Finite Group Databasebeta

← #11801789

Subgroups — #11801789

Order 1152.

1149 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic
2C3×C4×C4⋊Dic3C211yesmaximal, characteristic
3C3×C42×Dic3C211yesmaximal, characteristic
4C4×#3724C212yesmaximal
5#10591222C212yesmaximal
6#10591213C212yesmaximal
7#10591212C212yesmaximal
8#10591197C214yesmaximal
9#73618—31nomaximal
10#73300—31nomaximal
11C22×#634C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3750C2212yes—
15C2×C4×C3⋊Dic3C2212yes—
16C4×#634C418yescomplemented
17C2×C3×C4⋊Dic3C2212yes—
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2212yes—
20C2×C3×C4×Dic3C2212yes—
21C2×C3×C4×Dic3C2212yes—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×#3724C2214yes—
24C3×C3⋊#95C2212yes—
25#63579C2214yes—
26#63579C2214yes—
27#63579C2214yes—
28C2×C4×Dic6—31no—
29C2×C4×Dic6—31no—
30C2×C4×Dic6—61no—
31C3×C4×C4⋊C4—31no—
32C3×C43—31no—
33#4973—32no—
34#4972—32no—
35C4×C4⋊Dic3D311yescharacteristic
36#4933—34no—
37#4932—32no—
38#4932—32no—
39C4×Dic3⋊C4—32no—
40C4×Dic3⋊C4—32no—
41C42×Dic3D311yescharacteristic
42#4929—32no—
43#4928—32no—
44#4652—34no—
45C22×C32×C4C2311yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3C2312yes—
49C22×C3⋊Dic3C2312yes—
50C2×#634—24no—
51C2×#634C2×C414yes—
52C22×C3×Dic3C2314yes—
53C22×C3×Dic3C2312yes—
54C22×C3×Dic3C2312yes—
55C32×C42C2×C414yes—
56C4⋊(C3⋊Dic3)C2×C414yes—
57#3750C2×C418yes—
58C4×C3⋊Dic3C2×C418yes—
59C3×C4⋊Dic3—24no—
60C3×C4×Dic3—24no—
61C3×C4×Dic3—22no—
62C3×C4×Dic3—24no—
63C3×C4×Dic3—24no—
64C3×C4×Dic3Q814yescomplemented
65#3724—28no—
66#2295—91noSylow
67C22×Dic6—31no—
68C22×Dic6—31no—
69C22×Dic6—61no—
70C2×C3×C4⋊C4—32no—
71C2×C3×C42—21no—
72C2×C3×C42—31no—
73C2×C3×C42—32no—
74C2×C3×C42—31no—
75C2×C3×C42—32no—
76C2×C3×C42—32no—
77C2×C3×C42C2×D311yescharacteristic
78C2×C3×C42C2×D311yescharacteristic
79C2×C4⋊Dic3—31no—
80C2×C4⋊Dic3—31no—
81C2×C4⋊Dic3—61no—
82C2×C4⋊Dic3C2×D312yes—
83C2×Dic3⋊C4—32no—
84C2×Dic3⋊C4—32no—
85C2×Dic3⋊C4—34no—
86C2×Dic3⋊C4—34no—
87C2×Dic3⋊C4—62no—
88C2×C4×Dic3—32no—
89C2×C4×Dic3—32no—
90C2×C4×Dic3—62no—
91C2×C4×Dic3C2×D312yes—
92C2×C4×Dic3C2×D311yescharacteristic
93C2×C4×Dic3C2×D312yes—
94C2×C4×Dic3C2×D312yes—
95C2×C4×Dic3C2×D311yescharacteristic
96C4×Dic6—38no—
97C4×Dic6—38no—
98C4×Dic6—68no—
99C3×#95—32no—
100C3⋊#95—34no—
101C3⋊#95—34no—
102C3⋊#95—34no—
103C3⋊#95—34no—
104C3⋊#95—34no—
105C3⋊#95—34no—
106C3⋊#95C2×D312yes—
107C23×C32C2411yescharacteristic
108C2×C32×C4—22no—
109C2×C32×C4C22×C412yes—
110C2×C32×C4C22×C412yes—
111C2×C32×C4C22×C412yes—
112C2×C32×C4C2×Q812yes—
113C2×C32×C4#4114yes—
114C2×C32×C4#4112yes—
115C2×C3⋊Dic3—24no—
116C2×C3⋊Dic3—24no—
117C2×C3⋊Dic3C22×C414yes—
118C2×C3⋊Dic3C22×C414yes—
119#634—28no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—22no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—24no—
125C2×C3×Dic3—24no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3C2×Q814yes—
128C2×C3×Dic3#4114yes—
129C2×C4×Q8—91no—
130#391—92no—
131#389—92no—
132#387—94no—
133C4×C4⋊C4—31no—
134C4×C4⋊C4—92no—
135#376—92no—
136C43—31no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—32no—
141C22×C3×C4—32no—
142C22×C3×C4—34no—
143C22×C3×C4C22×D311yescharacteristic
144C22×C3×C4C22×D311yescharacteristic
145C22×C3×C4C22×D311yescharacteristic
146C22×C3×C4C22×D311yescharacteristic
147C22×C3×C4C22×D311yescharacteristic
148C22×C3×C4C22×D311yescharacteristic
149C22×Dic3—32no—
150C22×Dic3—32no—
151C22×Dic3—32no—
152C22×Dic3—32no—
153C22×Dic3—62no—
154C22×Dic3—62no—
155C22×Dic3C22×D314yes—
156C22×Dic3C22×D312yes—
157C22×Dic3C22×D312yes—
158C2×Dic6—34no—
159C2×Dic6—34no—
160C2×Dic6—64no—
161C2×Dic6—68no—
162C2×Dic6—64no—
163C2×Dic6—64no—
164C3×C4⋊C4—64no—
165C3×C42—24no—
166C3×C42—34no—
167C3×C42—64no—
168C3×C42—64no—
169C3×C42—64no—
170C3×C42—62no—
171C3×C42C4×D314yes—
172C3×C42C4×D314yes—
173C4⋊Dic3—24no—
174C4⋊Dic3—34no—
175C4⋊Dic3—34no—
176C4⋊Dic3—64no—
177Dic3⋊C4—38no—
178Dic3⋊C4—38no—
179Dic3⋊C4—68no—
180Dic3⋊C4—68no—
181Dic3⋊C4—68no—
182C4×Dic3—22no—
183C4×Dic3—24no—
184C4×Dic3—24no—
185C4×Dic3—24no—
186C4×Dic3—38no—
187C4×Dic3—38no—
188C4×Dic3—68no—
189C4×Dic3Dic614yescomplemented
190C22×C32C23×C411yescharacteristic
191C22×C32C22×Q811yescharacteristic
192C22×C32C2×#4112yes—
193C22×C32C2×#4111yescharacteristic
194C22×C32C2×#4112yes—
195C32×C4—22no—
196C32×C4#11714yes—
197C32×C4C4×Q814yes—
198C3⋊Dic3—24no—
199C3⋊Dic3—24no—
200C3×Dic3—24no—
201C3×Dic3—24no—
202C3×Dic3—44no—
203C22×Q8—91no—
204C4×Q8—98no—
205C2×C4⋊C4—32no—
206C2×C4⋊C4—92no—
207C2×C4⋊C4—91no—
208C2×C4⋊C4—94no—
209C2×C42—31no—
210C2×C42—32no—
211C2×C42—32no—
212C2×C42—31no—
213C2×C42—32no—
214C2×C42—92no—
215C2×C42D3211yescharacteristic
216#95—32no—
217#95—94no—
218#95—94no—
219#95—94no—
220C23×C3—21no—
221C23×C3C23×D311yescharacteristic
222C23×C3C23×D311yescharacteristic
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—24no—
228C2×C3×C4—22no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—34no—
232C2×C3×C4—34no—
233C2×C3×C4—42no—
234C2×C3×C4—62no—
235C2×C3×C4—62no—
236C2×C3×C4—62no—
237C2×C3×C4—62no—
238C2×C3×C4—64no—
239C2×C3×C4—64no—
240C2×C3×C4—64no—
241C2×C3×C4C2×Dic612yes—
242C2×C3×C4C2×C4×D312yes—
243C2×C3×C4C2×C4×D312yes—
244C2×C3×C4C2×C4×D312yes—
245C2×C3×C4C2×C4×D312yes—
246C2×C3×C4C2×C4×D312yes—
247C2×C3×C4C2×C4×D312yes—
248C2×C3×C4#23512yes—
249C2×C3×C4#23514yes—
250C2×C3×C4#23514yes—
251C2×C3×C4#23712yes—
252C2×C3×C4D3×Q812yes—
253C2×Dic3—22no—
254C2×Dic3—22no—
255C2×Dic3—22no—
256C2×Dic3—22no—
257C2×Dic3—24no—
258C2×Dic3—24no—
259C2×Dic3—24no—
260C2×Dic3—34no—
261C2×Dic3—34no—
262C2×Dic3—34no—
263C2×Dic3—34no—
264C2×Dic3—64no—
265C2×Dic3—64no—
266C2×Dic3—68no—
267C2×Dic3—64no—
268C2×Dic3—64no—
269C2×Dic3—64no—
270C2×Dic3—64no—
271C2×Dic3—124no—
272C2×Dic3C2×Dic614yes—
273C2×Dic3#23514yes—
274Dic6—616no—
275Dic6—68no—
276Dic6—68no—
277C2×C32C2×#11711yescharacteristic
278C2×C32C2×C4×Q811yescharacteristic
279C2×C32C4×#4111yescharacteristic
280C2×C32#52912yes—
281C2×C32#53312yes—
282C2×Q8—94no—
283C2×Q8—184no—
284C22×C4—32no—
285C22×C4—32no—
286C22×C4—34no—
287C22×C4—92no—
288C22×C4—92no—
289C22×C4C2×D3211yescharacteristic
290C22×C4C2×D3211yescharacteristic
291C22×C4C2×D3211yescharacteristic
292C4⋊C4—64no—
293C4⋊C4—98no—
294C4⋊C4—94no—
295C4⋊C4—188no—
296C42—34no—
297C42—64no—
298C42—62no—
299C42—64no—
300C42—64no—
301C42—98no—
302C42#62414yes—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—21no—
308C22×C3C22×Dic611yescharacteristic
309C22×C3C22×C4×D311yescharacteristic
310C22×C3C22×C4×D311yescharacteristic
311C22×C3C2×#23511yescharacteristic
312C22×C3C2×#23512yes—
313C22×C3C2×#23512yes—
314C22×C3C2×#23512yes—
315C22×C3C2×#23711yescharacteristic
316C22×C3C2×D3×Q811yescharacteristic
317C22×C3D3×#4112yes—
318C3×C4—22no—
319C3×C4—22no—
320C3×C4—24no—
321C3×C4—24no—
322C3×C4—42no—
323C3×C4—64no—
324C3×C4—64no—
325C3×C4—124no—
326C3×C4C4×Dic614yes—
327C3×C4#87214yes—
328C3×C4#87214yes—
329C3×C4#88714yes—
330Dic3—24no—
331Dic3—24no—
332Dic3—44no—
333Dic3—68no—
334Dic3—64no—
335Dic3—64no—
336Dic3—64no—
337Dic3—64no—
338Dic3—124no—
339C32#229511yescharacteristic, complemented, Sylow
340C23C22×D3211yescharacteristic
341Q8—188no—
342C2×C4—22no—
343C2×C4—34no—
344C2×C4—34no—
345C2×C4—62no—
346C2×C4—62no—
347C2×C4—62no—
348C2×C4—62no—
349C2×C4—64no—
350C2×C4—64no—
351C2×C4—64no—
352C2×C4—94no—
353C2×C4—94no—
354C2×C4—184no—
355C2×C4—184no—
356C2×C4D3×Dic612yes—
357C2×C4#379512yes—
358C2×C4#379814yes—
359C2×C4C2×#62412yes—
360C2×C4C2×#62412yes—
361C2×C4C2×#62412yes—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—22no—
365C2×C3—21no—
366C2×C3—22no—
367C2×C3C2×C4×Dic611yescharacteristic
368C2×C3#547012yes—
369C2×C3C2×#87211yescharacteristic
370C2×C3C2×#87211yescharacteristic
371C2×C3C4×#23511yescharacteristic
372C2×C3#547912yes—
373C2×C3C2×#88711yescharacteristic
374C2×C3#552211yescharacteristic
375C2×C3#555712yes—
376C2×C3#557812yes—
377C22C2×D3×Dic611yescharacteristic
378C22C2×#379511yescharacteristic
379C22C2×#379812yes—
380C22D3×#23512yes—
381C22C22×#62411yescharacteristic
382C4—22no—
383C4—64no—
384C4—64no—
385C4—124no—
386C4—184no—
387C4—184no—
388C4#6384414yes—
389C4#6387414yes—
390C3—21no—
391C3#7330011yescharacteristic, complemented
392C3#7361811yescharacteristic, complemented
393C2#1059387312yes—
394C2#1059397412yes—
395C2C2×#6384411yescharacteristic
396C2C2×#6387411yescharacteristic
397C2#1059495411yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2295
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
16. C4×#634C4semidirect
64. C3×C4×Dic3Q8semidirect
189. C4×Dic3Dic6semidirect
339. C32#2295semidirect
391. C3#73300semidirect
392. C3#73618semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C3×C4×C4⋊Dic32
C3×C42×Dic32
C4×#37242
#105912222
#105912132
#105912122
#105911972
#736183
#733003