Finite Group Databasebeta

← #11895349

Subgroups — #11895349

Order 1152.

842 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#10596056C211yesmaximal, characteristic, complemented
2#10593956C211yesmaximal, characteristic, complemented
3C3×C4×#215C211yesmaximal, characteristic, complemented
4C3×#5021C211yesmaximal, characteristic, complemented
5#10591570C212yesmaximal, complemented
6#10591539C212yesmaximal, complemented
7#10590459C212yesmaximal, complemented
8#10590435C212yesmaximal, complemented
9#10590349C211yesmaximal, characteristic
10#10590281C211yesmaximal, characteristic, complemented
11#10590254C211yesmaximal, characteristic, complemented
12#81134—31nomaximal
13#79621—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15#64156C2212yes—
16#64103—22no—
17#64102C2212yes—
18#64084—21no—
19#64083C2211yescharacteristic
20C4×C4⋊(C3⋊D3)—21no—
21C4×#634C2211yescharacteristic
22C2×C3×#215C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×#869C2211yescharacteristic
25#63898C2212yes—
26D3×C4⋊Dic3—21no—
27#63887—22no—
28#63872C2212yes—
29#63857—21no—
30C2×#3714C2212yes—
31C3×#835C2211yescharacteristic
32C3×#835C2212yes—
33C3×#809C2211yescharacteristic
34C3×#808C2211yescharacteristic
35C3×#807C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38#63572C2212yes—
39#63564C2212yes—
40#63564C2212yes—
41#63564C2212yes—
42#63553C2212yes—
43#5730—31no—
44#5585—31no—
45#5585—31no—
46#5585—61no—
47#5543—31no—
48C3×#477—31no—
49C3×C4×SD16—31no—
50#5165—32no—
51#5088—31no—
52C4×#215D311yescharacteristic, complemented
53#5021D311yescharacteristic, complemented
54#5015—31no—
55#4891—32no—
56#4872—32no—
57#4871—32no—
58#4843—31no—
59#4830—31no—
60#4819—32no—
61#4800—32no—
62#4800—32no—
63#4756—32no—
64#4694—31no—
65C8×Dic6—31no—
66C2×C32×Q8C2311yescharacteristic
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C4×C3⋊D3—22no—
71C2×#634D411yescharacteristic
72C2×C3×D12C2311yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×Dic6—21no—
75C2×D3×Dic3—22no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4C2311yescharacteristic
78C32×C42—21no—
79C32×C42C2311yescharacteristic
80#3752—22no—
81#3752—22no—
82#3752—22no—
83C4⋊(C3⋊Dic3)D411yescharacteristic
84#3750D412yes—
85C4×C3⋊Dic3C2312yes—
86C3×#215—22no—
87C3×(C2×D3)⋊C4—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2312yes—
90C3×C4⋊Dic3C2311yescharacteristic
91C2×C3×C3⋊C8C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2312yes—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97#3714—24no—
98#3361—91noSylow
99C2×C3×SD16—31no—
100C3×C4⋊Q8—31no—
101C3×C4×Q8—21no—
102C3×C4×Q8C2×D311yescharacteristic
103C3×C4×Q8C2×D311yescharacteristic
104C3×C4×D4—31no—
105#947—32no—
106#947—32no—
107#947—62no—
108#946—62no—
109C2×#215C2×D311yescharacteristic
110D4×Dic3—32no—
111C2×#213—32no—
112C2×C4⋊Dic3—61no—
113#924—61no—
114C2×D24—32no—
115#897—61no—
116#894—62no—
117#894—62no—
118#894—64no—
119#893—32no—
120#893—32no—
121#893—32no—
122#893—62no—
123D3×C4⋊C4—61no—
124#890—32no—
125#890—32no—
126#878—62no—
127#875—61no—
128#875—61no—
129#875—62no—
130#874—31no—
131#874—31no—
132#874—61no—
133C4×D12—61no—
134C4×D12—61no—
135C4×D12—62no—
136C4×D12C2×D311yescharacteristic
137#869C2×D311yescharacteristic
138C4×Dic6—31no—
139C4×Dic6—31no—
140C4×Dic6—61no—
141C3×#107—32no—
142C3×#106—31no—
143C3×C4⋊C8—31no—
144C3×#103—31no—
145C3×#103—32no—
146C3×#102—31no—
147C3×C4×C8—31no—
148#835C2×D312yes—
149#835C2×D311yescharacteristic
150#821—32no—
151#821—32no—
152#821—32no—
153Dic3⋊C8—32no—
154Dic3⋊C8—32no—
155C8×Dic3—32no—
156C8×Dic3—32no—
157#809—32no—
158#809—32no—
159#809—32no—
160#809C2×D311yescharacteristic
161#808C2×D311yescharacteristic
162#807C2×D312yes—
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C4×C3⋊C8C2×D311yescharacteristic
165C22×C3⋊D3—22no—
166C22×C3×D3—21no—
167C32×Q8—21no—
168C32×Q8—21no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3C2×D412yes—
175C2×C3⋊Dic3C2×D412yes—
176C4⋊(C3⋊D3)—22no—
177C4⋊(C3⋊D3)—22no—
178C4⋊(C3⋊D3)—42no—
179C4⋊(C3⋊D3)—81no—
180C4×C3⋊D3—82no—
181#634—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—21no—
184C3×D12—21no—
185C3×D12#4112yes—
186C3×C4×D3—42no—
187C3×Dic6—81no—
188D3×Dic3—82no—
189C3×C3⋊C8—22no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192#559—91no—
193#554—91no—
194#488—92no—
195#486—91no—
196#478—92no—
197#477—31no—
198#463—92no—
199#459—91no—
200C8×Q8—91no—
201C4×SD16—31no—
202C4×D8—92no—
203C2×C3×Q8—21no—
204C2×C3×Q8—61no—
205C2×C3×Q8C22×D311yescharacteristic
206C2×C3×Q8C22×D311yescharacteristic
207C2×C3×D4—31no—
208C22×C3×C4—61no—
209C22×Dic3—62no—
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×D12C22×D311yescharacteristic
220C2×C4×D3—21no—
221C2×C4×D3—62no—
222C2×C4×D3—62no—
223C2×C4×D3—62no—
224C2×C4×D3—64no—
225C2×Dic6—21no—
226C2×Dic6—31no—
227C2×Dic6—31no—
228C2×Dic6—61no—
229C3×SD16—62no—
230C2×C3×C8—31no—
231C2×C3×C8—32no—
232C2×C3×C8—31no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4C22×D311yescharacteristic
241C3×C4⋊C4C22×D311yescharacteristic
242C3×C22⋊C4—61no—
243C3×C42—22no—
244C3×C42—21no—
245C3×C42—21no—
246C3×C42—21no—
247C3×C42C22×D311yescharacteristic
248C3×C42C22×D311yescharacteristic
249#217—62no—
250#215—22no—
251#213—64no—
252(C2×D3)⋊C4—21no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—62no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—62no—
258(C2×D3)⋊C4—62no—
259(C2×D3)⋊C4—62no—
260(C2×D3)⋊C4—64no—
261(C2×D3)⋊C4—64no—
262(C2×D3)⋊C4—64no—
263C4⋊Dic3—21no—
264C4⋊Dic3—31no—
265C4⋊Dic3—31no—
266C4⋊Dic3—61no—
267C4⋊Dic3—62no—
268C4⋊Dic3—62no—
269C4⋊Dic3C22×D312yes—
270C4⋊Dic3C22×D311yescharacteristic
271Dic3⋊C4—32no—
272Dic3⋊C4—32no—
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276C4×Dic3—32no—
277C4×Dic3—32no—
278C4×Dic3—62no—
279C2×C3⋊C8C22×D311yescharacteristic
280C2×C3⋊C8C22×D311yescharacteristic
281C2×C3⋊C8C22×D312yes—
282D24—64no—
283C22×C32C22×D411yescharacteristic
284C2×C3⋊D3—42no—
285C2×C3⋊D3—42no—
286C2×C3⋊D3—42no—
287C2×C3×D3—22no—
288C2×C3×D3—41no—
289C2×C3×D3—41no—
290C32×C4—21no—
291C32×C4—41no—
292C32×C4—41no—
293C32×C4#13512yes—
294C32×C4C2×#4111yescharacteristic
295C32×C42−1+411yescharacteristic
296C3⋊Dic3—22no—
297C3⋊Dic3—22no—
298C3×Dic3—41no—
299C3×Dic3—42no—
300C2×SD16—31no—
301C2×D8—92no—
302C4⋊Q8—31no—
303#127—91no—
304#125—92no—
305#124—92no—
306#124—181no—
307#123—182no—
308C22⋊Q8—182no—
309C22⋊Q8—181no—
310C4×Q8—91no—
311C4×Q8D3211yescharacteristic
312C4×D4—31no—
313C4×D4—92no—
314C4×D4—92no—
315C4×D4—181no—
316C2×C4⋊C4—181no—
317#107—32no—
318#106—31no—
319C4⋊C8—31no—
320C4⋊C8—92no—
321#103—31no—
322#103—32no—
323#102—31no—
324#102—92no—
325#102—92no—
326#102—92no—
327C4×C8—31no—
328C4×C8—92no—
329C23×C3—61no—
330C22×D3—21no—
331C22×D3—64no—
332C22×D3—62no—
333C22×D3—62no—
334C3×Q8—21no—
335C3×Q8—21no—
336C3×Q8—21no—
337C3×Q8—21no—
338C3×Q8—41no—
339C3×Q8—41no—
340C3×Q8—241no—
341C3×D4—32no—
342C3×D4—61no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—61no—
353C2×C3×C4—62no—
354C2×C3×C4—122no—
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361C2×Dic3—21no—
362C2×Dic3—22no—
363C2×Dic3—32no—
364C2×Dic3—32no—
365C2×Dic3—32no—
366C2×Dic3—32no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—242no—
370D12—21no—
371D12—62no—
372D12—62no—
373D12—62no—
374D12—62no—
375D12—122no—
376D12—122no—
377D12—124no—
378D12—122no—
379D12—122no—
380D12—241no—
381D12—241no—
382D12—242no—
383D12#23512yes—
384C4×D3—42no—
385C4×D3—242no—
386C4×D3—242no—
387C4×D3—242no—
388C4×D3—244no—
389Dic6—62no—
390Dic6—62no—
391Dic6—81no—
392Dic6—122no—
393C3×C8—62no—
394C3×C8—61no—
395C3×C8—61no—
396C3⋊C8—21no—
397C3⋊C8—22no—
398C3⋊C8—21no—
399C2×C32#54811yescharacteristic
400C2×C32C2×#13511yescharacteristic
401C2×C32#57611yescharacteristic
402C3⋊D3—82no—
403C3×D3—42no—
404C2×Q8—61no—
405C2×Q8—91no—
406C2×Q8C2×D3211yescharacteristic
407C2×D4—31no—
408C2×D4—92no—
409C2×D4—181no—
410C2×D4—181no—
411C22×C4—61no—
412C22×C4—182no—
413C22×C4—182no—
414SD16—62no—
415D8—184no—
416C2×C8—31no—
417C2×C8—31no—
418C2×C8—32no—
419C4⋊C4—21no—
420C4⋊C4—31no—
421C4⋊C4—32no—
422C4⋊C4—61no—
423C4⋊C4—91no—
424C4⋊C4—92no—
425C4⋊C4—182no—
426C4⋊C4—182no—
427C4⋊C4C2×D3211yescharacteristic
428C22⋊C4—61no—
429C22⋊C4—182no—
430C22⋊C4—182no—
431C22⋊C4—182no—
432C22⋊C4—182no—
433C42—21no—
434C42—92no—
435C42C2×D3211yescharacteristic
436C22×C3—21no—
437C22×C3—62no—
438C22×C3—121no—
439C22×C3—121no—
440C22×C3C2×D3×D411yescharacteristic
441C22×C3C2×D3×D411yescharacteristic
442C2×D3—22no—
443C2×D3—41no—
444C2×D3—41no—
445C2×D3—124no—
446C2×D3—124no—
447C2×D3—124no—
448C2×D3—122no—
449C2×D3—122no—
450C2×D3—122no—
451C2×D3—122no—
452C2×D3—122no—
453C2×D3—122no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—22no—
459C3×C4—41no—
460C3×C4—42no—
461C3×C4—42no—
462C3×C4—41no—
463C3×C4—41no—
464C3×C4—41no—
465C3×C4—41no—
466C3×C4—121no—
467C3×C4—122no—
468C3×C4#91612yes—
469C3×C4#91912yes—
470C3×C4C2×#23511yescharacteristic
471C3×C4#100711yescharacteristic
472C3×C4D3×#4111yescharacteristic
473C3×C4#101011yescharacteristic
474Dic3—41no—
475Dic3—42no—
476Dic3—62no—
477Dic3—62no—
478Dic3—62no—
479Dic3—62no—
480Dic3—122no—
481Dic3—122no—
482C32#336111yescharacteristic, complemented, Sylow
483C23—61no—
484C23—182no—
485Q8—21no—
486Q8—21no—
487Q8—182no—
488Q8—241no—
489D4—32no—
490D4—61no—
491D4—182no—
492D4—182no—
493D4—362no—
494D4—721no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—61no—
498C2×C4—62no—
499C2×C4—92no—
500C2×C4—92no—
501C2×C4—122no—
502C2×C4—722no—
503C2×C4—722no—
504C2×C4#381111yescharacteristic
505C2×C4#381111yescharacteristic
506C2×C4C22×D3211yescharacteristic
507C8—61no—
508C8—62no—
509C8—61no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—122no—
514C2×C3#555211yescharacteristic
515C2×C3#563311yescharacteristic
516C2×C3C2×#91611yescharacteristic
517C2×C3C2×#91911yescharacteristic
518C2×C3#576911yescharacteristic
519C2×C3#577411yescharacteristic
520D3—42no—
521D3—244no—
522D3—242no—
523D3—242no—
524C22—62no—
525C22—121no—
526C22—121no—
527C22—362no—
528C22—362no—
529C22—362no—
530C22C2×#381111yescharacteristic
531C4—21no—
532C4—41no—
533C4—41no—
534C4—121no—
535C4—122no—
536C4—182no—
537C4—182no—
538C4#6395012yes—
539C4#6429711yescharacteristic
540C4D3×#23511yescharacteristic
541C3—21no—
542C3#7962111yescharacteristic, complemented
543C3#8113411yescharacteristic, complemented
544C2—122no—
545C2—722no—
546C2#1059491611yescharacteristic
547C2C2×#6395011yescharacteristic
548C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10590349C2
hypercenterC4×Q8D32
hypocenterC32#3361
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. #10596056C2semidirect
2. #10593956C2semidirect
3. C3×C4×#215C2semidirect
4. C3×#5021C2semidirect
5. #10591570C2semidirect
6. #10591539C2semidirect
7. #10590459C2semidirect
8. #10590435C2semidirect
10. #10590281C2semidirect
11. #10590254C2semidirect
52. C4×#215D3semidirect
53. #5021D3semidirect
482. C32#3361semidirect
542. C3#79621semidirect
543. C3#81134semidirect

Maximal subgroups

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

subgroupindex
#105960562
#105939562
C3×C4×#2152
C3×#50212
#105915702
#105915392
#105904592
#105904352
#105903492
#105902812
#105902542
#811343
#796213