Finite Group Databasebeta

← #11788758

Subgroups — #11788758

Order 1152.

855 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596301C211yesmaximal, characteristic
2C3×#5819C211yesmaximal, characteristic, complemented
3C3×#5240C211yesmaximal, characteristic, complemented
4#10591096C212yesmaximal, complemented
5#10589158C212yesmaximal, complemented
6#72025—31nomaximal
7#70047—31nomaximal
8C2×C32×#41C2211yescharacteristic
9C22×C4⋊(C3⋊D3)C2211yescharacteristic
10#64156C412yescomplemented
11#64149C412yescomplemented
12#64146—22no—
13#64139—22no—
14#64135C2211yescharacteristic
15C3×#948—24no—
16C3×#926C2212yes—
17C2×C3×#208—22no—
18C2×C3×#208C2212yes—
19C3×#834—22no—
20#63564—24no—
21C3×#568—31no—
22#5830—31no—
23#5830—31no—
24#5830—61no—
25#5819D311yescharacteristic, complemented
26C3×#410—31no—
27#5240D311yescharacteristic, complemented
28#5131—32no—
29#5001—32no—
30#4557—32no—
31#4531—32no—
32C23×C3⋊D3—21no—
33C32×#41—22no—
34C32×#41—22no—
35C2×C32×Q8C2×C411yescharacteristic
36C2×C32×D4C2×C411yescharacteristic
37C2×C32×D4D412yes—
38C22×C32×C4D412yes—
39C22×C32×C4C2311yescharacteristic
40C2×#638—24no—
41C2×C4⋊(C3⋊D3)—22no—
42C2×C4⋊(C3⋊D3)—22no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)C2×C412yes—
45#3757—21no—
46#3752—24no—
47C4⋊(C3⋊Dic3)—21no—
48C4×C3⋊Dic3C2×C412yes—
49C3×#217—22no—
50C3×C4⋊Dic3—22no—
51C3×C4×Dic3—22no—
52C3×#208—24no—
53C3×#208—22no—
54C3×#208—22no—
55C2×C3×C3⋊C8—24no—
56C2×C3×C3⋊C8D414yescomplemented
57#1910—91noSylow
58C2×C3×#41—21no—
59C2×C3×#41C2×D311yescharacteristic
60C2×C3×#41C2×D311yescharacteristic
61C22×D12—31no—
62C22×D12—31no—
63C22×D12—61no—
64C3×#131—64no—
65C2×C3×M16—32no—
66C2×C3×M16—62no—
67C3×#117—32no—
68#948—24no—
69#947—32no—
70#947—32no—
71#947—62no—
72#940—32no—
73#940—32no—
74#940—62no—
75#937—64no—
76#937—62no—
77#937—62no—
78#930—64no—
79#930—62no—
80#930—62no—
81#926—31no—
82#926—31no—
83#926—61no—
84#926C2×D312yes—
85C2×#208—22no—
86C2×#208C2×D312yes—
87C3×#99—62no—
88#834—22no—
89#821—64no—
90#809—64no—
91C23×C32C22⋊C412yes—
92C23×C32C2×D411yescharacteristic
93C22×C3⋊D3—22no—
94C22×C3⋊D3—42no—
95C22×C3⋊D3—82no—
96C32×Q8—22no—
97C32×D4—24no—
98C32×D4—22no—
99C2×C32×C4—22no—
100C2×C32×C4—22no—
101C2×C32×C4C22⋊C412yes—
102C2×C32×C4C22×C411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D412yes—
105C2×C32×C4#4112yes—
106#638—84no—
107C2×C3⋊Dic3—22no—
108C4⋊(C3⋊D3)—24no—
109C4⋊(C3⋊D3)—41no—
110C4⋊(C3⋊D3)—41no—
111C2×C3×Dic3—42no—
112C3×C3⋊C8—24no—
113#568—31no—
114#535—91no—
115#418—92no—
116#410—31no—
117H(3,ℤ/4)—92no—
118C23×D3—62no—
119C23×D3—61no—
120C23×D3—61no—
121C3×#41—22no—
122C3×#41—22no—
123C3×#41—22no—
124C3×#41—22no—
125C3×#41—42no—
126C3×#41—42no—
127C2×C3×Q8—21no—
128C2×C3×Q8C4×D311yescharacteristic
129C2×C3×Q8C4×D311yescharacteristic
130C2×C3×D4—21no—
131C2×C3×D4—22no—
132C2×C3×D4C4×D311yescharacteristic
133C2×C3×D4C4×D311yescharacteristic
134C2×C3×D4D1212yes—
135C2×C3×D4#6712yes—
136C22×C3×C4—22no—
137C22×C3×C4—21no—
138C22×C3×C4D1212yes—
139C22×C3×C4#6712yes—
140C22×C3×C4C22×D311yescharacteristic
141C22×C3×C4C22×D311yescharacteristic
142C2×#67—68no—
143C2×#67—64no—
144C2×#67—64no—
145C2×D12—32no—
146C2×D12—32no—
147C2×D12—62no—
148C2×D12—62no—
149C2×D12—62no—
150C2×D12—62no—
151C2×D12—62no—
152C2×D12—62no—
153C2×D12—61no—
154C2×D12—61no—
155C2×D12—122no—
156C2×D12—122no—
157C3×M16—64no—
158C3×M16—62no—
159C3×M16—62no—
160C2×C3×C8—34no—
161C2×C3×C8—64no—
162C3×C4⋊C4—62no—
163C3×C22⋊C4—62no—
164C3×C42—62no—
165#217—22no—
166#217—62no—
167#217—61no—
168#217—61no—
169(C2×D3)⋊C4—68no—
170(C2×D3)⋊C4—64no—
171(C2×D3)⋊C4—64no—
172C4⋊Dic3—22no—
173C4⋊Dic3—62no—
174C4⋊Dic3—61no—
175C4⋊Dic3—61no—
176C4×Dic3—22no—
177C4×Dic3—32no—
178C4×Dic3—32no—
179C4×Dic3—62no—
180#208—24no—
181#208—22no—
182#208—22no—
183C2×C3⋊C8—24no—
184C2×C3⋊C8#6714yescomplemented
185C22×C32—22no—
186C22×C32—41no—
187C22×C32—42no—
188C22×C32C2×C22⋊C411yescharacteristic
189C22×C32#12112yes—
190C2×C3⋊D3—44no—
191C2×C3⋊D3—42no—
192C2×C3⋊D3—84no—
193C32×C4—22no—
194C32×C4C4×D412yes—
195C32×C4#12011yescharacteristic
196C32×C4#12311yescharacteristic
197C3⋊Dic3—42no—
198C3×Dic3—82no—
199C2×#41D3211yescharacteristic
200C22×D4—91no—
201#131—64no—
202C2×M16—32no—
203C2×M16—62no—
204#127—92no—
205#124—92no—
206#121—182no—
207#120—182no—
208#117—32no—
209#117—91no—
210#102—184no—
211#99—62no—
212C23×C3—22no—
213C23×C3—21no—
214C23×C3(C2×D3)⋊C412yes—
215C23×C3(C2×D3)⋊C412yes—
216C23×C3C2×D1211yescharacteristic
217C23×C3C2×#6711yescharacteristic
218C22×D3—64no—
219C22×D3—62no—
220C22×D3—62no—
221C22×D3—124no—
222C22×D3—122no—
223C22×D3—122no—
224C22×D3—242no—
225C22×D3—242no—
226C22×D3—244no—
227C3×Q8—22no—
228C3×Q8—22no—
229C3×Q8—42no—
230C3×D4—24no—
231C3×D4—24no—
232C3×D4—22no—
233C3×D4—22no—
234C3×D4—42no—
235C3×D4—44no—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—22no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—22no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—22no—
245C2×C3×C4—42no—
246C2×C3×C4—42no—
247C2×C3×C4—122no—
248C2×C3×C4(C2×D3)⋊C412yes—
249C2×C3×C4(C2×D3)⋊C412yes—
250C2×C3×C4C2×C4×D311yescharacteristic
251C2×C3×C4C2×C4×D311yescharacteristic
252C2×C3×C4C2×D1211yescharacteristic
253C2×C3×C4#23512yes—
254C2×C3×C4D3×D412yes—
255C2×C3×C4#23712yes—
256C2×C3×C4C2×#6711yescharacteristic
257C2×C3×C4C2×#6712yes—
258#67—244no—
259#67—244no—
260#67—248no—
261C2×Dic3—42no—
262C2×Dic3—64no—
263C2×Dic3—62no—
264C2×Dic3—62no—
265D12—64no—
266D12—64no—
267D12—124no—
268D12—122no—
269D12—122no—
270D12—121no—
271D12—121no—
272D12—121no—
273D12—121no—
274C3×C8—64no—
275C3⋊C8—24no—
276C2×C32—21no—
277C2×C32—22no—
278C2×C32—42no—
279C2×C32#38611yescharacteristic
280C3⋊D3—82no—
281C24—181no—
282#41—22no—
283#41—22no—
284C2×Q8#62411yescharacteristic
285C2×D4—92no—
286C2×D4—184no—
287C2×D4—182no—
288C2×D4—181no—
289C2×D4—182no—
290C2×D4#62411yescharacteristic
291C2×D4#62612yes—
292C22×C4#62612yes—
293C22×C4C2×D3211yescharacteristic
294M16—64no—
295M16—62no—
296M16—62no—
297C2×C8—34no—
298C2×C8—64no—
299C4⋊C4—62no—
300C4⋊C4—181no—
301C22⋊C4—62no—
302C22⋊C4—181no—
303C22⋊C4—184no—
304C42—62no—
305C42—92no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—21no—
309C22×C3—22no—
310C22×C3—42no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—42no—
314C22×C3—42no—
315C22×C3—42no—
316C22×C3—44no—
317C22×C3C2×(C2×D3)⋊C411yescharacteristic
318C22×C3C2×(C2×D3)⋊C411yescharacteristic
319C22×C3#93012yes—
320C22×C3#93912yes—
321C2×D3—124no—
322C2×D3—128no—
323C2×D3—124no—
324C2×D3—124no—
325C2×D3—122no—
326C2×D3—122no—
327C2×D3—244no—
328C2×D3—244no—
329C2×D3—248no—
330C3×C4—22no—
331C3×C4—22no—
332C3×C4—22no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—42no—
336C3×C4—242no—
337C3×C4#67⋊C412yes—
338C3×C4#88211yescharacteristic
339C3×C4#88611yescharacteristic
340C3×C4C4×#6712yes—
341C3×C4#92911yescharacteristic
342C3×C4#95311yescharacteristic
343Dic3—82no—
344Dic3—124no—
345Dic3—122no—
346Dic3—122no—
347C32#191011yescharacteristic, complemented, Sylow
348C23—182no—
349C23—362no—
350C23—722no—
351C23#372212yes—
352C23C2×#62611yescharacteristic
353Q8—22no—
354D4—24no—
355D4—22no—
356D4—184no—
357D4—361no—
358D4—361no—
359D4—724no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—122no—
363C2×C4—182no—
364C2×C4#372212yes—
365C2×C4#380412yes—
366C2×C4C2×#62411yescharacteristic
367C2×C4C2×#62611yescharacteristic
368C2×C4D3×#6712yes—
369C8—64no—
370C2×C3—22no—
371C2×C3—21no—
372C2×C3—22no—
373C2×C3—22no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—42no—
377C2×C3—42no—
378C2×C3—42no—
379C2×C3—82no—
380C2×C3#495811yescharacteristic
381C2×C3#521311yescharacteristic
382D3—244no—
383D3—242no—
384D3—242no—
385C22—22no—
386C22—41no—
387C22—42no—
388C22—364no—
389C22—362no—
390C22—724no—
391C22C2×#372211yescharacteristic
392C22#6397812yes—
393C4—22no—
394C4—242no—
395C4—362no—
396C4#6395212yes—
397C4#6396611yescharacteristic
398C4#6397711yescharacteristic
399C3—21no—
400C3#7004711yescharacteristic, complemented
401C3#7202511yescharacteristic, complemented
402C2—22no—
403C2—21no—
404C2—42no—
405C2—722no—
406C2#1059171111yescharacteristic
subgroupG/H
centerC2#10591711
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#386
prime radical#10596301C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1910
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#5819C2semidirect
3. C3×#5240C2semidirect
4. #10591096C2semidirect
5. #10589158C2semidirect
10. #64156C4semidirect
11. #64149C4semidirect
25. #5819D3semidirect
27. #5240D3semidirect
56. C2×C3×C3⋊C8D4semidirect
184. C2×C3⋊C8#67semidirect
347. C32#1910semidirect
400. C3#70047semidirect
401. C3#72025semidirect

Maximal subgroups

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

subgroupindex
#105963012
C3×#58192
C3×#52402
#105910962
#105891582
#720253
#700473