Finite Group Databasebeta

← C3×#69694 #11792264

Subgroups — C3×#69694 #11792264

Order 1152.

833 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#942C212yesmaximal, complemented
2C3×#5510C211yesmaximal, characteristic
3C32×#391C211yesmaximal, characteristic, complemented
4C2×C3×#805C212yesmaximal, complemented
5C3×#4530C211yesmaximal, characteristic, complemented
6C3×#2007—31nomaximal
7#69694C311yesmaximal, characteristic, direct product factor
8C22×C32×Q8C2211yescharacteristic
9C2×C3×#235C2212yes—
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×C3×#216—22no—
13C3×#942—24no—
14C3×#942—24no—
15C2×C3×#215—22no—
16C3×#930—22no—
17C2×C3×#208C2212yes—
18C3×#897—22no—
19C3×#895—22no—
20C32×#95—22no—
21C3×#805—24no—
22C2×C3×#137—32no—
23C3×#537—31no—
24C2×#942C2×C312yescomplemented
25#5510C2×C311yescharacteristic
26C2×C3×#104—32no—
27C3×#391—21no—
28C3×#391D311yescharacteristic, complemented
29C3×#391C2×C311yescharacteristic, complemented
30C2×#805C2×C312yescomplemented
31C3×#343—31no—
32#4530C2×C311yescharacteristic, complemented
33C2×C32×Q8—21no—
34C2×C32×Q8—22no—
35C2×C32×Q8—22no—
36C2×C32×Q8D412yescomplemented
37C22×C32×C4—21no—
38C22×C32×C4—21no—
39C22×C32×C4D412yes—
40C22×C32×C4C2311yescharacteristic
41C2×C3×#67—22no—
42C3×#235—22no—
43C3×#235—22no—
44C3×#235—22no—
45C3×#235—22no—
46C2×C3×D12—22no—
47C2×C3×D12D412yes—
48C2×C3×C4×D3—22no—
49C2×C3×Dic6D412yes—
50C32×C4⋊C4—22no—
51C32×C42—22no—
52C3×#216—28no—
53C3×#215—28no—
54C3×(C2×D3)⋊C4—24no—
55C3×C4⋊Dic3—22no—
56C3×#208—22no—
57C3×#208D414yescomplemented
58C2×C3×C3⋊C8—22no—
59#2007—31noSylow
60C2×C3×#41—32no—
61C22×C3×Q8—21no—
62C22×C3×Q8C2×D311yescharacteristic
63C22×C3×Q8C22×C311yescharacteristic
64C2×#235C22×C312yes—
65C3×#137—64no—
66C3×#137—64no—
67C2×C3×Q16—62no—
68C2×C3×SD16—62no—
69C2×C3×M16—32no—
70C3×C22⋊Q8—62no—
71C3×#121—62no—
72C3×#121—62no—
73C2×C3×C4⋊C4—21no—
74C2×C3×C4⋊C4C2×D311yescharacteristic
75C2×C3×C4⋊C4C22×C311yescharacteristic
76C2×C3×C42—21no—
77C2×C3×C42C2×D311yescharacteristic
78C2×C3×C42C22×C311yescharacteristic
79C2×#216—22no—
80#942—24no—
81#942—24no—
82C2×#215—22no—
83#930—22no—
84C2×#208C22×C312yes—
85#897—22no—
86#895—22no—
87C3×#104—64no—
88C3×#95—24no—
89C3×#95—22no—
90C3×#95—22no—
91#805—24no—
92C23×C32C2×D411yescharacteristic
93C22×C3×D3—22no—
94C32×Q8—24no—
95C32×Q8—42no—
96C2×C32×C4—22no—
97C2×C32×C4—22no—
98C2×C32×C4—22no—
99C2×C32×C4—41no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C32×C4—42no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D412yes—
106C2×C32×C4C2×D412yes—
107C2×C32×C4#4111yescharacteristic
108C3×#67—42no—
109C3×#67—42no—
110C2×C3×Dic3—22no—
111C3×D12—22no—
112C3×D12—22no—
113C3×D12—82no—
114C3×C4×D3—42no—
115C3×C4×D3—42no—
116C3×Dic6—22no—
117C3×Dic6—22no—
118C3×C3⋊C8—24no—
119C2×#137—32no—
120#537—31no—
121C2×#104—32no—
122#391C3×D311yescharacteristic, complemented
123#343—31no—
124C3×#41—62no—
125C3×#41—62no—
126C3×#41—62no—
127C3×#41—62no—
128C2×C3×Q8—22no—
129C2×C3×Q8—21no—
130C2×C3×Q8—21no—
131C2×C3×Q8—22no—
132C2×C3×Q8—22no—
133C2×C3×Q8—22no—
134C2×C3×Q8—22no—
135C2×C3×Q8—22no—
136C2×C3×Q8—32no—
137C2×C3×Q8—42no—
138C2×C3×Q8—42no—
139C2×C3×Q8D1212yescomplemented
140C2×C3×Q8C3×D412yescomplemented
141C2×C3×D4—32no—
142C2×C3×D4—62no—
143C2×C3×D4—62no—
144C22×C3×C4—22no—
145C22×C3×C4—22no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—22no—
151C22×C3×C4—21no—
152C22×C3×C4—62no—
153C22×C3×C4#6712yes—
154C22×C3×C4C3×D412yes—
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C23×C311yescharacteristic
157C2×#67—22no—
158#235—22no—
159#235—22no—
160#235—22no—
161#235—22no—
162C2×D12—22no—
163C2×D12C3×D412yes—
164C2×C4×D3—22no—
165C2×Dic6C3×D412yes—
166C3×Q16—68no—
167C3×SD16—68no—
168C3×M16—34no—
169C3×M16—62no—
170C2×C3×C8—62no—
171C3×C4⋊C4—22no—
172C3×C4⋊C4—22no—
173C3×C4⋊C4—42no—
174C3×C4⋊C4—62no—
175C3×C22⋊C4—64no—
176C3×C42—22no—
177C3×C42—22no—
178C3×C42—42no—
179#216—28no—
180#215—28no—
181(C2×D3)⋊C4—24no—
182C4⋊Dic3—22no—
183#208—22no—
184#208C3×D414yescomplemented
185C2×C3⋊C8—22no—
186C22×C32—21no—
187C22×C32—21no—
188C22×C32#12011yescharacteristic
189C22×C32#12111yescharacteristic
190C22×C32#12711yescharacteristic
191C2×C3×D3—42no—
192C2×C3×D3—42no—
193C2×C3×D3—42no—
194C32×C4—42no—
195C32×C4—42no—
196C32×C4—42no—
197C32×C4#12012yes—
198C32×C4#12112yes—
199C3×Dic3—42no—
200C2×#41—32no—
201C22×Q8C2×C3×D311yescharacteristic
202#137—64no—
203#137—64no—
204C2×Q16—62no—
205C2×SD16—62no—
206C2×M16—32no—
207C22⋊Q8—62no—
208#121—62no—
209#121—62no—
210C2×C4⋊C4C2×C3×D311yescharacteristic
211C2×C42C2×C3×D311yescharacteristic
212#104—64no—
213#95—22no—
214C23×C3—21no—
215C23×C3—62no—
216C23×C3C2×#6711yescharacteristic
217C23×C3C2×C3×D411yescharacteristic
218C22×D3—22no—
219C3×Q8—24no—
220C3×Q8—24no—
221C3×Q8—44no—
222C3×Q8—44no—
223C3×Q8—42no—
224C3×Q8—42no—
225C3×Q8—62no—
226C3×Q8—62no—
227C3×D4—62no—
228C3×D4—62no—
229C3×D4—122no—
230C3×D4—122no—
231C3×D4—242no—
232C2×C3×C4—24no—
233C2×C3×C4—22no—
234C2×C3×C4—22no—
235C2×C3×C4—24no—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—22no—
239C2×C3×C4—22no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—42no—
245C2×C3×C4—42no—
246C2×C3×C4—42no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—42no—
250C2×C3×C4—42no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—42no—
258C2×C3×C4—42no—
259C2×C3×C4—44no—
260C2×C3×C4—62no—
261C2×C3×C4—122no—
262C2×C3×C4—122no—
263C2×C3×C4C2×D1211yescharacteristic
264C2×C3×C4#23511yescharacteristic
265C2×C3×C4D3×D412yes—
266C2×C3×C4D3×D412yes—
267C2×C3×C4C2×C3×D411yescharacteristic
268C2×C3×C4C2×C3×D412yes—
269C2×C3×C4C2×C3×D412yes—
270C2×C3×C4C3×#4111yescharacteristic
271#67—42no—
272#67—42no—
273C2×Dic3—22no—
274D12—22no—
275D12—22no—
276D12—82no—
277C4×D3—42no—
278C4×D3—42no—
279Dic6—22no—
280Dic6—22no—
281C3×C8—64no—
282C3⋊C8—24no—
283C2×C32—21no—
284C2×C32—21no—
285C2×C32#39211yescharacteristic
286C2×C32#45511yescharacteristic
287C2×C32#45611yescharacteristic
288C3×D3—82no—
289#41—62no—
290#41—62no—
291#41—62no—
292#41—62no—
293C2×Q8—21no—
294C2×Q8—22no—
295C2×Q8—22no—
296C2×Q8—32no—
297C2×Q8C3×D1212yescomplemented
298C2×D4—32no—
299C2×D4—62no—
300C2×D4—62no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—62no—
304C22×C4C3×#6712yes—
305C22×C4C22×C3×D311yescharacteristic
306Q16—68no—
307SD16—68no—
308M16—34no—
309M16—62no—
310C2×C8—62no—
311C4⋊C4—22no—
312C4⋊C4—62no—
313C22⋊C4—64no—
314C42—22no—
315C22×C3—22no—
316C22×C3—22no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—122no—
325C22×C3—122no—
326C22×C3—122no—
327C22×C3#93011yescharacteristic
328C22×C3#93711yescharacteristic
329C22×C3#94011yescharacteristic
330C22×C3C3×#12011yescharacteristic
331C22×C3C3×#12111yescharacteristic
332C22×C3C3×#12711yescharacteristic
333C2×D3—42no—
334C2×D3—42no—
335C2×D3—42no—
336C3×C4—22no—
337C3×C4—22no—
338C3×C4—44no—
339C3×C4—44no—
340C3×C4—42no—
341C3×C4—42no—
342C3×C4—42no—
343C3×C4—42no—
344C3×C4—42no—
345C3×C4—42no—
346C3×C4—82no—
347C3×C4—122no—
348C3×C4#88212yes—
349C3×C4#88412yes—
350C3×C4C3×#12012yes—
351C3×C4C3×#12112yes—
352Dic3—42no—
353C32#200711yescharacteristic, complemented, Sylow
354C23—62no—
355C23C2×C3×#6711yescharacteristic
356Q8—24no—
357Q8—42no—
358Q8—62no—
359Q8—62no—
360D4—62no—
361D4—62no—
362D4—122no—
363D4—122no—
364D4—242no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—62no—
374C2×C4—122no—
375C2×C4—122no—
376C2×C4C2×C3×D1211yescharacteristic
377C2×C4C3×#23511yescharacteristic
378C2×C4C3×D3×D412yes—
379C2×C4C3×D3×D412yes—
380C8—64no—
381C2×C3—22no—
382C2×C3—22no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—242no—
391C2×C3#496011yescharacteristic
392C2×C3#506111yescharacteristic
393C2×C3#509511yescharacteristic
394C2×C3C3×#39211yescharacteristic
395C2×C3C3×#45511yescharacteristic
396C2×C3C3×#45611yescharacteristic
397D3—82no—
398C22—21no—
399C22—21no—
400C22—122no—
401C22—122no—
402C22—122no—
403C22C3×#93011yescharacteristic
404C22C3×#93711yescharacteristic
405C22C3×#94011yescharacteristic
406C4—42no—
407C4—42no—
408C4—42no—
409C4—122no—
410C4C3×#88212yes—
411C4C3×#88412yes—
412C3—21no—
413C3#6969411yescharacteristic, direct product factor
414C3C3×#200711yescharacteristic, complemented
415C2—21no—
416C2—21no—
417C2—242no—
418C2C3×#496011yescharacteristic
419C2C3×#506111yescharacteristic
420C2C3×#509511yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#391C2
socleC22×C32#120
prime radicalC3×#5510C2
hypercenterC3×#391D3
hypocenterC3C3×#2007
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#391

Complements

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

NH ≅ G/Ntype
1. C2×C3×#942C2semidirect
3. C32×#391C2semidirect
4. C2×C3×#805C2semidirect
5. C3×#4530C2semidirect
7. #69694C3direct (N × H)
24. C2×#942C2×C3semidirect
28. C3×#391D3semidirect
29. C3×#391C2×C3semidirect
30. C2×#805C2×C3semidirect
32. #4530C2×C3semidirect
36. C2×C32×Q8D4semidirect
57. C3×#208D4semidirect
122. #391C3×D3semidirect
139. C2×C3×Q8D12semidirect
140. C2×C3×Q8C3×D4semidirect
184. #208C3×D4semidirect
297. C2×Q8C3×D12semidirect
353. C32#2007semidirect
413. C3#69694direct (N × H)
414. C3C3×#2007semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9422
C3×#55102
C32×#3912
C2×C3×#8052
C3×#45302
C3×#20073
#696943