Finite Group Databasebeta

← #11903688

Subgroups — #11903688

Order 1152.

2245 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic
2C3×#5570C212yesmaximal, complemented
3Q8×#624C212yesmaximal
4#10595351C212yesmaximal, complemented
5#10594482C216yesmaximal
6#10594324C216yesmaximal, complemented
7#10593909C213yesmaximal
8C4×#3797C213yesmaximal
9#10593864C216yesmaximal, complemented
10D3×#557—32nomaximal
11C2×Q8×C3⋊D3C2211yescharacteristic
12C2×#3797C2213yes—
13C32×C4×Q8C2211yescharacteristic
14Q8×C3⋊Dic3C2211yescharacteristic
15C4⋊C4×C3⋊D3C2213yes—
16#64096C2213yes—
17C42×C3⋊D3C2213yes—
18C4×#634C2213yes—
19C3×Q8×Dic3C2214yes—
20C3×#890C22112yes—
21C3×#869C2216yes—
22C3×C4×Dic6C2216yes—
23#63919C2216yes—
24#63919C2216yes—
25C4×#627C2216yes—
26#63900C2216yes—
27#63900C2211yescharacteristic
28#63900C2216yes—
29#63883C2216yes—
30C4×#624C2216yes—
31#63873C2216yes—
32#63869C22112yes—
33#63847C22124yes—
34#63844C22112yes—
35#63843C2216yes—
36#63838C2216yes—
37C3×#557—32no—
38D3×C4⋊Q8—36no—
39#5721—36no—
40D3×#125—312no—
41#5685—312no—
42C4×D3×Q8—32no—
43C4×D3×Q8—34no—
44C4×D3×Q8—36no—
45C4×D3×Q8—61no—
46#5570D312yescomplemented
47#5569—34no—
48#5567—36no—
49C2×C32×Q8C2311yescharacteristic
50Q8×C3⋊D3Q818yescomplemented
51C2×C4×C3⋊D3C2313yes—
52C2×C4×C3⋊D3C2313yes—
53C2×C4×C3⋊D3C2311yescharacteristic
54C2×#634C2313yes—
55C2×C3×Dic6C2316yes—
56C2×#627C2316yes—
57C2×#624C2316yes—
58C2×#624C2312yes—
59#3797—212no—
60C32×C4⋊C4C2313yes—
61C32×C42C2313yes—
62C4⋊(C3⋊Dic3)C2313yes—
63#3750C2316yes—
64C4×C3⋊Dic3C2313yes—
65C4×C3⋊Dic3C2313yes—
66C4×C3⋊Dic3C2313yes—
67C3×C4⋊Dic3C23112yes—
68C3×C4⋊Dic3C23112yes—
69C3×C4⋊Dic3C2312yes—
70C3×Dic3⋊C4C23112yes—
71C3×C4×Dic3C23112yes—
72#3724C2312yes—
73#3724C23112yes—
74#3724C23112yes—
75Dic3⋊Dic3C23112yes—
76Dic32C23112yes—
77C2×#557—91noSylow
78C2×D3×Q8—32no—
79C2×D3×Q8—36no—
80C2×D3×Q8—61no—
81C3×C4⋊Q8—36no—
82C3×#125—312no—
83C3×C4×Q8—21no—
84C3×C4×Q8—34no—
85C3×C4×Q8—36no—
86C3×C4×Q8C2×D312yes—
87Q8×Dic3—32no—
88Q8×Dic3—36no—
89Q8×Dic3—61no—
90Q8×Dic3C2×D314yes—
91#944—312no—
92D3×C4⋊C4—36no—
93D3×C4⋊C4—312no—
94D3×C4⋊C4—312no—
95D3×C4⋊C4—32no—
96D3×C4⋊C4—312no—
97D3×C4⋊C4—63no—
98#890—312no—
99#890C2×D3112yes—
100#889—324no—
101#889—324no—
102#888—312no—
103#888—312no—
104#887—36no—
105#887—36no—
106#887—312no—
107#887—312no—
108#887—63no—
109C42×D3—36no—
110C42×D3—312no—
111C42×D3—63no—
112#870—312no—
113#869C2×D316yes—
114C4×Dic6—36no—
115C4×Dic6—312no—
116C4×Dic6—312no—
117C4×Dic6—63no—
118C4×Dic6C2×D316yes—
119C22×C3⋊D3C2411yescharacteristic
120C32×Q8C2×Q814yescomplemented
121C2×C32×C4C2413yes—
122C2×C32×C4C2413yes—
123C2×C32×C4C2411yescharacteristic
124C2×C3⋊Dic3C2413yes—
125C2×C3⋊Dic3C2413yes—
126C2×C3⋊Dic3C2411yescharacteristic
127C4×C3⋊D3—26no—
128C4×C3⋊D3C2×Q8112yes—
129C4×C3⋊D3#4114yes—
130#634C2×Q8112yescomplemented
131C2×C3×Dic3C2414yes—
132C2×C3×Dic3C24112yes—
133C3×Dic6—212no—
134#627—212no—
135#624—212no—
136#624—24no—
137#557—32no—
138#557—92no—
139#557—96no—
140#557—96no—
141C2×C4⋊Q8—93no—
142C2×#125—96no—
143C2×C4×Q8—92no—
144C2×C4×Q8—93no—
145C2×C4×Q8—91no—
146C2×C3×Q8—21no—
147C2×C3×Q8—36no—
148C2×C3×Q8C22×D312yes—
149D3×Q8—316no—
150D3×Q8—68no—
151D3×Q8—624no—
152C2×C4×D3—36no—
153C2×C4×D3—32no—
154C2×C4×D3—36no—
155C2×C4×D3—34no—
156C2×C4×D3—312no—
157C2×C4×D3—61no—
158C2×C4×D3—63no—
159C2×C4×D3—63no—
160C2×Dic6—36no—
161C2×Dic6—312no—
162C2×Dic6—63no—
163C2×Dic6C22×D316yes—
164C3×C4⋊C4—23no—
165C3×C4⋊C4—32no—
166C3×C4⋊C4—312no—
167C3×C4⋊C4—312no—
168C3×C4⋊C4—312no—
169C3×C4⋊C4C22×D316yes—
170C3×C42—23no—
171C3×C42—312no—
172C3×C42C22×D316yes—
173C4⋊Dic3—36no—
174C4⋊Dic3—312no—
175C4⋊Dic3—63no—
176C4⋊Dic3C22×D3112yes—
177C4⋊Dic3C22×D312yes—
178C4⋊Dic3C22×D3112yes—
179Dic3⋊C4—312no—
180Dic3⋊C4—34no—
181Dic3⋊C4—312no—
182Dic3⋊C4—324no—
183Dic3⋊C4—324no—
184Dic3⋊C4—66no—
185Dic3⋊C4C22×D3112yes—
186C4×Dic3—36no—
187C4×Dic3—36no—
188C4×Dic3—36no—
189C4×Dic3—312no—
190C4×Dic3—312no—
191C4×Dic3—63no—
192C4×Dic3—63no—
193C4×Dic3—63no—
194C4×Dic3C22×D3112yes—
195C22×C32C2511yescharacteristic
196C2×C3⋊D3C22×Q812yes—
197C2×C3⋊D3C2×#4112yes—
198C2×C3⋊D32−1+412yes—
199C32×C4—23no—
200C32×C4C22×Q816yes—
201C32×C4C2×#4112yes—
202C3⋊Dic3—23no—
203C3⋊Dic3C22×Q816yes—
204C3⋊Dic3C2×#4112yes—
205C3×Dic3—212no—
206C3×Dic3—24no—
207C22×Q8—93no—
208C22×Q8—91no—
209C4⋊Q8—36no—
210C4⋊Q8—96no—
211C4⋊Q8—96no—
212C4⋊Q8—96no—
213#125—312no—
214#125—912no—
215#125—924no—
216C4×Q8—34no—
217C4×Q8—36no—
218C4×Q8—96no—
219C4×Q8—912no—
220C4×Q8—96no—
221C4×Q8—96no—
222C4×Q8—91no—
223C4×Q8—93no—
224C4×Q8—93no—
225C4×Q8D3211yescharacteristic
226C2×C4⋊C4—91no—
227C2×C4⋊C4—96no—
228C2×C4⋊C4—96no—
229C2×C4⋊C4—96no—
230C2×C4⋊C4—93no—
231C2×C42—96no—
232C2×C42—93no—
233C22×D3—32no—
234C22×D3—61no—
235C3×Q8—24no—
236C3×Q8—612no—
237C3×Q8D3×Q818yescomplemented
238C2×C3×C4—21no—
239C2×C3×C4—23no—
240C2×C3×C4—23no—
241C2×C3×C4—34no—
242C2×C3×C4—312no—
243C2×C3×C4C23×D316yes—
244C2×C3×C4C23×D316yes—
245C2×C3×C4C23×D312yes—
246C2×Dic3—36no—
247C2×Dic3—32no—
248C2×Dic3—36no—
249C2×Dic3—61no—
250C2×Dic3—63no—
251C2×Dic3—63no—
252C2×Dic3C23×D314yes—
253C2×Dic3C23×D3112yes—
254C4×D3—324no—
255C4×D3—38no—
256C4×D3—612no—
257C4×D3—64no—
258C4×D3—68no—
259C4×D3—624no—
260C4×D3—612no—
261C4×D3—126no—
262Dic6—212no—
263Dic6—324no—
264Dic6—612no—
265Dic6—624no—
266C2×C32C23×Q811yescharacteristic
267C2×C32C22×#4111yescharacteristic
268C2×C32C2×2−1+411yescharacteristic
269C3⋊D3#55714yescomplemented
270C2×Q8—36no—
271C2×Q8—96no—
272C2×Q8—98no—
273C2×Q8—93no—
274C2×Q8—1812no—
275C2×Q8C2×D3211yescharacteristic
276C22×C4—92no—
277C22×C4—96no—
278C22×C4—93no—
279C22×C4—91no—
280C22×C4—93no—
281C4⋊C4—32no—
282C4⋊C4—312no—
283C4⋊C4—312no—
284C4⋊C4—312no—
285C4⋊C4—92no—
286C4⋊C4—912no—
287C4⋊C4—912no—
288C4⋊C4—912no—
289C4⋊C4—96no—
290C4⋊C4—93no—
291C4⋊C4C2×D3213yes—
292C42—312no—
293C42—912no—
294C42—93no—
295C42—93no—
296C42—93no—
297C42C2×D3213yes—
298C22×C3—21no—
299C22×C3C24×D312yes—
300C2×D3—34no—
301C2×D3—34no—
302C2×D3—34no—
303C2×D3—62no—
304C2×D3—62no—
305C2×D3—62no—
306C3×C4—26no—
307C3×C4—26no—
308C3×C4—22no—
309C3×C4—43no—
310C3×C4—612no—
311C3×C4—64no—
312C3×C4C2×D3×Q8112yes—
313C3×C4D3×#4114yes—
314Dic3—212no—
315Dic3—24no—
316Dic3—312no—
317Dic3—34no—
318Dic3—66no—
319Dic3—62no—
320Dic3—66no—
321Dic3—123no—
322C32C2×#55711yescharacteristic, complemented, Sylow
323C23—91no—
324Q8—612no—
325Q8—912no—
326Q8—1812no—
327Q8#379714yescomplemented
328C2×C4—34no—
329C2×C4—312no—
330C2×C4—93no—
331C2×C4—91no—
332C2×C4—912no—
333C2×C4—94no—
334C2×C4—93no—
335C2×C4—186no—
336C2×C4—1812no—
337C2×C4—184no—
338C2×C4C22×D3213yes—
339C2×C4C22×D3213yes—
340C2×C4C22×D3211yescharacteristic
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3C22×D3×Q812yes—
345C2×C3C2×D3×#4112yes—
346C2×C3D3×2−1+412yes—
347D3—38no—
348D3—64no—
349C22—92no—
350C22—92no—
351C22—92no—
352C22C23×D3211yescharacteristic
353C4—23no—
354C4—612no—
355C4—64no—
356C4—96no—
357C4—92no—
358C4—183no—
359C4C2×#379716yes—
360C4#6431912yes—
361C3—21no—
362C3D3×#55712yescomplemented
363C2—94no—
364C2C22×#379711yescharacteristic
365C2C2×#6431911yescharacteristic
366C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC22×C3⋊D3C24
hypercenterC4×Q8D32
hypocenterC32C2×#557
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5570C2semidirect
4. #10595351C2semidirect
6. #10594324C2semidirect
9. #10593864C2semidirect
46. #5570D3semidirect
50. Q8×C3⋊D3Q8semidirect
120. C32×Q8C2×Q8semidirect
130. #634C2×Q8semidirect
237. C3×Q8D3×Q8semidirect
269. C3⋊D3#557semidirect
322. C32C2×#557semidirect
327. Q8#3797semidirect
362. C3D3×#557semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
C3×#55702
Q8×#6242
#105953512
#105944822
#105943242
#105939092
C4×#37972
#105938642
D3×#5573