Finite Group Databasebeta

← C3×#69964 #11792008

Subgroups — C3×#69964 #11792008

Order 1152.

885 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#924C212yesmaximal
2C22×C3×Dic12C211yesmaximal, characteristic, complemented
3C2×C32×C22⋊C8C211yesmaximal, characteristic
4C2×C3×#816C212yesmaximal, complemented
5C3×#4551C211yesmaximal, characteristic, complemented
6C3×#2001—31nomaximal
7#69964C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2211yescharacteristic
9C22×C3×Dic6C2212yes—
10C22×C32×C8C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C3×#217—22no—
13C2×C3×C4⋊Dic3C2212yes—
14C3×#924—24no—
15C3×#924—24no—
16C2×C3×Dic3⋊C4—22no—
17C2×C3×Dic12—24no—
18C2×C3×Dic12—22no—
19C32×C22⋊C8—22no—
20C3×#816—24no—
21C22×C3×Q16—31no—
22C2×C3×C22⋊Q8—32no—
23C2×#924C2×C312yes—
24C22×Dic12C2×C311yescharacteristic, complemented
25C2×C3×#103—32no—
26C2×C3×C22⋊C8—21no—
27C2×C3×C22⋊C8D311yescharacteristic
28C2×C3×C22⋊C8C2×C311yescharacteristic
29C2×#816C2×C312yescomplemented
30C3×#340—31no—
31#4551C2×C311yescharacteristic, complemented
32C24×C32D411yescharacteristic
33C22×C32×C4—21no—
34C22×C32×C4—22no—
35C22×C32×C4—22no—
36C22×C32×C4—21no—
37C22×C32×C4D411yescharacteristic
38C22×C32×C4C2311yescharacteristic
39C22×C3×Dic3—22no—
40C22×C3×Dic3—22no—
41C2×C3×Dic6—22no—
42C2×C3×Dic6—22no—
43C2×C3×Dic6—22no—
44C2×C3×Dic6—22no—
45C2×C3×Dic6—22no—
46C2×C3×Dic6D414yes—
47C2×C32×C8—22no—
48C2×C32×C8—21no—
49C2×C32×C8—22no—
50C2×C32×C8D412yes—
51C3×#217—28no—
52C3×C4⋊Dic3—22no—
53C3×C4⋊Dic3D414yes—
54C3×Dic3⋊C4—28no—
55C3×Dic12—28no—
56#2001—31noSylow
57C22×C3×Q8—32no—
58C23×C3×C4—21no—
59C23×C3×C4C2×D311yescharacteristic
60C23×C3×C4C22×C311yescharacteristic
61C22×Dic6C22×C312yes—
62C2×C3×Q16—64no—
63C2×C3×Q16—62no—
64C22×C3×C8—21no—
65C22×C3×C8—21no—
66C22×C3×C8C2×D311yescharacteristic
67C22×C3×C8C2×D311yescharacteristic
68C22×C3×C8C22×C311yescharacteristic
69C22×C3×C8C22×C311yescharacteristic
70C3×C22⋊Q8—64no—
71C3×C22⋊Q8—64no—
72C2×C3×C4⋊C4—32no—
73C2×C3×C4⋊C4—62no—
74C2×C3×C22⋊C4—62no—
75C2×#217—22no—
76C2×C4⋊Dic3C22×C312yes—
77#924—24no—
78#924—24no—
79C2×Dic3⋊C4—22no—
80C2×Dic12—24no—
81C2×Dic12—22no—
82C3×#103—64no—
83C3×C22⋊C8—24no—
84C3×C22⋊C8—22no—
85C3×C22⋊C8—22no—
86#816—24no—
87C23×C32—21no—
88C23×C32—21no—
89C23×C32—22no—
90C23×C32—22no—
91C23×C32Q1612yescomplemented
92C23×C32C2×D411yescharacteristic
93C2×C32×C4—21no—
94C2×C32×C4—22no—
95C2×C32×C4—41no—
96C2×C32×C4—42no—
97C2×C32×C4—41no—
98C2×C32×C4C2×D412yes—
99C2×C32×C4C2×D412yes—
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C3×Dic3—24no—
103C2×C3×Dic3—24no—
104C2×C3×Dic3—42no—
105C2×C3×Dic3—42no—
106C2×C3×Dic3—42no—
107C2×C3×Dic3—42no—
108C3×Dic6—24no—
109C3×Dic6—24no—
110C3×Dic6—42no—
111C3×Dic6—42no—
112C32×C8—22no—
113C32×C8—41no—
114C22×Q16—31no—
115C2×C22⋊Q8—32no—
116C2×#103—32no—
117C2×C22⋊C8C3×D311yescharacteristic
118#340—31no—
119C24×C3—21no—
120C24×C3D1211yescharacteristic
121C24×C3C3×D411yescharacteristic
122C2×C3×Q8—34no—
123C2×C3×Q8—62no—
124C2×C3×Q8—62no—
125C2×C3×Q8—62no—
126C2×C3×Q8—62no—
127C2×C3×Q8—62no—
128C22×C3×C4—22no—
129C22×C3×C4—22no—
130C22×C3×C4—21no—
131C22×C3×C4—22no—
132C22×C3×C4—22no—
133C22×C3×C4—21no—
134C22×C3×C4—21no—
135C22×C3×C4—22no—
136C22×C3×C4—22no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—42no—
141C22×C3×C4—42no—
142C22×C3×C4—62no—
143C22×C3×C4—62no—
144C22×C3×C4D1211yescharacteristic
145C22×C3×C4C3×D411yescharacteristic
146C22×C3×C4C22×D311yescharacteristic
147C22×C3×C4C23×C311yescharacteristic
148C22×Dic3—22no—
149C22×Dic3—22no—
150C2×Dic6—22no—
151C2×Dic6—22no—
152C2×Dic6—22no—
153C2×Dic6—22no—
154C2×Dic6—22no—
155C2×Dic6C3×D414yes—
156C3×Q16—68no—
157C2×C3×C8—22no—
158C2×C3×C8—22no—
159C2×C3×C8—22no—
160C2×C3×C8—22no—
161C2×C3×C8—21no—
162C2×C3×C8—22no—
163C2×C3×C8—21no—
164C2×C3×C8—22no—
165C2×C3×C8—42no—
166C2×C3×C8—42no—
167C2×C3×C8#6712yes—
168C2×C3×C8C3×D412yes—
169C3×C4⋊C4—34no—
170C3×C4⋊C4—68no—
171C3×C4⋊C4—62no—
172C3×C22⋊C4—68no—
173#217—28no—
174C4⋊Dic3—22no—
175C4⋊Dic3C3×D414yes—
176Dic3⋊C4—28no—
177Dic12—28no—
178C22×C32—22no—
179C22×C32—24no—
180C22×C32—41no—
181C22×C32—42no—
182C22×C32—41no—
183C22×C32#12012yes—
184C22×C32#12111yescharacteristic
185C22×C32C2×Q1611yescharacteristic
186C22×C32#13511yescharacteristic
187C22×C32#13712yes—
188C32×C4—41no—
189C32×C4#12011yescharacteristic
190C32×C4#12112yes—
191C32×C4#12711yescharacteristic
192C3×Dic3—44no—
193C3×Dic3—44no—
194C22×Q8—32no—
195C23×C4C2×C3×D311yescharacteristic
196C2×Q16—64no—
197C2×Q16—62no—
198C22×C8C2×C3×D311yescharacteristic
199C22×C8C2×C3×D311yescharacteristic
200C22⋊Q8—64no—
201C22⋊Q8—64no—
202C2×C4⋊C4—32no—
203C2×C4⋊C4—62no—
204C2×C22⋊C4—62no—
205#103—64no—
206C22⋊C8—22no—
207C23×C3—22no—
208C23×C3—22no—
209C23×C3—22no—
210C23×C3—21no—
211C23×C3—22no—
212C23×C3—21no—
213C23×C3—22no—
214C23×C3—21no—
215C23×C3—21no—
216C23×C3—22no—
217C23×C3—22no—
218C23×C3—21no—
219C23×C3—42no—
220C23×C3—42no—
221C23×C3Dic1212yescomplemented
222C23×C3C3×Q1612yescomplemented
223C23×C3C2×D1211yescharacteristic
224C23×C3C2×C3×D411yescharacteristic
225C3×Q8—64no—
226C3×Q8—64no—
227C3×Q8—122no—
228C3×Q8—122no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—21no—
232C2×C3×C4—22no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—22no—
236C2×C3×C4—22no—
237C2×C3×C4—21no—
238C2×C3×C4—42no—
239C2×C3×C4—44no—
240C2×C3×C4—42no—
241C2×C3×C4—42no—
242C2×C3×C4—42no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—41no—
246C2×C3×C4—42no—
247C2×C3×C4—41no—
248C2×C3×C4—64no—
249C2×C3×C4—64no—
250C2×C3×C4—122no—
251C2×C3×C4—122no—
252C2×C3×C4—122no—
253C2×C3×C4—122no—
254C2×C3×C4#23511yescharacteristic
255C2×C3×C4D3×D412yes—
256C2×C3×C4D3×D412yes—
257C2×C3×C4C2×#6711yescharacteristic
258C2×C3×C4C2×C3×D412yes—
259C2×C3×C4C2×C3×D412yes—
260C2×C3×C4C2×C3×D411yescharacteristic
261C2×C3×C4C3×#4111yescharacteristic
262C2×Dic3—24no—
263C2×Dic3—24no—
264C2×Dic3—42no—
265C2×Dic3—42no—
266C2×Dic3—42no—
267C2×Dic3—42no—
268Dic6—24no—
269Dic6—24no—
270Dic6—42no—
271Dic6—42no—
272C3×C8—22no—
273C3×C8—22no—
274C3×C8—42no—
275C3×C8—42no—
276C3×C8—41no—
277C3×C8—41no—
278C2×C32—42no—
279C2×C32#39211yescharacteristic
280C2×C32#45112yes—
281C2×C32#45212yes—
282C2×C32#46711yescharacteristic
283C2×C32#47011yescharacteristic
284C24C3×D1211yescharacteristic
285C2×Q8—34no—
286C2×Q8—62no—
287C2×Q8—62no—
288C2×Q8—62no—
289C2×Q8—62no—
290C2×Q8—62no—
291C22×C4—21no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—21no—
295C22×C4—62no—
296C22×C4—62no—
297C22×C4C3×D1211yescharacteristic
298C22×C4C22×C3×D311yescharacteristic
299Q16—68no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—21no—
303C2×C8C3×#6712yes—
304C4⋊C4—34no—
305C4⋊C4—68no—
306C4⋊C4—62no—
307C22⋊C4—68no—
308C22×C3—24no—
309C22×C3—24no—
310C22×C3—24no—
311C22×C3—22no—
312C22×C3—22no—
313C22×C3—22no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—22no—
317C22×C3—21no—
318C22×C3—44no—
319C22×C3—42no—
320C22×C3—44no—
321C22×C3—42no—
322C22×C3—41no—
323C22×C3—41no—
324C22×C3—42no—
325C22×C3—41no—
326C22×C3—42no—
327C22×C3—41no—
328C22×C3#88212yes—
329C22×C3#90411yescharacteristic
330C22×C3C2×Dic1211yescharacteristic
331C22×C3#90912yes—
332C22×C3#93011yescharacteristic
333C22×C3C3×#12012yes—
334C22×C3C3×#12111yescharacteristic
335C22×C3C2×C3×Q1611yescharacteristic
336C22×C3C3×#13511yescharacteristic
337C22×C3C3×#13712yes—
338C3×C4—22no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—42no—
342C3×C4—41no—
343C3×C4—41no—
344C3×C4—124no—
345C3×C4—124no—
346C3×C4#88412yes—
347C3×C4#93711yescharacteristic
348C3×C4#94011yescharacteristic
349C3×C4C3×#12011yescharacteristic
350C3×C4C3×#12112yes—
351C3×C4C3×#12711yescharacteristic
352Dic3—44no—
353Dic3—44no—
354C32#200111yescharacteristic, complemented, Sylow
355C23—22no—
356C23—21no—
357C23—22no—
358C23—21no—
359C23C3×Dic1212yescomplemented
360C23C2×C3×D1211yescharacteristic
361Q8—64no—
362Q8—64no—
363Q8—122no—
364Q8—122no—
365C2×C4—22no—
366C2×C4—21no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—64no—
371C2×C4—64no—
372C2×C4—122no—
373C2×C4—122no—
374C2×C4—122no—
375C2×C4—122no—
376C2×C4C3×#23511yescharacteristic
377C2×C4C3×D3×D412yes—
378C2×C4C3×D3×D412yes—
379C2×C4C2×C3×#6711yescharacteristic
380C8—22no—
381C8—41no—
382C2×C3—21no—
383C2×C3—22no—
384C2×C3—22no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—44no—
388C2×C3—42no—
389C2×C3—42no—
390C2×C3#473312yes—
391C2×C3#473912yes—
392C2×C3#496011yescharacteristic
393C2×C3#511611yescharacteristic
394C2×C3#513711yescharacteristic
395C2×C3C3×#39211yescharacteristic
396C2×C3C3×#45112yes—
397C2×C3C3×#45212yes—
398C2×C3C3×#46711yescharacteristic
399C2×C3C3×#47011yescharacteristic
400C22—24no—
401C22—22no—
402C22—41no—
403C22—42no—
404C22—41no—
405C22C3×#88212yes—
406C22C3×#90411yescharacteristic
407C22C2×C3×Dic1211yescharacteristic
408C22C3×#90912yes—
409C22C3×#93011yescharacteristic
410C4—41no—
411C4—124no—
412C4—124no—
413C4C3×#88412yes—
414C4C3×#93711yescharacteristic
415C4C3×#94011yescharacteristic
416C3—21no—
417C3#6996411yescharacteristic, direct product factor
418C3C3×#200111yescharacteristic, complemented
419C2—42no—
420C2C3×#473312yes—
421C2C3×#473912yes—
422C2C3×#496011yescharacteristic
423C2C3×#511611yescharacteristic
424C2C3×#513711yescharacteristic
subgroupG/H
centerC23×C3C2×D12
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C22⋊C8C2
socleC23×C32C2×D4
prime radicalC24×C32D4
hypercenterC2×C3×C22⋊C8D3
hypocenterC3C3×#2001
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C2×C3×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×C3×Dic12C2semidirect
4. C2×C3×#816C2semidirect
5. C3×#4551C2semidirect
7. #69964C3direct (N × H)
24. C22×Dic12C2×C3semidirect
29. C2×#816C2×C3semidirect
31. #4551C2×C3semidirect
91. C23×C32Q16semidirect
221. C23×C3Dic12semidirect
222. C23×C3C3×Q16semidirect
354. C32#2001semidirect
359. C23C3×Dic12semidirect
417. C3#69964direct (N × H)
418. C3C3×#2001semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9242
C22×C3×Dic122
C2×C32×C22⋊C82
C2×C3×#8162
C3×#45512
C3×#20013
#699643