Finite Group Databasebeta

← #11888008

Subgroups — #11888008

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#10596203C211yesmaximal, characteristic, complemented
2#10596026C211yesmaximal, characteristic
3C32×#474C211yesmaximal, characteristic, complemented
4#10592792C211yesmaximal, characteristic, complemented
5C4×#3754C211yesmaximal, characteristic, complemented
6#10592587C212yesmaximal, complemented
7#10592586C212yesmaximal, complemented
8#10592548C211yesmaximal, characteristic, complemented
9#10592533C211yesmaximal, characteristic, complemented
10#10592482C212yesmaximal, complemented
11#10592471C212yesmaximal, complemented
12#80981—34nomaximal
13C2×#3830C2212yes—
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4×D4C2211yescharacteristic
16#64156—21no—
17Q8×C3⋊Dic3—21no—
18C2×#3754C2211yescharacteristic
19#64139—21no—
20C2×C4⋊(C3⋊Dic3)—21no—
21C2×#3746C2212yes—
22C2×C8×C3⋊D3C2212yes—
23#64107—22no—
24#64106C2212yes—
25#64106C2212yes—
26#64101C2212yes—
27#64095—22no—
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29#64078C2211yescharacteristic
30C4×#634C2211yescharacteristic
31C32×#107C2212yes—
32C32×C4⋊C8C2211yescharacteristic
33C32×#102C2212yes—
34#63659C2211yescharacteristic
35#63647C2212yes—
36#63643C2212yes—
37#63637C2212yes—
38#63637C2212yes—
39#63637C2211yescharacteristic
40#63635C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42#5732—34no—
43#5555—34no—
44C3×#474D314yescomplemented
45#5093—34no—
46C4×#214—34no—
47#4888—38no—
48#4887—38no—
49#4849—34no—
50#4834—34no—
51#4783—38no—
52#4772—38no—
53C2×C32×Q8—21no—
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×#634C2311yescharacteristic
63C2×#634C2312yes—
64C2×C32×C8C2312yes—
65C32×C4⋊C4—21no—
66C32×C4⋊C4C2312yes—
67C32×C4⋊C4C2311yescharacteristic
68C32×C22⋊C4—21no—
69C32×C42C2311yescharacteristic
70#3754—22no—
71#3752—22no—
72#3752—22no—
73#3752—22no—
74#3752D412yes—
75C4⋊(C3⋊Dic3)—21no—
76C4⋊(C3⋊Dic3)—21no—
77C4⋊(C3⋊Dic3)—22no—
78C4⋊(C3⋊Dic3)—22no—
79C4⋊(C3⋊Dic3)D411yescharacteristic
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3750—21no—
82C4×C3⋊Dic3—21no—
83C4×C3⋊Dic3—22no—
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86#3746—42no—
87C8×C3⋊D3—42no—
88#3302—91noSylow
89C2×#237—38no—
90C3×C4⋊Q8C2×D314yes—
91C3×C4×D4C2×D314yes—
92#947—64no—
93Q8×Dic3—64no—
94C2×#214—34no—
95#930—64no—
96C2×C4⋊Dic3—64no—
97C2×Dic12—38no—
98C2×D3×C8—38no—
99#898—68no—
100#897—38no—
101#897—38no—
102#892—38no—
103#886—68no—
104C4×D12—34no—
105#869—34no—
106C4×Dic6—34no—
107C3×#107C2×D318yes—
108C3×C4⋊C8C2×D314yes—
109C3×#102C2×D318yes—
110#832—34no—
111(C2×D3)⋊C8—38no—
112#816—38no—
113#810—34no—
114#810—38no—
115#810—38no—
116#808—34no—
117C4×C3⋊C8—34no—
118C23×C32—21no—
119C22×C3⋊D3C2×D412yes—
120C32×Q8—42no—
121C32×D4—21no—
122C32×D4#4112yes—
123C2×C32×C4—22no—
124C2×C32×C4—21no—
125C2×C32×C4—42no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2411yescharacteristic
129#638—44no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—44no—
134C2×C3⋊Dic3C2×D412yes—
135C4⋊(C3⋊D3)—22no—
136C4×C3⋊D3—22no—
137C4×C3⋊D3—22no—
138#634—21no—
139#634—22no—
140#634—21no—
141#634—22no—
142C32×C8—22no—
143C3⋊(C3⋊C8)—21no—
144C3⋊(C3⋊C8)—21no—
145#556—91no—
146#547—91no—
147#487—91no—
148#485—92no—
149#474C3⋊D311yescharacteristic, complemented
150#467—92no—
151#462—91no—
152#452—92no—
153C4×SD16—91no—
154C8×D4—91no—
155#416—92no—
156C2×C3×Q8—24no—
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—34no—
167C2×C3×C8C22×D318yes—
168C3×C4⋊C4—24no—
169C3×C4⋊C4C22×D314yes—
170C3×C4⋊C4C22×D318yes—
171C3×C22⋊C4—24no—
172C3×C42C22×D314yes—
173#214—68no—
174(C2×D3)⋊C4—38no—
175(C2×D3)⋊C4—68no—
176(C2×D3)⋊C4—68no—
177(C2×D3)⋊C4—68no—
178C4⋊Dic3—34no—
179C4⋊Dic3—34no—
180C4⋊Dic3—68no—
181C4⋊Dic3—68no—
182C4⋊Dic3—64no—
183C4⋊Dic3—64no—
184Dic3⋊C4—64no—
185C4×Dic3—68no—
186C4×Dic3—64no—
187C2×C3⋊C8—34no—
188C2×C3⋊C8—34no—
189Dic12—128no—
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—42no—
201C32×C4#13512yes—
202C32×C4C2×#4111yescharacteristic
203C32×C4H(5,𝔽2)11yescharacteristic
204C3⋊Dic3—22no—
205C3⋊Dic3—41no—
206C3⋊Dic3—42no—
207C3⋊Dic3—41no—
208C2×#41—92no—
209C2×Q16—92no—
210C2×SD16—91no—
211C22×C8—92no—
212C4⋊Q8—91no—
213C4⋊Q8C2×C3⋊D311yescharacteristic
214#126—182no—
215#124—181no—
216#123—182no—
217C22⋊Q8—92no—
218C22⋊Q8—92no—
219#121—181no—
220C4×Q8—91no—
221C4×Q8—181no—
222C4×D4—91no—
223C4×D4C2×C3⋊D311yescharacteristic
224#117—92no—
225C2×C4⋊C4—181no—
226#107C2×C3⋊D312yes—
227#106—91no—
228C4⋊C8C2×C3⋊D311yescharacteristic
229#103—92no—
230#103—92no—
231#103—91no—
232#103—92no—
233#102—91no—
234#102C2×C3⋊D312yes—
235C22⋊C8—92no—
236C4×C8—91no—
237C23×C3—24no—
238C22×D3—38no—
239C3×Q8—48no—
240C3×D4—24no—
241C3×D4#23918yes—
242C2×C3×C4—28no—
243C2×C3×C4—24no—
244C2×C3×C4—48no—
245C2×C3×C4D3×D414yes—
246C2×C3×C4D3×D414yes—
247C2×C3×C4C23×D314yes—
248#67—1216no—
249C2×Dic3—38no—
250C2×Dic3—64no—
251C2×Dic3—64no—
252C2×Dic3—68no—
253C2×Dic3—1216no—
254D12—68no—
255C4×D3—68no—
256C4×D3—68no—
257Dic6—64no—
258Dic6—68no—
259Dic6—64no—
260Dic6—68no—
261C3×C8—28no—
262C3⋊C8—64no—
263C3⋊C8—64no—
264C2×C32—42no—
265C2×C32#54611yescharacteristic
266C2×C32C2×#13511yescharacteristic
267C2×C32#57811yescharacteristic
268C3⋊D3—42no—
269#41—184no—
270#41—362no—
271C2×Q8—21no—
272C2×Q8—92no—
273C2×Q8—91no—
274C2×D4—91no—
275C2×D4—182no—
276C2×D4C22×C3⋊D311yescharacteristic
277C22×C4—21no—
278C22×C4—92no—
279C22×C4—182no—
280Q16—362no—
281SD16—182no—
282C2×C8—91no—
283C2×C8—91no—
284C2×C8—362no—
285C2×C8C22×C3⋊D312yes—
286C4⋊C4—21no—
287C4⋊C4—91no—
288C4⋊C4—91no—
289C4⋊C4—182no—
290C4⋊C4—182no—
291C4⋊C4—181no—
292C4⋊C4—181no—
293C4⋊C4—181no—
294C4⋊C4C22×C3⋊D312yes—
295C4⋊C4C22×C3⋊D311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—92no—
298C22⋊C4—182no—
299C22⋊C4—182no—
300C22⋊C4—182no—
301C42—182no—
302C42—181no—
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—48no—
314C3×C4#91218yes—
315C3×C4C2×#23914yes—
316C3×C4#100914yes—
317Dic3—68no—
318Dic3—124no—
319Dic3—128no—
320Dic3—124no—
321C32#330211yescharacteristic, complemented, Sylow
322C23—21no—
323C23—92no—
324Q8—42no—
325Q8—181no—
326Q8—182no—
327Q8—181no—
328Q8—182no—
329D4—21no—
330D4—182no—
331D4—364no—
332D4#383212yes—
333C2×C4—22no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—92no—
337C2×C4—182no—
338C2×C4—182no—
339C2×C4—181no—
340C2×C4—181no—
341C2×C4—182no—
342C2×C4—364no—
343C2×C4D4×C3⋊D311yescharacteristic
344C2×C4D4×C3⋊D311yescharacteristic
345C2×C4C23×C3⋊D311yescharacteristic
346C8—22no—
347C8—181no—
348C8—181no—
349C2×C3—48no—
350C2×C3#563014yes—
351C2×C3C2×#91214yes—
352C2×C3#577914yes—
353D3—128no—
354C22—22no—
355C22—41no—
356C22—41no—
357C22—182no—
358C22—182no—
359C22—182no—
360C22C2×D4×C3⋊D311yescharacteristic
361C4—21no—
362C4—41no—
363C4—42no—
364C4—182no—
365C4—362no—
366C4—361no—
367C4—361no—
368C4#6412112yes—
369C4C2×#383211yescharacteristic
370C4#6436611yescharacteristic
371C3#8098114yescomplemented
372C2—42no—
373C2—362no—
374C2#1059610111yescharacteristic
375C2C2×#6412111yescharacteristic
376C2#1059625011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#474C2
socleC22×C32C22×D4
prime radical#10596026C2
hypercenter#474C3⋊D3
hypocenterC32#3302
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #10596203C2semidirect
3. C32×#474C2semidirect
4. #10592792C2semidirect
5. C4×#3754C2semidirect
6. #10592587C2semidirect
7. #10592586C2semidirect
8. #10592548C2semidirect
9. #10592533C2semidirect
10. #10592482C2semidirect
11. #10592471C2semidirect
44. C3×#474D3semidirect
149. #474C3⋊D3semidirect
321. C32#3302semidirect
371. C3#80981semidirect

Maximal subgroups

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

subgroupindex
#105962032
#105960262
C32×#4742
#105927922
C4×#37542
#105925872
#105925862
#105925482
#105925332
#105924822
#105924712
#809813