Finite Group Databasebeta

← #11898291

Subgroups — #11898291

Order 1152.

1212 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596189C211yesmaximal, characteristic
2#10596038C211yesmaximal, characteristic, complemented
3C32×#460C211yesmaximal, characteristic, complemented
4#10592874C212yesmaximal, complemented
5#10592861C212yesmaximal, complemented
6#10592775C211yesmaximal, characteristic, complemented
7C4×#3755C211yesmaximal, characteristic, complemented
8#10592540C211yesmaximal, characteristic, complemented
9#10592529C211yesmaximal, characteristic, complemented
10#10592461C212yesmaximal, complemented
11#10592457C212yesmaximal, complemented
12#80378—34nomaximal
13C2×#3830—21no—
14C2×C32×SD16C2212yes—
15C32×#127C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17#64153C2212yes—
18C2×#3755C2211yescharacteristic
19#64149C2212yes—
20#64148—22no—
21#64147—21no—
22D4×C3⋊Dic3C2212yes—
23C2×#3754C2212yes—
24C2×#3754C2212yes—
25C2×#3744C2212yes—
26#64098—22no—
27#64096C2212yes—
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29#64079—21no—
30#64078C2211yescharacteristic
31C4×#634—21no—
32C4×#634C2211yescharacteristic
33C32×C4⋊C8C2211yescharacteristic
34C32×#102C2212yes—
35#63662C2211yescharacteristic
36#63643C2212yes—
37#63641C2212yes—
38C8×C3⋊Dic3C2212yes—
39#63636C2211yescharacteristic
40#63635C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42#5718—34no—
43#5567—34no—
44C3×#460D314yescomplemented
45#5175—38no—
46#5162—38no—
47#5076—34no—
48C4×#215—34no—
49#4841—34no—
50#4830—34no—
51#4762—38no—
52#4758—38no—
53C2×C32×Q8C2311yescharacteristic
54C2×C32×D4—21no—
55C2×C32×D4—21no—
56C2×C32×D4C2312yes—
57C2×#638—22no—
58C2×#638—22no—
59C22×C3⋊Dic3—22no—
60#3830—44no—
61C2×C4⋊(C3⋊D3)C2311yescharacteristic
62C2×C4×C3⋊D3—21no—
63C2×#634D411yescharacteristic
64C2×#634C2312yes—
65C32×SD16—42no—
66C2×C32×C8C2312yes—
67C32×C4⋊C4—21no—
68C32×C4⋊C4C2311yescharacteristic
69C32×C42—21no—
70C32×C42C2311yescharacteristic
71#3757—22no—
72#3755—22no—
73#3754—24no—
74#3754—42no—
75#3752—21no—
76C4⋊(C3⋊Dic3)—21no—
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)D411yescharacteristic
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80#3750—22no—
81#3750—22no—
82#3750—22no—
83#3750D412yes—
84C4×C3⋊Dic3—22no—
85C4×C3⋊Dic3C2312yes—
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88#3744—42no—
89#3392—91noSylow
90C2×#237—64no—
91C2×C3×SD16C2×D318yes—
92C3×#127C2×D314yes—
93C3×C4×Q8C2×D314yes—
94#944—38no—
95C2×#215—34no—
96#940—38no—
97#939—68no—
98#938—64no—
99D4×Dic3—38no—
100C2×#214—38no—
101C2×#214—38no—
102C2×#204—38no—
103#889—68no—
104#887—38no—
105C4×D12—34no—
106#870—64no—
107#869—34no—
108C4×Dic6—34no—
109C4×Dic6—64no—
110C3×C4⋊C8C2×D314yes—
111C3×#102C2×D318yes—
112#835—34no—
113#816—38no—
114Dic3⋊C8—38no—
115C8×Dic3—38no—
116#809—34no—
117#808—34no—
118C4×C3⋊C8—34no—
119C23×C32—22no—
120C22×C3⋊D3—21no—
121C32×Q8—21no—
122C32×Q8—21no—
123C32×D4—22no—
124C32×D4—22no—
125C32×D4—42no—
126C32×D4—81no—
127C2×C32×C4—21no—
128C2×C32×C4—21no—
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2411yescharacteristic
132#638—44no—
133#638—82no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—44no—
137C2×C3⋊Dic3C2×D412yes—
138C2×C3⋊Dic3C2×D412yes—
139C4⋊(C3⋊D3)—21no—
140C4⋊(C3⋊D3)—21no—
141C4×C3⋊D3—42no—
142#634—22no—
143#634—22no—
144#634SD1614yescomplemented
145C32×C8—22no—
146C3⋊(C3⋊C8)—21no—
147C3⋊(C3⋊C8)#4112yescomplemented
148#557—91no—
149#550—91no—
150#492—92no—
151#492—91no—
152#461—92no—
153#461—91no—
154#460—92no—
155#460C3⋊D311yescharacteristic, complemented
156C8×Q8—91no—
157C4×SD16—91no—
158C4×SD16—92no—
159C2×C3×Q8C22×D314yes—
160C2×C3×D4—24no—
161C2×C3×D4—24no—
162C2×C3×D4C22×D318yes—
163C2×#67—68no—
164C2×#67—68no—
165C22×Dic3—68no—
166#237—1216no—
167C2×D12—34no—
168C2×C4×D3—64no—
169C2×Dic6—34no—
170C2×Dic6—38no—
171C3×SD16—48no—
172C2×C3×C8C22×D318yes—
173C3×C4⋊C4—24no—
174C3×C4⋊C4C22×D314yes—
175C3×C42—24no—
176C3×C42C22×D314yes—
177#217—68no—
178#215—68no—
179#214—616no—
180#214—128no—
181(C2×D3)⋊C4—64no—
182C4⋊Dic3—34no—
183C4⋊Dic3—34no—
184C4⋊Dic3—64no—
185C4⋊Dic3—64no—
186Dic3⋊C4—38no—
187Dic3⋊C4—68no—
188Dic3⋊C4—68no—
189Dic3⋊C4—68no—
190C4×Dic3—38no—
191C4×Dic3—68no—
192C2×C3⋊C8—34no—
193C2×C3⋊C8—34no—
194#204—128no—
195C22×C32—42no—
196C22×C32—42no—
197C22×C32—42no—
198C22×C32C22×D411yescharacteristic
199C2×C3⋊D3—41no—
200C2×C3⋊D3—41no—
201C2×C3⋊D3—41no—
202C32×C4—21no—
203C32×C4—41no—
204C32×C4—41no—
205C32×C4C2×SD1612yes—
206C32×C4C2×#4111yescharacteristic
207C32×C4H(5,𝔽2)11yescharacteristic
208C3⋊Dic3—22no—
209C3⋊Dic3—42no—
210C3⋊Dic3—41no—
211C3⋊Dic3C2×SD1614yes—
212C2×#41—181no—
213C2×SD16—91no—
214C2×SD16—92no—
215C2×SD16—92no—
216C2×SD16—92no—
217C2×SD16C2×C3⋊D312yes—
218C4⋊Q8—92no—
219C4⋊Q8—91no—
220#127—92no—
221#127C2×C3⋊D311yescharacteristic
222#125—181no—
223#125—182no—
224#121—181no—
225#121—182no—
226C4×Q8—91no—
227C4×Q8—92no—
228C4×Q8—181no—
229C4×Q8C2×C3⋊D311yescharacteristic
230C4×D4—92no—
231C4×D4—91no—
232#106—91no—
233C4⋊C8—92no—
234C4⋊C8C2×C3⋊D311yescharacteristic
235#103—91no—
236#103—92no—
237#102—91no—
238#102C2×C3⋊D312yes—
239C4×C8—92no—
240C4×C8—91no—
241C23×C3—28no—
242C22×D3—64no—
243C3×Q8—24no—
244C3×Q8—24no—
245C3×D4—28no—
246C3×D4—28no—
247C3×D4—48no—
248C3×D4—84no—
249C2×C3×C4—24no—
250C2×C3×C4—24no—
251C2×C3×C4D3×D414yes—
252C2×C3×C4D3×D414yes—
253C2×C3×C4C23×D314yes—
254#67—1216no—
255#67—248no—
256C2×Dic3—38no—
257C2×Dic3—38no—
258C2×Dic3—68no—
259C2×Dic3—64no—
260C2×Dic3—1216no—
261D12—64no—
262D12—64no—
263C4×D3—128no—
264Dic6—316no—
265Dic6—68no—
266Dic6—68no—
267C3×C8—28no—
268C3⋊C8—38no—
269C3⋊C8—64no—
270C2×C32—82no—
271C2×C32#55011yescharacteristic
272C2×C32C22×SD1611yescharacteristic
273C2×C32#57711yescharacteristic
274C3⋊D3—81no—
275#41—364no—
276C2×Q8—91no—
277C2×Q8—92no—
278C2×Q8C22×C3⋊D311yescharacteristic
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—91no—
282C2×D4—182no—
283C2×D4—182no—
284C2×D4C22×C3⋊D312yes—
285C22×C4—182no—
286C22×C4—181no—
287SD16—42no—
288SD16—184no—
289SD16—182no—
290SD16—362no—
291SD16—362no—
292C2×C8—91no—
293C2×C8—91no—
294C2×C8C22×C3⋊D312yes—
295C4⋊C4—21no—
296C4⋊C4—92no—
297C4⋊C4—91no—
298C4⋊C4—91no—
299C4⋊C4—182no—
300C4⋊C4—182no—
301C4⋊C4—182no—
302C4⋊C4—181no—
303C4⋊C4—181no—
304C4⋊C4C22×C3⋊D311yescharacteristic
305C22⋊C4—182no—
306C22⋊C4—181no—
307C42—21no—
308C42—92no—
309C42—182no—
310C42C22×C3⋊D311yescharacteristic
311C22×C3—48no—
312C22×C3—48no—
313C22×C3—48no—
314C22×C3C2×D3×D414yes—
315C2×D3—124no—
316C2×D3—124no—
317C2×D3—124no—
318C3×C4—24no—
319C3×C4—44no—
320C3×C4—44no—
321C3×C4D3×SD1618yes—
322C3×C4#100414yes—
323C3×C4D3×#4114yes—
324Dic3—316no—
325Dic3—68no—
326Dic3—124no—
327Dic3—128no—
328C32#339211yescharacteristic, complemented, Sylow
329C23—22no—
330C23—181no—
331Q8—21no—
332Q8—21no—
333Q8—94no—
334Q8—182no—
335Q8—182no—
336D4—22no—
337D4—22no—
338D4—42no—
339D4—81no—
340D4—181no—
341D4—181no—
342D4—364no—
343D4—722no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—92no—
347C2×C4—92no—
348C2×C4—182no—
349C2×C4—181no—
350C2×C4—364no—
351C2×C4—362no—
352C2×C4D4×C3⋊D311yescharacteristic
353C2×C4D4×C3⋊D311yescharacteristic
354C2×C4C23×C3⋊D311yescharacteristic
355C8—22no—
356C8—92no—
357C8—181no—
358C2×C3—88no—
359C2×C3#559914yes—
360C2×C3C2×D3×SD1614yes—
361C2×C3#577514yes—
362D3—244no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—361no—
367C22—361no—
368C22—361no—
369C22C2×D4×C3⋊D311yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—94no—
374C4—182no—
375C4—361no—
376C4—362no—
377C4SD16×C3⋊D312yes—
378C4#6436111yescharacteristic
379C4#41×C3⋊D311yescharacteristic
380C3#8037814yescomplemented
381C2—82no—
382C2—721no—
383C2#1059607011yescharacteristic
384C2C2×SD16×C3⋊D311yescharacteristic
385C2#1059624611yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#460C2
socleC22×C32C22×D4
prime radical#10596189C2
hypercenter#460C3⋊D3
hypocenterC32#3392
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. #10596038C2semidirect
3. C32×#460C2semidirect
4. #10592874C2semidirect
5. #10592861C2semidirect
6. #10592775C2semidirect
7. C4×#3755C2semidirect
8. #10592540C2semidirect
9. #10592529C2semidirect
10. #10592461C2semidirect
11. #10592457C2semidirect
44. C3×#460D3semidirect
144. #634SD16semidirect
147. C3⋊(C3⋊C8)#41semidirect
155. #460C3⋊D3semidirect
328. C32#3392semidirect
380. C3#80378semidirect

Maximal subgroups

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

subgroupindex
#105961892
#105960382
C32×#4602
#105928742
#105928612
#105927752
C4×#37552
#105925402
#105925292
#105924612
#105924572
#803783