Finite Group Databasebeta

← #11786741

Subgroups — #11786741

Order 1152.

653 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
2#10592931C211yesmaximal, characteristic
3C2×C3×#837C211yesmaximal, characteristic
4#10591224C211yesmaximal, characteristic, complemented
5#10591131C211yesmaximal, characteristic, complemented
6#10589167C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#71665—31nomaximal
9#70364—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
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#63662—21no—
23#63659—21no—
24C3×#837C414yescomplemented
25#63579—22no—
26#63575—21no—
27#63573—21no—
28C3×#520—31no—
29#5827D311yescharacteristic
30C2×C3×#104—31no—
31C2×#837D311yescharacteristic
32#5232—31no—
33#5232—31no—
34#5232—61no—
35#5121—31no—
36#4995—31no—
37#4977—31no—
38#4936—31no—
39#4554—31no—
40#4532—31no—
41#4530—31no—
42#4523—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—21no—
54C22×C3×Dic3—22no—
55C22×C3×Dic3D412yes—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—21no—
58#3748—21no—
59#3748—21no—
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⋊Dic3D411yescharacteristic
67C3×C4⋊Dic3D411yescharacteristic
68C3×C4×Dic3—22no—
69C3×C4×Dic3—21no—
70C3×C4×Dic3—21no—
71C3×C4×Dic3C2×C412yescomplemented
72C3×#208—21no—
73C3×#208C2×C412yescomplemented
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—61no—
87C2×C3×C42—31no—
88Q8×Dic3—21no—
89D4×Dic3—21no—
90D4×Dic3—22no—
91#926—21no—
92#926C2×D311yescharacteristic
93C2×C4⋊Dic3—21no—
94C2×C4⋊Dic3—31no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—61no—
97C2×C4⋊Dic3C2×D311yescharacteristic
98C2×C4×Dic3C2×D311yescharacteristic
99C2×#208—31no—
100C2×#208—31no—
101C2×#208—61no—
102C2×#208C2×D311yescharacteristic
103C3×#104—34no—
104#837Dic314yescomplemented
105#835—62no—
106#835—61no—
107#835—61no—
108#832—62no—
109#832—61no—
110#832—61no—
111C3⋊#95—62no—
112C3⋊#95—62no—
113#818—61no—
114#817—61no—
115#808—61no—
116#807—61no—
117C23×C32—21no—
118C23×C32C2×D411yescharacteristic
119C32×Q8—21no—
120C32×Q8C4⋊C412yes—
121C32×D4—22no—
122C32×D4—22no—
123C32×D4—21no—
124C32×D4C4⋊C412yes—
125C2×C32×C4—21no—
126C2×C32×C4—22no—
127C2×C32×C4—22no—
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×Q811yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C3⋊Dic3—41no—
135C2×C3⋊Dic3—42no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—42no—
143C2×C3×Dic3—82no—
144C3⋊(C3⋊C8)—41no—
145C3×C3⋊C8—22no—
146#520—31no—
147#428—91no—
148C2×#104—31no—
149#417—91no—
150#382—91no—
151#343—91no—
152#339—91no—
153C3×#41—21no—
154C3×#41—21no—
155C3×#41—21no—
156C3×#41—21no—
157C3×#41—22no—
158C3×#41—22no—
159C3×#41—41no—
160C3×#41—41no—
161C3×#41Dic612yes—
162C3×#41Dic612yes—
163C3×#41C4×D312yes—
164C3×#41C2×Dic312yes—
165C2×C3×Q8—21no—
166C2×C3×Q8D1211yescharacteristic
167C2×C3×Q8#6711yescharacteristic
168C2×C3×D4—21no—
169C2×C3×D4—21no—
170C2×C3×D4—21no—
171C2×C3×D4—41no—
172C2×C3×D4D1211yescharacteristic
173C2×C3×D4#6711yescharacteristic
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—32no—
178C22×C3×C4—41no—
179C22×C3×C4—61no—
180C22×C3×C4—62no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C22×Dic3—21no—
184C22×Dic3—22no—
185C22×Dic3—61no—
186C22×Dic3—61no—
187C22×Dic3—121no—
188C22×Dic3#6712yes—
189C3×M16—32no—
190C3×M16—61no—
191C2×C3×C8—61no—
192C3×C4⋊C4—31no—
193C3×C4⋊C4—31no—
194C3×C4⋊C4—62no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4—61no—
197C3×C22⋊C4—62no—
198C3×C22⋊C4—61no—
199C3×C42—32no—
200C3×C42—62no—
201C3×C42—61no—
202C3×C42—61no—
203#217—22no—
204#217—21no—
205C4⋊Dic3—22no—
206C4⋊Dic3—21no—
207C4⋊Dic3—21no—
208C4⋊Dic3—62no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3—61no—
213C4⋊Dic3—121no—
214C4⋊Dic3#6711yescharacteristic
215C4⋊Dic3#6711yescharacteristic
216C4×Dic3—22no—
217C4×Dic3—21no—
218C4×Dic3—21no—
219C4×Dic3C2×Dic312yescomplemented
220#208—21no—
221#208—61no—
222#208—61no—
223#208—61no—
224#208—61no—
225#208—121no—
226#208—121no—
227#208C2×Dic312yescomplemented
228C2×C3⋊C8—21no—
229C2×C3⋊C8—62no—
230C2×C3⋊C8—61no—
231C2×C3⋊C8—61no—
232C22×C32—21no—
233C22×C32—21no—
234C22×C32—22no—
235C22×C32—41no—
236C22×C32—41no—
237C22×C32C4×D411yescharacteristic
238C22×C32#12011yescharacteristic
239C22×C32C22⋊Q811yescharacteristic
240C32×C4—22no—
241C32×C4C2×C4⋊C411yescharacteristic
242C32×C4C4×D411yescharacteristic
243C32×C4C22⋊Q811yescharacteristic
244C32×C4#12311yescharacteristic
245C3⋊Dic3—81no—
246C3×Dic3—42no—
247C3×Dic3—41no—
248C3×Dic3—42no—
249C3×Dic3—41no—
250C2×#41D3211yescharacteristic
251C2×M16—31no—
252C2×M16—91no—
253C4×Q8—61no—
254C4×D4—62no—
255C4×D4—61no—
256#117—31no—
257#117—61no—
258C2×C4⋊C4—31no—
259C2×C4⋊C4—61no—
260C2×C4⋊C4—91no—
261C2×C42—31no—
262#107—181no—
263#106—181no—
264#104—34no—
265#103—181no—
266#102—181no—
267#95—182no—
268C23×C3—21no—
269C23×C3—21no—
270C23×C3—21no—
271C23×C3—41no—
272C23×C3D3×D411yescharacteristic
273C23×C3C2×#6711yescharacteristic
274C3×Q8—21no—
275C3×Q8—21no—
276C3×Q8—22no—
277C3×Q8—41no—
278C3×Q8Dic3⋊C412yes—
279C3×Q8C4⋊Dic312yes—
280C3×D4—22no—
281C3×D4—22no—
282C3×D4—22no—
283C3×D4—22no—
284C3×D4—21no—
285C3×D4—21no—
286C3×D4—22no—
287C3×D4—41no—
288C3×D4—42no—
289C3×D4—42no—
290C3×D4Dic3⋊C412yes—
291C3×D4C4⋊Dic312yes—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—42no—
305C2×C3×C4—42no—
306C2×C3×C4—41no—
307C2×C3×C4—61no—
308C2×C3×C4—61no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4—121no—
312C2×C3×C4—121no—
313C2×C3×C4—122no—
314C2×C3×C4—242no—
315C2×C3×C4C2×Dic611yescharacteristic
316C2×C3×C4C2×Dic611yescharacteristic
317C2×C3×C4C2×C4×D311yescharacteristic
318C2×C3×C4C2×D1211yescharacteristic
319C2×C3×C4#23511yescharacteristic
320C2×C3×C4#23511yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4#23711yescharacteristic
323C2×C3×C4#23711yescharacteristic
324C2×C3×C4C22×Dic311yescharacteristic
325C2×C3×C4C2×#6711yescharacteristic
326C2×C3×C4C2×#6711yescharacteristic
327C2×Dic3—22no—
328C2×Dic3—21no—
329C2×Dic3—22no—
330C2×Dic3—21no—
331C2×Dic3—41no—
332C2×Dic3—41no—
333C2×Dic3—42no—
334C2×Dic3—82no—
335C2×Dic3—122no—
336C2×Dic3—122no—
337C2×Dic3—122no—
338C2×Dic3—121no—
339C2×Dic3—121no—
340C2×Dic3—242no—
341C3×C8—62no—
342C3⋊C8—22no—
343C3⋊C8—122no—
344C3⋊C8—121no—
345C3⋊C8—121no—
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#41D3×Dic312yes—
355#41#62712yes—
356C2×Q8#62611yescharacteristic
357C2×D4—21no—
358C2×D4#62611yescharacteristic
359C22×C4—21no—
360C22×C4—32no—
361C22×C4—61no—
362C22×C4—62no—
363C22×C4—181no—
364C22×C4C2×D3211yescharacteristic
365M16—32no—
366M16—61no—
367M16—181no—
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—181no—
377C4⋊C4—181no—
378C22⋊C4—62no—
379C22⋊C4—61no—
380C42—32no—
381C42—62no—
382C42—61no—
383C42—61no—
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#88211yescharacteristic
404C22×C3#92411yescharacteristic
405C22×C3C4×#6711yescharacteristic
406C22×C3D4×Dic311yescharacteristic
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—122no—
416C3×C4—122no—
417C3×C4—121no—
418C3×C4—121no—
419C3×C4#87811yescharacteristic
420C3×C4#88611yescharacteristic
421C3×C4C2×Dic3⋊C411yescharacteristic
422C3×C4#92411yescharacteristic
423C3×C4C2×C4⋊Dic311yescharacteristic
424C3×C4C4×#6711yescharacteristic
425C3×C4#92911yescharacteristic
426C3×C4D4×Dic311yescharacteristic
427Dic3—42no—
428Dic3—42no—
429Dic3—41no—
430Dic3—41no—
431Dic3—242no—
432Dic3—241no—
433Dic3—241no—
434C32#186011yescharacteristic, complemented, Sylow
435C23—21no—
436C23D3×#6711yescharacteristic
437Q8—21no—
438Q8Dic3⋊Dic312yes—
439D4—22no—
440D4—22no—
441D4—21no—
442D4Dic3⋊Dic312yes—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—62no—
447C2×C4—61no—
448C2×C4—61no—
449C2×C4—62no—
450C2×C4—121no—
451C2×C4—121no—
452C2×C4—122no—
453C2×C4—242no—
454C2×C4—362no—
455C2×C4—361no—
456C2×C4C2×D3×Dic311yescharacteristic
457C2×C4#380411yescharacteristic
458C2×C4#380411yescharacteristic
459C2×C4C2×#62611yescharacteristic
460C2×C4C2×#62711yescharacteristic
461C2×C4D3×#6711yescharacteristic
462C8—62no—
463C8—361no—
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#482511yescharacteristic
477C2×C3#482711yescharacteristic
478C2×C3#495011yescharacteristic
479C2×C3#521011yescharacteristic
480C2×C3#524211yescharacteristic
481C2×C3#524511yescharacteristic
482C22—21no—
483C22—21no—
484C22—22no—
485C22—41no—
486C22—41no—
487C22#6396411yescharacteristic
488C22Dic3×#6711yescharacteristic
489C22#6397711yescharacteristic
490C4—22no—
491C4—122no—
492C4—121no—
493C4—122no—
494C4—121no—
495C4—721no—
496C4#6396411yescharacteristic
497C4C2×Dic3⋊Dic311yescharacteristic
498C4#6396611yescharacteristic
499C4Dic3×#6711yescharacteristic
500C3—21no—
501C3#7036411yescharacteristic, complemented
502C3#7166511yescharacteristic, complemented
503C2—21no—
504C2—21no—
505C2—42no—
506C2#1059168511yescharacteristic
507C2#1059168811yescharacteristic
508C2#1059171811yescharacteristic
subgroupG/H
centerC22#63977
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. #10591224C2semidirect
5. #10591131C2semidirect
6. #10589167C2semidirect
7. #10589161C2semidirect
24. C3×#837C4semidirect
71. C3×C4×Dic3C2×C4semidirect
73. C3×#208C2×C4semidirect
104. #837Dic3semidirect
219. C4×Dic3C2×Dic3semidirect
227. #208C2×Dic3semidirect
434. C32#1860semidirect
501. C3#70364semidirect
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
#105929312
C2×C3×#8372
#105912242
#105911312
#105891672
#105891612
#716653
#703643