Finite Group Databasebeta

← D3×#5427 #11922445

Subgroups — D3×#5427 #11922445

Order 1152.

755 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 755 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C2×D3×#41⋊C3C211yesmaximal, characteristic, complemented
2C2×D3×GL(2,𝔽3)C211yesmaximal, characteristic, complemented
3#10593661C211yesmaximal, characteristic, complemented
4C3×#5427C211yesmaximal, characteristic, complemented
5D3×#859C211yesmaximal, characteristic, complemented
6#10593206C211yesmaximal, characteristic, complemented
7#10593203C211yesmaximal, characteristic, complemented
8C2×#5427—31nomaximal
9D3×#449—31nomaximal
10C2×C3×#41⋊C3C2211yescharacteristic, complemented
11D3×#41⋊C3—22no—
12C2×D3×SL(2,𝔽3)C2211yescharacteristic
13C2×C3⋊(#41⋊C3)C2211yescharacteristic, complemented
14C2×C3⋊GL(2,𝔽3)C2211yescharacteristic, complemented
15C2×C3×GL(2,𝔽3)C2211yescharacteristic, complemented
16D3×GL(2,𝔽3)—22no—
17D3×(C2×D3)⋊C4—41nomaximal
18C3⋊#859C2211yescharacteristic, complemented
19C3×#859C2211yescharacteristic, complemented
20C2×D3×#41D311yescharacteristic, complemented
21C22×#41⋊C3—31no—
22C22×GL(2,𝔽3)—31no—
23C2×D3×SD16—31no—
24C2×D3×D8—31no—
25D3×#121—31no—
26#5427—31no—
27#5427—31no—
28#5427—31no—
29#5427—61no—
30#5427D311yescharacteristic, direct product factor
31C2×#859—31no—
32C3×#449—31no—
33#5238—31no—
34#5172—31no—
35#5158—31no—
36#5037—31no—
37#4810—31no—
38D3×#103—31no—
39#4781—31no—
40D3×#102—31no—
41#4734—31no—
42D3×C22⋊C8—31no—
43C22×D32—41no—
44C2×C3×C4×D3—41no—
45C3×#41⋊C3—21no—
46C2×C3×SL(2,𝔽3)C2311yescharacteristic
47C2×D3×Dic3—41no—
48D3×SL(2,𝔽3)D412yescomplemented
49C3⋊(#41⋊C3)—21no—
50C3⋊GL(2,𝔽3)—21no—
51C3×GL(2,𝔽3)—21no—
52#3752—41no—
53C3×(C2×D3)⋊C4—41no—
54#3722—41no—
55(C2×D3)⋊Dic3—41no—
56C2×#449—91noSylow
57C2×C3×#41C2×D311yescharacteristic, complemented
58D3×#41—22no—
59D3×#41—62no—
60C2×#239C2×D311yescharacteristic, complemented
61C2×D3×Q8C2×D311yescharacteristic
62C2×#237—31no—
63C2×D3×D4—31no—
64C2×D3×D4—31no—
65C2×D3×D4—61no—
66C2×#235—31no—
67C22×C4×D3—31no—
68C2×#41⋊C3—21no—
69C2×#41⋊C3—31no—
70C2×#41⋊C3—62no—
71C2×#41⋊C3C2×D311yescharacteristic, complemented
72C22×SL(2,𝔽3)—31no—
73C2×GL(2,𝔽3)—31no—
74C2×GL(2,𝔽3)—61no—
75C2×GL(2,𝔽3)—62no—
76C2×GL(2,𝔽3)C2×D311yescharacteristic, complemented
77C2×C3×SD16—31no—
78C2×C3×D8—31no—
79C3×#121—31no—
80C2×#215—31no—
81#939—61no—
82#938—31no—
83C2×#214—31no—
84C2×#213—31no—
85C2×#213—31no—
86#930—31no—
87C2×(C2×D3)⋊C4—121no—
88D3×SD16—62no—
89D3×SD16—62no—
90D3×D8—64no—
91C2×D24—31no—
92C2×#204—31no—
93C2×D3×C8—31no—
94C2×D3×C8—31no—
95#895—31no—
96D3×C4⋊C4—31no—
97#884—61no—
98D3×C22⋊C4—61no—
99#859—31no—
100#859—61no—
101#859C2×D311yescharacteristic, complemented
102C3×#103—31no—
103C3×#102—31no—
104C3×C22⋊C8—31no—
105#835—31no—
106#832—31no—
107#830—31no—
108#821—31no—
109(C2×D3)⋊C8—31no—
110(C2×D3)⋊C8—31no—
111#816—31no—
112#810—31no—
113#809—31no—
114C22×C3⋊D3—41no—
115C22×C3×D3—41no—
116C22×C3×D3—41no—
117C2×D32—44no—
118C2×D32—82no—
119C2×D32—82no—
120C2×C32×C4—41no—
121C2×C3⋊Dic3—41no—
122C2×C3×Dic3—41no—
123C2×C3×Dic3—41no—
124C3×C4×D3—82no—
125C3×SL(2,𝔽3)C2×D411yescharacteristic, complemented
126D3×Dic3—82no—
127C22×#41—31no—
128C22×SD16—91no—
129C22×D8—91no—
130C2×#121—91no—
131#449—31no—
132#449—91no—
133#449—91no—
134#449—91no—
135#449—91no—
136#449—91no—
137#449—91no—
138#449—91no—
139C2×#103—91no—
140C2×#102—91no—
141C2×C22⋊C8—91no—
142C23×D3—31no—
143C23×D3—61no—
144C23×D3—121no—
145C3×#41—21no—
146C3×#41—61no—
147C2×C3×Q8C22×D311yescharacteristic
148C2×C3×D4—31no—
149C2×C3×D4—31no—
150C2×C3×D4—61no—
151C22×C3×C4—31no—
152C22×C3×C4—121no—
153C2×#67—61no—
154C2×#67—61no—
155C2×#67—61no—
156C2×#67—61no—
157C22×Dic3—31no—
158C22×Dic3—121no—
159#239—21no—
160#239—61no—
161D3×Q8—32no—
162D3×Q8#6712yes—
163#237—62no—
164#237—62no—
165D3×D4—34no—
166D3×D4—62no—
167D3×D4—62no—
168D3×D4—62no—
169D3×D4—124no—
170#235—62no—
171#235—62no—
172C2×D12—31no—
173C2×D12—31no—
174C2×D12—61no—
175C2×C4×D3—31no—
176C2×C4×D3—31no—
177C2×C4×D3—31no—
178C2×C4×D3—62no—
179C2×C4×D3—62no—
180C2×C4×D3—61no—
181C2×C4×D3S411yescharacteristic
182C2×Dic6—31no—
183#41⋊C3—21no—
184#41⋊C3—41no—
185#41⋊C3—61no—
186C2×SL(2,𝔽3)—21no—
187C2×SL(2,𝔽3)—32no—
188C2×SL(2,𝔽3)C22×D311yescharacteristic
189GL(2,𝔽3)—21no—
190GL(2,𝔽3)—61no—
191GL(2,𝔽3)—121no—
192C3×SD16—61no—
193C3×SD16—61no—
194C3×D8—62no—
195C2×C3×C8—31no—
196C2×C3×C8—31no—
197C3×C4⋊C4—31no—
198C3×C22⋊C4—61no—
199#217—61no—
200#215—61no—
201#215—61no—
202#214—62no—
203#213—62no—
204#213—62no—
205(C2×D3)⋊C4—41no—
206(C2×D3)⋊C4—61no—
207(C2×D3)⋊C4—61no—
208(C2×D3)⋊C4—121no—
209(C2×D3)⋊C4—121no—
210(C2×D3)⋊C4—121no—
211(C2×D3)⋊C4—241no—
212C4⋊Dic3—31no—
213Dic3⋊C4—61no—
214C2×C3⋊C8—31no—
215C2×C3⋊C8—31no—
216D24—62no—
217#204—62no—
218D3×C8—62no—
219D3×C8—62no—
220C22×C32—41no—
221C2×C3⋊D3—42no—
222C2×C3⋊D3—81no—
223C2×C3⋊D3—81no—
224C2×C3×D3—42no—
225C2×C3×D3—42no—
226C2×C3×D3—42no—
227C2×C3×D3—42no—
228C2×C3×D3—81no—
229C2×C3×D3—81no—
230D32—88no—
231C32×C4—81no—
232C3⋊Dic3—81no—
233C3×Dic3—81no—
234C3×Dic3—81no—
235C2×#41—31no—
236C2×#41—62no—
237C2×#41—91no—
238C2×#41—91no—
239C2×#41—182no—
240C2×#41D3211yescharacteristic, complemented
241C22×Q8—31no—
242C22×D4—91no—
243C22×D4—91no—
244C22×D4—181no—
245C23×C4—91no—
246C2×SD16—31no—
247C2×SD16—91no—
248C2×SD16—91no—
249C2×SD16—91no—
250C2×SD16—182no—
251C2×SD16—182no—
252C2×D8—31no—
253C2×D8—91no—
254C2×D8—91no—
255C2×D8—91no—
256C2×D8—184no—
257C22×C8—91no—
258C22×C8—91no—
259#121—31no—
260#121—91no—
261#121—91no—
262#121—91no—
263#121—181no—
264#121—181no—
265C2×C4⋊C4—91no—
266C2×C22⋊C4—181no—
267#103—31no—
268#103—91no—
269#103—91no—
270#103—91no—
271#102—31no—
272#102—91no—
273#102—91no—
274#102—91no—
275C22⋊C8—31no—
276C22⋊C8—91no—
277C22⋊C8—91no—
278C22⋊C8—91no—
279C23×C3—31no—
280C23×C3—61no—
281C23×C3—121no—
282C22×D3—31no—
283C22×D3—41no—
284C22×D3—62no—
285C22×D3—62no—
286C22×D3—62no—
287C22×D3—61no—
288C22×D3—121no—
289C22×D3—124no—
290C22×D3—122no—
291C22×D3—122no—
292C22×D3—122no—
293C22×D3—241no—
294C22×D3—242no—
295C22×D3—242no—
296C22×D3C2×S411yescharacteristic
297C3×Q8—31no—
298C3×Q8C2×#6711yescharacteristic
299C3×D4—32no—
300C3×D4—61no—
301C3×D4—61no—
302C3×D4—61no—
303C3×D4—122no—
304C2×C3×C4—31no—
305C2×C3×C4—41no—
306C2×C3×C4—61no—
307C2×C3×C4—61no—
308C2×C3×C4—61no—
309C2×C3×C4—81no—
310C2×C3×C4—121no—
311C2×C3×C4—242no—
312C2×C3×C4C2×S411yescharacteristic
313#67—64no—
314#67—122no—
315#67—122no—
316#67—122no—
317C2×Dic3—31no—
318C2×Dic3—41no—
319C2×Dic3—62no—
320C2×Dic3—61no—
321C2×Dic3—121no—
322C2×Dic3—241no—
323C2×Dic3—242no—
324C2×Dic3C2×S411yescharacteristic
325D12—32no—
326D12—61no—
327D12—61no—
328D12—61no—
329D12—122no—
330C4×D3—22no—
331C4×D3—32no—
332C4×D3—32no—
333C4×D3—61no—
334C4×D3—61no—
335C4×D3—62no—
336C4×D3—122no—
337Dic6—32no—
338Dic6—61no—
339SL(2,𝔽3)—21no—
340SL(2,𝔽3)D3×D411yescharacteristic, complemented
341C3×C8—61no—
342C3×C8—61no—
343C3⋊C8—61no—
344C3⋊C8—61no—
345C2×C32—41no—
346C2×C32—41no—
347C2×C32—41no—
348C3⋊D3—82no—
349C3×D3—44no—
350C3×D3—82no—
351C24—91no—
352C24—181no—
353#41—21no—
354#41—61no—
355#41—61no—
356#41—182no—
357#41—182no—
358#41—182no—
359#41—182no—
360#41—181no—
361C2×Q8—32no—
362C2×Q8—91no—
363C2×Q8—92no—
364C2×Q8C2×D3211yescharacteristic
365C2×D4—31no—
366C2×D4—31no—
367C2×D4—61no—
368C2×D4—91no—
369C2×D4—91no—
370C2×D4—94no—
371C2×D4—181no—
372C2×D4—182no—
373C2×D4—182no—
374C2×D4—182no—
375C2×D4—181no—
376C2×D4—181no—
377C2×D4—181no—
378C2×D4—181no—
379C2×D4—364no—
380C22×C4—31no—
381C22×C4—31no—
382C22×C4—91no—
383C22×C4—91no—
384C22×C4—91no—
385C22×C4—91no—
386C22×C4—182no—
387C22×C4—182no—
388C22×C4—181no—
389SD16—61no—
390SD16—61no—
391SD16—182no—
392SD16—182no—
393SD16—181no—
394SD16—181no—
395D8—62no—
396D8—182no—
397D8—182no—
398D8—182no—
399C2×C8—31no—
400C2×C8—31no—
401C2×C8—91no—
402C2×C8—91no—
403C2×C8—182no—
404C2×C8—182no—
405C4⋊C4—31no—
406C4⋊C4—91no—
407C4⋊C4—181no—
408C22⋊C4—61no—
409C22⋊C4—181no—
410C22⋊C4—181no—
411C22⋊C4—181no—
412C22×C3—41no—
413C22×C3—61no—
414C22×C3—61no—
415C22×C3—61no—
416C22×C3—81no—
417C22×C3—122no—
418C22×C3—122no—
419C22×C3—122no—
420C22×C3—121no—
421C22×C3—121no—
422C22×C3—121no—
423C22×C3C22×S411yescharacteristic
424C2×D3—42no—
425C2×D3—61no—
426C2×D3—61no—
427C2×D3—61no—
428C2×D3—81no—
429C2×D3—81no—
430C2×D3—124no—
431C2×D3—122no—
432C2×D3—121no—
433C2×D3—121no—
434C2×D3—121no—
435C2×D3—241no—
436C2×D3—241no—
437C2×D3—242no—
438C2×D3—248no—
439C2×D3—244no—
440C2×D3—481no—
441C2×D3—481no—
442C2×D3#98512yes—
443C2×D3#98612yes—
444C2×D3GL(2,ℤ/4)12yes—
445C3×C4—21no—
446C3×C4—31no—
447C3×C4—31no—
448C3×C4—81no—
449C3×C4—121no—
450C3×C4—161no—
451C3×C4—241no—
452Dic3—21no—
453Dic3—32no—
454Dic3—81no—
455Dic3—121no—
456Dic3—241no—
457Dic3—481no—
458C32—41noSylow
459C23—31no—
460C23—31no—
461C23—61no—
462C23—91no—
463C23—182no—
464C23—182no—
465C23—182no—
466C23—181no—
467C23—362no—
468C23—362no—
469C23—362no—
470Q8—31no—
471Q8—92no—
472Q8—181no—
473Q8D3×#6711yescharacteristic
474D4—32no—
475D4—61no—
476D4—61no—
477D4—61no—
478D4—92no—
479D4—122no—
480D4—181no—
481D4—181no—
482D4—181no—
483D4—184no—
484D4—362no—
485D4—362no—
486D4—362no—
487D4—362no—
488C2×C4—31no—
489C2×C4—31no—
490C2×C4—61no—
491C2×C4—61no—
492C2×C4—62no—
493C2×C4—61no—
494C2×C4—92no—
495C2×C4—92no—
496C2×C4—91no—
497C2×C4—182no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—182no—
501C2×C4—181no—
502C2×C4—362no—
503C2×C4D3×S411yescharacteristic
504C8—61no—
505C8—61no—
506C8—181no—
507C8—181no—
508C2×C3—41no—
509C2×C3—41no—
510C2×C3—41no—
511C2×C3—81no—
512C2×C3—81no—
513C2×C3—81no—
514C2×C3—124no—
515C2×C3—121no—
516C2×C3—241no—
517C2×C3C2×#98511yescharacteristic
518C2×C3C2×#98611yescharacteristic
519C2×C3C2×GL(2,ℤ/4)11yescharacteristic
520D3—82no—
521D3—121no—
522D3—242no—
523D3—241no—
524D3—482no—
525D3#542714yesdirect product factor
526C22—32no—
527C22—32no—
528C22—32no—
529C22—61no—
530C22—61no—
531C22—61no—
532C22—121no—
533C22—121no—
534C22—121no—
535C22—181no—
536C22—181no—
537C22—181no—
538C22—364no—
539C22—361no—
540C22—361no—
541C22—361no—
542C22—724no—
543C22C2×D3×S411yescharacteristic
544C4—21no—
545C4—31no—
546C4—31no—
547C4—61no—
548C4—92no—
549C4—121no—
550C4—361no—
551C3—41no—
552C3—81no—
553C3C2×#542711yescharacteristic, complemented
554C2—34no—
555C2—121no—
556C2—241no—
557C2—361no—
558C2—721no—
559C2D3×#98511yescharacteristic
560C2D3×#98611yescharacteristic
561C2D3×GL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutator, cosocleC2×C3×SL(2,𝔽3)C23
FittingC2×C3×#41C2×D3
socleC22×C3C22×S4
hypercenterC2×C4D3×S4
hypocenterC3×SL(2,𝔽3)C2×D4
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×D3×#41⋊C3C2semidirect
2. C2×D3×GL(2,𝔽3)C2semidirect
3. #10593661C2semidirect
4. C3×#5427C2semidirect
5. D3×#859C2semidirect
6. #10593206C2semidirect
7. #10593203C2semidirect
10. C2×C3×#41⋊C3C22semidirect
13. C2×C3⋊(#41⋊C3)C22semidirect
14. C2×C3⋊GL(2,𝔽3)C22semidirect
15. C2×C3×GL(2,𝔽3)C22semidirect
18. C3⋊#859C22semidirect
19. C3×#859C22semidirect
20. C2×D3×#41D3semidirect
30. #5427D3direct (N × H)
48. D3×SL(2,𝔽3)D4semidirect
57. C2×C3×#41C2×D3semidirect
60. C2×#239C2×D3semidirect
71. C2×#41⋊C3C2×D3semidirect
76. C2×GL(2,𝔽3)C2×D3semidirect
101. #859C2×D3semidirect
125. C3×SL(2,𝔽3)C2×D4semidirect
240. C2×#41D32semidirect
340. SL(2,𝔽3)D3×D4semidirect
525. D3#5427direct (N × H)
553. C3C2×#5427semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#41⋊C32
C2×D3×GL(2,𝔽3)2
#105936612
C3×#54272
D3×#8592
#105932062
#105932032
C2×#54273
D3×#4493
D3×(C2×D3)⋊C44