Finite Group Databasebeta

← C3×#70354 #11783901

Subgroups — C3×#70354 #11783901

Order 1152.

725 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Dic3×#41C211yesmaximal, characteristic
2C2×C32×#104C211yesmaximal, characteristic
3C2×C3×#837C211yesmaximal, characteristic
4C3×Dic3×M16C211yesmaximal, characteristic, complemented
5C3×#4932C211yesmaximal, characteristic, complemented
6C3×#4555C211yesmaximal, characteristic, complemented
7C3×#4523C211yesmaximal, characteristic, complemented
8C3×#1759—31nomaximal
9#70354C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C3×Q8×Dic3C412yescomplemented
14C3×D4×Dic3—22no—
15C3×D4×Dic3C412yescomplemented
16C3×#926—21no—
17C3×#926C2211yescharacteristic
18C2×C3×C4×Dic3—21no—
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C32×#104C414yescomplemented
23C3×#837C414yescomplemented
24C3×C3⋊#95—22no—
25C3×#815—21no—
26C3×C8×Dic3—21no—
27C3×C4×#41—31no—
28Dic3×#41C2×C311yescharacteristic
29C2×C3×#104—21no—
30C2×C3×#104—31no—
31C2×C3×#104D311yescharacteristic
32C2×C3×#104C2×C311yescharacteristic
33C3×C4×M16—31no—
34C3×#376—31no—
35C2×#837C2×C311yescharacteristic
36Dic3×M16C2×C311yescharacteristic, complemented
37#4932C2×C311yescharacteristic, complemented
38C3×#339—31no—
39C3×#339—31no—
40#4555C2×C311yescharacteristic, complemented
41#4523C2×C311yescharacteristic, complemented
42C32×#41—21no—
43C32×#41—21no—
44C32×#41C2×C412yes—
45C32×#41C2×C412yes—
46C2×C32×Q8C2×C411yescharacteristic
47C2×C32×D4—21no—
48C2×C32×D4C2×C411yescharacteristic
49C22×C32×C4—21no—
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3×Dic3—21no—
53C22×C3×Dic3—22no—
54C22×C3×Dic3D412yes—
55C32×M16—21no—
56C32×M16C2×C412yescomplemented
57C2×C32×C8—21no—
58C32×C42—21no—
59C32×C42C2×C412yescomplemented
60C3×#217—21no—
61C3×#217—22no—
62C3×C4⋊Dic3—22no—
63C3×C4⋊Dic3C2×C412yes—
64C3×C4×Dic3—21no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3—22no—
67C3×C4×Dic3C2×C412yes—
68C3×C4×Dic3C2×C412yescomplemented
69C3×C4×Dic3D411yescharacteristic
70C3×C4×Dic3D411yescharacteristic
71C3×#208—21no—
72C3×#208C2×C412yescomplemented
73C2×C3×C3⋊C8—21no—
74#1759—31noSylow
75C2×C3×#41—21no—
76C2×C3×#41C2×D311yescharacteristic
77C2×C3×#41C22×C311yescharacteristic
78C2×C3×M16—21no—
79C2×C3×M16—31no—
80C2×C3×M16C2×D311yescharacteristic
81C2×C3×M16C22×C311yescharacteristic
82C3×C4×Q8—32no—
83C3×C4×D4—32no—
84C3×C4×D4—62no—
85C3×#117—31no—
86C3×#117—61no—
87C2×C3×C42—21no—
88C2×C3×C42—31no—
89C2×C3×C42—31no—
90C2×C3×C42—61no—
91C2×C3×C42C2×D311yescharacteristic
92C2×C3×C42C22×C311yescharacteristic
93Q8×Dic3C3×C412yescomplemented
94D4×Dic3—22no—
95D4×Dic3C3×C412yescomplemented
96#926—21no—
97#926C22×C311yescharacteristic
98C2×C4×Dic3—21no—
99C2×C4×Dic3C22×C311yescharacteristic
100C2×C4×Dic3C22×C311yescharacteristic
101C2×#208C22×C311yescharacteristic
102C3×#104—24no—
103C3×#104—34no—
104C3×#104Dic314yescomplemented
105C3×#104C3×C414yescomplemented
106C3×#97—61no—
107C3×C4×C8—61no—
108C3×#95—62no—
109#837C3×C414yescomplemented
110C3⋊#95—22no—
111#815—21no—
112C8×Dic3—21no—
113C23×C32—21no—
114C23×C32C2×D411yescharacteristic
115C32×Q8—21no—
116C32×Q8C4212yes—
117C32×D4—22no—
118C32×D4—22no—
119C32×D4—21no—
120C32×D4C4212yes—
121C2×C32×C4—21no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4—22no—
125C2×C32×C4—42no—
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C22×C411yescharacteristic
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C3×Dic3—22no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—42no—
135C2×C3×Dic3—44no—
136C2×C3×Dic3—42no—
137C2×C3×Dic3C22⋊C412yes—
138C2×C3×Dic3C22⋊C412yes—
139C32×C8—22no—
140C3×C3⋊C8—22no—
141C4×#41—31no—
142C2×#104—31no—
143C2×#104C3×D311yescharacteristic
144C4×M16—31no—
145#376—31no—
146#339—31no—
147#339—31no—
148C3×#41—21no—
149C3×#41—21no—
150C3×#41—21no—
151C3×#41—21no—
152C3×#41—22no—
153C3×#41—22no—
154C3×#41—41no—
155C3×#41—41no—
156C3×#41C4×D312yes—
157C3×#41C2×Dic312yes—
158C3×#41C2×C3×C412yes—
159C3×#41C2×C3×C412yes—
160C2×C3×Q8—21no—
161C2×C3×Q8C4×D311yescharacteristic
162C2×C3×Q8C2×C3×C411yescharacteristic
163C2×C3×D4—21no—
164C2×C3×D4—21no—
165C2×C3×D4—21no—
166C2×C3×D4—41no—
167C2×C3×D4C4×D311yescharacteristic
168C2×C3×D4C2×C3×C411yescharacteristic
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—32no—
175C22×C3×C4—41no—
176C22×C3×C4—41no—
177C22×C3×C4—62no—
178C22×C3×C4—61no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C23×C311yescharacteristic
181C22×Dic3—21no—
182C22×Dic3—22no—
183C22×Dic3C3×D412yes—
184C3×M16—21no—
185C3×M16—21no—
186C3×M16—22no—
187C3×M16—32no—
188C3×M16—41no—
189C3×M16—61no—
190C3×M16C2×Dic312yescomplemented
191C3×M16C2×C3×C412yescomplemented
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C2×C3×C8—41no—
195C2×C3×C8—61no—
196C3×C4⋊C4—32no—
197C3×C4⋊C4—62no—
198C3×C22⋊C4—62no—
199C3×C22⋊C4—61no—
200C3×C42—21no—
201C3×C42—21no—
202C3×C42—22no—
203C3×C42—32no—
204C3×C42—31no—
205C3×C42—31no—
206C3×C42—32no—
207C3×C42—41no—
208C3×C42—62no—
209C3×C42—61no—
210C3×C42—61no—
211C3×C42C2×Dic312yescomplemented
212C3×C42C2×C3×C412yescomplemented
213#217—21no—
214#217—22no—
215C4⋊Dic3—22no—
216C4⋊Dic3C2×C3×C412yes—
217C4×Dic3—21no—
218C4×Dic3—21no—
219C4×Dic3—22no—
220C4×Dic3C2×C3×C412yes—
221C4×Dic3C2×C3×C412yescomplemented
222C4×Dic3C3×D411yescharacteristic
223C4×Dic3C3×D411yescharacteristic
224#208—21no—
225#208C2×C3×C412yescomplemented
226C2×C3⋊C8—21no—
227C22×C32—22no—
228C22×C32—22no—
229C22×C32—42no—
230C22×C32C2×C22⋊C411yescharacteristic
231C22×C32C4×D411yescharacteristic
232C22×C32C4×D411yescharacteristic
233C32×C4—22no—
234C32×C4—42no—
235C32×C4C2×C4211yescharacteristic
236C32×C4#11711yescharacteristic
237C32×C4C4×D411yescharacteristic
238C32×C4C4×D411yescharacteristic
239C3×Dic3—22no—
240C3×Dic3—22no—
241C3×Dic3—42no—
242C3×Dic3—42no—
243C2×#41C2×C3×D311yescharacteristic
244C2×M16—31no—
245C2×M16C2×C3×D311yescharacteristic
246C4×Q8—32no—
247C4×D4—32no—
248C4×D4—62no—
249#117—31no—
250#117—61no—
251C2×C42—31no—
252C2×C42—31no—
253C2×C42—61no—
254C2×C42C2×C3×D311yescharacteristic
255#104—34no—
256#104C3×Dic314yescomplemented
257#97—61no—
258C4×C8—61no—
259#95—62no—
260C23×C3—21no—
261C23×C3—21no—
262C23×C3—21no—
263C23×C3—41no—
264C23×C3D3×D411yescharacteristic
265C23×C3C2×C3×D411yescharacteristic
266C3×Q8—21no—
267C3×Q8—21no—
268C3×Q8—22no—
269C3×Q8—41no—
270C3×Q8C4×Dic312yes—
271C3×Q8C3×C4212yes—
272C3×D4—22no—
273C3×D4—22no—
274C3×D4—22no—
275C3×D4—22no—
276C3×D4—21no—
277C3×D4—21no—
278C3×D4—22no—
279C3×D4—41no—
280C3×D4—42no—
281C3×D4—42no—
282C3×D4C4×Dic312yes—
283C3×D4C3×C4212yes—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—32no—
299C2×C3×C4—32no—
300C2×C3×C4—42no—
301C2×C3×C4—42no—
302C2×C3×C4—42no—
303C2×C3×C4—41no—
304C2×C3×C4—42no—
305C2×C3×C4—42no—
306C2×C3×C4—44no—
307C2×C3×C4—62no—
308C2×C3×C4—62no—
309C2×C3×C4—122no—
310C2×C3×C4—124no—
311C2×C3×C4—122no—
312C2×C3×C4C2×C4×D311yescharacteristic
313C2×C3×C4C2×C4×D311yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4#23711yescharacteristic
316C2×C3×C4#23711yescharacteristic
317C2×C3×C4C22×Dic311yescharacteristic
318C2×C3×C4C22×C3×C411yescharacteristic
319C2×C3×C4C22×C3×C411yescharacteristic
320C2×C3×C4C22×C3×C411yescharacteristic
321C2×C3×C4C2×C3×D411yescharacteristic
322C2×C3×C4C3×#4111yescharacteristic
323C2×C3×C4C3×#4111yescharacteristic
324C2×Dic3—22no—
325C2×Dic3—22no—
326C2×Dic3—42no—
327C2×Dic3—44no—
328C2×Dic3—42no—
329C2×Dic3C3×C22⋊C412yes—
330C2×Dic3C3×C22⋊C412yes—
331C3×C8—22no—
332C3×C8—22no—
333C3×C8—42no—
334C3×C8—62no—
335C3⋊C8—22no—
336C2×C32—21no—
337C2×C32—21no—
338C2×C32—42no—
339C2×C32C4×C22⋊C411yescharacteristic
340C2×C32#42112yes—
341#41—21no—
342#41—21no—
343#41C3×C4×D312yes—
344#41C2×C3×Dic312yes—
345C2×Q8C3×C4×D311yescharacteristic
346C2×D4—21no—
347C2×D4C3×C4×D311yescharacteristic
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—32no—
351C22×C4—62no—
352C22×C4—61no—
353C22×C4C22×C3×D311yescharacteristic
354M16—21no—
355M16—32no—
356M16—61no—
357M16C2×C3×Dic312yescomplemented
358C2×C8—21no—
359C2×C8—61no—
360C4⋊C4—32no—
361C4⋊C4—62no—
362C22⋊C4—62no—
363C22⋊C4—61no—
364C42—21no—
365C42—32no—
366C42—31no—
367C42—31no—
368C42—32no—
369C42—62no—
370C42—61no—
371C42—61no—
372C42C2×C3×Dic312yescomplemented
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—22no—
376C22×C3—22no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—42no—
381C22×C3—42no—
382C22×C3—42no—
383C22×C3—42no—
384C22×C3—82no—
385C22×C3D3×C22⋊C411yescharacteristic
386C22×C3#67⋊C411yescharacteristic
387C22×C3D4×Dic311yescharacteristic
388C22×C3C2×C3×C22⋊C411yescharacteristic
389C22×C3C3×C4×D411yescharacteristic
390C22×C3C3×C4×D411yescharacteristic
391C3×C4—22no—
392C3×C4—22no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—42no—
398C3×C4—42no—
399C3×C4—42no—
400C3×C4—44no—
401C3×C4—62no—
402C3×C4—62no—
403C3×C4—122no—
404C3×C4—122no—
405C3×C4#87711yescharacteristic
406C3×C4#67⋊C411yescharacteristic
407C3×C4C2×C4×Dic311yescharacteristic
408C3×C4D4×Dic311yescharacteristic
409C3×C4C2×C3×C4211yescharacteristic
410C3×C4C3×#11711yescharacteristic
411C3×C4C3×C4×D411yescharacteristic
412C3×C4C3×C4×D411yescharacteristic
413Dic3—22no—
414Dic3—22no—
415Dic3—42no—
416Dic3—42no—
417C32#175911yescharacteristic, complemented, Sylow
418C23—21no—
419C23C3×D3×D411yescharacteristic
420Q8—21no—
421Q8C3×C4×Dic312yes—
422D4—22no—
423D4—22no—
424D4—21no—
425D4C3×C4×Dic312yes—
426C2×C4—21no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—32no—
431C2×C4—32no—
432C2×C4—42no—
433C2×C4—62no—
434C2×C4—62no—
435C2×C4—122no—
436C2×C4—124no—
437C2×C4—122no—
438C2×C4C2×C3×C4×D311yescharacteristic
439C2×C4C2×C3×C4×D311yescharacteristic
440C2×C4C3×D3×D411yescharacteristic
441C2×C4C3×#23711yescharacteristic
442C2×C4C3×#23711yescharacteristic
443C2×C4C22×C3×Dic311yescharacteristic
444C8—22no—
445C8—62no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—22no—
452C2×C3—41no—
453C2×C3—41no—
454C2×C3—42no—
455C2×C3—42no—
456C2×C3—82no—
457C2×C3#482112yes—
458C2×C3Dic3×C22⋊C411yescharacteristic
459C2×C3C3×C4×C22⋊C411yescharacteristic
460C2×C3C3×#42112yes—
461C22—22no—
462C22—22no—
463C22—42no—
464C22C3×D3×C22⋊C411yescharacteristic
465C22C3×#67⋊C411yescharacteristic
466C22C3×D4×Dic311yescharacteristic
467C4—22no—
468C4—42no—
469C4—62no—
470C4—62no—
471C4—122no—
472C4—122no—
473C4C3×#87711yescharacteristic
474C4C3×#67⋊C411yescharacteristic
475C4C2×C3×C4×Dic311yescharacteristic
476C4C3×D4×Dic311yescharacteristic
477C3—21no—
478C3#7035411yescharacteristic, direct product factor
479C3C3×#175911yescharacteristic, complemented
480C2—21no—
481C2—21no—
482C2—42no—
483C2C3×#482112yes—
484C2C3×Dic3×C22⋊C411yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC3×C4C2×C3×C42
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#104C2
socleC22×C32C2×C22⋊C4
prime radicalC2×C32×#41C22
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#104D3
hypocenterC3C3×#1759
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#104

Complements

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

NH ≅ G/Ntype
4. C3×Dic3×M16C2semidirect
5. C3×#4932C2semidirect
6. C3×#4555C2semidirect
7. C3×#4523C2semidirect
9. #70354C3direct (N × H)
13. C3×Q8×Dic3C4semidirect
15. C3×D4×Dic3C4semidirect
22. C32×#104C4semidirect
23. C3×#837C4semidirect
36. Dic3×M16C2×C3semidirect
37. #4932C2×C3semidirect
40. #4555C2×C3semidirect
41. #4523C2×C3semidirect
56. C32×M16C2×C4semidirect
59. C32×C42C2×C4semidirect
68. C3×C4×Dic3C2×C4semidirect
72. C3×#208C2×C4semidirect
93. Q8×Dic3C3×C4semidirect
95. D4×Dic3C3×C4semidirect
104. C3×#104Dic3semidirect
105. C3×#104C3×C4semidirect
109. #837C3×C4semidirect
190. C3×M16C2×Dic3semidirect
191. C3×M16C2×C3×C4semidirect
211. C3×C42C2×Dic3semidirect
212. C3×C42C2×C3×C4semidirect
221. C4×Dic3C2×C3×C4semidirect
225. #208C2×C3×C4semidirect
256. #104C3×Dic3semidirect
357. M16C2×C3×Dic3semidirect
372. C42C2×C3×Dic3semidirect
417. C32#1759semidirect
478. C3#70354direct (N × H)
479. C3C3×#1759semidirect

Maximal subgroups

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

subgroupindex
C3×Dic3×#412
C2×C32×#1042
C2×C3×#8372
C3×Dic3×M162
C3×#49322
C3×#45552
C3×#45232
C3×#17593
#703543