Finite Group Databasebeta

← C3×#69488 #11791482

Subgroups — C3×#69488 #11791482

Order 1152.

785 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#875C211yesmaximal, characteristic
2C32×C4×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#810C212yesmaximal, complemented
4C2×C3×#809C212yesmaximal
5C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C3×#1983—31nomaximal
7#69488C311yesmaximal, characteristic, direct product factor
8C22×C3×D12C2211yescharacteristic
9C22×C3×Dic6C2211yescharacteristic
10C2×C32×C4⋊C4C2212yes—
11C2×C32×C42—21no—
12C2×C32×C42C2211yescharacteristic
13C2×C3×(C2×D3)⋊C4—21no—
14C2×C3×(C2×D3)⋊C4—21no—
15C22×C3×C3⋊C8C2212yes—
16C3×#875—22no—
17C3×#875C414yescomplemented
18C32×#95—21no—
19C3×#810—24no—
20C3×#809—24no—
21C3×C4⋊(C3⋊C8)—22no—
22C2×C3×#124—31no—
23C2×#875C2×C311yescharacteristic
24C2×C3×C4⋊C8—31no—
25C2×C3×#103—32no—
26C2×C3×#102—32no—
27C3×C4×C4⋊C4—21no—
28C3×C4×C4⋊C4D311yescharacteristic, complemented
29C3×C4×C4⋊C4C2×C311yescharacteristic, complemented
30C2×#810C2×C312yescomplemented
31C2×#809C2×C312yes—
32C2×C4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
33C23×C3×D3—21no—
34C22×C32×C4—22no—
35C22×C32×C4D411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4C2311yescharacteristic
38C22×C3×Dic3—21no—
39C2×C3×D12—22no—
40C2×C3×D12—22no—
41C2×C3×D12—21no—
42C2×C3×D12C2×C412yes—
43C2×C3×Dic6—22no—
44C2×C3×Dic6—22no—
45C2×C3×Dic6—21no—
46C2×C3×Dic6C2×C412yes—
47C32×C4⋊C4—22no—
48C32×C4⋊C4D414yes—
49C32×C42—42no—
50C32×C42C2×C412yes—
51C32×C42D412yes—
52C3×(C2×D3)⋊C4—24no—
53C3×(C2×D3)⋊C4—24no—
54C2×C3×C3⋊C8—22no—
55C2×C3×C3⋊C8—22no—
56C2×C3×C3⋊C8—22no—
57#1983—31noSylow
58C22×C3×Q8—31no—
59C22×C3×D4—31no—
60C22×D12C22×C311yescharacteristic
61C22×Dic6C22×C311yescharacteristic
62C22×C3×C8—32no—
63C3×#124—34no—
64C3×#124—62no—
65C2×C3×C4⋊C4—22no—
66C2×C3×C4⋊C4C2×D312yes—
67C2×C3×C4⋊C4C22×C312yes—
68C2×C3×C22⋊C4—61no—
69C2×C3×C22⋊C4—61no—
70C2×C3×C42—22no—
71C2×C3×C42—21no—
72C2×C3×C42—21no—
73C2×C3×C42—21no—
74C2×C3×C42C2×D311yescharacteristic
75C2×C3×C42C22×C311yescharacteristic
76C2×(C2×D3)⋊C4—21no—
77C2×(C2×D3)⋊C4—21no—
78C22×C3⋊C8C22×C312yes—
79#875—22no—
80#875C3×C414yescomplemented
81C3×C4⋊C8—62no—
82C3×#103—64no—
83C3×#102—64no—
84C3×#95—22no—
85C3×#95—21no—
86C3×#95—21no—
87#810—24no—
88#809—24no—
89C4⋊(C3⋊C8)—22no—
90C23×C32C2×D411yescharacteristic
91C22×C3×D3—22no—
92C22×C3×D3—42no—
93C22×C3×D3—42no—
94C22×C3×D3—41no—
95C22×C3×D3—41no—
96C2×C32×C4—21no—
97C2×C32×C4—21no—
98C2×C32×C4—24no—
99C2×C32×C4—22no—
100C2×C32×C4—42no—
101C2×C32×C4—42no—
102C2×C32×C4C22⋊C412yes—
103C2×C32×C4C22⋊C412yes—
104C2×C32×C4C22×C411yescharacteristic
105C2×C32×C4C2×D412yes—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4#4112yes—
108C2×C3×Dic3—22no—
109C2×C3×Dic3—42no—
110C3×D12—24no—
111C3×D12—41no—
112C3×D12—41no—
113C3×Dic6—24no—
114C3×Dic6—41no—
115C3×Dic6—41no—
116C3×C3⋊C8—42no—
117C2×#124—31no—
118C2×C4⋊C8—31no—
119C2×#103—32no—
120C2×#102—32no—
121C4×C4⋊C4C3×D311yescharacteristic, complemented
122C24×C3—61no—
123C23×D3—21no—
124C2×C3×Q8—32no—
125C2×C3×Q8—61no—
126C2×C3×Q8—62no—
127C2×C3×Q8—62no—
128C2×C3×D4—32no—
129C2×C3×D4—62no—
130C2×C3×D4—61no—
131C2×C3×D4—62no—
132C22×C3×C4—24no—
133C22×C3×C4—22no—
134C22×C3×C4—22no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—61no—
139C22×C3×C4#6711yescharacteristic
140C22×C3×C4#6711yescharacteristic
141C22×C3×C4C3×D411yescharacteristic
142C22×C3×C4C3×D411yescharacteristic
143C22×C3×C4C22×D311yescharacteristic
144C22×C3×C4C23×C311yescharacteristic
145C22×Dic3—21no—
146C2×D12—22no—
147C2×D12—22no—
148C2×D12—21no—
149C2×D12C2×C3×C412yes—
150C2×Dic6—22no—
151C2×Dic6—22no—
152C2×Dic6—21no—
153C2×Dic6C2×C3×C412yes—
154C2×C3×C8—62no—
155C2×C3×C8—62no—
156C2×C3×C8—62no—
157C3×C4⋊C4—24no—
158C3×C4⋊C4—22no—
159C3×C4⋊C4—22no—
160C3×C4⋊C4—24no—
161C3×C4⋊C4D1214yes—
162C3×C4⋊C4C3×D414yes—
163C3×C22⋊C4—64no—
164C3×C22⋊C4—64no—
165C3×C42—22no—
166C3×C42—22no—
167C3×C42—44no—
168C3×C42—42no—
169C3×C42—42no—
170C3×C42C4×D312yes—
171C3×C42D1212yes—
172C3×C42C2×C3×C412yes—
173C3×C42C3×D412yes—
174(C2×D3)⋊C4—24no—
175(C2×D3)⋊C4—24no—
176C2×C3⋊C8—22no—
177C2×C3⋊C8—22no—
178C2×C3⋊C8—22no—
179C22×C32C2×C22⋊C411yescharacteristic
180C22×C32#12112yes—
181C22×C32#13512yes—
182C22×C32AGL(1,ℤ/8)11yescharacteristic
183C22×C32#13711yescharacteristic
184C2×C3×D3—42no—
185C2×C3×D3—42no—
186C2×C3×D3—42no—
187C2×C3×D3—82no—
188C2×C3×D3—82no—
189C32×C4—22no—
190C32×C4—22no—
191C32×C4—44no—
192C32×C4C4×D412yes—
193C32×C4#12411yescharacteristic
194C32×C4#12711yescharacteristic
195C3×Dic3—42no—
196C22×Q8—31no—
197C22×D4—31no—
198C22×C8—32no—
199#124—34no—
200#124—62no—
201C2×C4⋊C4C2×C3×D312yes—
202C2×C22⋊C4—61no—
203C2×C22⋊C4—61no—
204C2×C42—21no—
205C2×C42C2×C3×D311yescharacteristic
206C4⋊C8—62no—
207#103—64no—
208#102—64no—
209#95—21no—
210C23×C3—21no—
211C23×C3—62no—
212C23×C3—122no—
213C23×C3—121no—
214C23×C3—121no—
215C23×C3—122no—
216C23×C3C2×#6711yescharacteristic
217C23×C3C2×C3×D411yescharacteristic
218C22×D3—22no—
219C22×D3—42no—
220C22×D3—42no—
221C22×D3—41no—
222C22×D3—41no—
223C3×Q8—64no—
224C3×Q8—121no—
225C3×Q8—121no—
226C3×D4—64no—
227C3×D4—121no—
228C3×D4—121no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—22no—
234C2×C3×C4—22no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—28no—
238C2×C3×C4—24no—
239C2×C3×C4—24no—
240C2×C3×C4—22no—
241C2×C3×C4—22no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—42no—
247C2×C3×C4—44no—
248C2×C3×C4—44no—
249C2×C3×C4—42no—
250C2×C3×C4—42no—
251C2×C3×C4—42no—
252C2×C3×C4—42no—
253C2×C3×C4—62no—
254C2×C3×C4—122no—
255C2×C3×C4(C2×D3)⋊C412yes—
256C2×C3×C4(C2×D3)⋊C412yes—
257C2×C3×C4C3×C22⋊C412yes—
258C2×C3×C4C3×C22⋊C412yes—
259C2×C3×C4C2×C4×D311yescharacteristic
260C2×C3×C4C2×D1212yes—
261C2×C3×C4C2×D1211yescharacteristic
262C2×C3×C4#23512yes—
263C2×C3×C4C22×C3×C411yescharacteristic
264C2×C3×C4C2×C3×D412yes—
265C2×C3×C4C2×C3×D411yescharacteristic
266C2×C3×C4C3×#4112yes—
267C2×Dic3—22no—
268C2×Dic3—42no—
269D12—24no—
270D12—41no—
271D12—41no—
272Dic6—24no—
273Dic6—41no—
274Dic6—41no—
275C3×C8—122no—
276C3⋊C8—42no—
277C2×C32#39011yescharacteristic
278C2×C32#41611yescharacteristic
279C2×C32#41711yescharacteristic
280C2×C32#46312yes—
281C2×C32#46412yes—
282C3×D3—82no—
283C24—61no—
284C2×Q8—32no—
285C2×Q8—61no—
286C2×Q8—62no—
287C2×Q8—62no—
288C2×D4—32no—
289C2×D4—62no—
290C2×D4—61no—
291C2×D4—62no—
292C22×C4—22no—
293C22×C4—61no—
294C22×C4C3×#6711yescharacteristic
295C22×C4C3×#6711yescharacteristic
296C22×C4C22×C3×D311yescharacteristic
297C2×C8—62no—
298C2×C8—62no—
299C2×C8—62no—
300C4⋊C4—22no—
301C4⋊C4C3×D1214yes—
302C22⋊C4—64no—
303C22⋊C4—64no—
304C42—42no—
305C42C3×C4×D312yes—
306C42C3×D1212yes—
307C22×C3—21no—
308C22×C3—22no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—22no—
312C22×C3—122no—
313C22×C3—122no—
314C22×C3—122no—
315C22×C3—242no—
316C22×C3—242no—
317C22×C3C2×(C2×D3)⋊C411yescharacteristic
318C22×C3#93012yes—
319C22×C3#93211yescharacteristic
320C22×C3#94211yescharacteristic
321C22×C3#95012yes—
322C22×C3C2×C3×C22⋊C411yescharacteristic
323C22×C3C3×#12112yes—
324C22×C3C3×#13512yes—
325C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
326C22×C3C3×#13711yescharacteristic
327C2×D3—42no—
328C2×D3—42no—
329C2×D3—42no—
330C2×D3—82no—
331C2×D3—82no—
332C3×C4—24no—
333C3×C4—22no—
334C3×C4—22no—
335C3×C4—22no—
336C3×C4—22no—
337C3×C4—22no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—42no—
341C3×C4—48no—
342C3×C4—44no—
343C3×C4—44no—
344C3×C4—122no—
345C3×C4C4×D1212yes—
346C3×C4#87411yescharacteristic
347C3×C4#87511yescharacteristic
348C3×C4C3×C4×D412yes—
349C3×C4C3×#12411yescharacteristic
350C3×C4C3×#12711yescharacteristic
351Dic3—42no—
352C32#198311yescharacteristic, complemented, Sylow
353C23—62no—
354C23—122no—
355C23—121no—
356C23—121no—
357C23—122no—
358C23C2×C3×#6711yescharacteristic
359Q8—64no—
360Q8—121no—
361Q8—121no—
362D4—64no—
363D4—121no—
364D4—121no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—24no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—62no—
372C2×C4—122no—
373C2×C4C3×(C2×D3)⋊C412yes—
374C2×C4C3×(C2×D3)⋊C412yes—
375C2×C4C2×C3×C4×D311yescharacteristic
376C2×C4C2×C3×D1212yes—
377C2×C4C2×C3×D1211yescharacteristic
378C2×C4C3×#23512yes—
379C8—122no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—22no—
384C2×C3—22no—
385C2×C3—242no—
386C2×C3#493911yescharacteristic
387C2×C3#496611yescharacteristic
388C2×C3#500211yescharacteristic
389C2×C3#501612yes—
390C2×C3#502812yes—
391C2×C3C3×#39011yescharacteristic
392C2×C3C3×#41611yescharacteristic
393C2×C3C3×#41711yescharacteristic
394C2×C3C3×#46312yes—
395C2×C3C3×#46412yes—
396D3—82no—
397C22—122no—
398C22—122no—
399C22—122no—
400C22—242no—
401C22—242no—
402C22C2×C3×(C2×D3)⋊C411yescharacteristic
403C22C3×#93012yes—
404C22C3×#93211yescharacteristic
405C22C3×#94211yescharacteristic
406C22C3×#95012yes—
407C4—22no—
408C4—22no—
409C4—44no—
410C4—122no—
411C4C3×C4×D1212yes—
412C4C3×#87411yescharacteristic
413C4C3×#87511yescharacteristic
414C3—21no—
415C3#6948811yescharacteristic, direct product factor
416C3C3×#198311yescharacteristic, complemented
417C2—242no—
418C2C3×#493911yescharacteristic
419C2C3×#496611yescharacteristic
420C2C3×#500211yescharacteristic
421C2C3×#501612yes—
422C2C3×#502812yes—
subgroupG/H
centerC23×C3C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×C4×C4⋊C4C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C3×C4C23×C3
hypercenterC3×C4×C4⋊C4D3
hypocenterC3C3×#1983
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C3×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C32×C4×C4⋊C4C2semidirect
3. C2×C3×#810C2semidirect
5. C2×C3×C4⋊(C3⋊C8)C2semidirect
7. #69488C3direct (N × H)
17. C3×#875C4semidirect
28. C3×C4×C4⋊C4D3semidirect
29. C3×C4×C4⋊C4C2×C3semidirect
30. C2×#810C2×C3semidirect
32. C2×C4⋊(C3⋊C8)C2×C3semidirect
80. #875C3×C4semidirect
121. C4×C4⋊C4C3×D3semidirect
352. C32#1983semidirect
415. C3#69488direct (N × H)
416. C3C3×#1983semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8752
C32×C4×C4⋊C42
C2×C3×#8102
C2×C3×#8092
C2×C3×C4⋊(C3⋊C8)2
C3×#19833
#694883