Finite Group Databasebeta

← C3×#69147 #11798676

Subgroups — C3×#69147 #11798676

Order 1152.

563 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 563 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5720C211yesmaximal, characteristic, complemented
2C3×#5077C211yesmaximal, characteristic, complemented
3C3×#4742C211yesmaximal, characteristic, complemented
4C3×#4741C211yesmaximal, characteristic, complemented
5C32×#353C211yesmaximal, characteristic, complemented
6C3×#4472C211yesmaximal, characteristic, complemented
7C3×#4471C211yesmaximal, characteristic, complemented
8C3×#2200—31nomaximal
9#69147C311yesmaximal, characteristic, direct product factor
10C3×#1004C2211yescharacteristic
11C32×#127C2211yescharacteristic
12C3×#939—21no—
13C3×#939—21no—
14C3×#939—21no—
15C3×#937—21no—
16C3×#937C2211yescharacteristic
17C3×#935—21no—
18C3×#935C2211yescharacteristic
19C3×#932—21no—
20C3×#886—21no—
21C3×#882—21no—
22C3×#876—21no—
23C32×#99C2211yescharacteristic
24C32×#99C2211yescharacteristic
25C3×#833C2211yescharacteristic
26C3×#806—21no—
27C3×#806—21no—
28C3×#805—21no—
29C3×#560—31no—
30#5720C2×C311yescharacteristic, complemented
31C3×#458—31no—
32C3×B(4,𝔽2)—31no—
33C3×#453—31no—
34#5077C2×C311yescharacteristic, complemented
35#4742C2×C311yescharacteristic, complemented
36#4741C2×C311yescharacteristic, complemented
37C3×#353—21no—
38C3×#353D311yescharacteristic, complemented
39C3×#353C2×C311yescharacteristic, complemented
40C3×#352—31no—
41C3×AΣL(1,𝔽16)—31no—
42#4472C2×C311yescharacteristic, complemented
43#4471C2×C311yescharacteristic, complemented
44C23×C3×D3D411yescharacteristic
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4D411yescharacteristic, complemented
48C2×C32×D4C2311yescharacteristic
49C2×C3×#67—21no—
50C2×C3×#67—21no—
51C2×C3×#67—21no—
52C2×C3×#67—21no—
53C2×C3×#67—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3D411yescharacteristic, complemented
56C3×#237—41no—
57C3×D3×D4—41no—
58C3×#235—21no—
59C2×C3×D12—41no—
60C32×C22⋊C4—21no—
61C32×C22⋊C4—21no—
62C32×C42D411yescharacteristic, complemented
63C3×#217—21no—
64C3×#217—21no—
65C3×#217D411yescharacteristic
66C3×#217D411yescharacteristic, complemented
67C3×#214—41no—
68C3×#213—41no—
69C3×(C2×D3)⋊C4—21no—
70C3×(C2×D3)⋊C4—21no—
71C3×(C2×D3)⋊C4—21no—
72C3×(C2×D3)⋊C4—41no—
73C3×(C2×D3)⋊C4—41no—
74C3×C4⋊Dic3—41no—
75C3×Dic3⋊C4—21no—
76C3×Dic3⋊C4—21no—
77C3×Dic3⋊C4—21no—
78C3×#208—21no—
79#2200—31noSylow
80C3×H(5,𝔽2)—31no—
81#1004C22×C311yescharacteristic
82C3×AGL(1,ℤ/8)—61no—
83C3×#127—21no—
84C3×#127C2×D311yescharacteristic
85C3×#127C22×C311yescharacteristic
86C3×#126—61no—
87C3×#123—31no—
88C3×#123—61no—
89C3×#123—61no—
90C3×#121—61no—
91C3×#121—61no—
92C3×#121—61no—
93C3×#120—31no—
94C3×#120—61no—
95C3×#120—61no—
96#939—21no—
97#939—21no—
98#939—21no—
99#937—21no—
100#937C22×C311yescharacteristic
101#935—21no—
102#935C22×C311yescharacteristic
103#932—21no—
104#886—21no—
105#882—21no—
106#876—21no—
107C3×#104—61no—
108C3×#100—31no—
109C3×#99—21no—
110C3×#99—21no—
111C3×#99—61no—
112C3×#99—61no—
113C3×#99C2×D311yescharacteristic
114C3×#99C2×D311yescharacteristic
115C3×#99C22×C311yescharacteristic
116C3×#99C22×C311yescharacteristic
117#833C22×C311yescharacteristic
118#806—21no—
119#806—21no—
120#805—21no—
121C23×C32—21no—
122C23×C32C2×D411yescharacteristic
123C23×C32C2×D411yescharacteristic
124C22×C3×D3—21no—
125C22×C3×D3—21no—
126C22×C3×D3—21no—
127C22×C3×D3—41no—
128C22×C3×D3—81no—
129C32×D4—41no—
130C32×D4—41no—
131C32×D4—81no—
132C32×D4—81no—
133C2×C32×C4—21no—
134C2×C32×C4—41no—
135C2×C32×C4—41no—
136C2×C32×C4C2×D411yescharacteristic
137C3×#67—41no—
138C3×#67—41no—
139C3×#67—41no—
140C3×#67—81no—
141C3×#67—81no—
142C3×#67—81no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—81no—
150C3×D12—21no—
151C3×D12—82no—
152C3×C4×D3—41no—
153C3×Dic6—21no—
154C3×C3⋊C8—41no—
155#560—31no—
156#458—31no—
157B(4,𝔽2)—31no—
158#453—31no—
159#353C3×D311yescharacteristic, complemented
160#352—31no—
161AΣL(1,𝔽16)—31no—
162C24×C3—31no—
163C23×D3C3×D411yescharacteristic
164C3×#41—61no—
165C3×#41—121no—
166C2×C3×D4—21no—
167C2×C3×D4—21no—
168C2×C3×D4—21no—
169C2×C3×D4—21no—
170C2×C3×D4—21no—
171C2×C3×D4—21no—
172C2×C3×D4—41no—
173C2×C3×D4—41no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—121no—
180C2×C3×D4—121no—
181C2×C3×D4D1211yescharacteristic, complemented
182C2×C3×D4C3×D411yescharacteristic, complemented
183C2×C3×D4C22×D311yescharacteristic
184C2×C3×D4C23×C311yescharacteristic
185C22×C3×C4—31no—
186C22×C3×C4—61no—
187C2×#67—21no—
188C2×#67—21no—
189C2×#67—21no—
190C2×#67—21no—
191C2×#67—21no—
192C22×Dic3—21no—
193C22×Dic3C3×D411yescharacteristic, complemented
194#237—41no—
195D3×D4—41no—
196#235—21no—
197C2×D12—41no—
198C3×SD16—121no—
199C3×D8—121no—
200C3×M16—61no—
201C3×C4⋊C4—61no—
202C3×C4⋊C4—61no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4—121no—
205C3×C22⋊C4—21no—
206C3×C22⋊C4—21no—
207C3×C22⋊C4—21no—
208C3×C22⋊C4—21no—
209C3×C22⋊C4—31no—
210C3×C22⋊C4—31no—
211C3×C22⋊C4—41no—
212C3×C22⋊C4—41no—
213C3×C22⋊C4—61no—
214C3×C22⋊C4—61no—
215C3×C22⋊C4—61no—
216C3×C22⋊C4—61no—
217C3×C22⋊C4—61no—
218C3×C22⋊C4—121no—
219C3×C22⋊C4—121no—
220C3×C42—21no—
221C3×C42D1211yescharacteristic, complemented
222C3×C42C3×D411yescharacteristic, complemented
223#217—21no—
224#217—21no—
225#217C3×D411yescharacteristic
226#217C3×D411yescharacteristic, complemented
227#214—41no—
228#213—41no—
229(C2×D3)⋊C4—21no—
230(C2×D3)⋊C4—21no—
231(C2×D3)⋊C4—21no—
232(C2×D3)⋊C4—41no—
233(C2×D3)⋊C4—41no—
234C4⋊Dic3—41no—
235Dic3⋊C4—21no—
236Dic3⋊C4—21no—
237Dic3⋊C4—21no—
238#208—21no—
239C22×C32—21no—
240C22×C32—21no—
241C22×C32—41no—
242C22×C32—41no—
243C22×C32—41no—
244C22×C32—41no—
245C22×C32—41no—
246C22×C32#12011yescharacteristic
247C2×C3×D3—41no—
248C2×C3×D3—41no—
249C2×C3×D3—42no—
250C2×C3×D3—41no—
251C2×C3×D3—41no—
252C2×C3×D3—81no—
253C2×C3×D3—81no—
254C2×C3×D3—81no—
255C32×C4—21no—
256C32×C4—41no—
257C32×C4—81no—
258C32×C4—81no—
259C3×Dic3—41no—
260C3×Dic3—41no—
261C3×Dic3—41no—
262C3×Dic3—41no—
263H(5,𝔽2)—31no—
264AGL(1,ℤ/8)—61no—
265#127C2×C3×D311yescharacteristic
266#126—61no—
267#123—31no—
268#123—61no—
269#123—61no—
270#121—61no—
271#121—61no—
272#121—61no—
273#120—31no—
274#120—61no—
275#120—61no—
276#104—61no—
277#100—31no—
278#99—61no—
279#99—61no—
280#99C2×C3×D311yescharacteristic
281#99C2×C3×D311yescharacteristic
282C23×C3—21no—
283C23×C3—21no—
284C23×C3—21no—
285C23×C3—21no—
286C23×C3—41no—
287C23×C3—61no—
288C23×C3—61no—
289C23×C3—61no—
290C23×C3—121no—
291C23×C3—241no—
292C23×C3D3×D411yescharacteristic
293C23×C3D3×D411yescharacteristic
294C23×C3C2×C3×D411yescharacteristic
295C23×C3C2×C3×D411yescharacteristic
296C22×D3—21no—
297C22×D3—21no—
298C22×D3—21no—
299C22×D3—41no—
300C22×D3—81no—
301C3×Q8—61no—
302C3×D4—41no—
303C3×D4—41no—
304C3×D4—41no—
305C3×D4—41no—
306C3×D4—61no—
307C3×D4—81no—
308C3×D4—81no—
309C3×D4—81no—
310C3×D4—81no—
311C3×D4—81no—
312C3×D4—81no—
313C3×D4—82no—
314C3×D4—82no—
315C3×D4—121no—
316C3×D4—121no—
317C3×D4—121no—
318C3×D4—242no—
319C3×D4—241no—
320C3×D4—241no—
321C3×D4—241no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4—41no—
329C2×C3×C4—41no—
330C2×C3×C4—61no—
331C2×C3×C4—61no—
332C2×C3×C4—61no—
333C2×C3×C4—61no—
334C2×C3×C4—61no—
335C2×C3×C4—81no—
336C2×C3×C4—81no—
337C2×C3×C4—121no—
338C2×C3×C4—121no—
339C2×C3×C4—241no—
340C2×C3×C4C2×D1211yescharacteristic
341C2×C3×C4C2×C3×D411yescharacteristic
342#67—41no—
343#67—41no—
344#67—41no—
345#67—81no—
346#67—81no—
347#67—81no—
348C2×Dic3—21no—
349C2×Dic3—21no—
350C2×Dic3—21no—
351C2×Dic3—21no—
352C2×Dic3—21no—
353C2×Dic3—41no—
354C2×Dic3—81no—
355D12—21no—
356D12—82no—
357C4×D3—41no—
358Dic6—21no—
359C3×C8—121no—
360C3⋊C8—41no—
361C2×C32—21no—
362C2×C32—41no—
363C2×C32—41no—
364C2×C32—81no—
365C2×C32B(4,𝔽2)11yescharacteristic
366C3×D3—81no—
367C3×D3—81no—
368C24—31no—
369#41—61no—
370#41—121no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—61no—
374C2×D4—61no—
375C2×D4—61no—
376C2×D4—61no—
377C2×D4—61no—
378C2×D4—121no—
379C2×D4—121no—
380C2×D4C3×D1211yescharacteristic, complemented
381C2×D4C22×C3×D311yescharacteristic
382C22×C4—31no—
383C22×C4—61no—
384SD16—121no—
385D8—121no—
386M16—61no—
387C4⋊C4—61no—
388C4⋊C4—61no—
389C4⋊C4—61no—
390C4⋊C4—121no—
391C22⋊C4—21no—
392C22⋊C4—21no—
393C22⋊C4—31no—
394C22⋊C4—31no—
395C22⋊C4—61no—
396C22⋊C4—61no—
397C22⋊C4—61no—
398C22⋊C4—61no—
399C22⋊C4—61no—
400C22⋊C4—121no—
401C22⋊C4—121no—
402C42C3×D1211yescharacteristic, complemented
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—41no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3—41no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3—41no—
420C22×C3—81no—
421C22×C3—81no—
422C22×C3—81no—
423C22×C3—81no—
424C22×C3—81no—
425C22×C3—121no—
426C22×C3—121no—
427C22×C3—122no—
428C22×C3—121no—
429C22×C3—121no—
430C22×C3—241no—
431C22×C3—241no—
432C22×C3—241no—
433C22×C3#88211yescharacteristic
434C22×C3C3×#12011yescharacteristic
435C2×D3—41no—
436C2×D3—41no—
437C2×D3—42no—
438C2×D3—41no—
439C2×D3—41no—
440C2×D3—81no—
441C2×D3—81no—
442C2×D3—81no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—41no—
446C3×C4—41no—
447C3×C4—41no—
448C3×C4—42no—
449C3×C4—81no—
450C3×C4—81no—
451C3×C4—81no—
452C3×C4—81no—
453C3×C4—121no—
454C3×C4—121no—
455C3×C4—121no—
456C3×C4—121no—
457C3×C4—161no—
458C3×C4—161no—
459Dic3—41no—
460Dic3—41no—
461Dic3—41no—
462Dic3—41no—
463C32#220011yescharacteristic, complemented, Sylow
464C23—21no—
465C23—61no—
466C23—61no—
467C23—61no—
468C23—121no—
469C23—241no—
470C23C3×D3×D411yescharacteristic
471C23C3×D3×D411yescharacteristic
472Q8—61no—
473D4—41no—
474D4—41no—
475D4—61no—
476D4—81no—
477D4—81no—
478D4—121no—
479D4—121no—
480D4—121no—
481D4—242no—
482D4—241no—
483D4—241no—
484D4—241no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—61no—
489C2×C4—61no—
490C2×C4—61no—
491C2×C4—61no—
492C2×C4—61no—
493C2×C4—121no—
494C2×C4—121no—
495C2×C4—241no—
496C2×C4C2×C3×D1211yescharacteristic
497C8—121no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—41no—
502C2×C3—41no—
503C2×C3—41no—
504C2×C3—41no—
505C2×C3—41no—
506C2×C3—81no—
507C2×C3—81no—
508C2×C3—81no—
509C2×C3—81no—
510C2×C3—161no—
511C2×C3—241no—
512C2×C3—241no—
513C2×C3#474111yescharacteristic
514C2×C3C3×B(4,𝔽2)11yescharacteristic
515D3—81no—
516D3—81no—
517C22—21no—
518C22—21no—
519C22—41no—
520C22—41no—
521C22—41no—
522C22—41no—
523C22—41no—
524C22—121no—
525C22—121no—
526C22—122no—
527C22—121no—
528C22—121no—
529C22—241no—
530C22—241no—
531C22—241no—
532C22C3×#88211yescharacteristic
533C4—21no—
534C4—41no—
535C4—81no—
536C4—81no—
537C4—121no—
538C4—121no—
539C4—121no—
540C4—121no—
541C3—21no—
542C3#6914711yescharacteristic, direct product factor
543C3C3×#220011yescharacteristic, complemented
544C2—21no—
545C2—41no—
546C2—41no—
547C2—81no—
548C2—241no—
549C2—241no—
550C2C3×#474111yescharacteristic
subgroupG/H
centerC2×C3#4741
commutator, cosocleC2×C3×D4C23×C3
FrattiniC2×D4C22×C3×D3
FittingC32×#353C2
socleC2×C32B(4,𝔽2)
hypercenterC3×#353D3
hypocenterC3C3×#2200
LCSG ▷ C2×C3×D4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#353

Complements

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

NH ≅ G/Ntype
1. C3×#5720C2semidirect
2. C3×#5077C2semidirect
3. C3×#4742C2semidirect
4. C3×#4741C2semidirect
5. C32×#353C2semidirect
6. C3×#4472C2semidirect
7. C3×#4471C2semidirect
9. #69147C3direct (N × H)
30. #5720C2×C3semidirect
34. #5077C2×C3semidirect
35. #4742C2×C3semidirect
36. #4741C2×C3semidirect
38. C3×#353D3semidirect
39. C3×#353C2×C3semidirect
42. #4472C2×C3semidirect
43. #4471C2×C3semidirect
47. C2×C32×D4D4semidirect
55. C22×C3×Dic3D4semidirect
62. C32×C42D4semidirect
66. C3×#217D4semidirect
159. #353C3×D3semidirect
181. C2×C3×D4D12semidirect
182. C2×C3×D4C3×D4semidirect
193. C22×Dic3C3×D4semidirect
221. C3×C42D12semidirect
222. C3×C42C3×D4semidirect
226. #217C3×D4semidirect
380. C2×D4C3×D12semidirect
402. C42C3×D12semidirect
463. C32#2200semidirect
542. C3#69147direct (N × H)
543. C3C3×#2200semidirect

Maximal subgroups

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

subgroupindex
C3×#57202
C3×#50772
C3×#47422
C3×#47412
C32×#3532
C3×#44722
C3×#44712
C3×#22003
#691473