Finite Group Databasebeta

← #11898411

Subgroups — #11898411

Order 1152.

1116 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596056C211yesmaximal, characteristic, complemented
2#10596013C211yesmaximal, characteristic, complemented
3C32×C4×SD16C211yesmaximal, characteristic, complemented
4#10592867C212yesmaximal, complemented
5#10592730C211yesmaximal, characteristic, complemented
6#10592714C211yesmaximal, characteristic
7#10592551C212yesmaximal, complemented
8#10592497C212yesmaximal, complemented
9#10592486C212yesmaximal, complemented
10#10592392C211yesmaximal, characteristic, complemented
11C8×#634C211yesmaximal, characteristic, complemented
12#79638—34nomaximal
13C2×C32×SD16C2211yescharacteristic
14C32×C4×Q8C2211yescharacteristic
15C32×C4×D4C2211yescharacteristic
16#64156C2212yes—
17C2×#3756C2212yes—
18#64145C2212yes—
19C2×#3753C2212yes—
20#64135—21no—
21#64133—21no—
22C2×#3744C2212yes—
23C2×#3744C2212yes—
24#64103—22no—
25#64102C2212yes—
26#64096C2212yes—
27#64088—22no—
28#64084—21no—
29#64083C2211yescharacteristic
30C4×C4⋊(C3⋊D3)—21no—
31#64078C2211yescharacteristic
32C4×#634C2211yescharacteristic
33C32×#106C2211yescharacteristic
34C32×#103C2211yescharacteristic
35C32×#102C2211yescharacteristic
36C32×C4×C8C2211yescharacteristic
37#63641C2212yes—
38C8×C3⋊Dic3C2212yes—
39#63637C2212yes—
40#63636C2212yes—
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
42#5585—34no—
43#5542—34no—
44C3×C4×SD16D314yescomplemented
45#5168—38no—
46#5031—34no—
47#5015—34no—
48#4852—38no—
49#4798—38no—
50#4787—38no—
51#4693—34no—
52C8×Dic6—34no—
53C2×C32×Q8C2311yescharacteristic
54C2×C32×D4C2311yescharacteristic
55C22×C32×C4—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)C2312yes—
59C2×C4×C3⋊D3—22no—
60C2×#634D411yescharacteristic
61C2×#634C2312yes—
62C32×SD16—22no—
63C2×C32×C8C2311yescharacteristic
64C2×C32×C8C2311yescharacteristic
65C32×C4⋊C4—21no—
66C32×C4⋊C4C2311yescharacteristic
67C32×C4⋊C4C2311yescharacteristic
68C32×C22⋊C4—21no—
69C32×C42—21no—
70C32×C42C2311yescharacteristic
71#3757—22no—
72#3757—22no—
73#3756—42no—
74#3753—42no—
75#3752—22no—
76#3752—22no—
77#3752—22no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)D411yescharacteristic
81#3750—22no—
82#3750D412yes—
83C4×C3⋊Dic3—22no—
84C4×C3⋊Dic3C2312yes—
85C2×C3⋊(C3⋊C8)C2312yes—
86#3744—24no—
87#3744—42no—
88#3394—91noSylow
89C2×C3×SD16C2×D314yes—
90C3×C4×Q8C2×D314yes—
91C3×C4×D4C2×D314yes—
92#947—38no—
93C2×#216—38no—
94#936—38no—
95C2×#213—38no—
96#926—64no—
97#924—64no—
98C2×#204—38no—
99C2×#204—38no—
100#894—68no—
101#893—38no—
102#887—38no—
103#879—68no—
104#875—64no—
105#874—34no—
106C4×D12—64no—
107#869—34no—
108C4×Dic6—34no—
109C3×#106C2×D314yes—
110C3×#103C2×D314yes—
111C3×#102C2×D314yes—
112C3×C4×C8C2×D314yes—
113Dic3⋊C8—38no—
114C8×Dic3—38no—
115#810—38no—
116#809—38no—
117C4⋊(C3⋊C8)—34no—
118C23×C32—21no—
119C22×C3⋊D3—22no—
120C32×Q8—21no—
121C32×Q8—21no—
122C32×D4—21no—
123C32×D4—21no—
124C2×C32×C4—21no—
125C2×C32×C4—21no—
126C2×C32×C4—21no—
127C2×C32×C4—42no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2411yescharacteristic
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3C2×D412yes—
133C2×C3⋊Dic3C2×D412yes—
134C4⋊(C3⋊D3)—22no—
135C4⋊(C3⋊D3)—22no—
136C4⋊(C3⋊D3)—42no—
137C4⋊(C3⋊D3)—81no—
138C4×C3⋊D3—82no—
139#634—22no—
140#634—22no—
141#634—22no—
142C32×C8—21no—
143C32×C8#4112yes—
144C3⋊(C3⋊C8)—22no—
145#559—91no—
146#556—91no—
147#495—92no—
148#492—91no—
149#464—92no—
150#463—92no—
151#462—91no—
152#459—91no—
153C8×Q8—91no—
154C4×SD16—92no—
155C4×SD16C3⋊D311yescharacteristic, complemented
156C2×C3×Q8C22×D314yes—
157C2×C3×D4C22×D314yes—
158C22×C3×C4—24no—
159C2×D12—38no—
160C2×D12—64no—
161C2×D12—64no—
162C2×C4×D3—68no—
163C2×Dic6—34no—
164C2×Dic6—38no—
165C3×SD16—28no—
166C2×C3×C8C22×D314yes—
167C2×C3×C8C22×D314yes—
168C3×C4⋊C4—24no—
169C3×C4⋊C4C22×D314yes—
170C3×C4⋊C4C22×D314yes—
171C3×C22⋊C4—24no—
172C3×C42—24no—
173C3×C42C22×D314yes—
174#217—68no—
175#217—68no—
176#216—128no—
177#213—128no—
178(C2×D3)⋊C4—68no—
179(C2×D3)⋊C4—68no—
180(C2×D3)⋊C4—68no—
181C4⋊Dic3—34no—
182C4⋊Dic3—64no—
183C4⋊Dic3—64no—
184Dic3⋊C4—38no—
185Dic3⋊C4—68no—
186C4×Dic3—38no—
187C4×Dic3—68no—
188C2×C3⋊C8—38no—
189#204—616no—
190#204—128no—
191C22×C32—41no—
192C22×C32—41no—
193C22×C32—41no—
194C22×C32C22×D411yescharacteristic
195C2×C3⋊D3—42no—
196C2×C3⋊D3—42no—
197C2×C3⋊D3—42no—
198C32×C4—21no—
199C32×C4—41no—
200C32×C4—41no—
201C32×C4—41no—
202C32×C4#13512yes—
203C32×C4C2×#4111yescharacteristic
204C32×C4H(5,𝔽2)11yescharacteristic
205C3⋊Dic3—22no—
206C3⋊Dic3—22no—
207C3⋊Dic3—42no—
208C2×Q16—92no—
209C2×SD16—92no—
210C2×SD16—92no—
211C2×SD16C2×C3⋊D311yescharacteristic
212C2×D8—92no—
213C4⋊Q8—91no—
214#127—91no—
215#126—182no—
216#124—92no—
217#124—92no—
218#124—181no—
219#123—182no—
220C22⋊Q8—181no—
221C4×Q8—91no—
222C4×Q8—92no—
223C4×Q8C2×C3⋊D311yescharacteristic
224C4×D4—92no—
225C4×D4—181no—
226C4×D4C2×C3⋊D311yescharacteristic
227#117—181no—
228#106C2×C3⋊D311yescharacteristic
229C4⋊C8—92no—
230C4⋊C8—91no—
231#103—92no—
232#103C2×C3⋊D311yescharacteristic
233#102—92no—
234#102C2×C3⋊D311yescharacteristic
235C4×C8—92no—
236C4×C8C2×C3⋊D311yescharacteristic
237C23×C3—24no—
238C22×D3—68no—
239C3×Q8—24no—
240C3×Q8—24no—
241C3×D4—24no—
242C3×D4—24no—
243C2×C3×C4—24no—
244C2×C3×C4—24no—
245C2×C3×C4—24no—
246C2×C3×C4—48no—
247C2×C3×C4D3×D414yes—
248C2×C3×C4D3×D414yes—
249C2×C3×C4C23×D314yes—
250C2×Dic3—38no—
251C2×Dic3—38no—
252C2×Dic3—68no—
253D12—68no—
254D12—68no—
255D12—128no—
256D12—244no—
257C4×D3—248no—
258Dic6—68no—
259Dic6—68no—
260Dic6—68no—
261C3×C8—24no—
262C3×C8#23518yes—
263C3⋊C8—68no—
264C2×C32—81no—
265C2×C32#55011yescharacteristic
266C2×C32C2×#13511yescharacteristic
267C2×C32#57711yescharacteristic
268C3⋊D3—82no—
269C2×Q8—91no—
270C2×Q8—92no—
271C2×Q8C22×C3⋊D311yescharacteristic
272C2×D4—92no—
273C2×D4—181no—
274C2×D4—181no—
275C2×D4C22×C3⋊D311yescharacteristic
276C22×C4—21no—
277C22×C4—182no—
278Q16—362no—
279SD16—22no—
280SD16—184no—
281SD16—362no—
282D8—362no—
283C2×C8—92no—
284C2×C8C22×C3⋊D311yescharacteristic
285C2×C8C22×C3⋊D311yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—91no—
288C4⋊C4—92no—
289C4⋊C4—182no—
290C4⋊C4—181no—
291C4⋊C4—181no—
292C4⋊C4C22×C3⋊D311yescharacteristic
293C4⋊C4C22×C3⋊D311yescharacteristic
294C22⋊C4—21no—
295C22⋊C4—182no—
296C22⋊C4—182no—
297C22⋊C4—182no—
298C22⋊C4—182no—
299C22⋊C4—182no—
300C42—21no—
301C42—92no—
302C42—182no—
303C42C22×C3⋊D311yescharacteristic
304C22×C3—44no—
305C22×C3—44no—
306C22×C3—44no—
307C22×C3C2×D3×D414yes—
308C2×D3—128no—
309C2×D3—128no—
310C2×D3—128no—
311C3×C4—24no—
312C3×C4—44no—
313C3×C4—44no—
314C3×C4—44no—
315C3×C4#91618yes—
316C3×C4C2×#23514yes—
317C3×C4#100914yes—
318Dic3—68no—
319Dic3—68no—
320Dic3—128no—
321C32#339411yescharacteristic, complemented, Sylow
322C23—21no—
323C23—182no—
324Q8—21no—
325Q8—21no—
326Q8—182no—
327Q8—182no—
328Q8—182no—
329D4—21no—
330D4—21no—
331D4—182no—
332D4—182no—
333D4—362no—
334D4—721no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—92no—
340C2×C4—92no—
341C2×C4—182no—
342C2×C4—722no—
343C2×C4D4×C3⋊D311yescharacteristic
344C2×C4D4×C3⋊D311yescharacteristic
345C2×C4C23×C3⋊D311yescharacteristic
346C8—21no—
347C8—182no—
348C8#382812yes—
349C2×C3—84no—
350C2×C3#555314yes—
351C2×C3C2×#91614yes—
352C2×C3#577014yes—
353D3—248no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—362no—
358C22—362no—
359C22—362no—
360C22C2×D4×C3⋊D311yescharacteristic
361C4—21no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—182no—
366C4—182no—
367C4—362no—
368C4#6412512yes—
369C4C2×#382811yescharacteristic
370C4#6436611yescharacteristic
371C3#7963814yescomplemented
372C2—81no—
373C2—722no—
374C2#1059602411yescharacteristic
375C2C2×#6412511yescharacteristic
376C2#1059624111yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radical#10592714C2
hypercenterC4×SD16C3⋊D3
hypocenterC32#3394
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #10596056C2semidirect
2. #10596013C2semidirect
3. C32×C4×SD16C2semidirect
4. #10592867C2semidirect
5. #10592730C2semidirect
7. #10592551C2semidirect
8. #10592497C2semidirect
9. #10592486C2semidirect
10. #10592392C2semidirect
11. C8×#634C2semidirect
44. C3×C4×SD16D3semidirect
155. C4×SD16C3⋊D3semidirect
321. C32#3394semidirect
371. C3#79638semidirect

Maximal subgroups

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

subgroupindex
#105960562
#105960132
C32×C4×SD162
#105928672
#105927302
#105927142
#105925512
#105924972
#105924862
#105923922
C8×#6342
#796383