Finite Group Databasebeta

← #11857277

Subgroups — #11857277

Order 1152.

1209 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5522C211yesmaximal, characteristic
2C2×#63815C211yesmaximal, characteristic
3C2×#63814C211yesmaximal, characteristic
4#10592696C211yesmaximal, characteristic, complemented
5C3×#4997C211yesmaximal, characteristic, complemented
6Dic3×#208C211yesmaximal, characteristic, complemented
7C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
8#10590334C212yesmaximal, complemented
9#10590319C212yesmaximal, complemented
10#10590318C212yesmaximal, complemented
11C4×D3×C3⋊C8C212yesmaximal, complemented
12C4×#948—31nomaximal
13#78549—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#893C412yes—
22C3×#887C412yes—
23C3×#67⋊C4C414yes—
24C3×#872C2212yes—
25C3×C42×D3C2212yes—
26C2×#3711C2212yes—
27C2×#3711C2212yes—
28#63815C418yescomplemented
29#63814C418yescomplemented
30C2×D3×C3⋊C8C2212yes—
31C2×D3×C3⋊C8C2212yes—
32#63630C2212yes—
33C4×C3⋊(C3⋊C8)C2212yes—
34C3×#803C2212yes—
35C3×C4×C3⋊C8C2212yes—
36#63554C2212yes—
37Dic3×C3⋊C8C2211yescharacteristic
38Dic3×C3⋊C8C2211yescharacteristic
39Dic3×C3⋊C8C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41Dic3×C3⋊C8C2212yes—
42C3×C4×#41—31no—
43C2×#948—31no—
44C2×#948—31no—
45C2×#907—31no—
46C2×#901—31no—
47#5522D311yescharacteristic
48C3×#405—31no—
49Dic3×M16—31no—
50C2×C8×Dic3—31no—
51#4997—31no—
52#4997—31no—
53#4997—32no—
54#4997—32no—
55#4997—61no—
56#4997D311yescharacteristic, complemented
57C4×#208—31no—
58C4×#208—32no—
59C2×C4×C3⋊C8—31no—
60C2×C4×C3⋊C8—32no—
61#4708—32no—
62#4707—32no—
63#4689—32no—
64C4×D3×C8—32no—
65C22×C32×C4C2311yescharacteristic
66C2×C3×#67C2×C412yes—
67C22×C3×Dic3C2×C412yes—
68C3×#235C2×C414yes—
69C3×#235C2×C414yes—
70C2×C3×D12C2×C411yescharacteristic
71C2×C3×C4×D3C2×C414yes—
72C2×C3×C4×D3C2312yes—
73C2×C3×Dic6C2×C411yescharacteristic
74C32×C4⋊C4C2×C412yes—
75C32×C22⋊C4C2×C412yes—
76C32×C42C2312yes—
77#3748C2×C414yescomplemented
78C2×C3⋊(C3⋊C8)C2×C414yescomplemented
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2312yes—
82C3×(C2×D3)⋊C4C2×C414yes—
83C3×Dic3⋊C4C2×C414yes—
84C3×C4×Dic3C2×C414yes—
85C3×C4×Dic3C2×C412yes—
86C3×C4×Dic3C2311yescharacteristic
87C3×C4×Dic3C2311yescharacteristic
88C3×#208C2×C414yescomplemented
89C2×C3×C3⋊C8C2×C414yescomplemented
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2311yescharacteristic
92C2×C3×C3⋊C8C2312yes—
93#3711C2×C418yescomplemented
94#3711C2×C418yescomplemented
95D3×C3⋊C8C2×C418yescomplemented
96D3×C3⋊C8C2×C418yescomplemented
97C4×#131—91noSylow
98C2×C3×#41—31no—
99C2×#235C2×D311yescharacteristic
100C2×C3×M16—31no—
101C22×C3×C8—31no—
102C3×C4×Q8—32no—
103C3×C4×D4—32no—
104C3×C4×D4—34no—
105C3×#117—21no—
106C3×#117—32no—
107C3×#117C2×D311yescharacteristic
108C3×#117C2×D311yescharacteristic
109C2×C3×C42—31no—
110C2×C3×C42—32no—
111#948—38no—
112#948—38no—
113C2×C4×Dic3C2×D311yescharacteristic
114C2×#208—31no—
115C2×#208—31no—
116C2×#208—32no—
117C2×#208—32no—
118C2×#208—61no—
119C2×#208C2×D311yescharacteristic
120C22×C3⋊C8—31no—
121C22×C3⋊C8—31no—
122C22×C3⋊C8—32no—
123C22×C3⋊C8—32no—
124C22×C3⋊C8—61no—
125C22×C3⋊C8C2×D311yescharacteristic
126#907—38no—
127#901—38no—
128C2×ΓL(1,𝔽25)—32no—
129C2×ΓL(1,𝔽25)—32no—
130C2×D3×C8—32no—
131C2×D3×C8—32no—
132#893Dic312yes—
133#887Dic312yes—
134#67⋊C4Dic314yes—
135#872C2×D312yes—
136C42×D3C2×D312yes—
137C3×#97—32no—
138C3×C4×C8—32no—
139#815—32no—
140C8×Dic3—31no—
141C8×Dic3—32no—
142C8×Dic3—31no—
143C8×Dic3—31no—
144C8×Dic3—31no—
145#803—32no—
146#803—32no—
147#803—32no—
148#803—62no—
149#803C2×D312yes—
150C4×C3⋊C8—32no—
151C4×C3⋊C8—32no—
152C4×C3⋊C8—31no—
153C4×C3⋊C8—31no—
154C4×C3⋊C8—32no—
155C4×C3⋊C8—31no—
156C4×C3⋊C8—31no—
157C4×C3⋊C8—62no—
158C4×C3⋊C8C2×D312yes—
159C23×C32C22×C411yescharacteristic
160C22×C3×D3C22×C412yes—
161C2×C32×C4C22×C412yes—
162C2×C32×C4C22×C412yes—
163C2×C32×C4C22×C414yes—
164C2×C32×C4C22×C411yescharacteristic
165C2×C32×C4C2411yescharacteristic
166C3×#67C4218yes—
167C2×C3×Dic3—24no—
168C2×C3×Dic3C22×C412yes—
169C2×C3×Dic3C22×C412yes—
170C2×C3×Dic3C22×C412yes—
171C3×D12C4214yes—
172C3×C4×D3—28no—
173C3×C4×D3C22×C414yes—
174C3×C4×D3C22×C414yes—
175C3×Dic6C4214yes—
176C3⋊(C3⋊C8)C22×C412yes—
177C3⋊(C3⋊C8)C22×C414yes—
178C3⋊(C3⋊C8)C22×C412yes—
179C3×C3⋊C8C22×C412yes—
180C3×C3⋊C8C22×C414yes—
181C3×C3⋊C8C22×C412yes—
182C2×#131—91no—
183C2×#131—91no—
184C4×#41—31no—
185#405—31no—
186#405—92no—
187#405—92no—
188#405—91no—
189C4×M16—92no—
190C4×M16—91no—
191C2×C4×C8—92no—
192C2×C4×C8—91no—
193C3×#41—34no—
194C3×#41—34no—
195C2×C3×Q8—31no—
196C2×C3×D4—32no—
197C2×C3×D4—31no—
198C22×C3×C4—21no—
199C22×C3×C4—32no—
200C22×C3×C4—32no—
201C22×C3×C4—34no—
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C2×#67C2×Dic312yes—
205C22×Dic3C2×Dic312yes—
206#235C4×D314yes—
207#235C4×D314yes—
208C2×D12C2×Dic311yescharacteristic
209C2×C4×D3C2×Dic314yes—
210C2×C4×D3C22×D312yes—
211C2×Dic6C2×Dic311yescharacteristic
212C3×M16—34no—
213C2×C3×C8—34no—
214C2×C3×C8—31no—
215C2×C3×C8—31no—
216C2×C3×C8—32no—
217C3×C4⋊C4—22no—
218C3×C4⋊C4—34no—
219C3×C4⋊C4C4×D312yes—
220C3×C4⋊C4C2×Dic312yes—
221C3×C22⋊C4—22no—
222C3×C22⋊C4—34no—
223C3×C22⋊C4C4×D312yes—
224C3×C22⋊C4C2×Dic312yes—
225C3×C42—22no—
226C3×C42—34no—
227C3×C42—32no—
228C3×C42—31no—
229C3×C42—31no—
230C3×C42C22×D312yes—
231C3×C42C22×D312yes—
232(C2×D3)⋊C4C2×Dic314yes—
233Dic3⋊C4C2×Dic314yes—
234C4×Dic3C2×Dic314yes—
235C4×Dic3C2×Dic312yes—
236C4×Dic3C22×D311yescharacteristic
237C4×Dic3C22×D311yescharacteristic
238#208—34no—
239#208—34no—
240#208—38no—
241#208—38no—
242#208—64no—
243#208C4×D314yescomplemented
244C2×C3⋊C8—34no—
245C2×C3⋊C8—34no—
246C2×C3⋊C8—31no—
247C2×C3⋊C8—32no—
248C2×C3⋊C8—31no—
249C2×C3⋊C8—31no—
250C2×C3⋊C8—32no—
251C2×C3⋊C8—31no—
252C2×C3⋊C8—38no—
253C2×C3⋊C8—38no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—62no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—64no—
258C2×C3⋊C8C4×D314yescomplemented
259C2×C3⋊C8C22×D311yescharacteristic
260C2×C3⋊C8C22×D311yescharacteristic
261C2×C3⋊C8C22×D312yes—
262ΓL(1,𝔽25)—38no—
263ΓL(1,𝔽25)—38no—
264D3×C8—38no—
265D3×C8—38no—
266C22×C32—22no—
267C22×C32C2×C4212yes—
268C22×C32C23×C411yescharacteristic
269C2×C3×D3—24no—
270C2×C3×D3C2×C4214yes—
271C32×C4—24no—
272C32×C4C2×C4212yes—
273C32×C4C23×C411yescharacteristic
274C32×C4C23×C411yescharacteristic
275C3×Dic3—22no—
276C3×Dic3C2×C4214yes—
277C3×Dic3#13114yescomplemented
278C2×#41—31no—
279#131—98no—
280#131—98no—
281C2×M16—31no—
282C2×M16—92no—
283C2×M16—92no—
284C2×M16—91no—
285C22×C8—31no—
286C22×C8—92no—
287C22×C8—92no—
288C22×C8—91no—
289C4×Q8—32no—
290C4×D4—32no—
291C4×D4—34no—
292#117—32no—
293#117D3211yescharacteristic
294C2×C42—31no—
295C2×C42—32no—
296#97—32no—
297#97—92no—
298#97—92no—
299C4×C8—32no—
300C4×C8—91no—
301C4×C8—92no—
302C4×C8—91no—
303C4×C8—91no—
304C4×C8—91no—
305C4×C8—92no—
306C23×C3—21no—
307C23×C3—32no—
308C23×C3C2×C4×D311yescharacteristic
309C23×C3C22×Dic311yescharacteristic
310C22×D3C22×Dic312yes—
311C3×Q8—34no—
312C3×D4—38no—
313C3×D4—34no—
314C2×C3×C4—21no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—21no—
318C2×C3×C4—24no—
319C2×C3×C4—32no—
320C2×C3×C4—32no—
321C2×C3×C4—34no—
322C2×C3×C4—34no—
323C2×C3×C4—32no—
324C2×C3×C4—68no—
325C2×C3×C4—64no—
326C2×C3×C4C2×C4×D312yes—
327C2×C3×C4C2×C4×D312yes—
328C2×C3×C4C2×C4×D312yes—
329C2×C3×C4C2×C4×D312yes—
330C2×C3×C4C2×C4×D314yes—
331C2×C3×C4C2×C4×D311yescharacteristic
332C2×C3×C4C22×Dic314yes—
333C2×C3×C4C22×Dic311yescharacteristic
334C2×C3×C4C23×D311yescharacteristic
335C2×C3×C4C23×D311yescharacteristic
336#67C4×Dic318yes—
337C2×Dic3—24no—
338C2×Dic3C22×Dic312yes—
339C2×Dic3C22×Dic312yes—
340C2×Dic3C22×Dic312yes—
341D12C4×Dic314yes—
342C4×D3—28no—
343C4×D3C2×C4×D314yes—
344C4×D3C2×C4×D314yes—
345Dic6C4×Dic314yes—
346C3×C8—32no—
347C3×C8—34no—
348C3×C8—32no—
349C3⋊C8—32no—
350C3⋊C8—34no—
351C3⋊C8—32no—
352C3⋊C8—32no—
353C3⋊C8—34no—
354C3⋊C8—32no—
355C3⋊C8—62no—
356C3⋊C8—62no—
357C3⋊C8—64no—
358C3⋊C8C2×C4×D312yes—
359C3⋊C8C2×C4×D314yes—
360C3⋊C8C2×C4×D312yes—
361C2×C32—22no—
362C2×C32C22×C4211yescharacteristic
363C2×C32C2×#13112yes—
364C3×D3—24no—
365#41—34no—
366#41—34no—
367C2×Q8—31no—
368C2×D4—32no—
369C2×D4—31no—
370C22×C4—32no—
371C22×C4—32no—
372C22×C4—34no—
373C22×C4C2×D3211yescharacteristic
374M16—34no—
375M16—98no—
376M16—98no—
377M16—94no—
378C2×C8—31no—
379C2×C8—32no—
380C2×C8—31no—
381C2×C8—34no—
382C2×C8—98no—
383C2×C8—98no—
384C2×C8—91no—
385C2×C8—91no—
386C2×C8—92no—
387C2×C8—94no—
388C4⋊C4—34no—
389C4⋊C4D3×Dic312yes—
390C22⋊C4—34no—
391C22⋊C4D3×Dic312yes—
392C42—31no—
393C42—31no—
394C42—34no—
395C42—32no—
396C42C2×D3212yes—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—21no—
400C22×C3—22no—
401C22×C3—34no—
402C22×C3—42no—
403C22×C3—64no—
404C22×C3C42×D312yes—
405C22×C3C2×C4×Dic312yes—
406C22×C3C22×C4×D311yescharacteristic
407C22×C3C23×Dic311yescharacteristic
408C2×D3—24no—
409C2×D3C2×C4×Dic314yes—
410C3×C4—24no—
411C3×C4—24no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—22no—
415C3×C4—34no—
416C3×C4—34no—
417C3×C4—44no—
418C3×C4—62no—
419C3×C4C42×D312yes—
420C3×C4C2×C4×Dic312yes—
421C3×C4C22×C4×D311yescharacteristic
422C3×C4C22×C4×D311yescharacteristic
423C3×C4C22×C4×D311yescharacteristic
424C3×C4C22×C4×D311yescharacteristic
425Dic3—22no—
426Dic3C2×C4×Dic314yes—
427Dic3#94814yescomplemented
428C32C4×#13111yescharacteristic, complemented, Sylow
429C23—32no—
430C23C2×D3×Dic311yescharacteristic
431Q8—34no—
432D4—38no—
433D4—34no—
434C2×C4—32no—
435C2×C4—32no—
436C2×C4—34no—
437C2×C4—34no—
438C2×C4—32no—
439C2×C4—68no—
440C2×C4—64no—
441C2×C4C4×D3212yes—
442C2×C4C4×D3212yes—
443C2×C4C2×D3×Dic314yes—
444C2×C4C2×D3×Dic311yescharacteristic
445C2×C4C22×D3211yescharacteristic
446C8—32no—
447C8—32no—
448C8—34no—
449C8—92no—
450C8—94no—
451C8—92no—
452C2×C3—22no—
453C2×C3—22no—
454C2×C3—21no—
455C2×C3—22no—
456C2×C3—42no—
457C2×C3—64no—
458C2×C3C2×C42×D311yescharacteristic
459C2×C3D3×#13112yes—
460C2×C3C22×C4×Dic311yescharacteristic
461C2×C3C2×#94812yes—
462D3—24no—
463C22—22no—
464C22—34no—
465C22—64no—
466C22C4×D3×Dic312yes—
467C22C22×D3×Dic311yescharacteristic
468C4—24no—
469C4—34no—
470C4—34no—
471C4—62no—
472C4C4×D3×Dic312yes—
473C4C2×C4×D3211yescharacteristic
474C4C2×C4×D3211yescharacteristic
475C3—21no—
476C3#7854911yescharacteristic, complemented
477C3C4×#94811yescharacteristic, complemented
478C2—22no—
479C2—64no—
480C2C2×C4×D3×Dic311yescharacteristic
481C2D3×#94812yes—
subgroupG/H
center, FrattiniC2×C4C22×D32
commutatorC2×C32C22×C42
FittingC32×#117C22
socleC22×C32C23×C4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32C4×#131
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #10592696C2semidirect
5. C3×#4997C2semidirect
6. Dic3×#208C2semidirect
7. C2×Dic3×C3⋊C8C2semidirect
8. #10590334C2semidirect
9. #10590319C2semidirect
10. #10590318C2semidirect
11. C4×D3×C3⋊C8C2semidirect
28. #63815C4semidirect
29. #63814C4semidirect
56. #4997D3semidirect
77. #3748C2×C4semidirect
78. C2×C3⋊(C3⋊C8)C2×C4semidirect
88. C3×#208C2×C4semidirect
89. C2×C3×C3⋊C8C2×C4semidirect
93. #3711C2×C4semidirect
94. #3711C2×C4semidirect
95. D3×C3⋊C8C2×C4semidirect
96. D3×C3⋊C8C2×C4semidirect
243. #208C4×D3semidirect
258. C2×C3⋊C8C4×D3semidirect
277. C3×Dic3#131semidirect
427. Dic3#948semidirect
428. C32C4×#131semidirect
476. C3#78549semidirect
477. C3C4×#948semidirect

Maximal subgroups

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

subgroupindex
C3×#55222
C2×#638152
C2×#638142
#105926962
C3×#49972
Dic3×#2082
C2×Dic3×C3⋊C82
#105903342
#105903192
#105903182
C4×D3×C3⋊C82
C4×#9483
#785493