Finite Group Databasebeta

← #11788178

Subgroups — #11788178

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 459 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C3×#5791C211yesmaximal, characteristic
3C3×#5207C211yesmaximal, characteristic, complemented
4C2×#63568C212yesmaximal, complemented
5#10589160C212yesmaximal, complemented
6#71711—31nomaximal
7#69965—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3—21no—
10C2×C3×#235C2211yescharacteristic
11C2×C4×C3⋊Dic3—21no—
12C2×C4×C3⋊Dic3—24no—
13C2×C4×C3⋊Dic3C2212yes—
14C3×#953—21no—
15C3×#930C412yescomplemented
16C3×#929—21no—
17C3×C4×#67—22no—
18C3×#926C2211yescharacteristic
19C3×#924C412yescomplemented
20C2×C3×#208C2212yes—
21C3×#830—22no—
22#63568—24no—
23C3×#525—31no—
24#5791D311yescharacteristic
25C22×C4×Dic3—31no—
26C22×C4×Dic3—31no—
27C22×C4×Dic3—61no—
28C3×#407—31no—
29C2×#837—32no—
30#5207D311yescharacteristic, complemented
31C2×#825—32no—
32#4555—32no—
33#4532—32no—
34C24×C32D411yescharacteristic
35C22×C32×C4—22no—
36C22×C32×C4—22no—
37C22×C32×C4C2×C412yes—
38C22×C32×C4D411yescharacteristic
39C22×C32×C4D412yes—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3—28no—
42C22×C3⋊Dic3—24no—
43C22×C3⋊Dic3—22no—
44C2×C3×#67—22no—
45C2×C3×#67—21no—
46C3×#235—22no—
47C3×#235—22no—
48C2×C3×D12C2×C411yescharacteristic, complemented
49C2×C3×C4×D3—21no—
50C2×C3×Dic6C2×C411yescharacteristic, complemented
51C4×C3⋊Dic3—24no—
52C4×C3⋊Dic3—22no—
53C4×C3⋊Dic3D414yescomplemented
54C3×#217—22no—
55C3×#217—21no—
56C3×(C2×D3)⋊C4—22no—
57C3×C4⋊Dic3C2×C412yescomplemented
58C3×Dic3⋊C4—22no—
59C3×C4×Dic3—21no—
60C3×#208—22no—
61C3×#208—22no—
62C2×C3×C3⋊C8—22no—
63#1896—91noSylow
64C2×C3×#41—31no—
65C23×C3×C4—21no—
66C23×C3×C4C2×D311yescharacteristic
67C23×C3×C4C2×D311yescharacteristic
68C23×Dic3—62no—
69C23×Dic3—61no—
70C23×Dic3—61no—
71C2×#235C2×D311yescharacteristic
72C2×C3×M16—32no—
73C3×#123—61no—
74C3×C22⋊Q8—32no—
75C3×#121—32no—
76C3×#120—61no—
77C3×C4×D4—62no—
78C3×#117—31no—
79#953—21no—
80#930Dic312yescomplemented
81#929—21no—
82C4×#67—22no—
83#926C2×D311yescharacteristic
84#924Dic312yescomplemented
85C2×C4×Dic3—32no—
86C2×C4×Dic3—32no—
87C2×C4×Dic3—62no—
88C2×C4×Dic3—64no—
89C2×C4×Dic3—64no—
90C2×C4×Dic3—68no—
91C2×C4×Dic3—62no—
92C2×C4×Dic3—61no—
93C2×C4×Dic3—61no—
94C2×#208C2×D312yes—
95C3×C22⋊C8—62no—
96#837—64no—
97#830—22no—
98#825—64no—
99C23×C32—24no—
100C23×C32—21no—
101C23×C32—21no—
102C23×C32C22⋊C412yes—
103C23×C32C2×D411yescharacteristic
104C22×C3×D3—21no—
105C2×C32×C4—21no—
106C2×C32×C4—21no—
107C2×C32×C4—24no—
108C2×C32×C4—24no—
109C2×C32×C4C22⋊C412yes—
110C2×C32×C4C22×C411yescharacteristic
111C2×C32×C4C2×D412yes—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4#4112yes—
114C2×C3⋊Dic3—216no—
115C2×C3⋊Dic3—28no—
116C2×C3⋊Dic3—24no—
117C3×#67—44no—
118C3×#67—41no—
119C3×#67—41no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—21no—
122C3×D12—22no—
123C3×C4×D3—42no—
124C3×Dic6—22no—
125C3×C3⋊C8—42no—
126#525—31no—
127C22×C42—91no—
128C2×#104—92no—
129#407—31no—
130#339—92no—
131C24×C3—21no—
132C24×C3D1211yescharacteristic
133C24×C3#6711yescharacteristic
134C3×#41—62no—
135C3×#41—62no—
136C2×C3×Q8—31no—
137C2×C3×D4—31no—
138C2×C3×D4—62no—
139C2×C3×D4—61no—
140C22×C3×C4—24no—
141C22×C3×C4—24no—
142C22×C3×C4—22no—
143C22×C3×C4—22no—
144C22×C3×C4—22no—
145C22×C3×C4—22no—
146C22×C3×C4—22no—
147C22×C3×C4—22no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—61no—
151C22×C3×C4C4×D312yes—
152C22×C3×C4D1211yescharacteristic
153C22×C3×C4C2×Dic312yes—
154C22×C3×C4#6712yes—
155C22×C3×C4#6712yes—
156C22×C3×C4#6711yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C2×#67—22no—
160C2×#67—21no—
161C22×Dic3—68no—
162C22×Dic3—64no—
163C22×Dic3—64no—
164C22×Dic3—64no—
165C22×Dic3—616no—
166C22×Dic3—68no—
167C22×Dic3—68no—
168C22×Dic3—62no—
169C22×Dic3—62no—
170#235—22no—
171#235—22no—
172C2×D12C2×Dic311yescharacteristic, complemented
173C2×C4×D3—21no—
174C2×Dic6C2×Dic311yescharacteristic, complemented
175C3×M16—62no—
176C3×M16—62no—
177C2×C3×C8—62no—
178C3×C4⋊C4—32no—
179C3×C4⋊C4—62no—
180C3×C22⋊C4—62no—
181C3×C22⋊C4—61no—
182C3×C22⋊C4—62no—
183C3×C42—61no—
184#217—22no—
185#217—21no—
186(C2×D3)⋊C4—22no—
187C4⋊Dic3C2×Dic312yescomplemented
188Dic3⋊C4—22no—
189C4×Dic3—21no—
190C4×Dic3—34no—
191C4×Dic3—34no—
192C4×Dic3—64no—
193C4×Dic3—68no—
194C4×Dic3—64no—
195C4×Dic3—64no—
196C4×Dic3—64no—
197C4×Dic3—62no—
198C4×Dic3—62no—
199#208—22no—
200#208—22no—
201C2×C3⋊C8—22no—
202C22×C32—24no—
203C22×C32—24no—
204C22×C32—22no—
205C22×C32—22no—
206C22×C32—22no—
207C22×C32#10414yescomplemented
208C22×C32C2×C22⋊C411yescharacteristic
209C22×C32#12011yescharacteristic
210C22×C32#12311yescharacteristic
211C2×C3×D3—41no—
212C2×C3×D3—42no—
213C32×C4—22no—
214C32×C4C4×D412yes—
215C32×C4#12112yes—
216C3⋊Dic3—28no—
217C3×Dic3—41no—
218C3×Dic3—42no—
219C2×#41—31no—
220C23×C4—181no—
221C23×C4D3211yescharacteristic
222C2×M16—32no—
223#123—61no—
224C22⋊Q8—32no—
225#121—32no—
226#120—61no—
227C4×D4—62no—
228#117—31no—
229C2×C42—92no—
230C2×C42—184no—
231C2×C42—181no—
232#104—184no—
233C22⋊C8—62no—
234C23×C3—22no—
235C23×C3—28no—
236C23×C3—22no—
237C23×C3—24no—
238C23×C3—24no—
239C23×C3—21no—
240C23×C3—21no—
241C23×C3—21no—
242C23×C3—21no—
243C23×C3—22no—
244C23×C3—21no—
245C23×C3—61no—
246C23×C3(C2×D3)⋊C412yes—
247C23×C3#21712yes—
248C23×C3C2×D1211yescharacteristic
249C23×C3C2×#6711yescharacteristic
250C22×D3—21no—
251C3×Q8—62no—
252C3×D4—62no—
253C3×D4—124no—
254C3×D4—121no—
255C3×D4—121no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—28no—
259C2×C3×C4—28no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—24no—
265C2×C3×C4—24no—
266C2×C3×C4—24no—
267C2×C3×C4—24no—
268C2×C3×C4—22no—
269C2×C3×C4—21no—
270C2×C3×C4—22no—
271C2×C3×C4—21no—
272C2×C3×C4—22no—
273C2×C3×C4—62no—
274C2×C3×C4—61no—
275C2×C3×C4—122no—
276C2×C3×C4(C2×D3)⋊C412yes—
277C2×C3×C4#21712yes—
278C2×C3×C4C2×C4×D311yescharacteristic
279C2×C3×C4D3×D412yes—
280C2×C3×C4D3×D412yes—
281C2×C3×C4#23712yes—
282C2×C3×C4#23712yes—
283C2×C3×C4C22×Dic311yescharacteristic
284C2×C3×C4C2×#6711yescharacteristic
285C2×C3×C4C2×#6711yescharacteristic
286#67—44no—
287#67—41no—
288#67—41no—
289C2×Dic3—22no—
290C2×Dic3—21no—
291C2×Dic3—68no—
292C2×Dic3—632no—
293C2×Dic3—616no—
294C2×Dic3—616no—
295C2×Dic3—616no—
296C2×Dic3—68no—
297C2×Dic3—68no—
298C2×Dic3—64no—
299C2×Dic3—64no—
300D12—22no—
301C4×D3—42no—
302Dic6—22no—
303C3×C8—122no—
304C3⋊C8—42no—
305C2×C32—21no—
306C2×C32—24no—
307C2×C32—21no—
308C2×C32#38611yescharacteristic
309C2×C32C2×#10412yes—
310C3×D3—81no—
311C24#62611yescharacteristic
312#41—62no—
313#41—62no—
314C2×Q8—31no—
315C2×D4—31no—
316C2×D4—62no—
317C2×D4—61no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—61no—
321C22×C4—184no—
322C22×C4—188no—
323C22×C4—182no—
324C22×C4D3×Dic312yes—
325C22×C4#62512yes—
326C22×C4#62611yescharacteristic
327C22×C4C2×D3211yescharacteristic
328M16—62no—
329M16—62no—
330C2×C8—62no—
331C4⋊C4—32no—
332C4⋊C4—62no—
333C22⋊C4—62no—
334C22⋊C4—61no—
335C22⋊C4—62no—
336C42—61no—
337C42—94no—
338C42—184no—
339C42—182no—
340C22×C3—28no—
341C22×C3—24no—
342C22×C3—24no—
343C22×C3—24no—
344C22×C3—24no—
345C22×C3—28no—
346C22×C3—24no—
347C22×C3—24no—
348C22×C3—24no—
349C22×C3—22no—
350C22×C3—22no—
351C22×C3—22no—
352C22×C3—22no—
353C22×C3—22no—
354C22×C3—22no—
355C22×C3—24no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—122no—
360C22×C3—121no—
361C22×C3#82514yescomplemented
362C22×C3#83714yescomplemented
363C22×C3#88211yescharacteristic
364C22×C3#88611yescharacteristic
365C22×C3C2×(C2×D3)⋊C411yescharacteristic
366C22×C3#93511yescharacteristic
367C22×C3#93711yescharacteristic
368C22×C3C2×#21711yescharacteristic
369C2×D3—41no—
370C2×D3—42no—
371C3×C4—24no—
372C3×C4—22no—
373C3×C4—22no—
374C3×C4—22no—
375C3×C4—22no—
376C3×C4—122no—
377C3×C4—121no—
378C3×C4#67⋊C412yes—
379C3×C4D4×Dic312yes—
380C3×C4#93912yes—
381C3×C4#93912yes—
382Dic3—41no—
383Dic3—42no—
384Dic3—616no—
385Dic3—68no—
386Dic3—68no—
387C32#189611yescharacteristic, complemented, Sylow
388C23—24no—
389C23—21no—
390C23—21no—
391C23—61no—
392C23(C2×D3)⋊Dic312yes—
393C23C2×#62611yescharacteristic
394Q8—62no—
395D4—62no—
396D4—124no—
397D4—121no—
398D4—121no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—62no—
404C2×C4—61no—
405C2×C4—122no—
406C2×C4—1816no—
407C2×C4—188no—
408C2×C4—184no—
409C2×C4(C2×D3)⋊Dic312yes—
410C2×C4C2×D3×Dic311yescharacteristic
411C2×C4#380512yes—
412C2×C4C2×#62511yescharacteristic
413C2×C4#381112yes—
414C8—122no—
415C2×C3—22no—
416C2×C3—28no—
417C2×C3—22no—
418C2×C3—21no—
419C2×C3—24no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—24no—
423C2×C3—21no—
424C2×C3—22no—
425C2×C3—21no—
426C2×C3—241no—
427C2×C3#495811yescharacteristic
428C2×C3C2×#82512yes—
429C2×C3#522011yescharacteristic
430C2×C3C2×#83712yes—
431D3—81no—
432C22—24no—
433C22—24no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—122no—
438C22—121no—
439C22#6356814yescomplemented
440C22C2×(C2×D3)⋊Dic311yescharacteristic
441C22#6396211yescharacteristic
442C22#6398111yescharacteristic
443C4—22no—
444C4—122no—
445C4—121no—
446C4—188no—
447C4#67⋊Dic312yes—
448C4#6398012yes—
449C3—21no—
450C3#6996511yescharacteristic, complemented
451C3#7171111yescharacteristic, complemented
452C2—21no—
453C2—24no—
454C2—21no—
455C2—241no—
456C2C2×#6356812yes—
457C2#1059171311yescharacteristic
subgroupG/H
centerC2×C4C2×#625
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#5791C2
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1896
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C3⋊Dic3C2semidirect
3. C3×#5207C2semidirect
4. C2×#63568C2semidirect
5. #10589160C2semidirect
15. C3×#930C4semidirect
19. C3×#924C4semidirect
30. #5207D3semidirect
48. C2×C3×D12C2×C4semidirect
50. C2×C3×Dic6C2×C4semidirect
53. C4×C3⋊Dic3D4semidirect
57. C3×C4⋊Dic3C2×C4semidirect
80. #930Dic3semidirect
84. #924Dic3semidirect
172. C2×D12C2×Dic3semidirect
174. C2×Dic6C2×Dic3semidirect
187. C4⋊Dic3C2×Dic3semidirect
207. C22×C32#104semidirect
361. C22×C3#825semidirect
362. C22×C3#837semidirect
387. C32#1896semidirect
439. C22#63568semidirect
450. C3#69965semidirect
451. C3#71711semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊Dic32
C3×#57912
C3×#52072
C2×#635682
#105891602
#717113
#699653