Finite Group Databasebeta

← #11904575

Subgroups — #11904575

Order 1152.

3469 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64364C211yesmaximal, characteristic, complemented
2C22×C3×#239C211yesmaximal, characteristic, complemented
3C3×#5812C211yesmaximal, characteristic, complemented
4#10595414C218yesmaximal, complemented
5#10595410C218yesmaximal, complemented
6#10595042C216yesmaximal, complemented
7#10595023C216yesmaximal, complemented
8#87274—31nomaximal
9#85874—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11#64364—28no—
12C2×#3832C2214yescomplemented
13C2×Q8×C3⋊D3C2214yescomplemented
14C2×#3828C2216yes—
15C2×C3×#239—28no—
16C2×C3×#239C2218yes—
17C22×C3×D12C2213yes—
18C22×C3×C4×D3C2213yes—
19C3×Q8×Dic3C2218yescomplemented
20C3×#926C2216yes—
21#63977C22112yes—
22#63966C2214yes—
23#63916C22124yescomplemented
24#63911C22112yescomplemented
25#63909C22112yescomplemented
26C4×#626C22124yescomplemented
27#63860C22112yescomplemented
28#63857C22112yescomplemented
29C22×C3×#41—31no—
30C2×#1007—31no—
31C2×#1007—31no—
32C2×#1007—61no—
33C22×#239D311yescharacteristic, complemented
34C3×#519—31no—
35#5834—38no—
36#5831—38no—
37#5812D311yescharacteristic, complemented
38#5805—36no—
39#5791—36no—
40#5577—38no—
41#5576—38no—
42#5525—36no—
43#5524—36no—
44C23×C3×D3C2313yes—
45C2×C32×Q8D418yescomplemented
46C2×C32×Q8C2314yes—
47C22×C32×C4C2313yes—
48C2×#638C2314yes—
49#3832—216no—
50Q8×C3⋊D3—216no—
51#3828—224no—
52C2×C4⋊(C3⋊D3)C2316yes—
53C2×C4×C3⋊D3C23112yes—
54C2×#634C2316yes—
55C22×C3×Dic3C2311yescharacteristic
56C3×#239—232no—
57C2×C3×D12—212no—
58C2×C3×D12C23112yes—
59C2×C3×C4×D3—212no—
60C2×C3×C4×D3C23112yes—
61C2×#626C23124yes—
62C3×#217C2314yes—
63C3×C4⋊Dic3C23112yes—
64C3×C4×Dic3C23112yes—
65Dic3⋊Dic3C2318yes—
66#3722C2318yes—
67(C2×D3)⋊Dic3C23124yes—
68#3487—91noSylow
69C2×C3×#41—38no—
70C2×C3×#41—68no—
71C22×C3×Q8—21no—
72C22×C3×Q8C2×D311yescharacteristic
73C22×C3×Q8C2×D311yescharacteristic
74C22×C3×D4—33no—
75C23×C3×C4—33no—
76#1007—616no—
77#1007—68no—
78#1007—68no—
79C2×#239—28no—
80C2×#239—34no—
81C2×#239—34no—
82C2×#239—64no—
83C2×#239C2×D318yes—
84C2×D3×Q8—34no—
85C2×D3×Q8—34no—
86C2×D3×Q8—64no—
87C2×#235—36no—
88C2×#235—36no—
89C2×#235—66no—
90C22×D12C2×D313yes—
91C22×C4×D3C2×D313yes—
92C3×C4×Q8—38no—
93C3×#117—36no—
94#953—312no—
95Q8×Dic3C2×D318yescomplemented
96#940—312no—
97#938—324no—
98#936—312no—
99#930—312no—
100#929—34no—
101C4×#67—324no—
102#926C2×D316yes—
103#924—312no—
104#897—312no—
105#895—324no—
106#895—312no—
107#886—34no—
108#882—312no—
109#875—312no—
110#874—312no—
111C4×D12—324no—
112C23×C32C2411yescharacteristic
113C22×C3⋊D3C2414yes—
114C22×C3×D3—26no—
115C22×C3×D3—46no—
116C22×C3×D3C2416yes—
117C32×Q8C2×D4116yes—
118C2×C32×C4C2×D4112yes—
119C2×C32×C4C2416yes—
120#638—28no—
121C2×C3⋊Dic3C2414yes—
122C4⋊(C3⋊D3)—212no—
123C4×C3⋊D3—224no—
124#634—212no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3C2418yes—
127C2×C3×Dic3C2412yes—
128C3×D12—224no—
129C3×C4×D3—224no—
130#626—424no—
131C2×2−1+4—91no—
132C22×#41—31no—
133#550—98no—
134#548—98no—
135#535—96no—
136#525—96no—
137#519—31no—
138C24×C3—33no—
139C23×D3C22×D313yes—
140C3×#41—632no—
141C2×C3×Q8—28no—
142C2×C3×Q8—24no—
143C2×C3×Q8D1218yescomplemented
144C2×C3×Q8#6718yescomplemented
145C2×C3×Q8C22×D314yes—
146C2×C3×Q8C22×D314yes—
147C2×C3×D4—312no—
148C2×C3×D4—612no—
149C22×C3×C4—23no—
150C22×C3×C4—31no—
151C22×C3×C4—312no—
152C22×C3×C4—612no—
153C22×C3×C4C22×D313yes—
154C22×C3×C4C22×D313yes—
155C2×#67—34no—
156C2×#67—34no—
157C2×#67—324no—
158C2×#67—64no—
159C22×Dic3C22×D311yescharacteristic
160#239—232no—
161#239—632no—
162#239—616no—
163#239—616no—
164D3×Q8—632no—
165D3×Q8—616no—
166D3×Q8—616no—
167#235—648no—
168#235—624no—
169#235—624no—
170C2×D12—212no—
171C2×D12—36no—
172C2×D12—36no—
173C2×D12—324no—
174C2×D12—66no—
175C2×D12C22×D3112yes—
176C2×C4×D3—212no—
177C2×C4×D3—312no—
178C2×C4×D3—312no—
179C2×C4×D3—612no—
180C2×C4×D3C22×D3112yes—
181C2×Dic6—36no—
182C2×Dic6—36no—
183C2×Dic6—66no—
184C3×C4⋊C4—312no—
185C3×C22⋊C4—34no—
186C3×C42—312no—
187#217—324no—
188#217C22×D314yes—
189(C2×D3)⋊C4—324no—
190(C2×D3)⋊C4—38no—
191(C2×D3)⋊C4—38no—
192C4⋊Dic3—38no—
193C4⋊Dic3C22×D3112yes—
194Dic3⋊C4—38no—
195C4×Dic3C22×D3112yes—
196C22×C32—22no—
197C22×C32C22×D412yes—
198C22×C32C2511yescharacteristic
199C2×C3⋊D3—24no—
200C2×C3⋊D3—28no—
201C2×C3×D3—26no—
202C2×C3×D3—212no—
203C2×C3×D3—412no—
204C32×C4C22×D4112yes—
205C3⋊Dic3—24no—
206C3×Dic3—22no—
207C3×Dic3—28no—
2082−1+4—188no—
209C2×#41—38no—
210C2×#41—68no—
211C2×#41—94no—
212C2×#41—96no—
213C22×Q8—94no—
214C22×Q8D3211yescharacteristic
215C22×D4—33no—
216C23×C4—33no—
217#127—912no—
218#124—912no—
219#123—94no—
220C22⋊Q8—912no—
221#121—912no—
222#121—924no—
223#120—912no—
224C4×Q8—38no—
225C4×D4—924no—
226#117—36no—
227C23×C3—21no—
228C23×C3—36no—
229C23×C3—66no—
230C23×C3—126no—
231C23×C3C23×D311yescharacteristic
232C23×C3C23×D311yescharacteristic
233C22×D3—26no—
234C22×D3—34no—
235C22×D3—34no—
236C22×D3—46no—
237C22×D3—64no—
238C22×D3C23×D316yes—
239C3×Q8—216no—
240C3×Q8C2×D12116yes—
241C3×Q8C2×#67116yes—
242C3×D4—624no—
243C2×C3×C4—26no—
244C2×C3×C4—212no—
245C2×C3×C4—32no—
246C2×C3×C4—38no—
247C2×C3×C4—62no—
248C2×C3×C4—624no—
249C2×C3×C4C2×D12112yes—
250C2×C3×C4C2×#67112yes—
251C2×C3×C4C23×D316yes—
252C2×C3×C4C23×D316yes—
253#67—616no—
254#67—68no—
255#67—68no—
256#67—1224no—
257C2×Dic3—22no—
258C2×Dic3—34no—
259C2×Dic3—34no—
260C2×Dic3—64no—
261C2×Dic3C23×D318yes—
262C2×Dic3C23×D312yes—
263D12—224no—
264D12—624no—
265D12—612no—
266D12—612no—
267D12—1224no—
268C4×D3—224no—
269C4×D3—648no—
270C4×D3—624no—
271C4×D3—624no—
272Dic6—624no—
273Dic6—612no—
274Dic6—612no—
275C2×C32—22no—
276C2×C32C23×D411yescharacteristic
277C2×C32#58512yes—
278C3⋊D3—44no—
279C3×D3—46no—
280C24—33no—
281#41—632no—
282#41—1816no—
283#41—1824no—
284C2×Q8—96no—
285C2×Q8—1816no—
286C2×Q8#62618yescomplemented
287C2×Q8C2×D3214yes—
288C2×D4—312no—
289C2×D4—612no—
290C2×D4—924no—
291C2×D4—94no—
292C2×D4—96no—
293C22×C4—31no—
294C22×C4—312no—
295C22×C4—612no—
296C22×C4—912no—
297C22×C4C2×D3213yes—
298C4⋊C4—312no—
299C4⋊C4—98no—
300C22⋊C4—34no—
301C22⋊C4—98no—
302C22⋊C4—924no—
303C42—312no—
304C22×C3—22no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—21no—
308C22×C3—42no—
309C22×C3—66no—
310C22×C3—612no—
311C22×C3—1212no—
312C22×C3C22×D1212yes—
313C22×C3C22×#6712yes—
314C22×C3C24×D311yescharacteristic
315C22×C3C24×D311yescharacteristic
316C2×D3—212no—
317C2×D3—26no—
318C2×D3—412no—
319C2×D3—68no—
320C2×D3—64no—
321C2×D3—68no—
322C2×D3—68no—
323C2×D3—64no—
324C2×D3—128no—
325C3×C4—212no—
326C3×C4—62no—
327C3×C4—68no—
328C3×C4C22×D12112yes—
329C3×C4C22×#67112yes—
330Dic3—28no—
331Dic3—22no—
332Dic3—68no—
333Dic3—64no—
334Dic3—64no—
335C32#348711yescharacteristic, complemented, Sylow
336C23—36no—
337C23—66no—
338C23—94no—
339C23—126no—
340C23C22×D3211yescharacteristic
341Q8—1812no—
342Q8C2×#626116yes—
343D4—624no—
344D4—188no—
345D4—1812no—
346D4—3624no—
347C2×C4—38no—
348C2×C4—32no—
349C2×C4—62no—
350C2×C4—624no—
351C2×C4—94no—
352C2×C4—1824no—
353C2×C4C2×#626112yes—
354C2×C4C22×D3216yes—
355C2×C3—22no—
356C2×C3—22no—
357C2×C3—22no—
358C2×C3—21no—
359C2×C3—42no—
360C2×C3—126no—
361C2×C3C23×D1211yescharacteristic
362C2×C3#596412yes—
363C2×C3#596812yes—
364C2×C3C23×#6711yescharacteristic
365D3—46no—
366D3—128no—
367D3—124no—
368D3—124no—
369C22—22no—
370C22—612no—
371C22—66no—
372C22—1212no—
373C22—188no—
374C22—184no—
375C22C22×#62612yes—
376C22C23×D3211yescharacteristic
377C4—68no—
378C4—62no—
379C4—184no—
380C4C22×#626112yes—
381C3—21no—
382C3#8587411yescharacteristic, complemented
383C3#8727411yescharacteristic, complemented
384C2—22no—
385C2—126no—
386C2—364no—
387C2#1059668812yes—
388C2C23×#62611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32#3487
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64364C2semidirect
2. C22×C3×#239C2semidirect
3. C3×#5812C2semidirect
4. #10595414C2semidirect
5. #10595410C2semidirect
6. #10595042C2semidirect
7. #10595023C2semidirect
12. C2×#3832C22semidirect
13. C2×Q8×C3⋊D3C22semidirect
19. C3×Q8×Dic3C22semidirect
23. #63916C22semidirect
24. #63911C22semidirect
25. #63909C22semidirect
26. C4×#626C22semidirect
27. #63860C22semidirect
28. #63857C22semidirect
33. C22×#239D3semidirect
37. #5812D3semidirect
45. C2×C32×Q8D4semidirect
95. Q8×Dic3C2×D3semidirect
143. C2×C3×Q8D12semidirect
144. C2×C3×Q8#67semidirect
286. C2×Q8#626semidirect
335. C32#3487semidirect
382. C3#85874semidirect
383. C3#87274semidirect

Maximal subgroups

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

subgroupindex
C2×#643642
C22×C3×#2392
C3×#58122
#105954142
#105954102
#105950422
#105950232
#872743
#858743