Finite Group Databasebeta

← C3×#69691 #11792625

Subgroups — C3×#69691 #11792625

Order 1152.

833 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#216C212yesmaximal
2C2×C3×#869C211yesmaximal, characteristic
3C32×#391C211yesmaximal, characteristic
4C2×C3×#810C212yesmaximal
5C3×#4524C211yesmaximal, characteristic
6C3×#2016—31nomaximal
7#69691C311yesmaximal, characteristic, direct product factor
8C22×C32×Q8C2211yescharacteristic
9C22×C3×Dic6C2212yes—
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×C3×#216—24no—
13C2×C3×#216—24no—
14C2×C3×#216—24no—
15C2×C3×C4⋊Dic3—22no—
16C22×C3×C3⋊C8C2212yes—
17C3×#869—24no—
18C32×#95—22no—
19C3×#810—24no—
20C22×C3×Q16—32no—
21C2×C3×C4⋊Q8—31no—
22C22×#216C2×C312yes—
23C2×#869C2×C311yescharacteristic
24C2×C3×#103—32no—
25C3×#391—21no—
26C3×#391D311yescharacteristic
27C3×#391C2×C311yescharacteristic
28C2×#810C2×C312yes—
29C3×#336—31no—
30#4524C2×C311yescharacteristic
31C2×C32×Q8—21no—
32C2×C32×Q8—22no—
33C2×C32×Q8—22no—
34C2×C32×Q8D412yes—
35C22×C32×C4—21no—
36C22×C32×C4—21no—
37C22×C32×C4D412yes—
38C22×C32×C4C2311yescharacteristic
39C22×C3×Dic3—22no—
40C2×C3×Dic6—22no—
41C2×C3×Dic6—22no—
42C2×C3×Dic6—22no—
43C2×C3×Dic6—22no—
44C2×C3×Dic6—22no—
45C2×C3×Dic6D414yes—
46C32×C4⋊C4—22no—
47C32×C42—22no—
48C3×#216—216no—
49C3×C4⋊Dic3—28no—
50C2×C3×C3⋊C8—22no—
51C2×C3×C3⋊C8—22no—
52C2×C3×C3⋊C8D414yes—
53#2016—31noSylow
54C22×C3×Q8—21no—
55C22×C3×Q8—32no—
56C22×C3×Q8C2×D311yescharacteristic
57C22×C3×Q8C22×C311yescharacteristic
58C22×Dic6C22×C312yes—
59C2×C3×Q16—64no—
60C2×C3×Q16—64no—
61C2×C3×Q16—64no—
62C22×C3×C8—32no—
63C3×C4⋊Q8—64no—
64C2×C3×C4⋊C4—21no—
65C2×C3×C4⋊C4—62no—
66C2×C3×C4⋊C4C2×D311yescharacteristic
67C2×C3×C4⋊C4C22×C311yescharacteristic
68C2×C3×C42—21no—
69C2×C3×C42C2×D311yescharacteristic
70C2×C3×C42C22×C311yescharacteristic
71C2×#216—24no—
72C2×#216—24no—
73C2×#216—24no—
74C2×C4⋊Dic3—22no—
75C22×C3⋊C8C22×C312yes—
76#869—24no—
77C3×#103—64no—
78C3×#95—24no—
79C3×#95—22no—
80C3×#95—22no—
81#810—24no—
82C23×C32C2×D411yescharacteristic
83C32×Q8—24no—
84C32×Q8—42no—
85C2×C32×C4—22no—
86C2×C32×C4—22no—
87C2×C32×C4—22no—
88C2×C32×C4—41no—
89C2×C32×C4—41no—
90C2×C32×C4—41no—
91C2×C32×C4—42no—
92C2×C32×C4Q1614yescomplemented
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D412yes—
95C2×C32×C4C2×D412yes—
96C2×C32×C4#4111yescharacteristic
97C2×C3×Dic3—24no—
98C2×C3×Dic3—42no—
99C2×C3×Dic3—42no—
100C3×Dic6—24no—
101C3×Dic6—24no—
102C3×Dic6—42no—
103C3×Dic6—42no—
104C3×C3⋊C8—24no—
105C22×Q16—32no—
106C2×C4⋊Q8—31no—
107C2×#103—32no—
108#391C3×D311yescharacteristic
109#336—31no—
110C2×C3×Q8—22no—
111C2×C3×Q8—21no—
112C2×C3×Q8—21no—
113C2×C3×Q8—22no—
114C2×C3×Q8—22no—
115C2×C3×Q8—22no—
116C2×C3×Q8—22no—
117C2×C3×Q8—22no—
118C2×C3×Q8—34no—
119C2×C3×Q8—42no—
120C2×C3×Q8—42no—
121C2×C3×Q8—62no—
122C2×C3×Q8—62no—
123C2×C3×Q8—62no—
124C2×C3×Q8—62no—
125C2×C3×Q8—62no—
126C2×C3×Q8D1212yes—
127C2×C3×Q8C3×D412yes—
128C22×C3×C4—22no—
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—22no—
132C22×C3×C4—21no—
133C22×C3×C4—21no—
134C22×C3×C4—22no—
135C22×C3×C4—21no—
136C22×C3×C4—62no—
137C22×C3×C4#6712yes—
138C22×C3×C4C3×D412yes—
139C22×C3×C4C22×D311yescharacteristic
140C22×C3×C4C23×C311yescharacteristic
141C22×Dic3—22no—
142C2×Dic6—22no—
143C2×Dic6—22no—
144C2×Dic6—22no—
145C2×Dic6—22no—
146C2×Dic6—22no—
147C2×Dic6C3×D414yes—
148C3×Q16—616no—
149C2×C3×C8—34no—
150C2×C3×C8—62no—
151C2×C3×C8—62no—
152C3×C4⋊C4—22no—
153C3×C4⋊C4—22no—
154C3×C4⋊C4—42no—
155C3×C4⋊C4—68no—
156C3×C42—22no—
157C3×C42—22no—
158C3×C42—42no—
159#216—216no—
160C4⋊Dic3—28no—
161C2×C3⋊C8—22no—
162C2×C3⋊C8—22no—
163C2×C3⋊C8C3×D414yes—
164C22×C32#12011yescharacteristic
165C22×C32#12111yescharacteristic
166C22×C32#12711yescharacteristic
167C22×C32C2×Q1612yes—
168C22×C32#13712yes—
169C32×C4—24no—
170C32×C4—42no—
171C32×C4—81no—
172C32×C4#12012yes—
173C32×C4#12112yes—
174C3×Dic3—44no—
175C22×Q8—32no—
176C22×Q8C2×C3×D311yescharacteristic
177C2×Q16—64no—
178C2×Q16—64no—
179C2×Q16—64no—
180C22×C8—32no—
181C4⋊Q8—64no—
182C2×C4⋊C4—62no—
183C2×C4⋊C4C2×C3×D311yescharacteristic
184C2×C42C2×C3×D311yescharacteristic
185#103—64no—
186#95—22no—
187C23×C3—21no—
188C23×C3C2×#6711yescharacteristic
189C23×C3C2×C3×D411yescharacteristic
190C3×Q8—24no—
191C3×Q8—24no—
192C3×Q8—44no—
193C3×Q8—44no—
194C3×Q8—42no—
195C3×Q8—42no—
196C3×Q8—64no—
197C3×Q8—64no—
198C3×Q8—122no—
199C3×Q8—122no—
200C2×C3×C4—22no—
201C2×C3×C4—22no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—24no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—24no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—22no—
211C2×C3×C4—22no—
212C2×C3×C4—42no—
213C2×C3×C4—42no—
214C2×C3×C4—42no—
215C2×C3×C4—42no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—41no—
219C2×C3×C4—41no—
220C2×C3×C4—42no—
221C2×C3×C4—44no—
222C2×C3×C4—41no—
223C2×C3×C4—42no—
224C2×C3×C4—41no—
225C2×C3×C4—42no—
226C2×C3×C4—64no—
227C2×C3×C4—122no—
228C2×C3×C4—122no—
229C2×C3×C4#21614yescomplemented
230C2×C3×C4C3×Q1614yescomplemented
231C2×C3×C4C2×D1211yescharacteristic
232C2×C3×C4#23511yescharacteristic
233C2×C3×C4D3×D412yes—
234C2×C3×C4D3×D412yes—
235C2×C3×C4C2×C3×D411yescharacteristic
236C2×C3×C4C2×C3×D412yes—
237C2×C3×C4C2×C3×D412yes—
238C2×C3×C4C3×#4111yescharacteristic
239C2×Dic3—24no—
240C2×Dic3—42no—
241C2×Dic3—42no—
242Dic6—24no—
243Dic6—24no—
244Dic6—42no—
245Dic6—42no—
246C3×C8—64no—
247C3⋊C8—24no—
248C2×C32#39211yescharacteristic
249C2×C32#45112yes—
250C2×C32#46212yes—
251C2×C32#49411yescharacteristic
252C2×C32#49711yescharacteristic
253C2×Q8—21no—
254C2×Q8—22no—
255C2×Q8—22no—
256C2×Q8—34no—
257C2×Q8—62no—
258C2×Q8—62no—
259C2×Q8—62no—
260C2×Q8—62no—
261C2×Q8—62no—
262C2×Q8C3×D1212yes—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—62no—
266C22×C4C3×#6712yes—
267C22×C4C22×C3×D311yescharacteristic
268Q16—616no—
269C2×C8—34no—
270C2×C8—62no—
271C2×C8—62no—
272C4⋊C4—22no—
273C4⋊C4—68no—
274C42—22no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—22no—
279C22×C3—22no—
280C22×C3#93011yescharacteristic
281C22×C3#93711yescharacteristic
282C22×C3#94011yescharacteristic
283C22×C3C2×#21612yes—
284C22×C3#95112yes—
285C22×C3C3×#12011yescharacteristic
286C22×C3C3×#12111yescharacteristic
287C22×C3C3×#12711yescharacteristic
288C22×C3C2×C3×Q1612yes—
289C22×C3C3×#13712yes—
290C3×C4—24no—
291C3×C4—24no—
292C3×C4—22no—
293C3×C4—22no—
294C3×C4—44no—
295C3×C4—44no—
296C3×C4—42no—
297C3×C4—42no—
298C3×C4—82no—
299C3×C4—81no—
300C3×C4—81no—
301C3×C4—124no—
302C3×C4#88212yes—
303C3×C4#88412yes—
304C3×C4C3×#12012yes—
305C3×C4C3×#12112yes—
306Dic3—44no—
307C32#201611yescharacteristic, complemented, Sylow
308C23C2×C3×#6711yescharacteristic
309Q8—24no—
310Q8—42no—
311Q8—64no—
312Q8—64no—
313Q8—122no—
314Q8—122no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—64no—
323C2×C4—122no—
324C2×C4—122no—
325C2×C4C3×#21614yescomplemented
326C2×C4C2×C3×D1211yescharacteristic
327C2×C4C3×#23511yescharacteristic
328C2×C4C3×D3×D412yes—
329C2×C4C3×D3×D412yes—
330C8—64no—
331C2×C3—21no—
332C2×C3—22no—
333C2×C3—22no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3#496011yescharacteristic
337C2×C3#503112yes—
338C2×C3#505012yes—
339C2×C3#506011yescharacteristic
340C2×C3#509211yescharacteristic
341C2×C3C3×#39211yescharacteristic
342C2×C3C3×#45112yes—
343C2×C3C3×#46212yes—
344C2×C3C3×#49411yescharacteristic
345C2×C3C3×#49711yescharacteristic
346C22C3×#93011yescharacteristic
347C22C3×#93711yescharacteristic
348C22C3×#94011yescharacteristic
349C22C2×C3×#21612yes—
350C22C3×#95112yes—
351C4—24no—
352C4—42no—
353C4—81no—
354C4—124no—
355C4C3×#88212yes—
356C4C3×#88412yes—
357C3—21no—
358C3#6969111yescharacteristic, direct product factor
359C3C3×#201611yescharacteristic, complemented
360C2C3×#496011yescharacteristic
361C2C3×#503112yes—
362C2C3×#505012yes—
363C2C3×#506011yescharacteristic
364C2C3×#509211yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#391C2
socle, prime radicalC23×C32C2×D4
hypercenterC3×#391D3
hypocenterC3C3×#2016
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C3×#391

Complements

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

NH ≅ G/Ntype
7. #69691C3direct (N × H)
92. C2×C32×C4Q16semidirect
229. C2×C3×C4#216semidirect
230. C2×C3×C4C3×Q16semidirect
307. C32#2016semidirect
325. C2×C4C3×#216semidirect
358. C3#69691direct (N × H)
359. C3C3×#2016semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2162
C2×C3×#8692
C32×#3912
C2×C3×#8102
C3×#45242
C3×#20163
#696913