Finite Group Databasebeta

← #11857268

Subgroups — #11857268

Order 1152.

1225 conjugacy classes of subgroups.

The subgroup lattice has 491 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#901C211yesmaximal, characteristic
2#10594958C211yesmaximal, characteristic
3C2×#63815C211yesmaximal, characteristic
4C2×C8×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×#5101C211yesmaximal, characteristic, complemented
6#10591060C211yesmaximal, characteristic, complemented
7#10591057C211yesmaximal, characteristic, complemented
8#10590909C212yesmaximal, complemented
9#10590692C212yesmaximal, complemented
10#10590667C212yesmaximal, complemented
11D3×C8×Dic3C212yesmaximal, complemented
12Dic3×#131—31nomaximal
13#78549—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C3×#901C418yescomplemented
22C2×C3×ΓL(1,𝔽25)C2212yes—
23C2×C3×D3×C8C2212yes—
24#67⋊Dic3C414yes—
25#63898C412yes—
26C4×D3×Dic3C2212yes—
27#63855C2212yes—
28#63843C412yes—
29C2×#3711C2212yes—
30#63815C418yescomplemented
31C2×D3×C3⋊C8C2212yes—
32C8×C3⋊Dic3C2211yescharacteristic
33C8×C3⋊Dic3C2211yescharacteristic
34C8×C3⋊Dic3C2211yescharacteristic
35C8×C3⋊Dic3C2211yescharacteristic
36C3×#815C2212yes—
37C3×C8×Dic3C2212yes—
38#63555C2212yes—
39#63554C2212yes—
40#63553C2212yes—
41Dic3×C3⋊C8C2212yes—
42C2×C3×#131—31no—
43Dic3×#41—31no—
44C2×#948—31no—
45C2×#907—31no—
46C2×#901D311yescharacteristic
47#5522—31no—
48C3×#405—31no—
49#5122—31no—
50#5122—32no—
51Dic3×M16—31no—
52Dic3×M16—31no—
53Dic3×M16—32no—
54#5101—32no—
55#5101D311yescharacteristic, complemented
56C2×C8×Dic3—31no—
57C2×C8×Dic3—31no—
58C2×C8×Dic3—32no—
59C2×C8×Dic3—61no—
60#4997—31no—
61#4708—32no—
62#4707—32no—
63#4689—32no—
64C4×D3×C8—32no—
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2×C412yes—
67C2×C3×#67C2×C412yes—
68C3×#235C2×C414yes—
69C3×#235C2×C414yes—
70C2×C3×D12C2×C411yescharacteristic
71C2×C3×C4×D3C2312yes—
72C2×C3×Dic6C2×C411yescharacteristic
73C2×D3×Dic3C2×C414yes—
74C2×C32×C8C2×C414yescomplemented
75C2×C32×C8C2311yescharacteristic
76C2×C32×C8C2311yescharacteristic
77C4×C3⋊Dic3C2×C412yes—
78C4×C3⋊Dic3C2311yescharacteristic
79C4×C3⋊Dic3C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2×C414yescomplemented
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C3×#217C2×C412yes—
84C3×C4⋊Dic3C2×C412yes—
85C3×C4×Dic3C2312yes—
86C3×#208C2×C414yescomplemented
87C3×#208C2×C414yescomplemented
88C2×C3×C3⋊C8C2312yes—
89C2×C3×C3⋊C8C2312yes—
90C3×ΓL(1,𝔽25)C2×C418yescomplemented
91C3×D3×C8C2×C418yescomplemented
92Dic3⋊Dic3C2×C414yes—
93(C2×D3)⋊Dic3C2×C414yes—
94Dic32C2×C414yes—
95#3711C2×C418yescomplemented
96D3×C3⋊C8C2×C418yescomplemented
97C4×#131—91noSylow
98C2×C3×#41—31no—
99C2×#235C2×D311yescharacteristic
100C3×#131—38no—
101C2×C3×M16—31no—
102C2×C3×M16—31no—
103C2×C3×M16—32no—
104C22×C3×C8—21no—
105C22×C3×C8—32no—
106C22×C3×C8C2×D311yescharacteristic
107C22×C3×C8C2×D311yescharacteristic
108C3×#117—31no—
109#948—38no—
110Q8×Dic3—32no—
111D4×Dic3—34no—
112D4×Dic3—32no—
113#926—32no—
114#926C2×D311yescharacteristic
115C2×C4×Dic3—31no—
116C2×C4×Dic3—31no—
117C2×C4×Dic3—32no—
118C2×C4×Dic3—61no—
119C2×#208—32no—
120C2×#208C2×D311yescharacteristic
121C2×#208C2×D311yescharacteristic
122C22×C3⋊C8—31no—
123C22×C3⋊C8—31no—
124C22×C3⋊C8—32no—
125C22×C3⋊C8—61no—
126#907—38no—
127#901Dic318yescomplemented
128C2×ΓL(1,𝔽25)—32no—
129C2×ΓL(1,𝔽25)C2×D312yes—
130C2×D3×C8—32no—
131C2×D3×C8C2×D312yes—
132#893—32no—
133#887—32no—
134#67⋊C4—34no—
135#872—32no—
136C42×D3—32no—
137C3×#97—32no—
138C3×C4×C8—32no—
139#815—32no—
140#815—32no—
141#815—32no—
142#815C2×D312yes—
143C8×Dic3—31no—
144C8×Dic3—31no—
145C8×Dic3—31no—
146C8×Dic3—31no—
147C8×Dic3—31no—
148C8×Dic3—31no—
149C8×Dic3—31no—
150C8×Dic3—31no—
151C8×Dic3—32no—
152C8×Dic3—32no—
153C8×Dic3—32no—
154C8×Dic3—61no—
155C8×Dic3—61no—
156C8×Dic3—61no—
157C8×Dic3—61no—
158C8×Dic3C2×D312yes—
159#803—32no—
160C4×C3⋊C8—32no—
161C23×C32C22×C411yescharacteristic
162C22×C3×D3C22×C412yes—
163C2×C32×C4C22×C411yescharacteristic
164C2×C32×C4C22×C412yes—
165C2×C32×C4C22×C412yes—
166C2×C32×C4C2411yescharacteristic
167C2×C3⋊Dic3—24no—
168C2×C3⋊Dic3C22×C412yes—
169C2×C3⋊Dic3C22×C412yes—
170C3×#67C4218yes—
171C2×C3×Dic3C22×C414yes—
172C2×C3×Dic3C22×C412yes—
173C3×D12C4214yes—
174C3×C4×D3C22×C414yes—
175C3×C4×D3C22×C414yes—
176C3×Dic6C4214yes—
177D3×Dic3—28no—
178C32×C8C22×C412yes—
179C32×C8C22×C412yes—
180C3⋊(C3⋊C8)C22×C412yes—
181C3⋊(C3⋊C8)C22×C412yes—
182C3×C3⋊C8C22×C414yes—
183C3×C3⋊C8C22×C414yes—
184C2×#131—31no—
185C2×#131—91no—
186C4×#41—91no—
187#405—31no—
188#405—92no—
189#405—92no—
190#405—91no—
191C4×M16—92no—
192C4×M16—91no—
193C2×C4×C8—92no—
194C2×C4×C8—91no—
195C3×#41—34no—
196C3×#41—34no—
197C2×C3×Q8—31no—
198C2×C3×D4—32no—
199C2×C3×D4—31no—
200C22×C3×C4—21no—
201C22×C3×C4—32no—
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C2×#67C4×D312yes—
205C22×Dic3—32no—
206C22×Dic3—32no—
207C22×Dic3—34no—
208C22×Dic3—62no—
209#235C4×D314yes—
210#235C2×Dic314yes—
211C2×D12C4×D311yescharacteristic
212C2×C4×D3—34no—
213C2×C4×D3C22×D312yes—
214C2×Dic6C4×D311yescharacteristic
215C3×M16—34no—
216C3×M16—34no—
217C3×M16—38no—
218C2×C3×C8—24no—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—32no—
222C2×C3×C8—32no—
223C2×C3×C8—38no—
224C2×C3×C8C4×D314yescomplemented
225C2×C3×C8C2×Dic314yescomplemented
226C2×C3×C8C22×D311yescharacteristic
227C2×C3×C8C22×D311yescharacteristic
228C2×C3×C8C22×D311yescharacteristic
229C2×C3×C8C22×D311yescharacteristic
230C3×C4⋊C4—32no—
231C3×C22⋊C4—32no—
232C3×C42—32no—
233#217—34no—
234#217C4×D312yes—
235(C2×D3)⋊C4—34no—
236C4⋊Dic3—34no—
237C4⋊Dic3C4×D312yes—
238Dic3⋊C4—34no—
239C4×Dic3—32no—
240C4×Dic3—32no—
241C4×Dic3—31no—
242C4×Dic3—31no—
243C4×Dic3—31no—
244C4×Dic3—31no—
245C4×Dic3—34no—
246C4×Dic3—34no—
247C4×Dic3—61no—
248C4×Dic3—61no—
249C4×Dic3—62no—
250C4×Dic3C22×D312yes—
251#208—38no—
252#208C4×D314yescomplemented
253#208C2×Dic314yescomplemented
254C2×C3⋊C8—34no—
255C2×C3⋊C8—34no—
256C2×C3⋊C8—31no—
257C2×C3⋊C8—31no—
258C2×C3⋊C8—31no—
259C2×C3⋊C8—31no—
260C2×C3⋊C8—38no—
261C2×C3⋊C8—61no—
262C2×C3⋊C8—61no—
263C2×C3⋊C8—64no—
264C2×C3⋊C8C22×D312yes—
265C2×C3⋊C8C22×D312yes—
266ΓL(1,𝔽25)—38no—
267ΓL(1,𝔽25)C2×Dic318yescomplemented
268D3×C8—38no—
269D3×C8C2×Dic318yescomplemented
270C22×C32—22no—
271C22×C32C2×C4212yes—
272C22×C32C23×C411yescharacteristic
273C2×C3×D3—24no—
274C2×C3×D3C2×C4214yes—
275C32×C4C2×C4212yes—
276C32×C4C23×C411yescharacteristic
277C32×C4C23×C411yescharacteristic
278C3⋊Dic3—22no—
279C3⋊Dic3#13114yescomplemented
280C3×Dic3—24no—
281C3×Dic3C2×C4214yes—
282C2×#41—31no—
283#131—38no—
284#131—98no—
285C2×M16—31no—
286C2×M16—31no—
287C2×M16—32no—
288C2×M16—92no—
289C22×C8—32no—
290C22×C8—92no—
291C22×C8—91no—
292C22×C8D3211yescharacteristic
293C4×Q8—92no—
294C4×D4—94no—
295C4×D4—92no—
296#117—31no—
297#117—92no—
298C2×C42—92no—
299C2×C42—91no—
300#97—32no—
301#97—92no—
302#97—92no—
303C4×C8—32no—
304C4×C8—92no—
305C4×C8—92no—
306C4×C8—91no—
307C4×C8—91no—
308C4×C8—91no—
309C4×C8—91no—
310C23×C3—21no—
311C23×C3—32no—
312C23×C3C2×C4×D311yescharacteristic
313C23×C3C2×C4×D311yescharacteristic
314C22×D3C2×C4×D312yes—
315C3×Q8—34no—
316C3×D4—38no—
317C3×D4—34no—
318C2×C3×C4—21no—
319C2×C3×C4—22no—
320C2×C3×C4—21no—
321C2×C3×C4—22no—
322C2×C3×C4—32no—
323C2×C3×C4—34no—
324C2×C3×C4—34no—
325C2×C3×C4—34no—
326C2×C3×C4C2×C4×D311yescharacteristic
327C2×C3×C4C2×C4×D312yes—
328C2×C3×C4C2×C4×D311yescharacteristic
329C2×C3×C4C2×C4×D312yes—
330C2×C3×C4C2×C4×D312yes—
331C2×C3×C4C22×Dic312yes—
332C2×C3×C4C23×D311yescharacteristic
333C2×C3×C4C23×D311yescharacteristic
334#67C4×Dic318yes—
335C2×Dic3—32no—
336C2×Dic3—32no—
337C2×Dic3—32no—
338C2×Dic3—32no—
339C2×Dic3—62no—
340C2×Dic3—62no—
341C2×Dic3—68no—
342C2×Dic3—64no—
343C2×Dic3—64no—
344C2×Dic3—68no—
345C2×Dic3C2×C4×D314yes—
346C2×Dic3C2×C4×D312yes—
347D12C4×Dic314yes—
348C4×D3—68no—
349C4×D3C2×C4×D314yes—
350C4×D3C22×Dic314yes—
351Dic6C4×Dic314yes—
352C3×C8—22no—
353C3×C8—22no—
354C3×C8—34no—
355C3×C8—34no—
356C3×C8C2×C4×D312yes—
357C3×C8C2×C4×D312yes—
358C3×C8C22×Dic312yes—
359C3×C8C22×Dic312yes—
360C3⋊C8—32no—
361C3⋊C8—32no—
362C3⋊C8—32no—
363C3⋊C8—32no—
364C3⋊C8—62no—
365C3⋊C8—62no—
366C3⋊C8C2×C4×D314yes—
367C3⋊C8C22×Dic314yes—
368C2×C32—22no—
369C2×C32C22×C4211yescharacteristic
370C2×C32C2×#13112yes—
371C3×D3—24no—
372#41—34no—
373#41—34no—
374C2×Q8—31no—
375C2×D4—32no—
376C2×D4—31no—
377C22×C4—32no—
378C22×C4—94no—
379C22×C4—92no—
380C22×C4C2×D3211yescharacteristic
381M16—34no—
382M16—34no—
383M16—38no—
384M16—98no—
385C2×C8—32no—
386C2×C8—32no—
387C2×C8—38no—
388C2×C8—98no—
389C2×C8—91no—
390C2×C8—91no—
391C2×C8—94no—
392C2×C8D3×Dic314yescomplemented
393C2×C8C2×D3211yescharacteristic
394C2×C8C2×D3211yescharacteristic
395C4⋊C4—32no—
396C4⋊C4—94no—
397C22⋊C4—32no—
398C22⋊C4—94no—
399C42—32no—
400C42—94no—
401C42—91no—
402C42—91no—
403C42—92no—
404C22×C3—24no—
405C22×C3—22no—
406C22×C3—22no—
407C22×C3—21no—
408C22×C3—22no—
409C22×C3—34no—
410C22×C3—64no—
411C22×C3C42×D312yes—
412C22×C3C2×C4×Dic312yes—
413C22×C3C22×C4×D311yescharacteristic
414C22×C3C22×C4×D311yescharacteristic
415C2×D3—24no—
416C2×D3C2×C4×Dic314yes—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—22no—
420C3×C4—34no—
421C3×C4—64no—
422C3×C4C42×D312yes—
423C3×C4C2×C4×Dic312yes—
424C3×C4C22×C4×D311yescharacteristic
425C3×C4C22×C4×D311yescharacteristic
426C3×C4C22×C4×D311yescharacteristic
427C3×C4C23×Dic311yescharacteristic
428Dic3—24no—
429Dic3—34no—
430Dic3—34no—
431Dic3—64no—
432Dic3—64no—
433Dic3—62no—
434Dic3—62no—
435Dic3C2×C4×Dic314yes—
436C32C4×#13111yescharacteristic, complemented, Sylow
437C23—32no—
438C23C4×D3211yescharacteristic
439Q8—34no—
440D4—38no—
441D4—34no—
442C2×C4—32no—
443C2×C4—34no—
444C2×C4—34no—
445C2×C4—34no—
446C2×C4—92no—
447C2×C4—92no—
448C2×C4—188no—
449C2×C4—184no—
450C2×C4C4×D3212yes—
451C2×C4C4×D3211yescharacteristic
452C2×C4C2×D3×Dic312yes—
453C2×C4C22×D3211yescharacteristic
454C8—34no—
455C8—34no—
456C8—92no—
457C8—92no—
458C8C2×D3×Dic312yes—
459C8C2×D3×Dic312yes—
460C2×C3—24no—
461C2×C3—22no—
462C2×C3—22no—
463C2×C3—21no—
464C2×C3—22no—
465C2×C3—64no—
466C2×C3C2×C42×D311yescharacteristic
467C2×C3D3×#13112yes—
468C2×C3D3×#13112yes—
469C2×C3C22×C4×Dic311yescharacteristic
470D3—24no—
471C22—22no—
472C22—34no—
473C22—64no—
474C22C4×D3×Dic312yes—
475C22C2×C4×D3211yescharacteristic
476C4—34no—
477C4—64no—
478C4—94no—
479C4—182no—
480C4C4×D3×Dic312yes—
481C4C2×C4×D3211yescharacteristic
482C4C22×D3×Dic311yescharacteristic
483C3—21no—
484C3#7854911yescharacteristic, complemented
485C3Dic3×#13111yescharacteristic, complemented
486C2—22no—
487C2—64no—
488C2#1059466912yes—
489C2C2×C4×D3×Dic311yescharacteristic
subgroupG/H
centerC2×C8C2×D32
commutatorC2×C32C22×C42
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C23×C4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C4×#131
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
4. C2×C8×C3⋊Dic3C2semidirect
5. C3×#5101C2semidirect
6. #10591060C2semidirect
7. #10591057C2semidirect
8. #10590909C2semidirect
9. #10590692C2semidirect
10. #10590667C2semidirect
11. D3×C8×Dic3C2semidirect
21. C3×#901C4semidirect
30. #63815C4semidirect
55. #5101D3semidirect
74. C2×C32×C8C2×C4semidirect
80. C2×C3⋊(C3⋊C8)C2×C4semidirect
86. C3×#208C2×C4semidirect
87. C3×#208C2×C4semidirect
90. C3×ΓL(1,𝔽25)C2×C4semidirect
91. C3×D3×C8C2×C4semidirect
95. #3711C2×C4semidirect
96. D3×C3⋊C8C2×C4semidirect
127. #901Dic3semidirect
224. C2×C3×C8C4×D3semidirect
225. C2×C3×C8C2×Dic3semidirect
252. #208C4×D3semidirect
253. #208C2×Dic3semidirect
267. ΓL(1,𝔽25)C2×Dic3semidirect
269. D3×C8C2×Dic3semidirect
279. C3⋊Dic3#131semidirect
392. C2×C8D3×Dic3semidirect
436. C32C4×#131semidirect
484. C3#78549semidirect
485. C3Dic3×#131semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9012
#105949582
C2×#638152
C2×C8×C3⋊Dic32
C3×#51012
#105910602
#105910572
#105909092
#105906922
#105906672
D3×C8×Dic32
Dic3×#1313
#785493