Finite Group Databasebeta

← #11904514

Subgroups — #11904514

Order 1152.

3409 conjugacy classes of subgroups.

The subgroup lattice has 397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×#1007C211yesmaximal, characteristic, complemented
3C3×#5812C211yesmaximal, characteristic, complemented
4#10595414C218yesmaximal, complemented
5Q8×#626C218yesmaximal, complemented
6#10595034C216yesmaximal, complemented
7#10594856C216yesmaximal, complemented
8#87294—31nomaximal
9#85881—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×Q8×C3⋊D3—28no—
12C2×Q8×C3⋊D3C2218yes—
13C22×C4×C3⋊D3C2213yes—
14C22×#634C2213yes—
15C3×#1007—28no—
16C2×C3×#239C2214yescomplemented
17C2×C3×D3×Q8C2214yescomplemented
18C2×C3×#235C2216yes—
19C3×Q8×Dic3C2218yescomplemented
20C3×#926C2216yes—
21#63981C2214yes—
22#63962C22112yes—
23#63916C22112yes—
24C4×#626C22124yes—
25#63871C22112yes—
26#63866C22112yescomplemented
27#63860C22112yescomplemented
28#63857C22124yescomplemented
29C2×C3×2−1+4—31no—
30C2×#1007D311yescharacteristic, complemented
31C22×D3×Q8—31no—
32C22×D3×Q8—31no—
33C22×D3×Q8—61no—
34C3×#519—31no—
35#5831—38no—
36#5828—36no—
37#5825—36no—
38Q8×#67—38no—
39#5812D311yescharacteristic, complemented
40#5576—38no—
41Q8×D12—38no—
42#5526—36no—
43#5524—36no—
44C23×C3⋊D3C2311yescharacteristic
45C2×C32×Q8D418yescomplemented
46C2×C32×Q8C2314yes—
47C22×C32×C4C2313yes—
48C22×C3⋊Dic3C2313yes—
49Q8×C3⋊D3—232no—
50C2×C4×C3⋊D3—212no—
51C2×C4×C3⋊D3C23112yes—
52C2×#634—212no—
53C2×#634C23112yes—
54C2×C3×#67C2314yes—
55C3×#239—216no—
56C3×D3×Q8—216no—
57C3×#235—224no—
58C2×C3×D12C2316yes—
59C2×C3×C4×D3C23112yes—
60C2×C3×Dic6C2316yes—
61C2×#626C2318yes—
62C3×#217C2314yes—
63C3×C4⋊Dic3C23112yes—
64C3×C4×Dic3C23112yes—
65Dic3⋊Dic3C23124yes—
66#3722C2318yes—
67(C2×D3)⋊Dic3C23124yes—
68#3486—91noSylow
69C3×2−1+4—68no—
70C2×C3×#41—34no—
71C2×C3×#41—36no—
72C22×C3×Q8—21no—
73C22×C3×Q8—34no—
74C22×C3×Q8C2×D311yescharacteristic
75C22×C3×Q8C2×D311yescharacteristic
76#1007—28no—
77C2×#239C2×D314yescomplemented
78C2×D3×Q8—38no—
79C2×D3×Q8—38no—
80C2×D3×Q8—68no—
81C2×D3×Q8—616no—
82C2×D3×Q8—68no—
83C2×D3×Q8—68no—
84C2×D3×Q8C2×D314yescomplemented
85C2×#235C2×D316yes—
86C22×C4×D3—33no—
87C22×C4×D3—33no—
88C22×C4×D3—63no—
89C22×Dic6—33no—
90C22×Dic6—33no—
91C22×Dic6—63no—
92C3×C4×Q8—38no—
93C3×#117—36no—
94#946—312no—
95Q8×Dic3C2×D318yescomplemented
96#944—312no—
97#938—312no—
98#937—34no—
99#936—312no—
100#935—312no—
101C4×#67—324no—
102#926C2×D316yes—
103#924—324no—
104#897—324no—
105#897—312no—
106#895—312no—
107#886—312no—
108#882—34no—
109#875—312no—
110C4×D12—324no—
111#869—312no—
112C23×C32C2411yescharacteristic
113C22×C3⋊D3—22no—
114C22×C3⋊D3—24no—
115C22×C3⋊D3C2412yes—
116C22×C3×D3C2414yes—
117C32×Q8C2×D4116yes—
118C2×C32×C4C2×D4112yes—
119C2×C32×C4C2416yes—
120C2×C3⋊Dic3—26no—
121C2×C3⋊Dic3C2416yes—
122C4×C3⋊D3—224no—
123#634—224no—
124C3×#67—28no—
125C2×C3×Dic3C2418yes—
126C2×C3×Dic3C2414yes—
127C3×D12—212no—
128C3×C4×D3—224no—
129C3×Dic6—212no—
130#626—216no—
131C2×2−1+4—31no—
132C23×Q8—91no—
133D4×Q8—98no—
134#548—98no—
135#536—96no—
136#525—96no—
137#519—31no—
138C23×D3—31no—
139C23×D3—31no—
140C23×D3—61no—
141C3×#41—616no—
142C3×#41—624no—
143C2×C3×Q8—28no—
144C2×C3×Q8—24no—
145C2×C3×Q8—36no—
146C2×C3×Q8—616no—
147C2×C3×Q8D1218yescomplemented
148C2×C3×Q8#6718yescomplemented
149C2×C3×Q8C22×D314yes—
150C2×C3×Q8C22×D314yes—
151C2×C3×D4—34no—
152C2×C3×D4—36no—
153C22×C3×C4—23no—
154C22×C3×C4—312no—
155C22×C3×C4C22×D313yes—
156C22×C3×C4C22×D313yes—
157C2×#67—38no—
158C2×#67C22×D314yes—
159C22×Dic3—33no—
160C22×Dic3—33no—
161C22×Dic3—63no—
162#239—216no—
163D3×Q8—216no—
164D3×Q8—664no—
165D3×Q8—632no—
166D3×Q8—632no—
167#235—224no—
168C2×D12—38no—
169C2×D12C22×D316yes—
170C2×C4×D3—312no—
171C2×C4×D3—312no—
172C2×C4×D3—612no—
173C2×C4×D3—624no—
174C2×C4×D3—612no—
175C2×C4×D3—612no—
176C2×C4×D3C22×D3112yes—
177C2×Dic6—312no—
178C2×Dic6—312no—
179C2×Dic6—612no—
180C2×Dic6—624no—
181C2×Dic6—612no—
182C2×Dic6—612no—
183C2×Dic6C22×D316yes—
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—324no—
193C4⋊Dic3C22×D3112yes—
194Dic3⋊C4—324no—
195C4×Dic3C22×D3112yes—
196C22×C32—22no—
197C22×C32C22×D412yes—
198C22×C32C2511yescharacteristic
199C2×C3⋊D3—28no—
200C2×C3⋊D3—22no—
201C2×C3⋊D3—22no—
202C2×C3⋊D32−1+414yescomplemented
203C2×C3×D3—24no—
204C2×C3×D3—28no—
205C32×C4C22×D4112yes—
206C3⋊Dic3—26no—
207C3×Dic3—24no—
208C3×Dic3—28no—
2092−1+4—68no—
210C2×#41—34no—
211C2×#41—36no—
212C22×Q8—34no—
213C22×Q8—98no—
214C22×Q8—93no—
215C22×Q8—188no—
216C22×Q8D3211yescharacteristic
217C23×C4—93no—
218C4⋊Q8—912no—
219#124—912no—
220#123—912no—
221C22⋊Q8—924no—
222C22⋊Q8—912no—
223#121—912no—
224#120—94no—
225C4×Q8—38no—
226C4×D4—924no—
227#117—36no—
228C23×C3—21no—
229C23×C3—34no—
230C23×C3C23×D311yescharacteristic
231C23×C3C23×D311yescharacteristic
232C22×D3—32no—
233C22×D3—32no—
234C22×D3—62no—
235C22×D3—64no—
236C22×D3—64no—
237C22×D3—64no—
238C22×D3—68no—
239C22×D3—62no—
240C22×D3—62no—
241C22×D3C23×D314yes—
242C3×Q8—216no—
243C3×Q8—612no—
244C3×Q8C2×D12116yes—
245C3×Q8C2×#67116yes—
246C3×D4—68no—
247C3×D4—612no—
248C2×C3×C4—26no—
249C2×C3×C4—212no—
250C2×C3×C4—34no—
251C2×C3×C4—38no—
252C2×C3×C4—624no—
253C2×C3×C4C2×D12112yes—
254C2×C3×C4C2×#67112yes—
255C2×C3×C4C23×D316yes—
256C2×C3×C4C23×D316yes—
257#67—28no—
258#67—616no—
259C2×Dic3—36no—
260C2×Dic3—36no—
261C2×Dic3—66no—
262C2×Dic3—612no—
263C2×Dic3—66no—
264C2×Dic3—66no—
265C2×Dic3C23×D318yes—
266C2×Dic3C23×D314yes—
267D12—212no—
268D12—616no—
269C4×D3—224no—
270C4×D3—648no—
271C4×D3—624no—
272C4×D3—624no—
273Dic6—212no—
274Dic6—648no—
275Dic6—624no—
276Dic6—624no—
277C2×C32—22no—
278C2×C32C23×D411yescharacteristic
279C2×C32C2×2−1+412yes—
280C3⋊D3—24no—
281C3×D3—44no—
282C24—91no—
283#41—616no—
284#41—624no—
285C2×Q8—36no—
286C2×Q8—616no—
287C2×Q8—912no—
288C2×Q8—1832no—
289C2×Q8—1812no—
290C2×Q8#62618yescomplemented
291C2×Q8C2×D3214yes—
292C2×D4—34no—
293C2×D4—36no—
294C2×D4—98no—
295C22×C4—312no—
296C22×C4—93no—
297C22×C4—912no—
298C22×C4—1812no—
299C22×C4C2×D3213yes—
300C4⋊C4—312no—
301C4⋊C4—924no—
302C22⋊C4—34no—
303C22⋊C4—98no—
304C22⋊C4—924no—
305C42—312no—
306C22×C3—24no—
307C22×C3—22no—
308C22×C3—22no—
309C22×C3—22no—
310C22×C3—21no—
311C22×C3—64no—
312C22×C3—68no—
313C22×C3C22×D1212yes—
314C22×C3C22×#6712yes—
315C22×C3C24×D311yescharacteristic
316C22×C3C24×D311yescharacteristic
317C2×D3—28no—
318C2×D3—24no—
319C2×D3—34no—
320C2×D3—34no—
321C2×D3—64no—
322C2×D3—64no—
323C2×D3—616no—
324C2×D3—68no—
325C2×D3—68no—
326C2×D3—64no—
327C2×D3—62no—
328C2×D3—62no—
329C2×D3—62no—
330C2×D3—62no—
331C3×C4—212no—
332C3×C4—64no—
333C3×C4—68no—
334C3×C4C22×D12112yes—
335C3×C4C22×#67112yes—
336Dic3—28no—
337Dic3—24no—
338Dic3—612no—
339Dic3—66no—
340Dic3—66no—
341C32#348611yescharacteristic, complemented, Sylow
342C23—34no—
343C23—92no—
344C23—184no—
345C23—182no—
346C23C22×D3211yescharacteristic
347Q8—612no—
348Q8—1824no—
349Q8C2×#626116yes—
350D4—68no—
351D4—612no—
352D4—1816no—
353C2×C4—38no—
354C2×C4—34no—
355C2×C4—624no—
356C2×C4—96no—
357C2×C4—186no—
358C2×C4—1824no—
359C2×C4C2×#626112yes—
360C2×C4C22×D3216yes—
361C2×C3—24no—
362C2×C3—22no—
363C2×C3—22no—
364C2×C3—22no—
365C2×C3—21no—
366C2×C3—124no—
367C2×C3C23×D1211yescharacteristic
368C2×C3D3×2−1+412yes—
369C2×C3D3×2−1+412yes—
370C2×C3C23×#6711yescharacteristic
371D3—44no—
372D3—68no—
373D3—64no—
374D3—64no—
375C22—22no—
376C22—68no—
377C22—64no—
378C22—94no—
379C22—188no—
380C22—182no—
381C22—182no—
382C22C22×#62612yes—
383C22C23×D3211yescharacteristic
384C4—68no—
385C4—64no—
386C4—186no—
387C4C22×#626112yes—
388C3—21no—
389C3#8588111yescharacteristic, complemented
390C3#8729411yescharacteristic, complemented
391C2—22no—
392C2—124no—
393C2—184no—
394C2#1059668712yes—
395C2C23×#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. C22×Q8×C3⋊D3C2semidirect
2. C2×C3×#1007C2semidirect
3. C3×#5812C2semidirect
4. #10595414C2semidirect
5. Q8×#626C2semidirect
6. #10595034C2semidirect
7. #10594856C2semidirect
16. C2×C3×#239C22semidirect
17. C2×C3×D3×Q8C22semidirect
19. C3×Q8×Dic3C22semidirect
26. #63866C22semidirect
27. #63860C22semidirect
28. #63857C22semidirect
30. C2×#1007D3semidirect
39. #5812D3semidirect
45. C2×C32×Q8D4semidirect
77. C2×#239C2×D3semidirect
84. C2×D3×Q8C2×D3semidirect
95. Q8×Dic3C2×D3semidirect
147. C2×C3×Q8D12semidirect
148. C2×C3×Q8#67semidirect
202. C2×C3⋊D32−1+4semidirect
290. C2×Q8#626semidirect
341. C32#3486semidirect
389. C3#85881semidirect
390. C3#87294semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×C3⋊D32
C2×C3×#10072
C3×#58122
#105954142
Q8×#6262
#105950342
#105948562
#872943
#858813