Finite Group Databasebeta

← C3×#71548 #11773333

Subgroups — C3×#71548 #11773333

Order 1152.

1809 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C22⋊C4C211yesmaximal, characteristic
2C22×C3×#217C212yesmaximal
3C2×C3×C3⋊#95C214yesmaximal, complemented
4C3×#1440—31nomaximal
5#71548C311yesmaximal, characteristic, direct product factor
6C25×C32C2211yescharacteristic
7C23×C32×C4C2212yes—
8C23×C3×Dic3C2214yes—
9C2×C32×C22⋊C4—24no—
10C2×C32×C22⋊C4C414yescomplemented
11C2×C3×#217—28no—
12C2×C3×#217—24no—
13C3×C3⋊#95—28no—
14C22×C3×C22⋊C4—21no—
15C22×C3×C22⋊C4—32no—
16C22×C3×C22⋊C4D311yescharacteristic
17C22×C3×C22⋊C4C2×C311yescharacteristic
18C22×#217C2×C312yes—
19C2×C3×#95—34no—
20C2×C3⋊#95C2×C314yescomplemented
21C24×C32—24no—
22C24×C32—24no—
23C24×C32—24no—
24C24×C32C2×C412yes—
25C24×C32D414yes—
26C24×C32C2311yescharacteristic
27C22×C32×C4—22no—
28C22×C32×C4—22no—
29C22×C32×C4—24no—
30C22×C32×C4—24no—
31C22×C32×C4C2×C414yes—
32C22×C3×Dic3—24no—
33C22×C3×Dic3—24no—
34C22×C3×Dic3—24no—
35C22×C3×Dic3—24no—
36C22×C3×Dic3—24no—
37C22×C3×Dic3—24no—
38C22×C3×Dic3D418yes—
39C32×C22⋊C4—28no—
40C3×#217—216no—
41#1440—31noSylow
42C25×C3—21no—
43C25×C3C2×D311yescharacteristic
44C25×C3C22×C311yescharacteristic
45C23×C3×C4—22no—
46C23×C3×C4—34no—
47C23×C3×C4C2×D312yes—
48C23×C3×C4C22×C312yes—
49C23×Dic3C22×C314yes—
50C2×C3×C22⋊C4—28no—
51C2×C3×C22⋊C4—24no—
52C2×C3×C22⋊C4—24no—
53C2×C3×C22⋊C4—24no—
54C2×C3×C22⋊C4—68no—
55C2×C3×C22⋊C4—64no—
56C2×C3×C22⋊C4Dic314yescomplemented
57C2×C3×C22⋊C4C3×C414yescomplemented
58C2×#217—24no—
59C2×#217—28no—
60C3×#95—68no—
61C3⋊#95—28no—
62C23×C32—24no—
63C23×C32—28no—
64C23×C32—28no—
65C23×C32—24no—
66C23×C32—28no—
67C23×C32—24no—
68C23×C32—44no—
69C23×C32—44no—
70C23×C32—44no—
71C23×C32—44no—
72C23×C32C22⋊C414yes—
73C23×C32C22×C411yescharacteristic
74C23×C32C2×D414yes—
75C23×C32C2×D412yes—
76C23×C32#4114yes—
77C23×C32#4114yes—
78C2×C32×C4—24no—
79C2×C32×C4—28no—
80C2×C32×C4—42no—
81C2×C32×C4—44no—
82C2×C32×C4—42no—
83C2×C3×Dic3—28no—
84C2×C3×Dic3—28no—
85C2×C3×Dic3—28no—
86C2×C3×Dic3—44no—
87C2×C3×Dic3—44no—
88C2×C3×Dic3—44no—
89C2×C3×Dic3—44no—
90C22×C22⋊C4—32no—
91C22×C22⋊C4C3×D311yescharacteristic
92C2×#95—34no—
93C24×C3—28no—
94C24×C3—24no—
95C24×C3—24no—
96C24×C3—24no—
97C24×C3—24no—
98C24×C3—24no—
99C24×C3—24no—
100C24×C3—22no—
101C24×C3—24no—
102C24×C3—21no—
103C24×C3—44no—
104C24×C3—44no—
105C24×C3C2×Dic312yes—
106C24×C3#6714yes—
107C24×C3C2×C3×C412yes—
108C24×C3C3×D414yes—
109C24×C3C22×D311yescharacteristic
110C24×C3C23×C311yescharacteristic
111C22×C3×C4—24no—
112C22×C3×C4—24no—
113C22×C3×C4—24no—
114C22×C3×C4—24no—
115C22×C3×C4—22no—
116C22×C3×C4—22no—
117C22×C3×C4—24no—
118C22×C3×C4—22no—
119C22×C3×C4—22no—
120C22×C3×C4—24no—
121C22×C3×C4—24no—
122C22×C3×C4—38no—
123C22×C3×C4—44no—
124C22×C3×C4—44no—
125C22×C3×C4—64no—
126C22×C3×C4—64no—
127C22×C3×C4—64no—
128C22×C3×C4—64no—
129C22×C3×C4—64no—
130C22×C3×C4—64no—
131C22×C3×C4C2×Dic314yes—
132C22×C3×C4C2×C3×C414yes—
133C22×Dic3—24no—
134C22×Dic3—24no—
135C22×Dic3—24no—
136C22×Dic3—24no—
137C22×Dic3—24no—
138C22×Dic3—24no—
139C22×Dic3C3×D418yes—
140C3×C22⋊C4—216no—
141C3×C22⋊C4—28no—
142C3×C22⋊C4—28no—
143C3×C22⋊C4—616no—
144#217—216no—
145C22×C32—24no—
146C22×C32—28no—
147C22×C32—48no—
148C22×C32—48no—
149C22×C32—48no—
150C22×C32C2×C22⋊C411yescharacteristic
151C22×C32#11712yes—
152C22×C32C4×D414yes—
153C22×C32#12012yes—
154C22×C32#12114yes—
155C22×C32#12114yes—
156C22×C32#12314yes—
157C22×C32#12314yes—
158C22×C32#12312yes—
159C22×C32#12414yes—
160C22×C32#12614yes—
161C32×C4—44no—
162C3×Dic3—48no—
163C25C2×C3×D311yescharacteristic
164C23×C4—34no—
165C23×C4C2×C3×D312yes—
166C2×C22⋊C4—24no—
167C2×C22⋊C4—68no—
168C2×C22⋊C4—64no—
169C2×C22⋊C4C3×Dic314yescomplemented
170#95—68no—
171C23×C3—28no—
172C23×C3—216no—
173C23×C3—24no—
174C23×C3—28no—
175C23×C3—28no—
176C23×C3—24no—
177C23×C3—24no—
178C23×C3—28no—
179C23×C3—24no—
180C23×C3—28no—
181C23×C3—24no—
182C23×C3—28no—
183C23×C3—28no—
184C23×C3—24no—
185C23×C3—24no—
186C23×C3—24no—
187C23×C3—24no—
188C23×C3—24no—
189C23×C3—21no—
190C23×C3—22no—
191C23×C3—48no—
192C23×C3—44no—
193C23×C3—44no—
194C23×C3—48no—
195C23×C3—48no—
196C23×C3—48no—
197C23×C3—48no—
198C23×C3—48no—
199C23×C3—44no—
200C23×C3—44no—
201C23×C3—44no—
202C23×C3—44no—
203C23×C3—44no—
204C23×C3—44no—
205C23×C3—44no—
206C23×C3—44no—
207C23×C3#21714yes—
208C23×C3C3×C22⋊C414yes—
209C23×C3#23514yes—
210C23×C3D3×D414yes—
211C23×C3#23714yes—
212C23×C3C22×Dic311yescharacteristic
213C23×C3C2×#6712yes—
214C23×C3C22×C3×C411yescharacteristic
215C23×C3C2×C3×D414yes—
216C23×C3C2×C3×D412yes—
217C23×C3C3×#4114yes—
218C23×C3C3×#4114yes—
219C2×C3×C4—28no—
220C2×C3×C4—28no—
221C2×C3×C4—24no—
222C2×C3×C4—24no—
223C2×C3×C4—28no—
224C2×C3×C4—48no—
225C2×C3×C4—44no—
226C2×C3×C4—44no—
227C2×C3×C4—48no—
228C2×C3×C4—42no—
229C2×C3×C4—42no—
230C2×C3×C4—44no—
231C2×C3×C4—42no—
232C2×C3×C4—44no—
233C2×C3×C4—42no—
234C2×C3×C4—68no—
235C2×C3×C4—68no—
236C2×C3×C4—68no—
237C2×C3×C4—124no—
238C2×C3×C4—124no—
239C2×C3×C4—124no—
240C2×C3×C4—124no—
241C2×Dic3—28no—
242C2×Dic3—28no—
243C2×Dic3—28no—
244C2×Dic3—44no—
245C2×Dic3—44no—
246C2×Dic3—44no—
247C2×Dic3—44no—
248C2×C32—44no—
249C2×C32#38111yescharacteristic
250C2×C32#38612yes—
251C2×C32#38814yes—
252C2×C32#39414yes—
253C2×C32#39714yes—
254C24—24no—
255C24—24no—
256C24—24no—
257C24C2×C3×Dic312yes—
258C24C3×#6714yes—
259C24C22×C3×D311yescharacteristic
260C22×C4—24no—
261C22×C4—24no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—38no—
265C22×C4—64no—
266C22×C4—64no—
267C22×C4—64no—
268C22×C4—64no—
269C22×C4—64no—
270C22×C4—64no—
271C22×C4C2×C3×Dic314yes—
272C22⋊C4—28no—
273C22⋊C4—616no—
274C22×C3—28no—
275C22×C3—24no—
276C22×C3—28no—
277C22×C3—24no—
278C22×C3—28no—
279C22×C3—24no—
280C22×C3—24no—
281C22×C3—24no—
282C22×C3—24no—
283C22×C3—22no—
284C22×C3—24no—
285C22×C3—24no—
286C22×C3—22no—
287C22×C3—22no—
288C22×C3—24no—
289C22×C3—21no—
290C22×C3—48no—
291C22×C3—416no—
292C22×C3—416no—
293C22×C3—416no—
294C22×C3—48no—
295C22×C3—48no—
296C22×C3—48no—
297C22×C3—48no—
298C22×C3—48no—
299C22×C3—48no—
300C22×C3#87914yes—
301C22×C3#88314yes—
302C22×C3#88414yes—
303C22×C3#88514yes—
304C22×C3#92612yes—
305C22×C3#92914yes—
306C22×C3D4×Dic314yes—
307C22×C3#93512yes—
308C22×C3#93712yes—
309C22×C3#93914yes—
310C22×C3C2×#21711yescharacteristic
311C22×C3C2×C3×C22⋊C411yescharacteristic
312C22×C3C3×#11712yes—
313C22×C3C3×C4×D414yes—
314C22×C3C3×#12012yes—
315C22×C3C3×#12114yes—
316C22×C3C3×#12114yes—
317C22×C3C3×#12314yes—
318C22×C3C3×#12314yes—
319C22×C3C3×#12312yes—
320C22×C3C3×#12414yes—
321C22×C3C3×#12614yes—
322C3×C4—48no—
323C3×C4—44no—
324C3×C4—44no—
325C3×C4—128no—
326Dic3—48no—
327C32#144011yescharacteristic, complemented, Sylow
328C23—24no—
329C23—28no—
330C23—28no—
331C23—24no—
332C23—24no—
333C23—28no—
334C23—44no—
335C23—44no—
336C23—44no—
337C23—44no—
338C23C3×#21714yes—
339C23C3×#23514yes—
340C23C3×D3×D414yes—
341C23C3×#23714yes—
342C23C22×C3×Dic311yescharacteristic
343C23C2×C3×#6712yes—
344C2×C4—28no—
345C2×C4—24no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—44no—
349C2×C4—68no—
350C2×C4—68no—
351C2×C4—68no—
352C2×C4—124no—
353C2×C4—124no—
354C2×C4—124no—
355C2×C4—124no—
356C2×C3—24no—
357C2×C3—24no—
358C2×C3—21no—
359C2×C3—24no—
360C2×C3—22no—
361C2×C3—48no—
362C2×C3—44no—
363C2×C3—44no—
364C2×C3#495114yes—
365C2×C3#495214yes—
366C2×C3#495914yes—
367C2×C3#521111yescharacteristic
368C2×C3#522012yes—
369C2×C3C3×#38111yescharacteristic
370C2×C3C3×#38612yes—
371C2×C3C3×#38814yes—
372C2×C3C3×#39414yes—
373C2×C3C3×#39714yes—
374C22—24no—
375C22—28no—
376C22—48no—
377C22—48no—
378C22—48no—
379C22C3×#87914yes—
380C22C3×#88314yes—
381C22C3×#88414yes—
382C22C3×#88514yes—
383C22C3×#92612yes—
384C22C3×#92914yes—
385C22C3×D4×Dic314yes—
386C22C3×#93512yes—
387C22C3×#93712yes—
388C22C3×#93914yes—
389C22C2×C3×#21711yescharacteristic
390C4—44no—
391C4—128no—
392C3—21no—
393C3#7154811yescharacteristic, direct product factor
394C3C3×#144011yescharacteristic, complemented
395C2—44no—
396C2C3×#495114yes—
397C2C3×#495214yes—
398C2C3×#495914yes—
399C2C3×#521111yescharacteristic
400C2C3×#522012yes—
subgroupG/H
centerC24×C3C22×D3
commutatorC23×C3C22×C3×C4
FrattiniC24C22×C3×D3
FittingC22×C32×C22⋊C4C2
socleC24×C32C23
prime radicalC25×C32C22
cosocleC24×C3C23×C3
hypercenterC22×C3×C22⋊C4D3
hypocenterC3C3×#1440
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C22×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C3×C3⋊#95C2semidirect
5. #71548C3direct (N × H)
10. C2×C32×C22⋊C4C4semidirect
20. C2×C3⋊#95C2×C3semidirect
56. C2×C3×C22⋊C4Dic3semidirect
57. C2×C3×C22⋊C4C3×C4semidirect
169. C2×C22⋊C4C3×Dic3semidirect
327. C32#1440semidirect
393. C3#71548direct (N × H)
394. C3C3×#1440semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C22⋊C42
C22×C3×#2172
C2×C3×C3⋊#952
C3×#14403
#715483