Finite Group Databasebeta

← #11888023

Subgroups — #11888023

Order 1152.

1158 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#10596055C211yesmaximal, characteristic, complemented
2#10596026C211yesmaximal, characteristic
3C32×C4×SD16C211yesmaximal, characteristic, complemented
4#10592872C212yesmaximal, complemented
5#10592730C211yesmaximal, characteristic, complemented
6#10592706C211yesmaximal, characteristic, complemented
7#10592567C212yesmaximal, complemented
8#10592512C212yesmaximal, complemented
9#10592471C212yesmaximal, complemented
10C8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
11#10592380C211yesmaximal, characteristic, complemented
12#79680—34nomaximal
13C2×#3830C2212yes—
14C2×C32×SD16C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17#64155C2212yes—
18C2×#3756C2212yes—
19#64139—21no—
20C2×C4⋊(C3⋊Dic3)—21no—
21C2×C8×C3⋊D3C2212yes—
22#64107—22no—
23#64106C2212yes—
24#64101C2212yes—
25#64095—22no—
26#64084—21no—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28#64078C2211yescharacteristic
29#64078C2211yescharacteristic
30C4×#634—21no—
31C32×#106C2211yescharacteristic
32C32×#103C2211yescharacteristic
33C32×#102C2211yescharacteristic
34C32×C4×C8C2211yescharacteristic
35#63659C2212yes—
36#63647C2212yes—
37#63643C2212yes—
38#63643C2212yes—
39#63637C2212yes—
40#63634C2212yes—
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
42#5584—34no—
43#5555—34no—
44C3×C4×SD16D314yescomplemented
45#5173—38no—
46#5031—34no—
47#5007—34no—
48#4868—38no—
49#4813—38no—
50#4772—38no—
51C8×D12—34no—
52#4681—34no—
53C2×C32×Q8C2311yescharacteristic
54C2×C32×D4C2311yescharacteristic
55C22×C32×C4—21no—
56C2×#638—22no—
57C22×C3⋊Dic3—22no—
58#3830—24no—
59#3830—42no—
60C2×C4⋊(C3⋊D3)D411yescharacteristic
61C2×C4×C3⋊D3C2312yes—
62C2×#634—21no—
63C2×#634C2312yes—
64C32×SD16—22no—
65C2×C32×C8C2311yescharacteristic
66C2×C32×C8C2311yescharacteristic
67C32×C4⋊C4—21no—
68C32×C4⋊C4C2311yescharacteristic
69C32×C4⋊C4C2311yescharacteristic
70C32×C22⋊C4—21no—
71C32×C42—21no—
72C32×C42C2311yescharacteristic
73#3756—42no—
74#3752—22no—
75#3752—22no—
76#3752—22no—
77#3752D412yes—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)—22no—
82C4⋊(C3⋊Dic3)D411yescharacteristic
83C4⋊(C3⋊Dic3)C2312yes—
84#3750—22no—
85C4×C3⋊Dic3—22no—
86C2×C3⋊(C3⋊C8)C2312yes—
87C8×C3⋊D3—42no—
88#3302—91noSylow
89C2×#237—38no—
90C2×C3×SD16C2×D314yes—
91C3×C4×Q8C2×D314yes—
92C3×C4×D4C2×D314yes—
93#946—38no—
94C2×#216—38no—
95#930—64no—
96C2×C4⋊Dic3—64no—
97C2×D3×C8—38no—
98#898—68no—
99#897—38no—
100#892—38no—
101#886—68no—
102#875—64no—
103C4×D12—34no—
104#869—34no—
105#869—34no—
106C4×Dic6—64no—
107C3×#106C2×D314yes—
108C3×#103C2×D314yes—
109C3×#102C2×D314yes—
110C3×C4×C8C2×D314yes—
111#832—38no—
112(C2×D3)⋊C8—38no—
113#816—38no—
114#816—38no—
115#810—38no—
116#807—38no—
117C4⋊(C3⋊C8)—34no—
118C23×C32—21no—
119C22×C3⋊D3C2×D412yes—
120C32×Q8—21no—
121C32×Q8—21no—
122C32×D4—21no—
123C32×D4#4112yes—
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
131#638—44no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—44no—
135C2×C3⋊Dic3C2×D412yes—
136C4⋊(C3⋊D3)—22no—
137C4×C3⋊D3—22no—
138C4×C3⋊D3—22no—
139#634—22no—
140#634—22no—
141#634—42no—
142C32×C8—21no—
143C32×C8—21no—
144C3⋊(C3⋊C8)—22no—
145#556—91no—
146#547—91no—
147#487—91no—
148#485—92no—
149#474—91no—
150#467—92no—
151#462—91no—
152#452—92no—
153C4×SD16C3⋊D311yescharacteristic, complemented
154C8×D4—91no—
155#416—92no—
156C2×C3×Q8C22×D314yes—
157C2×C3×D4C22×D314yes—
158C22×C3×C4—24no—
159C2×#67—68no—
160C22×Dic3—68no—
161#237—616no—
162#237—128no—
163C2×D12—34no—
164C2×C4×D3—38no—
165C2×Dic6—38no—
166C2×Dic6—64no—
167C3×SD16—28no—
168C2×C3×C8C22×D314yes—
169C2×C3×C8C22×D314yes—
170C3×C4⋊C4—24no—
171C3×C4⋊C4C22×D314yes—
172C3×C4⋊C4C22×D314yes—
173C3×C22⋊C4—24no—
174C3×C42—24no—
175C3×C42C22×D314yes—
176#216—128no—
177(C2×D3)⋊C4—38no—
178(C2×D3)⋊C4—68no—
179(C2×D3)⋊C4—68no—
180(C2×D3)⋊C4—68no—
181C4⋊Dic3—34no—
182C4⋊Dic3—38no—
183C4⋊Dic3—68no—
184C4⋊Dic3—64no—
185C4⋊Dic3—64no—
186C4⋊Dic3—64no—
187Dic3⋊C4—68no—
188C4×Dic3—68no—
189C2×C3⋊C8—38no—
190D3×C8—128no—
191C22×C32—22no—
192C22×C32—41no—
193C22×C32—41no—
194C22×C32C22×D411yescharacteristic
195C2×C3⋊D3—22no—
196C2×C3⋊D3—22no—
197C2×C3⋊D3—22no—
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—42no—
207C3⋊Dic3—42no—
208C2×#41—92no—
209C2×Q16—92no—
210C2×SD16C2×C3⋊D311yescharacteristic
211C22×C8—92no—
212C4⋊Q8—91no—
213C4⋊Q8—91no—
214#126—182no—
215#124—181no—
216#123—182no—
217C22⋊Q8—92no—
218C22⋊Q8—92no—
219#121—181no—
220C4×Q8—181no—
221C4×Q8C2×C3⋊D311yescharacteristic
222C4×D4—91no—
223C4×D4C2×C3⋊D311yescharacteristic
224#117—92no—
225C2×C4⋊C4—181no—
226#107—92no—
227#106C2×C3⋊D311yescharacteristic
228C4⋊C8—91no—
229#103—92no—
230#103—92no—
231#103—92no—
232#103C2×C3⋊D311yescharacteristic
233#102—92no—
234#102C2×C3⋊D311yescharacteristic
235C22⋊C8—92no—
236C4×C8C2×C3⋊D311yescharacteristic
237C23×C3—24no—
238C22×D3—38no—
239C3×Q8—24no—
240C3×Q8—24no—
241C3×D4—24no—
242C3×D4#23518yes—
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—
250#67—1216no—
251C2×Dic3—38no—
252C2×Dic3—68no—
253C2×Dic3—68no—
254C2×Dic3—1216no—
255D12—68no—
256C4×D3—68no—
257C4×D3—68no—
258Dic6—68no—
259Dic6—68no—
260Dic6—128no—
261C3×C8—24no—
262C3×C8—24no—
263C3⋊C8—68no—
264C2×C32—42no—
265C2×C32#54611yescharacteristic
266C2×C32C2×#13511yescharacteristic
267C2×C32#57811yescharacteristic
268C3⋊D3—42no—
269#41—184no—
270#41—362no—
271C2×Q8—92no—
272C2×Q8—181no—
273C2×Q8C22×C3⋊D311yescharacteristic
274C2×D4—91no—
275C2×D4—182no—
276C2×D4C22×C3⋊D311yescharacteristic
277C22×C4—21no—
278C22×C4—92no—
279C22×C4—182no—
280Q16—362no—
281SD16—22no—
282C2×C8—92no—
283C2×C8—362no—
284C2×C8C22×C3⋊D311yescharacteristic
285C2×C8C22×C3⋊D311yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—91no—
288C4⋊C4—92no—
289C4⋊C4—182no—
290C4⋊C4—182no—
291C4⋊C4—181no—
292C4⋊C4—181no—
293C4⋊C4—181no—
294C4⋊C4C22×C3⋊D311yescharacteristic
295C4⋊C4C22×C3⋊D311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—92no—
298C22⋊C4—182no—
299C22⋊C4—182no—
300C22⋊C4—182no—
301C42—21no—
302C42—182no—
303C42C22×C3⋊D311yescharacteristic
304C22×C3—28no—
305C22×C3—44no—
306C22×C3—44no—
307C22×C3C2×D3×D414yes—
308C2×D3—68no—
309C2×D3—68no—
310C2×D3—68no—
311C3×C4—24no—
312C3×C4—44no—
313C3×C4—44no—
314C3×C4—44no—
315C3×C4#91618yes—
316C3×C4C2×#23514yes—
317C3×C4#100914yes—
318Dic3—68no—
319Dic3—128no—
320Dic3—128no—
321C32#330211yescharacteristic, complemented, Sylow
322C23—21no—
323C23—92no—
324Q8—21no—
325Q8—21no—
326Q8—182no—
327Q8—182no—
328Q8—362no—
329D4—21no—
330D4—182no—
331D4—364no—
332D4#382812yes—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—92no—
338C2×C4—182no—
339C2×C4—182no—
340C2×C4—182no—
341C2×C4—182no—
342C2×C4—364no—
343C2×C4D4×C3⋊D311yescharacteristic
344C2×C4D4×C3⋊D311yescharacteristic
345C2×C4C23×C3⋊D311yescharacteristic
346C8—21no—
347C8—21no—
348C8—182no—
349C2×C3—48no—
350C2×C3#555014yes—
351C2×C3C2×#91614yes—
352C2×C3#577114yes—
353D3—128no—
354C22—22no—
355C22—41no—
356C22—41no—
357C22—182no—
358C22—182no—
359C22—182no—
360C22C2×D4×C3⋊D311yescharacteristic
361C4—21no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—182no—
366C4—362no—
367C4—362no—
368C4#6412512yes—
369C4C2×#382811yescharacteristic
370C4#6436611yescharacteristic
371C3#7968014yescomplemented
372C2—42no—
373C2—362no—
374C2#1059602111yescharacteristic
375C2C2×#6412511yescharacteristic
376C2#1059624211yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radical#10596026C2
hypercenterC4×SD16C3⋊D3
hypocenterC32#3302
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. #10596055C2semidirect
3. C32×C4×SD16C2semidirect
4. #10592872C2semidirect
5. #10592730C2semidirect
6. #10592706C2semidirect
7. #10592567C2semidirect
8. #10592512C2semidirect
9. #10592471C2semidirect
10. C8×C4⋊(C3⋊D3)C2semidirect
11. #10592380C2semidirect
44. C3×C4×SD16D3semidirect
153. C4×SD16C3⋊D3semidirect
321. C32#3302semidirect
371. C3#79680semidirect

Maximal subgroups

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

subgroupindex
#105960552
#105960262
C32×C4×SD162
#105928722
#105927302
#105927062
#105925672
#105925122
#105924712
C8×C4⋊(C3⋊D3)2
#105923802
#796803