Finite Group Databasebeta

← #11786743

Subgroups — #11786743

Order 1152.

657 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5827C211yesmaximal, characteristic
2C2×#63664C211yesmaximal, characteristic
3C3×#5232C211yesmaximal, characteristic
4#10591230C211yesmaximal, characteristic, complemented
5#10591139C211yesmaximal, characteristic, complemented
6#10589167C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#71665—31nomaximal
9#70298—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×Q8×Dic3—21no—
14C3×D4×Dic3—21no—
15C3×D4×Dic3—22no—
16C3×#926—21no—
17C3×#926C2211yescharacteristic
18C2×C3×C4⋊Dic3—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22#63664C414yescomplemented
23C3×#835—21no—
24C3×#832—21no—
25#63579—22no—
26#63576—21no—
27#63574—21no—
28C3×#520—31no—
29#5827D311yescharacteristic
30C3×#417—31no—
31C2×#837—31no—
32C2×#837—31no—
33C2×#837—61no—
34#5232D311yescharacteristic
35#4995—31no—
36#4977—31no—
37#4977—31no—
38#4964—31no—
39#4555—31no—
40#4554—31no—
41#4532—31no—
42#4530—31no—
43C32×#41—21no—
44C32×#41—21no—
45C32×#41C2×C412yes—
46C32×#41Q812yes—
47C2×C32×Q8D411yescharacteristic
48C2×C32×D4—21no—
49C2×C32×D4D411yescharacteristic
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C22×C3×Dic3—22no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3D412yes—
56C4×C3⋊Dic3—21no—
57C4×C3⋊Dic3C2×C412yescomplemented
58#3748—21no—
59#3748C2×C412yescomplemented
60C2×C3⋊(C3⋊C8)—21no—
61C3×#217—22no—
62C3×#217—21no—
63C3×C4⋊Dic3—22no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3D411yescharacteristic
69C3×C4⋊Dic3D411yescharacteristic
70C3×C4×Dic3—22no—
71C3×C4×Dic3—21no—
72C3×#208—21no—
73C3×#208—21no—
74C2×C3×C3⋊C8—21no—
75#1860—91noSylow
76C2×C3×#41—21no—
77C2×C3×#41C2×D311yescharacteristic
78C2×C3×#41C2×D311yescharacteristic
79C2×C3×M16—31no—
80C3×C4×Q8—61no—
81C3×C4×D4—62no—
82C3×C4×D4—61no—
83C3×#117—31no—
84C3×#117—61no—
85C2×C3×C4⋊C4—31no—
86C2×C3×C4⋊C4—31no—
87C2×C3×C4⋊C4—61no—
88Q8×Dic3—21no—
89D4×Dic3—21no—
90D4×Dic3—22no—
91#926—21no—
92#926C2×D311yescharacteristic
93C2×C4⋊Dic3—21no—
94C2×C4⋊Dic3C2×D311yescharacteristic
95C2×C4⋊Dic3C2×D311yescharacteristic
96C2×C4×Dic3—31no—
97C2×C4×Dic3—31no—
98C2×C4×Dic3—61no—
99C2×#208—31no—
100C2×#208—31no—
101C2×#208—61no—
102C2×#208C2×D311yescharacteristic
103C3×#103—61no—
104C3×#102—61no—
105#837—34no—
106#837—34no—
107#837—64no—
108#835—21no—
109#832—21no—
110C3⋊#95—62no—
111C3⋊#95—62no—
112#808—61no—
113#808—61no—
114#807—61no—
115#807—61no—
116C23×C32—21no—
117C23×C32C2×D411yescharacteristic
118C32×Q8—21no—
119C32×Q8C4⋊C412yes—
120C32×D4—22no—
121C32×D4—22no—
122C32×D4—21no—
123C32×D4C4⋊C412yes—
124C2×C32×C4—21no—
125C2×C32×C4—22no—
126C2×C32×C4—22no—
127C2×C32×C4C22×C411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×Q811yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—41no—
135C2×C3⋊Dic3—41no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—42no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—82no—
143C3⋊(C3⋊C8)—22no—
144C3×C3⋊C8—41no—
145#520—31no—
146#428—91no—
147C2×#104—91no—
148#417—31no—
149#382—91no—
150#343—91no—
151#339—91no—
152C3×#41—21no—
153C3×#41—21no—
154C3×#41—21no—
155C3×#41—21no—
156C3×#41—22no—
157C3×#41—22no—
158C3×#41—41no—
159C3×#41—41no—
160C3×#41Dic612yes—
161C3×#41Dic612yes—
162C3×#41C4×D312yes—
163C3×#41C4×D312yes—
164C2×C3×Q8—21no—
165C2×C3×Q8#6711yescharacteristic
166C2×C3×Q8#6711yescharacteristic
167C2×C3×D4—21no—
168C2×C3×D4—21no—
169C2×C3×D4—21no—
170C2×C3×D4—41no—
171C2×C3×D4#6711yescharacteristic
172C2×C3×D4#6711yescharacteristic
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—32no—
177C22×C3×C4—41no—
178C22×C3×C4—62no—
179C22×C3×C4—61no—
180C22×C3×C4C22×D311yescharacteristic
181C22×C3×C4C22×D311yescharacteristic
182C22×Dic3—22no—
183C22×Dic3—21no—
184C22×Dic3—61no—
185C22×Dic3—61no—
186C22×Dic3—121no—
187C22×Dic3#6712yes—
188C3×M16—61no—
189C3×M16—61no—
190C2×C3×C8—61no—
191C3×C4⋊C4—31no—
192C3×C4⋊C4—31no—
193C3×C4⋊C4—62no—
194C3×C4⋊C4—61no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4—61no—
198C3×C22⋊C4—62no—
199C3×C22⋊C4—61no—
200C3×C42—62no—
201C3×C42—61no—
202#217—22no—
203#217—21no—
204C4⋊Dic3—22no—
205C4⋊Dic3—21no—
206C4⋊Dic3—21no—
207C4⋊Dic3—21no—
208C4⋊Dic3—21no—
209C4⋊Dic3#6711yescharacteristic
210C4⋊Dic3#6711yescharacteristic
211C4×Dic3—22no—
212C4×Dic3—21no—
213C4×Dic3—32no—
214C4×Dic3—32no—
215C4×Dic3—62no—
216C4×Dic3—61no—
217C4×Dic3—61no—
218C4×Dic3—121no—
219#208—21no—
220#208—21no—
221#208—32no—
222#208—32no—
223#208—62no—
224#208—61no—
225#208—61no—
226#208—121no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—61no—
230C2×C3⋊C8—121no—
231C22×C32—21no—
232C22×C32—21no—
233C22×C32—22no—
234C22×C32—41no—
235C22×C32—41no—
236C22×C32C4×D411yescharacteristic
237C22×C32#12011yescharacteristic
238C22×C32C22⋊Q811yescharacteristic
239C32×C4—22no—
240C32×C4C2×C4⋊C411yescharacteristic
241C32×C4C4×D411yescharacteristic
242C32×C4C22⋊Q811yescharacteristic
243C32×C4#12311yescharacteristic
244C3⋊Dic3—42no—
245C3×Dic3—41no—
246C3×Dic3—42no—
247C3×Dic3—41no—
248C3×Dic3—81no—
249C2×#41D3211yescharacteristic
250C2×M16—31no—
251C2×M16—91no—
252C4×Q8—61no—
253C4×D4—62no—
254C4×D4—61no—
255#117—31no—
256#117—61no—
257C2×C4⋊C4—31no—
258C2×C4⋊C4—31no—
259C2×C4⋊C4—61no—
260C2×C42—91no—
261#107—181no—
262#106—181no—
263#104—94no—
264#103—61no—
265#102—61no—
266#95—182no—
267C23×C3—21no—
268C23×C3—21no—
269C23×C3—21no—
270C23×C3—41no—
271C23×C3D3×D411yescharacteristic
272C23×C3C2×#6711yescharacteristic
273C3×Q8—21no—
274C3×Q8—21no—
275C3×Q8—22no—
276C3×Q8—41no—
277C3×Q8Dic3⋊C412yes—
278C3×Q8Dic3⋊C412yes—
279C3×D4—22no—
280C3×D4—22no—
281C3×D4—22no—
282C3×D4—22no—
283C3×D4—21no—
284C3×D4—21no—
285C3×D4—22no—
286C3×D4—41no—
287C3×D4—42no—
288C3×D4—42no—
289C3×D4Dic3⋊C412yes—
290C3×D4Dic3⋊C412yes—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—42no—
304C2×C3×C4—42no—
305C2×C3×C4—41no—
306C2×C3×C4—61no—
307C2×C3×C4—61no—
308C2×C3×C4—62no—
309C2×C3×C4—122no—
310C2×C3×C4—122no—
311C2×C3×C4—121no—
312C2×C3×C4—242no—
313C2×C3×C4C2×Dic611yescharacteristic
314C2×C3×C4C2×Dic611yescharacteristic
315C2×C3×C4C2×C4×D311yescharacteristic
316C2×C3×C4C2×C4×D311yescharacteristic
317C2×C3×C4#23511yescharacteristic
318C2×C3×C4#23511yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4#23711yescharacteristic
321C2×C3×C4#23711yescharacteristic
322C2×C3×C4C2×#6711yescharacteristic
323C2×C3×C4C2×#6711yescharacteristic
324C2×C3×C4C2×#6711yescharacteristic
325C2×Dic3—21no—
326C2×Dic3—22no—
327C2×Dic3—21no—
328C2×Dic3—42no—
329C2×Dic3—42no—
330C2×Dic3—41no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—82no—
334C2×Dic3—122no—
335C2×Dic3—121no—
336C2×Dic3—121no—
337C2×Dic3—121no—
338C2×Dic3—121no—
339C2×Dic3—122no—
340C2×Dic3—122no—
341C3×C8—121no—
342C3⋊C8—41no—
343C3⋊C8—62no—
344C3⋊C8—62no—
345C3⋊C8—122no—
346C2×C32—21no—
347C2×C32—21no—
348C2×C32—42no—
349C2×C32#38511yescharacteristic
350C2×C32#45411yescharacteristic
351C2×C32#45511yescharacteristic
352#41—21no—
353#41—21no—
354#41#62412yes—
355#41#62712yes—
356C2×Q8#62511yescharacteristic
357C2×D4—21no—
358C2×D4#62511yescharacteristic
359C22×C4—21no—
360C22×C4—32no—
361C22×C4—62no—
362C22×C4—61no—
363C22×C4—181no—
364C22×C4C2×D3211yescharacteristic
365M16—61no—
366M16—61no—
367M16—92no—
368M16—181no—
369C2×C8—61no—
370C2×C8—181no—
371C4⋊C4—31no—
372C4⋊C4—31no—
373C4⋊C4—62no—
374C4⋊C4—61no—
375C4⋊C4—61no—
376C4⋊C4—61no—
377C4⋊C4—61no—
378C22⋊C4—62no—
379C22⋊C4—61no—
380C42—62no—
381C42—61no—
382C42—92no—
383C42—181no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—22no—
389C22×C3—22no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—41no—
394C22×C3—41no—
395C22×C3—42no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—81no—
401C22×C3—81no—
402C22×C3#87811yescharacteristic
403C22×C3#67⋊C411yescharacteristic
404C22×C3#92411yescharacteristic
405C22×C3C4×#6711yescharacteristic
406C22×C3#93711yescharacteristic
407C22×C3#95311yescharacteristic
408C3×C4—22no—
409C3×C4—22no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—42no—
415C3×C4—121no—
416C3×C4—122no—
417C3×C4—121no—
418C3×C4—241no—
419C3×C4#87811yescharacteristic
420C3×C4#67⋊C411yescharacteristic
421C3×C4C2×Dic3⋊C411yescharacteristic
422C3×C4C2×Dic3⋊C411yescharacteristic
423C3×C4#92411yescharacteristic
424C3×C4C4×#6711yescharacteristic
425C3×C4#92911yescharacteristic
426C3×C4#93511yescharacteristic
427Dic3—42no—
428Dic3—41no—
429Dic3—41no—
430Dic3—81no—
431Dic3—122no—
432Dic3—122no—
433Dic3—124no—
434C32#186011yescharacteristic, complemented, Sylow
435C23—21no—
436C23D3×#6711yescharacteristic
437Q8—21no—
438Q8#372412yes—
439D4—22no—
440D4—22no—
441D4—21no—
442D4#372412yes—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—61no—
447C2×C4—61no—
448C2×C4—62no—
449C2×C4—122no—
450C2×C4—122no—
451C2×C4—121no—
452C2×C4—182no—
453C2×C4—242no—
454C2×C4—361no—
455C2×C4—361no—
456C2×C4#380411yescharacteristic
457C2×C4#380411yescharacteristic
458C2×C4C2×#62411yescharacteristic
459C2×C4C2×#62511yescharacteristic
460C2×C4C2×#62711yescharacteristic
461C2×C4D3×#6711yescharacteristic
462C8—121no—
463C8—182no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—41no—
472C2×C3—41no—
473C2×C3—42no—
474C2×C3—42no—
475C2×C3—82no—
476C2×C3#494611yescharacteristic
477C2×C3#520111yescharacteristic
478C2×C3#520211yescharacteristic
479C2×C3#521011yescharacteristic
480C2×C3#524211yescharacteristic
481C2×C3#524511yescharacteristic
482C22—21no—
483C22—21no—
484C22—22no—
485C22—41no—
486C22—41no—
487C22#6395211yescharacteristic
488C22#6396411yescharacteristic
489C22#6397611yescharacteristic
490C4—22no—
491C4—122no—
492C4—121no—
493C4—121no—
494C4—241no—
495C4—362no—
496C4#6395211yescharacteristic
497C4#6396111yescharacteristic
498C4#6396411yescharacteristic
499C4C2×#372411yescharacteristic
500C3—21no—
501C3#7029811yescharacteristic, complemented
502C3#7166511yescharacteristic, complemented
503C2—21no—
504C2—21no—
505C2—42no—
506C2#1059166411yescharacteristic
507C2#1059168411yescharacteristic
508C2#1059169311yescharacteristic
subgroupG/H
centerC22#63976
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32#120
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1860
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. #10591230C2semidirect
5. #10591139C2semidirect
6. #10589167C2semidirect
7. #10589160C2semidirect
22. #63664C4semidirect
57. C4×C3⋊Dic3C2×C4semidirect
59. #3748C2×C4semidirect
434. C32#1860semidirect
501. C3#70298semidirect
502. C3#71665semidirect

Maximal subgroups

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

subgroupindex
C3×#58272
C2×#636642
C3×#52322
#105912302
#105911392
#105891672
#105891602
#716653
#702983