Finite Group Databasebeta

← #11895418

Subgroups — #11895418

Order 1152.

843 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5718C211yesmaximal, characteristic
2Dic62C211yesmaximal, characteristic, complemented
3#10592769C211yesmaximal, characteristic, complemented
4C3×#5075C211yesmaximal, characteristic, complemented
5#10591487C212yesmaximal, complemented
6#10591438C212yesmaximal, complemented
7Dic3×#214C212yesmaximal, complemented
8#10591408C212yesmaximal, complemented
9C4×#3715C211yesmaximal, characteristic, complemented
10#10590268C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12#83586—31nomaximal
13#80369—31nomaximal
14C2×C3×#237—21no—
15C32×#127C2211yescharacteristic
16#64078C2211yescharacteristic
17C3×#940C2212yes—
18C3×#939—22no—
19C3×#938—21no—
20C3×D4×Dic3C2212yes—
21C2×C3×#214C2212yes—
22C3×C4×D12C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63918—21no—
26#63918C2212yes—
27Dic3×Dic6—21no—
28Dic3×Dic6C2212yes—
29#63840—22no—
30C2×#3715C2211yescharacteristic
31#63659C2212yes—
32#63659C2212yes—
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#832C2212yes—
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36#63574C2211yescharacteristic
37#63573C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63565C2211yescharacteristic
40#63563C2212yes—
41#63562C2211yescharacteristic
42Dic3×C3⋊C8C2212yes—
43C3×#550—31no—
44#5718D311yescharacteristic
45Q8×Dic6—31no—
46Q8×Dic6—31no—
47C3×#460—31no—
48#5163—32no—
49Dic3×SD16—32no—
50#5075—32no—
51#5075D311yescharacteristic, complemented
52#5070—31no—
53#5070—31no—
54#5070—32no—
55#5070—61no—
56C4×#215—31no—
57Q8×C3⋊C8—31no—
58C4×#214—32no—
59C4×#214—31no—
60#5008—32no—
61#5008—31no—
62#4842—31no—
63#4830—31no—
64#4761—32no—
65#4760—32no—
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4C2312yes—
69C2×#634—21no—
70C2×C3×#67—22no—
71C2×C3×#67—22no—
72C22×C3×Dic3—22no—
73C3×#237—44no—
74C2×C3×D12C2311yescharacteristic
75C2×C3×C4×D3—21no—
76C2×C3×Dic6D411yescharacteristic
77C2×C3×Dic6C2311yescharacteristic
78C2×#627—22no—
79C32×C42C2311yescharacteristic
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)C2312yes—
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C3×#217—22no—
85C3×#214—24no—
86C3×(C2×D3)⋊C4—21no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2311yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—21no—
91C3×Dic3⋊C4D412yes—
92C3×C4×Dic3—21no—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8C2312yes—
95Dic3⋊Dic3—22no—
96Dic3⋊Dic3—22no—
97Dic32—22no—
98#3715—22no—
99#3362—91noSylow
100C2×C3×#41—61no—
101C2×#237—21no—
102C2×C3×SD16—32no—
103C3×#127—21no—
104C3×#127—32no—
105C3×#127C2×D311yescharacteristic
106C3×#127C2×D311yescharacteristic
107C3×#121—61no—
108C3×#121—62no—
109C3×C4×Q8—31no—
110C3×C4×Q8—31no—
111C3×C4×D4—32no—
112C3×C4×D4—31no—
113Q8×Dic3—32no—
114Q8×Dic3—61no—
115C2×#215—31no—
116#940C2×D312yes—
117#939—22no—
118#938—21no—
119D4×Dic3C2×D312yes—
120C2×#214—31no—
121C2×#214C2×D312yes—
122#888—32no—
123#888—61no—
124#888—62no—
125#888—62no—
126C4×D12C2×D311yescharacteristic
127#869—31no—
128#869—31no—
129#869—32no—
130#869—61no—
131#869—61no—
132C4×Dic6—32no—
133C4×Dic6—61no—
134C4×Dic6C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×C4⋊C8—31no—
137C3×#102—32no—
138#835—31no—
139#832—32no—
140#832—32no—
141#832—32no—
142#832—32no—
143#832—31no—
144#832—32no—
145#832—62no—
146#832—62no—
147#832C2×D312yes—
148#821—32no—
149#817—32no—
150Dic3⋊C8—32no—
151C8×Dic3—32no—
152#810—31no—
153#809—31no—
154#808—31no—
155#808—31no—
156#808—32no—
157C4⋊(C3⋊C8)—32no—
158C4⋊(C3⋊C8)C2×D311yescharacteristic
159C4×C3⋊C8—31no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—32no—
162C4×C3⋊C8—61no—
163C23×C32—22no—
164C22×C3×D3—21no—
165C32×D4—22no—
166C32×D4—22no—
167C32×D4—42no—
168C32×D4—81no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—22no—
173#634—81no—
174C3×#67—44no—
175C3×#67—82no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—44no—
180C2×C3×Dic3C2×D412yes—
181C2×C3×Dic3C2×D412yes—
182C3×D12—21no—
183C3×D12—21no—
184C3×C4×D3—42no—
185C3×Dic6—21no—
186C3×Dic6SD1614yescomplemented
187C3×Dic6#4112yescomplemented
188#627—82no—
189C3⋊(C3⋊C8)—21no—
190C3⋊(C3⋊C8)—21no—
191C3×C3⋊C8—22no—
192Q82—91no—
193#550—31no—
194#486—92no—
195#486—91no—
196#476—92no—
197#476—91no—
198#460—31no—
199#460—92no—
200C8×Q8—91no—
201C4×SD16—91no—
202C4×SD16—92no—
203C3×#41—124no—
204C2×C3×Q8—31no—
205C2×C3×Q8—31no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—22no—
211C2×C3×D4—31no—
212C2×C3×D4—41no—
213C2×C3×D4—41no—
214C2×C3×D4—62no—
215C2×C3×D4—62no—
216C2×C3×D4C22×D312yes—
217C2×C3×D4C22×D312yes—
218C22×C3×C4—62no—
219C22×C3×C4—61no—
220C2×#67—22no—
221C2×#67—22no—
222C22×Dic3—22no—
223#237—44no—
224C2×D12C22×D311yescharacteristic
225C2×C4×D3—21no—
226C2×Dic6—62no—
227C2×Dic6—61no—
228C2×Dic6—61no—
229C2×Dic6—62no—
230C2×Dic6—121no—
231C2×Dic6#6711yescharacteristic
232C2×Dic6C22×D311yescharacteristic
233C3×SD16—64no—
234C2×C3×C8—32no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—31no—
239C3×C4⋊C4—61no—
240C3×C22⋊C4—62no—
241C3×C22⋊C4—61no—
242C3×C42—21no—
243C3×C42—32no—
244C3×C42—61no—
245C3×C42C22×D311yescharacteristic
246C3×C42C22×D311yescharacteristic
247#217—22no—
248#215—62no—
249#214—24no—
250#214—62no—
251(C2×D3)⋊C4—21no—
252C4⋊Dic3—32no—
253C4⋊Dic3—32no—
254C4⋊Dic3—62no—
255C4⋊Dic3—62no—
256C4⋊Dic3—61no—
257C4⋊Dic3—61no—
258C4⋊Dic3—62no—
259C4⋊Dic3—121no—
260C4⋊Dic3#6711yescharacteristic
261C4⋊Dic3C22×D311yescharacteristic
262C4⋊Dic3C22×D311yescharacteristic
263Dic3⋊C4—21no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4#6712yes—
267C4×Dic3—21no—
268C4×Dic3—62no—
269C4×Dic3—62no—
270C4×Dic3C22×D312yes—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—61no—
276C2×C3⋊C8—61no—
277C2×C3⋊C8C22×D312yes—
278C22×C32—42no—
279C22×C32—42no—
280C22×C32—42no—
281C22×C32C22×D411yescharacteristic
282C2×C3×D3—41no—
283C2×C3×D3—41no—
284C2×C3×D3—41no—
285C32×C4—21no—
286C32×C4C2×SD1612yes—
287C32×C4C2×#4111yescharacteristic
288C32×C42−1+411yescharacteristic
289C3⋊Dic3—42no—
290C3×Dic3—22no—
291C3×Dic3—22no—
292C3×Dic3—41no—
293C3×Dic3—41no—
294C3×Dic3C2×SD1614yes—
295C2×#41—61no—
296C2×SD16—32no—
297C2×SD16—91no—
298C4⋊Q8—92no—
299C4⋊Q8—91no—
300C4⋊Q8—181no—
301C4⋊Q8—182no—
302#127—32no—
303#127D3211yescharacteristic
304#121—61no—
305#121—62no—
306C4×Q8—31no—
307C4×Q8—31no—
308C4×Q8—92no—
309C4×Q8—181no—
310C4×D4—32no—
311C4×D4—31no—
312#106—91no—
313#106—92no—
314C4⋊C8—31no—
315C4⋊C8—92no—
316#103—91no—
317#102—32no—
318#102—91no—
319#102—92no—
320#102—92no—
321#102—92no—
322C4×C8—92no—
323C4×C8—91no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—42no—
327C23×C3—61no—
328C22×D3—21no—
329C3×Q8—34no—
330C3×Q8—32no—
331C3×Q8—61no—
332C3×D4—22no—
333C3×D4—22no—
334C3×D4—22no—
335C3×D4—22no—
336C3×D4—42no—
337C3×D4—42no—
338C3×D4—42no—
339C3×D4—42no—
340C3×D4—61no—
341C3×D4—61no—
342C3×D4—82no—
343C3×D4—81no—
344C3×D4—81no—
345C3×D4—82no—
346C3×D4—124no—
347C3×D4—242no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—32no—
352C2×C3×C4—32no—
353C2×C3×C4—61no—
354C2×C3×C4—61no—
355C2×C3×C4—61no—
356C2×C3×C4—124no—
357C2×C3×C4—122no—
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C23×D311yescharacteristic
363C2×C3×C4C23×D311yescharacteristic
364#67—44no—
365#67—82no—
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—21no—
369C2×Dic3—44no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—122no—
373C2×Dic3C2×#6712yes—
374C2×Dic3C2×#6712yes—
375D12—21no—
376D12—21no—
377C4×D3—42no—
378Dic6—21no—
379Dic6—242no—
380Dic6—242no—
381Dic6—241no—
382Dic6—241no—
383Dic6—242no—
384Dic6#21414yescomplemented
385Dic6#23712yescomplemented
386C3×C8—62no—
387C3⋊C8—22no—
388C3⋊C8—61no—
389C3⋊C8—61no—
390C3⋊C8—61no—
391C3⋊C8—61no—
392C3⋊C8—121no—
393C3⋊C8—121no—
394C2×C32—82no—
395C2×C32#54811yescharacteristic
396C2×C32C22×SD1611yescharacteristic
397C2×C32#57611yescharacteristic
398C3×D3—81no—
399#41—124no—
400C2×Q8—31no—
401C2×Q8—31no—
402C2×Q8—182no—
403C2×Q8—181no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—31no—
407C2×D4—62no—
408C2×D4—62no—
409C2×D4C2×D3212yes—
410C22×C4—62no—
411C22×C4—61no—
412SD16—64no—
413SD16—182no—
414C2×C8—32no—
415C2×C8—91no—
416C2×C8—91no—
417C4⋊C4—32no—
418C4⋊C4—31no—
419C4⋊C4—31no—
420C4⋊C4—31no—
421C4⋊C4—61no—
422C4⋊C4—92no—
423C4⋊C4—182no—
424C4⋊C4—182no—
425C4⋊C4—181no—
426C22⋊C4—62no—
427C22⋊C4—61no—
428C42—32no—
429C42—61no—
430C42—182no—
431C42C2×D3211yescharacteristic
432C22×C3—21no—
433C22×C3—42no—
434C22×C3—42no—
435C22×C3—42no—
436C22×C3—42no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—82no—
440C22×C3—82no—
441C22×C3—82no—
442C22×C3—121no—
443C22×C3—121no—
444C22×C3—121no—
445C22×C3C2×D3×D411yescharacteristic
446C22×C3C22×#6711yescharacteristic
447C2×D3—41no—
448C2×D3—41no—
449C2×D3—41no—
450C3×C4—22no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—22no—
456C3×C4—34no—
457C3×C4—62no—
458C3×C4—62no—
459C3×C4—121no—
460C3×C4—121no—
461C3×C4D3×SD1612yes—
462C3×C4C2×#21412yes—
463C3×C4C2×#23711yescharacteristic
464C3×C4D3×#4111yescharacteristic
465C3×C4#101011yescharacteristic
466C3×C4#101011yescharacteristic
467Dic3—22no—
468Dic3—22no—
469Dic3—41no—
470Dic3—41no—
471Dic3—122no—
472Dic3—122no—
473Dic3—242no—
474Dic3C2×#21414yes—
475C32#336211yescharacteristic, complemented, Sylow
476C23—22no—
477C23—61no—
478Q8—34no—
479Q8—32no—
480Q8—61no—
481Q8—721no—
482Q8—722no—
483D4—22no—
484D4—22no—
485D4—42no—
486D4—61no—
487D4—61no—
488D4—81no—
489D4—124no—
490D4—242no—
491C2×C4—32no—
492C2×C4—32no—
493C2×C4—61no—
494C2×C4—61no—
495C2×C4—61no—
496C2×C4—124no—
497C2×C4—122no—
498C2×C4—182no—
499C2×C4D3×#6711yescharacteristic
500C2×C4D3×#6711yescharacteristic
501C2×C4C22×D3211yescharacteristic
502C8—62no—
503C8—181no—
504C8—181no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—82no—
509C2×C3—82no—
510C2×C3—162no—
511C2×C3—241no—
512C2×C3#559811yescharacteristic
513C2×C3C2×D3×SD1611yescharacteristic
514C2×C3#577411yescharacteristic
515C2×C3C22×#21411yescharacteristic
516C2×C3#583111yescharacteristic
517C2×C3#583511yescharacteristic
518D3—81no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—121no—
523C22—121no—
524C22—121no—
525C22C2×D3×#6711yescharacteristic
526C4—21no—
527C4—34no—
528C4—62no—
529C4—62no—
530C4—121no—
531C4—121no—
532C4—362no—
533C4D3×#21412yes—
534C4#6430911yescharacteristic
535C4D3×#23711yescharacteristic
536C3—21no—
537C3#8036911yescharacteristic, complemented
538C3#8358611yescharacteristic, complemented
539C2—82no—
540C2—241no—
541C2#1059509711yescharacteristic
542C2C2×D3×#21411yescharacteristic
543C2#1059515711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
prime radicalC3×#5718C2
hypercenter#127D32
hypocenterC32#3362
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. Dic62C2semidirect
3. #10592769C2semidirect
4. C3×#5075C2semidirect
5. #10591487C2semidirect
6. #10591438C2semidirect
7. Dic3×#214C2semidirect
8. #10591408C2semidirect
9. C4×#3715C2semidirect
10. #10590268C2semidirect
11. #10590250C2semidirect
51. #5075D3semidirect
186. C3×Dic6SD16semidirect
187. C3×Dic6#41semidirect
384. Dic6#214semidirect
385. Dic6#237semidirect
475. C32#3362semidirect
537. C3#80369semidirect
538. C3#83586semidirect

Maximal subgroups

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

subgroupindex
C3×#57182
Dic622
#105927692
C3×#50752
#105914872
#105914382
Dic3×#2142
#105914082
C4×#37152
#105902682
#105902502
#835863
#803693