Finite Group Databasebeta

← C3×#70985 #11798664

Subgroups — C3×#70985 #11798664

Order 1152.

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

normal subgroups only

This group has 604 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
2C32×#453C211yesmaximal, characteristic, complemented
3C3×#5244C211yesmaximal, characteristic, complemented
4C3×#5243C211yesmaximal, characteristic, complemented
5C3×#4545C211yesmaximal, characteristic, complemented
6C3×#4476C211yesmaximal, characteristic, complemented
7C3×#4475C211yesmaximal, characteristic, complemented
8C3×#2200—31nomaximal
9#70985C311yesmaximal, characteristic, direct product factor
10C32×H(5,𝔽2)C2211yescharacteristic
11C32×AGL(1,ℤ/8)—21no—
12C32×#127C2211yescharacteristic
13C3×#939—21no—
14C3×#939—21no—
15C3×#939—21no—
16C3×#937—21no—
17C3×#937—21no—
18C3×#937C2211yescharacteristic
19C3×#935—21no—
20C3×#935—21no—
21C3×#935C2211yescharacteristic
22C3×#876—21no—
23C32×#104—21no—
24C32×#100C2211yescharacteristic
25C3×#834—21no—
26C3×#834—21no—
27C3×#834C2211yescharacteristic
28C3×#834C2211yescharacteristic
29C3×#560—31no—
30#5720C2×C311yescharacteristic, complemented
31C3×#458—31no—
32C3×B(4,𝔽2)—31no—
33C3×#453—21no—
34C3×#453D311yescharacteristic, complemented
35C3×#453C2×C311yescharacteristic, complemented
36#5244C2×C311yescharacteristic, complemented
37#5243C2×C311yescharacteristic, complemented
38C3×#353—31no—
39C3×#352—31no—
40C3×AΣL(1,𝔽16)—31no—
41#4545C2×C311yescharacteristic, complemented
42#4476C2×C311yescharacteristic, complemented
43#4475C2×C311yescharacteristic, complemented
44C23×C3×D3D411yescharacteristic
45C32×#41—21no—
46C32×#41—41no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4—21no—
51C2×C32×D4—41no—
52C2×C32×D4D411yescharacteristic, complemented
53C2×C32×D4C2311yescharacteristic
54C2×C3×#67—21no—
55C2×C3×#67—21no—
56C2×C3×#67—21no—
57C2×C3×#67—41no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3D411yescharacteristic, complemented
60C32×SD16—41no—
61C32×D8—41no—
62C32×M16—21no—
63C32×C42D411yescharacteristic, complemented
64C3×#217—21no—
65C3×#217—21no—
66C3×#217—21no—
67C3×#217—21no—
68C3×#217—41no—
69C3×#217D411yescharacteristic
70C3×#217D411yescharacteristic, complemented
71C3×(C2×D3)⋊C4—21no—
72C3×(C2×D3)⋊C4—21no—
73C3×(C2×D3)⋊C4—21no—
74C3×(C2×D3)⋊C4—41no—
75C3×Dic3⋊C4—21no—
76C3×Dic3⋊C4—21no—
77C3×Dic3⋊C4—21no—
78C3×Dic3⋊C4—41no—
79#2200—31noSylow
80C3×H(5,𝔽2)—21no—
81C3×H(5,𝔽2)C2×D311yescharacteristic
82C3×H(5,𝔽2)C22×C311yescharacteristic
83C3×AGL(1,ℤ/8)—22no—
84C3×AGL(1,ℤ/8)—21no—
85C3×AGL(1,ℤ/8)—21no—
86C3×#127—21no—
87C3×#127C2×D311yescharacteristic
88C3×#127C22×C311yescharacteristic
89C3×#126—61no—
90C3×#123—31no—
91C3×#123—61no—
92C3×#123—61no—
93C3×#121—61no—
94C3×#121—61no—
95C3×#121—61no—
96C3×#120—31no—
97C3×#120—61no—
98C3×#120—61no—
99#939—21no—
100#939—21no—
101#939—21no—
102#937—21no—
103#937—21no—
104#937C22×C311yescharacteristic
105#935—21no—
106#935—21no—
107#935C22×C311yescharacteristic
108#876—21no—
109C3×#104—22no—
110C3×#104—21no—
111C3×#104—21no—
112C3×#100—21no—
113C3×#100C2×D311yescharacteristic
114C3×#100C22×C311yescharacteristic
115C3×#99—31no—
116C3×#99—31no—
117C3×#99—61no—
118C3×#99—61no—
119#834—21no—
120#834—21no—
121#834C22×C311yescharacteristic
122#834C22×C311yescharacteristic
123C23×C32—21no—
124C23×C32—21no—
125C23×C32—21no—
126C23×C32C2×D411yescharacteristic
127C23×C32C2×D411yescharacteristic
128C22×C3×D3—21no—
129C22×C3×D3—41no—
130C22×C3×D3—81no—
131C32×Q8—21no—
132C32×D4—21no—
133C32×D4—41no—
134C32×D4—41no—
135C32×D4—41no—
136C32×D4—41no—
137C32×D4—41no—
138C32×D4—81no—
139C32×D4—81no—
140C2×C32×C4—21no—
141C2×C32×C4—21no—
142C2×C32×C4—21no—
143C2×C32×C4—41no—
144C2×C32×C4C2×D411yescharacteristic
145C3×#67—81no—
146C3×#67—81no—
147C3×#67—81no—
148C3×#67—82no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—81no—
156C32×C8—41no—
157#560—31no—
158#458—31no—
159B(4,𝔽2)—31no—
160#453C3×D311yescharacteristic, complemented
161#353—31no—
162#352—31no—
163AΣL(1,𝔽16)—31no—
164C24×C3—31no—
165C23×D3C3×D411yescharacteristic
166C3×#41—22no—
167C3×#41—21no—
168C3×#41—21no—
169C3×#41—41no—
170C3×#41—41no—
171C3×#41—42no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4—21no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×C3×D4—41no—
183C2×C3×D4—41no—
184C2×C3×D4—41no—
185C2×C3×D4—41no—
186C2×C3×D4—41no—
187C2×C3×D4—41no—
188C2×C3×D4—42no—
189C2×C3×D4—61no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C2×C3×D4—121no—
193C2×C3×D4#6711yescharacteristic, complemented
194C2×C3×D4C3×D411yescharacteristic, complemented
195C2×C3×D4C22×D311yescharacteristic
196C2×C3×D4C23×C311yescharacteristic
197C22×C3×C4—31no—
198C22×C3×C4—61no—
199C2×#67—21no—
200C2×#67—21no—
201C2×#67—21no—
202C2×#67—41no—
203C22×Dic3—21no—
204C22×Dic3C3×D411yescharacteristic, complemented
205C3×SD16—41no—
206C3×SD16—41no—
207C3×SD16—42no—
208C3×D8—41no—
209C3×D8—41no—
210C3×D8—42no—
211C3×M16—22no—
212C3×M16—21no—
213C3×M16—21no—
214C3×C4⋊C4—61no—
215C3×C4⋊C4—61no—
216C3×C4⋊C4—61no—
217C3×C4⋊C4—121no—
218C3×C22⋊C4—31no—
219C3×C22⋊C4—31no—
220C3×C22⋊C4—61no—
221C3×C22⋊C4—61no—
222C3×C22⋊C4—61no—
223C3×C22⋊C4—61no—
224C3×C22⋊C4—61no—
225C3×C22⋊C4—61no—
226C3×C22⋊C4—61no—
227C3×C22⋊C4—121no—
228C3×C22⋊C4—121no—
229C3×C42—21no—
230C3×C42#6711yescharacteristic, complemented
231C3×C42C3×D411yescharacteristic, complemented
232#217—21no—
233#217—21no—
234#217—21no—
235#217—21no—
236#217—41no—
237#217C3×D411yescharacteristic
238#217C3×D411yescharacteristic, complemented
239(C2×D3)⋊C4—21no—
240(C2×D3)⋊C4—21no—
241(C2×D3)⋊C4—21no—
242(C2×D3)⋊C4—41no—
243Dic3⋊C4—21no—
244Dic3⋊C4—21no—
245Dic3⋊C4—21no—
246Dic3⋊C4—41no—
247C22×C32—21no—
248C22×C32—21no—
249C22×C32—41no—
250C22×C32—41no—
251C22×C32—41no—
252C22×C32—41no—
253C22×C32—41no—
254C22×C32—41no—
255C22×C32—81no—
256C22×C32—81no—
257C22×C32#12011yescharacteristic
258C2×C3×D3—41no—
259C2×C3×D3—41no—
260C2×C3×D3—42no—
261C2×C3×D3—41no—
262C2×C3×D3—81no—
263C32×C4—21no—
264C32×C4—41no—
265C32×C4—41no—
266C3×Dic3—41no—
267C3×Dic3—41no—
268C3×Dic3—41no—
269C3×Dic3—81no—
270C3×Dic3—81no—
271H(5,𝔽2)C2×C3×D311yescharacteristic
272AGL(1,ℤ/8)—21no—
273#127C2×C3×D311yescharacteristic
274#126—61no—
275#123—31no—
276#123—61no—
277#123—61no—
278#121—61no—
279#121—61no—
280#121—61no—
281#120—31no—
282#120—61no—
283#120—61no—
284#104—21no—
285#100C2×C3×D311yescharacteristic
286#99—31no—
287#99—31no—
288#99—61no—
289#99—61no—
290C23×C3—21no—
291C23×C3—21no—
292C23×C3—21no—
293C23×C3—21no—
294C23×C3—21no—
295C23×C3—21no—
296C23×C3—21no—
297C23×C3—21no—
298C23×C3—41no—
299C23×C3—41no—
300C23×C3—41no—
301C23×C3—61no—
302C23×C3—121no—
303C23×C3—241no—
304C23×C3D3×D411yescharacteristic
305C23×C3D3×D411yescharacteristic
306C23×C3C2×C3×D411yescharacteristic
307C23×C3C2×C3×D411yescharacteristic
308C22×D3—21no—
309C22×D3—41no—
310C22×D3—81no—
311C3×Q8—22no—
312C3×Q8—21no—
313C3×Q8—21no—
314C3×D4—22no—
315C3×D4—21no—
316C3×D4—21no—
317C3×D4—41no—
318C3×D4—41no—
319C3×D4—41no—
320C3×D4—41no—
321C3×D4—42no—
322C3×D4—42no—
323C3×D4—41no—
324C3×D4—41no—
325C3×D4—41no—
326C3×D4—41no—
327C3×D4—42no—
328C3×D4—42no—
329C3×D4—42no—
330C3×D4—41no—
331C3×D4—41no—
332C3×D4—81no—
333C3×D4—81no—
334C3×D4—81no—
335C3×D4—81no—
336C3×D4—82no—
337C3×D4—82no—
338C3×D4—241no—
339C3×D4—241no—
340C3×D4—241no—
341C3×D4—242no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—42no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—61no—
356C2×C3×C4—61no—
357C2×C3×C4—61no—
358C2×C3×C4—121no—
359C2×C3×C4—121no—
360C2×C3×C4—121no—
361C2×C3×C4—241no—
362C2×C3×C4C2×#6711yescharacteristic
363C2×C3×C4C2×C3×D411yescharacteristic
364#67—81no—
365#67—81no—
366#67—81no—
367#67—82no—
368C2×Dic3—21no—
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—41no—
372C2×Dic3—41no—
373C2×Dic3—41no—
374C2×Dic3—81no—
375C3×C8—42no—
376C3×C8—41no—
377C3×C8—41no—
378C2×C32—21no—
379C2×C32—41no—
380C2×C32—41no—
381C2×C32—81no—
382C2×C32—81no—
383C2×C32B(4,𝔽2)11yescharacteristic
384C3×D3—81no—
385C24—31no—
386#41—21no—
387#41—41no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—41no—
393C2×D4—61no—
394C2×D4—61no—
395C2×D4—61no—
396C2×D4—121no—
397C2×D4C3×#6711yescharacteristic, complemented
398C2×D4C22×C3×D311yescharacteristic
399C22×C4—31no—
400C22×C4—61no—
401SD16—41no—
402D8—41no—
403M16—21no—
404C4⋊C4—61no—
405C4⋊C4—61no—
406C4⋊C4—61no—
407C4⋊C4—121no—
408C22⋊C4—31no—
409C22⋊C4—31no—
410C22⋊C4—61no—
411C22⋊C4—61no—
412C22⋊C4—61no—
413C22⋊C4—61no—
414C22⋊C4—61no—
415C22⋊C4—61no—
416C22⋊C4—61no—
417C22⋊C4—121no—
418C22⋊C4—121no—
419C42C3×#6711yescharacteristic, complemented
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—41no—
426C22×C3—41no—
427C22×C3—41no—
428C22×C3—41no—
429C22×C3—41no—
430C22×C3—41no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3—42no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—81no—
441C22×C3—81no—
442C22×C3—81no—
443C22×C3—81no—
444C22×C3—81no—
445C22×C3—81no—
446C22×C3—81no—
447C22×C3—81no—
448C22×C3—81no—
449C22×C3—121no—
450C22×C3—121no—
451C22×C3—122no—
452C22×C3—121no—
453C22×C3—161no—
454C22×C3—161no—
455C22×C3—241no—
456C22×C3#93711yescharacteristic
457C22×C3C3×#12011yescharacteristic
458C2×D3—41no—
459C2×D3—41no—
460C2×D3—42no—
461C2×D3—41no—
462C2×D3—81no—
463C3×C4—22no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—41no—
467C3×C4—41no—
468C3×C4—42no—
469C3×C4—42no—
470C3×C4—41no—
471C3×C4—41no—
472C3×C4—121no—
473C3×C4—121no—
474C3×C4—121no—
475C3×C4—241no—
476C3×C4—241no—
477Dic3—41no—
478Dic3—41no—
479Dic3—41no—
480Dic3—81no—
481Dic3—81no—
482C32#220011yescharacteristic, complemented, Sylow
483C23—21no—
484C23—21no—
485C23—21no—
486C23—61no—
487C23—121no—
488C23—241no—
489C23C3×D3×D411yescharacteristic
490C23C3×D3×D411yescharacteristic
491Q8—21no—
492D4—21no—
493D4—41no—
494D4—41no—
495D4—41no—
496D4—41no—
497D4—41no—
498D4—81no—
499D4—81no—
500D4—241no—
501D4—241no—
502D4—241no—
503D4—242no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—61no—
509C2×C4—61no—
510C2×C4—61no—
511C2×C4—121no—
512C2×C4—121no—
513C2×C4—121no—
514C2×C4—241no—
515C2×C4C2×C3×#6711yescharacteristic
516C8—41no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—41no—
521C2×C3—41no—
522C2×C3—41no—
523C2×C3—41no—
524C2×C3—41no—
525C2×C3—81no—
526C2×C3—81no—
527C2×C3—82no—
528C2×C3—81no—
529C2×C3—81no—
530C2×C3—81no—
531C2×C3—81no—
532C2×C3—161no—
533C2×C3—241no—
534C2×C3#503211yescharacteristic
535C2×C3C3×B(4,𝔽2)11yescharacteristic
536D3—81no—
537C22—21no—
538C22—21no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—81no—
546C22—81no—
547C22—121no—
548C22—121no—
549C22—122no—
550C22—121no—
551C22—241no—
552C22C3×#93711yescharacteristic
553C4—21no—
554C4—41no—
555C4—41no—
556C4—121no—
557C4—121no—
558C4—121no—
559C4—241no—
560C4—241no—
561C3—21no—
562C3#7098511yescharacteristic, direct product factor
563C3C3×#220011yescharacteristic, complemented
564C2—21no—
565C2—41no—
566C2—41no—
567C2—81no—
568C2—81no—
569C2—241no—
570C2C3×#503211yescharacteristic
subgroupG/H
centerC2×C3#5032
commutator, cosocleC2×C3×D4C23×C3
FrattiniC2×D4C22×C3×D3
FittingC32×#453C2
socleC2×C32B(4,𝔽2)
hypercenterC3×#453D3
hypocenterC3C3×#2200
LCSG ▷ C2×C3×D4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#453

Complements

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

NH ≅ G/Ntype
1. C3×#5720C2semidirect
2. C32×#453C2semidirect
3. C3×#5244C2semidirect
4. C3×#5243C2semidirect
5. C3×#4545C2semidirect
6. C3×#4476C2semidirect
7. C3×#4475C2semidirect
9. #70985C3direct (N × H)
30. #5720C2×C3semidirect
34. C3×#453D3semidirect
35. C3×#453C2×C3semidirect
36. #5244C2×C3semidirect
37. #5243C2×C3semidirect
41. #4545C2×C3semidirect
42. #4476C2×C3semidirect
43. #4475C2×C3semidirect
52. C2×C32×D4D4semidirect
59. C22×C3×Dic3D4semidirect
63. C32×C42D4semidirect
70. C3×#217D4semidirect
160. #453C3×D3semidirect
193. C2×C3×D4#67semidirect
194. C2×C3×D4C3×D4semidirect
204. C22×Dic3C3×D4semidirect
230. C3×C42#67semidirect
231. C3×C42C3×D4semidirect
238. #217C3×D4semidirect
397. C2×D4C3×#67semidirect
419. C42C3×#67semidirect
482. C32#2200semidirect
562. C3#70985direct (N × H)
563. C3C3×#2200semidirect

Maximal subgroups

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

subgroupindex
C3×#57202
C32×#4532
C3×#52442
C3×#52432
C3×#45452
C3×#44762
C3×#44752
C3×#22003
#709853