Finite Group Databasebeta

← #11888014

Subgroups — #11888014

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#10596197C211yesmaximal, characteristic
3C32×#487C211yesmaximal, characteristic, complemented
4#10592789C211yesmaximal, characteristic, complemented
5#10592786C211yesmaximal, characteristic, complemented
6#10592514C212yesmaximal, complemented
7#10592512C212yesmaximal, complemented
8#10592507C212yesmaximal, complemented
9#10592503C212yesmaximal, complemented
10C4×#3744C211yesmaximal, characteristic, complemented
11C8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
12#81614—34nomaximal
13C2×#3832C2212yes—
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4⋊Q8C2211yescharacteristic
16#64156—21no—
17#64155C2212yes—
18Q8×C3⋊Dic3—21no—
19C2×#3756C2212yes—
20C2×#3744C2211yescharacteristic
21C2×C8×C3⋊D3C2212yes—
22#64107—22no—
23#64106C2212yes—
24#64104—21no—
25#64103—22no—
26#64101C2212yes—
27C4⋊C4×C3⋊D3—21no—
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C4×C4⋊(C3⋊D3)C2211yescharacteristic
30C4×#634C2211yescharacteristic
31C32×#103C2212yes—
32C32×#103C2212yes—
33C32×C4×C8C2211yescharacteristic
34#63662C2212yes—
35#63648C2211yescharacteristic
36#63647C2212yes—
37#63644C2211yescharacteristic
38#63643C2211yescharacteristic
39#63636C2212yes—
40#63634C2212yes—
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
42#5732—34no—
43#5726—34no—
44C3×#487D314yescomplemented
45#5090—34no—
46#5087—34no—
47#4815—38no—
48#4813—38no—
49#4808—38no—
50#4804—38no—
51C4×#204—34no—
52C8×D12—34no—
53C2×C32×Q8—21no—
54C2×C32×Q8C2312yes—
55#3832—24no—
56#3832—42no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)D411yescharacteristic
59C2×C4⋊(C3⋊D3)C2311yescharacteristic
60C2×C4×C3⋊D3—21no—
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3C2312yes—
63C2×#634C2311yescharacteristic
64C2×C32×C8C2311yescharacteristic
65C2×C32×C8C2311yescharacteristic
66C32×C4⋊C4—21no—
67C32×C4⋊C4—21no—
68C32×C4⋊C4—21no—
69C32×C4⋊C4C2312yes—
70C32×C42C2311yescharacteristic
71#3756—42no—
72#3752—22no—
73#3752—22no—
74#3752—22no—
75#3752—21no—
76#3752D412yes—
77C4⋊(C3⋊Dic3)—22no—
78C4⋊(C3⋊Dic3)D411yescharacteristic
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3750—21no—
82#3750—22no—
83C4×C3⋊Dic3—21no—
84C4×C3⋊Dic3—22no—
85C2×C3⋊(C3⋊C8)C2312yes—
86#3744—22no—
87C8×C3⋊D3—42no—
88#3302—91noSylow
89C2×#239—38no—
90C3×C4⋊Q8C2×D314yes—
91C3×C4⋊Q8C2×D314yes—
92#947—64no—
93#946—38no—
94Q8×Dic3—64no—
95C2×#216—38no—
96C2×#204—34no—
97C2×D3×C8—38no—
98#898—68no—
99#897—38no—
100#895—64no—
101#894—68no—
102#892—38no—
103D3×C4⋊C4—64no—
104C4×D12—34no—
105C4×D12—34no—
106C4×Dic6—34no—
107C3×#103C2×D318yes—
108C3×#103C2×D318yes—
109C3×C4×C8C2×D314yes—
110#835—38no—
111#821—34no—
112(C2×D3)⋊C8—38no—
113#817—34no—
114#816—34no—
115#809—38no—
116#807—38no—
117C4⋊(C3⋊C8)—34no—
118C22×C3⋊D3—21no—
119C22×C3⋊D3C2×D412yes—
120C32×Q8—22no—
121C32×Q8—22no—
122C32×Q8—42no—
123C2×C32×C4—22no—
124C2×C32×C4—22no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2411yescharacteristic
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3C2×D412yes—
132C4⋊(C3⋊D3)—22no—
133C4⋊(C3⋊D3)—21no—
134C4⋊(C3⋊D3)—44no—
135C4⋊(C3⋊D3)#4112yes—
136C4×C3⋊D3—22no—
137C4×C3⋊D3—22no—
138C4×C3⋊D3—44no—
139C4×C3⋊D3—42no—
140#634—21no—
141#634—21no—
142C32×C8—21no—
143C32×C8—21no—
144C3⋊(C3⋊C8)—22no—
145#556—91no—
146#547—91no—
147#487C3⋊D311yescharacteristic, complemented
148#485—92no—
149#474—91no—
150#467—92no—
151#462—91no—
152#452—92no—
153C4×SD16—91no—
154C8×D4—91no—
155#416—92no—
156C2×C3×Q8—24no—
157C2×C3×Q8C22×D318yes—
158#239—616no—
159#239—128no—
160C2×D12—34no—
161C2×D12—34no—
162C2×D12—68no—
163C2×C4×D3—38no—
164C2×C4×D3—68no—
165C2×C4×D3—64no—
166C2×Dic6—34no—
167C2×C3×C8C22×D314yes—
168C2×C3×C8C22×D314yes—
169C3×C4⋊C4—24no—
170C3×C4⋊C4—24no—
171C3×C4⋊C4—24no—
172C3×C4⋊C4C22×D318yes—
173C3×C42C22×D314yes—
174#216—128no—
175(C2×D3)⋊C4—38no—
176(C2×D3)⋊C4—68no—
177(C2×D3)⋊C4—68no—
178(C2×D3)⋊C4—68no—
179(C2×D3)⋊C4—64no—
180C4⋊Dic3—34no—
181C4⋊Dic3—34no—
182C4⋊Dic3—34no—
183C4⋊Dic3—68no—
184Dic3⋊C4—68no—
185Dic3⋊C4—64no—
186C4×Dic3—68no—
187C4×Dic3—64no—
188C2×C3⋊C8—38no—
189#204—68no—
190D3×C8—128no—
191C22×C32C22×D411yescharacteristic
192C2×C3⋊D3—22no—
193C2×C3⋊D3—22no—
194C2×C3⋊D3—22no—
195C2×C3⋊D3—22no—
196C2×C3⋊D3—41no—
197C2×C3⋊D3—41no—
198C32×C4—21no—
199C32×C4—42no—
200C32×C4—42no—
201C32×C4#13512yes—
202C32×C4C2×#4111yescharacteristic
203C32×C4H(5,𝔽2)11yescharacteristic
204C3⋊Dic3—22no—
205C3⋊Dic3—41no—
206C3⋊Dic3—41no—
207C3⋊Dic3—41no—
208C2×#41—92no—
209C2×Q16—92no—
210C2×SD16—91no—
211C22×C8—92no—
212C4⋊Q8C2×C3⋊D311yescharacteristic
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×D4—91no—
224#117—92no—
225C2×C4⋊C4—181no—
226#107—92no—
227#106—91no—
228C4⋊C8—91no—
229#103—92no—
230#103—91no—
231#103C2×C3⋊D312yes—
232#103C2×C3⋊D312yes—
233#102—91no—
234#102—92no—
235C22⋊C8—92no—
236C4×C8C2×C3⋊D311yescharacteristic
237C22×D3—38no—
238C22×D3—64no—
239C3×Q8—28no—
240C3×Q8—28no—
241C3×Q8—48no—
242C2×C3×C4—28no—
243C2×C3×C4—28no—
244C2×C3×C4D3×D414yes—
245C2×C3×C4D3×D414yes—
246C2×C3×C4C23×D314yes—
247C2×Dic3—38no—
248C2×Dic3—64no—
249C2×Dic3—64no—
250C2×Dic3—64no—
251D12—38no—
252D12—68no—
253D12—64no—
254D12—1216no—
255C4×D3—68no—
256C4×D3—68no—
257C4×D3—1216no—
258C4×D3—128no—
259Dic6—64no—
260Dic6—64no—
261C3×C8—24no—
262C3×C8—24no—
263C3⋊C8—68no—
264C2×C32#54611yescharacteristic
265C2×C32C2×#13511yescharacteristic
266C2×C32#57811yescharacteristic
267C3⋊D3—42no—
268C3⋊D3—42no—
269#41—184no—
270#41—362no—
271C2×Q8—21no—
272C2×Q8—91no—
273C2×Q8C22×C3⋊D312yes—
274C2×D4—91no—
275C2×D4—91no—
276C2×D4—182no—
277C22×C4—92no—
278C22×C4—182no—
279C22×C4—181no—
280Q16—362no—
281SD16—182no—
282C2×C8—92no—
283C2×C8—362no—
284C2×C8C22×C3⋊D311yescharacteristic
285C2×C8C22×C3⋊D311yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—91no—
290C4⋊C4—91no—
291C4⋊C4—91no—
292C4⋊C4—182no—
293C4⋊C4—182no—
294C4⋊C4—181no—
295C4⋊C4C22×C3⋊D312yes—
296C22⋊C4—92no—
297C22⋊C4—182no—
298C22⋊C4—182no—
299C22⋊C4—182no—
300C22⋊C4—181no—
301C42—182no—
302C42—181no—
303C42C22×C3⋊D311yescharacteristic
304C22×C3C2×D3×D414yes—
305C2×D3—68no—
306C2×D3—68no—
307C2×D3—68no—
308C2×D3—68no—
309C2×D3—124no—
310C2×D3—124no—
311C3×C4—24no—
312C3×C4—48no—
313C3×C4—48no—
314C3×C4#91618yes—
315C3×C4D3×#4114yes—
316C3×C4#100914yes—
317Dic3—68no—
318Dic3—124no—
319Dic3—124no—
320Dic3—124no—
321C32#330211yescharacteristic, complemented, Sylow
322C23—92no—
323C23—181no—
324Q8—22no—
325Q8—22no—
326Q8—42no—
327Q8—181no—
328Q8—181no—
329D4—92no—
330D4—181no—
331D4—182no—
332D4—364no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—92no—
336C2×C4—182no—
337C2×C4—182no—
338C2×C4—181no—
339C2×C4—181no—
340C2×C4—181no—
341C2×C4—364no—
342C2×C4—362no—
343C2×C4D4×C3⋊D311yescharacteristic
344C2×C4D4×C3⋊D311yescharacteristic
345C2×C4C23×C3⋊D311yescharacteristic
346C8—21no—
347C8—21no—
348C8—182no—
349C2×C3#567614yes—
350C2×C3C2×#91614yes—
351C2×C3#576614yes—
352D3—128no—
353D3—128no—
354C22—182no—
355C22—182no—
356C22—182no—
357C22—182no—
358C22—361no—
359C22—361no—
360C22C2×D4×C3⋊D311yescharacteristic
361C4—21no—
362C4—42no—
363C4—42no—
364C4—182no—
365C4—361no—
366C4—361no—
367C4—361no—
368C4#6412512yes—
369C4#41×C3⋊D311yescharacteristic
370C4#6436611yescharacteristic
371C3#8161414yescomplemented
372C2—362no—
373C2—362no—
374C2#1059614711yescharacteristic
375C2C2×#6412511yescharacteristic
376C2#1059623711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#487C2
socleC22×C32C22×D4
prime radical#10596197C2
hypercenter#487C3⋊D3
hypocenterC32#3302
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #10596203C2semidirect
3. C32×#487C2semidirect
4. #10592789C2semidirect
5. #10592786C2semidirect
6. #10592514C2semidirect
7. #10592512C2semidirect
8. #10592507C2semidirect
9. #10592503C2semidirect
10. C4×#3744C2semidirect
11. C8×C4⋊(C3⋊D3)C2semidirect
44. C3×#487D3semidirect
147. #487C3⋊D3semidirect
321. C32#3302semidirect
371. C3#81614semidirect

Maximal subgroups

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

subgroupindex
#105962032
#105961972
C32×#4872
#105927892
#105927862
#105925142
#105925122
#105925072
#105925032
C4×#37442
C8×C4⋊(C3⋊D3)2
#816143