Finite Group Databasebeta

← D4×C3⋊(#41⋊C3) #11923252

Subgroups — D4×C3⋊(#41⋊C3) #11923252

Order 1152.

831 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 831 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×C3⋊(#41⋊C3)C212yesmaximal, complemented
2C3×D4×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
3#5817⋊C3C212yesmaximal, complemented
4C4⋊(C3⋊(#41⋊C3))C211yesmaximal, characteristic, complemented
5C4×C3⋊(#41⋊C3)C211yesmaximal, characteristic, complemented
6D4×#239C311yesmaximal, characteristic, complemented
7D4×#41⋊C3—31nomaximal
8C22×C3×SL(2,𝔽3)C2212yescomplemented
9C2×C3⋊(#41⋊C3)—24no—
10C2×C3⋊(#41⋊C3)C2211yescharacteristic
11C2×C3⋊(#41⋊C3)C2212yescomplemented
12C3×D4×Dic3—41nomaximal
13C3×C4×SL(2,𝔽3)C2211yescharacteristic, complemented
14Dic3×SL(2,𝔽3)C2211yescharacteristic, complemented
15C22×#239C2×C312yescomplemented
16C22×#41⋊C3—32no—
17C3×D4×Q8C2×C311yescharacteristic
18#5817C2×C312yescomplemented
19#5726—31no—
20#5725—31no—
21#5630—32no—
22#5627—32no—
23#5577C2×C311yescharacteristic, complemented
24C4×#239C2×C311yescharacteristic, complemented
25D4×D12—31no—
26C4×D3×D4—31no—
27C4⋊(#41⋊C3)—31no—
28D4×SL(2,𝔽3)—21no—
29D4×SL(2,𝔽3)D311yescharacteristic, complemented
30#548⋊C3—32no—
31C4×#41⋊C3—31no—
32C2×C32×D4—41no—
33C22×C3×Dic3—42no—
34C2×C3×SL(2,𝔽3)—22no—
35C2×C3×SL(2,𝔽3)C2311yescharacteristic
36C3⋊(#41⋊C3)—22no—
37C3⋊(#41⋊C3)D412yesdirect product factor
38C3×#217—42no—
39C3×C4⋊Dic3—41no—
40C3×C4×Dic3—41no—
41D4×#41—31noSylow
42C22×C3×Q8C22×C312yes—
43C2×#239—24no—
44C2×#239—32no—
45C2×#239—32no—
46C2×#239—64no—
47C2×#239C22×C312yes—
48C2×#239C22×C311yescharacteristic
49C2×D3×D4—31no—
50C22×D12—32no—
51C22×C4×D3—32no—
52C2×#41⋊C3—31no—
53C2×#41⋊C3—32no—
54C2×#41⋊C3—64no—
55C22×SL(2,𝔽3)—22no—
56C22×SL(2,𝔽3)C2×D312yescomplemented
57C3×C4⋊Q8—31no—
58C3×C22⋊Q8—32no—
59C3×C4×Q8C22×C311yescharacteristic
60C3×C4×D4—31no—
61C3×C4×D4—121no—
62#947—32no—
63#946—32no—
64Q8×Dic3C22×C311yescharacteristic
65D4×Dic3A411yescharacteristic
66#930—32no—
67C4×#67—32no—
68#895—32no—
69#895—32no—
70#895—32no—
71#894—34no—
72#893—32no—
73#893—31no—
74#893—31no—
75#892—31no—
76D3×C4⋊C4—31no—
77#882—34no—
78#67⋊C4—32no—
79D3×C22⋊C4—32no—
80#874—31no—
81C4×D12—31no—
82C4×D12—31no—
83C42×D3—31no—
84C4×SL(2,𝔽3)—21no—
85C4×SL(2,𝔽3)—31no—
86C4×SL(2,𝔽3)C2×D311yescharacteristic, complemented
87C23×C32—42no—
88C32×D4—44no—
89C2×C32×C4—41no—
90C2×C3×Dic3—41no—
91C2×C3×Dic3—41no—
92C2×C3×Dic3—42no—
93C2×C3×Dic3—84no—
94C3×SL(2,𝔽3)C2×D411yescharacteristic, complemented
95C22×#41—32no—
96#550—31no—
97D4×Q8C3×D311yescharacteristic
98#548—32no—
99#547—91no—
100#546—92no—
101D42—91no—
102#532—91no—
103#525—92no—
104C4×#41—31no—
105C2×C4×D4—91no—
106C23×D3—32no—
107C2×C3×Q8—22no—
108C2×C3×Q8—32no—
109C2×C3×Q8—62no—
110C2×C3×Q8C23×C311yescharacteristic
111C2×C3×D4—41no—
112C2×C3×D4—81no—
113C2×C3×D4C2×A411yescharacteristic
114C22×C3×C4—32no—
115C22×C3×C4—122no—
116C2×#67—32no—
117C22×Dic3C2×A412yes—
118#239—22no—
119#239—32no—
120#239—64no—
121#239—64no—
122#239—64no—
123#239—64no—
124#239—62no—
125#239C3×D412yescomplemented
126D3×D4—64no—
127C2×D12—31no—
128C2×D12—32no—
129C2×D12—34no—
130C2×D12—31no—
131C2×D12—32no—
132C2×D12—64no—
133C2×D12—64no—
134C2×C4×D3—31no—
135C2×C4×D3—31no—
136C2×C4×D3—32no—
137C2×C4×D3—32no—
138C2×C4×D3—32no—
139C2×C4×D3—31no—
140C2×C4×D3—64no—
141C2×C4×D3—64no—
142#41⋊C3—32no—
143#41⋊C3—62no—
144C2×SL(2,𝔽3)—22no—
145C2×SL(2,𝔽3)—21no—
146C2×SL(2,𝔽3)—42no—
147C2×SL(2,𝔽3)C22×D311yescharacteristic
148C3×C4⋊C4—31no—
149C3×C4⋊C4—32no—
150C3×C4⋊C4—31no—
151C3×C4⋊C4—121no—
152C3×C22⋊C4—32no—
153C3×C22⋊C4—122no—
154C3×C42—31no—
155C3×C42—121no—
156#217C2×A412yes—
157(C2×D3)⋊C4—32no—
158(C2×D3)⋊C4—34no—
159(C2×D3)⋊C4—32no—
160(C2×D3)⋊C4—32no—
161C4⋊Dic3—31no—
162C4⋊Dic3C2×A411yescharacteristic
163Dic3⋊C4—32no—
164C4×Dic3—31no—
165C4×Dic3—31no—
166C4×Dic3C2×A411yescharacteristic
167C22×C32—44no—
168C22×C32—41no—
169C22×C32—82no—
170C22×C32—82no—
171C32×C4—42no—
172C3×Dic3—42no—
173C3×Dic3—81no—
174C3×Dic3—82no—
175C2×#41—31no—
176C2×#41—32no—
177C2×#41—64no—
178C2×#41—92no—
179C2×#41—92no—
180C2×#41—184no—
181C22×Q8C2×C3×D312yes—
182C22×D4—92no—
183C22×D4—91no—
184C23×C4—92no—
185C4⋊Q8—31no—
186#127—91no—
187#124—92no—
188#123—94no—
189C22⋊Q8—32no—
190C22⋊Q8—92no—
191#121—92no—
192#121—92no—
193#121—92no—
194#121—92no—
195#120—94no—
196C4×Q8—31no—
197C4×Q8C2×C3×D311yescharacteristic
198C4×D4—31no—
199C4×D4—31no—
200C4×D4—91no—
201C4×D4—91no—
202C4×D4—91no—
203C4×D4—92no—
204C4×D4—92no—
205C4×D4—92no—
206C4×D4—91no—
207#117—91no—
208C2×C4⋊C4—91no—
209C2×C22⋊C4—92no—
210C2×C42—91no—
211C23×C3—42no—
212C23×C3—82no—
213C23×C3C22×A412yes—
214C22×D3—31no—
215C22×D3—32no—
216C22×D3—64no—
217C22×D3—64no—
218C22×D3—122no—
219C3×Q8—31no—
220C3×Q8—62no—
221C3×Q8—62no—
222C3×Q8C2×C3×D411yescharacteristic
223C3×D4—44no—
224C3×D4—84no—
225C3×D4#41⋊C314yescomplemented
226C2×C3×C4—31no—
227C2×C3×C4—31no—
228C2×C3×C4—32no—
229C2×C3×C4—41no—
230C2×C3×C4—62no—
231C2×C3×C4—62no—
232C2×C3×C4—81no—
233C2×C3×C4—121no—
234C2×C3×C4—121no—
235C2×C3×C4—122no—
236C2×C3×C4—244no—
237C2×C3×C4C22×A411yescharacteristic
238#67—64no—
239C2×Dic3—24no—
240C2×Dic3—31no—
241C2×Dic3C22×A411yescharacteristic
242C2×Dic3C22×A412yes—
243C2×Dic3C22×A411yescharacteristic
244D12—32no—
245D12—32no—
246D12—62no—
247D12—62no—
248D12—68no—
249D12—62no—
250D12—122no—
251C4×D3—32no—
252C4×D3—32no—
253C4×D3—62no—
254C4×D3—62no—
255C4×D3—64no—
256C4×D3—62no—
257C4×D3—64no—
258C4×D3—121no—
259SL(2,𝔽3)—21no—
260SL(2,𝔽3)D3×D411yescharacteristic, complemented
261C2×C32—41no—
262C2×C32—41no—
263C2×C32—41no—
264C2×C32—84no—
265C24—92no—
266#41—32no—
267#41—62no—
268#41—92no—
269#41—184no—
270#41—184no—
271#41—184no—
272#41—184no—
273#41—182no—
274C2×Q8—22no—
275C2×Q8—32no—
276C2×Q8—62no—
277C2×Q8C22×C3×D311yescharacteristic
278C2×D4—91no—
279C2×D4—92no—
280C2×D4—94no—
281C2×D4—92no—
282C2×D4—92no—
283C2×D4—91no—
284C2×D4—184no—
285C2×D4—184no—
286C2×D4—184no—
287C2×D4D3×A411yescharacteristic
288C22×C4—32no—
289C22×C4—32no—
290C22×C4—91no—
291C22×C4—92no—
292C22×C4—92no—
293C22×C4—92no—
294C22×C4—91no—
295C22×C4—91no—
296C22×C4—184no—
297C22×C4—184no—
298C4⋊C4—31no—
299C4⋊C4—32no—
300C4⋊C4—31no—
301C4⋊C4—31no—
302C4⋊C4—92no—
303C4⋊C4—91no—
304C22⋊C4—32no—
305C22⋊C4—32no—
306C22⋊C4—92no—
307C22⋊C4—92no—
308C22⋊C4—92no—
309C22⋊C4—94no—
310C42—31no—
311C42—31no—
312C42—91no—
313C42—91no—
314C22×C3—22no—
315C22×C3—22no—
316C22×C3—44no—
317C22×C3—41no—
318C22×C3—82no—
319C22×C3—82no—
320C22×C3—84no—
321C22×C3—81no—
322C22×C3—162no—
323C22×C3—162no—
324C22×C3C2×#41⋊C314yescomplemented
325C22×C3C23×A411yescharacteristic
326C2×D3—32no—
327C2×D3—61no—
328C2×D3—61no—
329C2×D3—62no—
330C2×D3—62no—
331C2×D3—62no—
332C2×D3—128no—
333C3×C4—31no—
334C3×C4—31no—
335C3×C4—42no—
336C3×C4—62no—
337C3×C4—61no—
338C3×C4—82no—
339C3×C4—122no—
340C3×C4—242no—
341C3×C4—241no—
342C3×C4C2×#41⋊C312yescomplemented
343Dic3—22no—
344Dic3—21no—
345Dic3—61no—
346Dic3D4×A412yes—
347C32—41noSylow
348C23—91no—
349C23—92no—
350C23—184no—
351C23—184no—
352C23—362no—
353C23C2×D3×A412yes—
354Q8—31no—
355Q8—62no—
356Q8—62no—
357Q8C3×D3×D411yescharacteristic
358D4—92no—
359D4—92no—
360D4—182no—
361D4—182no—
362D4—188no—
363D4—184no—
364D4—182no—
365D4—362no—
366D4C3⋊(#41⋊C3)14yesdirect product factor
367C2×C4—31no—
368C2×C4—31no—
369C2×C4—31no—
370C2×C4—31no—
371C2×C4—32no—
372C2×C4—32no—
373C2×C4—62no—
374C2×C4—62no—
375C2×C4—64no—
376C2×C4—92no—
377C2×C4—92no—
378C2×C4—91no—
379C2×C4—182no—
380C2×C4—182no—
381C2×C4—184no—
382C2×C4—184no—
383C2×C4—182no—
384C2×C4—361no—
385C2×C4C2×D3×A411yescharacteristic
386C2×C3—24no—
387C2×C3—41no—
388C2×C3—41no—
389C2×C3—41no—
390C2×C3—84no—
391C2×C3—81no—
392C2×C3—81no—
393C2×C3—81no—
394C2×C3—164no—
395C2×C3C2×D4×A411yescharacteristic
396C2×C3C22×#41⋊C311yescharacteristic
397C2×C3#594511yescharacteristic
398D3—62no—
399D3—122no—
400C22—22no—
401C22—22no—
402C22—92no—
403C22—181no—
404C22—181no—
405C22—182no—
406C22—182no—
407C22—182no—
408C22—368no—
409C22C2×C3⋊(#41⋊C3)14yescomplemented
410C22C22×D3×A411yescharacteristic
411C4—31no—
412C4—31no—
413C4—32no—
414C4—62no—
415C4—62no—
416C4—61no—
417C4—61no—
418C4—181no—
419C4C2×C3⋊(#41⋊C3)12yescomplemented
420C3—41no—
421C3—81no—
422C3D4×#41⋊C311yescharacteristic, complemented
423C2—24no—
424C2—182no—
425C2—362no—
426C2D3×D4×A411yescharacteristic
427C2C22×C3⋊(#41⋊C3)11yescharacteristic
428C2#5968⋊C311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, cosocleC2×C3×Q8C23×C3
FittingC3×D4×Q8C2×C3
socleC22×C3C23×A4
hypercenterC2×D4D3×A4
hypocenterC3×Q8C2×C3×D4
LCSG ▷ C2×C3×Q8 ▷ C3×Q8
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3⋊(#41⋊C3)C2semidirect
2. C3×D4×SL(2,𝔽3)C2semidirect
3. #5817⋊C3C2semidirect
4. C4⋊(C3⋊(#41⋊C3))C2semidirect
5. C4×C3⋊(#41⋊C3)C2semidirect
6. D4×#239C3semidirect
8. C22×C3×SL(2,𝔽3)C22semidirect
11. C2×C3⋊(#41⋊C3)C22semidirect
13. C3×C4×SL(2,𝔽3)C22semidirect
14. Dic3×SL(2,𝔽3)C22semidirect
15. C22×#239C2×C3semidirect
18. #5817C2×C3semidirect
23. #5577C2×C3semidirect
24. C4×#239C2×C3semidirect
29. D4×SL(2,𝔽3)D3semidirect
37. C3⋊(#41⋊C3)D4direct (N × H)
56. C22×SL(2,𝔽3)C2×D3semidirect
86. C4×SL(2,𝔽3)C2×D3semidirect
94. C3×SL(2,𝔽3)C2×D4semidirect
125. #239C3×D4semidirect
225. C3×D4#41⋊C3semidirect
260. SL(2,𝔽3)D3×D4semidirect
324. C22×C3C2×#41⋊C3semidirect
342. C3×C4C2×#41⋊C3semidirect
366. D4C3⋊(#41⋊C3)direct (N × H)
409. C22C2×C3⋊(#41⋊C3)semidirect
419. C4C2×C3⋊(#41⋊C3)semidirect
422. C3D4×#41⋊C3semidirect

Maximal subgroups

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

subgroupindex
C22×C3⋊(#41⋊C3)2
C3×D4×SL(2,𝔽3)2
#5817⋊C32
C4⋊(C3⋊(#41⋊C3))2
C4×C3⋊(#41⋊C3)2
D4×#2393
D4×#41⋊C33
C3×D4×Dic34