Finite Group Databasebeta

← #11904513

Subgroups — #11904513

Order 1152.

3381 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64364C211yesmaximal, characteristic, complemented
2C22×C3×D3×Q8C211yesmaximal, characteristic, complemented
3C3×#5812C211yesmaximal, characteristic, complemented
4Q8×#626C218yesmaximal, complemented
5#10595342C218yesmaximal, complemented
6#10595023C216yesmaximal, complemented
7#10594866C216yesmaximal, complemented
8#87251—31nomaximal
9#85881—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11#64364—28no—
12C2×#3832C2214yescomplemented
13C2×Q8×C3⋊D3C2214yescomplemented
14C2×#3828C2216yes—
15C2×C3×D3×Q8—28no—
16C2×C3×D3×Q8C2218yes—
17C22×C3×C4×D3C2213yes—
18C22×C3×Dic6C2213yes—
19C3×Q8×Dic3C2218yescomplemented
20C3×#926C2216yes—
21#63977C2214yes—
22#63966C22112yes—
23#63909C22112yes—
24C4×#626C22124yes—
25#63871C22124yescomplemented
26#63866C22112yescomplemented
27#63864C22112yescomplemented
28#63857C22112yes—
29C23×C3×Q8—31no—
30C2×#1007—31no—
31C2×#1007—31no—
32C2×#1007—61no—
33C22×D3×Q8D311yescharacteristic, complemented
34C3×#519—31no—
35#5817—38no—
36#5816—36no—
37Q8×#67—38no—
38#5812D311yescharacteristic, complemented
39#5791—36no—
40#5576—38no—
41Q8×D12—38no—
42#5526—36no—
43#5524—36no—
44C23×C3×D3C2311yescharacteristic
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×Dic3C2313yes—
56C3×D3×Q8—232no—
57C2×C3×C4×D3—212no—
58C2×C3×C4×D3C23112yes—
59C2×C3×Dic6—212no—
60C2×C3×Dic6C23112yes—
61C2×#626C2318yes—
62C3×#217C2314yes—
63C3×C4⋊Dic3C23112yes—
64C3×C4×Dic3C23112yes—
65Dic3⋊Dic3C23124yes—
66#3722C23124yes—
67(C2×D3)⋊Dic3C2318yes—
68#3486—91noSylow
69C22×C3×Q8—21no—
70C22×C3×Q8—38no—
71C22×C3×Q8—33no—
72C22×C3×Q8—68no—
73C22×C3×Q8C2×D311yescharacteristic
74C22×C3×Q8C2×D311yescharacteristic
75C23×C3×C4—33no—
76#1007—616no—
77#1007—68no—
78#1007—68no—
79C2×#239—34no—
80C2×#239—34no—
81C2×#239—64no—
82C2×D3×Q8—28no—
83C2×D3×Q8—34no—
84C2×D3×Q8—34no—
85C2×D3×Q8—64no—
86C2×D3×Q8C2×D318yes—
87C2×#235—36no—
88C2×#235—36no—
89C2×#235—66no—
90C22×C4×D3C2×D313yes—
91C22×Dic6C2×D313yes—
92C3×C4×Q8—38no—
93C3×#117—36no—
94#953—34no—
95#947—312no—
96#946—324no—
97Q8×Dic3C2×D318yescomplemented
98#944—312no—
99#930—312no—
100#929—312no—
101C4×#67—324no—
102#926C2×D316yes—
103#924—312no—
104#897—312no—
105#897—324no—
106#895—312no—
107#886—312no—
108#882—34no—
109#875—312no—
110C4×D12—324no—
111#869—312no—
112C23×C32C2411yescharacteristic
113C22×C3⋊D3C2414yes—
114C22×C3×D3—22no—
115C22×C3×D3—24no—
116C22×C3×D3C2412yes—
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—26no—
126C2×C3×Dic3C2418yes—
127C2×C3×Dic3C2416yes—
128C3×C4×D3—224no—
129C3×Dic6—224no—
130#626—216no—
131C2×2−1+4—91no—
132C23×Q8—31no—
133D4×Q8—98no—
134#548—98no—
135#536—96no—
136#525—96no—
137#519—31no—
138C24×C3—31no—
139C23×D3C22×D311yescharacteristic
140C2×C3×Q8—28no—
141C2×C3×Q8—24no—
142C2×C3×Q8—312no—
143C2×C3×Q8—632no—
144C2×C3×Q8—612no—
145C2×C3×Q8D1218yescomplemented
146C2×C3×Q8#6718yescomplemented
147C2×C3×Q8C22×D314yes—
148C2×C3×Q8C22×D314yes—
149C22×C3×C4—23no—
150C22×C3×C4—33no—
151C22×C3×C4—312no—
152C22×C3×C4—612no—
153C22×C3×C4C22×D313yes—
154C22×C3×C4C22×D313yes—
155C2×#67—34no—
156C2×#67—34no—
157C2×#67—38no—
158C2×#67—64no—
159C22×Dic3C22×D313yes—
160#239—632no—
161#239—616no—
162#239—616no—
163D3×Q8—232no—
164D3×Q8—632no—
165D3×Q8—616no—
166D3×Q8—616no—
167#235—648no—
168#235—624no—
169#235—624no—
170C2×D12—38no—
171C2×D12—36no—
172C2×D12—36no—
173C2×D12—66no—
174C2×C4×D3—212no—
175C2×C4×D3—312no—
176C2×C4×D3—312no—
177C2×C4×D3—612no—
178C2×C4×D3C22×D3112yes—
179C2×Dic6—212no—
180C2×Dic6—36no—
181C2×Dic6—36no—
182C2×Dic6—66no—
183C2×Dic6C22×D3112yes—
184C3×C4⋊C4—312no—
185C3×C22⋊C4—34no—
186C3×C42—312no—
187#217—38no—
188#217C22×D314yes—
189(C2×D3)⋊C4—38no—
190(C2×D3)⋊C4—324no—
191(C2×D3)⋊C4—324no—
192C4⋊Dic3—324no—
193C4⋊Dic3C22×D3112yes—
194Dic3⋊C4—324no—
195C4×Dic3C22×D3112yes—
196C22×C32—22no—
197C22×C32C22×D412yes—
198C22×C32C2511yescharacteristic
199C2×C3⋊D3—24no—
200C2×C3⋊D3—28no—
201C2×C3×D3—28no—
202C2×C3×D3—22no—
203C2×C3×D3—22no—
204C2×C3×D32−1+414yescomplemented
205C32×C4C22×D4112yes—
206C3⋊Dic3—24no—
207C3×Dic3—26no—
208C3×Dic3—28no—
2092−1+4—188no—
210C2×#41—94no—
211C2×#41—96no—
212C22×Q8—38no—
213C22×Q8—33no—
214C22×Q8—68no—
215C22×Q8—94no—
216C22×Q8D3211yescharacteristic
217C23×C4—33no—
218C4⋊Q8—912no—
219#124—912no—
220#123—912no—
221C22⋊Q8—912no—
222C22⋊Q8—924no—
223#121—912no—
224#120—94no—
225C4×Q8—38no—
226C4×D4—924no—
227#117—36no—
228C23×C3—21no—
229C23×C3—32no—
230C23×C3—64no—
231C23×C3—62no—
232C23×C3C23×D311yescharacteristic
233C23×C3C23×D311yescharacteristic
234C22×D3—22no—
235C22×D3—24no—
236C22×D3—34no—
237C22×D3—34no—
238C22×D3—64no—
239C22×D3C23×D312yes—
240C3×Q8—216no—
241C3×Q8—624no—
242C3×Q8C2×D12116yes—
243C3×Q8C2×#67116yes—
244C2×C3×C4—26no—
245C2×C3×C4—212no—
246C2×C3×C4—36no—
247C2×C3×C4—38no—
248C2×C3×C4—66no—
249C2×C3×C4—624no—
250C2×C3×C4C2×D12112yes—
251C2×C3×C4C2×#67112yes—
252C2×C3×C4C23×D316yes—
253C2×C3×C4C23×D316yes—
254#67—616no—
255#67—616no—
256#67—68no—
257#67—68no—
258C2×Dic3—26no—
259C2×Dic3—34no—
260C2×Dic3—34no—
261C2×Dic3—64no—
262C2×Dic3C23×D318yes—
263C2×Dic3C23×D316yes—
264D12—624no—
265D12—616no—
266D12—612no—
267D12—612no—
268C4×D3—224no—
269C4×D3—648no—
270C4×D3—624no—
271C4×D3—624no—
272Dic6—224no—
273Dic6—624no—
274Dic6—612no—
275Dic6—612no—
276C2×C32—22no—
277C2×C32C23×D411yescharacteristic
278C2×C32C2×2−1+412yes—
279C3⋊D3—44no—
280C3×D3—24no—
281C24—31no—
282#41—1816no—
283#41—1824no—
284C2×Q8—312no—
285C2×Q8—632no—
286C2×Q8—612no—
287C2×Q8—96no—
288C2×Q8—1816no—
289C2×Q8#62618yescomplemented
290C2×Q8C2×D3214yes—
291C2×D4—98no—
292C2×D4—94no—
293C2×D4—96no—
294C22×C4—33no—
295C22×C4—312no—
296C22×C4—612no—
297C22×C4—912no—
298C22×C4C2×D3213yes—
299C4⋊C4—312no—
300C4⋊C4—924no—
301C22⋊C4—34no—
302C22⋊C4—924no—
303C22⋊C4—98no—
304C42—312no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—21no—
309C22×C3—34no—
310C22×C3—42no—
311C22×C3—68no—
312C22×C3—62no—
313C22×C3—62no—
314C22×C3C22×D1212yes—
315C22×C3C22×#6712yes—
316C22×C3C24×D311yescharacteristic
317C22×C3C24×D311yescharacteristic
318C2×D3—28no—
319C2×D3—22no—
320C2×D3—22no—
321C2×D3—68no—
322C2×D3—64no—
323C2×D3—68no—
324C2×D3—68no—
325C2×D3—64no—
326C2×D3—128no—
327C2×D3#100714yescomplemented
328C3×C4—212no—
329C3×C4—66no—
330C3×C4—68no—
331C3×C4C22×D12112yes—
332C3×C4C22×#67112yes—
333Dic3—28no—
334Dic3—26no—
335Dic3—68no—
336Dic3—64no—
337Dic3—64no—
338C32#348611yescharacteristic, complemented, Sylow
339C23—32no—
340C23—64no—
341C23—62no—
342C23—94no—
343C23C22×D3211yescharacteristic
344Q8—624no—
345Q8—1812no—
346Q8C2×#626116yes—
347D4—1816no—
348D4—188no—
349D4—1812no—
350C2×C4—38no—
351C2×C4—36no—
352C2×C4—66no—
353C2×C4—624no—
354C2×C4—94no—
355C2×C4—1824no—
356C2×C4C2×#626112yes—
357C2×C4C22×D3216yes—
358C2×C3—22no—
359C2×C3—22no—
360C2×C3—22no—
361C2×C3—21no—
362C2×C3—42no—
363C2×C3—64no—
364C2×C3C23×D1211yescharacteristic
365C2×C3C2×#100712yes—
366C2×C3D3×2−1+412yes—
367C2×C3C23×#6711yescharacteristic
368D3—24no—
369D3—128no—
370D3—124no—
371D3—124no—
372C22—22no—
373C22—34no—
374C22—68no—
375C22—62no—
376C22—62no—
377C22—188no—
378C22—184no—
379C22C22×#62612yes—
380C22C23×D3211yescharacteristic
381C4—68no—
382C4—66no—
383C4—184no—
384C4C22×#626112yes—
385C3—21no—
386C3#8588111yescharacteristic, complemented
387C3#8725111yescharacteristic, complemented
388C2—22no—
389C2—64no—
390C2—364no—
391C2D3×#100712yes—
392C2C23×#62611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32#3486
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×D3×Q8C2semidirect
3. C3×#5812C2semidirect
4. Q8×#626C2semidirect
5. #10595342C2semidirect
6. #10595023C2semidirect
7. #10594866C2semidirect
12. C2×#3832C22semidirect
13. C2×Q8×C3⋊D3C22semidirect
19. C3×Q8×Dic3C22semidirect
25. #63871C22semidirect
26. #63866C22semidirect
27. #63864C22semidirect
33. C22×D3×Q8D3semidirect
38. #5812D3semidirect
45. C2×C32×Q8D4semidirect
97. Q8×Dic3C2×D3semidirect
145. C2×C3×Q8D12semidirect
146. C2×C3×Q8#67semidirect
204. C2×C3×D32−1+4semidirect
289. C2×Q8#626semidirect
327. C2×D3#1007semidirect
338. C32#3486semidirect
386. C3#85881semidirect
387. C3#87251semidirect

Maximal subgroups

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

subgroupindex
C2×#643642
C22×C3×D3×Q82
C3×#58122
Q8×#6262
#105953422
#105950232
#105948662
#872513
#858813