Finite Group Databasebeta

← #11858676

Subgroups — #11858676

Order 1152.

931 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5745C211yesmaximal, characteristic
2#10594776C211yesmaximal, characteristic
3C2×#63814C211yesmaximal, characteristic
4#10592823C211yesmaximal, characteristic, complemented
5C2×C3×#822C211yesmaximal, characteristic, complemented
6#10591143C211yesmaximal, characteristic, complemented
7C2×#63577C211yesmaximal, characteristic, complemented
8#10590973C214yesmaximal, complemented
9D3×#822C214yesmaximal, complemented
10#83810—31nomaximal
11#79252—31nomaximal
12C2×C3×#235C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C3×#907—22no—
20C3×D3×M16C2214yes—
21C3×#901—22no—
22C2×#3711C2212yes—
23#63815—22no—
24#63814—22no—
25#63814C414yes—
26#63814C414yes—
27D3×#208C2214yes—
28C2×D3×C3⋊C8C2212yes—
29#63649C2214yes—
30C3×#822C2212yes—
31C3×#822C2212yes—
32#63578C2214yes—
33#63577C2212yes—
34#63577C2212yes—
35C3×#568—31no—
36#5819—31no—
37C2×#948—31no—
38#5745—31no—
39#5745D311yescharacteristic
40C2×#901—31no—
41C2×C3×#108—31no—
42#5124—31no—
43#5124—31no—
44#5124—31no—
45#5124—31no—
46#5124—34no—
47#5124—61no—
48C2×#822—31no—
49C2×#822—34no—
50C2×#822D311yescharacteristic, complemented
51C2×#819—31no—
52#4893—34no—
53D3×#108—34no—
54C22×C32×C4C2311yescharacteristic
55C2×C3×#67Q812yes—
56C3×#235C2×C412yes—
57C3×#235C2×C412yes—
58C3×#235D412yes—
59C3×#235D412yes—
60C2×C3×D12Q811yescharacteristic
61C2×C3×C4×D3C2312yes—
62C2×C3×Dic6Q811yescharacteristic
63C32×M16—21no—
64C32×M16C2312yes—
65C2×C32×C8—21no—
66#3748—21no—
67#3748C2×C412yes—
68#3748C2×C412yes—
69#3748C2312yes—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)C2312yes—
72C3×#208—21no—
73C3×#208—21no—
74C3×#208C2312yes—
75C3×#208C2312yes—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8C2×C412yes—
79C2×C3×C3⋊C8C2×C412yes—
80C2×C3×C3⋊C8C2311yescharacteristic
81C2×C3×C3⋊C8C2311yescharacteristic
82C3×ΓL(1,𝔽25)—24no—
83C3×D3×C8—24no—
84#3711—24no—
85#3711C2×C418yes—
86D3×C3⋊C8—24no—
87D3×C3⋊C8C2×C418yes—
88#2916—91noSylow
89C2×C3×#41—31no—
90C2×#235C2×D311yescharacteristic
91C3×#131—62no—
92C3×#131—62no—
93C2×C3×M16—21no—
94C2×C3×M16—31no—
95C2×C3×M16—31no—
96C2×C3×M16—34no—
97C2×C3×M16C2×D311yescharacteristic
98C2×C3×M16C2×D311yescharacteristic
99C22×C3×C8—31no—
100#948—34no—
101#948—34no—
102#948—62no—
103#948—62no—
104C2×#208—31no—
105C2×#208—31no—
106C2×#208—32no—
107C2×#208—31no—
108C2×#208—31no—
109C2×#208—34no—
110C2×#208—61no—
111C2×#208—61no—
112C2×#208C2×D311yescharacteristic
113C2×#208C2×D311yescharacteristic
114C22×C3⋊C8—32no—
115C22×C3⋊C8C2×D311yescharacteristic
116#907—22no—
117#907—62no—
118D3×M16—34no—
119D3×M16C2×D314yes—
120#901—22no—
121#901—34no—
122#901—34no—
123#901—62no—
124C2×ΓL(1,𝔽25)—32no—
125C2×D3×C8—32no—
126C3×#108—32no—
127C3×#108—32no—
128#822—34no—
129#822—34no—
130#822—34no—
131#822—34no—
132#822—32no—
133#822—32no—
134#822—64no—
135#822C2×D312yes—
136#822C2×D312yes—
137#819—32no—
138#819—32no—
139C23×C32C2×Q811yescharacteristic
140C22×C3×D3C2×Q812yes—
141C2×C32×C4C22×C411yescharacteristic
142C2×C32×C4C22×C411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×Q811yescharacteristic
146C2×C32×C4C2411yescharacteristic
147C3×#67C4⋊C414yes—
148C3×#67C4⋊C414yes—
149C2×C3×Dic3C2×Q812yes—
150C3×D12C4⋊C412yes—
151C3×D12C4⋊C412yes—
152C3×C4×D3C22×C414yes—
153C3×C4×D3C2×D414yes—
154C3×Dic6C4⋊C412yes—
155C3×Dic6C4⋊C412yes—
156C32×C8—22no—
157C3⋊(C3⋊C8)—22no—
158C3⋊(C3⋊C8)C22×C414yes—
159C3×C3⋊C8—22no—
160C3×C3⋊C8—22no—
161C3×C3⋊C8C22×C412yes—
162C3×C3⋊C8C22×C412yes—
163#568—31no—
164#568—91no—
165C2×#131—91no—
166#430—94no—
167#430—91no—
168#430—91no—
169C2×#108—31no—
170C2×#108—94no—
171C2×#108—91no—
172C3×#41—32no—
173C3×#41—32no—
174C3×#41—32no—
175C3×#41—32no—
176C2×C3×Q8—31no—
177C2×C3×D4—32no—
178C2×C3×D4—31no—
179C22×C3×C4—21no—
180C22×C3×C4—32no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C2×#67Dic612yes—
184#235C4×D312yes—
185#235C4×D312yes—
186#235#6712yes—
187#235#6712yes—
188C2×D12Dic611yescharacteristic
189C2×C4×D3C22×D312yes—
190C2×Dic6Dic611yescharacteristic
191C3×M16—21no—
192C3×M16—21no—
193C3×M16—22no—
194C3×M16—32no—
195C3×M16—32no—
196C3×M16—41no—
197C3×M16—64no—
198C3×M16—61no—
199C3×M16—61no—
200C3×M16C22×D312yes—
201C3×M16C22×D312yes—
202C2×C3×C8—21no—
203C2×C3×C8—21no—
204C2×C3×C8—32no—
205C2×C3×C8—32no—
206C2×C3×C8—31no—
207C2×C3×C8—31no—
208C2×C3×C8—41no—
209C2×C3×C8—64no—
210C2×C3×C8—61no—
211C2×C3×C8—61no—
212#208—21no—
213#208—21no—
214#208—32no—
215#208—32no—
216#208—32no—
217#208—32no—
218#208—38no—
219#208—32no—
220#208—32no—
221#208—62no—
222#208—62no—
223#208—62no—
224#208—64no—
225#208—61no—
226#208—61no—
227#208—121no—
228#208C22×D312yes—
229#208C22×D312yes—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—21no—
232C2×C3⋊C8—32no—
233C2×C3⋊C8—32no—
234C2×C3⋊C8—38no—
235C2×C3⋊C8—62no—
236C2×C3⋊C8—64no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—121no—
240C2×C3⋊C8C4×D312yes—
241C2×C3⋊C8C4×D312yes—
242C2×C3⋊C8C22×D311yescharacteristic
243C2×C3⋊C8C22×D311yescharacteristic
244ΓL(1,𝔽25)—24no—
245ΓL(1,𝔽25)—38no—
246ΓL(1,𝔽25)—64no—
247D3×C8—24no—
248D3×C8—38no—
249D3×C8—64no—
250C22×C32—41no—
251C22×C32C2×C4⋊C411yescharacteristic
252C22×C32C2×C4⋊C411yescharacteristic
253C22×C32C22×Q811yescharacteristic
254C2×C3×D3—42no—
255C2×C3×D3C2×C4⋊C414yes—
256C32×C4C2×C4⋊C411yescharacteristic
257C32×C4C2×C4⋊C411yescharacteristic
258C32×C4C23×C411yescharacteristic
259C32×C4C22×D411yescharacteristic
260C3×Dic3C2×C4⋊C414yes—
261C2×#41—31no—
262#131—62no—
263#131—62no—
264#131—94no—
265#131—94no—
266#131—182no—
267#131—182no—
268C2×M16—31no—
269C2×M16—31no—
270C2×M16—34no—
271C2×M16—92no—
272C2×M16—91no—
273C2×M16—94no—
274C2×M16—91no—
275C2×M16D3211yescharacteristic
276C22×C8—31no—
277C22×C8—92no—
278#108—32no—
279#108—32no—
280#108—92no—
281#108—92no—
282#108—94no—
283#108—94no—
284C23×C3—21no—
285C23×C3—32no—
286C23×C3C2×Dic611yescharacteristic
287C23×C3D3×Q811yescharacteristic
288C22×D3C2×Dic612yes—
289C3×Q8—32no—
290C3×Q8—32no—
291C3×D4—34no—
292C3×D4—34no—
293C3×D4—32no—
294C3×D4—32no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—32no—
302C2×C3×C4—34no—
303C2×C3×C4—34no—
304C2×C3×C4C2×Dic611yescharacteristic
305C2×C3×C4C2×C4×D311yescharacteristic
306C2×C3×C4C2×C4×D311yescharacteristic
307C2×C3×C4C2×C4×D311yescharacteristic
308C2×C3×C4C2×C4×D311yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4D3×Q811yescharacteristic
312C2×C3×C4C2×#6711yescharacteristic
313C2×C3×C4C2×#6711yescharacteristic
314C2×C3×C4C23×D311yescharacteristic
315C2×C3×C4C23×D311yescharacteristic
316#67Dic3⋊C414yes—
317#67Dic3⋊C414yes—
318C2×Dic3C2×Dic612yes—
319D12Dic3⋊C412yes—
320D12Dic3⋊C412yes—
321C4×D3C2×C4×D314yes—
322C4×D3C2×#6714yes—
323Dic6Dic3⋊C412yes—
324Dic6Dic3⋊C412yes—
325C3×C8—22no—
326C3×C8—22no—
327C3×C8—32no—
328C3×C8—32no—
329C3×C8—42no—
330C3×C8—62no—
331C3×C8—62no—
332C3⋊C8—22no—
333C3⋊C8—22no—
334C3⋊C8—34no—
335C3⋊C8—34no—
336C3⋊C8—64no—
337C3⋊C8—62no—
338C3⋊C8—62no—
339C3⋊C8—122no—
340C3⋊C8C2×C4×D312yes—
341C3⋊C8C2×C4×D312yes—
342C2×C32—21no—
343C2×C32—21no—
344C2×C32—21no—
345C2×C32C22×C4⋊C411yescharacteristic
346C3×D3—24no—
347#41—32no—
348#41—32no—
349#41—32no—
350#41—32no—
351C2×Q8—31no—
352C2×D4—32no—
353C2×D4—31no—
354C22×C4—32no—
355C22×C4C2×D3211yescharacteristic
356M16—21no—
357M16—32no—
358M16—32no—
359M16—64no—
360M16—61no—
361M16—61no—
362M16—98no—
363M16—92no—
364M16—92no—
365M16—92no—
366M16—184no—
367M16—181no—
368M16C2×D3212yes—
369C2×C8—21no—
370C2×C8—31no—
371C2×C8—31no—
372C2×C8—32no—
373C2×C8—32no—
374C2×C8—64no—
375C2×C8—61no—
376C2×C8—61no—
377C2×C8—98no—
378C2×C8—92no—
379C2×C8—184no—
380C2×C8—181no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—34no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—81no—
388C22×C3—122no—
389C22×C3D3×C4⋊C411yescharacteristic
390C22×C3D3×C4⋊C411yescharacteristic
391C22×C3C2×Dic3⋊C411yescharacteristic
392C22×C3C2×Dic3⋊C411yescharacteristic
393C22×C3C22×Dic611yescharacteristic
394C22×C3C2×D3×Q811yescharacteristic
395C2×D3—42no—
396C2×D3C2×Dic3⋊C414yes—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—34no—
402C3×C4D3×C4⋊C411yescharacteristic
403C3×C4D3×C4⋊C411yescharacteristic
404C3×C4C2×Dic3⋊C411yescharacteristic
405C3×C4C2×Dic3⋊C411yescharacteristic
406C3×C4C22×C4×D311yescharacteristic
407C3×C4C22×C4×D311yescharacteristic
408C3×C4C2×D3×D411yescharacteristic
409C3×C4C22×#6711yescharacteristic
410Dic3C2×Dic3⋊C414yes—
411C32#291611yescharacteristic, complemented, Sylow
412C23—32no—
413C23D3×Dic611yescharacteristic
414Q8—32no—
415Q8—32no—
416D4—34no—
417D4—34no—
418D4—32no—
419D4—32no—
420C2×C4—32no—
421C2×C4—34no—
422C2×C4—34no—
423C2×C4D3×Dic611yescharacteristic
424C2×C4C4×D3211yescharacteristic
425C2×C4C4×D3211yescharacteristic
426C2×C4D3×#6711yescharacteristic
427C2×C4D3×#6711yescharacteristic
428C2×C4C22×D3211yescharacteristic
429C8—22no—
430C8—32no—
431C8—32no—
432C8—62no—
433C8—62no—
434C8—94no—
435C8—182no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—41no—
444C2×C3—41no—
445C2×C3—41no—
446C2×C3—64no—
447C2×C3C2×D3×C4⋊C411yescharacteristic
448C2×C3C22×Dic3⋊C411yescharacteristic
449D3—24no—
450C22—34no—
451C22—41no—
452C22—122no—
453C22D3×Dic3⋊C411yescharacteristic
454C22D3×Dic3⋊C411yescharacteristic
455C22C2×D3×Dic611yescharacteristic
456C4—34no—
457C4D3×Dic3⋊C411yescharacteristic
458C4D3×Dic3⋊C411yescharacteristic
459C4C2×C4×D3211yescharacteristic
460C4C2×D3×#6711yescharacteristic
461C3—21no—
462C3#7925211yescharacteristic, complemented
463C3#8381011yescharacteristic, complemented
464C2—21no—
465C2—21no—
466C2—21no—
467C2—64no—
468C2C2×D3×Dic3⋊C411yescharacteristic
subgroupG/H
centerC4C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC2×C32C22×C4⋊C4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2916
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #10592823C2semidirect
5. C2×C3×#822C2semidirect
6. #10591143C2semidirect
7. C2×#63577C2semidirect
8. #10590973C2semidirect
9. D3×#822C2semidirect
50. C2×#822D3semidirect
411. C32#2916semidirect
462. C3#79252semidirect
463. C3#83810semidirect

Maximal subgroups

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

subgroupindex
C3×#57452
#105947762
C2×#638142
#105928232
C2×C3×#8222
#105911432
C2×#635772
#105909732
D3×#8222
#838103
#792523