Finite Group Databasebeta

← #11805750

Subgroups — #11805750

Order 1152.

1764 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic
2C32×C4×C22⋊C4C211yesmaximal, characteristic, complemented
3#10592910C211yesmaximal, characteristic, complemented
4#10592655C212yesmaximal
5#10592643C212yesmaximal, complemented
6C4×#3752C212yesmaximal, complemented
7#10592632C212yesmaximal, complemented
8#10592366C211yesmaximal, characteristic, complemented
9C3⋊D3×#95C211yesmaximal, characteristic, complemented
10#10592350C211yesmaximal, characteristic, complemented
11#10592347C211yesmaximal, characteristic, complemented
12#73576—34nomaximal
13C23×C32×C4C2211yescharacteristic
14C22×#638C2211yescharacteristic
15C22×C4×C3⋊D3C2212yes—
16C22×C4×C3⋊D3C2211yescharacteristic
17C2×C32×C22⋊C4C2212yes—
18C2×C32×C42C2212yes—
19C2×#3757C2212yes—
20C2×#3757C2211yescharacteristic
21C4×#638C418yescomplemented
22C2×#3752C2212yes—
23C2×#3752C2211yescharacteristic
24C2×#3750C2212yes—
25C2×#3750C2211yescharacteristic
26C2×C4×C3⋊Dic3C2212yes—
27C2×C4×C3⋊Dic3C2211yescharacteristic
28C32×#95C2211yescharacteristic
29C32×#95C2211yescharacteristic
30#63658C2211yescharacteristic
31#63658C2212yes—
32#63658C2211yescharacteristic
33#63658C2212yes—
34#63658C2212yes—
35#63658C2212yes—
36#63658C2212yes—
37C2×C4×#67—34no—
38C3×C4×C22⋊C4D314yescomplemented
39#5211—34no—
40#4956—38no—
41#4944—38no—
42C4×(C2×D3)⋊C4—38no—
43#4933—38no—
44#4667—34no—
45D3×#95—34no—
46#4651—34no—
47#4648—34no—
48C24×C32C2311yescharacteristic
49C23×C3⋊D3C2311yescharacteristic
50C22×C32×C4—42no—
51C22×C32×C4C2×C414yescomplemented
52C22×C32×C4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2312yes—
56C2×#638—22no—
57C2×#638—22no—
58C2×#638C2×C414yes—
59C22×C3⋊Dic3C2312yes—
60C22×C3⋊Dic3C2312yes—
61C22×C3⋊Dic3C2311yescharacteristic
62C22×C3⋊Dic3C2311yescharacteristic
63C22×C3⋊Dic3C2311yescharacteristic
64C2×C4×C3⋊D3—24no—
65C2×C4×C3⋊D3—24no—
66C2×C4×C3⋊D3—42no—
67C2×C4×C3⋊D3—42no—
68C2×C4×C3⋊D3C2×C414yes—
69C32×C22⋊C4—24no—
70C32×C42—42no—
71#3757—42no—
72#3757C2×C414yescomplemented
73#3752—24no—
74#3752C2×C414yes—
75#3750—42no—
76#3750C2×C414yescomplemented
77C4×C3⋊Dic3—24no—
78C4×C3⋊Dic3C2×C414yescomplemented
79#2353—91noSylow
80C23×C3×C4C2×D314yes—
81C22×#67—34no—
82C22×C4×D3—34no—
83C22×C4×D3—38no—
84C2×C3×C22⋊C4C2×D318yes—
85C2×C3×C42C2×D318yes—
86C2×#217—34no—
87C2×#217—38no—
88C4×#67—332no—
89C2×(C2×D3)⋊C4—34no—
90C2×(C2×D3)⋊C4—38no—
91C2×Dic3⋊C4—34no—
92C2×Dic3⋊C4—38no—
93C2×C4×Dic3—34no—
94C2×C4×Dic3—38no—
95C3×#95C2×D314yes—
96C3×#95C2×D314yes—
97C3⋊#95—34no—
98C3⋊#95—38no—
99C3⋊#95—34no—
100C3⋊#95—38no—
101C3⋊#95—38no—
102C3⋊#95—38no—
103C3⋊#95—38no—
104C23×C32—22no—
105C23×C32—21no—
106C23×C32—21no—
107C23×C32—22no—
108C23×C32C22×C412yes—
109C23×C32C2411yescharacteristic
110C22×C3⋊D3—22no—
111C22×C3⋊D3—22no—
112C22×C3⋊D3C22×C412yes—
113C22×C3⋊D3#4112yes—
114C22×C3⋊D3#4112yes—
115C2×C32×C4—22no—
116C2×C32×C4—22no—
117C2×C32×C4—22no—
118C2×C32×C4—22no—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—44no—
123C2×C32×C4C22×C412yes—
124C2×C32×C4C22×C412yes—
125C2×C32×C4#4114yes—
126#638—28no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3C22×C412yes—
138C2×C3⋊Dic3C22×C412yes—
139C2×C3⋊Dic3C22×C412yes—
140C4×C3⋊D3—44no—
141C4×C3⋊D3—48no—
142C2×C4×D4—91no—
143#388—92no—
144#387—92no—
145#386—92no—
146#383—91no—
147#381—91no—
148#380—91no—
149C4×C22⋊C4—92no—
150C4×C22⋊C4C3⋊D311yescharacteristic, complemented
151#376—91no—
152C2×#95—91no—
153C24×C3C22×D314yes—
154C23×D3—34no—
155C22×C3×C4—48no—
156C22×C3×C4C4×D3116yescomplemented
157C22×C3×C4C22×D318yes—
158C22×C3×C4C22×D314yes—
159C22×C3×C4C22×D314yes—
160C22×C3×C4C22×D318yes—
161C2×#67—316no—
162C2×#67—68no—
163C2×#67—68no—
164C22×Dic3—34no—
165C22×Dic3—34no—
166C22×Dic3—34no—
167C22×Dic3—38no—
168C22×Dic3—38no—
169C2×C4×D3—316no—
170C2×C4×D3—616no—
171C2×C4×D3—616no—
172C2×C4×D3—128no—
173C2×C4×D3—128no—
174C3×C22⋊C4—216no—
175C3×C42—48no—
176#217—316no—
177#217—128no—
178(C2×D3)⋊C4—316no—
179(C2×D3)⋊C4—616no—
180Dic3⋊C4—316no—
181Dic3⋊C4—128no—
182C4×Dic3—316no—
183C4×Dic3—616no—
184C22×C32—22no—
185C22×C32—22no—
186C22×C32—22no—
187C22×C32—42no—
188C22×C32—42no—
189C22×C32C23×C411yescharacteristic
190C22×C32C2×#4112yes—
191C22×C32C2×#4111yescharacteristic
192C22×C32C2×#4111yescharacteristic
193C22×C32H(5,𝔽2)12yes—
194C2×C3⋊D3—22no—
195C2×C3⋊D3—22no—
196C2×C3⋊D3—24no—
197C2×C3⋊D3—24no—
198C2×C3⋊D3#11714yes—
199C32×C4—22no—
200C32×C4—22no—
201C32×C4—24no—
202C32×C4—42no—
203C3⋊Dic3—22no—
204C3⋊Dic3—22no—
205C3⋊Dic3—22no—
206C3⋊Dic3—42no—
207C3⋊Dic3—42no—
208C22×D4—91no—
209C23×C4—91no—
210C23×C4—92no—
211C23×C4C2×C3⋊D311yescharacteristic
212C4×D4—98no—
213C2×C4⋊C4—91no—
214C2×C4⋊C4—92no—
215C2×C22⋊C4—91no—
216C2×C22⋊C4—91no—
217C2×C22⋊C4—92no—
218C2×C22⋊C4—92no—
219C2×C22⋊C4C2×C3⋊D312yes—
220C2×C42—91no—
221C2×C42—92no—
222C2×C42C2×C3⋊D312yes—
223#95—91no—
224#95—92no—
225#95—91no—
226#95—92no—
227#95—92no—
228#95—92no—
229#95—92no—
230#95C2×C3⋊D311yescharacteristic
231#95C2×C3⋊D311yescharacteristic
232C23×C3—28no—
233C23×C3—28no—
234C23×C3—24no—
235C23×C3—24no—
236C23×C3C2×C4×D318yes—
237C23×C3C23×D314yes—
238C22×D3—38no—
239C22×D3—38no—
240C22×D3—38no—
241C22×D3—68no—
242C22×D3—68no—
243C2×C3×C4—28no—
244C2×C3×C4—28no—
245C2×C3×C4—28no—
246C2×C3×C4—28no—
247C2×C3×C4—28no—
248C2×C3×C4—28no—
249C2×C3×C4—28no—
250C2×C3×C4—416no—
251C2×C3×C4C2×C4×D318yes—
252C2×C3×C4C2×C4×D318yes—
253C2×C3×C4#235116yes—
254#67—632no—
255C2×Dic3—38no—
256C2×Dic3—38no—
257C2×Dic3—38no—
258C2×Dic3—68no—
259C2×Dic3—68no—
260C2×Dic3—64no—
261C2×Dic3—64no—
262C2×Dic3—68no—
263C2×Dic3—68no—
264C2×Dic3—68no—
265C2×Dic3—68no—
266C2×Dic3—68no—
267C2×Dic3—68no—
268C4×D3—1216no—
269C4×D3—1232no—
270C2×C32—42no—
271C2×C32C2×#11711yescharacteristic
272C2×C32C4×#4111yescharacteristic
273C2×C32#51811yescharacteristic
274C2×C32#55112yes—
275C2×C32#55312yes—
276C3⋊D3—24no—
277C24—91no—
278C24C22×C3⋊D311yescharacteristic
279C2×D4—94no—
280C2×D4—182no—
281C2×D4—182no—
282C22×C4—42no—
283C22×C4—91no—
284C22×C4—91no—
285C22×C4—91no—
286C22×C4—94no—
287C22×C4—92no—
288C22×C4—92no—
289C22×C4—184no—
290C22×C4—184no—
291C22×C4—362no—
292C22×C4—362no—
293C22×C4C4×C3⋊D314yescomplemented
294C22×C4C22×C3⋊D312yes—
295C22×C4C22×C3⋊D311yescharacteristic
296C22×C4C22×C3⋊D311yescharacteristic
297C22×C4C22×C3⋊D312yes—
298C4⋊C4—94no—
299C4⋊C4—362no—
300C22⋊C4—24no—
301C22⋊C4—94no—
302C22⋊C4—94no—
303C22⋊C4—184no—
304C22⋊C4—362no—
305C42—42no—
306C42—94no—
307C42—184no—
308C22×C3—28no—
309C22×C3—28no—
310C22×C3—28no—
311C22×C3—48no—
312C22×C3—48no—
313C22×C3C22×C4×D314yes—
314C22×C3C2×#23518yes—
315C22×C3#100418yes—
316C22×C3D3×#4114yes—
317C22×C3D3×#4114yes—
318C2×D3—316no—
319C2×D3—68no—
320C2×D3—68no—
321C2×D3—616no—
322C2×D3—616no—
323C3×C4—28no—
324C3×C4—28no—
325C3×C4—216no—
326C3×C4—48no—
327Dic3—68no—
328Dic3—68no—
329Dic3—68no—
330Dic3—128no—
331Dic3—128no—
332C32#235311yescharacteristic, complemented, Sylow
333C23—22no—
334C23—22no—
335C23—21no—
336C23—21no—
337C23—92no—
338C23—92no—
339C23—92no—
340C23—182no—
341C23—182no—
342C23C2×C4×C3⋊D312yes—
343C23C23×C3⋊D311yescharacteristic
344D4—188no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—44no—
353C2×C4—92no—
354C2×C4—92no—
355C2×C4—92no—
356C2×C4—182no—
357C2×C4—182no—
358C2×C4—181no—
359C2×C4—181no—
360C2×C4—182no—
361C2×C4—182no—
362C2×C4—182no—
363C2×C4—182no—
364C2×C4—182no—
365C2×C4—182no—
366C2×C4—364no—
367C2×C4—368no—
368C2×C4C2×C4×C3⋊D312yes—
369C2×C4C2×C4×C3⋊D312yes—
370C2×C4#382814yes—
371C2×C3—48no—
372C2×C3C4×#23514yes—
373C2×C3#548614yes—
374C2×C3D3×#11714yes—
375C2×C3#555618yes—
376C2×C3#555818yes—
377D3—616no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—42no—
382C22—42no—
383C22—94no—
384C22—182no—
385C22—182no—
386C22—184no—
387C22—184no—
388C22C22×C4×C3⋊D311yescharacteristic
389C22C2×#382812yes—
390C22#6436112yes—
391C22#41×C3⋊D311yescharacteristic
392C22#41×C3⋊D311yescharacteristic
393C4—22no—
394C4—22no—
395C4—24no—
396C4—42no—
397C4—182no—
398C4—182no—
399C4—182no—
400C4—362no—
401C4—362no—
402C3#7357614yescomplemented
403C2—42no—
404C2—184no—
405C2C4×#382811yescharacteristic
406C2#1059595711yescharacteristic
407C2C3⋊D3×#11711yescharacteristic
408C2#1059602712yes—
409C2#1059602912yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×C4×C22⋊C4C2
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC4×C22⋊C4C3⋊D3
hypocenterC32#2353
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C32×C4×C22⋊C4C2semidirect
3. #10592910C2semidirect
5. #10592643C2semidirect
6. C4×#3752C2semidirect
7. #10592632C2semidirect
8. #10592366C2semidirect
9. C3⋊D3×#95C2semidirect
10. #10592350C2semidirect
11. #10592347C2semidirect
21. C4×#638C4semidirect
38. C3×C4×C22⋊C4D3semidirect
51. C22×C32×C4C2×C4semidirect
72. #3757C2×C4semidirect
76. #3750C2×C4semidirect
78. C4×C3⋊Dic3C2×C4semidirect
150. C4×C22⋊C4C3⋊D3semidirect
156. C22×C3×C4C4×D3semidirect
293. C22×C4C4×C3⋊D3semidirect
332. C32#2353semidirect
402. C3#73576semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C32×C4×C22⋊C42
#105929102
#105926552
#105926432
C4×#37522
#105926322
#105923662
C3⋊D3×#952
#105923502
#105923472
#735763