Finite Group Databasebeta

← C3×#71817 #11787771

Subgroups — C3×#71817 #11787771

Order 1152.

819 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#532C211yesmaximal, characteristic
2C3×#5819C211yesmaximal, characteristic, complemented
3C3×#5240C211yesmaximal, characteristic, complemented
4C3×#5236C212yesmaximal, complemented
5C3×#4523C212yesmaximal, complemented
6C3×#1884—31nomaximal
7#71817C311yesmaximal, characteristic, direct product factor
8C2×C32×#41C2211yescharacteristic
9C2×C32×#41C2211yescharacteristic
10C32×C4⋊Q8C411yescharacteristic, complemented
11C32×#127C411yescharacteristic, complemented
12C32×#124C411yescharacteristic, complemented
13C32×#124C411yescharacteristic, complemented
14C32×#121—22no—
15C32×C4×D4—22no—
16C2×C32×C42C2211yescharacteristic
17C3×#948—24no—
18C3×#926C2212yes—
19C2×C3×#208—22no—
20C2×C3×#208C2212yes—
21C3×#837—24no—
22C3×#834—22no—
23C3×#568—31no—
24C3×#532—21no—
25C3×#532D311yescharacteristic
26C3×#532C2×C311yescharacteristic
27#5819C2×C311yescharacteristic, complemented
28C3×#421—32no—
29C3×#410—31no—
30#5240C2×C311yescharacteristic, complemented
31#5236C2×C312yescomplemented
32C3×#339—32no—
33#4523C2×C312yescomplemented
34C32×#41—22no—
35C32×#41—22no—
36C32×#41—22no—
37C32×#41—22no—
38C2×C32×Q8C2×C411yescharacteristic
39C2×C32×Q8C2×C411yescharacteristic
40C2×C32×D4—22no—
41C2×C32×D4—21no—
42C2×C32×D4C2×C411yescharacteristic
43C2×C32×D4C2×C411yescharacteristic
44C2×C32×D4D412yes—
45C22×C32×C4—21no—
46C22×C32×C4—21no—
47C22×C32×C4D412yes—
48C22×C32×C4C2311yescharacteristic
49C32×C4⋊C4—22no—
50C32×C22⋊C4—22no—
51C32×C22⋊C4—22no—
52C32×C42—21no—
53C32×C42C2×C411yescharacteristic
54C32×C42C2×C411yescharacteristic
55C3×#217—22no—
56C3×C4⋊Dic3—22no—
57C3×C4×Dic3—22no—
58C3×#208—24no—
59C3×#208—22no—
60C3×#208D414yescomplemented
61C2×C3×C3⋊C8—24no—
62C2×C3×C3⋊C8—22no—
63#1884—31noSylow
64C2×C3×#41—21no—
65C2×C3×#41—21no—
66C2×C3×#41C2×D311yescharacteristic
67C2×C3×#41C2×D311yescharacteristic
68C2×C3×#41C22×C311yescharacteristic
69C2×C3×#41C22×C311yescharacteristic
70C3×#131—64no—
71C2×C3×M16—32no—
72C2×C3×M16—62no—
73C3×C4⋊Q8—21no—
74C3×C4⋊Q8Dic311yescharacteristic, complemented
75C3×C4⋊Q8C3×C411yescharacteristic, complemented
76C3×#127—21no—
77C3×#127Dic311yescharacteristic, complemented
78C3×#127C3×C411yescharacteristic, complemented
79C3×#124—21no—
80C3×#124—21no—
81C3×#124Dic311yescharacteristic, complemented
82C3×#124Dic311yescharacteristic, complemented
83C3×#124C3×C411yescharacteristic, complemented
84C3×#124C3×C411yescharacteristic, complemented
85C3×#121—24no—
86C3×#121—22no—
87C3×#121—22no—
88C3×C4×D4—24no—
89C3×C4×D4—22no—
90C3×C4×D4—22no—
91C3×#117—32no—
92C2×C3×C42—21no—
93C2×C3×C42C2×D311yescharacteristic
94C2×C3×C42C22×C311yescharacteristic
95#948—24no—
96#926C22×C312yes—
97C2×#208—22no—
98C2×#208C22×C312yes—
99C3×#104—64no—
100C3×#99—62no—
101#837—24no—
102#834—22no—
103C23×C32—21no—
104C23×C32C22⋊C412yes—
105C23×C32C2×D411yescharacteristic
106C32×Q8—22no—
107C32×Q8—22no—
108C32×D4—24no—
109C32×D4—22no—
110C32×D4—22no—
111C32×D4—44no—
112C32×D4—42no—
113C2×C32×C4—21no—
114C2×C32×C4—21no—
115C2×C32×C4—21no—
116C2×C32×C4—22no—
117C2×C32×C4—22no—
118C2×C32×C4—42no—
119C2×C32×C4—41no—
120C2×C32×C4—41no—
121C2×C32×C4C22⋊C412yes—
122C2×C32×C4C22×C411yescharacteristic
123C2×C32×C4C2×D412yes—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4#4112yes—
126C2×C3×Dic3—42no—
127C3×C3⋊C8—24no—
128#568—31no—
129#532C3×D311yescharacteristic
130#421—32no—
131#410—31no—
132#339—32no—
133C3×#41—22no—
134C3×#41—22no—
135C3×#41—22no—
136C3×#41—22no—
137C3×#41—22no—
138C3×#41—22no—
139C3×#41—22no—
140C3×#41—22no—
141C3×#41—42no—
142C3×#41—42no—
143C3×#41—42no—
144C3×#41—42no—
145C2×C3×Q8—21no—
146C2×C3×Q8—21no—
147C2×C3×Q8C2×Dic311yescharacteristic
148C2×C3×Q8C2×Dic311yescharacteristic
149C2×C3×Q8C2×C3×C411yescharacteristic
150C2×C3×Q8C2×C3×C411yescharacteristic
151C2×C3×D4—24no—
152C2×C3×D4—22no—
153C2×C3×D4—22no—
154C2×C3×D4—22no—
155C2×C3×D4—21no—
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×C3×D4—22no—
160C2×C3×D4C2×Dic311yescharacteristic
161C2×C3×D4C2×Dic311yescharacteristic
162C2×C3×D4#6712yes—
163C2×C3×D4C2×C3×C411yescharacteristic
164C2×C3×D4C2×C3×C411yescharacteristic
165C2×C3×D4C3×D412yes—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—22no—
173C22×C3×C4—21no—
174C22×C3×C4#6712yes—
175C22×C3×C4C3×D412yes—
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C23×C311yescharacteristic
178C3×M16—34no—
179C3×M16—64no—
180C3×M16—62no—
181C2×C3×C8—64no—
182C2×C3×C8—62no—
183C3×C4⋊C4—24no—
184C3×C4⋊C4—22no—
185C3×C4⋊C4—22no—
186C3×C4⋊C4—62no—
187C3×C22⋊C4—24no—
188C3×C22⋊C4—24no—
189C3×C22⋊C4—22no—
190C3×C22⋊C4—22no—
191C3×C22⋊C4—22no—
192C3×C22⋊C4—22no—
193C3×C22⋊C4—62no—
194C3×C42—22no—
195C3×C42—21no—
196C3×C42—21no—
197C3×C42—21no—
198C3×C42—21no—
199C3×C42—62no—
200C3×C42C2×Dic311yescharacteristic
201C3×C42C2×Dic311yescharacteristic
202C3×C42C2×C3×C411yescharacteristic
203C3×C42C2×C3×C411yescharacteristic
204#217—22no—
205C4⋊Dic3—22no—
206C4×Dic3—22no—
207#208—24no—
208#208—22no—
209#208C3×D414yescomplemented
210C2×C3⋊C8—24no—
211C2×C3⋊C8—22no—
212C22×C32—22no—
213C22×C32—41no—
214C22×C32—42no—
215C22×C32—42no—
216C22×C32—41no—
217C22×C32C2×C22⋊C411yescharacteristic
218C22×C32#12112yes—
219C32×C4—22no—
220C32×C4—22no—
221C32×C4—41no—
222C32×C4—41no—
223C32×C4C4×D412yes—
224C32×C4#12011yescharacteristic
225C32×C4#12311yescharacteristic
226C3×Dic3—82no—
227C2×#41C2×C3×D311yescharacteristic
228C2×#41C2×C3×D311yescharacteristic
229#131—64no—
230C2×M16—32no—
231C2×M16—62no—
232C4⋊Q8C3×Dic311yescharacteristic, complemented
233#127C3×Dic311yescharacteristic, complemented
234#124C3×Dic311yescharacteristic, complemented
235#124C3×Dic311yescharacteristic, complemented
236#121—22no—
237C4×D4—22no—
238#117—32no—
239C2×C42C2×C3×D311yescharacteristic
240#104—64no—
241#99—62no—
242C23×C3—22no—
243C23×C3—21no—
244C23×C3—21no—
245C23×C3—22no—
246C23×C3—21no—
247C23×C3#21712yes—
248C23×C3C3×C22⋊C412yes—
249C23×C3C2×#6711yescharacteristic
250C23×C3C2×C3×D411yescharacteristic
251C3×Q8—22no—
252C3×Q8—22no—
253C3×Q8—22no—
254C3×Q8—22no—
255C3×Q8—42no—
256C3×Q8—42no—
257C3×D4—24no—
258C3×D4—24no—
259C3×D4—22no—
260C3×D4—22no—
261C3×D4—22no—
262C3×D4—22no—
263C3×D4—42no—
264C3×D4—42no—
265C3×D4—44no—
266C3×D4—44no—
267C3×D4—44no—
268C3×D4—48no—
269C3×D4—44no—
270C3×D4—42no—
271C3×D4—42no—
272C2×C3×C4—22no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—42no—
291C2×C3×C4—42no—
292C2×C3×C4—42no—
293C2×C3×C4—42no—
294C2×C3×C4—44no—
295C2×C3×C4—42no—
296C2×C3×C4—42no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—122no—
302C2×C3×C4#21712yes—
303C2×C3×C4C3×C22⋊C412yes—
304C2×C3×C4D3×D412yes—
305C2×C3×C4#23712yes—
306C2×C3×C4C22×Dic311yescharacteristic
307C2×C3×C4C2×#6711yescharacteristic
308C2×C3×C4C22×C3×C411yescharacteristic
309C2×C3×C4C2×C3×D412yes—
310C2×C3×C4C2×C3×D411yescharacteristic
311C2×C3×C4C3×#4112yes—
312C2×Dic3—42no—
313C3×C8—64no—
314C3⋊C8—24no—
315C2×C32—21no—
316C2×C32—22no—
317C2×C32—42no—
318C2×C32—81no—
319C2×C32#38611yescharacteristic
320#41—22no—
321#41—22no—
322#41—22no—
323#41—22no—
324C2×Q8C2×C3×Dic311yescharacteristic
325C2×Q8C2×C3×Dic311yescharacteristic
326C2×D4—22no—
327C2×D4—21no—
328C2×D4C2×C3×Dic311yescharacteristic
329C2×D4C2×C3×Dic311yescharacteristic
330C2×D4C3×#6712yes—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4C3×#6712yes—
334C22×C4C22×C3×D311yescharacteristic
335M16—34no—
336M16—64no—
337M16—62no—
338C2×C8—64no—
339C2×C8—62no—
340C4⋊C4—22no—
341C4⋊C4—62no—
342C22⋊C4—22no—
343C22⋊C4—22no—
344C22⋊C4—62no—
345C42—21no—
346C42—62no—
347C42C2×C3×Dic311yescharacteristic
348C42C2×C3×Dic311yescharacteristic
349C22×C3—22no—
350C22×C3—22no—
351C22×C3—22no—
352C22×C3—21no—
353C22×C3—42no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—42no—
357C22×C3—42no—
358C22×C3—42no—
359C22×C3—42no—
360C22×C3—44no—
361C22×C3—44no—
362C22×C3—42no—
363C22×C3—42no—
364C22×C3—41no—
365C22×C3—41no—
366C22×C3#93912yes—
367C22×C3C2×#21711yescharacteristic
368C22×C3C2×C3×C22⋊C411yescharacteristic
369C22×C3C3×#12112yes—
370C3×C4—24no—
371C3×C4—22no—
372C3×C4—22no—
373C3×C4—22no—
374C3×C4—22no—
375C3×C4—22no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—42no—
379C3×C4—42no—
380C3×C4—42no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—41no—
384C3×C4—41no—
385C3×C4—242no—
386C3×C4D4×Dic312yes—
387C3×C4#93511yescharacteristic
388C3×C4#93711yescharacteristic
389C3×C4C3×C4×D412yes—
390C3×C4C3×#12011yescharacteristic
391C3×C4C3×#12311yescharacteristic
392Dic3—82no—
393C32#188411yescharacteristic, complemented, Sylow
394C23—21no—
395C23C3×#21712yes—
396C23C2×C3×#6711yescharacteristic
397Q8—22no—
398Q8—22no—
399D4—24no—
400D4—22no—
401D4—22no—
402D4—44no—
403D4—42no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—122no—
413C2×C4C3×#21712yes—
414C2×C4C3×D3×D412yes—
415C2×C4C3×#23712yes—
416C2×C4C22×C3×Dic311yescharacteristic
417C2×C4C2×C3×#6711yescharacteristic
418C8—64no—
419C2×C3—22no—
420C2×C3—21no—
421C2×C3—22no—
422C2×C3—22no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—42no—
426C2×C3—42no—
427C2×C3—42no—
428C2×C3—82no—
429C2×C3—82no—
430C2×C3—81no—
431C2×C3—81no—
432C2×C3#522011yescharacteristic
433C2×C3C3×#38611yescharacteristic
434C22—22no—
435C22—41no—
436C22—42no—
437C22—42no—
438C22—41no—
439C22C3×#93912yes—
440C22C2×C3×#21711yescharacteristic
441C4—22no—
442C4—22no—
443C4—41no—
444C4—41no—
445C4—242no—
446C4C3×D4×Dic312yes—
447C4C3×#93511yescharacteristic
448C4C3×#93711yescharacteristic
449C3—21no—
450C3#7181711yescharacteristic, direct product factor
451C3C3×#188411yescharacteristic, complemented
452C2—21no—
453C2—22no—
454C2—42no—
455C2—81no—
456C2C3×#522011yescharacteristic
subgroupG/H
centerC3×C4#937
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
Fitting, prime radicalC32×#532C2
socleC2×C32#386
cosocleC22×C3×C4C23×C3
hypercenterC3×#532D3
hypocenterC3C3×#1884
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#532

Complements

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

NH ≅ G/Ntype
2. C3×#5819C2semidirect
3. C3×#5240C2semidirect
4. C3×#5236C2semidirect
5. C3×#4523C2semidirect
7. #71817C3direct (N × H)
10. C32×C4⋊Q8C4semidirect
11. C32×#127C4semidirect
12. C32×#124C4semidirect
13. C32×#124C4semidirect
27. #5819C2×C3semidirect
30. #5240C2×C3semidirect
31. #5236C2×C3semidirect
33. #4523C2×C3semidirect
60. C3×#208D4semidirect
74. C3×C4⋊Q8Dic3semidirect
75. C3×C4⋊Q8C3×C4semidirect
77. C3×#127Dic3semidirect
78. C3×#127C3×C4semidirect
81. C3×#124Dic3semidirect
82. C3×#124Dic3semidirect
83. C3×#124C3×C4semidirect
84. C3×#124C3×C4semidirect
209. #208C3×D4semidirect
232. C4⋊Q8C3×Dic3semidirect
233. #127C3×Dic3semidirect
234. #124C3×Dic3semidirect
235. #124C3×Dic3semidirect
393. C32#1884semidirect
450. C3#71817direct (N × H)
451. C3C3×#1884semidirect

Maximal subgroups

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

subgroupindex
C32×#5322
C3×#58192
C3×#52402
C3×#52362
C3×#45232
C3×#18843
#718173