Finite Group Databasebeta

← #11860907

Subgroups — #11860907

Order 1152.

1023 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#919C211yesmaximal, characteristic
2#10595394C212yesmaximal, complemented
3Q16×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C3×Dic3×Q16C211yesmaximal, characteristic, complemented
5#10591572C212yesmaximal, complemented
6#10591566C212yesmaximal, complemented
7#10591550C212yesmaximal, complemented
8#10590777C211yesmaximal, characteristic, complemented
9Dic3×D24C211yesmaximal, characteristic, complemented
10#10590692C211yesmaximal, characteristic, complemented
11D3×#818C211yesmaximal, characteristic, complemented
12#83898—31nomaximal
13#79721—31nomaximal
14C2×C3×#239C2212yes—
15C2×C32×Q16C2211yescharacteristic
16Q8×C3⋊Dic3C2212yes—
17C3×Q8×Dic3C2212yes—
18C2×C3×#215C2212yes—
19C3×#919C418yescomplemented
20C2×C3×D24C2211yescharacteristic
21C2×C3×D3×C8C2211yescharacteristic
22#63898—22no—
23#63898C2212yes—
24Dic3×D12—22no—
25Dic3×D12C2212yes—
26D3×C4⋊Dic3—22no—
27D3×C4⋊Dic3C2212yes—
28#63855—22no—
29#63855C2211yescharacteristic
30C2×#3711C2211yescharacteristic
31#63662C2212yes—
32#63645C2211yescharacteristic
33C8×C3⋊Dic3C2211yescharacteristic
34C3×#835C2212yes—
35C3×#818C2211yescharacteristic
36C3×C8×Dic3C2211yescharacteristic
37#63575C2212yes—
38#63563C2212yes—
39#63562C2212yes—
40#63555C2211yescharacteristic
41#63554C2211yescharacteristic
42C2×C3×#135—31no—
43#5827—32no—
44C2×#919D311yescharacteristic
45#5574—32no—
46C3×C4×Q16—31no—
47#5232—32no—
48Dic3×Q16—31no—
49Dic3×Q16—31no—
50Dic3×Q16—61no—
51Dic3×Q16D311yescharacteristic, complemented
52#5164—32no—
53#5164—32no—
54Dic3×D8—31no—
55Dic3×D8—31no—
56C2×#818—31no—
57#5101—31no—
58#5026—32no—
59D3×#107—31no—
60#4872—31no—
61#4817—32no—
62#4803—32no—
63C4×D24—31no—
64#4689—31no—
65C2×C32×Q8C2312yes—
66C3×#239—24no—
67C3×#239C2×C418yescomplemented
68C2×C3×D12—22no—
69C2×C3×D12C2312yes—
70C2×C3×C4×D3—22no—
71C2×C3×C4×D3C2311yescharacteristic
72C2×D3×Dic3—22no—
73C2×D3×Dic3—22no—
74C2×D3×Dic3—22no—
75C32×Q16C2×C414yescomplemented
76C2×C32×C8C2311yescharacteristic
77C4⋊(C3⋊Dic3)—22no—
78C4⋊(C3⋊Dic3)C2312yes—
79C4×C3⋊Dic3—22no—
80C4×C3⋊Dic3C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C3×#215C2×C418yescomplemented
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3C2312yes—
85C3×C4×Dic3—22no—
86C3×C4×Dic3C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C2×C3×C3⋊C8C2311yescharacteristic
89C3×D24C2×C414yescomplemented
90C3×D3×C8C2×C414yescomplemented
91Dic3⋊Dic3—22no—
92Dic3⋊Dic3D411yescharacteristic
93Dic3⋊Dic3D411yescharacteristic
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96(C2×D3)⋊Dic3D411yescharacteristic
97(C2×D3)⋊Dic3D411yescharacteristic
98#3711—22no—
99#2951—91noSylow
100C2×C3×#41—32no—
101C2×#239C2×D312yes—
102C3×#135—38no—
103C2×C3×Q16—21no—
104C2×C3×Q16C2×D311yescharacteristic
105C2×C3×Q16C2×D311yescharacteristic
106C2×C3×SD16—32no—
107C2×C3×D8—31no—
108C22×C3×C8—31no—
109C3×C4×Q8—32no—
110Q8×Dic3—32no—
111Q8×Dic3—32no—
112Q8×Dic3—62no—
113Q8×Dic3C2×D312yes—
114C2×#215C2×D312yes—
115D4×Dic3—32no—
116D4×Dic3—32no—
117D4×Dic3—62no—
118D4×Dic3—62no—
119#926—31no—
120#926—62no—
121C2×C4⋊Dic3—32no—
122C2×C4⋊Dic3—62no—
123C2×#208—31no—
124#919Dic318yescomplemented
125C2×D24C2×D311yescharacteristic
126C2×ΓL(1,𝔽25)—31no—
127C2×D3×C8C2×D311yescharacteristic
128#893—32no—
129#893—62no—
130D3×C4⋊C4—32no—
131D3×C4⋊C4—62no—
132C4×D12—32no—
133C4×D12—62no—
134#872—31no—
135#872—62no—
136C3×#107—31no—
137C3×#103—32no—
138C3×C4×C8—31no—
139#835—32no—
140#835—32no—
141#835—62no—
142#835C2×D312yes—
143#832—32no—
144#832—32no—
145#821—32no—
146#818—31no—
147#818—31no—
148#818—32no—
149#818—61no—
150#818C2×D311yescharacteristic
151#815—31no—
152#815—31no—
153#815—31no—
154C8×Dic3—31no—
155C8×Dic3—31no—
156C8×Dic3—61no—
157C8×Dic3C2×D311yescharacteristic
158#809—32no—
159#807—32no—
160#803—31no—
161C22×C3×D3—22no—
162C22×C3×D3C2×D411yescharacteristic
163C32×Q8—22no—
164C32×Q8C22×C414yes—
165C2×C32×C4—22no—
166C2×C32×C4C2411yescharacteristic
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3C2×D411yescharacteristic
169C2×C3⋊Dic3C2×D411yescharacteristic
170C2×C3×Dic3—22no—
171C2×C3×Dic3C2×D411yescharacteristic
172C2×C3×Dic3C2×D411yescharacteristic
173C2×C3×Dic3C2×D411yescharacteristic
174C3×D12—28no—
175C3×D12—22no—
176C3×D12C22×C414yes—
177C3×C4×D3—28no—
178C3×C4×D3C22×C412yes—
179C3×C4×D3#4112yes—
180D3×Dic3—82no—
181D3×Dic3—82no—
182D3×Dic3—82no—
183C32×C8C22×C412yes—
184C3⋊(C3⋊C8)—21no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8C22×C412yes—
187C2×#135—31no—
188#520—92no—
189#440—92no—
190#440—92no—
191C4×Q16—31no—
192C4×Q16—91no—
193C4×D8—91no—
194C4×D8—91no—
195C2×#107—91no—
196#417—92no—
197#405—91no—
198C3×#41—38no—
199C3×#41—64no—
200C2×C3×Q8—22no—
201C2×C3×Q8C22×D312yes—
202C2×C3×Q8C22×D312yes—
203C2×C3×D4—32no—
204C2×C3×D4—62no—
205C22×C3×C4—31no—
206C22×C3×C4—62no—
207C22×Dic3—62no—
208C22×Dic3—62no—
209C22×Dic3—62no—
210#239—24no—
211#239C2×Dic318yescomplemented
212C2×D12—22no—
213C2×D12C22×D312yes—
214C2×C4×D3—22no—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×C4×D3C22×D311yescharacteristic
219C3×Q16—24no—
220C3×Q16C4×D314yescomplemented
221C3×Q16C2×Dic314yescomplemented
222C3×SD16—38no—
223C3×D8—34no—
224C2×C3×C8—21no—
225C2×C3×C8—31no—
226C2×C3×C8—34no—
227C2×C3×C8—31no—
228C2×C3×C8C22×D311yescharacteristic
229C2×C3×C8C22×D311yescharacteristic
230C3×C4⋊C4—32no—
231C3×C4⋊C4—62no—
232C3×C42—31no—
233C3×C42—62no—
234#217—31no—
235#217—31no—
236#217—62no—
237#217—62no—
238#215C2×Dic318yescomplemented
239(C2×D3)⋊C4—31no—
240(C2×D3)⋊C4—31no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—62no—
243C4⋊Dic3—22no—
244C4⋊Dic3—31no—
245C4⋊Dic3—31no—
246C4⋊Dic3—32no—
247C4⋊Dic3—32no—
248C4⋊Dic3—62no—
249C4⋊Dic3—62no—
250C4⋊Dic3—62no—
251C4⋊Dic3—62no—
252C4⋊Dic3—122no—
253C4⋊Dic3C22×D312yes—
254Dic3⋊C4—31no—
255Dic3⋊C4—31no—
256Dic3⋊C4—62no—
257C4×Dic3—22no—
258C4×Dic3—31no—
259C4×Dic3—31no—
260C4×Dic3—61no—
261C4×Dic3—62no—
262C4×Dic3—62no—
263C4×Dic3—122no—
264C4×Dic3C22×D311yescharacteristic
265#208—62no—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—61no—
269C2×C3⋊C8C22×D311yescharacteristic
270C2×C3⋊C8C22×D311yescharacteristic
271D24C2×Dic314yescomplemented
272ΓL(1,𝔽25)—62no—
273D3×C8C2×Dic314yescomplemented
274C22×C32C22×D411yescharacteristic
275C2×C3×D3—21no—
276C2×C3×D3—21no—
277C2×C3×D3—24no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C2×C3×D3C4×D412yes—
281C32×C4—24no—
282C32×C4C23×C411yescharacteristic
283C32×C4C2×#4111yescharacteristic
284C3⋊Dic3—21no—
285C3⋊Dic3—21no—
286C3⋊Dic3—42no—
287C3×Dic3—21no—
288C3×Dic3—21no—
289C3×Dic3—42no—
290C3×Dic3C4×D412yes—
291C2×#41—32no—
292#135—38no—
293C2×Q16D3211yescharacteristic
294C2×SD16—32no—
295C2×D8—31no—
296C2×M16—91no—
297C22×C8—31no—
298C4×Q8—32no—
299C4×Q8—92no—
300C4×D4—92no—
301C4×D4—92no—
302C4×D4—182no—
303C4×D4—182no—
304#117—91no—
305#117—182no—
306C2×C4⋊C4—92no—
307C2×C4⋊C4—182no—
308#107—31no—
309#107—92no—
310#107—91no—
311#103—32no—
312#103—92no—
313#102—92no—
314#102—92no—
315#97—91no—
316#97—91no—
317C4×C8—31no—
318C4×C8—91no—
319C23×C3—31no—
320C23×C3—62no—
321C22×D3—22no—
322C22×D3D3×D411yescharacteristic
323C3×Q8—22no—
324C3×Q8—22no—
325C3×Q8—24no—
326C3×Q8—42no—
327C3×Q8C2×C4×D314yes—
328C3×Q8C22×Dic314yes—
329C3×D4—34no—
330C3×D4—68no—
331C3×D4—62no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—21no—
335C2×C3×C4—31no—
336C2×C3×C4—32no—
337C2×C3×C4—32no—
338C2×C3×C4—31no—
339C2×C3×C4—31no—
340C2×C3×C4—42no—
341C2×C3×C4—68no—
342C2×C3×C4—62no—
343C2×C3×C4C23×D311yescharacteristic
344C2×C3×C4C23×D311yescharacteristic
345C2×Dic3—22no—
346C2×Dic3—31no—
347C2×Dic3—31no—
348C2×Dic3—31no—
349C2×Dic3—31no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—122no—
355C2×Dic3—242no—
356C2×Dic3—242no—
357C2×Dic3—242no—
358C2×Dic3D3×D411yescharacteristic
359C2×Dic3D3×D411yescharacteristic
360C2×Dic3D3×D411yescharacteristic
361D12—28no—
362D12—22no—
363D12C22×Dic314yes—
364C4×D3—28no—
365C4×D3—242no—
366C4×D3—242no—
367C4×D3—242no—
368C4×D3#23712yes—
369C4×D3C22×Dic312yes—
370C3×C8—22no—
371C3×C8—32no—
372C3×C8—61no—
373C3×C8C2×C4×D312yes—
374C3×C8C22×Dic312yes—
375C3⋊C8—21no—
376C3⋊C8—61no—
377C3⋊C8—61no—
378C3⋊C8—121no—
379C3⋊C8C22×Dic312yes—
380C2×C32C2×C4×D411yescharacteristic
381C2×C32#57611yescharacteristic
382C2×C32#57811yescharacteristic
383C3×D3—22no—
384C3×D3—44no—
385#41—38no—
386#41—64no—
387C2×Q8C2×D3212yes—
388C2×D4—32no—
389C2×D4—62no—
390C22×C4—31no—
391C22×C4—62no—
392C22×C4—182no—
393C22×C4—182no—
394C22×C4—182no—
395Q16D3×Dic314yescomplemented
396SD16—38no—
397D8—34no—
398M16—182no—
399C2×C8—31no—
400C2×C8—34no—
401C2×C8—31no—
402C2×C8—91no—
403C2×C8C2×D3211yescharacteristic
404C4⋊C4—32no—
405C4⋊C4—62no—
406C4⋊C4—91no—
407C4⋊C4—91no—
408C4⋊C4—92no—
409C4⋊C4—182no—
410C4⋊C4—182no—
411C22⋊C4—91no—
412C22⋊C4—91no—
413C22⋊C4—182no—
414C22⋊C4—182no—
415C42—31no—
416C42—62no—
417C42—91no—
418C42—182no—
419C22×C3—21no—
420C22×C3—32no—
421C22×C3—61no—
422C22×C3—61no—
423C22×C3—64no—
424C22×C3—122no—
425C22×C3—122no—
426C22×C3C2×D3×D411yescharacteristic
427C22×C3C2×D3×D411yescharacteristic
428C2×D3—21no—
429C2×D3—21no—
430C2×D3—24no—
431C2×D3—42no—
432C2×D3—42no—
433C2×D3D4×Dic312yes—
434C3×C4—24no—
435C3×C4—24no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—32no—
439C3×C4—44no—
440C3×C4—61no—
441C3×C4—61no—
442C3×C4—122no—
443C3×C4C22×C4×D311yescharacteristic
444C3×C4C2×#23711yescharacteristic
445C3×C4D3×#4111yescharacteristic
446C3×C4C23×Dic311yescharacteristic
447Dic3—21no—
448Dic3—21no—
449Dic3—42no—
450Dic3—62no—
451Dic3—61no—
452Dic3—61no—
453Dic3—61no—
454Dic3—61no—
455Dic3—121no—
456Dic3—122no—
457Dic3—122no—
458Dic3—242no—
459Dic3D4×Dic312yes—
460C32#295111yescharacteristic, complemented, Sylow
461C23—31no—
462C23—62no—
463Q8—22no—
464Q8C2×D3×Dic314yes—
465D4—34no—
466D4—68no—
467D4—62no—
468C2×C4—22no—
469C2×C4—31no—
470C2×C4—32no—
471C2×C4—32no—
472C2×C4—31no—
473C2×C4—31no—
474C2×C4—68no—
475C2×C4—62no—
476C2×C4—91no—
477C2×C4—91no—
478C2×C4—182no—
479C2×C4—722no—
480C2×C4—722no—
481C2×C4—722no—
482C2×C4C22×D3211yescharacteristic
483C8—32no—
484C8—61no—
485C8—181no—
486C8C2×D3×Dic312yes—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—62no—
491C2×C3—124no—
492C2×C3C4×D3×D411yescharacteristic
493C2×C3#576611yescharacteristic
494C2×C3#576911yescharacteristic
495C2×C3#576911yescharacteristic
496C2×C3#577111yescharacteristic
497C2×C3C2×D4×Dic311yescharacteristic
498D3—22no—
499D3—44no—
500C22—32no—
501C22—61no—
502C22—61no—
503C22—64no—
504C22—122no—
505C22—122no—
506C22D32×D411yescharacteristic
507C4—24no—
508C4—32no—
509C4—61no—
510C4—61no—
511C4—122no—
512C4—181no—
513C4—181no—
514C4—362no—
515C4D3×#23711yescharacteristic
516C4C22×D3×Dic311yescharacteristic
517C3—21no—
518C3#7972111yescharacteristic, complemented
519C3#8389811yescharacteristic, complemented
520C2—62no—
521C2—124no—
522C2#1059476811yescharacteristic
523C2#1059477111yescharacteristic
524C2D3×D4×Dic311yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC2×C3×#919C2
cosocleC2×C32×C4C24
hypercenterC2×Q16D32
hypocenterC32#2951
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. #10595394C2semidirect
3. Q16×C3⋊Dic3C2semidirect
4. C3×Dic3×Q16C2semidirect
5. #10591572C2semidirect
6. #10591566C2semidirect
7. #10591550C2semidirect
8. #10590777C2semidirect
9. Dic3×D24C2semidirect
10. #10590692C2semidirect
11. D3×#818C2semidirect
19. C3×#919C4semidirect
51. Dic3×Q16D3semidirect
67. C3×#239C2×C4semidirect
75. C32×Q16C2×C4semidirect
82. C3×#215C2×C4semidirect
89. C3×D24C2×C4semidirect
90. C3×D3×C8C2×C4semidirect
124. #919Dic3semidirect
211. #239C2×Dic3semidirect
220. C3×Q16C4×D3semidirect
221. C3×Q16C2×Dic3semidirect
238. #215C2×Dic3semidirect
271. D24C2×Dic3semidirect
273. D3×C8C2×Dic3semidirect
395. Q16D3×Dic3semidirect
460. C32#2951semidirect
518. C3#79721semidirect
519. C3#83898semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9192
#105953942
Q16×C3⋊Dic32
C3×Dic3×Q162
#105915722
#105915662
#105915502
#105907772
Dic3×D242
#105906922
D3×#8182
#838983
#797213