Finite Group Databasebeta

← C3×#69946 #11775602

Subgroups — C3×#69946 #11775602

Order 1152.

677 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#924C211yesmaximal, characteristic
2C2×C32×C22⋊C8C211yesmaximal, characteristic
3C3×#5212C211yesmaximal, characteristic
4C3×#4467C214yesmaximal, complemented
5C3×#1520—31nomaximal
6#69946C311yesmaximal, characteristic, direct product factor
7C23×C32×C4C2211yescharacteristic
8C22×C3×Dic6C411yescharacteristic, complemented
9C22×C32×C8—21no—
10C2×C3×#217—21no—
11C2×C3×#217—21no—
12C2×C3×C4⋊Dic3—21no—
13C2×C3×C4⋊Dic3C411yescharacteristic, complemented
14C3×#924—21no—
15C3×#924—21no—
16C3×#924C412yescomplemented
17C3×#924C2212yes—
18C2×C3×Dic3⋊C4—21no—
19C32×C22⋊C8—21no—
20C32×C22⋊C8C2212yes—
21C3×C3⋊#95C2212yes—
22C2×C3×C22⋊Q8—31no—
23C2×#924C2×C311yescharacteristic
24C2×C3×C22⋊C8—21no—
25C2×C3×C22⋊C8D311yescharacteristic
26C2×C3×C22⋊C8C2×C311yescharacteristic
27C3×#380—31no—
28#5212C2×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—
45C2×C32×C8—22no—
46C2×C32×C8—42no—
47C3×#217—22no—
48C3×#217—22no—
49C3×#217—42no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—42no—
52C3×C4⋊Dic3C2×C412yes—
53C3×Dic3⋊C4—22no—
54C3×Dic3⋊C4—22no—
55#1520—31noSylow
56C22×C3×Q8—31no—
57C23×C3×C4—21no—
58C23×C3×C4C2×D311yescharacteristic
59C23×C3×C4C22×C311yescharacteristic
60C22×Dic6C3×C411yescharacteristic, complemented
61C22×C3×C8—22no—
62C22×C3×C8—21no—
63C22×C3×C8—21no—
64C3×C22⋊Q8—32no—
65C3×C22⋊Q8—32no—
66C3×C22⋊Q8—61no—
67C3×C22⋊Q8—61no—
68C2×C3×C4⋊C4—31no—
69C2×C3×C4⋊C4—61no—
70C2×C3×C4⋊C4—61no—
71C2×C3×C22⋊C4—61no—
72C2×C3×C22⋊C4—61no—
73C2×#217—21no—
74C2×#217—21no—
75C2×C4⋊Dic3—21no—
76C2×C4⋊Dic3C3×C411yescharacteristic, complemented
77#924—21no—
78#924—21no—
79#924C3×C412yescomplemented
80#924C22×C312yes—
81C2×Dic3⋊C4—21no—
82C3×C22⋊C8—22no—
83C3×C22⋊C8—21no—
84C3×C22⋊C8—21no—
85C3×C22⋊C8—22no—
86C3×C22⋊C8C2×D312yes—
87C3×C22⋊C8C22×C312yes—
88C3×#95—32no—
89C3⋊#95C22×C312yes—
90C23×C32—41no—
91C23×C32—41no—
92C23×C32C22⋊C411yescharacteristic
93C23×C32C22⋊C411yescharacteristic
94C23×C32SD1612yes—
95C23×C32Q1612yes—
96C23×C32C2×D411yescharacteristic
97C2×C32×C4—22no—
98C2×C32×C4—22no—
99C2×C32×C4—22no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C32×C4C22⋊C411yescharacteristic
104C2×C32×C4C22⋊C411yescharacteristic
105C2×C32×C4C22×C411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C3×Dic3—22no—
108C2×C3×Dic3—22no—
109C2×C3×Dic3—42no—
110C2×C3×Dic3—42no—
111C2×C3×Dic3—42no—
112C2×C3×Dic3—42no—
113C2×C3×Dic3—42no—
114C3×Dic6—42no—
115C3×Dic6—42no—
116C32×C8—42no—
117C2×C22⋊Q8—31no—
118C2×C22⋊C8C3×D311yescharacteristic
119#380—31no—
120#328—34no—
121C24×C3—21no—
122C24×C3D1211yescharacteristic
123C24×C3C3×D411yescharacteristic
124C2×C3×Q8—32no—
125C2×C3×Q8—61no—
126C2×C3×Q8—122no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—42no—
134C22×C3×C4—42no—
135C22×C3×C4—44no—
136C22×C3×C4—61no—
137C22×C3×C4—61no—
138C22×C3×C4—62no—
139C22×C3×C4C4×D311yescharacteristic
140C22×C3×C4C4×D311yescharacteristic
141C22×C3×C4D1211yescharacteristic
142C22×C3×C4#6711yescharacteristic
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—
153C22×Dic3—22no—
154C2×Dic6—21no—
155C2×Dic6—42no—
156C2×Dic6C2×C3×C412yes—
157C2×C3×C8—24no—
158C2×C3×C8—22no—
159C2×C3×C8—22no—
160C2×C3×C8—44no—
161C2×C3×C8—42no—
162C2×C3×C8—42no—
163C3×C4⋊C4—32no—
164C3×C4⋊C4—62no—
165C3×C4⋊C4—61no—
166C3×C4⋊C4—62no—
167C3×C4⋊C4—122no—
168C3×C22⋊C4—62no—
169C3×C22⋊C4—62no—
170C3×C22⋊C4—122no—
171#217—22no—
172#217—22no—
173#217—42no—
174C4⋊Dic3—21no—
175C4⋊Dic3—42no—
176C4⋊Dic3C2×C3×C412yes—
177Dic3⋊C4—22no—
178Dic3⋊C4—22no—
179C22×C32—21no—
180C22×C32—21no—
181C22×C32—21no—
182C22×C32—21no—
183C22×C32—21no—
184C22×C32—21no—
185C22×C32—42no—
186C22×C32—42no—
187C22×C32#10312yes—
188C22×C32#10312yes—
189C22×C32C2×C22⋊C411yescharacteristic
190C22×C32C2×SD1611yescharacteristic
191C22×C32C2×Q1611yescharacteristic
192C32×C4—21no—
193C32×C4—21no—
194C32×C4—21no—
195C32×C4#9912yes—
196C3×Dic3—42no—
197C3×Dic3—42no—
198C3×Dic3—82no—
199C22×Q8—31no—
200C23×C4C2×C3×D311yescharacteristic
201C22×C8—21no—
202C22⋊Q8—32no—
203C22⋊Q8—32no—
204C22⋊Q8—61no—
205C22⋊Q8—61no—
206C2×C4⋊C4—31no—
207C2×C4⋊C4—61no—
208C2×C4⋊C4—61no—
209C2×C22⋊C4—61no—
210C2×C22⋊C4—61no—
211C22⋊C8—21no—
212C22⋊C8C2×C3×D312yes—
213#95—32no—
214C23×C3—22no—
215C23×C3—22no—
216C23×C3—21no—
217C23×C3—21no—
218C23×C3—21no—
219C23×C3—41no—
220C23×C3—41no—
221C23×C3—41no—
222C23×C3—41no—
223C23×C3—42no—
224C23×C3—42no—
225C23×C3#20412yes—
226C23×C3Dic1212yes—
227C23×C3(C2×D3)⋊C411yescharacteristic
228C23×C3(C2×D3)⋊C411yescharacteristic
229C23×C3C3×C22⋊C411yescharacteristic
230C23×C3C3×C22⋊C411yescharacteristic
231C23×C3C3×SD1612yes—
232C23×C3C3×Q1612yes—
233C23×C3C2×D1211yescharacteristic
234C23×C3C2×C3×D411yescharacteristic
235C3×Q8—122no—
236C3×Q8—122no—
237C2×C3×C4—24no—
238C2×C3×C4—22no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—42no—
249C2×C3×C4—42no—
250C2×C3×C4—41no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—42no—
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—122no—
264C2×C3×C4—122no—
265C2×C3×C4—122no—
266C2×C3×C4(C2×D3)⋊C411yescharacteristic
267C2×C3×C4(C2×D3)⋊C411yescharacteristic
268C2×C3×C4C3×C22⋊C411yescharacteristic
269C2×C3×C4C3×C22⋊C411yescharacteristic
270C2×C3×C4C2×C4×D311yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×C3×C4C22×C3×C411yescharacteristic
273C2×C3×C4C2×C3×D411yescharacteristic
274C2×Dic3—22no—
275C2×Dic3—22no—
276C2×Dic3—42no—
277C2×Dic3—42no—
278C2×Dic3—42no—
279C2×Dic3—42no—
280C2×Dic3—42no—
281Dic6—42no—
282Dic6—42no—
283C3×C8—44no—
284C3×C8—42no—
285C3×C8—42no—
286C2×C32—22no—
287C2×C32—21no—
288C2×C32—22no—
289C2×C32—21no—
290C2×C32C2×#9911yescharacteristic
291C2×C32C2×#10311yescharacteristic
292C2×C32#42111yescharacteristic
293C24C3×D1211yescharacteristic
294C2×Q8—32no—
295C2×Q8—61no—
296C2×Q8—122no—
297C22×C4—42no—
298C22×C4—61no—
299C22×C4—61no—
300C22×C4—62no—
301C22×C4C3×C4×D311yescharacteristic
302C22×C4C3×C4×D311yescharacteristic
303C22×C4C3×D1211yescharacteristic
304C22×C4C3×#6711yescharacteristic
305C22×C4C3×#6711yescharacteristic
306C22×C4C22×C3×D311yescharacteristic
307C2×C8—22no—
308C2×C8—42no—
309C4⋊C4—32no—
310C4⋊C4—61no—
311C4⋊C4—62no—
312C4⋊C4—62no—
313C4⋊C4—122no—
314C22⋊C4—62no—
315C22⋊C4—62no—
316C22⋊C4—122no—
317C22×C3—22no—
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—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—22no—
335C22×C3—22no—
336C22×C3—41no—
337C22×C3—41no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3—42no—
341C22×C3—42no—
342C22×C3—42no—
343C22×C3—42no—
344C22×C3—44no—
345C22×C3—44no—
346C22×C3#81612yes—
347C22×C3#81612yes—
348C22×C3C3×#10312yes—
349C22×C3C3×#10312yes—
350C22×C3C2×#20411yescharacteristic
351C22×C3C2×Dic1211yescharacteristic
352C22×C3C2×(C2×D3)⋊C411yescharacteristic
353C22×C3C2×C3×C22⋊C411yescharacteristic
354C22×C3C2×C3×SD1611yescharacteristic
355C22×C3C2×C3×Q1611yescharacteristic
356C3×C4—22no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—22no—
364C3×C4—41no—
365C3×C4—41no—
366C3×C4—122no—
367C3×C4—122no—
368C3×C4—242no—
369C3×C4#80612yes—
370C3×C4C3×#9912yes—
371Dic3—42no—
372Dic3—42no—
373Dic3—82no—
374C32#152011yescharacteristic, complemented, Sylow
375C23—41no—
376C23—41no—
377C23C3×#20412yes—
378C23C3×Dic1212yes—
379C23C3×(C2×D3)⋊C411yescharacteristic
380C23C3×(C2×D3)⋊C411yescharacteristic
381C23C2×C3×D1211yescharacteristic
382Q8—122no—
383Q8—122no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—62no—
391C2×C4—62no—
392C2×C4—122no—
393C2×C4—122no—
394C2×C4—122no—
395C2×C4—122no—
396C2×C4—122no—
397C2×C4C3×(C2×D3)⋊C411yescharacteristic
398C2×C4C3×(C2×D3)⋊C411yescharacteristic
399C2×C4C2×C3×C4×D311yescharacteristic
400C2×C4C2×C3×#6711yescharacteristic
401C8—42no—
402C2×C3—24no—
403C2×C3—21no—
404C2×C3—22no—
405C2×C3—22no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—22no—
409C2×C3—22no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—41no—
415C2×C3—41no—
416C2×C3—42no—
417C2×C3C2×#80611yescharacteristic
418C2×C3C2×#81611yescharacteristic
419C2×C3#513911yescharacteristic
420C2×C3C2×C3×#9911yescharacteristic
421C2×C3C2×C3×#10311yescharacteristic
422C2×C3C3×#42111yescharacteristic
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—42no—
430C22—42no—
431C22C3×#81612yes—
432C22C3×#81612yes—
433C22C2×C3×#20411yescharacteristic
434C22C2×C3×Dic1211yescharacteristic
435C22C2×C3×(C2×D3)⋊C411yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—122no—
440C4—122no—
441C4—242no—
442C4C3×#80612yes—
443C3—21no—
444C3#6994611yescharacteristic, direct product factor
445C3C3×#152011yescharacteristic, complemented
446C2—21no—
447C2—21no—
448C2—22no—
449C2—22no—
450C2C2×C3×#80611yescharacteristic
451C2C2×C3×#81611yescharacteristic
452C2C3×#513911yescharacteristic
subgroupG/H
centerC22×C3C2×(C2×D3)⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C22⋊C8C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32D4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C22⋊C8D3
hypocenterC3C3×#1520
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C2×C3×C22⋊C8

Complements

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

NH ≅ G/Ntype
4. C3×#4467C2semidirect
6. #69946C3direct (N × H)
8. C22×C3×Dic6C4semidirect
13. C2×C3×C4⋊Dic3C4semidirect
16. C3×#924C4semidirect
30. #4467C2×C3semidirect
60. C22×Dic6C3×C4semidirect
76. C2×C4⋊Dic3C3×C4semidirect
79. #924C3×C4semidirect
374. C32#1520semidirect
444. C3#69946direct (N × H)
445. C3C3×#1520semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9242
C2×C32×C22⋊C82
C3×#52122
C3×#44672
C3×#15203
#699463