Finite Group Databasebeta

← #11808540

Subgroups — #11808540

Order 1152.

1680 conjugacy classes of subgroups.

The subgroup lattice has 414 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
3C4×#3757C211yesmaximal, characteristic, complemented
4#10592692C211yesmaximal, characteristic, complemented
5#10592691C211yesmaximal, characteristic, complemented
6#10592684C211yesmaximal, characteristic, complemented
7#10592682C211yesmaximal, characteristic, complemented
8#10592658C212yesmaximal
9#10592651C212yesmaximal, complemented
10C4×#3752C212yesmaximal, complemented
11C4×#3750C212yesmaximal, complemented
12#82274—34nomaximal
13C23×C32×C4C2211yescharacteristic
14C22×#638C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C32×#117—24no—
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C32×C22⋊C4C2212yes—
20C2×C32×C42C2212yes—
21C2×#3757C2211yescharacteristic
22C2×#3757C2212yes—
23C4×#638—24no—
24C2×#3752C2212yes—
25C2×#3752C2212yes—
26C2×#3752C2211yescharacteristic
27C2×#3750C2212yes—
28C2×#3750C2212yes—
29C2×#3750C2211yescharacteristic
30C2×C4×C3⋊Dic3C2211yescharacteristic
31C2×C4×C3⋊Dic3C2212yes—
32#63658C2212yes—
33#63658C2212yes—
34#63658C2212yes—
35#63658C2212yes—
36#63658C2211yescharacteristic
37#63658C2211yescharacteristic
38C2×C3×#117D314yescomplemented
39C2×C4×#67—34no—
40C4×#217—34no—
41#4993—34no—
42#4992—34no—
43#4985—34no—
44#4983—34no—
45#4959—38no—
46#4952—38no—
47C4×(C2×D3)⋊C4—38no—
48C4×Dic3⋊C4—38no—
49C24×C32C2311yescharacteristic
50C23×C3⋊D3C2311yescharacteristic
51C22×C32×C4—24no—
52C22×C32×C4D414yes—
53C22×C32×C4C2312yes—
54C22×C32×C4C2312yes—
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C2×#638—22no—
58C2×#638—22no—
59C2×#638—22no—
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3⋊Dic3C2311yescharacteristic
62C22×C3⋊Dic3C2312yes—
63C22×C3⋊Dic3C2311yescharacteristic
64C22×C3⋊Dic3C2312yes—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3—24no—
67C32×C4⋊C4—22no—
68C32×C4⋊C4—22no—
69C32×C22⋊C4—24no—
70C32×C42—24no—
71#3757—22no—
72#3757—24no—
73#3752—24no—
74#3752—22no—
75#3752—24no—
76#3750—22no—
77#3750—24no—
78#3750—24no—
79C4×C3⋊Dic3—22no—
80C4×C3⋊Dic3—24no—
81#2395—91noSylow
82C23×C3×C4C2×D314yes—
83C22×#67—34no—
84C22×C4×D3—34no—
85C3×#117—216no—
86C2×C3×C4⋊C4C2×D314yes—
87C2×C3×C4⋊C4C2×D314yes—
88C2×C3×C22⋊C4C2×D318yes—
89C2×C3×C42C2×D318yes—
90C2×#217—34no—
91C2×#217—38no—
92C4×#67—616no—
93C2×(C2×D3)⋊C4—38no—
94C2×(C2×D3)⋊C4—38no—
95C2×(C2×D3)⋊C4—34no—
96C2×Dic3⋊C4—38no—
97C2×Dic3⋊C4—38no—
98C2×Dic3⋊C4—34no—
99C2×C4×Dic3—34no—
100C2×C4×Dic3—38no—
101C3⋊#95—38no—
102C3⋊#95—38no—
103C3⋊#95—38no—
104C3⋊#95—38no—
105C3⋊#95—34no—
106C3⋊#95—34no—
107C23×C32—22no—
108C23×C32—21no—
109C23×C32—21no—
110C23×C32—22no—
111C23×C32C2×D412yes—
112C23×C32C2411yescharacteristic
113C22×C3⋊D3—21no—
114C22×C3⋊D3—22no—
115C22×C3⋊D3—22no—
116C22×C3⋊D3—21no—
117C22×C3⋊D3#4112yes—
118C2×C32×C4—22no—
119C2×C32×C4—28no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4C2×D412yes—
127C2×C32×C4C2×D412yes—
128C2×C32×C4#4114yes—
129#638—28no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3#4112yes—
142C2×C3⋊Dic3#4114yes—
143C4×C3⋊D3—44no—
144C2×C4×D4—91no—
145C2×#117C3⋊D311yescharacteristic, complemented
146#400—91no—
147#399—91no—
148#398—91no—
149#397—91no—
150#397—92no—
151#394—92no—
152C4×C4⋊C4—92no—
153C4×C22⋊C4—91no—
154C4×C22⋊C4—92no—
155C24×C3C22×D314yes—
156C23×D3—34no—
157C22×C3×C4—216no—
158C22×C3×C4#67116yes—
159C22×C3×C4C22×D318yes—
160C22×C3×C4C22×D318yes—
161C22×C3×C4C22×D314yes—
162C22×C3×C4C22×D314yes—
163C2×#67—68no—
164C2×#67—68no—
165C2×#67—68no—
166C22×Dic3—34no—
167C22×Dic3—38no—
168C22×Dic3—38no—
169C22×Dic3—34no—
170C22×Dic3—34no—
171C2×C4×D3—616no—
172C2×C4×D3—68no—
173C3×C4⋊C4—28no—
174C3×C4⋊C4—28no—
175C3×C22⋊C4—216no—
176C3×C42—216no—
177#217—616no—
178#217—68no—
179(C2×D3)⋊C4—616no—
180(C2×D3)⋊C4—616no—
181(C2×D3)⋊C4—68no—
182Dic3⋊C4—616no—
183Dic3⋊C4—616no—
184Dic3⋊C4—68no—
185C4×Dic3—616no—
186C4×Dic3—68no—
187C22×C32—22no—
188C22×C32—22no—
189C22×C32—22no—
190C22×C32—42no—
191C22×C32—42no—
192C22×C32C22×D411yescharacteristic
193C22×C32C2×#4112yes—
194C22×C32C2×#4111yescharacteristic
195C22×C32C2×#4111yescharacteristic
196C22×C32C2×#4112yes—
197C2×C3⋊D3—22no—
198C2×C3⋊D3—24no—
199C2×C3⋊D3—41no—
200C2×C3⋊D3—42no—
201C2×C3⋊D3—41no—
202C32×C4—22no—
203C32×C4—42no—
204C32×C4—42no—
205C32×C4#12314yes—
206C3⋊Dic3—22no—
207C3⋊Dic3—24no—
208C3⋊Dic3—41no—
209C3⋊Dic3—42no—
210C3⋊Dic3—41no—
211C22×D4—91no—
212C23×C4—91no—
213C23×C4C2×C3⋊D311yescharacteristic
214C4×D4—184no—
215#117—24no—
216C2×C4⋊C4—91no—
217C2×C4⋊C4—92no—
218C2×C4⋊C4—92no—
219C2×C4⋊C4C2×C3⋊D311yescharacteristic
220C2×C4⋊C4C2×C3⋊D311yescharacteristic
221C2×C22⋊C4—91no—
222C2×C22⋊C4—92no—
223C2×C22⋊C4—91no—
224C2×C22⋊C4—92no—
225C2×C22⋊C4—92no—
226C2×C22⋊C4C2×C3⋊D312yes—
227C2×C42—91no—
228C2×C42—92no—
229C2×C42C2×C3⋊D312yes—
230#95—92no—
231#95—91no—
232#95—92no—
233#95—91no—
234#95—92no—
235#95—92no—
236C23×C3—28no—
237C23×C3—28no—
238C23×C3—24no—
239C23×C3—24no—
240C23×C3C2×#6718yes—
241C23×C3C23×D314yes—
242C22×D3—38no—
243C22×D3—68no—
244C22×D3—68no—
245C22×D3—64no—
246C22×D3—64no—
247C2×C3×C4—28no—
248C2×C3×C4—232no—
249C2×C3×C4—28no—
250C2×C3×C4—28no—
251C2×C3×C4—28no—
252C2×C3×C4—28no—
253C2×C3×C4—28no—
254C2×C3×C4—28no—
255C2×C3×C4#235116yes—
256C2×C3×C4C2×#6718yes—
257C2×C3×C4C2×#6718yes—
258#67—632no—
259C2×Dic3—38no—
260C2×Dic3—316no—
261C2×Dic3—68no—
262C2×Dic3—68no—
263C2×Dic3—64no—
264C2×Dic3—64no—
265C2×Dic3—68no—
266C2×Dic3—68no—
267C2×Dic3—68no—
268C2×Dic3—68no—
269C2×Dic3—68no—
270C2×Dic3—64no—
271C2×Dic3—64no—
272C4×D3—1216no—
273C2×C32—42no—
274C2×C32C2×#12311yescharacteristic
275C2×C32#52511yescharacteristic
276C2×C32#52912yes—
277C2×C32#52912yes—
278C2×C32#53211yescharacteristic
279C3⋊D3—42no—
280C24—91no—
281C24C22×C3⋊D311yescharacteristic
282C2×D4—182no—
283C2×D4—182no—
284C2×D4—182no—
285C22×C4—24no—
286C22×C4—92no—
287C22×C4—91no—
288C22×C4—92no—
289C22×C4—91no—
290C22×C4—91no—
291C22×C4—184no—
292C22×C4—182no—
293C22×C4#63814yes—
294C22×C4C22×C3⋊D312yes—
295C22×C4C22×C3⋊D312yes—
296C22×C4C22×C3⋊D311yescharacteristic
297C22×C4C22×C3⋊D311yescharacteristic
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—184no—
301C4⋊C4—184no—
302C4⋊C4—182no—
303C22⋊C4—24no—
304C22⋊C4—184no—
305C22⋊C4—184no—
306C22⋊C4—184no—
307C22⋊C4—182no—
308C22⋊C4—182no—
309C42—24no—
310C42—184no—
311C42—182no—
312C22×C3—28no—
313C22×C3—28no—
314C22×C3—28no—
315C22×C3—48no—
316C22×C3—48no—
317C22×C3C2×#23518yes—
318C22×C3D3×#4114yes—
319C22×C3D3×#4114yes—
320C22×C3D3×#4118yes—
321C22×C3C22×#6714yes—
322C2×D3—616no—
323C2×D3—68no—
324C2×D3—128no—
325C2×D3—124no—
326C2×D3—124no—
327C3×C4—28no—
328C3×C4—48no—
329C3×C4—48no—
330C3×C4#929116yes—
331Dic3—616no—
332Dic3—68no—
333Dic3—128no—
334Dic3—124no—
335Dic3—124no—
336C32#239511yescharacteristic, complemented, Sylow
337C23—22no—
338C23—22no—
339C23—21no—
340C23—21no—
341C23—92no—
342C23—182no—
343C23—182no—
344C23—181no—
345C23—181no—
346C23C2×#63812yes—
347C23C23×C3⋊D311yescharacteristic
348D4—188no—
349C2×C4—22no—
350C2×C4—28no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—94no—
358C2×C4—92no—
359C2×C4—182no—
360C2×C4—182no—
361C2×C4—181no—
362C2×C4—181no—
363C2×C4—182no—
364C2×C4—182no—
365C2×C4—182no—
366C2×C4—182no—
367C2×C4—182no—
368C2×C4—181no—
369C2×C4—181no—
370C2×C4—364no—
371C2×C4#382814yes—
372C2×C4C2×#63812yes—
373C2×C4C2×#63812yes—
374C2×C3—48no—
375C2×C3#552818yes—
376C2×C3#552818yes—
377C2×C3C2×#92914yes—
378C2×C3#582814yes—
379C2×C3#583214yes—
380D3—128no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—42no—
385C22—42no—
386C22—184no—
387C22—182no—
388C22—362no—
389C22—361no—
390C22—361no—
391C22C2×#382812yes—
392C22#41×C3⋊D311yescharacteristic
393C22#41×C3⋊D311yescharacteristic
394C22#41×C3⋊D312yes—
395C22C22×#63811yescharacteristic
396C4—22no—
397C4—42no—
398C4—42no—
399C4—184no—
400C4—182no—
401C4—362no—
402C4—361no—
403C4—361no—
404C4#6413814yes—
405C3#8227414yescomplemented
406C2—42no—
407C2—362no—
408C2#1059599912yes—
409C2#1059599912yes—
410C2C2×#6413811yescharacteristic
411C2#1059629911yescharacteristic
412C2#1059630311yescharacteristic
subgroupG/H
centerC22×C4C22×C3⋊D3
commutator, socle, cosocleC23×C32C24
FrattiniC23C23×C3⋊D3
FittingC2×C32×#117C2
prime radicalC22×#638C22
hypercenterC2×#117C3⋊D3
hypocenterC32#2395
LCSG ▷ C23×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. C4×#3757C2semidirect
4. #10592692C2semidirect
5. #10592691C2semidirect
6. #10592684C2semidirect
7. #10592682C2semidirect
9. #10592651C2semidirect
10. C4×#3752C2semidirect
11. C4×#3750C2semidirect
38. C2×C3×#117D3semidirect
145. C2×#117C3⋊D3semidirect
336. C32#2395semidirect
405. C3#82274semidirect

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
C4×#37572
#105926922
#105926912
#105926842
#105926822
#105926582
#105926512
C4×#37522
C4×#37502
#822743