Finite Group Databasebeta

← #11895980

Subgroups — #11895980

Order 1152.

823 conjugacy classes of subgroups.

The subgroup lattice has 541 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5721C211yesmaximal, characteristic, complemented
2#10593902C211yesmaximal, characteristic
3#10592787C211yesmaximal, characteristic, complemented
4C3×#5087C211yesmaximal, characteristic, complemented
5#10590550C212yesmaximal, complemented
6#10590549C212yesmaximal, complemented
7#10590468C212yesmaximal, complemented
8#10590457C212yesmaximal, complemented
9#10590367C211yesmaximal, characteristic, complemented
10C4×#3715C211yesmaximal, characteristic, complemented
11#10590259C211yesmaximal, characteristic, complemented
12#83690—31nomaximal
13#80995—31nomaximal
14C2×#3799—21no—
15C32×C4⋊Q8C2211yescharacteristic
16#64083C2211yescharacteristic
17C3×Q8×Dic3—21no—
18C3×#944—21no—
19C3×#890C2212yes—
20C3×#889—22no—
21C3×#887C2212yes—
22C3×C4×D12C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63911C2212yes—
26#63910—22no—
27#63909—21no—
28#63894C2212yes—
29C2×#3717C2212yes—
30C2×#3715C2211yescharacteristic
31#63636C2212yes—
32#63636C2212yes—
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#809C2212yes—
35C3×#807C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37#63574C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63565C2211yescharacteristic
40#63564C2212yes—
41#63562C2211yescharacteristic
42#63554C2212yes—
43C3×#557—31no—
44#5721D311yescharacteristic, complemented
45#5577—31no—
46#5553—31no—
47C3×#474—31no—
48#5088—31no—
49#5088—31no—
50#5088—61no—
51#5087D311yescharacteristic, complemented
52#5067—32no—
53#5066—32no—
54#5027—32no—
55#5027—31no—
56#5026—32no—
57C4×#215—31no—
58#5024—31no—
59C4×#214—31no—
60#4891—32no—
61#4889—32no—
62#4848—31no—
63#4831—31no—
64#4764—32no—
65#4762—32no—
66C2×C32×Q8—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6C2311yescharacteristic
74C2×#626—22no—
75C2×#626—22no—
76C2×#624—22no—
77#3799—44no—
78C32×C4⋊C4—21no—
79C32×C4⋊C4C2312yes—
80C32×C42C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C3×(C2×D3)⋊C4—21no—
84C3×C4⋊Dic3—22no—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2311yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—21no—
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4D412yes—
92C3×C4×Dic3—21no—
93C3×C4×Dic3—22no—
94C3×C4×Dic3C2312yes—
95C2×C3×C3⋊C8C2312yes—
96#3722—22no—
97#3717—24no—
98#3715—22no—
99#3368—91noSylow
100C2×#239—61no—
101C2×#235—61no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8—61no—
104C3×C4⋊Q8C2×D311yescharacteristic
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×#125—32no—
107C3×#125—62no—
108C3×C4×Q8—31no—
109C3×C4×Q8—32no—
110C3×C4×Q8—31no—
111C3×C4×Q8—61no—
112C3×C4×D4—31no—
113Q8×Dic3—21no—
114#944—21no—
115C2×#215—31no—
116C2×#215—32no—
117#940—32no—
118C2×#214—31no—
119#930—61no—
120C2×#204—32no—
121#895—62no—
122#895—61no—
123#893—32no—
124#890C2×D312yes—
125#889—22no—
126#887C2×D312yes—
127#884—62no—
128#874—32no—
129#874—31no—
130#874—31no—
131#874—61no—
132C4×D12—32no—
133C4×D12C2×D311yescharacteristic
134C4×Dic6C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×#107—32no—
137C3×C4⋊C8—31no—
138C3×#102—32no—
139#835—31no—
140#832—31no—
141#821—32no—
142#815—32no—
143Dic3⋊C8—32no—
144#810—31no—
145#809—31no—
146#809—32no—
147#809—32no—
148#809—32no—
149#809—32no—
150#809—32no—
151#809—62no—
152#809—62no—
153#809C2×D312yes—
154#808—31no—
155#808—31no—
156#807C2×D312yes—
157C4⋊(C3⋊C8)—32no—
158C4⋊(C3⋊C8)C2×D311yescharacteristic
159#803—32no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—31no—
162C4×C3⋊C8—61no—
163C22×C3⋊D3—22no—
164C22×C3×D3—21no—
165C32×Q8—42no—
166C2×C32×C4—22no—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C4⋊(C3⋊D3)—22no—
171C4⋊(C3⋊D3)—22no—
172C4⋊(C3⋊D3)—42no—
173C4⋊(C3⋊D3)—81no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D412yes—
179C3×D12—21no—
180C3×D12—21no—
181C3×C4×D3—42no—
182C3×Dic6—22no—
183C3×Dic6—21no—
184C3×Dic6#4112yescomplemented
185#626—44no—
186#626—82no—
187#624—44no—
188C3⋊(C3⋊C8)—21no—
189C3⋊(C3⋊C8)—21no—
190C3×C3⋊C8—22no—
191#557—31no—
192#550—91no—
193#490—92no—
194#486—91no—
195#478—92no—
196#474—31no—
197#460—92no—
198#460—91no—
199#446—91no—
200#440—92no—
201C4×SD16—91no—
202C2×C3×Q8—21no—
203C2×C3×Q8—21no—
204C2×C3×Q8—31no—
205C2×C3×Q8—31no—
206C2×C3×Q8—41no—
207C2×C3×D4—31no—
208C22×C3×C4—61no—
209C2×#67—62no—
210C2×#67—62no—
211#239—124no—
212#235—124no—
213C2×D12—32no—
214C2×D12—32no—
215C2×D12—62no—
216C2×D12—62no—
217C2×D12—61no—
218C2×D12—61no—
219C2×D12—62no—
220C2×D12—61no—
221C2×D12—61no—
222C2×D12—121no—
223C2×D12—121no—
224C2×D12C22×D311yescharacteristic
225C2×C4×D3—21no—
226C2×C4×D3—62no—
227C2×C4×D3—62no—
228C2×Dic6#6711yescharacteristic
229C2×Dic6C22×D311yescharacteristic
230C2×C3×C8—32no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—31no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—41no—
239C3×C4⋊C4—62no—
240C3×C4⋊C4—62no—
241C3×C4⋊C4—62no—
242C3×C4⋊C4—61no—
243C3×C4⋊C4C22×D312yes—
244C3×C4⋊C4C22×D312yes—
245C3×C22⋊C4—61no—
246C3×C42—21no—
247C3×C42—32no—
248C3×C42—62no—
249C3×C42—61no—
250C3×C42C22×D311yescharacteristic
251C3×C42C22×D311yescharacteristic
252#215—64no—
253#215—62no—
254#214—62no—
255(C2×D3)⋊C4—21no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—62no—
258C4⋊Dic3—22no—
259C4⋊Dic3#6711yescharacteristic
260C4⋊Dic3C22×D311yescharacteristic
261C4⋊Dic3C22×D311yescharacteristic
262Dic3⋊C4—21no—
263Dic3⋊C4—22no—
264Dic3⋊C4—22no—
265Dic3⋊C4#6712yes—
266C4×Dic3—21no—
267C4×Dic3—22no—
268C4×Dic3C22×D312yes—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—61no—
274C2×C3⋊C8—61no—
275C2×C3⋊C8C22×D312yes—
276#204—64no—
277C22×C32C22×D411yescharacteristic
278C2×C3⋊D3—42no—
279C2×C3⋊D3—42no—
280C2×C3⋊D3—42no—
281C2×C3×D3—41no—
282C2×C3×D3—41no—
283C2×C3×D3—41no—
284C32×C4—21no—
285C32×C4—42no—
286C32×C4AGL(1,ℤ/8)12yes—
287C32×C4C2×#4111yescharacteristic
288C32×C42−1+411yescharacteristic
289C3×Dic3—22no—
290C3×Dic3—22no—
291C3×Dic3—22no—
292C3×Dic3—41no—
293C3×Dic3—41no—
294C2×#41—181no—
295C2×SD16—92no—
296C2×SD16—91no—
297C4⋊Q8—61no—
298C4⋊Q8D3211yescharacteristic
299#127—92no—
300#127—91no—
301#125—32no—
302#125—62no—
303#121—182no—
304#121—181no—
305C4×Q8—31no—
306C4×Q8—32no—
307C4×Q8—31no—
308C4×Q8—61no—
309C4×D4—31no—
310C4×D4—92no—
311#107—32no—
312#106—91no—
313C4⋊C8—31no—
314C4⋊C8—92no—
315#103—91no—
316#102—32no—
317#102—92no—
318#102—91no—
319#102—92no—
320#102—92no—
321#97—92no—
322C4×C8—91no—
323C23×C3—61no—
324C22×D3—21no—
325C22×D3—62no—
326C22×D3—62no—
327C22×D3—122no—
328C3×Q8—32no—
329C3×Q8—42no—
330C3×Q8—42no—
331C3×Q8—62no—
332C3×Q8—61no—
333C3×Q8—82no—
334C3×D4—61no—
335C3×D4—61no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—32no—
342C2×C3×C4—32no—
343C2×C3×C4—42no—
344C2×C3×C4—61no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—122no—
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C2×#6711yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354#67—124no—
355#67—242no—
356C2×Dic3—21no—
357C2×Dic3—21no—
358C2×Dic3—21no—
359C2×Dic3C2×#6712yes—
360C2×Dic3C2×#6712yes—
361D12—21no—
362D12—21no—
363D12—62no—
364D12—62no—
365D12—62no—
366D12—62no—
367D12—122no—
368D12—122no—
369D12—124no—
370D12—122no—
371D12—122no—
372D12—242no—
373D12—241no—
374D12—241no—
375D12—242no—
376D12—242no—
377C4×D3—42no—
378C4×D3—124no—
379C4×D3—124no—
380Dic6—22no—
381Dic6—21no—
382Dic6#23912yescomplemented
383C3×C8—62no—
384C3⋊C8—22no—
385C3⋊C8—61no—
386C3⋊C8—61no—
387C3⋊C8—61no—
388C3⋊C8—61no—
389C3⋊C8—121no—
390C3⋊C8—121no—
391C2×C32#54811yescharacteristic
392C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
393C2×C32#57711yescharacteristic
394C3⋊D3—82no—
395C3×D3—81no—
396#41—364no—
397C2×Q8—21no—
398C2×Q8—31no—
399C2×Q8—31no—
400C2×D4—31no—
401C2×D4—92no—
402C2×D4—182no—
403C2×D4—182no—
404C2×D4—181no—
405C2×D4—181no—
406C22×C4—61no—
407C22×C4—182no—
408SD16—184no—
409SD16—182no—
410C2×C8—32no—
411C2×C8—91no—
412C2×C8—91no—
413C4⋊C4—21no—
414C4⋊C4—31no—
415C4⋊C4—32no—
416C4⋊C4—31no—
417C4⋊C4—31no—
418C4⋊C4—62no—
419C4⋊C4—62no—
420C4⋊C4—62no—
421C4⋊C4—61no—
422C4⋊C4C2×D3212yes—
423C22⋊C4—61no—
424C22⋊C4—182no—
425C42—32no—
426C42—62no—
427C42—61no—
428C42C2×D3211yescharacteristic
429C22×C3—21no—
430C22×C3—121no—
431C22×C3—121no—
432C22×C3—121no—
433C22×C3C2×D3×D411yescharacteristic
434C22×C3C22×#6711yescharacteristic
435C2×D3—41no—
436C2×D3—41no—
437C2×D3—41no—
438C2×D3—122no—
439C2×D3—122no—
440C2×D3—122no—
441C2×D3—122no—
442C2×D3—122no—
443C2×D3—122no—
444C2×D3—242no—
445C2×D3—242no—
446C2×D3—242no—
447C3×C4—22no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—22no—
453C3×C4—42no—
454C3×C4—42no—
455C3×C4—62no—
456C3×C4—62no—
457C3×C4—62no—
458C3×C4—82no—
459C3×C4—121no—
460C3×C4—121no—
461C3×C4#91112yes—
462C3×C4#94912yes—
463C3×C4C2×#23911yescharacteristic
464C3×C4#100711yescharacteristic
465C3×C4#100711yescharacteristic
466C3×C4D3×#4111yescharacteristic
467Dic3—22no—
468Dic3—22no—
469Dic3—22no—
470Dic3—41no—
471Dic3—41no—
472C32#336811yescharacteristic, complemented, Sylow
473C23—61no—
474C23—182no—
475Q8—32no—
476Q8—42no—
477Q8—61no—
478Q8—62no—
479D4—61no—
480D4—61no—
481D4—182no—
482D4—182no—
483D4—364no—
484D4—362no—
485D4—721no—
486D4—722no—
487C2×C4—22no—
488C2×C4—32no—
489C2×C4—32no—
490C2×C4—61no—
491C2×C4—61no—
492C2×C4—61no—
493C2×C4—122no—
494C2×C4—364no—
495C2×C4D3×#6711yescharacteristic
496C2×C4D3×#6711yescharacteristic
497C2×C4C22×D3211yescharacteristic
498C8—62no—
499C8—181no—
500C8—181no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—241no—
505C2×C3#563311yescharacteristic
506C2×C3C2×#91111yescharacteristic
507C2×C3#577811yescharacteristic
508C2×C3#581711yescharacteristic
509C2×C3C2×#94911yescharacteristic
510C2×C3#583711yescharacteristic
511D3—81no—
512D3—242no—
513D3—242no—
514D3—482no—
515C22—121no—
516C22—121no—
517C22—121no—
518C22—362no—
519C22—362no—
520C22—362no—
521C22C2×D3×#6711yescharacteristic
522C4—21no—
523C4—42no—
524C4—62no—
525C4—62no—
526C4—62no—
527C4—121no—
528C4—121no—
529C4#6392512yes—
530C4#6431611yescharacteristic
531C4D3×#23911yescharacteristic
532C3—21no—
533C3#8099511yescharacteristic, complemented
534C3#8369011yescharacteristic, complemented
535C2—241no—
536C2—722no—
537C2C2×#6392511yescharacteristic
538C2#1059531911yescharacteristic
539C2#1059540211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10593902C2
hypercenterC4⋊Q8D32
hypocenterC32#3368
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. C3×#5721C2semidirect
3. #10592787C2semidirect
4. C3×#5087C2semidirect
5. #10590550C2semidirect
6. #10590549C2semidirect
7. #10590468C2semidirect
8. #10590457C2semidirect
9. #10590367C2semidirect
10. C4×#3715C2semidirect
11. #10590259C2semidirect
44. #5721D3semidirect
51. #5087D3semidirect
184. C3×Dic6#41semidirect
382. Dic6#239semidirect
472. C32#3368semidirect
533. C3#80995semidirect
534. C3#83690semidirect

Maximal subgroups

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

subgroupindex
C3×#57212
#105939022
#105927872
C3×#50872
#105905502
#105905492
#105904682
#105904572
#105903672
C4×#37152
#105902592
#836903
#809953