Finite Group Databasebeta

← C3×#69975 #11785836

Subgroups — C3×#69975 #11785836

Order 1152.

707 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×#926C211yesmaximal, characteristic
2C32×#407C211yesmaximal, characteristic
3C3×C4×#217C211yesmaximal, characteristic
4C3×#4555C214yesmaximal, complemented
5C3×#1826—31nomaximal
6#69975C311yesmaximal, characteristic, direct product factor
7C23×C32×C4C2211yescharacteristic
8C2×C32×M16C2212yes—
9C2×C3×#217—21no—
10C2×C3×#217—21no—
11C3×#926—21no—
12C3×#926—21no—
13C3×#926C412yescomplemented
14C3×#926C2212yes—
15C2×C3×C4⋊Dic3C411yescharacteristic, complemented
16C2×C3×C4⋊Dic3C411yescharacteristic, complemented
17C2×C3×C4×Dic3—21no—
18C2×C3×C4×Dic3C2212yes—
19C32×C22⋊C8—21no—
20C32×C22⋊C8—21no—
21C3×C3⋊#95—21no—
22C2×C3×#117—31no—
23C2×#926C2×C311yescharacteristic
24C3×#407—21no—
25C3×#407D311yescharacteristic
26C3×#407C2×C311yescharacteristic
27C3×C4×C22⋊C4—31no—
28C4×#217C2×C311yescharacteristic
29C3×#339—34no—
30#4555C2×C314yescomplemented
31C24×C32D411yescharacteristic
32C22×C32×C4—24no—
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4D411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4C2311yescharacteristic
39C22×C3×Dic3—21no—
40C22×C3×Dic3—21no—
41C22×C3×Dic3—22no—
42C32×M16—24no—
43C2×C32×C8—22no—
44C3×#217—24no—
45C3×#217—22no—
46C3×#217—22no—
47C3×C4⋊Dic3—21no—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3C2×C412yes—
50C3×C4⋊Dic3C2×C412yes—
51C3×C4×Dic3—22no—
52C3×C4×Dic3—22no—
53C3×C4×Dic3—24no—
54#1826—31noSylow
55C23×C3×C4—21no—
56C23×C3×C4C2×D311yescharacteristic
57C23×C3×C4C22×C311yescharacteristic
58C2×C3×M16—22no—
59C2×C3×M16C2×D312yes—
60C2×C3×M16C22×C312yes—
61C3×#117—32no—
62C3×#117—32no—
63C3×#117—61no—
64C3×#117—61no—
65C2×C3×C4⋊C4—31no—
66C2×C3×C4⋊C4—31no—
67C2×C3×C22⋊C4—61no—
68C2×C3×C22⋊C4—61no—
69C2×C3×C42—32no—
70C2×C3×C42—61no—
71C2×#217—21no—
72C2×#217—21no—
73#926—21no—
74#926—21no—
75#926C3×C412yescomplemented
76#926C22×C312yes—
77C2×C4⋊Dic3C3×C411yescharacteristic, complemented
78C2×C4⋊Dic3C3×C411yescharacteristic, complemented
79C2×C4×Dic3—21no—
80C2×C4×Dic3C22×C312yes—
81C3×C22⋊C8—22no—
82C3×C22⋊C8—22no—
83C3×C22⋊C8—21no—
84C3×C22⋊C8—21no—
85C3×C22⋊C8—21no—
86C3×C22⋊C8—21no—
87C3×#95—61no—
88C3⋊#95—21no—
89C23×C32—22no—
90C23×C32—22no—
91C23×C32—41no—
92C23×C32C22⋊C411yescharacteristic
93C23×C32C22⋊C411yescharacteristic
94C23×C32C2×D411yescharacteristic
95C2×C32×C4—22no—
96C2×C32×C4—22no—
97C2×C32×C4—22no—
98C2×C32×C4—22no—
99C2×C32×C4—22no—
100C2×C32×C4C22⋊C411yescharacteristic
101C2×C32×C4C22⋊C411yescharacteristic
102C2×C32×C4C22×C411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4#4114yes—
105C2×C3×Dic3—24no—
106C2×C3×Dic3—22no—
107C2×C3×Dic3—22no—
108C2×C3×Dic3—42no—
109C2×C3×Dic3—42no—
110C2×C3×Dic3—42no—
111C2×C3×Dic3—42no—
112C32×C8—42no—
113C2×#117—31no—
114#407C3×D311yescharacteristic
115C4×C22⋊C4—31no—
116#339—34no—
117C24×C3—21no—
118C24×C3D1211yescharacteristic
119C24×C3C3×D411yescharacteristic
120C22×C3×C4—24no—
121C22×C3×C4—24no—
122C22×C3×C4—21no—
123C22×C3×C4—21no—
124C22×C3×C4—21no—
125C22×C3×C4—21no—
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—44no—
129C22×C3×C4—61no—
130C22×C3×C4—61no—
131C22×C3×C4—62no—
132C22×C3×C4C4×D311yescharacteristic
133C22×C3×C4C4×D311yescharacteristic
134C22×C3×C4D1211yescharacteristic
135C22×C3×C4#6711yescharacteristic
136C22×C3×C4#6711yescharacteristic
137C22×C3×C4C2×C3×C411yescharacteristic
138C22×C3×C4C2×C3×C411yescharacteristic
139C22×C3×C4C3×D411yescharacteristic
140C22×C3×C4C3×D411yescharacteristic
141C22×C3×C4C3×D411yescharacteristic
142C22×C3×C4C22×D311yescharacteristic
143C22×C3×C4C23×C311yescharacteristic
144C22×Dic3—21no—
145C22×Dic3—21no—
146C22×Dic3—22no—
147C3×M16—24no—
148C3×M16—24no—
149C3×M16—44no—
150C2×C3×C8—24no—
151C2×C3×C8—22no—
152C2×C3×C8—22no—
153C3×C4⋊C4—32no—
154C3×C4⋊C4—32no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4—61no—
157C3×C22⋊C4—64no—
158C3×C22⋊C4—62no—
159C3×C22⋊C4—62no—
160C3×C42—62no—
161C3×C42—62no—
162C3×C42—64no—
163#217—24no—
164#217—22no—
165#217—22no—
166C4⋊Dic3—21no—
167C4⋊Dic3—21no—
168C4⋊Dic3C2×C3×C412yes—
169C4⋊Dic3C2×C3×C412yes—
170C4×Dic3—22no—
171C4×Dic3—22no—
172C4×Dic3—24no—
173C22×C32—21no—
174C22×C32—21no—
175C22×C32—21no—
176C22×C32—21no—
177C22×C32—21no—
178C22×C32—21no—
179C22×C32—21no—
180C22×C32—44no—
181C22×C32#10412yes—
182C22×C32C2×C22⋊C411yescharacteristic
183C22×C32#12312yes—
184C32×C4—21no—
185C32×C4—21no—
186C32×C4#11712yes—
187C32×C4#12312yes—
188C3×Dic3—44no—
189C3×Dic3—42no—
190C3×Dic3—42no—
191C23×C4C2×C3×D311yescharacteristic
192C2×M16C2×C3×D312yes—
193#117—32no—
194#117—32no—
195#117—61no—
196#117—61no—
197C2×C4⋊C4—31no—
198C2×C4⋊C4—31no—
199C2×C22⋊C4—61no—
200C2×C22⋊C4—61no—
201C2×C42—32no—
202C2×C42—61no—
203C22⋊C8—21no—
204C22⋊C8—21no—
205#95—61no—
206C23×C3—22no—
207C23×C3—22no—
208C23×C3—22no—
209C23×C3—22no—
210C23×C3—21no—
211C23×C3—21no—
212C23×C3—21no—
213C23×C3—42no—
214C23×C3—42no—
215C23×C3—41no—
216C23×C3—41no—
217C23×C3—42no—
218C23×C3(C2×D3)⋊C411yescharacteristic
219C23×C3(C2×D3)⋊C411yescharacteristic
220C23×C3C3×C22⋊C411yescharacteristic
221C23×C3C3×C22⋊C411yescharacteristic
222C23×C3C2×D1211yescharacteristic
223C23×C3C2×C3×D411yescharacteristic
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—22no—
228C2×C3×C4—22no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—22no—
232C2×C3×C4—22no—
233C2×C3×C4—22no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—24no—
238C2×C3×C4—21no—
239C2×C3×C4—42no—
240C2×C3×C4—42no—
241C2×C3×C4—42no—
242C2×C3×C4—42no—
243C2×C3×C4—42no—
244C2×C3×C4—64no—
245C2×C3×C4—62no—
246C2×C3×C4—62no—
247C2×C3×C4—122no—
248C2×C3×C4—122no—
249C2×C3×C4—122no—
250C2×C3×C4—122no—
251C2×C3×C4(C2×D3)⋊C411yescharacteristic
252C2×C3×C4(C2×D3)⋊C411yescharacteristic
253C2×C3×C4C3×C22⋊C411yescharacteristic
254C2×C3×C4C3×C22⋊C411yescharacteristic
255C2×C3×C4C2×C4×D311yescharacteristic
256C2×C3×C4#23714yes—
257C2×C3×C4C2×#6711yescharacteristic
258C2×C3×C4C22×C3×C411yescharacteristic
259C2×C3×C4C2×C3×D411yescharacteristic
260C2×C3×C4C3×#4114yes—
261C2×Dic3—24no—
262C2×Dic3—22no—
263C2×Dic3—22no—
264C2×Dic3—42no—
265C2×Dic3—42no—
266C2×Dic3—42no—
267C2×Dic3—42no—
268C3×C8—44no—
269C3×C8—42no—
270C3×C8—42no—
271C2×C32—22no—
272C2×C32—22no—
273C2×C32—41no—
274C2×C32#38111yescharacteristic
275C2×C32C2×#10411yescharacteristic
276C2×C32#42111yescharacteristic
277C24C3×D1211yescharacteristic
278C22×C4—24no—
279C22×C4—61no—
280C22×C4—61no—
281C22×C4—62no—
282C22×C4C3×C4×D311yescharacteristic
283C22×C4C3×C4×D311yescharacteristic
284C22×C4C3×D1211yescharacteristic
285C22×C4C3×#6711yescharacteristic
286C22×C4C3×#6711yescharacteristic
287C22×C4C22×C3×D311yescharacteristic
288M16—24no—
289C2×C8—22no—
290C4⋊C4—32no—
291C4⋊C4—32no—
292C4⋊C4—61no—
293C4⋊C4—61no—
294C22⋊C4—64no—
295C22⋊C4—62no—
296C22⋊C4—62no—
297C42—62no—
298C42—62no—
299C42—64no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—21no—
306C22×C3—21no—
307C22×C3—21no—
308C22×C3—22no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—22no—
316C22×C3—21no—
317C22×C3—22no—
318C22×C3—41no—
319C22×C3—41no—
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—41no—
323C22×C3—41no—
324C22×C3—44no—
325C22×C3—44no—
326C22×C3—48no—
327C22×C3#82512yes—
328C22×C3C3×#10412yes—
329C22×C3#88612yes—
330C22×C3C2×(C2×D3)⋊C411yescharacteristic
331C22×C3C2×C3×C22⋊C411yescharacteristic
332C22×C3C3×#12312yes—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—22no—
338C3×C4—22no—
339C3×C4—41no—
340C3×C4—41no—
341C3×C4—124no—
342C3×C4—122no—
343C3×C4—122no—
344C3×C4#87712yes—
345C3×C4#93512yes—
346C3×C4C3×#11712yes—
347C3×C4C3×#12312yes—
348Dic3—44no—
349Dic3—42no—
350Dic3—42no—
351C32#182611yescharacteristic, complemented, Sylow
352C23—22no—
353C23—22no—
354C23—41no—
355C23C3×(C2×D3)⋊C411yescharacteristic
356C23C3×(C2×D3)⋊C411yescharacteristic
357C23C2×C3×D1211yescharacteristic
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—64no—
364C2×C4—62no—
365C2×C4—62no—
366C2×C4—122no—
367C2×C4—122no—
368C2×C4—122no—
369C2×C4—122no—
370C2×C4C3×(C2×D3)⋊C411yescharacteristic
371C2×C4C3×(C2×D3)⋊C411yescharacteristic
372C2×C4C2×C3×C4×D311yescharacteristic
373C2×C4C3×#23714yes—
374C2×C4C2×C3×#6711yescharacteristic
375C8—42no—
376C2×C3—22no—
377C2×C3—22no—
378C2×C3—22no—
379C2×C3—22no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—42no—
384C2×C3—42no—
385C2×C3—42no—
386C2×C3—41no—
387C2×C3—41no—
388C2×C3#494311yescharacteristic
389C2×C3C2×#82511yescharacteristic
390C2×C3#513911yescharacteristic
391C2×C3C3×#38111yescharacteristic
392C2×C3C2×C3×#10411yescharacteristic
393C2×C3C3×#42111yescharacteristic
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—44no—
402C22C3×#82512yes—
403C22C3×#88612yes—
404C22C2×C3×(C2×D3)⋊C411yescharacteristic
405C4—21no—
406C4—21no—
407C4—124no—
408C4—122no—
409C4—122no—
410C4C3×#87712yes—
411C4C3×#93512yes—
412C3—21no—
413C3#6997511yescharacteristic, direct product factor
414C3C3×#182611yescharacteristic, complemented
415C2—22no—
416C2—22no—
417C2—41no—
418C2C3×#494311yescharacteristic
419C2C2×C3×#82511yescharacteristic
420C2C3×#513911yescharacteristic
subgroupG/H
centerC2×C3×C4C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#407C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32D4
cosocleC22×C3×C4C23×C3
hypercenterC3×#407D3
hypocenterC3C3×#1826
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C3×#407

Complements

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

NH ≅ G/Ntype
4. C3×#4555C2semidirect
6. #69975C3direct (N × H)
13. C3×#926C4semidirect
15. C2×C3×C4⋊Dic3C4semidirect
16. C2×C3×C4⋊Dic3C4semidirect
30. #4555C2×C3semidirect
75. #926C3×C4semidirect
77. C2×C4⋊Dic3C3×C4semidirect
78. C2×C4⋊Dic3C3×C4semidirect
351. C32#1826semidirect
413. C3#69975direct (N × H)
414. C3C3×#1826semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9262
C32×#4072
C3×C4×#2172
C3×#45552
C3×#18263
#699753