Finite Group Databasebeta

← #11858204

Subgroups — #11858204

Order 1152.

1881 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596756C211yesmaximal, characteristic
2C3×Dic3×#41C211yesmaximal, characteristic, complemented
3C3×#5819C211yesmaximal, characteristic, complemented
4#10591113C216yesmaximal, complemented
5C2×#63570C216yesmaximal, complemented
6#83817—31nomaximal
7#82536—31nomaximal
8C2×C32×#41C2211yescharacteristic
9#64367C414yescomplemented
10#64366C414yescomplemented
11#41×C3⋊D3—24no—
12#64364—21no—
13#64361—23no—
14C2×#3828C2216yes—
15C3×#948—24no—
16C3×Q8×Dic3—21no—
17C3×D4×Dic3—23no—
18C3×#926C2213yescomplemented
19C2×C3×C4×Dic3C2213yescomplemented
20C2×C3×#208C2216yescomplemented
21#63570C2214yescomplemented
22#63570C22112yescomplemented
23#5964—31no—
24#5964—31no—
25#5964—61no—
26C3×#568—31no—
27C3×C4×#41—31no—
28Dic3×#41D311yescharacteristic, complemented
29#5819D311yescharacteristic, complemented
30#5139—36no—
31C2×#825—36no—
32#5005—36no—
33C2×#805—36no—
34C32×#41C2×C414yes—
35C32×#41D414yes—
36C2×C32×Q8D411yescharacteristic
37C2×C32×D4D413yes—
38C22×C32×C4C2313yes—
39C2×#638—26no—
40#3832—24no—
41Q8×C3⋊D3—24no—
42#3830—212no—
43D4×C3⋊D3—212no—
44#3828—26no—
45#3828—26no—
46#3828C2×C4112yescomplemented
47#3828C2314yes—
48C2×C4⋊(C3⋊D3)C2×C416yescomplemented
49C2×C4×C3⋊D3—26no—
50C2×#634C2×C416yescomplemented
51C22×C3×Dic3—23no—
52C3×#217—23no—
53C3×C4⋊Dic3—23no—
54C3×C4×Dic3—23no—
55C3×C4×Dic3C2311yescharacteristic
56C3×C4×Dic3C2313yes—
57C3×#208—26no—
58C3×#208C2314yes—
59C2×C3×C3⋊C8—26no—
60#2901—91noSylow
61C2×C3×#41—21no—
62C2×C3×#41C2×D311yescharacteristic
63C2×C3×#41C2×D311yescharacteristic
64#1010—34no—
65#1010—34no—
66#1010—64no—
67#1009—34no—
68#1009—34no—
69#1009—64no—
70D3×#41—68no—
71D3×#41—64no—
72D3×#41—64no—
73#1007—62no—
74#1007—61no—
75#1007—61no—
76#1004—66no—
77#1004—63no—
78#1004—63no—
79C2×#235—36no—
80C2×#235—36no—
81C2×#235—66no—
82C3×#131—64no—
83C2×C3×M16—36no—
84C3×C4×Q8—61no—
85C3×C4×D4—63no—
86C3×#117—33no—
87C2×C3×C42—33no—
88#948—24no—
89Q8×Dic3—21no—
90D4×Dic3—23no—
91#926C2×D313yescomplemented
92C2×C4×Dic3C2×D313yescomplemented
93C2×#208C2×D316yescomplemented
94#825—34no—
95#825—312no—
96#805—34no—
97#805—312no—
98C23×C32C2×D413yes—
99C22×C3⋊D3—26no—
100C32×Q8C22⋊C414yes—
101C32×D4C22⋊C4112yes—
102C2×C32×C4C22×C416yes—
103C2×C32×C4C2×D413yes—
104C2×C32×C4C2×D416yes—
105C2×C32×C4C2411yescharacteristic
106#638—212no—
107#638—24no—
108C2×C3⋊Dic3—26no—
109C4⋊(C3⋊D3)—26no—
110C4⋊(C3⋊D3)C22×C414yes—
111C4×C3⋊D3—212no—
112C4×C3⋊D3—24no—
113#634—26no—
114#634C22×C414yes—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—23no—
117C2×C3×Dic3—46no—
118C3×C3⋊C8—24no—
119#585—91no—
120#568—31no—
121C4×#41—31no—
122#421—96no—
123C2×#104—96no—
124C3×#41—24no—
125C3×#41—24no—
126C3×#41C4×D314yes—
127C3×#41C4×D314yes—
128C3×#41D1214yes—
129C3×#41#6714yes—
130C2×C3×Q8—21no—
131C2×C3×Q8D1211yescharacteristic
132C2×C3×Q8#6711yescharacteristic
133C2×C3×D4—23no—
134C2×C3×D4D1213yes—
135C2×C3×D4#6713yes—
136C22×C3×C4—23no—
137C22×C3×C4—63no—
138C22×C3×C4C22×D313yes—
139C22×C3×C4C22×D313yes—
140C2×#67—612no—
141C2×#67—66no—
142C2×#67—66no—
143C22×Dic3—23no—
144#239—68no—
145#239—64no—
146#239—64no—
147D3×Q8—68no—
148D3×Q8—64no—
149D3×Q8—64no—
150#237—624no—
151#237—612no—
152#237—612no—
153D3×D4—624no—
154D3×D4—612no—
155D3×D4—612no—
156#235—312no—
157#235—312no—
158#235—34no—
159#235—34no—
160#235—64no—
161#235—612no—
162#235—612no—
163#235—612no—
164#235—66no—
165#235—66no—
166#235—66no—
167#235—66no—
168C2×D12—36no—
169C2×D12—36no—
170C2×D12—66no—
171C2×C4×D3—612no—
172C2×C4×D3—66no—
173C2×C4×D3—66no—
174C2×Dic6—36no—
175C2×Dic6—36no—
176C2×Dic6—66no—
177C3×M16—34no—
178C3×M16—66no—
179C2×C3×C8—66no—
180C3×C4⋊C4—63no—
181C3×C22⋊C4—63no—
182C3×C42—31no—
183C3×C42—33no—
184C3×C42—63no—
185#217—23no—
186C4⋊Dic3—23no—
187C4×Dic3—23no—
188C4×Dic3C22×D311yescharacteristic
189C4×Dic3C22×D313yes—
190#208—26no—
191#208C22×D314yes—
192C2×C3⋊C8—26no—
193C22×C32—43no—
194C22×C32C2×C22⋊C416yes—
195C22×C32C22×D411yescharacteristic
196C2×C3⋊D3—24no—
197C2×C3⋊D3—86no—
198C32×C4C2×C22⋊C416yes—
199C32×C4C23×C411yescharacteristic
200C32×C4C22×D411yescharacteristic
201C3⋊Dic3—24no—
202C3×Dic3—22no—
203C3×Dic3—43no—
2042−1+4—94no—
2052−1+4—181no—
206H(5,𝔽2)—94no—
207H(5,𝔽2)—183no—
208C2×#41—96no—
209C2×#41—184no—
210C2×#41D3211yescharacteristic
211#131—64no—
212C2×M16—36no—
213C4×Q8—61no—
214C4×D4—63no—
215#117—33no—
216C2×C42—33no—
217#104—94no—
218#104—912no—
219C23×C3—23no—
220C23×C3C2×D1213yes—
221C23×C3C2×#6713yes—
222C22×D3—612no—
223C22×D3—66no—
224C22×D3—66no—
225C3×Q8—24no—
226C3×Q8(C2×D3)⋊C414yes—
227C3×Q8(C2×D3)⋊C414yes—
228C3×D4—212no—
229C3×D4(C2×D3)⋊C4112yes—
230C3×D4(C2×D3)⋊C4112yes—
231C2×C3×C4—21no—
232C2×C3×C4—26no—
233C2×C3×C4—26no—
234C2×C3×C4—23no—
235C2×C3×C4—61no—
236C2×C3×C4—63no—
237C2×C3×C4—126no—
238C2×C3×C4C2×C4×D316yes—
239C2×C3×C4C2×C4×D316yes—
240C2×C3×C4C2×D1213yes—
241C2×C3×C4C2×D1216yes—
242C2×C3×C4C2×#6713yes—
243C2×C3×C4C2×#6716yes—
244C2×C3×C4C23×D311yescharacteristic
245C2×C3×C4C23×D311yescharacteristic
246#67—68no—
247#67—624no—
248#67—612no—
249#67—612no—
250#67—64no—
251#67—64no—
252C2×Dic3—21no—
253C2×Dic3—23no—
254C2×Dic3—46no—
255C2×Dic3—612no—
256C2×Dic3—66no—
257C2×Dic3—66no—
258D12—34no—
259D12—34no—
260D12—64no—
261D12—612no—
262D12—66no—
263D12—66no—
264C4×D3—68no—
265C4×D3—624no—
266C4×D3—612no—
267C4×D3—612no—
268C4×D3—64no—
269C4×D3—64no—
270Dic6—34no—
271Dic6—34no—
272Dic6—64no—
273Dic6—612no—
274Dic6—66no—
275Dic6—66no—
276C3×C8—64no—
277C3⋊C8—24no—
278C2×C32—21no—
279C2×C32—26no—
280C2×C32C22×C22⋊C411yescharacteristic
281C3⋊D3—44no—
282#41—94no—
283#41—912no—
284#41—184no—
285#41—1812no—
286#41—186no—
287#41—186no—
288#41#62414yes—
289#41#62614yes—
290C2×Q8—96no—
291C2×Q8—184no—
292C2×Q8#62611yescharacteristic
293C2×D4—96no—
294C2×D4—186no—
295C2×D4—1812no—
296C2×D4#62613yes—
297C22×C4—63no—
298C22×C4—186no—
299C22×C4C2×D3213yes—
300M16—34no—
301M16—66no—
302C2×C8—66no—
303C4⋊C4—63no—
304C22⋊C4—63no—
305C42—31no—
306C42—33no—
307C42—63no—
308C22×C3—21no—
309C22×C3—26no—
310C22×C3—43no—
311C22×C3—43no—
312C22×C3—83no—
313C22×C3C2×(C2×D3)⋊C416yes—
314C22×C3C2×(C2×D3)⋊C416yes—
315C22×C3C22×D1211yescharacteristic
316C22×C3C22×#6711yescharacteristic
317C2×D3—68no—
318C2×D3—64no—
319C2×D3—64no—
320C2×D3—246no—
321C2×D3—246no—
322C2×D3—2412no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—26no—
326C3×C4—62no—
327C3×C4—123no—
328C3×C4C2×(C2×D3)⋊C416yes—
329C3×C4C2×(C2×D3)⋊C416yes—
330C3×C4C22×C4×D311yescharacteristic
331C3×C4C22×C4×D311yescharacteristic
332C3×C4C22×D1211yescharacteristic
333C3×C4C22×#6711yescharacteristic
334Dic3—22no—
335Dic3—43no—
336Dic3—68no—
337Dic3—64no—
338Dic3—64no—
339C32#290111yescharacteristic, complemented, Sylow
340C23—186no—
341C23C2×#62613yes—
342Q8—94no—
343Q8—186no—
344Q8#372214yes—
345D4—94no—
346D4—184no—
347D4—1812no—
348D4—186no—
349D4#3722112yes—
350C2×C4—61no—
351C2×C4—63no—
352C2×C4—126no—
353C2×C4—186no—
354C2×C4—184no—
355C2×C4—1812no—
356C2×C4C2×#62416yes—
357C2×C4C2×#62616yes—
358C2×C4C2×#62613yes—
359C2×C4C22×D3211yescharacteristic
360C8—64no—
361C2×C3—21no—
362C2×C3—26no—
363C2×C3—21no—
364C2×C3—26no—
365C2×C3—21no—
366C2×C3—46no—
367C2×C3—41no—
368C2×C3C22×(C2×D3)⋊C411yescharacteristic
369C2×C3C22×(C2×D3)⋊C411yescharacteristic
370D3—128no—
371D3—124no—
372D3—124no—
373C22—43no—
374C22—184no—
375C22—726no—
376C22C2×#372216yes—
377C22C22×#62611yescharacteristic
378C4—62no—
379C4—123no—
380C4—184no—
381C4C2×#372216yes—
382C4C22×#62411yescharacteristic
383C4C22×#62611yescharacteristic
384C3—21no—
385C3#8253611yescharacteristic, complemented
386C3#8381711yescharacteristic, complemented
387C2—21no—
388C2—26no—
389C2—364no—
390C2C22×#372211yescharacteristic
subgroupG/H
centerC4C22×#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C22×C22⋊C4
prime radical#10596756C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2901
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×Dic3×#41C2semidirect
3. C3×#5819C2semidirect
4. #10591113C2semidirect
5. C2×#63570C2semidirect
9. #64367C4semidirect
10. #64366C4semidirect
18. C3×#926C22semidirect
19. C2×C3×C4×Dic3C22semidirect
20. C2×C3×#208C22semidirect
21. #63570C22semidirect
22. #63570C22semidirect
28. Dic3×#41D3semidirect
29. #5819D3semidirect
46. #3828C2×C4semidirect
48. C2×C4⋊(C3⋊D3)C2×C4semidirect
50. C2×#634C2×C4semidirect
91. #926C2×D3semidirect
92. C2×C4×Dic3C2×D3semidirect
93. C2×#208C2×D3semidirect
339. C32#2901semidirect
385. C3#82536semidirect
386. C3#83817semidirect

Maximal subgroups

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

subgroupindex
#105967562
C3×Dic3×#412
C3×#58192
#105911132
C2×#635702
#838173
#825363