Finite Group Databasebeta

← #11897560

Subgroups — #11897560

Order 1152.

888 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C3×#5579C211yesmaximal, characteristic, complemented
3C3×#5024C211yesmaximal, characteristic, complemented
4#10590346C212yesmaximal
5C4×#3714C211yesmaximal, characteristic
6#10590308C212yesmaximal, complemented
7#10590306C212yesmaximal, complemented
8#10590303C211yesmaximal, characteristic, complemented
9#10590300C211yesmaximal, characteristic, complemented
10#10590272C211yesmaximal, characteristic, complemented
11#10590268C212yesmaximal, complemented
12#83630—31nomaximal
13#79975—31nomaximal
14C2×Q8×C3⋊D3—21no—
15C32×C4×Q8C2211yescharacteristic
16#64106—21no—
17#64106—22no—
18C4×C4⋊(C3⋊D3)C2211yescharacteristic
19C4×C4⋊(C3⋊D3)C2212yes—
20#64078C2212yes—
21#64078C2211yescharacteristic
22C3×#946—21no—
23C3×#896—22no—
24C3×D3×C4⋊C4—21no—
25C3×C4×D12C2212yes—
26C3×C4×D12C2211yescharacteristic
27C3×#870C2212yes—
28C3×#869C2211yescharacteristic
29C2×#3714C2211yescharacteristic
30C3×C4⋊(C3⋊C8)C2212yes—
31C3×C4⋊(C3⋊C8)C2211yescharacteristic
32C3×#803C2212yes—
33C3×C4×C3⋊C8C2211yescharacteristic
34#63575C2212yes—
35#63575C2211yescharacteristic
36#63573C2212yes—
37#63573C2212yes—
38#63573C2212yes—
39#63564C2212yes—
40#63564C2211yescharacteristic
41#63563C2211yescharacteristic
42#63563C2212yes—
43C3×#554—31no—
44#5579D311yescharacteristic, complemented
45Q8×D12—31no—
46Q8×D12—31no—
47Q8×D12—61no—
48C3×#446—31no—
49#5084—31no—
50#5080—31no—
51#5066—32no—
52#5064—32no—
53#5024D311yescharacteristic, complemented
54#5014—32no—
55C4×#213—31no—
56#5008—32no—
57#5007—31no—
58#4847—32no—
59#4846—31no—
60#4842—32no—
61#4842—31no—
62#4711—32no—
63#4702—32no—
64C4×D24—31no—
65#4680—31no—
66C2×C32×Q8D411yescharacteristic
67Q8×C3⋊D3—44no—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3—21no—
71C2×#634—22no—
72C2×#634—21no—
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—21no—
75C2×C3×C4×D3—22no—
76C2×C3×Dic6—21no—
77C32×C4⋊C4D411yescharacteristic
78C32×C4⋊C4D412yes—
79C32×C42C2311yescharacteristic
80C32×C42C2312yes—
81#3752—22no—
82#3752—21no—
83C4⋊(C3⋊Dic3)—22no—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86C4⋊(C3⋊Dic3)C2312yes—
87C3×(C2×D3)⋊C4—21no—
88C3×(C2×D3)⋊C4—22no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4—22no—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97#3714Q814yescomplemented
98#3384—91noSylow
99C2×D3×Q8—62no—
100C2×D3×Q8—61no—
101C2×D3×Q8—61no—
102C3×C4⋊Q8—31no—
103C3×#125—32no—
104C3×C22⋊Q8—61no—
105C3×C22⋊Q8—62no—
106C3×C4×Q8—21no—
107C3×C4×Q8C2×D311yescharacteristic
108C3×C4×Q8C2×D311yescharacteristic
109C3×C4×D4—31no—
110C3×C4×D4—32no—
111C2×C3×C4⋊C4—61no—
112#946—21no—
113C2×#213—31no—
114C2×D24—31no—
115#897—62no—
116#897—64no—
117#897—61no—
118#897—62no—
119#897—61no—
120#897—62no—
121#896—22no—
122D3×C4⋊C4—21no—
123C4×D12—31no—
124C4×D12—32no—
125C4×D12—31no—
126C4×D12—32no—
127C4×D12—61no—
128C4×D12—62no—
129C4×D12C2×D311yescharacteristic
130C4×D12C2×D312yes—
131#870C2×D312yes—
132#869—31no—
133#869—32no—
134#869—31no—
135#869—32no—
136#869—61no—
137#869—62no—
138#869C2×D311yescharacteristic
139C3×C4⋊C8—31no—
140C3×C4⋊C8—32no—
141C3×#97—32no—
142C3×C4×C8—31no—
143#832—32no—
144#832—31no—
145#821—31no—
146#821—32no—
147#821—31no—
148#821—32no—
149#818—31no—
150#818—32no—
151#817—32no—
152#817—32no—
153#817—32no—
154#809—31no—
155#809—32no—
156#808—32no—
157#808—32no—
158#808—32no—
159#807—32no—
160#807—31no—
161C4⋊(C3⋊C8)C2×D311yescharacteristic
162C4⋊(C3⋊C8)C2×D312yes—
163#803C2×D312yes—
164C4×C3⋊C8C2×D311yescharacteristic
165C22×C3⋊D3—21no—
166C22×C3×D3—21no—
167C32×Q8—22no—
168C2×C32×C4C2×D412yes—
169C2×C32×C4C2×D412yes—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—22no—
175C4⋊(C3⋊D3)—21no—
176C4⋊(C3⋊D3)C2×Q812yes—
177C4×C3⋊D3—44no—
178C4×C3⋊D3—42no—
179#634—44no—
180#634—42no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—22no—
183C3×D12—21no—
184C3×D12C2×Q812yescomplemented
185C3×C4×D3—42no—
186C3×C4×D3—82no—
187C3×Dic6—81no—
188C3×C3⋊C8—21no—
189C3×C3⋊C8—22no—
190C3×C3⋊C8C2×Q812yescomplemented
191#554—31no—
192D4×Q8—91no—
193#501—92no—
194#498—91no—
195#478—92no—
196#476—92no—
197#476—91no—
198#474—91no—
199#446—31no—
200#442—92no—
201C4×D8—91no—
202C2×C3×Q8—21no—
203C2×C3×Q8—61no—
204C2×C3×Q8D1211yescharacteristic
205C2×C3×Q8#6711yescharacteristic
206C2×C3×D4—31no—
207C22×C3×C4—61no—
208C22×C3×C4—62no—
209D3×Q8—128no—
210D3×Q8—124no—
211D3×Q8—124no—
212C2×D12—31no—
213C2×D12—31no—
214C2×D12—61no—
215C2×D12C22×D311yescharacteristic
216C2×C4×D3—21no—
217C2×C4×D3—22no—
218C2×C4×D3—64no—
219C2×C4×D3—62no—
220C2×C4×D3—62no—
221C2×C4×D3—61no—
222C2×C4×D3—62no—
223C2×C4×D3—61no—
224C2×Dic6—21no—
225C2×Dic6—64no—
226C2×Dic6—62no—
227C2×Dic6—62no—
228C2×Dic6—61no—
229C2×Dic6—62no—
230C2×Dic6—61no—
231C2×C3×C8—31no—
232C2×C3×C8—31no—
233C2×C3×C8—32no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—22no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—32no—
238C3×C4⋊C4—62no—
239C3×C4⋊C4—62no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4D1211yescharacteristic
242C3×C4⋊C4D1212yes—
243C3×C4⋊C4#6711yescharacteristic
244C3×C4⋊C4#6712yes—
245C3×C22⋊C4—61no—
246C3×C22⋊C4—62no—
247C3×C42—21no—
248C3×C42—22no—
249C3×C42C22×D311yescharacteristic
250C3×C42C22×D312yes—
251C3×C42C22×D311yescharacteristic
252C3×C42C22×D312yes—
253#213—34no—
254(C2×D3)⋊C4—21no—
255(C2×D3)⋊C4—22no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—61no—
259(C2×D3)⋊C4—62no—
260(C2×D3)⋊C4—62no—
261(C2×D3)⋊C4—61no—
262C4⋊Dic3—21no—
263C4⋊Dic3—32no—
264C4⋊Dic3—31no—
265C4⋊Dic3—32no—
266C4⋊Dic3—31no—
267C4⋊Dic3—61no—
268C4⋊Dic3—62no—
269C4⋊Dic3—62no—
270C4⋊Dic3—64no—
271C4⋊Dic3—61no—
272C4⋊Dic3—62no—
273C4⋊Dic3—62no—
274C4⋊Dic3—61no—
275C4⋊Dic3C22×D312yes—
276C4⋊Dic3C22×D311yescharacteristic
277Dic3⋊C4—22no—
278Dic3⋊C4—22no—
279C2×C3⋊C8C22×D311yescharacteristic
280C2×C3⋊C8C22×D312yes—
281C2×C3⋊C8C22×D311yescharacteristic
282D24—34no—
283C22×C32C22×D411yescharacteristic
284C2×C3⋊D3—22no—
285C2×C3⋊D3—41no—
286C2×C3⋊D3—41no—
287C2×C3×D3—22no—
288C2×C3×D3—41no—
289C2×C3×D3—41no—
290C32×C4—22no—
291C32×C4—21no—
292C32×C4—22no—
293C32×C4AGL(1,ℤ/8)12yes—
294C32×C4C22×Q811yescharacteristic
295C32×C42−1+411yescharacteristic
296C3⋊Dic3—41no—
297C3⋊Dic3—42no—
298C3×Dic3—41no—
299C3×Dic3—42no—
300C22×Q8—181no—
301C2×D8—91no—
302C4⋊Q8—31no—
303C4⋊Q8—91no—
304C4⋊Q8—92no—
305#125—32no—
306C22⋊Q8—61no—
307C22⋊Q8—62no—
308C22⋊Q8—181no—
309C22⋊Q8—182no—
310C4×Q8D3211yescharacteristic
311C4×D4—31no—
312C4×D4—32no—
313C4×D4—91no—
314C4×D4—92no—
315C2×C4⋊C4—61no—
316#107—91no—
317#107—92no—
318#106—92no—
319#106—92no—
320#106—92no—
321C4⋊C8—31no—
322C4⋊C8—32no—
323#102—91no—
324#102—92no—
325#102—91no—
326#102—92no—
327#97—32no—
328C4×C8—31no—
329C23×C3—61no—
330C22×D3—21no—
331C22×D3—62no—
332C22×D3—61no—
333C22×D3—61no—
334C3×Q8—24no—
335C3×Q8—22no—
336C3×Q8—22no—
337C3×Q8—241no—
338C3×D4—32no—
339C3×D4—61no—
340C2×C3×C4—21no—
341C2×C3×C4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—22no—
345C2×C3×C4—61no—
346C2×C3×C4—62no—
347C2×C3×C4—122no—
348C2×C3×C4—242no—
349C2×C3×C4C2×D1211yescharacteristic
350C2×C3×C4C2×D1212yes—
351C2×C3×C4C2×D1212yes—
352C2×C3×C4C2×D1211yescharacteristic
353C2×C3×C4C2×#6712yes—
354C2×C3×C4C2×#6712yes—
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359C2×Dic3—21no—
360C2×Dic3—22no—
361C2×Dic3—64no—
362C2×Dic3—62no—
363C2×Dic3—61no—
364C2×Dic3—62no—
365C2×Dic3—61no—
366C2×Dic3—62no—
367D12—21no—
368D12—32no—
369D12—32no—
370D12—62no—
371D12—62no—
372D12—61no—
373D12—61no—
374D12D3×Q812yescomplemented
375C4×D3—42no—
376C4×D3—82no—
377C4×D3—128no—
378C4×D3—124no—
379C4×D3—124no—
380C4×D3—124no—
381C4×D3—122no—
382C4×D3—122no—
383Dic6—81no—
384Dic6—128no—
385Dic6—124no—
386Dic6—124no—
387Dic6—124no—
388Dic6—122no—
389Dic6—122no—
390C3×C8—32no—
391C3×C8—61no—
392C3×C8—62no—
393C3⋊C8—21no—
394C3⋊C8—22no—
395C3⋊C8D3×Q812yescomplemented
396C2×C32D4×Q811yescharacteristic
397C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
398C2×C32#57711yescharacteristic
399C3⋊D3—42no—
400C3×D3—42no—
401C2×Q8—61no—
402C2×Q8—182no—
403C2×Q8—181no—
404C2×Q8—364no—
405C2×Q8#62611yescharacteristic
406C2×D4—31no—
407C2×D4—91no—
408C22×C4—61no—
409C22×C4—62no—
410C22×C4—182no—
411C22×C4—181no—
412D8—94no—
413C2×C8—31no—
414C2×C8—31no—
415C2×C8—32no—
416C4⋊C4—32no—
417C4⋊C4—31no—
418C4⋊C4—62no—
419C4⋊C4—61no—
420C4⋊C4—62no—
421C4⋊C4—91no—
422C4⋊C4—92no—
423C4⋊C4—181no—
424C4⋊C4—182no—
425C4⋊C4#62611yescharacteristic
426C4⋊C4#62612yes—
427C22⋊C4—61no—
428C22⋊C4—62no—
429C22⋊C4—181no—
430C22⋊C4—182no—
431C42C2×D3211yescharacteristic
432C42C2×D3212yes—
433C22×C3—21no—
434C22×C3—62no—
435C22×C3—121no—
436C22×C3—121no—
437C22×C3C22×D1211yescharacteristic
438C22×C3C22×#6711yescharacteristic
439C2×D3—22no—
440C2×D3—41no—
441C2×D3—41no—
442C2×D3—64no—
443C2×D3—62no—
444C2×D3—62no—
445C2×D3—122no—
446C2×D3—122no—
447C2×D3—121no—
448C2×D3—121no—
449C2×D3—121no—
450C2×D3—121no—
451C3×C4—24no—
452C3×C4—22no—
453C3×C4—22no—
454C3×C4—21no—
455C3×C4—22no—
456C3×C4—21no—
457C3×C4—22no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—22no—
461C3×C4—42no—
462C3×C4—41no—
463C3×C4—121no—
464C3×C4—122no—
465C3×C4#90812yes—
466C3×C4#94912yes—
467C3×C4C2×D3×Q811yescharacteristic
468C3×C4C2×D3×Q811yescharacteristic
469C3×C4#100711yescharacteristic
470C3×C4#101011yescharacteristic
471Dic3—41no—
472Dic3—42no—
473Dic3—124no—
474Dic3—122no—
475Dic3—121no—
476Dic3—122no—
477Dic3—121no—
478Dic3—122no—
479C32#338411yescharacteristic, complemented, Sylow
480C23—61no—
481C23—181no—
482Q8—22no—
483Q8—241no—
484Q8—364no—
485Q8—362no—
486D4—32no—
487D4—61no—
488D4—92no—
489D4—181no—
490C2×C4—61no—
491C2×C4—62no—
492C2×C4—122no—
493C2×C4—182no—
494C2×C4—181no—
495C2×C4—242no—
496C2×C4—364no—
497C2×C4—362no—
498C2×C4C2×#62611yescharacteristic
499C2×C4C2×#62612yes—
500C2×C4C2×#62612yes—
501C2×C4C2×#62611yescharacteristic
502C2×C4C22×D3211yescharacteristic
503C8—32no—
504C8—61no—
505C8—62no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—122no—
510C2×C3Q8×D1211yescharacteristic
511C2×C3C2×#90811yescharacteristic
512C2×C3#575111yescharacteristic
513C2×C3Q8×#6711yescharacteristic
514C2×C3C2×#94911yescharacteristic
515C2×C3#583611yescharacteristic
516D3—42no—
517D3—124no—
518D3—122no—
519D3—122no—
520C22—62no—
521C22—121no—
522C22—121no—
523C22—182no—
524C22—361no—
525C22—361no—
526C22C22×#62611yescharacteristic
527C4—22no—
528C4—21no—
529C4—22no—
530C4—122no—
531C4—121no—
532C4—362no—
533C4—361no—
534C4#6382512yes—
535C4#6431511yescharacteristic
536C4D32×Q811yescharacteristic
537C3—21no—
538C3#7997511yescharacteristic, complemented
539C3#8363011yescharacteristic, complemented
540C2—122no—
541C2—362no—
542C2C2×#6382511yescharacteristic
543C2Q8×#62611yescharacteristic
544C2#1059544711yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
hypercenterC4×Q8D32
hypocenterC32#3384
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. Q8×C4⋊(C3⋊D3)C2semidirect
2. C3×#5579C2semidirect
3. C3×#5024C2semidirect
6. #10590308C2semidirect
7. #10590306C2semidirect
8. #10590303C2semidirect
9. #10590300C2semidirect
10. #10590272C2semidirect
11. #10590268C2semidirect
44. #5579D3semidirect
53. #5024D3semidirect
97. #3714Q8semidirect
184. C3×D12C2×Q8semidirect
190. C3×C3⋊C8C2×Q8semidirect
374. D12D3×Q8semidirect
395. C3⋊C8D3×Q8semidirect
479. C32#3384semidirect
538. C3#79975semidirect
539. C3#83630semidirect

Maximal subgroups

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

subgroupindex
Q8×C4⋊(C3⋊D3)2
C3×#55792
C3×#50242
#105903462
C4×#37142
#105903082
#105903062
#105903032
#105903002
#105902722
#105902682
#836303
#799753