Finite Group Databasebeta

← C3×#83348 #11877017

Subgroups — C3×#83348 #11877017

Order 1152.

827 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#533C211yesmaximal, characteristic
2C3×#5470C211yesmaximal, characteristic
3C3×#5093C211yesmaximal, characteristic, complemented
4C3×#5092C211yesmaximal, characteristic, complemented
5C3×#5080C211yesmaximal, characteristic, complemented
6C3×#5079C211yesmaximal, characteristic, complemented
7C3×#5052C214yesmaximal
8C3×#5030C214yesmaximal, complemented
9C3×C4×#208C211yesmaximal, characteristic
10C3×#3185—31nomaximal
11#83348C311yesmaximal, characteristic, direct product factor
12C32×C4⋊Q8C2211yescharacteristic
13C32×C4⋊Q8C2211yescharacteristic
14C32×#125—21no—
15C32×C22⋊Q8—21no—
16C32×C22⋊Q8C2212yes—
17C32×C4×Q8—21no—
18C32×C4×Q8C2212yes—
19C32×#117—21no—
20C2×C32×C42C2211yescharacteristic
21C2×C3×#216C2214yes—
22C3×#926—21no—
23C3×#924—21no—
24C3×#924C2212yes—
25C2×C3×#208C2212yes—
26C3×#870—21no—
27C3×#869C2211yescharacteristic
28C3×#869C2211yescharacteristic
29C3×C4×Dic6—21no—
30C3×C4×Dic6C2212yes—
31C3×#835C2214yes—
32C3×#810C2214yes—
33C3×#808C2214yes—
34C3×#803C2212yes—
35C3×C4×C3⋊C8C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37C3×#533—21no—
38C3×#533—31no—
39C3×#533D311yescharacteristic
40C3×#533C2×C311yescharacteristic
41#5470C2×C311yescharacteristic
42C3×#498—31no—
43C3×#494—31no—
44C3×#487—31no—
45C3×#487—31no—
46C3×#470—34no—
47C3×#441—34no—
48C3×C4×M16—31no—
49#5093C2×C311yescharacteristic, complemented
50#5092C2×C311yescharacteristic, complemented
51#5080C2×C311yescharacteristic, complemented
52#5079C2×C311yescharacteristic, complemented
53#5052C2×C314yes—
54#5030C2×C314yescomplemented
55C4×#208C2×C311yescharacteristic
56C2×C32×Q8—21no—
57C2×C32×Q8C2312yes—
58C22×C32×C4D411yescharacteristic
59C22×C32×C4D411yescharacteristic
60C22×C32×C4C2311yescharacteristic
61C2×C3×Dic6—21no—
62C2×C3×Dic6C2312yes—
63C32×C4⋊C4—21no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4—22no—
67C32×C4⋊C4—22no—
68C32×C4⋊C4C2312yes—
69C32×C22⋊C4—22no—
70C32×C42—22no—
71C32×C42D411yescharacteristic
72C32×C42D411yescharacteristic
73C32×C42C2311yescharacteristic
74C32×C42C2311yescharacteristic
75C3×#217—22no—
76C3×#216—28no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3—21no—
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3C2312yes—
81C3×Dic3⋊C4—22no—
82C3×Dic3⋊C4—22no—
83C3×C4×Dic3—22no—
84C3×#208—24no—
85C2×C3×C3⋊C8C2312yes—
86C2×C3×C3⋊C8C2312yes—
87#3185—31noSylow
88C2×C3×Q16—34no—
89C2×C3×M16—32no—
90C3×C4⋊Q8—21no—
91C3×C4⋊Q8—21no—
92C3×C4⋊Q8—31no—
93C3×C4⋊Q8—31no—
94C3×C4⋊Q8C2×D311yescharacteristic
95C3×C4⋊Q8C2×D311yescharacteristic
96C3×C4⋊Q8C22×C311yescharacteristic
97C3×C4⋊Q8C22×C311yescharacteristic
98C3×#125—22no—
99C3×#125—21no—
100C3×#125—21no—
101C3×#125—61no—
102C3×C22⋊Q8—22no—
103C3×C22⋊Q8—21no—
104C3×C22⋊Q8—21no—
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8—32no—
107C3×C22⋊Q8—61no—
108C3×C22⋊Q8C2×D312yes—
109C3×C22⋊Q8C22×C312yes—
110C3×C4×Q8—22no—
111C3×C4×Q8—21no—
112C3×C4×Q8—21no—
113C3×C4×Q8—22no—
114C3×C4×Q8—32no—
115C3×C4×Q8—61no—
116C3×C4×Q8C2×D312yes—
117C3×C4×Q8C22×C312yes—
118C3×#117—22no—
119C3×#117—21no—
120C3×#117—21no—
121C3×#117—61no—
122C2×C3×C42—21no—
123C2×C3×C42C2×D311yescharacteristic
124C2×C3×C42C22×C311yescharacteristic
125C2×#216C22×C314yes—
126#926—21no—
127#924—21no—
128#924C22×C312yes—
129C2×#208C22×C312yes—
130#870—21no—
131#869C22×C311yescharacteristic
132#869C22×C311yescharacteristic
133C4×Dic6—21no—
134C4×Dic6C22×C312yes—
135C3×#106—34no—
136C3×#103—34no—
137C3×#103—34no—
138C3×#97—32no—
139C3×C4×C8—31no—
140C3×C4×C8—31no—
141#835C22×C314yes—
142#810C22×C314yes—
143#808C22×C314yes—
144#803C22×C312yes—
145C4×C3⋊C8C22×C311yescharacteristic
146C4×C3⋊C8C22×C311yescharacteristic
147C23×C32C2×D411yescharacteristic
148C32×Q8—24no—
149C32×Q8—42no—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—22no—
154C2×C32×C4—22no—
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2411yescharacteristic
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C3×Dic6—24no—
164C3×Dic6—42no—
165C3×C3⋊C8—22no—
166C3×C3⋊C8#4114yes—
167#533—31no—
168#533C3×D311yescharacteristic
169#498—31no—
170#494—31no—
171#487—31no—
172#487—31no—
173#470—34no—
174#441—34no—
175C4×M16—31no—
176C2×C3×Q8—22no—
177C2×C3×Q8—21no—
178C2×C3×Q8—21no—
179C2×C3×Q8—22no—
180C2×C3×Q8—32no—
181C2×C3×Q8—61no—
182C2×C3×Q8C22×D312yes—
183C2×C3×Q8C23×C312yes—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4#6711yescharacteristic
188C22×C3×C4#6711yescharacteristic
189C22×C3×C4C3×D411yescharacteristic
190C22×C3×C4C3×D411yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C23×C311yescharacteristic
193C2×Dic6—21no—
194C2×Dic6C23×C312yes—
195C3×Q16—68no—
196C3×M16—64no—
197C2×C3×C8—32no—
198C2×C3×C8—32no—
199C3×C4⋊C4—22no—
200C3×C4⋊C4—22no—
201C3×C4⋊C4—24no—
202C3×C4⋊C4—24no—
203C3×C4⋊C4—22no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—22no—
208C3×C4⋊C4—22no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—22no—
213C3×C4⋊C4—22no—
214C3×C4⋊C4—22no—
215C3×C4⋊C4—32no—
216C3×C4⋊C4—62no—
217C3×C4⋊C4—62no—
218C3×C4⋊C4—61no—
219C3×C4⋊C4—61no—
220C3×C4⋊C4—61no—
221C3×C4⋊C4C22×D312yes—
222C3×C4⋊C4C23×C312yes—
223C3×C22⋊C4—24no—
224C3×C22⋊C4—22no—
225C3×C22⋊C4—22no—
226C3×C22⋊C4—62no—
227C3×C42—24no—
228C3×C42—22no—
229C3×C42—22no—
230C3×C42—21no—
231C3×C42—21no—
232C3×C42—21no—
233C3×C42—21no—
234C3×C42—62no—
235C3×C42#6711yescharacteristic
236C3×C42#6711yescharacteristic
237C3×C42C3×D411yescharacteristic
238C3×C42C3×D411yescharacteristic
239C3×C42C22×D311yescharacteristic
240C3×C42C22×D311yescharacteristic
241C3×C42C23×C311yescharacteristic
242C3×C42C23×C311yescharacteristic
243#217—22no—
244#216—28no—
245C4⋊Dic3—21no—
246C4⋊Dic3—21no—
247C4⋊Dic3—21no—
248C4⋊Dic3C23×C312yes—
249Dic3⋊C4—22no—
250Dic3⋊C4—22no—
251C4×Dic3—22no—
252#208—24no—
253C2×C3⋊C8C23×C312yes—
254C2×C3⋊C8C23×C312yes—
255C22×C32—21no—
256C22×C32—21no—
257C22×C32—21no—
258C22×C32C22×D411yescharacteristic
259C32×C4—21no—
260C32×C4—21no—
261C32×C4—21no—
262C32×C4—42no—
263C32×C4—42no—
264C32×C4#13712yes—
265C32×C4#13712yes—
266C32×C4C2×#4112yes—
267C3×Dic3—42no—
268C3×Dic3—42no—
269C2×Q16—34no—
270C2×M16—32no—
271C4⋊Q8—31no—
272C4⋊Q8—31no—
273C4⋊Q8C2×C3×D311yescharacteristic
274C4⋊Q8C2×C3×D311yescharacteristic
275#125—21no—
276#125—61no—
277C22⋊Q8—21no—
278C22⋊Q8—32no—
279C22⋊Q8—61no—
280C22⋊Q8C2×C3×D312yes—
281C4×Q8—21no—
282C4×Q8—32no—
283C4×Q8—61no—
284C4×Q8C2×C3×D312yes—
285#117—21no—
286#117—61no—
287C2×C42C2×C3×D311yescharacteristic
288#106—34no—
289#103—34no—
290#103—34no—
291#97—32no—
292C4×C8—31no—
293C4×C8—31no—
294C23×C3—21no—
295C23×C3C2×#6711yescharacteristic
296C23×C3C2×C3×D411yescharacteristic
297C3×Q8—24no—
298C3×Q8—24no—
299C3×Q8—44no—
300C3×Q8—44no—
301C3×Q8—42no—
302C3×Q8—42no—
303C3×Q8—64no—
304C3×Q8—122no—
305C2×C3×C4—24no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—24no—
313C2×C3×C4—24no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—42no—
325C2×C3×C4—42no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4C2×#6711yescharacteristic
329C2×C3×C4C2×#6711yescharacteristic
330C2×C3×C4C2×#6711yescharacteristic
331C2×C3×C4C2×#6711yescharacteristic
332C2×C3×C4C2×#6711yescharacteristic
333C2×C3×C4C2×C3×D411yescharacteristic
334C2×C3×C4C2×C3×D411yescharacteristic
335C2×C3×C4C2×C3×D411yescharacteristic
336C2×C3×C4C2×C3×D411yescharacteristic
337C2×C3×C4C2×C3×D411yescharacteristic
338C2×C3×C4C23×D311yescharacteristic
339C2×C3×C4C24×C311yescharacteristic
340C2×Dic3—22no—
341C2×Dic3—22no—
342Dic6—24no—
343Dic6—42no—
344C3×C8—34no—
345C3×C8—62no—
346C3⋊C8—22no—
347C3⋊C8C3×#4114yes—
348C2×C32—41no—
349C2×C32#53211yescharacteristic
350C2×C32C2×#13711yescharacteristic
351C2×C32C2×#13711yescharacteristic
352C2×Q8—21no—
353C2×Q8—32no—
354C2×Q8—61no—
355C2×Q8C22×C3×D312yes—
356C22×C4C3×#6711yescharacteristic
357C22×C4C3×#6711yescharacteristic
358C22×C4C22×C3×D311yescharacteristic
359Q16—68no—
360M16—64no—
361C2×C8—32no—
362C2×C8—32no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—32no—
369C4⋊C4—61no—
370C4⋊C4—61no—
371C4⋊C4—62no—
372C4⋊C4—62no—
373C4⋊C4—61no—
374C4⋊C4C22×C3×D312yes—
375C22⋊C4—22no—
376C22⋊C4—62no—
377C42—22no—
378C42—62no—
379C42C3×#6711yescharacteristic
380C42C3×#6711yescharacteristic
381C42C22×C3×D311yescharacteristic
382C42C22×C3×D311yescharacteristic
383C22×C3—22no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3C22×#6711yescharacteristic
394C22×C3C22×C3×D411yescharacteristic
395C3×C4—22no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—22no—
403C3×C4—22no—
404C3×C4—22no—
405C3×C4—41no—
406C3×C4—41no—
407C3×C4—44no—
408C3×C4—44no—
409C3×C4—42no—
410C3×C4—42no—
411C3×C4—42no—
412C3×C4—42no—
413C3×C4—122no—
414C3×C4—122no—
415C3×C4#94212yes—
416C3×C4#95112yes—
417C3×C4C3×#13712yes—
418C3×C4C3×#13712yes—
419C3×C4D3×#4112yes—
420C3×C4C2×C3×#4112yes—
421Dic3—42no—
422Dic3—42no—
423C32#318511yescharacteristic, complemented, Sylow
424C23C2×C3×#6711yescharacteristic
425Q8—24no—
426Q8—42no—
427Q8—64no—
428Q8—122no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—62no—
435C2×C4—62no—
436C2×C4C2×C3×#6711yescharacteristic
437C2×C4C2×C3×#6711yescharacteristic
438C2×C4C2×C3×#6711yescharacteristic
439C2×C4C2×C3×#6711yescharacteristic
440C2×C4C2×C3×#6711yescharacteristic
441C2×C4C23×C3×D311yescharacteristic
442C8—34no—
443C8—62no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—42no—
448C2×C3—41no—
449C2×C3—41no—
450C2×C3C2×#94211yescharacteristic
451C2×C3C2×#95111yescharacteristic
452C2×C3#583211yescharacteristic
453C2×C3C3×#53211yescharacteristic
454C2×C3C2×C3×#13711yescharacteristic
455C2×C3C2×C3×#13711yescharacteristic
456C22—21no—
457C22—21no—
458C22—21no—
459C22C22×C3×#6711yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—42no—
464C4—42no—
465C4—122no—
466C4—122no—
467C4C3×#94212yes—
468C4C3×#95112yes—
469C4C3×D3×#4112yes—
470C3—21no—
471C3#8334811yescharacteristic, direct product factor
472C3C3×#318511yescharacteristic, complemented
473C2—41no—
474C2C2×C3×#94211yescharacteristic
475C2C2×C3×#95111yescharacteristic
476C2C3×#583211yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#533C2
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC3×#533D3
hypocenterC3C3×#3185
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C3×#533

Complements

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

NH ≅ G/Ntype
3. C3×#5093C2semidirect
4. C3×#5092C2semidirect
5. C3×#5080C2semidirect
6. C3×#5079C2semidirect
8. C3×#5030C2semidirect
11. #83348C3direct (N × H)
49. #5093C2×C3semidirect
50. #5092C2×C3semidirect
51. #5080C2×C3semidirect
52. #5079C2×C3semidirect
54. #5030C2×C3semidirect
423. C32#3185semidirect
471. C3#83348direct (N × H)
472. C3C3×#3185semidirect

Maximal subgroups

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

subgroupindex
C32×#5332
C3×#54702
C3×#50932
C3×#50922
C3×#50802
C3×#50792
C3×#50522
C3×#50302
C3×C4×#2082
C3×#31853
#833483