Finite Group Databasebeta

← #11895257

Subgroups — #11895257

Order 1152.

806 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596203C211yesmaximal, characteristic, complemented
2#10593956C211yesmaximal, characteristic, complemented
3C3×#5083C211yesmaximal, characteristic, complemented
4C3×#5079C211yesmaximal, characteristic, complemented
5#10591615C212yesmaximal, complemented
6#10591571C212yesmaximal, complemented
7#10591570C212yesmaximal
8#10591539C212yesmaximal, complemented
9C4×#3714C211yesmaximal, characteristic
10#10590300C211yesmaximal, characteristic, complemented
11#10590254C211yesmaximal, characteristic, complemented
12#81621—31nomaximal
13#80415—31nomaximal
14C32×C4⋊Q8C2211yescharacteristic
15#64156C2212yes—
16Q8×C3⋊Dic3C2212yes—
17#64107—22no—
18#64106—21no—
19#64101—21no—
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C2×C3×#215C2212yes—
23C3×C4×D12C2211yescharacteristic
24C3×#869C2211yescharacteristic
25#63898C2212yes—
26D3×C4⋊Dic3—21no—
27#63887—22no—
28#63872C2212yes—
29#63857—21no—
30C2×#3714C2211yescharacteristic
31C3×#835C2212yes—
32C3×#835C2212yes—
33C3×#835C2212yes—
34C3×C4⋊(C3⋊C8)C2211yescharacteristic
35C3×C4×C3⋊C8C2211yescharacteristic
36#63575C2211yescharacteristic
37#63573C2212yes—
38#63572C2212yes—
39#63564C2211yescharacteristic
40#63564C2212yes—
41#63563C2211yescharacteristic
42#63553C2212yes—
43#5732—31no—
44#5732—31no—
45#5732—61no—
46#5730—31no—
47#5543—31no—
48C3×#487—31no—
49C3×#461—31no—
50#5165—32no—
51Dic3×SD16—32no—
52#5084—31no—
53#5083D311yescharacteristic, complemented
54#5079D311yescharacteristic, complemented
55C4×#213—31no—
56#4842—31no—
57#4830—31no—
58#4819—32no—
59#4800—32no—
60#4800—32no—
61#4799—32no—
62#4796—32no—
63#4788—32no—
64C4×D24—31no—
65C8×Dic6—31no—
66C2×C32×Q8C2312yes—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×#634D411yescharacteristic
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6—21no—
73C2×D3×Dic3—22no—
74C32×C4⋊C4—21no—
75C32×C4⋊C4—21no—
76C32×C42C2311yescharacteristic
77#3752—21no—
78#3752—22no—
79#3752—22no—
80C4⋊(C3⋊Dic3)—22no—
81C4⋊(C3⋊Dic3)D411yescharacteristic
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83#3750D412yes—
84C4×C3⋊Dic3—22no—
85C4×C3⋊Dic3C2312yes—
86C3×#215—24no—
87C3×(C2×D3)⋊C4—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2312yes—
90C3×C4⋊Dic3C2311yescharacteristic
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97#3714—22no—
98#3360—91noSylow
99C2×C3×SD16—32no—
100C3×C4⋊Q8—21no—
101C3×C4⋊Q8—31no—
102C3×C4⋊Q8C2×D311yescharacteristic
103C3×C4⋊Q8C2×D311yescharacteristic
104C3×C4×D4—31no—
105#947—32no—
106#947—32no—
107#947—62no—
108#946—62no—
109Q8×Dic3—32no—
110Q8×Dic3—32no—
111Q8×Dic3—62no—
112C2×#215C2×D312yes—
113D4×Dic3—32no—
114C2×#213—31no—
115C2×C4⋊Dic3—61no—
116#924—61no—
117C2×D24—31no—
118#898—62no—
119#898—62no—
120#898—64no—
121#897—61no—
122#897—61no—
123#897—62no—
124#897—61no—
125#893—32no—
126#892—61no—
127#892—61no—
128#892—62no—
129D3×C4⋊C4—61no—
130#890—32no—
131#890—32no—
132#878—62no—
133C4×D12—31no—
134C4×D12—31no—
135C4×D12—61no—
136C4×D12C2×D311yescharacteristic
137#869C2×D311yescharacteristic
138C4×Dic6—31no—
139C4×Dic6—31no—
140C4×Dic6—61no—
141C3×C4⋊C8—31no—
142C3×#103—32no—
143C3×#103—32no—
144C3×#103—32no—
145C3×C4×C8—31no—
146#835C2×D312yes—
147#835C2×D312yes—
148#835C2×D312yes—
149#832—31no—
150#821—31no—
151#821—32no—
152#821—31no—
153#818—31no—
154#817—32no—
155Dic3⋊C8—32no—
156Dic3⋊C8—32no—
157C8×Dic3—32no—
158C8×Dic3—32no—
159#809—31no—
160#809—32no—
161#808—32no—
162#807—31no—
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C4×C3⋊C8C2×D311yescharacteristic
165C22×C3⋊D3—21no—
166C22×C3×D3—21no—
167C32×Q8—22no—
168C32×Q8—22no—
169C2×C32×C4—22no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3C2×D412yes—
175C2×C3⋊Dic3C2×D412yes—
176C4⋊(C3⋊D3)—21no—
177C4⋊(C3⋊D3)—21no—
178C4×C3⋊D3—42no—
179#634—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—21no—
182C3×D12—21no—
183C3×D12#4112yes—
184C3×C4×D3—42no—
185C3×Dic6—81no—
186D3×Dic3—82no—
187C3×C3⋊C8—21no—
188C3×C3⋊C8—22no—
189C3×C3⋊C8—21no—
190#556—91no—
191#554—91no—
192#488—92no—
193#487—31no—
194#479—92no—
195#476—91no—
196#463—92no—
197#461—31no—
198C8×Q8—91no—
199C4×SD16—92no—
200C4×D8—91no—
201C2×C3×Q8—22no—
202C2×C3×Q8—61no—
203C2×C3×Q8C22×D312yes—
204C2×C3×Q8C22×D312yes—
205C2×C3×D4—31no—
206C22×C3×C4—61no—
207C22×Dic3—62no—
208C2×D12—31no—
209C2×D12—31no—
210C2×D12—61no—
211C2×D12C22×D311yescharacteristic
212C2×C4×D3—21no—
213C2×C4×D3—62no—
214C2×C4×D3—61no—
215C2×C4×D3—61no—
216C2×C4×D3—62no—
217C2×Dic6—21no—
218C2×Dic6—31no—
219C2×Dic6—31no—
220C2×Dic6—61no—
221C3×SD16—64no—
222C2×C3×C8—31no—
223C2×C3×C8—32no—
224C2×C3×C8—31no—
225C3×C4⋊C4—22no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—31no—
232C3×C4⋊C4—32no—
233C3×C4⋊C4—61no—
234C3×C22⋊C4—61no—
235C3×C42—21no—
236C3×C42C22×D311yescharacteristic
237C3×C42C22×D311yescharacteristic
238#217—62no—
239#215—24no—
240#213—62no—
241(C2×D3)⋊C4—21no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250(C2×D3)⋊C4—61no—
251(C2×D3)⋊C4—61no—
252C4⋊Dic3—21no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—31no—
256C4⋊Dic3—31no—
257C4⋊Dic3—61no—
258C4⋊Dic3—61no—
259C4⋊Dic3—62no—
260C4⋊Dic3—62no—
261C4⋊Dic3—62no—
262C4⋊Dic3—62no—
263C4⋊Dic3—64no—
264C4⋊Dic3C22×D312yes—
265C4⋊Dic3C22×D311yescharacteristic
266Dic3⋊C4—32no—
267Dic3⋊C4—32no—
268Dic3⋊C4—62no—
269Dic3⋊C4—62no—
270Dic3⋊C4—62no—
271C4×Dic3—32no—
272C4×Dic3—32no—
273C4×Dic3—62no—
274C4×Dic3—62no—
275C4×Dic3—62no—
276C4×Dic3—64no—
277C2×C3⋊C8C22×D311yescharacteristic
278C2×C3⋊C8C22×D311yescharacteristic
279C2×C3⋊C8C22×D312yes—
280D24—62no—
281C22×C32C22×D411yescharacteristic
282C2×C3⋊D3—41no—
283C2×C3⋊D3—41no—
284C2×C3⋊D3—41no—
285C2×C3×D3—22no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C32×C4—21no—
289C32×C4—42no—
290C32×C4#13512yes—
291C32×C4C2×#4111yescharacteristic
292C32×C42−1+411yescharacteristic
293C3⋊Dic3—22no—
294C3⋊Dic3—22no—
295C3⋊Dic3—41no—
296C3×Dic3—41no—
297C3×Dic3—42no—
298C2×SD16—32no—
299C2×D8—91no—
300C4⋊Q8—31no—
301C4⋊Q8D3211yescharacteristic
302#126—182no—
303#125—92no—
304#124—92no—
305C22⋊Q8—182no—
306C22⋊Q8—181no—
307C22⋊Q8—181no—
308C4×Q8—91no—
309C4×Q8—92no—
310C4×D4—31no—
311C4×D4—92no—
312C4×D4—91no—
313#117—181no—
314C2×C4⋊C4—181no—
315#107—91no—
316#106—92no—
317C4⋊C8—31no—
318C4⋊C8—92no—
319#103—32no—
320#103—32no—
321#103—32no—
322#102—91no—
323#102—92no—
324#102—91no—
325C4×C8—31no—
326C4×C8—92no—
327C23×C3—61no—
328C22×D3—21no—
329C22×D3—62no—
330C22×D3—61no—
331C22×D3—61no—
332C3×Q8—22no—
333C3×Q8—22no—
334C3×Q8—22no—
335C3×Q8—22no—
336C3×Q8—42no—
337C3×Q8—42no—
338C3×Q8—241no—
339C3×D4—32no—
340C3×D4—61no—
341C2×C3×C4—24no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—61no—
348C2×C3×C4—62no—
349C2×C3×C4—122no—
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×Dic3—21no—
357C2×Dic3—22no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—32no—
361C2×Dic3—32no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—242no—
368D12—21no—
369D12—61no—
370D12—61no—
371D12—61no—
372D12—61no—
373D12—121no—
374D12—121no—
375D12#23712yes—
376C4×D3—42no—
377C4×D3—124no—
378C4×D3—122no—
379C4×D3—122no—
380C4×D3—242no—
381Dic6—62no—
382Dic6—62no—
383Dic6—81no—
384Dic6—122no—
385C3×C8—61no—
386C3×C8—62no—
387C3×C8—61no—
388C3⋊C8—22no—
389C3⋊C8—21no—
390C3⋊C8—21no—
391C2×C32#54811yescharacteristic
392C2×C32C2×#13511yescharacteristic
393C2×C32#57711yescharacteristic
394C3⋊D3—81no—
395C3×D3—42no—
396C2×Q8—61no—
397C2×Q8—91no—
398C2×Q8C2×D3212yes—
399C2×D4—31no—
400C2×D4—91no—
401C22×C4—61no—
402C22×C4—182no—
403C22×C4—181no—
404SD16—64no—
405D8—182no—
406C2×C8—31no—
407C2×C8—31no—
408C2×C8—32no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—32no—
412C4⋊C4—31no—
413C4⋊C4—61no—
414C4⋊C4—91no—
415C4⋊C4—92no—
416C4⋊C4—91no—
417C4⋊C4—182no—
418C4⋊C4—182no—
419C4⋊C4—182no—
420C22⋊C4—61no—
421C22⋊C4—182no—
422C22⋊C4—182no—
423C22⋊C4—182no—
424C22⋊C4—181no—
425C42—92no—
426C42—182no—
427C42C2×D3211yescharacteristic
428C22×C3—21no—
429C22×C3—62no—
430C22×C3—121no—
431C22×C3—121no—
432C22×C3C2×D3×D411yescharacteristic
433C22×C3C2×D3×D411yescharacteristic
434C2×D3—22no—
435C2×D3—41no—
436C2×D3—41no—
437C2×D3—122no—
438C2×D3—122no—
439C2×D3—122no—
440C2×D3—121no—
441C2×D3—121no—
442C2×D3—121no—
443C2×D3—121no—
444C2×D3—121no—
445C2×D3—121no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—22no—
451C3×C4—41no—
452C3×C4—44no—
453C3×C4—42no—
454C3×C4—42no—
455C3×C4—121no—
456C3×C4—122no—
457C3×C4#91612yes—
458C3×C4#91912yes—
459C3×C4C2×#23711yescharacteristic
460C3×C4D3×#4111yescharacteristic
461C3×C4#101011yescharacteristic
462C3×C4#101011yescharacteristic
463Dic3—41no—
464Dic3—42no—
465Dic3—62no—
466Dic3—62no—
467Dic3—62no—
468Dic3—62no—
469Dic3—122no—
470Dic3—122no—
471Dic3—122no—
472Dic3—121no—
473Dic3—121no—
474C32#336011yescharacteristic, complemented, Sylow
475C23—61no—
476C23—181no—
477Q8—22no—
478Q8—22no—
479Q8—182no—
480Q8—241no—
481D4—32no—
482D4—61no—
483D4—181no—
484D4—181no—
485C2×C4—22no—
486C2×C4—61no—
487C2×C4—62no—
488C2×C4—92no—
489C2×C4—92no—
490C2×C4—122no—
491C2×C4—181no—
492C2×C4—362no—
493C2×C4—722no—
494C2×C4#381111yescharacteristic
495C2×C4#381111yescharacteristic
496C2×C4C22×D3211yescharacteristic
497C8—61no—
498C8—61no—
499C8—62no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—122no—
504C2×C3#559811yescharacteristic
505C2×C3#567711yescharacteristic
506C2×C3C2×#91611yescharacteristic
507C2×C3#576211yescharacteristic
508C2×C3C2×#91911yescharacteristic
509C2×C3#577811yescharacteristic
510D3—42no—
511D3—242no—
512D3—241no—
513D3—241no—
514C22—62no—
515C22—121no—
516C22—121no—
517C22—361no—
518C22—361no—
519C22—361no—
520C22C2×#381111yescharacteristic
521C4—21no—
522C4—42no—
523C4—121no—
524C4—122no—
525C4—182no—
526C4—182no—
527C4—361no—
528C4#6395012yes—
529C4#6430911yescharacteristic
530C4D3×#23711yescharacteristic
531C3—21no—
532C3#8041511yescharacteristic, complemented
533C3#8162111yescharacteristic, complemented
534C2—122no—
535C2—721no—
536C2#1059516111yescharacteristic
537C2#1059532411yescharacteristic
538C2C2×#6395011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
hypercenterC4⋊Q8D32
hypocenterC32#3360
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. #10596203C2semidirect
2. #10593956C2semidirect
3. C3×#5083C2semidirect
4. C3×#5079C2semidirect
5. #10591615C2semidirect
6. #10591571C2semidirect
8. #10591539C2semidirect
10. #10590300C2semidirect
11. #10590254C2semidirect
53. #5083D3semidirect
54. #5079D3semidirect
474. C32#3360semidirect
532. C3#80415semidirect
533. C3#81621semidirect

Maximal subgroups

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

subgroupindex
#105962032
#105939562
C3×#50832
C3×#50792
#105916152
#105915712
#105915702
#105915392
C4×#37142
#105903002
#105902542
#816213
#804153