Finite Group Databasebeta

← #11898414

Subgroups — #11898414

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#10596203C211yesmaximal, characteristic, complemented
2#10596056C211yesmaximal, characteristic, complemented
3C32×#462C211yesmaximal, characteristic, complemented
4#10592890C212yesmaximal, complemented
5#10592884C212yesmaximal, complemented
6#10592784C211yesmaximal, characteristic, complemented
7C4×#3755C211yesmaximal, characteristic, complemented
8#10592542C211yesmaximal, characteristic
9#10592529C211yesmaximal, characteristic, complemented
10#10592518C212yesmaximal, complemented
11#10592487C212yesmaximal, complemented
12#80472—34nomaximal
13C2×C32×Q16C2212yes—
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16#64156C2212yes—
17#64156C2212yes—
18Q8×C3⋊Dic3C2212yes—
19C2×#3755C2212yes—
20C2×#3755C2211yescharacteristic
21C2×#3755C2212yes—
22C2×#3745C2212yes—
23#64107—22no—
24#64106—21no—
25#64103—22no—
26#64102C2212yes—
27#64101—21no—
28#64084—21no—
29#64083C2211yescharacteristic
30C4×C4⋊(C3⋊D3)—21no—
31C4×C4⋊(C3⋊D3)C2211yescharacteristic
32C4×#634C2211yescharacteristic
33C32×C4⋊C8C2211yescharacteristic
34C32×#103C2212yes—
35#63662C2211yescharacteristic
36#63648C2212yes—
37#63641C2212yes—
38C8×C3⋊Dic3C2212yes—
39#63636C2211yescharacteristic
40#63635C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42#5732—34no—
43#5585—34no—
44C3×#462D314yescomplemented
45#5191—38no—
46#5185—38no—
47#5085—34no—
48C4×#215—34no—
49#4843—34no—
50#4830—34no—
51#4819—38no—
52#4788—38no—
53C2×C32×Q8C2312yes—
54C2×C32×Q8C2311yescharacteristic
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)C2311yescharacteristic
58C2×C4⋊(C3⋊D3)C2312yes—
59C2×C4×C3⋊D3—21no—
60C2×C4×C3⋊D3—22no—
61C2×#634D411yescharacteristic
62C32×Q16—42no—
63C2×C32×C8C2312yes—
64C32×C4⋊C4—21no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4—21no—
67C32×C4⋊C4C2311yescharacteristic
68C32×C42—21no—
69C32×C42C2311yescharacteristic
70#3755—24no—
71#3755—22no—
72#3755—42no—
73#3752—21no—
74#3752—22no—
75#3752—22no—
76#3752—22no—
77#3752—22no—
78#3752—22no—
79C4⋊(C3⋊Dic3)—22no—
80C4⋊(C3⋊Dic3)D411yescharacteristic
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82#3750D412yes—
83C4×C3⋊Dic3—22no—
84C4×C3⋊Dic3C2312yes—
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87#3745—42no—
88#3394—91noSylow
89C2×C3×Q16C2×D318yes—
90C3×C4⋊Q8C2×D314yes—
91C3×C4×Q8C2×D314yes—
92#947—38no—
93#947—38no—
94Q8×Dic3—38no—
95C2×#215—34no—
96C2×#215—38no—
97C2×#215—38no—
98C2×D24—38no—
99#898—68no—
100#897—64no—
101#894—68no—
102#893—38no—
103#892—64no—
104#875—64no—
105#874—34no—
106C4×D12—34no—
107C4×D12—64no—
108C4×Dic6—34no—
109C3×C4⋊C8C2×D314yes—
110C3×#103C2×D318yes—
111#835—34no—
112#821—38no—
113Dic3⋊C8—38no—
114C8×Dic3—38no—
115#809—34no—
116#808—34no—
117C4×C3⋊C8—34no—
118C22×C3⋊D3—21no—
119C22×C3⋊D3—22no—
120C32×Q8—22no—
121C32×Q8—21no—
122C32×Q8—22no—
123C32×Q8—21no—
124C2×C32×C4—22no—
125C2×C32×C4—21no—
126C2×C32×C4—21no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2411yescharacteristic
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3C2×D412yes—
132C2×C3⋊Dic3C2×D412yes—
133C4⋊(C3⋊D3)—21no—
134C4⋊(C3⋊D3)—22no—
135C4⋊(C3⋊D3)—21no—
136C4⋊(C3⋊D3)—22no—
137C4⋊(C3⋊D3)—42no—
138C4⋊(C3⋊D3)—81no—
139C4×C3⋊D3—42no—
140C4×C3⋊D3—82no—
141#634—22no—
142C32×C8—22no—
143C3⋊(C3⋊C8)—21no—
144C3⋊(C3⋊C8)#4112yes—
145#559—91no—
146#556—91no—
147#495—92no—
148#492—91no—
149#464—92no—
150#463—92no—
151#462C3⋊D311yescharacteristic, complemented
152#459—91no—
153C8×Q8—91no—
154C4×SD16—91no—
155C4×SD16—92no—
156C2×C3×Q8C22×D314yes—
157C2×C3×Q8C22×D318yes—
158C2×D12—34no—
159C2×D12—38no—
160C2×D12—64no—
161C2×D12—64no—
162C2×C4×D3—64no—
163C2×C4×D3—68no—
164C2×Dic6—34no—
165C3×Q16—48no—
166C2×C3×C8C22×D318yes—
167C3×C4⋊C4—24no—
168C3×C4⋊C4—24no—
169C3×C4⋊C4—24no—
170C3×C4⋊C4C22×D314yes—
171C3×C42—24no—
172C3×C42C22×D314yes—
173#215—68no—
174#215—616no—
175#215—128no—
176(C2×D3)⋊C4—68no—
177(C2×D3)⋊C4—68no—
178(C2×D3)⋊C4—68no—
179(C2×D3)⋊C4—68no—
180(C2×D3)⋊C4—68no—
181(C2×D3)⋊C4—64no—
182C4⋊Dic3—34no—
183C4⋊Dic3—34no—
184C4⋊Dic3—68no—
185Dic3⋊C4—38no—
186C4×Dic3—38no—
187C4×Dic3—68no—
188C2×C3⋊C8—34no—
189C2×C3⋊C8—34no—
190D24—128no—
191C22×C32C22×D411yescharacteristic
192C2×C3⋊D3—41no—
193C2×C3⋊D3—42no—
194C2×C3⋊D3—41no—
195C2×C3⋊D3—42no—
196C2×C3⋊D3—42no—
197C2×C3⋊D3—41no—
198C32×C4—21no—
199C32×C4—42no—
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—41no—
208C2×Q16C2×C3⋊D312yes—
209C2×SD16—92no—
210C2×SD16—91no—
211C2×SD16—92no—
212C2×D8—92no—
213C4⋊Q8C2×C3⋊D311yescharacteristic
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—91no—
226C4×D4—181no—
227#117—181no—
228#106—91no—
229C4⋊C8—92no—
230C4⋊C8C2×C3⋊D311yescharacteristic
231#103—91no—
232#103C2×C3⋊D312yes—
233#102—92no—
234#102—91no—
235C4×C8—92no—
236C4×C8—91no—
237C22×D3—64no—
238C22×D3—68no—
239C3×Q8—28no—
240C3×Q8—24no—
241C3×Q8—24no—
242C3×Q8—28no—
243C2×C3×C4—28no—
244C2×C3×C4—24no—
245C2×C3×C4—24no—
246C2×C3×C4D3×D414yes—
247C2×C3×C4D3×D414yes—
248C2×C3×C4C23×D314yes—
249C2×Dic3—38no—
250C2×Dic3—38no—
251C2×Dic3—64no—
252D12—64no—
253D12—68no—
254D12—64no—
255D12—68no—
256D12—128no—
257D12—244no—
258C4×D3—128no—
259C4×D3—248no—
260Dic6—68no—
261C3×C8—28no—
262C3⋊C8—38no—
263C3⋊C8—64no—
264C2×C32#55011yescharacteristic
265C2×C32C2×#13511yescharacteristic
266C2×C32#57711yescharacteristic
267C3⋊D3—81no—
268C3⋊D3—82no—
269C2×Q8—91no—
270C2×Q8C22×C3⋊D311yescharacteristic
271C2×Q8C22×C3⋊D312yes—
272C2×D4—91no—
273C2×D4—92no—
274C2×D4—181no—
275C2×D4—181no—
276C22×C4—182no—
277C22×C4—181no—
278Q16—42no—
279SD16—184no—
280SD16—182no—
281SD16—362no—
282D8—362no—
283C2×C8—91no—
284C2×C8—91no—
285C2×C8C22×C3⋊D312yes—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—91no—
290C4⋊C4—92no—
291C4⋊C4—91no—
292C4⋊C4—182no—
293C4⋊C4C22×C3⋊D311yescharacteristic
294C22⋊C4—182no—
295C22⋊C4—182no—
296C22⋊C4—182no—
297C22⋊C4—182no—
298C22⋊C4—182no—
299C22⋊C4—181no—
300C42—21no—
301C42—92no—
302C42—182no—
303C42C22×C3⋊D311yescharacteristic
304C22×C3C2×D3×D414yes—
305C2×D3—124no—
306C2×D3—128no—
307C2×D3—128no—
308C2×D3—124no—
309C2×D3—124no—
310C2×D3—128no—
311C3×C4—24no—
312C3×C4—44no—
313C3×C4—48no—
314C3×C4—44no—
315C3×C4#91918yes—
316C3×C4#100414yes—
317C3×C4D3×#4114yes—
318Dic3—68no—
319Dic3—68no—
320Dic3—124no—
321C32#339411yescharacteristic, complemented, Sylow
322C23—181no—
323C23—182no—
324Q8—22no—
325Q8—21no—
326Q8—21no—
327Q8—22no—
328Q8—182no—
329D4—181no—
330D4—182no—
331D4—181no—
332D4—182no—
333D4—362no—
334D4—721no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—92no—
339C2×C4—92no—
340C2×C4—181no—
341C2×C4—362no—
342C2×C4—722no—
343C2×C4D4×C3⋊D311yescharacteristic
344C2×C4D4×C3⋊D311yescharacteristic
345C2×C4C23×C3⋊D311yescharacteristic
346C8—22no—
347C8—92no—
348C8—181no—
349C2×C3#559914yes—
350C2×C3C2×#91914yes—
351C2×C3#577814yes—
352D3—244no—
353D3—248no—
354C22—361no—
355C22—362no—
356C22—362no—
357C22—361no—
358C22—361no—
359C22—362no—
360C22C2×D4×C3⋊D311yescharacteristic
361C4—21no—
362C4—41no—
363C4—41no—
364C4—42no—
365C4—182no—
366C4—182no—
367C4—361no—
368C4#6412812yes—
369C4#6436111yescharacteristic
370C4#41×C3⋊D311yescharacteristic
371C3#8047214yescomplemented
372C2—721no—
373C2—722no—
374C2#1059607011yescharacteristic
375C2C2×#6412811yescharacteristic
376C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#462C2
socleC22×C32C22×D4
prime radical#10592542C2
hypercenter#462C3⋊D3
hypocenterC32#3394
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. #10596203C2semidirect
2. #10596056C2semidirect
3. C32×#462C2semidirect
4. #10592890C2semidirect
5. #10592884C2semidirect
6. #10592784C2semidirect
7. C4×#3755C2semidirect
9. #10592529C2semidirect
10. #10592518C2semidirect
11. #10592487C2semidirect
44. C3×#462D3semidirect
151. #462C3⋊D3semidirect
321. C32#3394semidirect
371. C3#80472semidirect

Maximal subgroups

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

subgroupindex
#105962032
#105960562
C32×#4622
#105928902
#105928842
#105927842
C4×#37552
#105925422
#105925292
#105925182
#105924872
#804723