Finite Group Databasebeta

← C3×#69494 #11785312

Subgroups — C3×#69494 #11785312

Order 1152.

721 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#235C211yesmaximal, characteristic
2C32×C4×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#805C212yesmaximal
4C3×#4924C211yesmaximal, characteristic, complemented
5C3×#4523C212yesmaximal, complemented
6C3×#1806—31nomaximal
7#69494C311yesmaximal, characteristic, direct product factor
8C2×C3×#235C2211yescharacteristic
9C2×C32×C4⋊C4—21no—
10C2×C32×C42C2212yes—
11C2×C32×C42C2211yescharacteristic
12C3×C4×#67—21no—
13C3×C4×#67—21no—
14C3×#926C2211yescharacteristic
15C2×C3×#208C2212yes—
16C3×C4×D12C411yescharacteristic, complemented
17C3×C4×D12C411yescharacteristic, complemented
18C3×#872—21no—
19C3×C42×D3—21no—
20C3×C4×Dic6C411yescharacteristic, complemented
21C3×C4×Dic6C411yescharacteristic, complemented
22C32×#95—21no—
23C3×#805—24no—
24C3×C4⋊(C3⋊C8)—21no—
25C3×C4⋊(C3⋊C8)—21no—
26C3×C4×#41—31no—
27C4×#235C2×C311yescharacteristic
28C3×#423—31no—
29C2×C3×#104—32no—
30C3×C4×C4⋊C4—21no—
31C3×C4×C4⋊C4D311yescharacteristic, complemented
32C3×C4×C4⋊C4C2×C311yescharacteristic, complemented
33C2×#805C2×C312yes—
34#4924C2×C311yescharacteristic, complemented
35C3×#339—32no—
36#4523C2×C312yescomplemented
37C22×C32×C4—22no—
38C22×C32×C4D411yescharacteristic
39C22×C32×C4D411yescharacteristic
40C22×C32×C4C2311yescharacteristic
41C2×C3×#67—21no—
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×C4⋊C4—24no—
52C32×C42—22no—
53C32×C42—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⋊Dic3C2×C411yescharacteristic
62C3×C4⋊Dic3C2×C411yescharacteristic
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3—21no—
67C3×C4×Dic3—21no—
68C3×#208—22no—
69C3×#208—22no—
70C2×C3×C3⋊C8—22no—
71#1806—31noSylow
72C2×C3×#41—31no—
73C2×#235C22×C311yescharacteristic
74C2×C3×M16—32no—
75C3×C4×Q8—31no—
76C3×C4×Q8—31no—
77C3×C4×D4—31no—
78C3×C4×D4—31no—
79C3×C4×D4—61no—
80C3×C4×D4—61no—
81C3×#117—31no—
82C3×#117—61no—
83C2×C3×C4⋊C4—22no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4—21no—
86C2×C3×C42—21no—
87C2×C3×C42—22no—
88C2×C3×C42—61no—
89C2×C3×C42C2×D312yes—
90C2×C3×C42C2×D311yescharacteristic
91C2×C3×C42C22×C312yes—
92C2×C3×C42C22×C311yescharacteristic
93C4×#67—21no—
94C4×#67—21no—
95#926C22×C311yescharacteristic
96C2×#208C22×C312yes—
97C4×D12C3×C411yescharacteristic, complemented
98C4×D12C3×C411yescharacteristic, complemented
99#872—21no—
100C42×D3—21no—
101C4×Dic6C3×C411yescharacteristic, complemented
102C4×Dic6C3×C411yescharacteristic, complemented
103C3×C4⋊C8—61no—
104C3×C4⋊C8—61no—
105C3×#104—64no—
106C3×#95—22no—
107C3×#95—21no—
108C3×#95—21no—
109#805—24no—
110C4⋊(C3⋊C8)—21no—
111C4⋊(C3⋊C8)—21no—
112C23×C32C2×D411yescharacteristic
113C22×C3×D3—21no—
114C2×C32×C4—22no—
115C2×C32×C4—24no—
116C2×C32×C4—41no—
117C2×C32×C4—42no—
118C2×C32×C4—42no—
119C2×C32×C4C22⋊C411yescharacteristic
120C2×C32×C4C22⋊C411yescharacteristic
121C2×C32×C4C22⋊C411yescharacteristic
122C2×C32×C4C22⋊C411yescharacteristic
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×Q811yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C3×#67—22no—
130C3×#67—22no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
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
142C3×C3⋊C8—42no—
143C4×#41—31no—
144#423—31no—
145C2×#104—32no—
146C4×C4⋊C4C3×D311yescharacteristic, complemented
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—24no—
156C22×C3×C4—22no—
157C22×C3×C4—22no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—61no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164C22×C3×C4#6711yescharacteristic
165C22×C3×C4#6711yescharacteristic
166C22×C3×C4C3×D411yescharacteristic
167C22×C3×C4C3×D411yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C23×C311yescharacteristic
170C2×#67—21no—
171#235—21no—
172#235—21no—
173#235C3×D412yes—
174#235C3×Q812yes—
175C2×D12C2×C3×C411yescharacteristic
176C2×C4×D3—21no—
177C2×C4×D3—21no—
178C2×C4×D3—21no—
179C2×Dic6C2×C3×C411yescharacteristic
180C3×M16—62no—
181C3×M16—62no—
182C2×C3×C8—62no—
183C3×C4⋊C4—28no—
184C3×C4⋊C4—24no—
185C3×C4⋊C4—24no—
186C3×C4⋊C4—31no—
187C3×C4⋊C4—31no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—61no—
190C3×C22⋊C4—61no—
191C3×C22⋊C4—61no—
192C3×C22⋊C4—61no—
193C3×C42—22no—
194C3×C42—22no—
195C3×C42—22no—
196C3×C42—22no—
197C3×C42—21no—
198C3×C42—21no—
199C3×C42—21no—
200C3×C42—21no—
201C3×C42—42no—
202C3×C42—42no—
203C3×C42—61no—
204C3×C42—61no—
205C3×C42—61no—
206C3×C42C4×D311yescharacteristic
207C3×C42C4×D311yescharacteristic
208C3×C42D1211yescharacteristic
209C3×C42D1211yescharacteristic
210C3×C42C2×C3×C411yescharacteristic
211C3×C42C2×C3×C411yescharacteristic
212C3×C42C3×D411yescharacteristic
213C3×C42C3×D411yescharacteristic
214#217—21no—
215(C2×D3)⋊C4—21no—
216(C2×D3)⋊C4—21no—
217C4⋊Dic3C2×C3×C411yescharacteristic
218C4⋊Dic3C2×C3×C411yescharacteristic
219Dic3⋊C4—21no—
220Dic3⋊C4—21no—
221C4×Dic3—21no—
222C4×Dic3—21no—
223C4×Dic3—21no—
224#208—22no—
225#208—22no—
226C2×C3⋊C8—22no—
227C22×C32—21no—
228C22×C32—21no—
229C22×C32C2×C22⋊C411yescharacteristic
230C22×C32#12111yescharacteristic
231C22×C32C22⋊Q811yescharacteristic
232C2×C3×D3—22no—
233C2×C3×D3—41no—
234C2×C3×D3—41no—
235C32×C4—21no—
236C32×C4—21no—
237C32×C4—21no—
238C32×C4—44no—
239C32×C4#10412yescomplemented
240C32×C4C2×C4⋊C411yescharacteristic
241C32×C4#11711yescharacteristic
242C32×C4#12111yescharacteristic
243C32×C4C22⋊Q811yescharacteristic
244C3×Dic3—22no—
245C3×Dic3—41no—
246C3×Dic3—41no—
247C2×#41—31no—
248C2×M16—32no—
249C4×Q8—31no—
250C4×Q8—31no—
251C4×D4—31no—
252C4×D4—31no—
253C4×D4—61no—
254C4×D4—61no—
255#117—31no—
256#117—61no—
257C2×C4⋊C4—21no—
258C2×C42—61no—
259C2×C42C2×C3×D312yes—
260C2×C42C2×C3×D311yescharacteristic
261C4⋊C8—61no—
262C4⋊C8—61no—
263#104—64no—
264#95—21no—
265C23×C3—21no—
266C23×C3—61no—
267C23×C3C2×#6711yescharacteristic
268C23×C3C2×C3×D411yescharacteristic
269C22×D3—21no—
270C3×Q8—32no—
271C3×Q8—61no—
272C3×D4—32no—
273C3×D4—62no—
274C3×D4—62no—
275C3×D4—61no—
276C2×C3×C4—24no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—28no—
280C2×C3×C4—24no—
281C2×C3×C4—24no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—44no—
295C2×C3×C4—42no—
296C2×C3×C4—44no—
297C2×C3×C4—42no—
298C2×C3×C4—42no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
301C2×C3×C4—61no—
302C2×C3×C4—62no—
303C2×C3×C4—62no—
304C2×C3×C4—61no—
305C2×C3×C4—61no—
306C2×C3×C4—122no—
307C2×C3×C4—122no—
308C2×C3×C4(C2×D3)⋊C411yescharacteristic
309C2×C3×C4(C2×D3)⋊C411yescharacteristic
310C2×C3×C4(C2×D3)⋊C411yescharacteristic
311C2×C3×C4(C2×D3)⋊C411yescharacteristic
312C2×C3×C4C3×C22⋊C411yescharacteristic
313C2×C3×C4C3×C22⋊C411yescharacteristic
314C2×C3×C4C3×C22⋊C411yescharacteristic
315C2×C3×C4C3×C22⋊C411yescharacteristic
316C2×C3×C4C2×C4×D311yescharacteristic
317C2×C3×C4C2×D1211yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4#23711yescharacteristic
320C2×C3×C4D3×Q811yescharacteristic
321C2×C3×C4#23911yescharacteristic
322C2×C3×C4C22×C3×C411yescharacteristic
323C2×C3×C4C2×C3×D411yescharacteristic
324C2×C3×C4C2×C3×D411yescharacteristic
325C2×C3×C4C2×C3×Q811yescharacteristic
326C2×C3×C4C3×#4111yescharacteristic
327C2×C3×C4C3×#4111yescharacteristic
328#67—22no—
329#67—22no—
330C2×Dic3—21no—
331C2×Dic3—21no—
332C2×Dic3—21no—
333D12—21no—
334D12C3×C4⋊C412yescomplemented
335C4×D3—22no—
336C4×D3—22no—
337C4×D3—42no—
338C4×D3—42no—
339Dic6—21no—
340Dic6C3×C4⋊C412yescomplemented
341C3×C8—122no—
342C3⋊C8—42no—
343C2×C32—21no—
344C2×C32—21no—
345C2×C32#38011yescharacteristic
346C2×C32C2×#10411yescharacteristic
347C2×C32#42111yescharacteristic
348C3×D3—42no—
349#41—32no—
350#41—32no—
351#41—61no—
352#41—61no—
353C2×Q8—31no—
354C2×D4—31no—
355C2×D4—61no—
356C22×C4—22no—
357C22×C4—61no—
358C22×C4—61no—
359C22×C4—61no—
360C22×C4C3×#6711yescharacteristic
361C22×C4C3×#6711yescharacteristic
362C22×C4C22×C3×D311yescharacteristic
363M16—62no—
364M16—62no—
365C2×C8—62no—
366C4⋊C4—24no—
367C4⋊C4—31no—
368C4⋊C4—31no—
369C4⋊C4—61no—
370C4⋊C4—61no—
371C22⋊C4—61no—
372C22⋊C4—61no—
373C22⋊C4—61no—
374C42—22no—
375C42—22no—
376C42—61no—
377C42—61no—
378C42—61no—
379C42C3×C4×D311yescharacteristic
380C42C3×C4×D311yescharacteristic
381C42C3×D1211yescharacteristic
382C42C3×D1211yescharacteristic
383C22×C3—22no—
384C22×C3—22no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—62no—
393C22×C3—121no—
394C22×C3—121no—
395C22×C3C2×(C2×D3)⋊C411yescharacteristic
396C22×C3#93811yescharacteristic
397C22×C3#94611yescharacteristic
398C22×C3C2×C3×C22⋊C411yescharacteristic
399C22×C3C3×#12111yescharacteristic
400C22×C3C3×C22⋊Q811yescharacteristic
401C2×D3—22no—
402C2×D3—41no—
403C2×D3—41no—
404C3×C4—22no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—22no—
416C3×C4—41no—
417C3×C4—41no—
418C3×C4—48no—
419C3×C4—44no—
420C3×C4—44no—
421C3×C4—62no—
422C3×C4—121no—
423C3×C4—121no—
424C3×C4#80512yescomplemented
425C3×C4C3×#10412yescomplemented
426C3×C4D3×C4⋊C411yescharacteristic
427C3×C4#89211yescharacteristic
428C3×C4#89511yescharacteristic
429C3×C4#89711yescharacteristic
430C3×C4C2×C3×C4⋊C411yescharacteristic
431C3×C4C3×#11711yescharacteristic
432C3×C4C3×#12111yescharacteristic
433C3×C4C3×C22⋊Q811yescharacteristic
434Dic3—22no—
435Dic3—41no—
436Dic3—41no—
437C32#180611yescharacteristic, complemented, Sylow
438C23—61no—
439C23C2×C3×#6711yescharacteristic
440Q8—32no—
441Q8—61no—
442D4—32no—
443D4—62no—
444D4—62no—
445D4—61no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—61no—
452C2×C4—62no—
453C2×C4—62no—
454C2×C4—61no—
455C2×C4—61no—
456C2×C4—122no—
457C2×C4—122no—
458C2×C4C3×(C2×D3)⋊C411yescharacteristic
459C2×C4C3×(C2×D3)⋊C411yescharacteristic
460C2×C4C3×(C2×D3)⋊C411yescharacteristic
461C2×C4C3×(C2×D3)⋊C411yescharacteristic
462C2×C4C2×C3×C4×D311yescharacteristic
463C2×C4C2×C3×D1211yescharacteristic
464C2×C4C3×D3×D411yescharacteristic
465C2×C4C3×#23711yescharacteristic
466C2×C4C3×D3×Q811yescharacteristic
467C2×C4C3×#23911yescharacteristic
468C8—122no—
469C2×C3—22no—
470C2×C3—22no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—122no—
479C2×C3C2×#80511yescharacteristic
480C2×C3#498711yescharacteristic
481C2×C3#500511yescharacteristic
482C2×C3C3×#38011yescharacteristic
483C2×C3C2×C3×#10411yescharacteristic
484C2×C3C3×#42111yescharacteristic
485D3—42no—
486C22—21no—
487C22—21no—
488C22—62no—
489C22—121no—
490C22—121no—
491C22C2×C3×(C2×D3)⋊C411yescharacteristic
492C22C3×#93811yescharacteristic
493C22C3×#94611yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—44no—
498C4—62no—
499C4—121no—
500C4—121no—
501C4C3×#80512yescomplemented
502C4C3×D3×C4⋊C411yescharacteristic
503C4C3×#89211yescharacteristic
504C4C3×#89511yescharacteristic
505C4C3×#89711yescharacteristic
506C3—21no—
507C3#6949411yescharacteristic, direct product factor
508C3C3×#180611yescharacteristic, complemented
509C2—21no—
510C2—21no—
511C2—122no—
512C2C2×C3×#80511yescharacteristic
513C2C3×#498711yescharacteristic
514C2C3×#500511yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D12
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×C4×C4⋊C4C2
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#235C22
cosocleC22×C3×C4C23×C3
hypercenterC3×C4×C4⋊C4D3
hypocenterC3C3×#1806
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C32×C4×C4⋊C4C2semidirect
4. C3×#4924C2semidirect
5. C3×#4523C2semidirect
7. #69494C3direct (N × H)
16. C3×C4×D12C4semidirect
17. C3×C4×D12C4semidirect
20. C3×C4×Dic6C4semidirect
21. C3×C4×Dic6C4semidirect
31. C3×C4×C4⋊C4D3semidirect
32. C3×C4×C4⋊C4C2×C3semidirect
34. #4924C2×C3semidirect
36. #4523C2×C3semidirect
97. C4×D12C3×C4semidirect
98. C4×D12C3×C4semidirect
101. C4×Dic6C3×C4semidirect
102. C4×Dic6C3×C4semidirect
135. C3×D12C4⋊C4semidirect
141. C3×Dic6C4⋊C4semidirect
146. C4×C4⋊C4C3×D3semidirect
239. C32×C4#104semidirect
334. D12C3×C4⋊C4semidirect
340. Dic6C3×C4⋊C4semidirect
424. C3×C4#805semidirect
425. C3×C4C3×#104semidirect
437. C32#1806semidirect
501. C4C3×#805semidirect
507. C3#69494direct (N × H)
508. 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×C4×C4⋊C42
C2×C3×#8052
C3×#49242
C3×#45232
C3×#18063
#694943