Finite Group Databasebeta

← #11801460

Subgroups — #11801460

Order 1152.

2088 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#117C211yesmaximal, characteristic, complemented
2C2×C4×#638C211yesmaximal, characteristic
3C2×C42×C3⋊D3C211yesmaximal, characteristic, complemented
4C4×#3757C211yesmaximal, characteristic, complemented
5#10592688C212yesmaximal, complemented
6#10592677C212yesmaximal, complemented
7#10592655C212yesmaximal
8#10592643C212yesmaximal, complemented
9C4×#3752C211yesmaximal, characteristic, complemented
10#10592631C211yesmaximal, characteristic, complemented
11C4×#3750C211yesmaximal, characteristic, complemented
12#82268—34nomaximal
13C23×C32×C4C2211yescharacteristic
14C22×#638C2211yescharacteristic
15C22×C4×C3⋊D3C2212yes—
16C22×C4×C3⋊D3C2211yescharacteristic
17C32×#117—24no—
18C2×C32×C4⋊C4C2212yes—
19C2×C32×C22⋊C4C2212yes—
20C2×C32×C42C2211yescharacteristic
21C2×C32×C42C2211yescharacteristic
22C2×#3757C2212yes—
23C2×#3757C2211yescharacteristic
24C4×#638C418yescomplemented
25C2×#3752C2212yes—
26C2×#3752C2211yescharacteristic
27C2×#3750C2212yes—
28C2×#3750C2211yescharacteristic
29C2×C4×C3⋊Dic3C2211yescharacteristic
30C2×C4×C3⋊Dic3C2212yes—
31C2×C4×C3⋊Dic3C2211yescharacteristic
32C2×C4×C3⋊Dic3C2211yescharacteristic
33C42×C3⋊D3—24no—
34#63658C2212yes—
35#63658C2212yes—
36#63658C2212yes—
37#63658C2212yes—
38#63658C2212yes—
39C2×C3×#117D314yescomplemented
40C2×C4×#67—34no—
41C2×C42×D3—34no—
42C4×#217—34no—
43#4989—38no—
44#4978—38no—
45#4956—38no—
46#4944—38no—
47C4×(C2×D3)⋊C4—34no—
48#4932—34no—
49C4×Dic3⋊C4—34no—
50C24×C32C2311yescharacteristic
51C23×C3⋊D3C2311yescharacteristic
52C22×C32×C4—22no—
53C22×C32×C4—22no—
54C22×C32×C4C2×C414yescomplemented
55C22×C32×C4C2312yes—
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2312yes—
58C22×C32×C4C2311yescharacteristic
59C2×#638—24no—
60C2×#638C2×C414yes—
61C22×C3⋊Dic3C2312yes—
62C22×C3⋊Dic3C2311yescharacteristic
63C22×C3⋊Dic3C2311yescharacteristic
64C22×C3⋊Dic3C2311yescharacteristic
65C22×C3⋊Dic3C2312yes—
66C2×C4×C3⋊D3—24no—
67C2×C4×C3⋊D3—24no—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3—24no—
71C2×C4×C3⋊D3C2×C414yes—
72C32×C4⋊C4—24no—
73C32×C22⋊C4—24no—
74C32×C42—22no—
75C32×C42D414yescomplemented
76#3757—24no—
77#3757C2×C414yescomplemented
78#3752—24no—
79#3752C2×C414yes—
80#3750—24no—
81#3750C2×C414yescomplemented
82C4×C3⋊Dic3—24no—
83C4×C3⋊Dic3—22no—
84C4×C3⋊Dic3—22no—
85C4×C3⋊Dic3C2×C414yescomplemented
86#2290—91noSylow
87C23×C3×C4C2×D314yes—
88C22×#67—34no—
89C22×C4×D3—34no—
90C22×C4×D3—38no—
91C3×#117—216no—
92C2×C3×C4⋊C4C2×D318yes—
93C2×C3×C22⋊C4C2×D318yes—
94C2×C3×C42C2×D314yes—
95C2×C3×C42C2×D314yes—
96C2×#217—34no—
97C2×#217—38no—
98C4×#67—332no—
99C2×(C2×D3)⋊C4—34no—
100C2×(C2×D3)⋊C4—38no—
101C2×Dic3⋊C4—34no—
102C2×Dic3⋊C4—38no—
103C2×C4×Dic3—34no—
104C2×C4×Dic3—34no—
105C2×C4×Dic3—34no—
106C2×C4×Dic3—38no—
107C42×D3—616no—
108C3⋊#95—38no—
109C3⋊#95—38no—
110C3⋊#95—38no—
111C3⋊#95—38no—
112C3⋊#95—38no—
113C23×C32—21no—
114C23×C32—22no—
115C23×C32—22no—
116C23×C32—21no—
117C23×C32C22×C412yes—
118C23×C32C2411yescharacteristic
119C22×C3⋊D3—21no—
120C22×C3⋊D3—21no—
121C22×C3⋊D3—22no—
122C22×C3⋊D3C22×C412yes—
123C22×C3⋊D3#4114yes—
124C2×C32×C4—21no—
125C2×C32×C4—22no—
126C2×C32×C4—22no—
127C2×C32×C4—21no—
128C2×C32×C4—28no—
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4—22no—
132C2×C32×C4C22×C412yes—
133C2×C32×C4C22×C412yes—
134C2×C32×C4C2×D414yes—
135C2×C32×C4C2×D412yes—
136C2×C32×C4#4112yes—
137#638—28no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3C22×C412yes—
148C2×C3⋊Dic3C22×C412yes—
149C2×C3⋊Dic3C22×C412yes—
150C2×C3⋊Dic3#4114yes—
151C4×C3⋊D3—216no—
152C4×C3⋊D3—28no—
153C2×C4×D4—91no—
154C2×#117C3⋊D311yescharacteristic, complemented
155C22×C42—91no—
156#388—92no—
157#387—92no—
158#386—92no—
159#385—92no—
160C4×C4⋊C4—91no—
161C4×C22⋊C4—91no—
162C4×C22⋊C4—91no—
163#376—91no—
164C24×C3C22×D314yes—
165C23×D3—34no—
166C22×C3×C4—28no—
167C22×C3×C4—28no—
168C22×C3×C4C4×D3116yescomplemented
169C22×C3×C4C22×D318yes—
170C22×C3×C4C22×D314yes—
171C22×C3×C4C22×D318yes—
172C22×C3×C4C22×D314yes—
173C2×#67—316no—
174C2×#67—616no—
175C22×Dic3—34no—
176C22×Dic3—34no—
177C22×Dic3—38no—
178C22×Dic3—34no—
179C22×Dic3—38no—
180C2×C4×D3—316no—
181C2×C4×D3—616no—
182C2×C4×D3—616no—
183C2×C4×D3—68no—
184C2×C4×D3—616no—
185C2×C4×D3—68no—
186C3×C4⋊C4—216no—
187C3×C22⋊C4—216no—
188C3×C42—28no—
189C3×C42#67116yescomplemented
190#217—316no—
191#217—616no—
192(C2×D3)⋊C4—316no—
193(C2×D3)⋊C4—616no—
194Dic3⋊C4—316no—
195Dic3⋊C4—616no—
196C4×Dic3—316no—
197C4×Dic3—68no—
198C4×Dic3—616no—
199C4×Dic3—68no—
200C22×C32—22no—
201C22×C32—22no—
202C22×C32—22no—
203C22×C32—42no—
204C22×C32—42no—
205C22×C32C23×C411yescharacteristic
206C22×C32C22×D411yescharacteristic
207C22×C32C2×#4111yescharacteristic
208C22×C32C2×#4112yes—
209C22×C32C2×#4112yes—
210C2×C3⋊D3—22no—
211C2×C3⋊D3—22no—
212C2×C3⋊D3—24no—
213C2×C3⋊D3—24no—
214C2×C3⋊D3#11714yescomplemented
215C32×C4—22no—
216C32×C4—24no—
217C32×C4—42no—
218C32×C4C4×D414yes—
219C3⋊Dic3—22no—
220C3⋊Dic3—22no—
221C3⋊Dic3—22no—
222C3⋊Dic3—24no—
223C3⋊Dic3—42no—
224C22×D4—91no—
225C23×C4—91no—
226C23×C4—92no—
227C23×C4C2×C3⋊D311yescharacteristic
228C4×D4—98no—
229#117—24no—
230C2×C4⋊C4—91no—
231C2×C4⋊C4—92no—
232C2×C4⋊C4C2×C3⋊D312yes—
233C2×C22⋊C4—91no—
234C2×C22⋊C4—91no—
235C2×C22⋊C4—92no—
236C2×C22⋊C4—92no—
237C2×C22⋊C4C2×C3⋊D312yes—
238C2×C42—91no—
239C2×C42—92no—
240C2×C42—91no—
241C2×C42—91no—
242C2×C42—184no—
243C2×C42C2×C3⋊D311yescharacteristic
244C2×C42C2×C3⋊D311yescharacteristic
245#95—92no—
246#95—92no—
247#95—92no—
248#95—92no—
249#95—92no—
250C23×C3—24no—
251C23×C3—28no—
252C23×C3—28no—
253C23×C3—24no—
254C23×C3C2×C4×D318yes—
255C23×C3C23×D314yes—
256C22×D3—38no—
257C22×D3—316no—
258C22×D3—64no—
259C22×D3—68no—
260C22×D3—64no—
261C2×C3×C4—24no—
262C2×C3×C4—28no—
263C2×C3×C4—28no—
264C2×C3×C4—24no—
265C2×C3×C4—232no—
266C2×C3×C4—28no—
267C2×C3×C4—28no—
268C2×C3×C4—28no—
269C2×C3×C4C2×C4×D318yes—
270C2×C3×C4C2×C4×D318yes—
271C2×C3×C4#23518yes—
272C2×C3×C4C2×#67116yes—
273C2×C3×C4C2×#6718yes—
274#67—632no—
275C2×Dic3—38no—
276C2×Dic3—38no—
277C2×Dic3—38no—
278C2×Dic3—316no—
279C2×Dic3—64no—
280C2×Dic3—68no—
281C2×Dic3—68no—
282C2×Dic3—68no—
283C2×Dic3—64no—
284C2×Dic3—68no—
285C2×Dic3—68no—
286C2×Dic3—68no—
287C2×Dic3—68no—
288C4×D3—664no—
289C4×D3—632no—
290C2×C32—42no—
291C2×C32C2×#11711yescharacteristic
292C2×C32C2×C4×D411yescharacteristic
293C2×C32C4×#4111yescharacteristic
294C2×C32#52512yes—
295C2×C32#52912yes—
296C3⋊D3—24no—
297C24—91no—
298C24C22×C3⋊D311yescharacteristic
299C2×D4—94no—
300C2×D4—184no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—91no—
304C22×C4—91no—
305C22×C4—92no—
306C22×C4—91no—
307C22×C4—94no—
308C22×C4—92no—
309C22×C4—184no—
310C22×C4—184no—
311C22×C4—182no—
312C22×C4—184no—
313C22×C4—182no—
314C22×C4C4×C3⋊D314yescomplemented
315C22×C4C22×C3⋊D312yes—
316C22×C4C22×C3⋊D311yescharacteristic
317C22×C4C22×C3⋊D312yes—
318C22×C4C22×C3⋊D311yescharacteristic
319C4⋊C4—24no—
320C4⋊C4—94no—
321C4⋊C4—184no—
322C22⋊C4—24no—
323C22⋊C4—94no—
324C22⋊C4—94no—
325C22⋊C4—184no—
326C22⋊C4—184no—
327C42—22no—
328C42—94no—
329C42—182no—
330C42—184no—
331C42—182no—
332C42#63814yescomplemented
333C22×C3—28no—
334C22×C3—28no—
335C22×C3—28no—
336C22×C3—48no—
337C22×C3—48no—
338C22×C3C22×C4×D314yes—
339C22×C3C2×#23514yes—
340C22×C3D3×#4118yes—
341C22×C3D3×#4118yes—
342C22×C3C22×#6714yes—
343C2×D3—316no—
344C2×D3—68no—
345C2×D3—616no—
346C2×D3—68no—
347C2×D3—616no—
348C3×C4—28no—
349C3×C4—216no—
350C3×C4—48no—
351C3×C4C4×#67116yes—
352Dic3—68no—
353Dic3—68no—
354Dic3—68no—
355Dic3—616no—
356Dic3—128no—
357C32#229011yescharacteristic, complemented, Sylow
358C23—21no—
359C23—22no—
360C23—22no—
361C23—21no—
362C23—92no—
363C23—94no—
364C23—181no—
365C23—182no—
366C23—181no—
367C23C2×C4×C3⋊D312yes—
368C23C23×C3⋊D311yescharacteristic
369D4—188no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—21no—
374C2×C4—28no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—92no—
379C2×C4—92no—
380C2×C4—92no—
381C2×C4—94no—
382C2×C4—1816no—
383C2×C4—181no—
384C2×C4—182no—
385C2×C4—182no—
386C2×C4—182no—
387C2×C4—181no—
388C2×C4—182no—
389C2×C4—188no—
390C2×C4—182no—
391C2×C4—182no—
392C2×C4—182no—
393C2×C4C2×C4×C3⋊D312yes—
394C2×C4C2×C4×C3⋊D312yes—
395C2×C4#382812yes—
396C2×C4C2×#63814yes—
397C2×C4C2×#63812yes—
398C2×C3—48no—
399C2×C3D3×#11714yes—
400C2×C3#552214yes—
401C2×C3#552818yes—
402C2×C3C2×C4×#6714yes—
403C2×C3#582818yes—
404D3—616no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—42no—
409C22—42no—
410C22—94no—
411C22—182no—
412C22—184no—
413C22—182no—
414C22—184no—
415C22C22×C4×C3⋊D311yescharacteristic
416C22C2×#382811yescharacteristic
417C22#41×C3⋊D312yes—
418C22#41×C3⋊D312yes—
419C22C22×#63811yescharacteristic
420C4—22no—
421C4—24no—
422C4—42no—
423C4—182no—
424C4—182no—
425C4—182no—
426C4—184no—
427C4—362no—
428C4C4×#63814yes—
429C3#8226814yescomplemented
430C2—42no—
431C2—184no—
432C2C3⋊D3×#11711yescharacteristic
433C2#1059599311yescharacteristic
434C2#1059599912yes—
435C2C2×C4×#63811yescharacteristic
436C2#1059629912yes—
subgroupG/H
centerC22×C4C22×C3⋊D3
commutatorC22×C32C23×C4
FrattiniC23C23×C3⋊D3
FittingC2×C32×#117C2
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC2×#117C3⋊D3
hypocenterC32#2290
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×C32×#117C2semidirect
3. C2×C42×C3⋊D3C2semidirect
4. C4×#3757C2semidirect
5. #10592688C2semidirect
6. #10592677C2semidirect
8. #10592643C2semidirect
9. C4×#3752C2semidirect
10. #10592631C2semidirect
11. C4×#3750C2semidirect
24. C4×#638C4semidirect
39. C2×C3×#117D3semidirect
54. C22×C32×C4C2×C4semidirect
75. C32×C42D4semidirect
77. #3757C2×C4semidirect
81. #3750C2×C4semidirect
85. C4×C3⋊Dic3C2×C4semidirect
154. C2×#117C3⋊D3semidirect
168. C22×C3×C4C4×D3semidirect
189. C3×C42#67semidirect
214. C2×C3⋊D3#117semidirect
314. C22×C4C4×C3⋊D3semidirect
332. C42#638semidirect
357. C32#2290semidirect
429. C3#82268semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1172
C2×C4×#6382
C2×C42×C3⋊D32
C4×#37572
#105926882
#105926772
#105926552
#105926432
C4×#37522
#105926312
C4×#37502
#822683