Finite Group Databasebeta

← #11895865

Subgroups — #11895865

Order 1152.

850 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596055C211yesmaximal, characteristic, complemented
2C3×Q8×D12C211yesmaximal, characteristic, complemented
3C3×#5024C211yesmaximal, characteristic, complemented
4#10590366C212yesmaximal
5#10590365C211yesmaximal, characteristic, complemented
6#10590360C212yesmaximal, complemented
7C4×#3714C211yesmaximal, characteristic
8#10590313C211yesmaximal, characteristic, complemented
9#10590294C212yesmaximal, complemented
10#10590288C211yesmaximal, characteristic, complemented
11#10590284C212yesmaximal, complemented
12#83563—31nomaximal
13#79970—31nomaximal
14C2×C3×D3×Q8—21no—
15C32×C4×Q8C2211yescharacteristic
16#64155—21no—
17#64107—22no—
18#64101—21no—
19#64084C2212yes—
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21#64078C2211yescharacteristic
22C4×#634C2212yes—
23C3×#897—21no—
24C3×#897—22no—
25C3×C4×D12C2211yescharacteristic
26C3×C4×D12C2212yes—
27C3×#869C2212yes—
28C3×#869C2211yescharacteristic
29C2×#3716C2212yes—
30C2×#3714C2211yescharacteristic
31C3×C4⋊(C3⋊C8)C2212yes—
32C3×C4⋊(C3⋊C8)C2211yescharacteristic
33C3×#803C2212yes—
34C3×C4×C3⋊C8C2211yescharacteristic
35#63575C2211yescharacteristic
36#63575C2212yes—
37#63567C2212yes—
38#63567C2212yes—
39#63567C2212yes—
40#63564C2211yescharacteristic
41#63564C2212yes—
42#63563C2211yescharacteristic
43C3×D4×Q8—31no—
44#5584—31no—
45#5584—31no—
46#5584—61no—
47Q8×D12D311yescharacteristic, complemented
48C3×#446—31no—
49#5093—31no—
50#5091—32no—
51#5089—32no—
52#5087—31no—
53#5024D311yescharacteristic, complemented
54#5019—31no—
55#5018—32no—
56#5016—32no—
57C4×#213—31no—
58#4850—32no—
59#4846—31no—
60#4844—32no—
61#4841—31no—
62#4714—32no—
63#4710—32no—
64C4×D24—31no—
65#4681—31no—
66C2×C32×Q8D411yescharacteristic
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×#634C2312yes—
70C3×D3×Q8—44no—
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3—21no—
74C2×C3×Dic6—22no—
75C2×C3×Dic6—21no—
76C32×C4⋊C4D411yescharacteristic
77C32×C4⋊C4D412yes—
78C32×C42C2312yes—
79C32×C42C2311yescharacteristic
80#3752—21no—
81#3752—22no—
82#3752—22no—
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86#3750—22no—
87C4×C3⋊Dic3—22no—
88C3×(C2×D3)⋊C4—22no—
89C3×(C2×D3)⋊C4—21no—
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4⋊Dic3C2312yes—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97#3716—24no—
98#3714—22no—
99#3367—91noSylow
100C22×C3×Q8—61no—
101C2×D3×Q8—21no—
102C3×C4⋊Q8—31no—
103C3×C4⋊Q8—32no—
104C3×C22⋊Q8—61no—
105C3×C22⋊Q8—62no—
106C3×C4×Q8—21no—
107C3×C4×Q8C2×D311yescharacteristic
108C3×C4×Q8C2×D311yescharacteristic
109C3×C4×D4—31no—
110C3×C4×D4—32no—
111#946—62no—
112#946—61no—
113#946—61no—
114C2×#214—32no—
115C2×#213—31no—
116C2×D24—31no—
117C2×#204—32no—
118#898—64no—
119#898—62no—
120#898—62no—
121#897—21no—
122#897—22no—
123#892—62no—
124#892—61no—
125#892—61no—
126#875—32no—
127#875—32no—
128#875—62no—
129C4×D12—31no—
130C4×D12—31no—
131C4×D12—61no—
132C4×D12C2×D311yescharacteristic
133C4×D12C2×D312yes—
134#869—31no—
135#869—31no—
136#869—61no—
137#869C2×D311yescharacteristic
138#869C2×D312yes—
139C4×Dic6—32no—
140C4×Dic6—32no—
141C4×Dic6—62no—
142C3×C4⋊C8—31no—
143C3×C4⋊C8—32no—
144C3×#97—32no—
145C3×C4×C8—31no—
146#832—31no—
147#821—31no—
148#821—31no—
149#821—32no—
150#818—31no—
151#818—32no—
152#816—32no—
153#816—32no—
154#816—32no—
155#810—32no—
156#810—32no—
157#810—32no—
158#809—31no—
159#809—32no—
160#807—31no—
161#807—32no—
162C4⋊(C3⋊C8)C2×D312yes—
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164#803C2×D312yes—
165C4×C3⋊C8C2×D311yescharacteristic
166C22×C3⋊D3—21no—
167C22×C3×D3—21no—
168C32×Q8—22no—
169C2×C32×C4C2×D412yes—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D412yes—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—22no—
176C4⋊(C3⋊D3)—21no—
177C4⋊(C3⋊D3)—21no—
178C4×C3⋊D3—42no—
179#634—22no—
180#634—22no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—22no—
183C3×D12—21no—
184C3×D12#4112yes—
185C3×C4×D3—44no—
186C3×C4×D3—42no—
187C3×Dic6—44no—
188C3×Dic6—42no—
189C3×C3⋊C8—21no—
190C3×C3⋊C8—22no—
191C3×C3⋊C8—21no—
192#556—91no—
193D4×Q8—31no—
194#489—92no—
195#487—91no—
196#477—92no—
197#474—91no—
198#463—92no—
199#461—91no—
200#446—31no—
201#440—92no—
202C4×D8—91no—
203C2×C3×Q8—21no—
204C2×C3×Q8—62no—
205C2×C3×Q8—61no—
206C2×C3×Q8—124no—
207C2×C3×Q8D1211yescharacteristic
208C2×C3×Q8#6711yescharacteristic
209C2×C3×D4—31no—
210C22×C3×C4—62no—
211C22×C3×C4—61no—
212D3×Q8—44no—
213C2×D12—31no—
214C2×D12—31no—
215C2×D12—61no—
216C2×D12C22×D311yescharacteristic
217C2×C4×D3—22no—
218C2×C4×D3—21no—
219C2×C4×D3—62no—
220C2×C4×D3—61no—
221C2×C4×D3—61no—
222C2×Dic6—22no—
223C2×Dic6—21no—
224C2×Dic6—32no—
225C2×Dic6—32no—
226C2×Dic6—62no—
227C2×C3×C8—31no—
228C2×C3×C8—31no—
229C2×C3×C8—32no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—22no—
232C3×C4⋊C4—31no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—62no—
235C3×C4⋊C4—61no—
236C3×C4⋊C4D1211yescharacteristic
237C3×C4⋊C4D1212yes—
238C3×C4⋊C4#6711yescharacteristic
239C3×C4⋊C4#6712yes—
240C3×C22⋊C4—62no—
241C3×C22⋊C4—61no—
242C3×C42—22no—
243C3×C42—21no—
244C3×C42C22×D311yescharacteristic
245C3×C42C22×D312yes—
246C3×C42C22×D311yescharacteristic
247C3×C42C22×D312yes—
248#214—64no—
249#213—62no—
250(C2×D3)⋊C4—22no—
251(C2×D3)⋊C4—21no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—64no—
255(C2×D3)⋊C4—61no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—62no—
258(C2×D3)⋊C4—61no—
259(C2×D3)⋊C4—62no—
260(C2×D3)⋊C4—62no—
261C4⋊Dic3—22no—
262C4⋊Dic3—21no—
263C4⋊Dic3—31no—
264C4⋊Dic3—31no—
265C4⋊Dic3—61no—
266C4⋊Dic3—62no—
267C4⋊Dic3—62no—
268C4⋊Dic3—61no—
269C4⋊Dic3—61no—
270C4⋊Dic3—61no—
271C4⋊Dic3—61no—
272C4⋊Dic3C22×D312yes—
273C4⋊Dic3C22×D311yescharacteristic
274Dic3⋊C4—64no—
275Dic3⋊C4—62no—
276Dic3⋊C4—62no—
277C4×Dic3—64no—
278C4×Dic3—62no—
279C4×Dic3—62no—
280C2×C3⋊C8C22×D311yescharacteristic
281C2×C3⋊C8C22×D311yescharacteristic
282C2×C3⋊C8C22×D312yes—
283D24—62no—
284#204—64no—
285C22×C32C22×D411yescharacteristic
286C2×C3⋊D3—41no—
287C2×C3⋊D3—41no—
288C2×C3⋊D3—41no—
289C2×C3×D3—22no—
290C2×C3×D3—41no—
291C2×C3×D3—41no—
292C32×C4—22no—
293C32×C4—22no—
294C32×C4—21no—
295C32×C4AGL(1,ℤ/8)12yes—
296C32×C4C2×#4111yescharacteristic
297C32×C42−1+411yescharacteristic
298C3⋊Dic3—42no—
299C3⋊Dic3—41no—
300C3×Dic3—41no—
301C3×Dic3—42no—
302C22×Q8—61no—
303C2×SD16—92no—
304C2×D8—91no—
305C4⋊Q8—31no—
306C4⋊Q8—32no—
307C4⋊Q8—91no—
308#126—182no—
309#124—92no—
310C22⋊Q8—61no—
311C22⋊Q8—62no—
312C22⋊Q8—181no—
313C4×Q8—92no—
314C4×Q8D3211yescharacteristic
315C4×D4—31no—
316C4×D4—32no—
317C4×D4—91no—
318#117—181no—
319#107—91no—
320#107—92no—
321C4⋊C8—31no—
322C4⋊C8—32no—
323#103—92no—
324#103—92no—
325#103—92no—
326#102—91no—
327#102—92no—
328#102—91no—
329#97—32no—
330C4×C8—31no—
331C23×C3—61no—
332C22×D3—21no—
333C22×D3—62no—
334C22×D3—61no—
335C22×D3—61no—
336C3×Q8—22no—
337C3×Q8—22no—
338C3×Q8—42no—
339C3×Q8—124no—
340C3×Q8—122no—
341C3×D4—32no—
342C3×D4—61no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—21no—
348C2×C3×C4—62no—
349C2×C3×C4—61no—
350C2×C3×C4—124no—
351C2×C3×C4—122no—
352C2×C3×C4C2×D1212yes—
353C2×C3×C4C2×D1212yes—
354C2×C3×C4C2×D1211yescharacteristic
355C2×C3×C4C2×D1211yescharacteristic
356C2×C3×C4C2×#6712yes—
357C2×C3×C4C2×#6712yes—
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361C2×C3×C4C23×D311yescharacteristic
362C2×Dic3—21no—
363C2×Dic3—22no—
364C2×Dic3—62no—
365C2×Dic3—64no—
366C2×Dic3—61no—
367C2×Dic3—62no—
368C2×Dic3—61no—
369C2×Dic3—62no—
370D12—21no—
371D12—61no—
372D12—61no—
373D12—61no—
374D12—61no—
375D12—121no—
376D12—121no—
377D12#23912yes—
378C4×D3—44no—
379C4×D3—42no—
380C4×D3—124no—
381C4×D3—122no—
382C4×D3—122no—
383Dic6—44no—
384Dic6—42no—
385Dic6—62no—
386Dic6—62no—
387Dic6—62no—
388Dic6—62no—
389Dic6—122no—
390Dic6—122no—
391C3×C8—62no—
392C3×C8—61no—
393C3×C8—61no—
394C3⋊C8—21no—
395C3⋊C8—21no—
396C3⋊C8—22no—
397C2×C32#54811yescharacteristic
398C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
399C2×C32#57811yescharacteristic
400C3⋊D3—81no—
401C3×D3—42no—
402C2×Q8—62no—
403C2×Q8—61no—
404C2×Q8—92no—
405C2×Q8—124no—
406C2×Q8#62611yescharacteristic
407C2×D4—31no—
408C2×D4—91no—
409C22×C4—62no—
410C22×C4—61no—
411C22×C4—181no—
412SD16—184no—
413D8—182no—
414C2×C8—31no—
415C2×C8—31no—
416C2×C8—32no—
417C4⋊C4—31no—
418C4⋊C4—32no—
419C4⋊C4—62no—
420C4⋊C4—61no—
421C4⋊C4—91no—
422C4⋊C4—181no—
423C4⋊C4—182no—
424C4⋊C4—181no—
425C4⋊C4#62611yescharacteristic
426C4⋊C4#62612yes—
427C22⋊C4—62no—
428C22⋊C4—61no—
429C22⋊C4—182no—
430C22⋊C4—181no—
431C22⋊C4—182no—
432C42—182no—
433C42C2×D3211yescharacteristic
434C42C2×D3212yes—
435C22×C3—21no—
436C22×C3—62no—
437C22×C3—121no—
438C22×C3—121no—
439C22×C3C22×D1211yescharacteristic
440C22×C3C22×#6711yescharacteristic
441C2×D3—22no—
442C2×D3—41no—
443C2×D3—41no—
444C2×D3—122no—
445C2×D3—122no—
446C2×D3—122no—
447C2×D3—121no—
448C2×D3—121no—
449C2×D3—121no—
450C2×D3—121no—
451C2×D3—121no—
452C2×D3—121no—
453C3×C4—22no—
454C3×C4—22no—
455C3×C4—21no—
456C3×C4—22no—
457C3×C4—22no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—22no—
462C3×C4—42no—
463C3×C4—42no—
464C3×C4—41no—
465C3×C4—122no—
466C3×C4—121no—
467C3×C4#90812yes—
468C3×C4#93212yes—
469C3×C4C2×#23911yescharacteristic
470C3×C4#100711yescharacteristic
471C3×C4#100711yescharacteristic
472C3×C4D3×#4111yescharacteristic
473Dic3—41no—
474Dic3—42no—
475Dic3—124no—
476Dic3—122no—
477Dic3—121no—
478Dic3—121no—
479Dic3—122no—
480Dic3—122no—
481C32#336711yescharacteristic, complemented, Sylow
482C23—61no—
483C23—181no—
484Q8—22no—
485Q8—124no—
486Q8—122no—
487Q8—182no—
488Q8—182no—
489D4—32no—
490D4—61no—
491D4—181no—
492D4—181no—
493C2×C4—62no—
494C2×C4—61no—
495C2×C4—124no—
496C2×C4—122no—
497C2×C4—181no—
498C2×C4—182no—
499C2×C4—362no—
500C2×C4C2×#62612yes—
501C2×C4C2×#62611yescharacteristic
502C2×C4C2×#62612yes—
503C2×C4C2×#62611yescharacteristic
504C2×C4C22×D3211yescharacteristic
505C8—61no—
506C8—61no—
507C8—62no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—122no—
512C2×C3#557611yescharacteristic
513C2×C3C2×#90811yescharacteristic
514C2×C3#575311yescharacteristic
515C2×C3C2×#93211yescharacteristic
516C2×C3#581711yescharacteristic
517C2×C3#583811yescharacteristic
518D3—42no—
519D3—242no—
520D3—241no—
521D3—241no—
522C22—62no—
523C22—121no—
524C22—121no—
525C22—361no—
526C22—361no—
527C22—361no—
528C22C22×#62611yescharacteristic
529C4—22no—
530C4—21no—
531C4—22no—
532C4—122no—
533C4—121no—
534C4—362no—
535C4—361no—
536C4#6383012yes—
537C4#6431611yescharacteristic
538C4D3×#23911yescharacteristic
539C3—21no—
540C3#7997011yescharacteristic, complemented
541C3#8356311yescharacteristic, complemented
542C2—122no—
543C2—721no—
544C2C2×#6383011yescharacteristic
545C2#1059534211yescharacteristic
546C2#1059545011yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
hypercenterC4×Q8D32
hypocenterC32#3367
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596055C2semidirect
2. C3×Q8×D12C2semidirect
3. C3×#5024C2semidirect
5. #10590365C2semidirect
6. #10590360C2semidirect
8. #10590313C2semidirect
9. #10590294C2semidirect
10. #10590288C2semidirect
11. #10590284C2semidirect
47. Q8×D12D3semidirect
53. #5024D3semidirect
481. C32#3367semidirect
540. C3#79970semidirect
541. C3#83563semidirect

Maximal subgroups

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

subgroupindex
#105960552
C3×Q8×D122
C3×#50242
#105903662
#105903652
#105903602
C4×#37142
#105903132
#105902942
#105902882
#105902842
#835633
#799703