Finite Group Databasebeta

← #11895422

Subgroups — #11895422

Order 1152.

845 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5553C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3C4×#3754C211yesmaximal, characteristic, complemented
4C3×#5008C211yesmaximal, characteristic, complemented
5#10591487C212yesmaximal, complemented
6#10591439C212yesmaximal, complemented
7#10590558C212yesmaximal, complemented
8#10590479C212yesmaximal, complemented
9#10590377C211yesmaximal, characteristic, complemented
10#10590277C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12#83586—31nomaximal
13#81090—31nomaximal
14C2×C3×#235—21no—
15C32×C4×D4C2211yescharacteristic
16C2×#3754C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C3×#940C2212yes—
19C3×#930—21no—
20C3×#893C2212yes—
21C3×#884—22no—
22C3×#874C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63919—21no—
26#63918C2212yes—
27#63844C2212yes—
28#63843—21no—
29#63839—22no—
30C2×#3716C2212yes—
31#63659C2211yescharacteristic
32#63637C2211yescharacteristic
33#63635C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#832C2212yes—
36C3×#808C2212yes—
37C3×C4⋊(C3⋊C8)C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63563C2212yes—
40#63562C2212yes—
41#63562C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#550—31no—
44#5722—31no—
45Q8×Dic6—31no—
46#5553D311yescharacteristic
47C3×#476—31no—
48#5088—31no—
49#5075—32no—
50#5075—31no—
51#5070—31no—
52#5070—32no—
53Q8×C3⋊C8—31no—
54C4×#214—31no—
55C4×#214—31no—
56C4×#214—32no—
57C4×#214—61no—
58#5008—32no—
59#5008D311yescharacteristic, complemented
60#4870—32no—
61#4852—32no—
62#4848—31no—
63#4830—31no—
64#4762—32no—
65#4760—32no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634C2311yescharacteristic
69C2×C3×#67—22no—
70C2×C3×#67—22no—
71C3×#235—44no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12C2312yes—
75C2×C3×C4×D3—22no—
76C2×C3×Dic6—21no—
77C2×C3×Dic6D411yescharacteristic
78C2×#627—22no—
79C32×C4⋊C4C2311yescharacteristic
80C32×C22⋊C4—21no—
81C32×C42C2311yescharacteristic
82#3754—22no—
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84#3750—21no—
85C4×C3⋊Dic3—21no—
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88C3×(C2×D3)⋊C4—22no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3D411yescharacteristic
91C3×C4⋊Dic3C2312yes—
92C3×Dic3⋊C4D412yes—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8C2312yes—
95#3724—22no—
96Dic3⋊Dic3—22no—
97Dic32—22no—
98#3716—24no—
99#3362—91noSylow
100C2×C3×#41—61no—
101C2×#235—21no—
102C3×C4⋊Q8—31no—
103C3×#127—32no—
104C3×#127—31no—
105C3×#121—62no—
106C3×#121—61no—
107C3×C4×Q8—31no—
108C3×C4×D4—21no—
109C3×C4×D4—32no—
110C3×C4×D4C2×D311yescharacteristic
111C3×C4×D4C2×D311yescharacteristic
112Q8×Dic3—61no—
113#944—62no—
114#940C2×D312yes—
115C2×#214—31no—
116C2×#214—31no—
117C2×#214—32no—
118C2×#214—61no—
119#930—21no—
120C2×#204—32no—
121#893C2×D312yes—
122#888—32no—
123#888—61no—
124#888—62no—
125#888—61no—
126#887—32no—
127#887—61no—
128#884—22no—
129#874C2×D311yescharacteristic
130#869—32no—
131#869C2×D311yescharacteristic
132C4×Dic6—31no—
133C4×Dic6—31no—
134C4×Dic6—32no—
135C4×Dic6—61no—
136C4×Dic6C2×D311yescharacteristic
137C3×#106—32no—
138C3×C4⋊C8—31no—
139C3×#102—32no—
140#832—31no—
141#832—31no—
142#832—32no—
143#832—32no—
144#832—32no—
145#832—61no—
146#832C2×D312yes—
147#821—32no—
148Dic3⋊C8—32no—
149C8×Dic3—32no—
150#810—31no—
151#810—31no—
152#810—61no—
153#809—32no—
154#809—32no—
155#808—31no—
156#808—31no—
157#808—61no—
158#808C2×D312yes—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)C2×D311yescharacteristic
161C4×C3⋊C8—31no—
162C4×C3⋊C8—31no—
163C4×C3⋊C8—32no—
164C4×C3⋊C8—61no—
165C23×C32—21no—
166C22×C3×D3—22no—
167C32×D4—21no—
168C32×D4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—42no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176#634—21no—
177#634#4112yescomplemented
178C3×#67—44no—
179C3×#67—82no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3C2×D412yes—
182C2×C3×Dic3C2×D412yes—
183C3×D12—22no—
184C3×D12—22no—
185C3×D12—42no—
186C3×D12—81no—
187C3×C4×D3—44no—
188C3×Dic6—81no—
189C3×Dic6SD1614yescomplemented
190#627—82no—
191C3⋊(C3⋊C8)—21no—
192C3⋊(C3⋊C8)—21no—
193C3×C3⋊C8—22no—
194Q82—91no—
195#550—31no—
196#486—92no—
197#486—91no—
198#476—31no—
199#476—92no—
200#460—92no—
201#460—91no—
202C8×Q8—91no—
203C4×SD16—92no—
204C4×SD16—91no—
205C3×#41—124no—
206C2×C3×Q8—31no—
207C2×C3×Q8—61no—
208C2×C3×D4—21no—
209C2×C3×D4—32no—
210C2×C3×D4—62no—
211C2×C3×D4—62no—
212C2×C3×D4—61no—
213C2×C3×D4—61no—
214C2×C3×D4C22×D311yescharacteristic
215C2×C3×D4C22×D311yescharacteristic
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—41no—
219C22×C3×C4—62no—
220C2×#67—22no—
221C2×#67—22no—
222#235—44no—
223C2×D12—21no—
224C2×D12—21no—
225C2×D12C22×D312yes—
226C2×C4×D3—22no—
227C2×Dic6—21no—
228C2×Dic6—31no—
229C2×Dic6—31no—
230C2×Dic6—61no—
231C2×Dic6—62no—
232C2×Dic6—62no—
233C2×Dic6#6711yescharacteristic
234C2×C3×C8—32no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—32no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4C22×D311yescharacteristic
241C3×C4⋊C4C22×D311yescharacteristic
242C3×C22⋊C4—21no—
243C3×C22⋊C4—21no—
244C3×C22⋊C4—41no—
245C3×C22⋊C4—62no—
246C3×C42—21no—
247C3×C42—32no—
248C3×C42C22×D311yescharacteristic
249C3×C42C22×D311yescharacteristic
250#214—64no—
251#214—62no—
252#214—62no—
253#214—64no—
254(C2×D3)⋊C4—22no—
255C4⋊Dic3—21no—
256C4⋊Dic3—31no—
257C4⋊Dic3—31no—
258C4⋊Dic3—61no—
259C4⋊Dic3—62no—
260C4⋊Dic3#6711yescharacteristic
261C4⋊Dic3C22×D312yes—
262Dic3⋊C4—62no—
263Dic3⋊C4—61no—
264Dic3⋊C4—61no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4—121no—
268Dic3⋊C4#6712yes—
269C4×Dic3—62no—
270C4×Dic3—61no—
271C4×Dic3—61no—
272C4×Dic3—62no—
273C4×Dic3—121no—
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—
282#204—64no—
283C22×C32—41no—
284C22×C32—41no—
285C22×C32—41no—
286C22×C32C22×D411yescharacteristic
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C2×C3×D3—42no—
290C32×C4—21no—
291C32×C4—41no—
292C32×C4C2×SD1612yes—
293C32×C4C2×#4111yescharacteristic
294C32×C42−1+411yescharacteristic
295C3⋊Dic3—22no—
296C3⋊Dic3—41no—
297C3×Dic3—22no—
298C3×Dic3—42no—
299C3×Dic3C2×SD1614yes—
300C2×#41—61no—
301C2×SD16—92no—
302C2×SD16—91no—
303C4⋊Q8—31no—
304C4⋊Q8—92no—
305C4⋊Q8—181no—
306C4⋊Q8—182no—
307#127—32no—
308#127—31no—
309#121—62no—
310#121—61no—
311C4×Q8—31no—
312C4×Q8—92no—
313C4×Q8—91no—
314C4×Q8—181no—
315C4×D4—32no—
316C4×D4D3211yescharacteristic
317#106—32no—
318#106—91no—
319C4⋊C8—31no—
320C4⋊C8—92no—
321#103—91no—
322#102—32no—
323#102—92no—
324#102—92no—
325#102—92no—
326#102—91no—
327C4×C8—92no—
328C4×C8—91no—
329C23×C3—21no—
330C23×C3—21no—
331C23×C3—41no—
332C23×C3—62no—
333C22×D3—22no—
334C3×Q8—34no—
335C3×Q8—241no—
336C3×D4—22no—
337C3×D4—21no—
338C3×D4—21no—
339C3×D4—21no—
340C3×D4—21no—
341C3×D4—41no—
342C3×D4—62no—
343C3×D4—62no—
344C3×D4—124no—
345C3×D4—122no—
346C3×D4—241no—
347C3×D4—242no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—32no—
354C2×C3×C4—32no—
355C2×C3×C4—41no—
356C2×C3×C4—42no—
357C2×C3×C4—42no—
358C2×C3×C4—62no—
359C2×C3×C4—82no—
360C2×C3×C4—124no—
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367#67—44no—
368#67—82no—
369C2×Dic3—22no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—121no—
375C2×Dic3—121no—
376C2×Dic3C2×#6712yes—
377C2×Dic3C2×#6712yes—
378D12—22no—
379D12—22no—
380D12—42no—
381D12—81no—
382C4×D3—44no—
383Dic6—32no—
384Dic6—32no—
385Dic6—62no—
386Dic6—61no—
387Dic6—61no—
388Dic6—81no—
389Dic6—121no—
390Dic6—242no—
391Dic6—242no—
392Dic6#21414yescomplemented
393C3×C8—62no—
394C3⋊C8—22no—
395C3⋊C8—62no—
396C3⋊C8—61no—
397C3⋊C8—61no—
398C3⋊C8—61no—
399C3⋊C8—61no—
400C3⋊C8—121no—
401C2×C32—81no—
402C2×C32#54811yescharacteristic
403C2×C32C22×SD1611yescharacteristic
404C2×C32#57611yescharacteristic
405C3×D3—82no—
406#41—124no—
407C2×Q8—31no—
408C2×Q8—61no—
409C2×Q8—91no—
410C2×Q8—182no—
411C2×D4—32no—
412C2×D4—62no—
413C2×D4—62no—
414C2×D4—61no—
415C2×D4—61no—
416C2×D4C2×D3211yescharacteristic
417C22×C4—21no—
418C22×C4—62no—
419SD16—184no—
420SD16—182no—
421C2×C8—32no—
422C2×C8—91no—
423C2×C8—91no—
424C4⋊C4—32no—
425C4⋊C4—31no—
426C4⋊C4—32no—
427C4⋊C4—61no—
428C4⋊C4—91no—
429C4⋊C4—182no—
430C4⋊C4—182no—
431C4⋊C4—181no—
432C4⋊C4C2×D3211yescharacteristic
433C22⋊C4—21no—
434C22⋊C4—62no—
435C42—32no—
436C42—182no—
437C42—181no—
438C42C2×D3211yescharacteristic
439C22×C3—21no—
440C22×C3—42no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—41no—
447C22×C3—81no—
448C22×C3—81no—
449C22×C3—122no—
450C22×C3—122no—
451C22×C3—122no—
452C22×C3C2×D3×D411yescharacteristic
453C22×C3C22×#6711yescharacteristic
454C2×D3—42no—
455C2×D3—42no—
456C2×D3—42no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—22no—
462C3×C4—34no—
463C3×C4—41no—
464C3×C4—41no—
465C3×C4—41no—
466C3×C4—62no—
467C3×C4—81no—
468C3×C4—122no—
469C3×C4D3×SD1612yes—
470C3×C4C2×#21412yes—
471C3×C4#100711yescharacteristic
472C3×C4D3×#4111yescharacteristic
473C3×C4D3×#4111yescharacteristic
474C3×C4#101011yescharacteristic
475Dic3—22no—
476Dic3—42no—
477Dic3—62no—
478Dic3—62no—
479Dic3—122no—
480Dic3—121no—
481Dic3—121no—
482Dic3—241no—
483Dic3C2×#21414yes—
484C32#336211yescharacteristic, complemented, Sylow
485C23—21no—
486C23—62no—
487Q8—34no—
488Q8—92no—
489Q8—181no—
490Q8—241no—
491Q8—722no—
492D4—21no—
493D4—21no—
494D4—62no—
495D4—62no—
496D4—124no—
497D4—122no—
498D4—241no—
499D4—242no—
500C2×C4—21no—
501C2×C4—32no—
502C2×C4—32no—
503C2×C4—42no—
504C2×C4—62no—
505C2×C4—124no—
506C2×C4—181no—
507C2×C4—181no—
508C2×C4D3×#6711yescharacteristic
509C2×C4D3×#6711yescharacteristic
510C2×C4C22×D3211yescharacteristic
511C8—62no—
512C8—181no—
513C8—181no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—82no—
518C2×C3—81no—
519C2×C3—81no—
520C2×C3—242no—
521C2×C3#563311yescharacteristic
522C2×C3C2×D3×SD1611yescharacteristic
523C2×C3#577411yescharacteristic
524C2×C3C22×#21411yescharacteristic
525C2×C3#583111yescharacteristic
526C2×C3#583511yescharacteristic
527D3—82no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—122no—
532C22—122no—
533C22—122no—
534C22C2×D3×#6711yescharacteristic
535C4—21no—
536C4—34no—
537C4—41no—
538C4—62no—
539C4—122no—
540C4—182no—
541C4—361no—
542C4D3×#21412yes—
543C4#6429711yescharacteristic
544C4#6430611yescharacteristic
545C3—21no—
546C3#8109011yescharacteristic, complemented
547C3#8358611yescharacteristic, complemented
548C2—81no—
549C2—242no—
550C2#1059483011yescharacteristic
551C2C2×D3×#21411yescharacteristic
552C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5553C2
hypercenterC4×D4D32
hypocenterC32#3362
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10593856C2semidirect
3. C4×#3754C2semidirect
4. C3×#5008C2semidirect
5. #10591487C2semidirect
6. #10591439C2semidirect
7. #10590558C2semidirect
8. #10590479C2semidirect
9. #10590377C2semidirect
10. #10590277C2semidirect
11. #10590250C2semidirect
59. #5008D3semidirect
177. #634#41semidirect
189. C3×Dic6SD16semidirect
392. Dic6#214semidirect
484. C32#3362semidirect
546. C3#81090semidirect
547. C3#83586semidirect

Maximal subgroups

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

subgroupindex
C3×#55532
#105938562
C4×#37542
C3×#50082
#105914872
#105914392
#105905582
#105904792
#105903772
#105902772
#105902502
#835863
#810903