Finite Group Databasebeta

← C3×#69981 #11775323

Subgroups — C3×#69981 #11775323

Order 1152.

643 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#924C211yesmaximal, characteristic
2C32×#407C211yesmaximal, characteristic
3C3×#5211C211yesmaximal, characteristic
4C3×#4467C214yesmaximal, complemented
5C3×#1511—31nomaximal
6#69981C311yesmaximal, characteristic, direct product factor
7C23×C32×C4C2211yescharacteristic
8C22×C3×Dic6C411yescharacteristic, complemented
9C2×C32×M16—21no—
10C2×C3×#217—21no—
11C2×C3×#217—21no—
12C2×C3×C4⋊Dic3C411yescharacteristic, complemented
13C3×#924—21no—
14C3×#924—21no—
15C3×#924C412yescomplemented
16C3×#924C2212yes—
17C2×C3×Dic3⋊C4—21no—
18C32×C22⋊C8—21no—
19C32×C22⋊C8C2212yes—
20C3×C3⋊#95—21no—
21C3×C3⋊#95C2212yes—
22C2×C3×C22⋊Q8—31no—
23C2×#924C2×C311yescharacteristic
24C3×#407—21no—
25C3×#407D311yescharacteristic
26C3×#407C2×C311yescharacteristic
27C3×#381—31no—
28#5211C2×C311yescharacteristic
29C3×#328—34no—
30#4467C2×C314yescomplemented
31C24×C32D411yescharacteristic
32C22×C32×C4—42no—
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—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—42no—
44C2×C3×Dic6C2×C412yes—
45C32×M16—42no—
46C2×C32×C8—22no—
47C3×#217—22no—
48C3×#217—22no—
49C3×#217—42no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3C2×C412yes—
52C3×Dic3⋊C4—22no—
53C3×Dic3⋊C4—22no—
54#1511—31noSylow
55C22×C3×Q8—31no—
56C23×C3×C4—21no—
57C23×C3×C4C2×D311yescharacteristic
58C23×C3×C4C22×C311yescharacteristic
59C22×Dic6C3×C411yescharacteristic, complemented
60C2×C3×M16—22no—
61C2×C3×M16—21no—
62C2×C3×M16—21no—
63C3×C22⋊Q8—32no—
64C3×C22⋊Q8—32no—
65C3×C22⋊Q8—61no—
66C3×C22⋊Q8—61no—
67C2×C3×C4⋊C4—31no—
68C2×C3×C4⋊C4—61no—
69C2×C3×C22⋊C4—61no—
70C2×C3×C22⋊C4—61no—
71C2×#217—21no—
72C2×#217—21no—
73C2×C4⋊Dic3C3×C411yescharacteristic, complemented
74#924—21no—
75#924—21no—
76#924C3×C412yescomplemented
77#924C22×C312yes—
78C2×Dic3⋊C4—21no—
79C3×C22⋊C8—22no—
80C3×C22⋊C8—21no—
81C3×C22⋊C8—21no—
82C3×C22⋊C8—22no—
83C3×C22⋊C8C2×D312yes—
84C3×C22⋊C8C22×C312yes—
85C3×#95—32no—
86C3×#95—61no—
87C3⋊#95—21no—
88C3⋊#95C22×C312yes—
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—41no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C32×C4—41no—
101C2×C32×C4C22⋊C411yescharacteristic
102C2×C32×C4C22⋊C411yescharacteristic
103C2×C32×C4C22×C411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C3×Dic3—22no—
106C2×C3×Dic3—22no—
107C2×C3×Dic3—42no—
108C2×C3×Dic3—42no—
109C2×C3×Dic3—42no—
110C2×C3×Dic3—42no—
111C2×C3×Dic3—42no—
112C3×Dic6—42no—
113C3×Dic6—42no—
114C32×C8—42no—
115C2×C22⋊Q8—31no—
116#407C3×D311yescharacteristic
117#381—31no—
118#328—34no—
119C24×C3—21no—
120C24×C3D1211yescharacteristic
121C24×C3C3×D411yescharacteristic
122C2×C3×Q8—32no—
123C2×C3×Q8—61no—
124C2×C3×Q8—122no—
125C22×C3×C4—21no—
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—42no—
132C22×C3×C4—42no—
133C22×C3×C4—44no—
134C22×C3×C4—61no—
135C22×C3×C4—61no—
136C22×C3×C4—62no—
137C22×C3×C4C4×D311yescharacteristic
138C22×C3×C4C4×D311yescharacteristic
139C22×C3×C4D1211yescharacteristic
140C22×C3×C4#6711yescharacteristic
141C22×C3×C4#6711yescharacteristic
142C22×C3×C4C2×C3×C411yescharacteristic
143C22×C3×C4C2×C3×C411yescharacteristic
144C22×C3×C4C3×D411yescharacteristic
145C22×C3×C4C3×D411yescharacteristic
146C22×C3×C4C3×D411yescharacteristic
147C22×C3×C4C22×D311yescharacteristic
148C22×C3×C4C23×C311yescharacteristic
149C22×Dic3—21no—
150C22×Dic3—21no—
151C22×Dic3—22no—
152C2×Dic6—21no—
153C2×Dic6—42no—
154C2×Dic6C2×C3×C412yes—
155C3×M16—44no—
156C3×M16—42no—
157C3×M16—42no—
158C2×C3×C8—24no—
159C2×C3×C8—22no—
160C2×C3×C8—22no—
161C3×C4⋊C4—32no—
162C3×C4⋊C4—62no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4—62no—
165C3×C22⋊C4—62no—
166C3×C22⋊C4—62no—
167C3×C22⋊C4—122no—
168#217—22no—
169#217—22no—
170#217—42no—
171C4⋊Dic3—21no—
172C4⋊Dic3C2×C3×C412yes—
173Dic3⋊C4—22no—
174Dic3⋊C4—22no—
175C22×C32—21no—
176C22×C32—21no—
177C22×C32—21no—
178C22×C32—21no—
179C22×C32—21no—
180C22×C32—21no—
181C22×C32—21no—
182C22×C32—44no—
183C22×C32#9912yes—
184C22×C32C2×C22⋊C411yescharacteristic
185C22×C32#13712yes—
186C32×C4—21no—
187C32×C4—21no—
188C32×C4—21no—
189C32×C4—21no—
190C3×Dic3—42no—
191C3×Dic3—42no—
192C3×Dic3—82no—
193C22×Q8—31no—
194C23×C4C2×C3×D311yescharacteristic
195C2×M16—21no—
196C22⋊Q8—32no—
197C22⋊Q8—32no—
198C22⋊Q8—61no—
199C22⋊Q8—61no—
200C2×C4⋊C4—31no—
201C2×C4⋊C4—61no—
202C2×C22⋊C4—61no—
203C2×C22⋊C4—61no—
204C22⋊C8—21no—
205C22⋊C8C2×C3×D312yes—
206#95—32no—
207#95—61no—
208C23×C3—22no—
209C23×C3—22no—
210C23×C3—22no—
211C23×C3—22no—
212C23×C3—21no—
213C23×C3—21no—
214C23×C3—21no—
215C23×C3—42no—
216C23×C3—42no—
217C23×C3—41no—
218C23×C3—41no—
219C23×C3—42no—
220C23×C3(C2×D3)⋊C411yescharacteristic
221C23×C3(C2×D3)⋊C411yescharacteristic
222C23×C3C3×C22⋊C411yescharacteristic
223C23×C3C3×C22⋊C411yescharacteristic
224C23×C3C2×D1211yescharacteristic
225C23×C3C2×C3×D411yescharacteristic
226C3×Q8—122no—
227C3×Q8—122no—
228C2×C3×C4—24no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—22no—
232C2×C3×C4—22no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—42no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—41no—
246C2×C3×C4—42no—
247C2×C3×C4—42no—
248C2×C3×C4—42no—
249C2×C3×C4—42no—
250C2×C3×C4—62no—
251C2×C3×C4—62no—
252C2×C3×C4—122no—
253C2×C3×C4—122no—
254C2×C3×C4—122no—
255C2×C3×C4—122no—
256C2×C3×C4—122no—
257C2×C3×C4(C2×D3)⋊C411yescharacteristic
258C2×C3×C4(C2×D3)⋊C411yescharacteristic
259C2×C3×C4C3×C22⋊C411yescharacteristic
260C2×C3×C4C3×C22⋊C411yescharacteristic
261C2×C3×C4C2×C4×D311yescharacteristic
262C2×C3×C4C2×#6711yescharacteristic
263C2×C3×C4C22×C3×C411yescharacteristic
264C2×C3×C4C2×C3×D411yescharacteristic
265C2×Dic3—22no—
266C2×Dic3—22no—
267C2×Dic3—42no—
268C2×Dic3—42no—
269C2×Dic3—42no—
270C2×Dic3—42no—
271C2×Dic3—42no—
272Dic6—42no—
273Dic6—42no—
274C3×C8—44no—
275C3×C8—42no—
276C3×C8—42no—
277C2×C32—22no—
278C2×C32—22no—
279C2×C32—41no—
280C2×C32C2×#9911yescharacteristic
281C2×C32#41911yescharacteristic
282C2×C32#42111yescharacteristic
283C24C3×D1211yescharacteristic
284C2×Q8—32no—
285C2×Q8—61no—
286C2×Q8—122no—
287C22×C4—42no—
288C22×C4—61no—
289C22×C4—61no—
290C22×C4—62no—
291C22×C4C3×C4×D311yescharacteristic
292C22×C4C3×C4×D311yescharacteristic
293C22×C4C3×D1211yescharacteristic
294C22×C4C3×#6711yescharacteristic
295C22×C4C3×#6711yescharacteristic
296C22×C4C22×C3×D311yescharacteristic
297M16—42no—
298C2×C8—22no—
299C4⋊C4—32no—
300C4⋊C4—61no—
301C4⋊C4—62no—
302C4⋊C4—62no—
303C22⋊C4—62no—
304C22⋊C4—62no—
305C22⋊C4—122no—
306C22×C3—21no—
307C22×C3—21no—
308C22×C3—21no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—22no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—22no—
322C22×C3—21no—
323C22×C3—22no—
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—41no—
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—44no—
331C22×C3—44no—
332C22×C3—48no—
333C22×C3#80612yes—
334C22×C3C3×#9912yes—
335C22×C3#90912yes—
336C22×C3C2×(C2×D3)⋊C411yescharacteristic
337C22×C3C2×C3×C22⋊C411yescharacteristic
338C22×C3C3×#13712yes—
339C3×C4—22no—
340C3×C4—22no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—41no—
350C3×C4—41no—
351C3×C4—122no—
352C3×C4—122no—
353C3×C4—242no—
354Dic3—42no—
355Dic3—42no—
356Dic3—82no—
357C32#151111yescharacteristic, complemented, Sylow
358C23—22no—
359C23—22no—
360C23—41no—
361C23C3×(C2×D3)⋊C411yescharacteristic
362C23C3×(C2×D3)⋊C411yescharacteristic
363C23C2×C3×D1211yescharacteristic
364Q8—122no—
365Q8—122no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—62no—
373C2×C4—62no—
374C2×C4—122no—
375C2×C4—122no—
376C2×C4—122no—
377C2×C4—122no—
378C2×C4—122no—
379C2×C4C3×(C2×D3)⋊C411yescharacteristic
380C2×C4C3×(C2×D3)⋊C411yescharacteristic
381C2×C4C2×C3×C4×D311yescharacteristic
382C2×C4C2×C3×#6711yescharacteristic
383C8—42no—
384C2×C3—22no—
385C2×C3—22no—
386C2×C3—22no—
387C2×C3—22no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—42no—
392C2×C3—42no—
393C2×C3—42no—
394C2×C3—41no—
395C2×C3—41no—
396C2×C3C2×#80611yescharacteristic
397C2×C3#512011yescharacteristic
398C2×C3#513911yescharacteristic
399C2×C3C2×C3×#9911yescharacteristic
400C2×C3C3×#41911yescharacteristic
401C2×C3C3×#42111yescharacteristic
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—44no—
410C22C3×#80612yes—
411C22C3×#90912yes—
412C22C2×C3×(C2×D3)⋊C411yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—122no—
418C4—122no—
419C4—242no—
420C3—21no—
421C3#6998111yescharacteristic, direct product factor
422C3C3×#151111yescharacteristic, complemented
423C2—22no—
424C2—22no—
425C2—41no—
426C2C2×C3×#80611yescharacteristic
427C2C3×#512011yescharacteristic
428C2C3×#513911yescharacteristic
subgroupG/H
centerC22×C3C2×(C2×D3)⋊C4
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×#1511
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#407

Complements

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

NH ≅ G/Ntype
4. C3×#4467C2semidirect
6. #69981C3direct (N × H)
8. C22×C3×Dic6C4semidirect
12. C2×C3×C4⋊Dic3C4semidirect
15. C3×#924C4semidirect
30. #4467C2×C3semidirect
59. C22×Dic6C3×C4semidirect
73. C2×C4⋊Dic3C3×C4semidirect
76. #924C3×C4semidirect
357. C32#1511semidirect
421. C3#69981direct (N × H)
422. C3C3×#1511semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9242
C32×#4072
C3×#52112
C3×#44672
C3×#15113
#699813