Finite Group Databasebeta

← #11860698

Subgroups — #11860698

Order 1152.

1225 conjugacy classes of subgroups.

The subgroup lattice has 487 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596269C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic
3#10594982C211yesmaximal, characteristic, complemented
4C3×#5215C211yesmaximal, characteristic, complemented
5#10591436C214yesmaximal, complemented
6#10591435C214yesmaximal, complemented
7#10591122C211yesmaximal, characteristic, complemented
8#10591086C211yesmaximal, characteristic, complemented
9#10591059C211yesmaximal, characteristic, complemented
10#83823—31nomaximal
11#78915—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C2×#3757—22no—
15D4×C3⋊Dic3—22no—
16D4×C3⋊Dic3C2214yescomplemented
17#64135C2211yescharacteristic
18#64135C2211yescharacteristic
19C2×C3×#213C418yescomplemented
20C2×C3×#213C2212yes—
21C2×C3×#213C2212yes—
22C3×#926C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25D3×#217—22no—
26#63898C2214yescomplemented
27Dic3×D12—22no—
28C3×#832C2214yescomplemented
29#63575C2212yescomplemented
30#63573C2212yescomplemented
31#63563C2214yescomplemented
32#63555C2212yescomplemented
33#63553C2212yescomplemented
34C22×C3×D8—31no—
35#5798—31no—
36#5798—31no—
37#5798—31no—
38#5798—61no—
39C22×#213D311yescharacteristic
40#5521—31no—
41C3×#418—31no—
42#5215—31no—
43#5215D311yescharacteristic, complemented
44#5152—34no—
45Dic3×D8—34no—
46#5131—31no—
47#5122—31no—
48#5106—31no—
49#5101—31no—
50#4998—31no—
51#4785—34no—
52#4756—34no—
53C24×C32—21no—
54C23×C3×D3—21no—
55C2×C32×D4—21no—
56C2×C32×D4—22no—
57C2×C32×D4C2×C414yescomplemented
58C2×C32×D4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3—24no—
61C2×C3×D12—21no—
62C2×C3×D12—22no—
63C2×C3×D12C2×C414yescomplemented
64C2×C3×D12C2312yes—
65C2×D3×Dic3—24no—
66#3757—21no—
67#3757—24no—
68#3757D412yes—
69C4⋊(C3⋊Dic3)D412yes—
70C4⋊(C3⋊Dic3)C2312yes—
71C4×C3⋊Dic3—21no—
72C4×C3⋊Dic3C2312yes—
73C3×#217—21no—
74C3×#213C2×C418yescomplemented
75C3×#213C2×C418yescomplemented
76C3×C4⋊Dic3C2312yes—
77C3×C4×Dic3—21no—
78C3×#208—22no—
79C2×C3×C3⋊C8C2×C414yescomplemented
80C2×C3×C3⋊C8C2312yes—
81C2×C3×C3⋊C8C2311yescharacteristic
82C2×C3×C3⋊C8C2311yescharacteristic
83(C2×D3)⋊Dic3—24no—
84#2948—91noSylow
85C22×C3×D4—21no—
86C22×C3×D4—31no—
87C22×C3×D4C2×D311yescharacteristic
88C22×C3×D4C2×D311yescharacteristic
89C22×D12C2×D311yescharacteristic
90C2×C3×D8—38no—
91C2×C3×D8—32no—
92C2×C3×D8—32no—
93C2×C3×M16—31no—
94C22×C3×C8—31no—
95C3×#117—31no—
96C2×#217—62no—
97C2×#217—62no—
98C2×#217—62no—
99C2×#217—64no—
100D4×Dic3—34no—
101D4×Dic3—34no—
102D4×Dic3—34no—
103D4×Dic3—64no—
104D4×Dic3—62no—
105D4×Dic3—62no—
106D4×Dic3—62no—
107D4×Dic3—64no—
108C2×#213Dic318yescomplemented
109C2×#213C2×D312yes—
110C2×#213C2×D312yes—
111#926—31no—
112#926—31no—
113#926—31no—
114#926—31no—
115#926—61no—
116#926—61no—
117#926C2×D311yescharacteristic
118C2×#208C2×D311yescharacteristic
119C22×C3⋊C8C2×D311yescharacteristic
120#893—34no—
121D3×C22⋊C4—62no—
122C4×D12—62no—
123C3×#102—34no—
124#832—34no—
125#832C2×D314yescomplemented
126#821—34no—
127#818—32no—
128#817—32no—
129#815—32no—
130#815—32no—
131C8×Dic3—32no—
132C8×Dic3—32no—
133#808—32no—
134#807—32no—
135C23×C32—22no—
136C23×C32—24no—
137C23×C32—82no—
138C23×C32C2×D411yescharacteristic
139C22×C3×D3—22no—
140C22×C3×D3—24no—
141C22×C3×D3—82no—
142C32×D4—24no—
143C32×D4—22no—
144C32×D4C22×C414yes—
145C2×C32×C4C22×C412yes—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4#4112yes—
148C2×C32×C4C2411yescharacteristic
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—84no—
151C2×C3⋊Dic3C2×D414yes—
152C2×C3×Dic3—22no—
153C3×D12—24no—
154C3×D12—22no—
155C3×D12C22×C414yes—
156D3×Dic3—84no—
157C3×C3⋊C8—22no—
158C3×C3⋊C8C22×C412yes—
159C3×C3⋊C8C22×C412yes—
160C22×D8—31no—
161#518—91no—
162#518—91no—
163#442—94no—
164C4×D8—94no—
165#427—91no—
166#418—31no—
167#418—91no—
168#405—91no—
169C24×C3—22no—
170C24×C3—21no—
171C24×C3—21no—
172C24×C3—61no—
173C23×D3—21no—
174C2×C3×D4—22no—
175C2×C3×D4—24no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4—22no—
179C2×C3×D4—22no—
180C2×C3×D4—24no—
181C2×C3×D4—22no—
182C2×C3×D4—34no—
183C2×C3×D4—32no—
184C2×C3×D4—61no—
185C2×C3×D4—62no—
186C2×C3×D4C4×D314yescomplemented
187C2×C3×D4C2×Dic314yescomplemented
188C2×C3×D4C22×D312yes—
189C2×C3×D4C22×D312yes—
190C22×C3×C4—21no—
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C22×Dic3—64no—
194C22×Dic3—64no—
195C22×Dic3—64no—
196C22×Dic3—68no—
197C2×D12—21no—
198C2×D12—22no—
199C2×D12C2×Dic314yescomplemented
200C2×D12C22×D312yes—
201C2×C4×D3—64no—
202C3×D8—38no—
203C3×D8—38no—
204C3×M16—62no—
205C2×C3×C8—34no—
206C2×C3×C8—31no—
207C2×C3×C8—31no—
208C2×C3×C8—32no—
209C3×C4⋊C4—32no—
210C3×C22⋊C4—61no—
211C3×C42—61no—
212#217—21no—
213#217—32no—
214#217—32no—
215#217—62no—
216#217—64no—
217#217—64no—
218#217—64no—
219#217—62no—
220#217—68no—
221#217—61no—
222#217—61no—
223#213C2×Dic318yescomplemented
224#213C2×Dic318yescomplemented
225(C2×D3)⋊C4—64no—
226C4⋊Dic3—32no—
227C4⋊Dic3—32no—
228C4⋊Dic3—32no—
229C4⋊Dic3—32no—
230C4⋊Dic3—62no—
231C4⋊Dic3—62no—
232C4⋊Dic3C22×D312yes—
233C4×Dic3—21no—
234C4×Dic3—32no—
235C4×Dic3—32no—
236C4×Dic3—62no—
237C4×Dic3—62no—
238C4×Dic3—61no—
239C4×Dic3—61no—
240#208—22no—
241C2×C3⋊C8C2×Dic314yescomplemented
242C2×C3⋊C8C22×D312yes—
243C2×C3⋊C8C22×D311yescharacteristic
244C2×C3⋊C8C22×D311yescharacteristic
245C22×C32—24no—
246C22×C32—22no—
247C22×C32—44no—
248C22×C32—84no—
249C22×C32C4×D412yes—
250C22×C32C22×D411yescharacteristic
251C2×C3×D3—24no—
252C2×C3×D3—44no—
253C2×C3×D3—84no—
254C32×C4C4×D412yes—
255C32×C4C23×C411yescharacteristic
256C32×C4C2×#4111yescharacteristic
257C3⋊Dic3—24no—
258C3⋊Dic3—42no—
259C3×Dic3—42no—
260C22×D4—31no—
261C22×D4D3211yescharacteristic
262C2×D8—38no—
263C2×D8—32no—
264C2×D8—32no—
265C2×M16—31no—
266C22×C8—31no—
267C4×D4—94no—
268C4×D4—94no—
269C4×D4—182no—
270C4×D4—182no—
271#117—31no—
272#117—91no—
273#117—91no—
274C2×C22⋊C4—182no—
275C2×C22⋊C4—182no—
276#107—92no—
277#106—92no—
278#102—34no—
279#102—94no—
280#97—92no—
281C4×C8—92no—
282C23×C3—24no—
283C23×C3—28no—
284C23×C3—22no—
285C23×C3—22no—
286C23×C3—24no—
287C23×C3—24no—
288C23×C3—21no—
289C23×C3—62no—
290C23×C3—64no—
291C23×C3—82no—
292C23×C3—82no—
293C23×C3—84no—
294C23×C3—242no—
295C23×C3D3×D411yescharacteristic
296C23×C3D3×D411yescharacteristic
297C22×D3—22no—
298C22×D3—24no—
299C22×D3—82no—
300C3×D4—24no—
301C3×D4—28no—
302C3×D4—24no—
303C3×D4—24no—
304C3×D4—22no—
305C3×D4—22no—
306C3×D4—24no—
307C3×D4—34no—
308C3×D4—64no—
309C3×D4—62no—
310C3×D4C2×C4×D314yes—
311C3×D4C22×Dic314yes—
312C2×C3×C4—21no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—21no—
316C2×C3×C4—62no—
317C2×C3×C4C2×C4×D312yes—
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4#23712yes—
321C2×C3×C4#23712yes—
322C2×C3×C4C22×Dic312yes—
323C2×C3×C4C23×D311yescharacteristic
324C2×C3×C4C23×D311yescharacteristic
325C2×Dic3—22no—
326C2×Dic3—34no—
327C2×Dic3—34no—
328C2×Dic3—64no—
329C2×Dic3—64no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—244no—
333C2×Dic3—244no—
334C2×Dic3—244no—
335C2×Dic3—248no—
336D12—24no—
337D12—22no—
338D12C22×Dic314yes—
339C4×D3—244no—
340C3×C8—32no—
341C3×C8—32no—
342C3×C8—62no—
343C3⋊C8—22no—
344C3⋊C8C22×Dic312yes—
345C3⋊C8C22×Dic312yes—
346C2×C32—22no—
347C2×C32—44no—
348C2×C32C2×C4×D411yescharacteristic
349C2×C32#57612yes—
350C3×D3—44no—
351C24—21no—
352C24—61no—
353C2×D4—22no—
354C2×D4—21no—
355C2×D4—32no—
356C2×D4—34no—
357C2×D4—62no—
358C2×D4—61no—
359C2×D4D3×Dic314yescomplemented
360C2×D4C2×D3212yes—
361C22×C4—184no—
362C22×C4—184no—
363C22×C4C2×D3211yescharacteristic
364D8—38no—
365D8—38no—
366M16—62no—
367C2×C8—31no—
368C2×C8—31no—
369C2×C8—34no—
370C2×C8—32no—
371C4⋊C4—32no—
372C4⋊C4—92no—
373C4⋊C4—92no—
374C22⋊C4—61no—
375C22⋊C4—92no—
376C22⋊C4—184no—
377C22⋊C4—184no—
378C22⋊C4—181no—
379C42—61no—
380C42—92no—
381C42—181no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—28no—
385C22×C3—24no—
386C22×C3—24no—
387C22×C3—21no—
388C22×C3—22no—
389C22×C3—42no—
390C22×C3—48no—
391C22×C3—44no—
392C22×C3—44no—
393C22×C3—64no—
394C22×C3—84no—
395C22×C3—84no—
396C22×C3—88no—
397C22×C3—124no—
398C22×C3—244no—
399C22×C3#67⋊C412yes—
400C22×C3D4×Dic312yes—
401C22×C3C2×D3×D411yescharacteristic
402C22×C3C2×D3×D411yescharacteristic
403C2×D3—24no—
404C2×D3—44no—
405C2×D3—84no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—22no—
409C3×C4—122no—
410C3×C4#67⋊C412yes—
411C3×C4D4×Dic312yes—
412C3×C4C22×C4×D311yescharacteristic
413C3×C4C2×#23711yescharacteristic
414C3×C4C2×#23711yescharacteristic
415C3×C4C23×Dic311yescharacteristic
416Dic3—42no—
417Dic3—64no—
418Dic3—64no—
419Dic3—124no—
420Dic3—124no—
421Dic3—122no—
422Dic3—122no—
423C32#294811yescharacteristic, complemented, Sylow
424C23—22no—
425C23—24no—
426C23—62no—
427C23—64no—
428C23—82no—
429C23—242no—
430C23#381111yescharacteristic
431D4—22no—
432D4—24no—
433D4—34no—
434D4—62no—
435D4—64no—
436D4C2×D3×Dic314yes—
437C2×C4—62no—
438C2×C4—94no—
439C2×C4—182no—
440C2×C4—724no—
441C2×C4—724no—
442C2×C4C2×D3×Dic312yes—
443C2×C4#380512yes—
444C2×C4#381111yescharacteristic
445C2×C4C22×D3211yescharacteristic
446C8—32no—
447C8—32no—
448C8—62no—
449C2×C3—22no—
450C2×C3—22no—
451C2×C3—22no—
452C2×C3—21no—
453C2×C3—42no—
454C2×C3—48no—
455C2×C3—44no—
456C2×C3—44no—
457C2×C3—124no—
458C2×C3C2×#67⋊C411yescharacteristic
459C2×C3#575712yes—
460C2×C3#577412yes—
461C2×C3C2×D4×Dic311yescharacteristic
462D3—44no—
463C22—22no—
464C22—24no—
465C22—44no—
466C22—64no—
467C22—84no—
468C22—124no—
469C22—244no—
470C22#67⋊Dic312yes—
471C22C2×#381111yescharacteristic
472C4—122no—
473C4—184no—
474C4—362no—
475C4#67⋊Dic312yes—
476C4C22×D3×Dic311yescharacteristic
477C4C2×#380511yescharacteristic
478C3—21no—
479C3#7891511yescharacteristic, complemented
480C3#8382311yescharacteristic, complemented
481C2—22no—
482C2—44no—
483C2—124no—
484C2#1059510212yes—
485C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC22×C3×#213C2
cosocleC2×C32×C4C24
hypercenterC22×D4D32
hypocenterC32#2948
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #10596269C2semidirect
3. #10594982C2semidirect
4. C3×#5215C2semidirect
5. #10591436C2semidirect
6. #10591435C2semidirect
7. #10591122C2semidirect
8. #10591086C2semidirect
9. #10591059C2semidirect
16. D4×C3⋊Dic3C22semidirect
19. C2×C3×#213C4semidirect
26. #63898C22semidirect
28. C3×#832C22semidirect
29. #63575C22semidirect
30. #63573C22semidirect
31. #63563C22semidirect
32. #63555C22semidirect
33. #63553C22semidirect
43. #5215D3semidirect
57. C2×C32×D4C2×C4semidirect
63. C2×C3×D12C2×C4semidirect
74. C3×#213C2×C4semidirect
75. C3×#213C2×C4semidirect
79. C2×C3×C3⋊C8C2×C4semidirect
108. C2×#213Dic3semidirect
125. #832C2×D3semidirect
186. C2×C3×D4C4×D3semidirect
187. C2×C3×D4C2×Dic3semidirect
199. C2×D12C2×Dic3semidirect
223. #213C2×Dic3semidirect
224. #213C2×Dic3semidirect
241. C2×C3⋊C8C2×Dic3semidirect
359. C2×D4D3×Dic3semidirect
423. C32#2948semidirect
479. C3#78915semidirect
480. C3#83823semidirect

Maximal subgroups

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

subgroupindex
#105962692
C22×C3×#2132
#105949822
C3×#52152
#105914362
#105914352
#105911222
#105910862
#105910592
#838233
#789153