Finite Group Databasebeta

← C3×#69009 #11792273

Subgroups — C3×#69009 #11792273

Order 1152.

789 conjugacy classes of subgroups.

The subgroup lattice has 407 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#909C212yesmaximal, complemented
2C3×#5510C211yesmaximal, characteristic
3C2×C3×#825C212yesmaximal, complemented
4C3×#4973C211yesmaximal, characteristic, complemented
5C32×#343C211yesmaximal, characteristic, complemented
6C3×#2007—31nomaximal
7#69009C311yesmaximal, characteristic, direct product factor
8C2×C3×#235C2212yes—
9C22×C3×Dic6C2211yescharacteristic
10C2×C32×M16C2212yes—
11C2×C32×C4⋊C4C2211yescharacteristic
12C3×#930—22no—
13C2×C3×C4×Dic3C2211yescharacteristic
14C3×#909—24no—
15C3×#909—24no—
16C2×C3×Dic12—22no—
17C2×C3×#204—22no—
18C3×#897—22no—
19C3×#895—22no—
20C3×C3⋊#95—22no—
21C3×#825—24no—
22C2×C3×#137—32no—
23C3×#537—31no—
24C2×#909C2×C312yescomplemented
25#5510C2×C311yescharacteristic
26C2×C3×#104—32no—
27C3×#391—31no—
28C2×#825C2×C312yescomplemented
29#4973C2×C311yescharacteristic, complemented
30C3×#343—21no—
31C3×#343D311yescharacteristic, complemented
32C3×#343C2×C311yescharacteristic, complemented
33C22×C32×C4D412yes—
34C22×C32×C4C2311yescharacteristic
35C2×C3×#67—22no—
36C22×C3×Dic3—21no—
37C22×C3×Dic3—21no—
38C3×#235—22no—
39C3×#235—22no—
40C3×#235—22no—
41C3×#235—22no—
42C2×C3×D12—22no—
43C2×C3×D12D412yes—
44C2×C3×C4×D3—22no—
45C2×C3×Dic6—22no—
46C2×C3×Dic6—22no—
47C2×C3×Dic6—21no—
48C2×C3×Dic6D412yes—
49C2×C3×Dic6D412yescomplemented
50C32×M16—22no—
51C32×M16D414yescomplemented
52C2×C32×C8—22no—
53C32×C4⋊C4—22no—
54C3×(C2×D3)⋊C4—24no—
55C3×C4⋊Dic3—22no—
56C3×C4×Dic3—22no—
57C3×Dic12—28no—
58C3×#204—28no—
59#2007—31noSylow
60C2×C3×#41—32no—
61C22×C3×Q8—31no—
62C2×#235C22×C312yes—
63C22×Dic6C22×C311yescharacteristic
64C3×#137—64no—
65C3×#137—64no—
66C2×C3×Q16—62no—
67C2×C3×SD16—62no—
68C2×C3×M16—22no—
69C2×C3×M16C2×D312yes—
70C2×C3×M16C22×C312yes—
71C3×C22⋊Q8—62no—
72C3×#121—62no—
73C3×#121—62no—
74C2×C3×C4⋊C4—21no—
75C2×C3×C4⋊C4C2×D311yescharacteristic
76C2×C3×C4⋊C4C22×C311yescharacteristic
77C2×C3×C42—31no—
78#930—22no—
79C2×C4×Dic3C22×C311yescharacteristic
80#909—24no—
81#909—24no—
82C2×Dic12—22no—
83C2×#204—22no—
84#897—22no—
85#895—22no—
86C3×#104—64no—
87C3×#95—62no—
88C3⋊#95—22no—
89#825—24no—
90C23×C32C2×D411yescharacteristic
91C22×C3×D3—22no—
92C2×C32×C4—22no—
93C2×C32×C4—42no—
94C2×C32×C4C2×D412yes—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D412yes—
97C2×C32×C4#4111yescharacteristic
98C3×#67—42no—
99C3×#67—42no—
100C2×C3×Dic3—22no—
101C2×C3×Dic3—22no—
102C2×C3×Dic3—22no—
103C2×C3×Dic3—41no—
104C2×C3×Dic3—41no—
105C2×C3×Dic3—41no—
106C2×C3×Dic3—41no—
107C3×D12—22no—
108C3×D12—22no—
109C3×D12—82no—
110C3×C4×D3—42no—
111C3×C4×D3—42no—
112C3×Dic6—24no—
113C3×Dic6—22no—
114C3×Dic6—22no—
115C3×Dic6—42no—
116C32×C8—24no—
117C2×#137—32no—
118#537—31no—
119C2×#104—32no—
120#391—31no—
121#343C3×D311yescharacteristic, complemented
122C3×#41—62no—
123C3×#41—62no—
124C3×#41—62no—
125C3×#41—62no—
126C2×C3×Q8—32no—
127C2×C3×Q8—32no—
128C2×C3×Q8—61no—
129C2×C3×Q8—62no—
130C2×C3×Q8—62no—
131C2×C3×D4—32no—
132C2×C3×D4—62no—
133C2×C3×D4—62no—
134C22×C3×C4—22no—
135C22×C3×C4—21no—
136C22×C3×C4—61no—
137C22×C3×C4—61no—
138C22×C3×C4—62no—
139C22×C3×C4D1212yes—
140C22×C3×C4C3×D412yes—
141C22×C3×C4C22×D311yescharacteristic
142C22×C3×C4C23×C311yescharacteristic
143C2×#67—22no—
144C22×Dic3—21no—
145C22×Dic3—21no—
146#235—22no—
147#235—22no—
148#235—22no—
149#235—22no—
150C2×D12—22no—
151C2×D12C3×D412yes—
152C2×C4×D3—22no—
153C2×Dic6—22no—
154C2×Dic6—22no—
155C2×Dic6—21no—
156C2×Dic6C3×D412yes—
157C2×Dic6C3×D412yescomplemented
158C3×Q16—68no—
159C3×SD16—68no—
160C3×M16—22no—
161C3×M16—22no—
162C3×M16—24no—
163C3×M16—42no—
164C3×M16D1214yescomplemented
165C3×M16C3×D414yescomplemented
166C2×C3×C8—22no—
167C2×C3×C8—22no—
168C2×C3×C8—42no—
169C3×C4⋊C4—22no—
170C3×C4⋊C4—22no—
171C3×C4⋊C4—42no—
172C3×C4⋊C4—62no—
173C3×C22⋊C4—64no—
174C3×C42—62no—
175(C2×D3)⋊C4—24no—
176C4⋊Dic3—22no—
177C4×Dic3—22no—
178Dic12—28no—
179#204—28no—
180C22×C32—21no—
181C22×C32—21no—
182C22×C32#12011yescharacteristic
183C22×C32#12111yescharacteristic
184C22×C32#12711yescharacteristic
185C2×C3×D3—42no—
186C2×C3×D3—42no—
187C2×C3×D3—42no—
188C32×C4—42no—
189C32×C4#12012yes—
190C32×C4#12112yes—
191C3×Dic3—42no—
192C3×Dic3—42no—
193C3×Dic3—42no—
194C2×#41—32no—
195C22×Q8—31no—
196#137—64no—
197#137—64no—
198C2×Q16—62no—
199C2×SD16—62no—
200C2×M16C2×C3×D312yes—
201C22⋊Q8—62no—
202#121—62no—
203#121—62no—
204C2×C4⋊C4C2×C3×D311yescharacteristic
205C2×C42—31no—
206#104—64no—
207#95—62no—
208C23×C3—21no—
209C23×C3—62no—
210C23×C3C2×D1211yescharacteristic
211C23×C3C2×C3×D411yescharacteristic
212C22×D3—22no—
213C3×Q8—64no—
214C3×Q8—62no—
215C3×Q8—62no—
216C3×Q8—122no—
217C3×D4—62no—
218C3×D4—62no—
219C3×D4—122no—
220C3×D4—122no—
221C3×D4—242no—
222C2×C3×C4—22no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—42no—
229C2×C3×C4—42no—
230C2×C3×C4—42no—
231C2×C3×C4—62no—
232C2×C3×C4—62no—
233C2×C3×C4—62no—
234C2×C3×C4—82no—
235C2×C3×C4—121no—
236C2×C3×C4—121no—
237C2×C3×C4—121no—
238C2×C3×C4—121no—
239C2×C3×C4—122no—
240C2×C3×C4—122no—
241C2×C3×C4C2×D1212yes—
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4D3×D412yes—
244C2×C3×C4#23911yescharacteristic
245C2×C3×C4C2×C3×D412yes—
246C2×C3×C4C2×C3×D411yescharacteristic
247C2×C3×C4C2×C3×D412yes—
248C2×C3×C4C3×#4111yescharacteristic
249#67—42no—
250#67—42no—
251C2×Dic3—22no—
252C2×Dic3—22no—
253C2×Dic3—22no—
254C2×Dic3—41no—
255C2×Dic3—41no—
256C2×Dic3—41no—
257C2×Dic3—41no—
258D12—22no—
259D12—22no—
260D12—82no—
261C4×D3—42no—
262C4×D3—42no—
263Dic6—24no—
264Dic6—22no—
265Dic6—22no—
266Dic6—42no—
267C3×C8—24no—
268C3×C8—24no—
269C3×C8—44no—
270C2×C32—21no—
271C2×C32—21no—
272C2×C32#39211yescharacteristic
273C2×C32#45511yescharacteristic
274C2×C32#45611yescharacteristic
275C3×D3—82no—
276#41—62no—
277#41—62no—
278#41—62no—
279#41—62no—
280C2×Q8—32no—
281C2×Q8—32no—
282C2×Q8—61no—
283C2×Q8—62no—
284C2×Q8—62no—
285C2×D4—32no—
286C2×D4—62no—
287C2×D4—62no—
288C22×C4—61no—
289C22×C4—61no—
290C22×C4—62no—
291C22×C4C3×D1212yes—
292C22×C4C22×C3×D311yescharacteristic
293Q16—68no—
294SD16—68no—
295M16—22no—
296M16C3×D1214yescomplemented
297C2×C8—22no—
298C4⋊C4—22no—
299C4⋊C4—62no—
300C22⋊C4—64no—
301C42—62no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—21no—
306C22×C3—21no—
307C22×C3—21no—
308C22×C3—21no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—122no—
312C22×C3—122no—
313C22×C3—122no—
314C22×C3#87411yescharacteristic
315C22×C3#88211yescharacteristic
316C22×C3#89511yescharacteristic
317C22×C3C3×#12011yescharacteristic
318C22×C3C3×#12111yescharacteristic
319C22×C3C3×#12711yescharacteristic
320C2×D3—42no—
321C2×D3—42no—
322C2×D3—42no—
323C3×C4—22no—
324C3×C4—22no—
325C3×C4—42no—
326C3×C4—42no—
327C3×C4—82no—
328C3×C4—122no—
329C3×C4—122no—
330C3×C4—122no—
331C3×C4#88212yes—
332C3×C4#89512yes—
333C3×C4C3×#12012yes—
334C3×C4C3×#12112yes—
335Dic3—42no—
336Dic3—42no—
337Dic3—42no—
338C32#200711yescharacteristic, complemented, Sylow
339C23—62no—
340C23C2×C3×D1211yescharacteristic
341Q8—64no—
342Q8—62no—
343Q8—62no—
344Q8—122no—
345D4—62no—
346D4—62no—
347D4—122no—
348D4—122no—
349D4—242no—
350C2×C4—22no—
351C2×C4—42no—
352C2×C4—62no—
353C2×C4—62no—
354C2×C4—62no—
355C2×C4—121no—
356C2×C4—121no—
357C2×C4—121no—
358C2×C4—121no—
359C2×C4—122no—
360C2×C4—122no—
361C2×C4C2×C3×D1212yes—
362C2×C4C3×D3×D411yescharacteristic
363C2×C4C3×D3×D412yes—
364C2×C4C3×#23911yescharacteristic
365C8—24no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—41no—
374C2×C3—41no—
375C2×C3—242no—
376C2×C3#467111yescharacteristic
377C2×C3#474611yescharacteristic
378C2×C3#475211yescharacteristic
379C2×C3C3×#39211yescharacteristic
380C2×C3C3×#45511yescharacteristic
381C2×C3C3×#45611yescharacteristic
382D3—82no—
383C22—21no—
384C22—21no—
385C22—122no—
386C22—122no—
387C22—122no—
388C22C3×#87411yescharacteristic
389C22C3×#88211yescharacteristic
390C22C3×#89511yescharacteristic
391C4—42no—
392C4—122no—
393C4—122no—
394C4—122no—
395C4C3×#88212yes—
396C4C3×#89512yes—
397C3—21no—
398C3#6900911yescharacteristic, direct product factor
399C3C3×#200711yescharacteristic, complemented
400C2—21no—
401C2—21no—
402C2—242no—
403C2C3×#467111yescharacteristic
404C2C3×#474611yescharacteristic
405C2C3×#475211yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#343C2
socleC22×C32#120
prime radicalC3×#5510C2
hypercenterC3×#343D3
hypocenterC3C3×#2007
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#343

Complements

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

NH ≅ G/Ntype
1. C2×C3×#909C2semidirect
3. C2×C3×#825C2semidirect
4. C3×#4973C2semidirect
5. C32×#343C2semidirect
7. #69009C3direct (N × H)
24. C2×#909C2×C3semidirect
28. C2×#825C2×C3semidirect
29. #4973C2×C3semidirect
31. C3×#343D3semidirect
32. C3×#343C2×C3semidirect
49. C2×C3×Dic6D4semidirect
51. C32×M16D4semidirect
121. #343C3×D3semidirect
157. C2×Dic6C3×D4semidirect
164. C3×M16D12semidirect
165. C3×M16C3×D4semidirect
296. M16C3×D12semidirect
338. C32#2007semidirect
398. C3#69009direct (N × H)
399. C3C3×#2007semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9092
C3×#55102
C2×C3×#8252
C3×#49732
C32×#3432
C3×#20073
#690093