Finite Group Databasebeta

← C3×#69533 #11775317

Subgroups — C3×#69533 #11775317

Order 1152.

657 conjugacy classes of subgroups.

The subgroup lattice has 433 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#924C211yesmaximal, characteristic
2C32×#381C211yesmaximal, characteristic
3C3×#5207C211yesmaximal, characteristic
4C3×#4452C214yesmaximal, complemented
5C3×#1511—31nomaximal
6#69533C311yesmaximal, characteristic, direct product factor
7C23×C32×C4C2211yescharacteristic
8C22×C3×Dic6C411yescharacteristic, complemented
9C2×C32×C22⋊C4—21no—
10C2×C3×#217—21no—
11C2×C3×C4⋊Dic3C411yescharacteristic, complemented
12C3×#924—21no—
13C3×#924—21no—
14C3×#924C412yescomplemented
15C3×#924C2212yes—
16C2×C3×Dic3⋊C4—21no—
17C2×C3×#208—21no—
18C32×#95—21no—
19C32×#95C2212yes—
20C3×#830—21no—
21C3×#830C2212yes—
22C2×C3×C22⋊Q8—31no—
23C2×#924C2×C311yescharacteristic
24C3×#407—31no—
25C3×#381—21no—
26C3×#381D311yescharacteristic
27C3×#381C2×C311yescharacteristic
28#5207C2×C311yescharacteristic
29C3×#328—34no—
30#4452C2×C314yescomplemented
31C24×C32D411yescharacteristic
32C22×C32×C4—22no—
33C22×C32×C4—42no—
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C32×C4C2311yescharacteristic
40C22×C3×Dic3—21no—
41C22×C3×Dic3—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—42no—
44C2×C3×Dic6C2×C412yes—
45C32×C22⋊C4—42no—
46C3×#217—22no—
47C3×#217—22no—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3C2×C412yes—
50C3×Dic3⋊C4—22no—
51C3×Dic3⋊C4—22no—
52C3×#208—42no—
53C2×C3×C3⋊C8—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—61no—
61C3×C22⋊Q8—32no—
62C3×C22⋊Q8—32no—
63C3×C22⋊Q8—61no—
64C3×C22⋊Q8—61no—
65C2×C3×C4⋊C4—31no—
66C2×C3×C4⋊C4—61no—
67C2×C3×C22⋊C4—22no—
68C2×C3×C22⋊C4—21no—
69C2×C3×C22⋊C4—21no—
70C2×C3×C22⋊C4—61no—
71C2×#217—21no—
72C2×C4⋊Dic3C3×C411yescharacteristic, complemented
73#924—21no—
74#924—21no—
75#924C3×C412yescomplemented
76#924C22×C312yes—
77C2×Dic3⋊C4—21no—
78C2×#208—21no—
79C3×C22⋊C8—32no—
80C3×C22⋊C8—61no—
81C3×#95—22no—
82C3×#95—21no—
83C3×#95—21no—
84C3×#95—22no—
85C3×#95C2×D312yes—
86C3×#95C22×C312yes—
87#830—21no—
88#830C22×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×C4—42no—
102C2×C32×C4—42no—
103C2×C32×C4—42no—
104C2×C32×C4C22⋊C411yescharacteristic
105C2×C32×C4C22⋊C411yescharacteristic
106C2×C32×C4C22×C411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C3×Dic3—22no—
109C2×C3×Dic3—22no—
110C2×C3×Dic3—42no—
111C2×C3×Dic3—42no—
112C3×Dic6—42no—
113C3×Dic6—42no—
114C3×C3⋊C8—42no—
115C2×C22⋊Q8—31no—
116#407—31no—
117#381C3×D311yescharacteristic
118#328—34no—
119C24×C3—21no—
120C24×C3#6711yescharacteristic
121C24×C3C3×D411yescharacteristic
122C2×C3×Q8—32no—
123C2×C3×Q8—61no—
124C2×C3×Q8—122no—
125C22×C3×C4—24no—
126C22×C3×C4—22no—
127C22×C3×C4—22no—
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—21no—
134C22×C3×C4—42no—
135C22×C3×C4—42no—
136C22×C3×C4—44no—
137C22×C3×C4—61no—
138C22×C3×C4—61no—
139C22×C3×C4C4×D311yescharacteristic
140C22×C3×C4C4×D311yescharacteristic
141C22×C3×C4D1211yescharacteristic
142C22×C3×C4D1211yescharacteristic
143C22×C3×C4#6711yescharacteristic
144C22×C3×C4C2×C3×C411yescharacteristic
145C22×C3×C4C2×C3×C411yescharacteristic
146C22×C3×C4C3×D411yescharacteristic
147C22×C3×C4C3×D411yescharacteristic
148C22×C3×C4C3×D411yescharacteristic
149C22×C3×C4C22×D311yescharacteristic
150C22×C3×C4C23×C311yescharacteristic
151C22×Dic3—21no—
152C22×Dic3—21no—
153C2×Dic6—21no—
154C2×Dic6—42no—
155C2×Dic6C2×C3×C412yes—
156C3×M16—122no—
157C2×C3×C8—62no—
158C3×C4⋊C4—32no—
159C3×C4⋊C4—62no—
160C3×C4⋊C4—61no—
161C3×C4⋊C4—62no—
162C3×C22⋊C4—44no—
163C3×C22⋊C4—42no—
164C3×C22⋊C4—42no—
165C3×C22⋊C4—62no—
166C3×C22⋊C4—62no—
167#217—22no—
168#217—22no—
169C4⋊Dic3—21no—
170C4⋊Dic3C2×C3×C412yes—
171Dic3⋊C4—22no—
172Dic3⋊C4—22no—
173#208—42no—
174C2×C3⋊C8—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—
190C32×C4—82no—
191C3×Dic3—42no—
192C3×Dic3—42no—
193C22×Q8—31no—
194C23×C4C2×C3×D311yescharacteristic
195C2×M16—61no—
196C22⋊Q8—32no—
197C22⋊Q8—32no—
198C22⋊Q8—61no—
199C22⋊Q8—61no—
200C2×C4⋊C4—31no—
201C2×C4⋊C4—61no—
202C2×C22⋊C4—21no—
203C2×C22⋊C4—61no—
204C22⋊C8—32no—
205C22⋊C8—61no—
206#95—21no—
207#95C2×C3×D312yes—
208C23×C3—24no—
209C23×C3—22no—
210C23×C3—22no—
211C23×C3—22no—
212C23×C3—22no—
213C23×C3—21no—
214C23×C3—21no—
215C23×C3—21no—
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×#6711yescharacteristic
225C23×C3C2×C3×D411yescharacteristic
226C3×Q8—122no—
227C3×Q8—122no—
228C2×C3×C4—22no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—22no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—42no—
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—44no—
251C2×C3×C4—42no—
252C2×C3×C4—42no—
253C2×C3×C4—44no—
254C2×C3×C4—42no—
255C2×C3×C4—42no—
256C2×C3×C4—44no—
257C2×C3×C4—42no—
258C2×C3×C4—42no—
259C2×C3×C4—62no—
260C2×C3×C4—62no—
261C2×C3×C4—122no—
262C2×C3×C4—122no—
263C2×C3×C4(C2×D3)⋊C411yescharacteristic
264C2×C3×C4(C2×D3)⋊C411yescharacteristic
265C2×C3×C4C3×C22⋊C411yescharacteristic
266C2×C3×C4C3×C22⋊C411yescharacteristic
267C2×C3×C4C2×C4×D311yescharacteristic
268C2×C3×C4C2×D1211yescharacteristic
269C2×C3×C4C22×C3×C411yescharacteristic
270C2×C3×C4C2×C3×D411yescharacteristic
271C2×Dic3—22no—
272C2×Dic3—22no—
273C2×Dic3—42no—
274C2×Dic3—42no—
275Dic6—42no—
276Dic6—42no—
277C3×C8—122no—
278C3⋊C8—42no—
279C2×C32—22no—
280C2×C32—22no—
281C2×C32—41no—
282C2×C32C2×#9911yescharacteristic
283C2×C32#41911yescharacteristic
284C2×C32#42111yescharacteristic
285C24C3×#6711yescharacteristic
286C2×Q8—32no—
287C2×Q8—61no—
288C2×Q8—122no—
289C22×C4—22no—
290C22×C4—42no—
291C22×C4—61no—
292C22×C4—61no—
293C22×C4C3×C4×D311yescharacteristic
294C22×C4C3×C4×D311yescharacteristic
295C22×C4C3×D1211yescharacteristic
296C22×C4C3×D1211yescharacteristic
297C22×C4C3×#6711yescharacteristic
298C22×C4C22×C3×D311yescharacteristic
299M16—122no—
300C2×C8—62no—
301C4⋊C4—32no—
302C4⋊C4—61no—
303C4⋊C4—62no—
304C4⋊C4—62no—
305C22⋊C4—42no—
306C22⋊C4—62no—
307C22⋊C4—62no—
308C22×C3—22no—
309C22×C3—22no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—22no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—22no—
327C22×C3—22no—
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—44no—
333C22×C3—44no—
334C22×C3—48no—
335C22×C3#80612yes—
336C22×C3C3×#9912yes—
337C22×C3C2×(C2×D3)⋊C411yescharacteristic
338C22×C3#95112yes—
339C22×C3C2×C3×C22⋊C411yescharacteristic
340C22×C3C3×#13712yes—
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—41no—
352C3×C4—41no—
353C3×C4—84no—
354C3×C4—82no—
355C3×C4—82no—
356C3×C4—122no—
357C3×C4—122no—
358Dic3—42no—
359Dic3—42no—
360C32#151111yescharacteristic, complemented, Sylow
361C23—22no—
362C23—22no—
363C23—41no—
364C23C3×(C2×D3)⋊C411yescharacteristic
365C23C3×(C2×D3)⋊C411yescharacteristic
366C23C2×C3×#6711yescharacteristic
367Q8—122no—
368Q8—122no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—62no—
379C2×C4—62no—
380C2×C4—122no—
381C2×C4—122no—
382C2×C4C3×(C2×D3)⋊C411yescharacteristic
383C2×C4C3×(C2×D3)⋊C411yescharacteristic
384C2×C4C2×C3×C4×D311yescharacteristic
385C2×C4C2×C3×D1211yescharacteristic
386C8—122no—
387C2×C3—24no—
388C2×C3—22no—
389C2×C3—22no—
390C2×C3—22no—
391C2×C3—22no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—42no—
396C2×C3—42no—
397C2×C3—41no—
398C2×C3—41no—
399C2×C3C2×#80611yescharacteristic
400C2×C3#500411yescharacteristic
401C2×C3#500511yescharacteristic
402C2×C3C2×C3×#9911yescharacteristic
403C2×C3C3×#41911yescharacteristic
404C2×C3C3×#42111yescharacteristic
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—44no—
413C22C3×#80612yes—
414C22C2×C3×(C2×D3)⋊C411yescharacteristic
415C22C3×#95112yes—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—82no—
421C4—122no—
422C4—122no—
423C3—21no—
424C3#6953311yescharacteristic, direct product factor
425C3C3×#151111yescharacteristic, complemented
426C2—22no—
427C2—22no—
428C2—41no—
429C2C2×C3×#80611yescharacteristic
430C2C3×#500411yescharacteristic
431C2C3×#500511yescharacteristic
subgroupG/H
centerC22×C3C2×(C2×D3)⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#381C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32D4
cosocleC22×C3×C4C23×C3
hypercenterC3×#381D3
hypocenterC3C3×#1511
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#381

Complements

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

NH ≅ G/Ntype
4. C3×#4452C2semidirect
6. #69533C3direct (N × H)
8. C22×C3×Dic6C4semidirect
11. C2×C3×C4⋊Dic3C4semidirect
14. C3×#924C4semidirect
30. #4452C2×C3semidirect
59. C22×Dic6C3×C4semidirect
72. C2×C4⋊Dic3C3×C4semidirect
75. #924C3×C4semidirect
360. C32#1511semidirect
424. C3#69533direct (N × H)
425. 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×#3812
C3×#52072
C3×#44522
C3×#15113
#695333