Finite Group Databasebeta

← #11783238

Subgroups — #11783238

Order 1152.

1233 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic
3C22×#3710C211yesmaximal, characteristic
4C3×#4529C212yesmaximal, complemented
5#10589164C212yesmaximal, complemented
6D3×#340—32nomaximal
7C22×C4×C3⋊D3—21no—
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×#624—21no—
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C2×#3750—21no—
13C4⋊C4×C3⋊D3—22no—
14C4⋊C4×C3⋊D3C414yescomplemented
15C2×C3×C4⋊Dic3C2212yes—
16C22×C3×C3⋊C8C2212yes—
17C2×#3724—21no—
18#63900—22no—
19#63900C414yescomplemented
20C2×#3710—22no—
21C2×#3710—22no—
22C2×#3710C414yescomplemented
23C22×D3×C8—32no—
24C2×D3×C4⋊C4—32no—
25C2×D3×C4⋊C4—32no—
26C2×D3×C4⋊C4—61no—
27C3×#340—32no—
28#4551—32no—
29#4529—32no—
30#4529D312yescomplemented
31C23×C3⋊D3D411yescharacteristic
32C22×C32×C4—21no—
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3—21no—
35C22×C3⋊Dic3D411yescharacteristic
36C2×C4×C3⋊D3—24no—
37C2×C4×C3⋊D3—42no—
38C2×C4×C3⋊D3—42no—
39C2×C4×C3⋊D3C2×C412yes—
40C2×C4×C3⋊D3C2×C412yes—
41C2×C4×C3⋊D3C2×C412yes—
42C2×C4×C3⋊D3D412yes—
43C2×C4×C3⋊D3D412yes—
44C2×C4×C3⋊D3Q812yes—
45C22×C3×Dic3—22no—
46C2×#624—24no—
47C2×#624—42no—
48C2×#624—42no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4C2×C412yescomplemented
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)C2×C412yescomplemented
53#3750—24no—
54C3×C4⋊Dic3—22no—
55C3×C4⋊Dic3C2×C414yescomplemented
56C2×C3×C3⋊C8—22no—
57C2×C3×C3⋊C8—22no—
58C2×C3×C3⋊C8C2×C414yescomplemented
59#3724—24no—
60#3710—28no—
61C2×#340—91noSylow
62C22×C4×D3—32no—
63C22×C4×D3—61no—
64C22×C4×D3—62no—
65C22×C4×D3—62no—
66C22×C4×D3—62no—
67C22×C3×C8—32no—
68C2×C3×C4⋊C4—21no—
69C2×C3×C4⋊C4—32no—
70C2×C3×C4⋊C4C2×D312yes—
71C2×C4⋊Dic3—32no—
72C2×C4⋊Dic3—61no—
73C2×C4⋊Dic3C2×D312yes—
74C2×Dic3⋊C4—62no—
75C2×Dic3⋊C4—62no—
76C2×Dic3⋊C4—62no—
77C22×C3⋊C8C2×D312yes—
78C2×D3×C8—38no—
79C2×D3×C8—64no—
80C2×D3×C8—64no—
81D3×C4⋊C4—38no—
82D3×C4⋊C4—38no—
83D3×C4⋊C4—64no—
84D3×C4⋊C4—64no—
85D3×C4⋊C4—64no—
86D3×C4⋊C4—64no—
87C23×C32C2×D411yescharacteristic
88C22×C3⋊D3C22⋊C412yes—
89C22×C3⋊D3C22⋊C412yes—
90C22×C3⋊D3C4⋊C412yes—
91C22×C3⋊D3D812yes—
92C22×C3⋊D3SD1612yes—
93C22×C3⋊D3SD1612yes—
94C22×C3⋊D3Q1612yes—
95C2×C32×C4—22no—
96C2×C32×C4—41no—
97C2×C32×C4—41no—
98C2×C32×C4C22×C411yescharacteristic
99C2×C32×C4C22×C411yescharacteristic
100C2×C32×C4C22×C411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×Q811yescharacteristic
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—41no—
106C2×C3⋊Dic3—41no—
107C2×C3⋊Dic3C22⋊C412yes—
108C2×C3⋊Dic3C22⋊C412yes—
109C2×C3⋊Dic3C4⋊C412yes—
110C4×C3⋊D3—48no—
111C4×C3⋊D3C4214yes—
112C4×C3⋊D3C22⋊C414yes—
113C4×C3⋊D3C4⋊C414yes—
114C4×C3⋊D3C4⋊C414yes—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—42no—
117C2×C3×Dic3—42no—
118#624—48no—
119C3×C3⋊C8—24no—
120C23×C8—91no—
121C22×C4⋊C4—91no—
122C22×C4⋊C4—91no—
123#340—32no—
124#340—92no—
125C23×D3—32no—
126C23×D3—61no—
127C22×C3×C4—22no—
128C22×C3×C4—22no—
129C22×C3×C4—21no—
130C22×C3×C4—62no—
131C22×C3×C4C22×D312yes—
132C22×Dic3—22no—
133C22×Dic3—32no—
134C22×Dic3—61no—
135C22×Dic3—62no—
136C22×Dic3—62no—
137C2×C4×D3—34no—
138C2×C4×D3—34no—
139C2×C4×D3—34no—
140C2×C4×D3—34no—
141C2×C4×D3—34no—
142C2×C4×D3—34no—
143C2×C4×D3—62no—
144C2×C4×D3—62no—
145C2×C4×D3—62no—
146C2×C4×D3—62no—
147C2×C4×D3—62no—
148C2×C4×D3—62no—
149C2×C4×D3—68no—
150C2×C4×D3—68no—
151C2×C4×D3—68no—
152C2×C4×D3—124no—
153C2×C4×D3—124no—
154C2×C4×D3—124no—
155C2×C4×D3—124no—
156C2×C4×D3—124no—
157C2×C4×D3—124no—
158C2×C3×C8—34no—
159C2×C3×C8—62no—
160C2×C3×C8—62no—
161C3×C4⋊C4—22no—
162C3×C4⋊C4—22no—
163C3×C4⋊C4—22no—
164C3×C4⋊C4—34no—
165C3×C4⋊C4—62no—
166C3×C4⋊C4C4×D314yescomplemented
167C4⋊Dic3—22no—
168C4⋊Dic3—34no—
169C4⋊Dic3—62no—
170C4⋊Dic3—62no—
171C4⋊Dic3—62no—
172C4⋊Dic3C4×D314yescomplemented
173Dic3⋊C4—68no—
174Dic3⋊C4—68no—
175Dic3⋊C4—68no—
176C2×C3⋊C8—22no—
177C2×C3⋊C8—22no—
178C2×C3⋊C8C4×D314yescomplemented
179D3×C8—616no—
180C22×C32C2×C22⋊C411yescharacteristic
181C22×C32C2×C22⋊C411yescharacteristic
182C22×C32C2×C4⋊C411yescharacteristic
183C22×C32C2×D811yescharacteristic
184C22×C32C2×SD1611yescharacteristic
185C22×C32C2×SD1611yescharacteristic
186C22×C32C2×Q1611yescharacteristic
187C2×C3⋊D3#9514yes—
188C2×C3⋊D3#10214yes—
189C2×C3⋊D3#10214yes—
190C2×C3⋊D3#10314yes—
191C2×C3⋊D3#10314yes—
192C2×C3⋊D3#10614yes—
193C2×C3⋊D3#10714yes—
194C32×C4—42no—
195C32×C4C2×C4211yescharacteristic
196C32×C4C2×C22⋊C411yescharacteristic
197C32×C4C2×C4⋊C411yescharacteristic
198C32×C4C2×C4⋊C411yescharacteristic
199C3⋊Dic3—42no—
200C3⋊Dic3#9514yes—
201C3×Dic3—44no—
202C23×C4—91no—
203C23×C4—181no—
204C23×C4—181no—
205C22×C8—32no—
206C22×C8—94no—
207C22×C8—182no—
208C22×C8—182no—
209C2×C4⋊C4—32no—
210C2×C4⋊C4—94no—
211C2×C4⋊C4—91no—
212C2×C4⋊C4—94no—
213C2×C4⋊C4—182no—
214C2×C4⋊C4—182no—
215C2×C4⋊C4—181no—
216C2×C4⋊C4—181no—
217C2×C4⋊C4D3211yescharacteristic
218C23×C3—21no—
219C23×C3D3×D412yes—
220C22×D3—34no—
221C22×D3—34no—
222C22×D3—34no—
223C22×D3—34no—
224C22×D3—34no—
225C22×D3—34no—
226C22×D3—34no—
227C22×D3—62no—
228C22×D3—62no—
229C22×D3—62no—
230C22×D3—62no—
231C22×D3—62no—
232C22×D3—62no—
233C22×D3—62no—
234C2×C3×C4—24no—
235C2×C3×C4—24no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—42no—
243C2×C3×C4—42no—
244C2×C3×C4—42no—
245C2×C3×C4—42no—
246C2×C3×C4—64no—
247C2×C3×C4—122no—
248C2×C3×C4—122no—
249C2×C3×C4C2×C4×D312yes—
250C2×C3×C4C2×C4×D312yes—
251C2×C3×C4C2×C4×D312yes—
252C2×C3×C4D3×D412yes—
253C2×C3×C4D3×D412yes—
254C2×C3×C4D3×Q812yes—
255C2×Dic3—24no—
256C2×Dic3—34no—
257C2×Dic3—34no—
258C2×Dic3—34no—
259C2×Dic3—42no—
260C2×Dic3—42no—
261C2×Dic3—62no—
262C2×Dic3—62no—
263C2×Dic3—62no—
264C2×Dic3—64no—
265C2×Dic3—64no—
266C2×Dic3—122no—
267C2×Dic3—122no—
268C2×Dic3—122no—
269C2×Dic3—122no—
270C4×D3—38no—
271C4×D3—38no—
272C4×D3—38no—
273C4×D3—38no—
274C4×D3—64no—
275C4×D3—64no—
276C4×D3—64no—
277C4×D3—64no—
278C4×D3—1216no—
279C4×D3—1216no—
280C4×D3—1216no—
281C3×C8—64no—
282C3⋊C8—24no—
283C2×C32C2×#9511yescharacteristic
284C2×C32C2×#10211yescharacteristic
285C2×C32C2×#10211yescharacteristic
286C2×C32C2×#10311yescharacteristic
287C2×C32C2×#10311yescharacteristic
288C2×C32C2×#10611yescharacteristic
289C2×C32C2×#10711yescharacteristic
290C3⋊D3#34018yescomplemented
291C24—91no—
292C22×C4—21no—
293C22×C4—62no—
294C22×C4—91no—
295C22×C4—92no—
296C22×C4—92no—
297C22×C4—92no—
298C22×C4—92no—
299C22×C4—92no—
300C22×C4—92no—
301C22×C4—184no—
302C22×C4—184no—
303C22×C4—181no—
304C22×C4—362no—
305C22×C4—362no—
306C22×C4—362no—
307C22×C4—362no—
308C22×C4C2×D3211yescharacteristic
309C2×C8—34no—
310C2×C8—62no—
311C2×C8—62no—
312C2×C8—188no—
313C4⋊C4—21no—
314C4⋊C4—34no—
315C4⋊C4—62no—
316C4⋊C4—92no—
317C4⋊C4—184no—
318C4⋊C4—184no—
319C4⋊C4—181no—
320C4⋊C4#62412yescomplemented
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3D3×C22⋊C412yes—
329C22×C3D3×C22⋊C412yes—
330C22×C3D3×C4⋊C412yes—
331C22×C3D3×D812yes—
332C22×C3D3×SD1612yes—
333C22×C3D3×SD1612yes—
334C22×C3D3×Q1612yes—
335C2×D3—38no—
336C2×D3—38no—
337C2×D3—38no—
338C2×D3—38no—
339C2×D3—38no—
340C2×D3—38no—
341C2×D3—38no—
342C2×D3—64no—
343C2×D3—64no—
344C2×D3—64no—
345C2×D3—64no—
346C2×D3—64no—
347C2×D3—64no—
348C2×D3—64no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—44no—
354C3×C4—44no—
355C3×C4—124no—
356C3×C4C42×D312yes—
357C3×C4D3×C22⋊C412yes—
358C3×C4D3×C4⋊C412yes—
359C3×C4D3×C4⋊C412yes—
360Dic3—38no—
361Dic3—44no—
362Dic3—64no—
363Dic3—124no—
364Dic3—124no—
365C32C2×#34011yescharacteristic, complemented, Sylow
366C23—92no—
367C23—92no—
368C23—92no—
369C23—92no—
370C23—92no—
371C23—92no—
372C23—92no—
373C23#381111yescharacteristic
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—64no—
378C2×C4—92no—
379C2×C4—92no—
380C2×C4—92no—
381C2×C4—94no—
382C2×C4—94no—
383C2×C4—94no—
384C2×C4—94no—
385C2×C4—122no—
386C2×C4—122no—
387C2×C4—182no—
388C2×C4—368no—
389C2×C4—368no—
390C2×C4—361no—
391C2×C4—361no—
392C2×C4#379711yescharacteristic
393C2×C4C4×D3211yescharacteristic
394C2×C4C4×D3211yescharacteristic
395C2×C4#380211yescharacteristic
396C2×C4C2×#62411yescharacteristic
397C2×C4#381111yescharacteristic
398C8—64no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3D3×#9512yes—
407C2×C3D3×#10212yes—
408C2×C3D3×#10212yes—
409C2×C3D3×#10312yes—
410C2×C3D3×#10312yes—
411C2×C3D3×#10612yes—
412C2×C3D3×#10712yes—
413D3—316no—
414D3—68no—
415C22—94no—
416C22—94no—
417C22—94no—
418C22—94no—
419C22—94no—
420C22—94no—
421C22—94no—
422C22#6388311yescharacteristic
423C22#6392111yescharacteristic
424C22#6392611yescharacteristic
425C22#6393011yescharacteristic
426C22#6394011yescharacteristic
427C22#6394411yescharacteristic
428C22#6397411yescharacteristic
429C4—42no—
430C4—94no—
431C4—124no—
432C4—362no—
433C4C4×#62411yescharacteristic
434C4#6388311yescharacteristic
435C4#6390011yescharacteristic
436C4#6392111yescharacteristic
437C3—21no—
438C3D3×#34012yescomplemented
439C2—98no—
440C2#1059057311yescharacteristic
441C2#1059057511yescharacteristic
442C2#1059059311yescharacteristic
443C2#1059060111yescharacteristic
444C2#1059137011yescharacteristic
445C2#1059141611yescharacteristic
446C2#1059155211yescharacteristic
subgroupG/H
centerC23#3811
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#340
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C3×#4529C2semidirect
5. #10589164C2semidirect
14. C4⋊C4×C3⋊D3C4semidirect
19. #63900C4semidirect
22. C2×#3710C4semidirect
30. #4529D3semidirect
50. C32×C4⋊C4C2×C4semidirect
52. C4⋊(C3⋊Dic3)C2×C4semidirect
55. C3×C4⋊Dic3C2×C4semidirect
58. C2×C3×C3⋊C8C2×C4semidirect
166. C3×C4⋊C4C4×D3semidirect
172. C4⋊Dic3C4×D3semidirect
178. C2×C3⋊C8C4×D3semidirect
290. C3⋊D3#340semidirect
320. C4⋊C4#624semidirect
365. C32C2×#340semidirect
438. C3D3×#340semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C2×#639002
C22×#37102
C3×#45292
#105891642
D3×#3403