Finite Group Databasebeta

← #11860762

Subgroups — #11860762

Order 1152.

1117 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596283C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic
3#10594982C211yesmaximal, characteristic
4C3×#5225C211yesmaximal, characteristic, complemented
5#10591572C214yesmaximal, complemented
6#10591571C214yesmaximal, complemented
7#10591122C211yesmaximal, characteristic, complemented
8#10591086C211yesmaximal, characteristic
9#10591059C211yesmaximal, characteristic, complemented
10#83843—31nomaximal
11#78947—31nomaximal
12C22×C32×Q8C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14Q8×C3⋊Dic3—22no—
15Q8×C3⋊Dic3C2214yescomplemented
16#64135—22no—
17#64135C2211yescharacteristic
18#64135C2211yescharacteristic
19C2×C3×#215C418yescomplemented
20C2×C3×#215C2212yes—
21C2×C3×#215C2212yes—
22C3×#926C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25D3×#217—22no—
26#63898C2214yes—
27Dic3×D12—22no—
28C3×#835C2214yescomplemented
29#63575C2212yescomplemented
30#63573C2212yescomplemented
31#63563C2214yes—
32#63555C2212yescomplemented
33#63553C2212yescomplemented
34C22×C3×SD16—31no—
35#5812—31no—
36#5812—31no—
37#5812—61no—
38C22×#215D311yescharacteristic
39#5798—31no—
40#5521—31no—
41C3×#419—31no—
42#5225D311yescharacteristic, complemented
43#5215—31no—
44#5164—34no—
45Dic3×SD16—34no—
46#5131—31no—
47#5122—31no—
48#5106—31no—
49#5101—31no—
50#4998—31no—
51#4817—34no—
52#4788—34no—
53C23×C3×D3—21no—
54C2×C32×Q8—21no—
55C2×C32×Q8—22no—
56C2×C32×Q8C2×C414yescomplemented
57C2×C32×Q8C2312yes—
58C22×C32×C4—21no—
59C22×C32×C4C2311yescharacteristic
60C2×C3×D12—21no—
61C2×C3×D12—22no—
62C2×C3×D12C2×C414yes—
63C2×C3×D12C2312yes—
64C2×D3×Dic3—24no—
65#3757—21no—
66#3757D412yes—
67C4⋊(C3⋊Dic3)—24no—
68C4⋊(C3⋊Dic3)D412yes—
69C4⋊(C3⋊Dic3)C2312yes—
70C4×C3⋊Dic3—21no—
71C4×C3⋊Dic3—24no—
72C4×C3⋊Dic3C2312yes—
73C3×#217—21no—
74C3×#215C2×C418yescomplemented
75C3×#215C2×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#2949—91noSylow
85C22×C3×Q8—21no—
86C22×C3×Q8C2×D311yescharacteristic
87C22×C3×Q8C2×D311yescharacteristic
88C22×C3×D4—31no—
89C22×D12C2×D311yescharacteristic
90C2×C3×SD16—38no—
91C2×C3×SD16—32no—
92C2×C3×SD16—32no—
93C2×C3×M16—31no—
94C22×C3×C8—31no—
95C3×#117—31no—
96C2×#217—62no—
97Q8×Dic3—34no—
98Q8×Dic3—34no—
99Q8×Dic3—64no—
100Q8×Dic3—62no—
101Q8×Dic3—62no—
102Q8×Dic3—64no—
103C2×#215Dic318yescomplemented
104C2×#215C2×D312yes—
105C2×#215C2×D312yes—
106D4×Dic3—34no—
107D4×Dic3—62no—
108#926—31no—
109#926—31no—
110#926—31no—
111#926—31no—
112#926—61no—
113#926—61no—
114#926—62no—
115#926—62no—
116#926—64no—
117#926C2×D311yescharacteristic
118C2×#208C2×D311yescharacteristic
119C22×C3⋊C8C2×D311yescharacteristic
120#893—34no—
121D3×C22⋊C4—62no—
122C4×D12—62no—
123C3×#103—34no—
124#835C2×D314yescomplemented
125#832—34no—
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×C32C2×D411yescharacteristic
136C22×C3×D3—22no—
137C22×C3×D3—24no—
138C22×C3×D3—82no—
139C32×Q8—24no—
140C32×Q8—22no—
141C32×Q8C22×C414yes—
142C2×C32×C4—24no—
143C2×C32×C4—22no—
144C2×C32×C4C22×C412yes—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4#4112yes—
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3C2×D414yes—
150C2×C3×Dic3—22no—
151C3×D12—24no—
152C3×D12—22no—
153C3×D12C22×C414yes—
154D3×Dic3—84no—
155C3×C3⋊C8—22no—
156C3×C3⋊C8C22×C412yes—
157C3×C3⋊C8C22×C412yes—
158C22×SD16—31no—
159#519—91no—
160#518—91no—
161#440—94no—
162C4×SD16—94no—
163#427—91no—
164#419—31no—
165#418—91no—
166#405—91no—
167C24×C3—61no—
168C23×D3—21no—
169C2×C3×Q8—22no—
170C2×C3×Q8—24no—
171C2×C3×Q8—21no—
172C2×C3×Q8—21no—
173C2×C3×Q8—22no—
174C2×C3×Q8—22no—
175C2×C3×Q8—24no—
176C2×C3×Q8—22no—
177C2×C3×Q8C4×D314yescomplemented
178C2×C3×Q8C2×Dic314yescomplemented
179C2×C3×Q8C22×D312yes—
180C2×C3×Q8C22×D312yes—
181C2×C3×D4—34no—
182C2×C3×D4—32no—
183C2×C3×D4—61no—
184C2×C3×D4—62no—
185C22×C3×C4—22no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C22×Dic3—64no—
192C2×D12—21no—
193C2×D12—22no—
194C2×D12C2×Dic314yes—
195C2×D12C22×D312yes—
196C2×C4×D3—64no—
197C3×SD16—38no—
198C3×SD16—38no—
199C3×M16—62no—
200C2×C3×C8—34no—
201C2×C3×C8—31no—
202C2×C3×C8—31no—
203C2×C3×C8—32no—
204C3×C4⋊C4—32no—
205C3×C22⋊C4—61no—
206C3×C42—61no—
207#217—21no—
208#217—32no—
209#217—32no—
210#217—62no—
211#217—64no—
212#217—62no—
213#217—61no—
214#217—61no—
215#215C2×Dic318yescomplemented
216#215C2×Dic318yescomplemented
217(C2×D3)⋊C4—64no—
218C4⋊Dic3—32no—
219C4⋊Dic3—32no—
220C4⋊Dic3—32no—
221C4⋊Dic3—32no—
222C4⋊Dic3—62no—
223C4⋊Dic3—62no—
224C4⋊Dic3—64no—
225C4⋊Dic3—64no—
226C4⋊Dic3—68no—
227C4⋊Dic3C22×D312yes—
228C4×Dic3—21no—
229C4×Dic3—32no—
230C4×Dic3—32no—
231C4×Dic3—62no—
232C4×Dic3—64no—
233C4×Dic3—64no—
234C4×Dic3—68no—
235C4×Dic3—62no—
236C4×Dic3—61no—
237C4×Dic3—61no—
238#208—22no—
239C2×C3⋊C8C2×Dic314yescomplemented
240C2×C3⋊C8C22×D312yes—
241C2×C3⋊C8C22×D311yescharacteristic
242C2×C3⋊C8C22×D311yescharacteristic
243C22×C32—22no—
244C22×C32C4×D412yes—
245C22×C32C22×D411yescharacteristic
246C2×C3×D3—24no—
247C2×C3×D3—44no—
248C2×C3×D3—84no—
249C32×C4—24no—
250C32×C4C4×D412yes—
251C32×C4C23×C411yescharacteristic
252C32×C4C2×#4111yescharacteristic
253C3⋊Dic3—24no—
254C3⋊Dic3—42no—
255C3×Dic3—42no—
256C22×Q8D3211yescharacteristic
257C22×D4—31no—
258C2×SD16—38no—
259C2×SD16—32no—
260C2×SD16—32no—
261C2×M16—31no—
262C22×C8—31no—
263C4×Q8—94no—
264C4×Q8—182no—
265C4×D4—94no—
266C4×D4—182no—
267#117—31no—
268#117—91no—
269#117—91no—
270#117—182no—
271C2×C22⋊C4—182no—
272#107—92no—
273#106—92no—
274#103—34no—
275#102—94no—
276#97—92no—
277C4×C8—92no—
278C23×C3—21no—
279C23×C3—62no—
280C23×C3—64no—
281C23×C3—242no—
282C23×C3D3×D411yescharacteristic
283C23×C3D3×D411yescharacteristic
284C22×D3—22no—
285C22×D3—24no—
286C22×D3—82no—
287C3×Q8—24no—
288C3×Q8—28no—
289C3×Q8—24no—
290C3×Q8—24no—
291C3×Q8—22no—
292C3×Q8—22no—
293C3×Q8—24no—
294C3×Q8C2×C4×D314yes—
295C3×Q8C22×Dic314yes—
296C3×D4—34no—
297C3×D4—64no—
298C3×D4—62no—
299C2×C3×C4—24no—
300C2×C3×C4—28no—
301C2×C3×C4—24no—
302C2×C3×C4—24no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—62no—
310C2×C3×C4C2×C4×D312yes—
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4#23712yes—
314C2×C3×C4#23712yes—
315C2×C3×C4C22×Dic312yes—
316C2×C3×C4C23×D311yescharacteristic
317C2×C3×C4C23×D311yescharacteristic
318C2×Dic3—22no—
319C2×Dic3—34no—
320C2×Dic3—34no—
321C2×Dic3—64no—
322C2×Dic3—64no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—244no—
326D12—24no—
327D12—22no—
328D12C22×Dic314yes—
329C4×D3—244no—
330C3×C8—32no—
331C3×C8—32no—
332C3×C8—62no—
333C3⋊C8—22no—
334C3⋊C8C22×Dic312yes—
335C3⋊C8C22×Dic312yes—
336C2×C32—22no—
337C2×C32C2×C4×D411yescharacteristic
338C2×C32#57712yes—
339C3×D3—44no—
340C24—61no—
341C2×Q8—22no—
342C2×Q8—21no—
343C2×Q8D3×Dic314yescomplemented
344C2×Q8C2×D3212yes—
345C2×D4—32no—
346C2×D4—34no—
347C2×D4—62no—
348C2×D4—61no—
349C22×C4—21no—
350C22×C4—184no—
351C22×C4C2×D3211yescharacteristic
352SD16—38no—
353SD16—38no—
354M16—62no—
355C2×C8—31no—
356C2×C8—31no—
357C2×C8—34no—
358C2×C8—32no—
359C4⋊C4—32no—
360C4⋊C4—92no—
361C4⋊C4—92no—
362C4⋊C4—184no—
363C22⋊C4—61no—
364C22⋊C4—92no—
365C22⋊C4—184no—
366C22⋊C4—181no—
367C42—61no—
368C42—92no—
369C42—184no—
370C42—181no—
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—21no—
374C22×C3—22no—
375C22×C3—42no—
376C22×C3—64no—
377C22×C3—124no—
378C22×C3—244no—
379C22×C3#67⋊C412yes—
380C22×C3D4×Dic312yes—
381C22×C3C2×D3×D411yescharacteristic
382C22×C3C2×D3×D411yescharacteristic
383C2×D3—24no—
384C2×D3—44no—
385C2×D3—84no—
386C3×C4—28no—
387C3×C4—24no—
388C3×C4—24no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—22no—
392C3×C4—122no—
393C3×C4#67⋊C412yes—
394C3×C4D4×Dic312yes—
395C3×C4C22×C4×D311yescharacteristic
396C3×C4C2×#23711yescharacteristic
397C3×C4C2×#23711yescharacteristic
398C3×C4C23×Dic311yescharacteristic
399Dic3—42no—
400Dic3—64no—
401Dic3—64no—
402Dic3—124no—
403Dic3—124no—
404Dic3—122no—
405Dic3—122no—
406C32#294911yescharacteristic, complemented, Sylow
407C23—62no—
408C23—64no—
409C23—242no—
410C23#381111yescharacteristic
411Q8—22no—
412Q8—24no—
413Q8C2×D3×Dic314yes—
414D4—34no—
415D4—62no—
416D4—64no—
417C2×C4—22no—
418C2×C4—24no—
419C2×C4—62no—
420C2×C4—94no—
421C2×C4—182no—
422C2×C4—724no—
423C2×C4C2×D3×Dic312yes—
424C2×C4#380512yes—
425C2×C4#381111yescharacteristic
426C2×C4C22×D3211yescharacteristic
427C8—32no—
428C8—32no—
429C8—62no—
430C2×C3—22no—
431C2×C3—22no—
432C2×C3—21no—
433C2×C3—22no—
434C2×C3—42no—
435C2×C3—124no—
436C2×C3C2×#67⋊C411yescharacteristic
437C2×C3#576212yes—
438C2×C3#577812yes—
439C2×C3C2×D4×Dic311yescharacteristic
440D3—44no—
441C22—22no—
442C22—64no—
443C22—124no—
444C22—244no—
445C22#67⋊Dic312yes—
446C22C2×#381111yescharacteristic
447C4—24no—
448C4—122no—
449C4—184no—
450C4—362no—
451C4#67⋊Dic312yes—
452C4C22×D3×Dic311yescharacteristic
453C4C2×#380511yescharacteristic
454C3—21no—
455C3#7894711yescharacteristic, complemented
456C3#8384311yescharacteristic, complemented
457C2—22no—
458C2—124no—
459C2#1059532412yes—
460C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
cosocleC2×C32×C4C24
hypercenterC22×Q8D32
hypocenterC32#2949
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. #10596283C2semidirect
4. C3×#5225C2semidirect
5. #10591572C2semidirect
6. #10591571C2semidirect
7. #10591122C2semidirect
9. #10591059C2semidirect
15. Q8×C3⋊Dic3C22semidirect
19. C2×C3×#215C4semidirect
28. C3×#835C22semidirect
29. #63575C22semidirect
30. #63573C22semidirect
32. #63555C22semidirect
33. #63553C22semidirect
42. #5225D3semidirect
56. C2×C32×Q8C2×C4semidirect
74. C3×#215C2×C4semidirect
75. C3×#215C2×C4semidirect
79. C2×C3×C3⋊C8C2×C4semidirect
103. C2×#215Dic3semidirect
124. #835C2×D3semidirect
177. C2×C3×Q8C4×D3semidirect
178. C2×C3×Q8C2×Dic3semidirect
215. #215C2×Dic3semidirect
216. #215C2×Dic3semidirect
239. C2×C3⋊C8C2×Dic3semidirect
343. C2×Q8D3×Dic3semidirect
406. C32#2949semidirect
455. C3#78947semidirect
456. C3#83843semidirect

Maximal subgroups

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

subgroupindex
#105962832
C22×C3×#2152
#105949822
C3×#52252
#105915722
#105915712
#105911222
#105910862
#105910592
#838433
#789473