Finite Group Databasebeta

← #11786589

Subgroups — #11786589

Order 1152.

707 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594982C211yesmaximal, characteristic
2#10592820C211yesmaximal, characteristic, complemented
3C2×C3×#823C211yesmaximal, characteristic
4#10591318C211yesmaximal, characteristic
5#10591131C211yesmaximal, characteristic, complemented
6C3×#4555C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#70068—31nomaximal
9#68758—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17D3×#217—22no—
18C2×(C2×D3)⋊Dic3—22no—
19#63898—21no—
20#63898—21no—
21Dic3×D12—21no—
22Dic3×D12—21no—
23#63645—21no—
24#63644—21no—
25C3×#823C414yescomplemented
26#63575—21no—
27#63573—21no—
28#5798—31no—
29#5521—31no—
30C2×C3×#100—31no—
31#5221—31no—
32C2×#823D311yescharacteristic
33#5121—31no—
34#5121—31no—
35#5121—31no—
36#5121—61no—
37#4995—31no—
38#4939—31no—
39C3×#339—31no—
40#4555—31no—
41#4555D311yescharacteristic, complemented
42#4523—31no—
43C23×C3×D3D412yes—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C22×C3×Dic3—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12C2×C412yes—
52C2×C3×D12Q812yes—
53C2×D3×Dic3—22no—
54C2×D3×Dic3—22no—
55C32×M16—21no—
56C32×M16C2×C412yescomplemented
57C2×C32×C8—21no—
58#3757—21no—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)D411yescharacteristic
62C4⋊(C3⋊Dic3)D411yescharacteristic
63C4×C3⋊Dic3—21no—
64C3×#217—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×C4⋊Dic3D411yescharacteristic
67C3×C4×Dic3—21no—
68C3×C4×Dic3—21no—
69C3×C4×Dic3—21no—
70C3×#208—21no—
71C3×#208C2×C412yescomplemented
72C2×C3×C3⋊C8—21no—
73(C2×D3)⋊Dic3—22no—
74(C2×D3)⋊Dic3—22no—
75(C2×D3)⋊Dic3—44no—
76#1856—91noSylow
77C22×C3×D4—31no—
78C22×D12C2×D311yescharacteristic
79C2×C3×M16—21no—
80C2×C3×M16—31no—
81C2×C3×M16C2×D311yescharacteristic
82C2×C3×M16C2×D311yescharacteristic
83C3×#117—31no—
84C2×C3×C42—31no—
85C2×#217—62no—
86C2×#217—62no—
87D4×Dic3—61no—
88D4×Dic3—61no—
89D4×Dic3—61no—
90D4×Dic3—61no—
91C2×(C2×D3)⋊C4—62no—
92#926—31no—
93#926—31no—
94#926—61no—
95#926C2×D311yescharacteristic
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—61no—
99C2×C4×Dic3C2×D311yescharacteristic
100C2×#208C2×D311yescharacteristic
101#893—61no—
102#893—61no—
103D3×C22⋊C4—62no—
104C4×D12—61no—
105C4×D12—61no—
106C3×#100—34no—
107#823Dic314yescomplemented
108#818—61no—
109#818—61no—
110#818—62no—
111#818—61no—
112#817—61no—
113#817—61no—
114#817—62no—
115#817—61no—
116#808—61no—
117#807—61no—
118C23×C32C2×D411yescharacteristic
119C22×C3×D3—22no—
120C22×C3×D3—22no—
121C22×C3×D3—42no—
122C22×C3×D3—42no—
123C22×C3×D3C4⋊C414yes—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×Q811yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—42no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C3×D12—22no—
140C3×D12—22no—
141C3×D12—22no—
142C3×D12—22no—
143D3×Dic3—82no—
144D3×Dic3—82no—
145C32×C8—22no—
146C3×C3⋊C8—22no—
147#518—91no—
148#428—91no—
149#428—91no—
150C2×#100—31no—
151#390—91no—
152#339—31no—
153#339—91no—
154C24×C3—32no—
155C23×D3D1212yes—
156C2×C3×D4—32no—
157C2×C3×D4—32no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C22×C3×C4—21no—
163C22×C3×C4—61no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C22×Dic3—21no—
167C22×Dic3—62no—
168C22×Dic3—62no—
169C22×Dic3—61no—
170C22×Dic3—61no—
171C22×Dic3—121no—
172C2×D12—21no—
173C2×D12—21no—
174C2×D12—21no—
175C2×D12—21no—
176C2×D12Dic612yes—
177C2×D12C2×Dic312yes—
178C2×C4×D3—62no—
179C2×C4×D3—62no—
180C3×M16—22no—
181C3×M16—21no—
182C3×M16—21no—
183C3×M16—22no—
184C3×M16—32no—
185C3×M16—61no—
186C3×M16C4×D312yescomplemented
187C3×M16C2×Dic312yescomplemented
188C2×C3×C8—22no—
189C2×C3×C8—21no—
190C2×C3×C8—21no—
191C2×C3×C8—61no—
192C3×C4⋊C4—31no—
193C3×C4⋊C4—31no—
194C3×C22⋊C4—61no—
195C3×C42—61no—
196C3×C42—61no—
197C3×C42—61no—
198#217—21no—
199#217—62no—
200#217—62no—
201#217—61no—
202#217—61no—
203#217—121no—
204#217—124no—
205(C2×D3)⋊C4—62no—
206(C2×D3)⋊C4—62no—
207(C2×D3)⋊C4—124no—
208C4⋊Dic3—31no—
209C4⋊Dic3—31no—
210C4⋊Dic3—31no—
211C4⋊Dic3—31no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214C4⋊Dic3—62no—
215C4⋊Dic3—61no—
216C4⋊Dic3—61no—
217C4⋊Dic3—61no—
218C4⋊Dic3—61no—
219C4⋊Dic3—121no—
220C4⋊Dic3D1211yescharacteristic
221C4⋊Dic3D1211yescharacteristic
222C4×Dic3—21no—
223C4×Dic3—21no—
224C4×Dic3—21no—
225C4×Dic3—61no—
226C4×Dic3—61no—
227C4×Dic3—121no—
228#208—21no—
229#208C2×Dic312yescomplemented
230C2×C3⋊C8—21no—
231C22×C32—21no—
232C22×C32—21no—
233C22×C32C2×C4⋊C411yescharacteristic
234C22×C32#12011yescharacteristic
235C22×C32#12311yescharacteristic
236C2×C3×D3—24no—
237C2×C3×D3—42no—
238C2×C3×D3—42no—
239C2×C3×D3—44no—
240C2×C3×D3—82no—
241C32×C4C4×D411yescharacteristic
242C32×C4C4×D411yescharacteristic
243C32×C4C22⋊Q811yescharacteristic
244C32×C4C22⋊Q811yescharacteristic
245C3⋊Dic3—41no—
246C3⋊Dic3—41no—
247C3⋊Dic3—81no—
248C3×Dic3—42no—
249C3×Dic3—41no—
250C3×Dic3—41no—
251C22×D4—31no—
252C2×M16—31no—
253C2×M16D3211yescharacteristic
254C4×D4—181no—
255C4×D4—181no—
256C4×D4—181no—
257C4×D4—181no—
258#117—31no—
259#117—91no—
260C2×C4⋊C4—91no—
261C2×C22⋊C4—182no—
262C2×C22⋊C4—182no—
263C2×C42—31no—
264#107—181no—
265#107—181no—
266#106—181no—
267#106—181no—
268#100—34no—
269C23×C3—21no—
270C23×C3—34no—
271C23×C3—62no—
272C23×C3—62no—
273C23×C3—122no—
274C23×C3—122no—
275C23×C3C2×D1211yescharacteristic
276C23×C3D3×D411yescharacteristic
277C22×D3—22no—
278C22×D3—22no—
279C22×D3—42no—
280C22×D3—42no—
281C22×D3C4⋊Dic314yes—
282C3×D4—62no—
283C3×D4—62no—
284C3×D4—62no—
285C3×D4—62no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—62no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4—121no—
296C2×C3×C4—121no—
297C2×C3×C4C2×Dic611yescharacteristic
298C2×C3×C4C2×C4×D311yescharacteristic
299C2×C3×C4C2×D1211yescharacteristic
300C2×C3×C4#23511yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4#23711yescharacteristic
305C2×C3×C4#23711yescharacteristic
306C2×C3×C4#23711yescharacteristic
307C2×C3×C4D3×Q811yescharacteristic
308C2×C3×C4C22×Dic311yescharacteristic
309C2×Dic3—22no—
310C2×Dic3—21no—
311C2×Dic3—21no—
312C2×Dic3—41no—
313C2×Dic3—41no—
314C2×Dic3—61no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—61no—
318C2×Dic3—121no—
319C2×Dic3—121no—
320C2×Dic3—122no—
321C2×Dic3—122no—
322C2×Dic3—122no—
323C2×Dic3—121no—
324C2×Dic3—121no—
325C2×Dic3—242no—
326C2×Dic3—242no—
327C2×Dic3—242no—
328D12—22no—
329D12—22no—
330D12—22no—
331D12—22no—
332C4×D3—242no—
333C4×D3—242no—
334C3×C8—24no—
335C3×C8—22no—
336C3×C8—22no—
337C3×C8—62no—
338C3⋊C8—22no—
339C2×C32—21no—
340C2×C32—21no—
341C2×C32#38511yescharacteristic
342C2×C32#45311yescharacteristic
343C2×C32#45511yescharacteristic
344C3×D3—44no—
345C24—32no—
346C2×D4—32no—
347C2×D4—32no—
348C2×D4—61no—
349C2×D4—61no—
350C2×D4—61no—
351C2×D4—61no—
352C22×C4—61no—
353C22×C4—182no—
354C22×C4—182no—
355C22×C4—181no—
356C22×C4C2×D3211yescharacteristic
357M16—21no—
358M16—32no—
359M16—61no—
360M16D3×Dic312yescomplemented
361C2×C8—21no—
362C2×C8—61no—
363C4⋊C4—31no—
364C4⋊C4—31no—
365C4⋊C4—91no—
366C4⋊C4—91no—
367C4⋊C4—181no—
368C4⋊C4—181no—
369C22⋊C4—61no—
370C22⋊C4—182no—
371C22⋊C4—182no—
372C22⋊C4—181no—
373C22⋊C4—364no—
374C42—61no—
375C42—61no—
376C42—61no—
377C42—181no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—64no—
388C22×C3—124no—
389C22×C3—122no—
390C22×C3—122no—
391C22×C3—242no—
392C22×C3#88211yescharacteristic
393C22×C3#88211yescharacteristic
394C22×C3#88311yescharacteristic
395C22×C3#88611yescharacteristic
396C22×C3D3×C4⋊C411yescharacteristic
397C22×C3C2×C4⋊Dic311yescharacteristic
398C2×D3—24no—
399C2×D3—42no—
400C2×D3—42no—
401C2×D3—44no—
402C2×D3—82no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—122no—
408C3×C4—121no—
409C3×C4—121no—
410C3×C4C4×D1211yescharacteristic
411C3×C4#87811yescharacteristic
412C3×C4#87811yescharacteristic
413C3×C4#67⋊C411yescharacteristic
414C3×C4#89611yescharacteristic
415C3×C4#89711yescharacteristic
416C3×C4D4×Dic311yescharacteristic
417C3×C4D4×Dic311yescharacteristic
418Dic3—42no—
419Dic3—41no—
420Dic3—41no—
421Dic3—121no—
422Dic3—121no—
423Dic3—121no—
424Dic3—121no—
425Dic3—241no—
426Dic3—241no—
427Dic3—242no—
428Dic3—241no—
429Dic3—241no—
430C32#185611yescharacteristic, complemented, Sylow
431C23—34no—
432C23—62no—
433C23—62no—
434C23—122no—
435C23—122no—
436C23D3×D1211yescharacteristic
437D4—62no—
438D4—62no—
439D4—62no—
440D4—62no—
441C2×C4—62no—
442C2×C4—61no—
443C2×C4—61no—
444C2×C4—121no—
445C2×C4—121no—
446C2×C4—181no—
447C2×C4—181no—
448C2×C4—362no—
449C2×C4—361no—
450C2×C4—722no—
451C2×C4—722no—
452C2×C4D3×Dic611yescharacteristic
453C2×C4#379511yescharacteristic
454C2×C4D3×D1211yescharacteristic
455C2×C4C2×D3×Dic311yescharacteristic
456C2×C4#380511yescharacteristic
457C2×C4#381111yescharacteristic
458C8—22no—
459C8—62no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—41no—
468C2×C3—41no—
469C2×C3—124no—
470C2×C3#466811yescharacteristic
471C2×C3#474611yescharacteristic
472C2×C3#474711yescharacteristic
473C2×C3#482211yescharacteristic
474C2×C3#482511yescharacteristic
475C2×C3#495011yescharacteristic
476D3—44no—
477C22—21no—
478C22—21no—
479C22—64no—
480C22—124no—
481C22—122no—
482C22—122no—
483C22—242no—
484C22D3×C4⋊Dic311yescharacteristic
485C22#6389111yescharacteristic
486C22#6392311yescharacteristic
487C4—122no—
488C4—121no—
489C4—121no—
490C4—361no—
491C4—361no—
492C4—721no—
493C4Dic3×D1211yescharacteristic
494C4#6389311yescharacteristic
495C4#6389611yescharacteristic
496C4#67⋊Dic311yescharacteristic
497C3—21no—
498C3#6875811yescharacteristic, complemented
499C3#7006811yescharacteristic, complemented
500C2—21no—
501C2—21no—
502C2—124no—
503C2#1059101511yescharacteristic
504C2#1059101611yescharacteristic
505C2#1059137911yescharacteristic
subgroupG/H
centerC22#63923
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#120
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1856
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10592820C2semidirect
5. #10591131C2semidirect
6. C3×#4555C2semidirect
7. #10589162C2semidirect
25. C3×#823C4semidirect
41. #4555D3semidirect
56. C32×M16C2×C4semidirect
71. C3×#208C2×C4semidirect
107. #823Dic3semidirect
186. C3×M16C4×D3semidirect
187. C3×M16C2×Dic3semidirect
229. #208C2×Dic3semidirect
360. M16D3×Dic3semidirect
430. C32#1856semidirect
498. C3#68758semidirect
499. C3#70068semidirect

Maximal subgroups

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

subgroupindex
#105949822
#105928202
C2×C3×#8232
#105913182
#105911312
C3×#45552
#105891622
#700683
#687583