Finite Group Databasebeta

← C3×#70529 #11785300

Subgroups — C3×#70529 #11785300

Order 1152.

687 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#235C211yesmaximal, characteristic
2C32×#423C211yesmaximal, characteristic, complemented
3C2×C3×#825C212yesmaximal
4C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C3×#4555C212yesmaximal, complemented
6C3×#1806—31nomaximal
7#70529C311yesmaximal, characteristic, direct product factor
8C2×C3×#235C2211yescharacteristic
9C2×C32×M16C2212yes—
10C2×C32×C42C2211yescharacteristic
11C3×C4×#67—21no—
12C3×C4×#67—21no—
13C3×#926C2211yescharacteristic
14C2×C3×C4⋊Dic3—21no—
15C2×C3×C4×Dic3C2212yes—
16C3×C4×D12C411yescharacteristic, complemented
17C3×C4×D12C411yescharacteristic, complemented
18C3×#872—21no—
19C3×C42×D3—21no—
20C3×C4×Dic6C411yescharacteristic, complemented
21C3×C4×Dic6C411yescharacteristic, complemented
22C32×C4⋊C8—21no—
23C32×C4⋊C8—21no—
24C3×C3⋊#95—21no—
25C3×#825—24no—
26C3×C4×#41—31no—
27C4×#235C2×C311yescharacteristic
28C3×#423—21no—
29C3×#423D311yescharacteristic, complemented
30C3×#423C2×C311yescharacteristic, complemented
31C2×C3×#104—32no—
32C3×C4×C4⋊C4—31no—
33C2×#825C2×C312yes—
34C4×C4⋊Dic3C2×C311yescharacteristic, complemented
35C3×#339—32no—
36#4555C2×C312yescomplemented
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C32×C4C2311yescharacteristic
40C2×C3×#67—21no—
41C22×C3×Dic3—22no—
42C3×#235—21no—
43C3×#235—21no—
44C3×#235D412yes—
45C3×#235Q812yes—
46C2×C3×D12C2×C411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3—21no—
50C2×C3×Dic6C2×C411yescharacteristic
51C32×M16—22no—
52C32×M16—22no—
53C2×C32×C8—22no—
54C32×C42C2×C411yescharacteristic
55C32×C42C2×C411yescharacteristic
56C32×C42D411yescharacteristic
57C32×C42D411yescharacteristic
58C3×#217—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3—24no—
62C3×C4⋊Dic3C2×C411yescharacteristic
63C3×C4⋊Dic3C2×C411yescharacteristic
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
66C3×C4×Dic3—21no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3—21no—
69C3×C4×Dic3—22no—
70C3×C4×Dic3—22no—
71#1806—31noSylow
72C2×C3×#41—31no—
73C2×#235C22×C311yescharacteristic
74C2×C3×M16—22no—
75C2×C3×M16C2×D312yes—
76C2×C3×M16C22×C312yes—
77C3×C4×Q8—31no—
78C3×C4×Q8—31no—
79C3×C4×D4—31no—
80C3×C4×D4—31no—
81C3×C4×D4—61no—
82C3×C4×D4—61no—
83C3×#117—31no—
84C3×#117—61no—
85C2×C3×C4⋊C4—61no—
86C2×C3×C42—21no—
87C2×C3×C42—32no—
88C2×C3×C42—61no—
89C2×C3×C42C2×D311yescharacteristic
90C2×C3×C42C22×C311yescharacteristic
91C4×#67—21no—
92C4×#67—21no—
93#926C22×C311yescharacteristic
94C2×C4⋊Dic3—21no—
95C2×C4×Dic3C22×C312yes—
96C4×D12C3×C411yescharacteristic, complemented
97C4×D12C3×C411yescharacteristic, complemented
98#872—21no—
99C42×D3—21no—
100C4×Dic6C3×C411yescharacteristic, complemented
101C4×Dic6C3×C411yescharacteristic, complemented
102C3×C4⋊C8—22no—
103C3×C4⋊C8—22no—
104C3×C4⋊C8—21no—
105C3×C4⋊C8—21no—
106C3×C4⋊C8—21no—
107C3×C4⋊C8—21no—
108C3×#104—64no—
109C3×#95—61no—
110C3⋊#95—21no—
111#825—24no—
112C23×C32C2×D411yescharacteristic
113C22×C3×D3—21no—
114C2×C32×C4—22no—
115C2×C32×C4—41no—
116C2×C32×C4C22⋊C411yescharacteristic
117C2×C32×C4C22⋊C411yescharacteristic
118C2×C32×C4C22⋊C411yescharacteristic
119C2×C32×C4C22⋊C411yescharacteristic
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×Q811yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C3×#67—22no—
127C3×#67—22no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—42no—
133C2×C3×Dic3—42no—
134C3×D12—21no—
135C3×D12C4⋊C412yescomplemented
136C3×C4×D3—22no—
137C3×C4×D3—22no—
138C3×C4×D3—42no—
139C3×C4×D3—42no—
140C3×Dic6—21no—
141C3×Dic6C4⋊C412yescomplemented
142C32×C8—42no—
143C4×#41—31no—
144#423C3×D311yescharacteristic, complemented
145C2×#104—32no—
146C4×C4⋊C4—31no—
147#339—32no—
148C3×#41—32no—
149C3×#41—32no—
150C3×#41—61no—
151C3×#41—61no—
152C2×C3×Q8—31no—
153C2×C3×D4—31no—
154C2×C3×D4—61no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—61no—
159C22×C3×C4—62no—
160C22×C3×C4—61no—
161C22×C3×C4—61no—
162C22×C3×C4D1211yescharacteristic
163C22×C3×C4D1211yescharacteristic
164C22×C3×C4C3×D411yescharacteristic
165C22×C3×C4C3×D411yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C23×C311yescharacteristic
168C2×#67—21no—
169C22×Dic3—22no—
170#235—21no—
171#235—21no—
172#235C3×D412yes—
173#235C3×Q812yes—
174C2×D12C2×C3×C411yescharacteristic
175C2×C4×D3—21no—
176C2×C4×D3—21no—
177C2×C4×D3—21no—
178C2×Dic6C2×C3×C411yescharacteristic
179C3×M16—22no—
180C3×M16—22no—
181C3×M16—22no—
182C3×M16—22no—
183C3×M16—42no—
184C3×M16—42no—
185C2×C3×C8—24no—
186C2×C3×C8—22no—
187C2×C3×C8—22no—
188C3×C4⋊C4—31no—
189C3×C4⋊C4—31no—
190C3×C4⋊C4—64no—
191C3×C4⋊C4—61no—
192C3×C4⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195C3×C22⋊C4—61no—
196C3×C42—21no—
197C3×C42—21no—
198C3×C42—21no—
199C3×C42—21no—
200C3×C42—61no—
201C3×C42—61no—
202C3×C42—61no—
203C3×C42—62no—
204C3×C42—62no—
205C3×C42C4×D311yescharacteristic
206C3×C42C4×D311yescharacteristic
207C3×C42#6711yescharacteristic
208C3×C42#6711yescharacteristic
209C3×C42C2×C3×C411yescharacteristic
210C3×C42C2×C3×C411yescharacteristic
211C3×C42C3×D411yescharacteristic
212C3×C42C3×D411yescharacteristic
213#217—21no—
214(C2×D3)⋊C4—21no—
215(C2×D3)⋊C4—21no—
216C4⋊Dic3—24no—
217C4⋊Dic3C2×C3×C411yescharacteristic
218C4⋊Dic3C2×C3×C411yescharacteristic
219Dic3⋊C4—21no—
220Dic3⋊C4—21no—
221C4×Dic3—21no—
222C4×Dic3—21no—
223C4×Dic3—21no—
224C4×Dic3—22no—
225C4×Dic3—22no—
226C22×C32—21no—
227C22×C32—21no—
228C22×C32C2×C22⋊C411yescharacteristic
229C22×C32#12111yescharacteristic
230C22×C32C22⋊Q811yescharacteristic
231C2×C3×D3—22no—
232C2×C3×D3—41no—
233C2×C3×D3—41no—
234C32×C4—21no—
235C32×C4—21no—
236C32×C4—21no—
237C32×C4#10412yescomplemented
238C32×C4C2×C4⋊C411yescharacteristic
239C32×C4#11711yescharacteristic
240C32×C4#12111yescharacteristic
241C32×C4C22⋊Q811yescharacteristic
242C3×Dic3—22no—
243C3×Dic3—44no—
244C3×Dic3—41no—
245C3×Dic3—41no—
246C2×#41—31no—
247C2×M16C2×C3×D312yes—
248C4×Q8—31no—
249C4×Q8—31no—
250C4×D4—31no—
251C4×D4—31no—
252C4×D4—61no—
253C4×D4—61no—
254#117—31no—
255#117—61no—
256C2×C4⋊C4—61no—
257C2×C42—32no—
258C2×C42—61no—
259C2×C42C2×C3×D311yescharacteristic
260C4⋊C8—21no—
261C4⋊C8—21no—
262#104—64no—
263#95—61no—
264C23×C3—21no—
265C23×C3—61no—
266C23×C3C2×D1211yescharacteristic
267C23×C3C2×C3×D411yescharacteristic
268C22×D3—21no—
269C3×Q8—32no—
270C3×Q8—61no—
271C3×D4—32no—
272C3×D4—62no—
273C3×D4—62no—
274C3×D4—61no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—42no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—42no—
291C2×C3×C4—61no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—64no—
295C2×C3×C4—61no—
296C2×C3×C4—61no—
297C2×C3×C4—122no—
298C2×C3×C4—122no—
299C2×C3×C4—122no—
300C2×C3×C4—122no—
301C2×C3×C4(C2×D3)⋊C411yescharacteristic
302C2×C3×C4(C2×D3)⋊C411yescharacteristic
303C2×C3×C4(C2×D3)⋊C411yescharacteristic
304C2×C3×C4(C2×D3)⋊C411yescharacteristic
305C2×C3×C4C3×C22⋊C411yescharacteristic
306C2×C3×C4C3×C22⋊C411yescharacteristic
307C2×C3×C4C3×C22⋊C411yescharacteristic
308C2×C3×C4C3×C22⋊C411yescharacteristic
309C2×C3×C4C2×C4×D311yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4#23711yescharacteristic
312C2×C3×C4D3×Q811yescharacteristic
313C2×C3×C4#23911yescharacteristic
314C2×C3×C4C2×#6711yescharacteristic
315C2×C3×C4C22×C3×C411yescharacteristic
316C2×C3×C4C2×C3×D411yescharacteristic
317C2×C3×C4C2×C3×D411yescharacteristic
318C2×C3×C4C2×C3×Q811yescharacteristic
319C2×C3×C4C3×#4111yescharacteristic
320C2×C3×C4C3×#4111yescharacteristic
321#67—22no—
322#67—22no—
323C2×Dic3—21no—
324C2×Dic3—24no—
325C2×Dic3—21no—
326C2×Dic3—21no—
327C2×Dic3—42no—
328C2×Dic3—42no—
329D12—21no—
330D12C3×C4⋊C412yescomplemented
331C4×D3—22no—
332C4×D3—22no—
333C4×D3—42no—
334C4×D3—42no—
335Dic6—21no—
336Dic6C3×C4⋊C412yescomplemented
337C3×C8—44no—
338C3×C8—42no—
339C3×C8—42no—
340C2×C32—21no—
341C2×C32—21no—
342C2×C32#38011yescharacteristic
343C2×C32C2×#10411yescharacteristic
344C2×C32#42111yescharacteristic
345C3×D3—42no—
346#41—32no—
347#41—32no—
348#41—61no—
349#41—61no—
350C2×Q8—31no—
351C2×D4—31no—
352C2×D4—61no—
353C22×C4—61no—
354C22×C4—62no—
355C22×C4—61no—
356C22×C4—61no—
357C22×C4C3×D1211yescharacteristic
358C22×C4C3×D1211yescharacteristic
359C22×C4C22×C3×D311yescharacteristic
360M16—22no—
361M16—22no—
362C2×C8—22no—
363C4⋊C4—31no—
364C4⋊C4—31no—
365C4⋊C4—64no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C22⋊C4—61no—
369C22⋊C4—61no—
370C22⋊C4—61no—
371C42—61no—
372C42—61no—
373C42—61no—
374C42—62no—
375C42—62no—
376C42C3×C4×D311yescharacteristic
377C42C3×C4×D311yescharacteristic
378C42C3×#6711yescharacteristic
379C42C3×#6711yescharacteristic
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3—62no—
390C22×C3—121no—
391C22×C3—121no—
392C22×C3#89511yescharacteristic
393C22×C3#89711yescharacteristic
394C22×C3C2×(C2×D3)⋊C411yescharacteristic
395C22×C3C2×C3×C22⋊C411yescharacteristic
396C22×C3C3×#12111yescharacteristic
397C22×C3C3×C22⋊Q811yescharacteristic
398C2×D3—22no—
399C2×D3—41no—
400C2×D3—41no—
401C3×C4—22no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—22no—
413C3×C4—41no—
414C3×C4—41no—
415C3×C4—62no—
416C3×C4—124no—
417C3×C4—121no—
418C3×C4—121no—
419C3×C4#82512yescomplemented
420C3×C4C3×#10412yescomplemented
421C3×C4D3×C4⋊C411yescharacteristic
422C3×C4#89211yescharacteristic
423C3×C4#93811yescharacteristic
424C3×C4#94611yescharacteristic
425C3×C4C2×C3×C4⋊C411yescharacteristic
426C3×C4C3×#11711yescharacteristic
427C3×C4C3×#12111yescharacteristic
428C3×C4C3×C22⋊Q811yescharacteristic
429Dic3—22no—
430Dic3—44no—
431Dic3—41no—
432Dic3—41no—
433C32#180611yescharacteristic, complemented, Sylow
434C23—61no—
435C23C2×C3×D1211yescharacteristic
436Q8—32no—
437Q8—61no—
438D4—32no—
439D4—62no—
440D4—62no—
441D4—61no—
442C2×C4—22no—
443C2×C4—41no—
444C2×C4—61no—
445C2×C4—62no—
446C2×C4—62no—
447C2×C4—64no—
448C2×C4—61no—
449C2×C4—61no—
450C2×C4—122no—
451C2×C4—122no—
452C2×C4—122no—
453C2×C4—122no—
454C2×C4C3×(C2×D3)⋊C411yescharacteristic
455C2×C4C3×(C2×D3)⋊C411yescharacteristic
456C2×C4C3×(C2×D3)⋊C411yescharacteristic
457C2×C4C3×(C2×D3)⋊C411yescharacteristic
458C2×C4C2×C3×C4×D311yescharacteristic
459C2×C4C3×D3×D411yescharacteristic
460C2×C4C3×#23711yescharacteristic
461C2×C4C3×D3×Q811yescharacteristic
462C2×C4C3×#23911yescharacteristic
463C2×C4C2×C3×#6711yescharacteristic
464C8—42no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—41no—
473C2×C3—41no—
474C2×C3—122no—
475C2×C3#498711yescharacteristic
476C2×C3C2×#82511yescharacteristic
477C2×C3#513911yescharacteristic
478C2×C3C3×#38011yescharacteristic
479C2×C3C2×C3×#10411yescharacteristic
480C2×C3C3×#42111yescharacteristic
481D3—42no—
482C22—21no—
483C22—21no—
484C22—62no—
485C22—121no—
486C22—121no—
487C22C3×#89511yescharacteristic
488C22C3×#89711yescharacteristic
489C22C2×C3×(C2×D3)⋊C411yescharacteristic
490C4—21no—
491C4—21no—
492C4—21no—
493C4—62no—
494C4—124no—
495C4—121no—
496C4—121no—
497C4C3×#82512yescomplemented
498C4C3×D3×C4⋊C411yescharacteristic
499C4C3×#89211yescharacteristic
500C4C3×#93811yescharacteristic
501C4C3×#94611yescharacteristic
502C3—21no—
503C3#7052911yescharacteristic, direct product factor
504C3C3×#180611yescharacteristic, complemented
505C2—21no—
506C2—21no—
507C2—122no—
508C2C3×#498711yescharacteristic
509C2C2×C3×#82511yescharacteristic
510C2C3×#513911yescharacteristic
subgroupG/H
centerC2×C3×C4C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#423C2
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#235C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#423D3
hypocenterC3C3×#1806
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×#423

Complements

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

NH ≅ G/Ntype
2. C32×#423C2semidirect
4. C3×C4×C4⋊Dic3C2semidirect
5. C3×#4555C2semidirect
7. #70529C3direct (N × H)
16. C3×C4×D12C4semidirect
17. C3×C4×D12C4semidirect
20. C3×C4×Dic6C4semidirect
21. C3×C4×Dic6C4semidirect
29. C3×#423D3semidirect
30. C3×#423C2×C3semidirect
34. C4×C4⋊Dic3C2×C3semidirect
36. #4555C2×C3semidirect
96. C4×D12C3×C4semidirect
97. C4×D12C3×C4semidirect
100. C4×Dic6C3×C4semidirect
101. C4×Dic6C3×C4semidirect
135. C3×D12C4⋊C4semidirect
141. C3×Dic6C4⋊C4semidirect
144. #423C3×D3semidirect
237. C32×C4#104semidirect
330. D12C3×C4⋊C4semidirect
336. Dic6C3×C4⋊C4semidirect
419. C3×C4#825semidirect
420. C3×C4C3×#104semidirect
433. C32#1806semidirect
497. C4C3×#825semidirect
503. C3#70529direct (N × H)
504. C3C3×#1806semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2352
C32×#4232
C2×C3×#8252
C3×C4×C4⋊Dic32
C3×#45552
C3×#18063
#705293