Finite Group Databasebeta

← #11895969

Subgroups — #11895969

Order 1152.

825 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
1C3×#5570C211yesmaximal, characteristic, complemented
2#10593900C211yesmaximal, characteristic
3C4×#3755C211yesmaximal, characteristic, complemented
4C3×#5027C211yesmaximal, characteristic, complemented
5#10591617C212yesmaximal, complemented
6#10591566C212yesmaximal, complemented
7#10590550C212yesmaximal, complemented
8#10590469C212yesmaximal, complemented
9#10590313C211yesmaximal, characteristic, complemented
10#10590277C211yesmaximal, characteristic, complemented
11#10590259C211yesmaximal, characteristic, complemented
12#83690—31nomaximal
13#80371—31nomaximal
14C2×#3796—21no—
15C32×C4×Q8C2211yescharacteristic
16C2×#3755C2211yescharacteristic
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×Q8×Dic3C2212yes—
19C2×C3×#215C2212yes—
20C3×#890—22no—
21C3×#890C2212yes—
22C3×#874C2211yescharacteristic
23C3×#869—21no—
24C3×#869C2211yescharacteristic
25C3×C4×Dic6—21no—
26C3×C4×Dic6C2211yescharacteristic
27#63916—21no—
28#63911C2212yes—
29Dic3×D12C2212yes—
30#63886—22no—
31#63662C2211yescharacteristic
32#63636C2211yescharacteristic
33#63635C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#809C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37#63575C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63564C2212yes—
40#63562C2212yes—
41#63562C2212yes—
42#63554C2212yes—
43C3×#557—31no—
44#5718—31no—
45#5577—31no—
46#5570D311yescharacteristic, complemented
47C3×#460—31no—
48#5164—32no—
49#5163—32no—
50#5088—31no—
51#5087—31no—
52#5070—31no—
53#5067—32no—
54#5066—32no—
55#5027—32no—
56#5027D311yescharacteristic, complemented
57#5026—32no—
58C4×#215—31no—
59C4×#215—31no—
60C4×#215—61no—
61#5024—31no—
62#4846—31no—
63#4831—31no—
64#4766—32no—
65#4764—32no—
66C2×C32×Q8C2311yescharacteristic
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×Dic6—21no—
73C2×C3×Dic6D411yescharacteristic
74C2×#626—22no—
75C2×#626—22no—
76C2×D3×Dic3—22no—
77#3796—44no—
78C32×C4⋊C4—21no—
79C32×C4⋊C4C2311yescharacteristic
80C32×C42—21no—
81C32×C42C2311yescharacteristic
82#3755—22no—
83#3752—21no—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C3×#215—24no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3D411yescharacteristic
92C3×C4⋊Dic3C2312yes—
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4D412yes—
95C3×C4×Dic3—22no—
96C3×C4×Dic3C2312yes—
97C2×C3×C3⋊C8C2312yes—
98(C2×D3)⋊Dic3—22no—
99#3368—91noSylow
100C2×#239—61no—
101C2×#237—61no—
102C2×C3×SD16—32no—
103C3×C4⋊Q8—31no—
104C3×C4⋊Q8—61no—
105C3×#127—31no—
106C3×#125—32no—
107C3×#125—62no—
108C3×C4×Q8—21no—
109C3×C4×Q8—31no—
110C3×C4×Q8—32no—
111C3×C4×Q8—61no—
112C3×C4×Q8C2×D311yescharacteristic
113C3×C4×Q8C2×D311yescharacteristic
114Q8×Dic3C2×D312yes—
115C2×#215—31no—
116C2×#215—31no—
117C2×#215—61no—
118C2×#215C2×D312yes—
119#940—32no—
120#939—62no—
121#938—61no—
122D4×Dic3—32no—
123#895—62no—
124#895—61no—
125#890—22no—
126#890C2×D312yes—
127#874—32no—
128#874C2×D311yescharacteristic
129C4×D12—32no—
130C4×D12—31no—
131C4×D12—31no—
132C4×D12—61no—
133#869—21no—
134#869C2×D311yescharacteristic
135C4×Dic6—21no—
136C4×Dic6C2×D311yescharacteristic
137C3×C4⋊C8—31no—
138C3×#102—32no—
139#835—31no—
140#835—31no—
141#835—61no—
142#832—32no—
143#832—32no—
144#821—32no—
145#818—32no—
146#815—32no—
147Dic3⋊C8—32no—
148#809—32no—
149#809—32no—
150#809—31no—
151#809—31no—
152#809—32no—
153#809—61no—
154#809C2×D312yes—
155#808—31no—
156#808—31no—
157#808—61no—
158#807—32no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)C2×D311yescharacteristic
161#803—32no—
162C4×C3⋊C8—31no—
163C4×C3⋊C8—31no—
164C4×C3⋊C8—61no—
165C22×C3⋊D3—21no—
166C22×C3×D3—22no—
167C32×Q8—21no—
168C32×Q8#4112yescomplemented
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—21no—
175C4⋊(C3⋊D3)—21no—
176C4⋊(C3⋊D3)—21no—
177C4×C3⋊D3—42no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3C2×D412yes—
180C2×C3×Dic3C2×D412yes—
181C3×D12—22no—
182C3×D12—22no—
183C3×D12—42no—
184C3×D12—81no—
185C3×Dic6—22no—
186C3×Dic6—42no—
187#626—44no—
188#626—82no—
189D3×Dic3—44no—
190C3⋊(C3⋊C8)—21no—
191C3⋊(C3⋊C8)—21no—
192C3×C3⋊C8—22no—
193#557—31no—
194#550—91no—
195#490—92no—
196#486—91no—
197#478—92no—
198#474—91no—
199#460—31no—
200#460—92no—
201#446—91no—
202#440—92no—
203C4×SD16—91no—
204C2×C3×Q8—21no—
205C2×C3×Q8—31no—
206C2×C3×Q8—61no—
207C2×C3×Q8C22×D311yescharacteristic
208C2×C3×Q8C22×D311yescharacteristic
209C2×C3×D4—32no—
210C2×C3×D4—61no—
211C2×C3×D4—61no—
212C2×#67—62no—
213C2×#67—62no—
214C22×Dic3—62no—
215#239—124no—
216#237—124no—
217C2×D12—21no—
218C2×D12—21no—
219C2×D12—31no—
220C2×D12—31no—
221C2×D12—61no—
222C2×D12—62no—
223C2×D12—62no—
224C2×D12C22×D312yes—
225C2×C4×D3—62no—
226C2×C4×D3—61no—
227C2×C4×D3—61no—
228C2×C4×D3—121no—
229C2×Dic6—21no—
230C2×Dic6#6711yescharacteristic
231C3×SD16—64no—
232C2×C3×C8—32no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—32no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—41no—
240C3×C4⋊C4—62no—
241C3×C4⋊C4—62no—
242C3×C4⋊C4—62no—
243C3×C4⋊C4—61no—
244C3×C4⋊C4C22×D311yescharacteristic
245C3×C4⋊C4C22×D311yescharacteristic
246C3×C42—21no—
247C3×C42—21no—
248C3×C42—21no—
249C3×C42—32no—
250C3×C42—41no—
251C3×C42—62no—
252C3×C42C22×D311yescharacteristic
253C3×C42C22×D311yescharacteristic
254#217—62no—
255#215—24no—
256#215—64no—
257#215—62no—
258#215—62no—
259(C2×D3)⋊C4—62no—
260(C2×D3)⋊C4—61no—
261(C2×D3)⋊C4—61no—
262(C2×D3)⋊C4—121no—
263C4⋊Dic3—21no—
264C4⋊Dic3—22no—
265C4⋊Dic3—22no—
266C4⋊Dic3—31no—
267C4⋊Dic3—31no—
268C4⋊Dic3—61no—
269C4⋊Dic3#6711yescharacteristic
270C4⋊Dic3C22×D312yes—
271Dic3⋊C4—22no—
272Dic3⋊C4#6712yes—
273C4×Dic3—22no—
274C4×Dic3C22×D312yes—
275C2×C3⋊C8—31no—
276C2×C3⋊C8—31no—
277C2×C3⋊C8—31no—
278C2×C3⋊C8—31no—
279C2×C3⋊C8—61no—
280C2×C3⋊C8—61no—
281C2×C3⋊C8C22×D312yes—
282C22×C32C22×D411yescharacteristic
283C2×C3⋊D3—41no—
284C2×C3⋊D3—41no—
285C2×C3⋊D3—41no—
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C32×C4—22no—
290C32×C4—21no—
291C32×C4—41no—
292C32×C4AGL(1,ℤ/8)12yes—
293C32×C4C2×#4111yescharacteristic
294C32×C42−1+411yescharacteristic
295C3⋊Dic3—41no—
296C3×Dic3—22no—
297C3×Dic3—22no—
298C3×Dic3—42no—
299C2×#41—181no—
300C2×SD16—32no—
301C2×SD16—91no—
302C4⋊Q8—31no—
303C4⋊Q8—61no—
304#127—31no—
305#127—92no—
306#125—32no—
307#125—62no—
308#121—181no—
309#121—182no—
310C4×Q8—31no—
311C4×Q8—32no—
312C4×Q8—61no—
313C4×Q8D3211yescharacteristic
314C4×D4—92no—
315C4×D4—91no—
316#107—92no—
317#106—91no—
318C4⋊C8—31no—
319C4⋊C8—92no—
320#103—91no—
321#102—32no—
322#102—92no—
323#102—92no—
324#102—92no—
325#102—91no—
326#97—92no—
327C4×C8—91no—
328C23×C3—62no—
329C22×D3—22no—
330C22×D3—61no—
331C22×D3—61no—
332C22×D3—121no—
333C3×Q8—21no—
334C3×Q8—21no—
335C3×Q8—22no—
336C3×Q8—41no—
337C3×Q8—62no—
338C3×Q8—122no—
339C3×Q8#23712yescomplemented
340C3×Q8#23912yescomplemented
341C3×D4—62no—
342C3×D4—62no—
343C3×D4—122no—
344C3×D4—241no—
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—32no—
353C2×C3×C4—32no—
354C2×C3×C4—41no—
355C2×C3×C4—41no—
356C2×C3×C4—62no—
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C23×D311yescharacteristic
362C2×C3×C4C23×D311yescharacteristic
363#67—124no—
364#67—242no—
365C2×Dic3—22no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—121no—
369C2×Dic3—124no—
370C2×Dic3C2×#6712yes—
371C2×Dic3C2×#6712yes—
372D12—22no—
373D12—22no—
374D12—42no—
375D12—62no—
376D12—61no—
377D12—61no—
378D12—61no—
379D12—61no—
380D12—81no—
381D12—121no—
382D12—124no—
383D12—242no—
384C4×D3—124no—
385C4×D3—122no—
386C4×D3—122no—
387C4×D3—242no—
388Dic6—22no—
389Dic6—42no—
390C3×C8—62no—
391C3⋊C8—22no—
392C3⋊C8—62no—
393C3⋊C8—61no—
394C3⋊C8—61no—
395C3⋊C8—61no—
396C3⋊C8—61no—
397C3⋊C8—121no—
398C2×C32#54811yescharacteristic
399C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
400C2×C32#57711yescharacteristic
401C3⋊D3—81no—
402C3×D3—82no—
403#41—364no—
404C2×Q8—31no—
405C2×Q8—61no—
406C2×Q8C2×D3211yescharacteristic
407C2×D4—32no—
408C2×D4—61no—
409C2×D4—61no—
410C2×D4—91no—
411C2×D4—182no—
412C2×D4—182no—
413C22×C4—182no—
414C22×C4—181no—
415SD16—64no—
416SD16—182no—
417C2×C8—32no—
418C2×C8—91no—
419C2×C8—91no—
420C4⋊C4—21no—
421C4⋊C4—31no—
422C4⋊C4—32no—
423C4⋊C4—32no—
424C4⋊C4—62no—
425C4⋊C4—62no—
426C4⋊C4—62no—
427C4⋊C4—61no—
428C4⋊C4—91no—
429C4⋊C4C2×D3211yescharacteristic
430C22⋊C4—182no—
431C22⋊C4—181no—
432C42—21no—
433C42—32no—
434C42—62no—
435C42C2×D3211yescharacteristic
436C22×C3—21no—
437C22×C3—122no—
438C22×C3—122no—
439C22×C3—122no—
440C22×C3C2×D3×D411yescharacteristic
441C22×C3C22×#6711yescharacteristic
442C2×D3—42no—
443C2×D3—42no—
444C2×D3—42no—
445C2×D3—122no—
446C2×D3—121no—
447C2×D3—121no—
448C2×D3—121no—
449C2×D3—121no—
450C2×D3—121no—
451C2×D3—121no—
452C2×D3—241no—
453C2×D3—241no—
454C3×C4—21no—
455C3×C4—22no—
456C3×C4—21no—
457C3×C4—22no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—22no—
461C3×C4—41no—
462C3×C4—42no—
463C3×C4—41no—
464C3×C4—41no—
465C3×C4—62no—
466C3×C4—62no—
467C3×C4—81no—
468C3×C4—122no—
469C3×C4#91412yes—
470C3×C4#94912yes—
471C3×C4C2×#23711yescharacteristic
472C3×C4C2×#23911yescharacteristic
473C3×C4#100711yescharacteristic
474C3×C4#101011yescharacteristic
475Dic3—22no—
476Dic3—22no—
477Dic3—42no—
478Dic3—121no—
479Dic3—121no—
480Dic3—241no—
481C32#336811yescharacteristic, complemented, Sylow
482C23—62no—
483C23—181no—
484Q8—21no—
485Q8—62no—
486Q8—122no—
487Q8#379612yescomplemented
488D4—62no—
489D4—62no—
490D4—122no—
491D4—181no—
492D4—181no—
493D4—241no—
494D4—364no—
495D4—722no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—32no—
499C2×C4—32no—
500C2×C4—62no—
501C2×C4—181no—
502C2×C4—364no—
503C2×C4—362no—
504C2×C4D3×#6711yescharacteristic
505C2×C4D3×#6711yescharacteristic
506C2×C4C22×D3211yescharacteristic
507C8—62no—
508C8—181no—
509C8—181no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—242no—
514C2×C3#559811yescharacteristic
515C2×C3C2×#91411yescharacteristic
516C2×C3#577511yescharacteristic
517C2×C3#581711yescharacteristic
518C2×C3C2×#94911yescharacteristic
519C2×C3#583711yescharacteristic
520D3—82no—
521D3—242no—
522D3—241no—
523D3—241no—
524C22—122no—
525C22—122no—
526C22—122no—
527C22—361no—
528C22—361no—
529C22—361no—
530C22C2×D3×#6711yescharacteristic
531C4—22no—
532C4—21no—
533C4—41no—
534C4—62no—
535C4—62no—
536C4—122no—
537C4—361no—
538C4#6393912yes—
539C4C2×#379611yescharacteristic
540C4#6429711yescharacteristic
541C3—21no—
542C3#8037111yescharacteristic, complemented
543C3#8369011yescharacteristic, complemented
544C2—242no—
545C2—721no—
546C2#1059490011yescharacteristic
547C2C2×#6393911yescharacteristic
548C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10593900C2
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. C4×#3755C2semidirect
4. C3×#5027C2semidirect
5. #10591617C2semidirect
6. #10591566C2semidirect
7. #10590550C2semidirect
8. #10590469C2semidirect
9. #10590313C2semidirect
10. #10590277C2semidirect
11. #10590259C2semidirect
46. #5570D3semidirect
56. #5027D3semidirect
168. C32×Q8#41semidirect
339. C3×Q8#237semidirect
340. C3×Q8#239semidirect
481. C32#3368semidirect
487. Q8#3796semidirect
542. C3#80371semidirect
543. C3#83690semidirect

Maximal subgroups

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

subgroupindex
C3×#55702
#105939002
C4×#37552
C3×#50272
#105916172
#105915662
#105905502
#105904692
#105903132
#105902772
#105902592
#836903
#803713