Finite Group Databasebeta

← #11895971

Subgroups — #11895971

Order 1152.

828 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5570C211yesmaximal, characteristic, complemented
2#10593902C211yesmaximal, characteristic
3#10592726C211yesmaximal, characteristic, complemented
4C3×C4×#215C211yesmaximal, characteristic, complemented
5#10591617C212yesmaximal, complemented
6#10591540C212yesmaximal, complemented
7#10590550C212yesmaximal, complemented
8#10590470C212yesmaximal, complemented
9#10590281C211yesmaximal, characteristic, complemented
10#10590269C211yesmaximal, characteristic, complemented
11#10590258C211yesmaximal, characteristic, complemented
12#83690—31nomaximal
13#79625—31nomaximal
14C2×#3799—21no—
15C32×C4×Q8C2211yescharacteristic
16C2×#3755C2212yes—
17#64083C2211yescharacteristic
18C3×Q8×Dic3C2212yes—
19C2×C3×#215C2211yescharacteristic
20C3×#890—22no—
21C3×#890C2212yes—
22C3×C4×D12C2211yescharacteristic
23C3×#869—21no—
24C3×#869C2211yescharacteristic
25C3×C4×Dic6—21no—
26C3×C4×Dic6C2211yescharacteristic
27#63911C2212yes—
28#63910—22no—
29#63909—21no—
30#63894C2212yes—
31#63636C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C3×#835C2211yescharacteristic
34C3×#809C2211yescharacteristic
35C3×#808C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63576C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63564C2212yes—
40#63564C2212yes—
41#63562C2212yes—
42#63554C2212yes—
43C3×#557—31no—
44#5577—31no—
45#5570D311yescharacteristic, complemented
46#5553—31no—
47C3×C4×SD16—31no—
48#5163—32no—
49#5088—31no—
50#5087—31no—
51#5067—32no—
52#5066—32no—
53#5027—31no—
54#5027—31no—
55#5027—32no—
56#5027—61no—
57#5026—32no—
58C4×#215D311yescharacteristic, complemented
59#5024—31no—
60#5007—31no—
61#4871—32no—
62#4817—32no—
63#4764—32no—
64#4694—31no—
65#4679—31no—
66C2×C32×Q8C2311yescharacteristic
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×Dic6—21no—
73C2×C3×Dic6D411yescharacteristic
74C2×#626—22no—
75C2×#626—22no—
76C2×#624—22no—
77#3799—44no—
78C32×C4⋊C4—21no—
79C32×C4⋊C4C2311yescharacteristic
80C32×C42—21no—
81C32×C42C2311yescharacteristic
82#3755—24no—
83C2×C3⋊(C3⋊C8)C2312yes—
84C3×#215—22no—
85C3×(C2×D3)⋊C4—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3—22no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4D412yes—
94C3×C4×Dic3—22no—
95C3×C4×Dic3C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98#3722—22no—
99#3368—91noSylow
100C2×#239—61no—
101C2×#235—61no—
102C2×C3×SD16—31no—
103C3×C4⋊Q8—31no—
104C3×C4⋊Q8—61no—
105C3×#125—32no—
106C3×#125—62no—
107C3×C4×Q8—21no—
108C3×C4×Q8—31no—
109C3×C4×Q8—32no—
110C3×C4×Q8—61no—
111C3×C4×Q8C2×D311yescharacteristic
112C3×C4×Q8C2×D311yescharacteristic
113C3×C4×D4—31no—
114Q8×Dic3C2×D312yes—
115C2×#215—32no—
116C2×#215—32no—
117C2×#215—62no—
118C2×#215C2×D311yescharacteristic
119#940—32no—
120#930—61no—
121#895—62no—
122#895—61no—
123#893—32no—
124#890—22no—
125#890C2×D312yes—
126#884—62no—
127#874—32no—
128#874—31no—
129#874—31no—
130#874—61no—
131C4×D12—32no—
132C4×D12C2×D311yescharacteristic
133#869—21no—
134#869C2×D311yescharacteristic
135C4×Dic6—21no—
136C4×Dic6C2×D311yescharacteristic
137C3×#106—31no—
138C3×#103—31no—
139C3×#102—31no—
140C3×C4×C8—31no—
141#835C2×D311yescharacteristic
142#832—32no—
143#821—32no—
144#821—32no—
145#815—32no—
146Dic3⋊C8—32no—
147#809—32no—
148#809—32no—
149#809—32no—
150#809—32no—
151#809—32no—
152#809—62no—
153#809C2×D311yescharacteristic
154#808C2×D311yescharacteristic
155#807—32no—
156#807—32no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—31no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)—61no—
161#803—32no—
162C4×C3⋊C8C2×D311yescharacteristic
163C22×C3⋊D3—22no—
164C22×C3×D3—21no—
165C32×Q8—21no—
166C32×Q8#4112yescomplemented
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C4⋊(C3⋊D3)—22no—
173C4⋊(C3⋊D3)—22no—
174C4⋊(C3⋊D3)—42no—
175C4⋊(C3⋊D3)—81no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×D12—21no—
181C3×D12—21no—
182C3×C4×D3—42no—
183C3×Dic6—22no—
184C3×Dic6—42no—
185#626—44no—
186#626—82no—
187#624—44no—
188C3⋊(C3⋊C8)—22no—
189C3×C3⋊C8—21no—
190C3×C3⋊C8—21no—
191#557—31no—
192#550—91no—
193#490—92no—
194#486—91no—
195#478—92no—
196#474—91no—
197#460—92no—
198#460—91no—
199#446—91no—
200#440—92no—
201C4×SD16—31no—
202C2×C3×Q8—21no—
203C2×C3×Q8—31no—
204C2×C3×Q8—61no—
205C2×C3×Q8C22×D311yescharacteristic
206C2×C3×Q8C22×D311yescharacteristic
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—21no—
229C2×Dic6#6711yescharacteristic
230C3×SD16—62no—
231C2×C3×C8—31no—
232C2×C3×C8—31no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—32no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—31no—
239C3×C4⋊C4—32no—
240C3×C4⋊C4—41no—
241C3×C4⋊C4—62no—
242C3×C4⋊C4—62no—
243C3×C4⋊C4—62no—
244C3×C4⋊C4—61no—
245C3×C4⋊C4C22×D311yescharacteristic
246C3×C4⋊C4C22×D311yescharacteristic
247C3×C22⋊C4—61no—
248C3×C42—21no—
249C3×C42—21no—
250C3×C42—21no—
251C3×C42—32no—
252C3×C42—41no—
253C3×C42—62no—
254C3×C42C22×D311yescharacteristic
255C3×C42C22×D311yescharacteristic
256#215—22no—
257#215—64no—
258#215—64no—
259#215—124no—
260(C2×D3)⋊C4—21no—
261(C2×D3)⋊C4—62no—
262(C2×D3)⋊C4—62no—
263C4⋊Dic3—21no—
264C4⋊Dic3—22no—
265C4⋊Dic3—22no—
266C4⋊Dic3#6711yescharacteristic
267C4⋊Dic3C22×D311yescharacteristic
268C4⋊Dic3C22×D312yes—
269Dic3⋊C4—22no—
270Dic3⋊C4#6712yes—
271C4×Dic3—22no—
272C4×Dic3C22×D312yes—
273C2×C3⋊C8—32no—
274C2×C3⋊C8—32no—
275C2×C3⋊C8—62no—
276C2×C3⋊C8C22×D311yescharacteristic
277C2×C3⋊C8C22×D311yescharacteristic
278C22×C32C22×D411yescharacteristic
279C2×C3⋊D3—42no—
280C2×C3⋊D3—42no—
281C2×C3⋊D3—42no—
282C2×C3×D3—41no—
283C2×C3×D3—41no—
284C2×C3×D3—41no—
285C32×C4—22no—
286C32×C4—21no—
287C32×C4—41no—
288C32×C4AGL(1,ℤ/8)12yes—
289C32×C4C2×#4111yescharacteristic
290C32×C42−1+411yescharacteristic
291C3×Dic3—22no—
292C3×Dic3—22no—
293C3×Dic3—41no—
294C3×Dic3—42no—
295C2×#41—181no—
296C2×SD16—31no—
297C2×SD16—92no—
298C4⋊Q8—31no—
299C4⋊Q8—61no—
300#127—92no—
301#127—91no—
302#125—32no—
303#125—62no—
304#121—182no—
305#121—181no—
306C4×Q8—31no—
307C4×Q8—32no—
308C4×Q8—61no—
309C4×Q8D3211yescharacteristic
310C4×D4—31no—
311C4×D4—92no—
312#107—92no—
313#106—31no—
314C4⋊C8—92no—
315C4⋊C8—91no—
316#103—31no—
317#102—31no—
318#102—92no—
319#102—92no—
320#102—92no—
321#102—92no—
322#97—92no—
323C4×C8—31no—
324C23×C3—61no—
325C22×D3—21no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—122no—
329C3×Q8—21no—
330C3×Q8—21no—
331C3×Q8—22no—
332C3×Q8—41no—
333C3×Q8—62no—
334C3×Q8—122no—
335C3×Q8#23512yescomplemented
336C3×Q8#23912yescomplemented
337C3×D4—61no—
338C3×D4—61no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—32no—
347C2×C3×C4—32no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—62no—
351C2×C3×C4—61no—
352C2×C3×C4—122no—
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359#67—124no—
360#67—242no—
361C2×Dic3—21no—
362C2×Dic3—22no—
363C2×Dic3C2×#6712yes—
364C2×Dic3C2×#6712yes—
365D12—21no—
366D12—21no—
367D12—62no—
368D12—62no—
369D12—62no—
370D12—62no—
371D12—122no—
372D12—122no—
373D12—124no—
374D12—122no—
375D12—122no—
376D12—242no—
377D12—241no—
378D12—241no—
379D12—242no—
380D12—242no—
381C4×D3—42no—
382C4×D3—124no—
383C4×D3—124no—
384Dic6—22no—
385Dic6—42no—
386C3×C8—61no—
387C3×C8—61no—
388C3⋊C8—21no—
389C3⋊C8—21no—
390C3⋊C8—62no—
391C3⋊C8—62no—
392C3⋊C8—122no—
393C2×C32#54811yescharacteristic
394C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
395C2×C32#57711yescharacteristic
396C3⋊D3—82no—
397C3×D3—81no—
398#41—364no—
399C2×Q8—31no—
400C2×Q8—61no—
401C2×Q8C2×D3211yescharacteristic
402C2×D4—31no—
403C2×D4—92no—
404C2×D4—182no—
405C2×D4—182no—
406C2×D4—181no—
407C2×D4—181no—
408C22×C4—61no—
409C22×C4—182no—
410SD16—62no—
411SD16—184no—
412C2×C8—31no—
413C2×C8—31no—
414C2×C8—92no—
415C4⋊C4—21no—
416C4⋊C4—31no—
417C4⋊C4—32no—
418C4⋊C4—32no—
419C4⋊C4—31no—
420C4⋊C4—62no—
421C4⋊C4—62no—
422C4⋊C4—62no—
423C4⋊C4—61no—
424C4⋊C4C2×D3211yescharacteristic
425C22⋊C4—61no—
426C22⋊C4—182no—
427C42—21no—
428C42—32no—
429C42—62no—
430C42C2×D3211yescharacteristic
431C22×C3—21no—
432C22×C3—121no—
433C22×C3—121no—
434C22×C3—121no—
435C22×C3C2×D3×D411yescharacteristic
436C22×C3C22×#6711yescharacteristic
437C2×D3—41no—
438C2×D3—41no—
439C2×D3—41no—
440C2×D3—122no—
441C2×D3—122no—
442C2×D3—122no—
443C2×D3—122no—
444C2×D3—122no—
445C2×D3—122no—
446C2×D3—242no—
447C2×D3—242no—
448C2×D3—242no—
449C3×C4—21no—
450C3×C4—22no—
451C3×C4—22no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—22no—
456C3×C4—41no—
457C3×C4—42no—
458C3×C4—41no—
459C3×C4—41no—
460C3×C4—62no—
461C3×C4—62no—
462C3×C4—81no—
463C3×C4—122no—
464C3×C4—121no—
465C3×C4#91412yes—
466C3×C4#94912yes—
467C3×C4C2×#23511yescharacteristic
468C3×C4C2×#23911yescharacteristic
469C3×C4#100711yescharacteristic
470C3×C4#101011yescharacteristic
471Dic3—22no—
472Dic3—22no—
473Dic3—41no—
474Dic3—42no—
475C32#336811yescharacteristic, complemented, Sylow
476C23—61no—
477C23—182no—
478Q8—21no—
479Q8—62no—
480Q8—122no—
481Q8#379912yescomplemented
482D4—61no—
483D4—61no—
484D4—182no—
485D4—182no—
486D4—364no—
487D4—362no—
488D4—721no—
489D4—722no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—32no—
493C2×C4—32no—
494C2×C4—62no—
495C2×C4—61no—
496C2×C4—122no—
497C2×C4—364no—
498C2×C4D3×#6711yescharacteristic
499C2×C4D3×#6711yescharacteristic
500C2×C4C22×D3211yescharacteristic
501C8—61no—
502C8—61no—
503C8—182no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—241no—
508C2×C3#555211yescharacteristic
509C2×C3C2×#91411yescharacteristic
510C2×C3#577011yescharacteristic
511C2×C3#581711yescharacteristic
512C2×C3C2×#94911yescharacteristic
513C2×C3#583711yescharacteristic
514D3—81no—
515D3—242no—
516D3—242no—
517D3—482no—
518C22—121no—
519C22—121no—
520C22—121no—
521C22—362no—
522C22—362no—
523C22—362no—
524C22C2×D3×#6711yescharacteristic
525C4—22no—
526C4—21no—
527C4—41no—
528C4—62no—
529C4—62no—
530C4—121no—
531C4—122no—
532C4#6393912yes—
533C4#6429711yescharacteristic
534C4C2×#379911yescharacteristic
535C3—21no—
536C3#7962511yescharacteristic, complemented
537C3#8369011yescharacteristic, complemented
538C2—241no—
539C2—722no—
540C2#1059490211yescharacteristic
541C2C2×#6393911yescharacteristic
542C2#1059545711yescharacteristic
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×#5570C2semidirect
3. #10592726C2semidirect
4. C3×C4×#215C2semidirect
5. #10591617C2semidirect
6. #10591540C2semidirect
7. #10590550C2semidirect
8. #10590470C2semidirect
9. #10590281C2semidirect
10. #10590269C2semidirect
11. #10590258C2semidirect
45. #5570D3semidirect
58. C4×#215D3semidirect
166. C32×Q8#41semidirect
335. C3×Q8#235semidirect
336. C3×Q8#239semidirect
475. C32#3368semidirect
481. Q8#3799semidirect
536. C3#79625semidirect
537. C3#83690semidirect

Maximal subgroups

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

subgroupindex
C3×#55702
#105939022
#105927262
C3×C4×#2152
#105916172
#105915402
#105905502
#105904702
#105902812
#105902692
#105902582
#836903
#796253