32C22×D411yescharacteristic
281C2×C3⋊D3—22no—
282C2×C3⋊D3—41no—
283C2×C3⋊D3—41no—
284C2×C3⋊D3—41no—
285C2×C3⋊D3—41no—
286C2×C3⋊D3—41no—
287C32×C4—21no—
288C32×C4AGL(1,ℤ/8)12yes—
289C32×C4C2×#4111yescharacteristic
290C32×C42−1+411yescharacteristic
291C3⋊Dic3—41no—
292C3⋊Dic3—41no—
293C3×Dic3—22no—
294C3×Dic3—22no—
295C3×Dic3—42no—
296C3×Dic3—42no—
297C22×Q8—181no—
298C2×SD16—92no—
299C2×D8—91no—
300C4⋊Q8—31no—
301C4⋊Q8—31no—
302C4⋊Q8—92no—
303#126—182no—
304#124—92no—
305C22⋊Q8—182no—
306C22⋊Q8—181no—
307C22⋊Q8—181no—
308C4×Q8—31no—
309C4×Q8—92no—
310C4×D4—92no—
311C4×D4—91no—
312C4×D4—91no—
313#117—181no—
314#107—92no—
315#107—91no—
316C4⋊C8—32no—
317C4⋊C8—31no—
318#103—32no—
319#103—32no—
320#103—92no—
321#102—92no—
322#102—91no—
323#102—91no—
324#97—32no—
325C4×C8D3211yescharacteristic
326C22×D3—61no—
327C22×D3—61no—
328C22×D3—61no—
329C22×D3—61no—
330C22×D3—121no—
331C22×D3—121no—
332C3×Q8—62no—
333C3×Q8—62no—
334C3×Q8—62no—
335C3×Q8—122no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—32no—
340C2×C3×C4—32no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4C2×D1211yescharacteristic
344C2×C3×C4C2×D1211yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349C2×Dic3—22no—
350C2×Dic3—22no—
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—32no—
360D12—32no—
361D12—62no—
362D12—62no—
363D12—61no—
364D12—61no—
365D12—61no—
366D12—61no—
367D12—61no—
368D12—61no—
369D12—121no—
370D12—121no—
371C4×D3—124no—
372C4×D3—124no—
373C4×D3—122no—
374C4×D3—122no—
375C4×D3—122no—
376C4×D3—122no—
377C4×D3—242no—
378C4×D3—242no—
379Dic6—22no—
380Dic6—22no—
381Dic6—22no—
382Dic6—42no—
383Dic6—124no—
384Dic6—124no—
385C3×C8—22no—
386C3×C8—21no—
387C3×C8—21no—
388C3×C8—21no—
389C3×C8—21no—
390C3×C8—41no—
391C3×C8—62no—
392C3⋊C8—22no—
393C2×C32#54811yescharacteristic
394C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
395C2×C32#57811yescharacteristic
396C3⋊D3—42no—
397C3⋊D3—81no—
398C2×Q8—31no—
399C2×Q8—32no—
400C2×Q8—61no—
401C2×Q8—182no—
402C2×Q8—364no—
403C2×D4—91no—
404C2×D4—91no—
405C22×C4—182no—
406C22×C4—181no—
407C22×C4—181no—
408SD16—184no—
409D8—182no—
410C2×C8—32no—
411C2×C8C2×D3211yescharacteristic
412C2×C8C2×D3211yescharacteristic
413C4⋊C4—31no—
414C4⋊C4—32no—
415C4⋊C4—32no—
416C4⋊C4—61no—
417C4⋊C4—61no—
418C4⋊C4—61no—
419C4⋊C4—91no—
420C4⋊C4—91no—
421C4⋊C4—182no—
422C4⋊C4—182no—
423C22⋊C4—182no—
424C22⋊C4—182no—
425C22⋊C4—182no—
426C22⋊C4—181no—
427C22⋊C4—181no—
428C42—32no—
429C42—182no—
430C42C2×D3211yescharacteristic
431C22×C3—21no—
432C22×C3C22×D1211yescharacteristic
433C22×C3C2×D3×D411yescharacteristic
434C2×D3—62no—
435C2×D3—62no—
436C2×D3—122no—
437C2×D3—121no—
438C2×D3—121no—
439C2×D3—121no—
440C2×D3—121no—
441C2×D3—122no—
442C2×D3—121no—
443C2×D3—121no—
444C2×D3—121no—
445C2×D3—121no—
446C2×D3—121no—
447C2×D3—121no—
448C2×D3—241no—
449C2×D3—241no—
450C2×D3—241no—
451C2×D3—241no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—22no—
456C3×C4—21no—
457C3×C4—41no—
458C3×C4—62no—
459C3×C4—62no—
460C3×C4—122no—
461C3×C4—122no—
462C3×C4#90812yes—
463C3×C4#91412yes—
464C3×C4#100711yescharacteristic
465C3×C4D3×#4111yescharacteristic
466C3×C4D3×#4111yescharacteristic
467C3×C4#101011yescharacteristic
468Dic3—22no—
469Dic3—22no—
470Dic3—42no—
471Dic3—42no—
472Dic3—121no—
473Dic3—121no—
474Dic3—121no—
475Dic3—121no—
476Dic3—241no—
477Dic3—241no—
478C32#336711yescharacteristic, complemented, Sylow
479C23—181no—
480C23—181no—
481Q8—62no—
482Q8—62no—
483Q8—62no—
484Q8—122no—
485Q8—364no—
486D4—92no—
487D4—181no—
488D4—181no—
489D4—181no—
490C2×C4—32no—
491C2×C4—32no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—364no—
497C2×C4—362no—
498C2×C4—362no—
499C2×C4D3×D1211yescharacteristic
500C2×C4D3×D1211yescharacteristic
501C2×C4C22×D3211yescharacteristic
502C8—21no—
503C8—21no—
504C8—62no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3#557611yescharacteristic
509C2×C3#567711yescharacteristic
510C2×C3C2×#90811yescharacteristic
511C2×C3#575311yescharacteristic
512C2×C3C2×#91411yescharacteristic
513C2×C3#576611yescharacteristic
514D3—122no—
515D3—122no—
516D3—242no—
517D3—242no—
518D3—241no—
519D3—241no—
520C22—182no—
521C22—361no—
522C22—361no—
523C22—361no—
524C22—361no—
525C22—361no—
526C22C2×D3×D1211yescharacteristic
527C4—21no—
528C4—62no—
529C4—62no—
530C4—122no—
531C4—122no—
532C4—361no—
533C4—361no—
534C4#6379412yes—
535C4#6429711yescharacteristic
536C4#6430611yescharacteristic
537C3—21no—
538C3#7997011yescharacteristic, complemented
539C3#8162211yescharacteristic, complemented
540C2—362no—
541C2—721no—
542C2#1059390111yescharacteristic
543C2C2×#6379411yescharacteristic
544C2#1059469111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×#3745C22
hypercenterC4×C8D32
hypocenterC32#3367
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
1. #10593903C2semidirect
2. #10593865C2semidirect
4. C3×#4681C2semidirect
5. C3×#4679C2semidirect
6. #10590893C2semidirect
7. #10590804C2semidirect
8. #10590795C2semidirect
10. #10590379C2semidirect
11. #10590313C2semidirect
64. #4681D3semidirect
65. #4679D3semidirect
478. C32#3367semidirect
538. C3#79970semidirect
539. C3#81622semidirect

Maximal subgroups

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

subgroupindex
#105939032
#105938652
C4×#37452
C3×#46812
C3×#46792
#105908932
#105908042
#105907952
#105907702
#105903792
#105903132
#816223
#799703