Finite Group Databasebeta

← #11887515

Subgroups — #11887515

Order 1152.

1260 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596198C211yesmaximal, characteristic, complemented
2#10596022C211yesmaximal, characteristic
3C32×#461C211yesmaximal, characteristic, complemented
4#10592870C212yesmaximal, complemented
5#10592869C212yesmaximal, complemented
6#10592778C211yesmaximal, characteristic, complemented
7C4×#3754C211yesmaximal, characteristic, complemented
8#10592550C211yesmaximal, characteristic, complemented
9#10592533C211yesmaximal, characteristic, complemented
10#10592504C212yesmaximal, complemented
11C3⋊D3×#103C212yesmaximal, complemented
12#80450—34nomaximal
13C2×Q8×C3⋊D3C2212yes—
14C2×#3828—21no—
15C2×C32×SD16C2212yes—
16C32×C4⋊Q8C2211yescharacteristic
17C32×C4×D4C2211yescharacteristic
18#64155C2212yes—
19#64147C2212yes—
20C2×#3754C2211yescharacteristic
21#64133—21no—
22C2×C8×C3⋊D3C2212yes—
23#64105—22no—
24#64102—21no—
25C4⋊C4×C3⋊D3C2212yes—
26#64097—21no—
27#64092—22no—
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29#64078C2211yescharacteristic
30C4×#634C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32C32×#103C2212yes—
33#63662C2212yes—
34#63662C2212yes—
35#63659C2211yescharacteristic
36#63647C2212yes—
37#63644C2212yes—
38#63643C2212yes—
39#63637C2211yescharacteristic
40#63635C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42#5727—34no—
43#5551—34no—
44C3×#461D314yescomplemented
45#5171—38no—
46#5170—38no—
47#5079—34no—
48C4×#214—34no—
49#4851—34no—
50#4834—34no—
51#4805—38no—
52D3×#103—38no—
53C2×C32×Q8C2312yes—
54C2×C32×D4C2311yescharacteristic
55C22×C32×C4—21no—
56C2×#638—22no—
57Q8×C3⋊D3—24no—
58Q8×C3⋊D3—42no—
59#3828—44no—
60C2×C4⋊(C3⋊D3)D411yescharacteristic
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3—22no—
63C2×C4×C3⋊D3C2312yes—
64C2×#634—21no—
65C2×#634—22no—
66C2×#634C2311yescharacteristic
67C32×SD16—42no—
68C2×C32×C8C2312yes—
69C32×C4⋊C4—21no—
70C32×C4⋊C4—21no—
71C32×C4⋊C4C2311yescharacteristic
72C32×C22⋊C4—21no—
73C32×C42C2311yescharacteristic
74#3757—22no—
75#3754—22no—
76#3752—22no—
77#3752D412yes—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)D411yescharacteristic
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81C4⋊(C3⋊Dic3)C2312yes—
82#3750—21no—
83#3750—22no—
84#3750—22no—
85C4×C3⋊Dic3—21no—
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88C8×C3⋊D3—42no—
89#3298—91noSylow
90C2×D3×Q8—38no—
91C2×#235—64no—
92C2×C3×SD16C2×D318yes—
93C3×C4⋊Q8C2×D314yes—
94C3×C4×D4C2×D314yes—
95#946—38no—
96#938—38no—
97C2×#214—34no—
98#924—64no—
99C2×D3×C8—38no—
100#896—68no—
101#893—64no—
102D3×C4⋊C4—38no—
103#888—64no—
104#883—68no—
105C4×D12—34no—
106#869—34no—
107C4×Dic6—34no—
108C3×C4⋊C8C2×D314yes—
109C3×#103C2×D318yes—
110#835—38no—
111#835—38no—
112#832—34no—
113(C2×D3)⋊C8—38no—
114#817—38no—
115#816—38no—
116#810—34no—
117#808—34no—
118C4×C3⋊C8—34no—
119C23×C32—21no—
120C22×C3⋊D3C2×D412yes—
121C32×Q8—22no—
122C32×Q8—22no—
123C32×D4—21no—
124C32×D4—21no—
125C2×C32×C4—21no—
126C2×C32×C4—22no—
127C2×C32×C4—42no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2411yescharacteristic
131#638—44no—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3C2×D412yes—
136C4⋊(C3⋊D3)SD1614yescomplemented
137C4×C3⋊D3—22no—
138C4×C3⋊D3—22no—
139C4×C3⋊D3—44no—
140C4×C3⋊D3—44no—
141#634—21no—
142#634—44no—
143#634—42no—
144#634#4112yescomplemented
145C32×C8—22no—
146C3⋊(C3⋊C8)—21no—
147C3⋊(C3⋊C8)—21no—
148D4×Q8—91no—
149#547—91no—
150#487—91no—
151#483—92no—
152#475—91no—
153#465—92no—
154#461C3⋊D311yescharacteristic, complemented
155#448—92no—
156C4×SD16—91no—
157C8×D4—91no—
158C2×#103—92no—
159C2×C3×Q8C22×D318yes—
160C2×C3×D4C22×D314yes—
161C22×C3×C4—24no—
162C2×#67—68no—
163D3×Q8—616no—
164D3×Q8—128no—
165#235—1216no—
166C2×D12—34no—
167C2×C4×D3—38no—
168C2×C4×D3—68no—
169C2×C4×D3—68no—
170C2×Dic6—34no—
171C2×Dic6—68no—
172C2×Dic6—64no—
173C3×SD16—48no—
174C2×C3×C8C22×D318yes—
175C3×C4⋊C4—24no—
176C3×C4⋊C4—24no—
177C3×C4⋊C4C22×D314yes—
178C3×C22⋊C4—24no—
179C3×C42C22×D314yes—
180#217—68no—
181#214—68no—
182(C2×D3)⋊C4—38no—
183(C2×D3)⋊C4—68no—
184C4⋊Dic3—34no—
185C4⋊Dic3—34no—
186C4⋊Dic3—38no—
187C4⋊Dic3—64no—
188Dic3⋊C4—68no—
189Dic3⋊C4—68no—
190Dic3⋊C4—64no—
191C4×Dic3—64no—
192C2×C3⋊C8—34no—
193C2×C3⋊C8—34no—
194D3×C8—128no—
195C22×C32—41no—
196C22×C32—41no—
197C22×C32—41no—
198C22×C32C22×D411yescharacteristic
199C2×C3⋊D3—22no—
200C2×C3⋊D3—22no—
201C2×C3⋊D3C2×SD1614yes—
202C32×C4—21no—
203C32×C4—42no—
204C32×C4—41no—
205C32×C4C2×SD1612yes—
206C32×C4C2×#4111yescharacteristic
207C32×C4H(5,𝔽2)11yescharacteristic
208C3⋊Dic3—22no—
209C3⋊Dic3—22no—
210C3⋊Dic3—42no—
211C3⋊Dic3—41no—
212C2×#41—181no—
213C22×Q8—92no—
214C2×SD16—91no—
215C2×SD16C2×C3⋊D312yes—
216C22×C8—92no—
217C4⋊Q8—91no—
218C4⋊Q8—181no—
219C4⋊Q8C2×C3⋊D311yescharacteristic
220#123—182no—
221C22⋊Q8—92no—
222C22⋊Q8—182no—
223C22⋊Q8—181no—
224#121—92no—
225C4×Q8—91no—
226C4×D4—91no—
227C4×D4—181no—
228C4×D4C2×C3⋊D311yescharacteristic
229C2×C4⋊C4—92no—
230#106—92no—
231#106—91no—
232C4⋊C8C2×C3⋊D311yescharacteristic
233#103—92no—
234#103—92no—
235#103—92no—
236#103—91no—
237#103C2×C3⋊D312yes—
238#102—91no—
239C22⋊C8—92no—
240C4×C8—91no—
241C23×C3—24no—
242C22×D3—38no—
243C3×Q8—28no—
244C3×Q8—28no—
245C3×D4—24no—
246C3×D4—24no—
247C2×C3×C4—24no—
248C2×C3×C4—28no—
249C2×C3×C4—48no—
250C2×C3×C4D3×D414yes—
251C2×C3×C4D3×D414yes—
252C2×C3×C4C23×D314yes—
253#67—1216no—
254C2×Dic3—38no—
255C2×Dic3—64no—
256C2×Dic3—64no—
257C2×Dic3—68no—
258D12—316no—
259C4×D3—68no—
260C4×D3—68no—
261C4×D3—1216no—
262C4×D3—1216no—
263Dic6—38no—
264Dic6—64no—
265Dic6—1216no—
266Dic6—128no—
267C3×C8—28no—
268C3⋊C8—64no—
269C3⋊C8—64no—
270C2×C32—81no—
271C2×C32#54611yescharacteristic
272C2×C32C22×SD1611yescharacteristic
273C2×C32#57811yescharacteristic
274C3⋊D3—24no—
275#41—364no—
276C2×Q8—91no—
277C2×Q8—182no—
278C2×Q8—181no—
279C2×Q8—184no—
280C2×Q8—362no—
281C2×Q8C22×C3⋊D312yes—
282C2×D4—91no—
283C2×D4—182no—
284C2×D4C22×C3⋊D311yescharacteristic
285C22×C4—21no—
286C22×C4—92no—
287C22×C4—182no—
288C22×C4—182no—
289SD16—42no—
290SD16—182no—
291C2×C8—91no—
292C2×C8—91no—
293C2×C8—362no—
294C2×C8C22×C3⋊D312yes—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—91no—
298C4⋊C4—91no—
299C4⋊C4—92no—
300C4⋊C4—182no—
301C4⋊C4—182no—
302C4⋊C4—181no—
303C4⋊C4—181no—
304C4⋊C4C22×C3⋊D311yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—92no—
307C22⋊C4—182no—
308C22⋊C4—182no—
309C42—181no—
310C42C22×C3⋊D311yescharacteristic
311C22×C3—44no—
312C22×C3—44no—
313C22×C3—44no—
314C22×C3C2×D3×D414yes—
315C2×D3—316no—
316C2×D3—68no—
317C2×D3—68no—
318C3×C4—24no—
319C3×C4—44no—
320C3×C4—48no—
321C3×C4D3×SD1618yes—
322C3×C4#100414yes—
323C3×C4D3×#4114yes—
324Dic3—68no—
325Dic3—68no—
326Dic3—128no—
327Dic3—124no—
328C32#329811yescharacteristic, complemented, Sylow
329C23—21no—
330C23—92no—
331Q8—22no—
332Q8—22no—
333Q8—92no—
334Q8—181no—
335Q8—364no—
336Q8—362no—
337D4—21no—
338D4—21no—
339D4—94no—
340D4—364no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—42no—
344C2×C4—92no—
345C2×C4—181no—
346C2×C4—182no—
347C2×C4—182no—
348C2×C4—181no—
349C2×C4—182no—
350C2×C4—364no—
351C2×C4—364no—
352C2×C4D4×C3⋊D311yescharacteristic
353C2×C4D4×C3⋊D311yescharacteristic
354C2×C4C23×C3⋊D311yescharacteristic
355C8—22no—
356C8—181no—
357C8—181no—
358C2×C3—84no—
359C2×C3#561214yes—
360C2×C3C2×D3×SD1614yes—
361C2×C3#577914yes—
362D3—616no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—94no—
367C22—182no—
368C22—182no—
369C22C2×D4×C3⋊D311yescharacteristic
370C4—21no—
371C4—41no—
372C4—42no—
373C4—182no—
374C4—182no—
375C4—362no—
376C4—361no—
377C4SD16×C3⋊D312yes—
378C4#6436111yescharacteristic
379C4#41×C3⋊D311yescharacteristic
380C3#8045014yescomplemented
381C2—81no—
382C2—184no—
383C2#1059608311yescharacteristic
384C2C2×SD16×C3⋊D311yescharacteristic
385C2#1059625011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#461C2
socleC22×C32C22×D4
prime radical#10596022C2
hypercenter#461C3⋊D3
hypocenterC32#3298
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #10596198C2semidirect
3. C32×#461C2semidirect
4. #10592870C2semidirect
5. #10592869C2semidirect
6. #10592778C2semidirect
7. C4×#3754C2semidirect
8. #10592550C2semidirect
9. #10592533C2semidirect
10. #10592504C2semidirect
11. C3⋊D3×#103C2semidirect
44. C3×#461D3semidirect
136. C4⋊(C3⋊D3)SD16semidirect
144. #634#41semidirect
154. #461C3⋊D3semidirect
328. C32#3298semidirect
380. C3#80450semidirect

Maximal subgroups

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

subgroupindex
#105961982
#105960222
C32×#4612
#105928702
#105928692
#105927782
C4×#37542
#105925502
#105925332
#105925042
C3⋊D3×#1032
#804503