Finite Group Databasebeta

← D12×#41⋊C3 #11923202

Subgroups — D12×#41⋊C3 #11923202

Order 1152.

819 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 819 conjugacy classes of subgroups — too many to draw. Only its 99 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⋊C3C212yesmaximal, complemented
2C3×C4×#41⋊C3C211yesmaximal, characteristic, complemented
3#5576⋊C3C212yesmaximal, complemented
4SL(2,𝔽3)×D12C211yesmaximal, characteristic, complemented
5C4⋊(C3⋊(#41⋊C3))C211yesmaximal, characteristic, complemented
6#41×D12C311yesmaximal, characteristic, complemented
7D4×#41⋊C3—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9D3×#41⋊C3—24no—
10C2×D3×SL(2,𝔽3)C2212yescomplemented
11C2×C3⋊(#41⋊C3)C2212yescomplemented
12C3×C4×D12—41nomaximal
13C3×C4×SL(2,𝔽3)C2211yescharacteristic, complemented
14C3×C4×SL(2,𝔽3)C2211yescharacteristic, complemented
15C2×D3×#41C2×C312yescomplemented
16C22×#41⋊C3—32no—
17C3×C4×#41C2×C311yescharacteristic, complemented
18#5577C2×C311yescharacteristic, complemented
19#5576C2×C312yescomplemented
20Q8×D12C2×C311yescharacteristic
21#5555—31no—
22#5554—32no—
23D4×D12—31no—
24#5524—32no—
25#5477—31no—
26C2×C4×D12—31no—
27C4⋊(#41⋊C3)—31no—
28D4×SL(2,𝔽3)—31no—
29#548⋊C3—32no—
30C4×#41⋊C3—21no—
31C4×#41⋊C3D311yescharacteristic, complemented
32C2×C3×D12—41no—
33C2×C3×C4×D3—42no—
34C3×#41⋊C3D412yescomplemented
35C2×C3×SL(2,𝔽3)C2311yescharacteristic
36D3×SL(2,𝔽3)—22no—
37C3⋊(#41⋊C3)—22no—
38C32×C42—41no—
39C3×(C2×D3)⋊C4—42no—
40C3×C4⋊Dic3—41no—
41D4×#41—31noSylow
42C2×C3×#41C22×C311yescharacteristic
43D3×#41—24no—
44D3×#41—64no—
45C2×#239C22×C312yes—
46C2×D3×Q8C22×C312yes—
47C2×#237—32no—
48C2×D3×D4—32no—
49C2×#235—32no—
50C22×D12—31no—
51C22×C4×D3—32no—
52C2×#41⋊C3—21no—
53C2×#41⋊C3—32no—
54C2×#41⋊C3—64no—
55C2×#41⋊C3C2×D311yescharacteristic
56C22×SL(2,𝔽3)—32no—
57C3×C4×Q8C22×C311yescharacteristic
58C3×C4×Q8C22×C311yescharacteristic
59C3×C4×D4—31no—
60C3×C4×D4—31no—
61C3×C4×D4—121no—
62C3×#117—31no—
63C2×C3×C42—31no—
64#930—32no—
65#930—32no—
66C2×(C2×D3)⋊C4—32no—
67C2×C4⋊Dic3—31no—
68#897—32no—
69#897—32no—
70#895—32no—
71#895—32no—
72#886—34no—
73#882—34no—
74#875—32no—
75#874—31no—
76C4×D12—32no—
77C4×D12—31no—
78C4×D12—32no—
79C4×D12—31no—
80C4×D12—32no—
81C4×D12—31no—
82C4×D12A411yescharacteristic
83#869—31no—
84C4×SL(2,𝔽3)—21no—
85C4×SL(2,𝔽3)—21no—
86C4×SL(2,𝔽3)C2×D311yescharacteristic, complemented
87C4×SL(2,𝔽3)C2×D311yescharacteristic, complemented
88C22×C3×D3—42no—
89C2×C32×C4—41no—
90C2×C32×C4—41no—
91C2×C32×C4—41no—
92C2×C3×Dic3—42no—
93C3×D12—44no—
94C3×C4×D3—84no—
95C3×SL(2,𝔽3)C2×D411yescharacteristic, complemented
96C22×#41—32no—
97#550—31no—
98D4×Q8—31no—
99#548—32no—
100#547—91no—
101#546—92no—
102D42—91no—
103#532—91no—
104#525—92no—
105C4×#41C3×D311yescharacteristic, complemented
106C2×C4×D4—91no—
107C23×D3—32no—
108C3×#41—32no—
109C3×#41C3×D412yescomplemented
110C2×C3×Q8C23×C311yescharacteristic
111C2×C3×D4—31no—
112C2×C3×D4—121no—
113C22×C3×C4—31no—
114C22×C3×C4—31no—
115C22×C3×C4—31no—
116C22×C3×C4—122no—
117C2×#67—34no—
118C22×Dic3—32no—
119#239—22no—
120#239—62no—
121D3×Q8—22no—
122D3×Q8—62no—
123#237—64no—
124#237—64no—
125D3×D4—64no—
126D3×D4—64no—
127#235—64no—
128#235—64no—
129C2×D12—32no—
130C2×D12—32no—
131C2×D12—31no—
132C2×D12—32no—
133C2×D12—64no—
134C2×D12C2×A411yescharacteristic
135C2×C4×D3—32no—
136C2×C4×D3—32no—
137C2×C4×D3—32no—
138C2×C4×D3—64no—
139C2×C4×D3—64no—
140C2×C4×D3C2×A412yes—
141C2×Dic6—32no—
142#41⋊C3—22no—
143#41⋊C3—62no—
144#41⋊C3D1212yesdirect product factor
145C2×SL(2,𝔽3)—21no—
146C2×SL(2,𝔽3)—62no—
147C2×SL(2,𝔽3)C22×D311yescharacteristic
148C3×C4⋊C4—31no—
149C3×C4⋊C4—31no—
150C3×C4⋊C4—121no—
151C3×C22⋊C4—32no—
152C3×C22⋊C4—122no—
153C3×C42—31no—
154C3×C42—31no—
155C3×C42—31no—
156C3×C42—41no—
157C3×C42—81no—
158C3×C42C2×A411yescharacteristic
159(C2×D3)⋊C4—34no—
160(C2×D3)⋊C4—32no—
161(C2×D3)⋊C4—32no—
162(C2×D3)⋊C4—32no—
163(C2×D3)⋊C4C2×A412yes—
164C4⋊Dic3—32no—
165C4⋊Dic3—31no—
166C4⋊Dic3—32no—
167C4⋊Dic3C2×A411yescharacteristic
168C22×C32—41no—
169C2×C3×D3—44no—
170C2×C3×D3—82no—
171C2×C3×D3—82no—
172C32×C4—42no—
173C32×C4—42no—
174C32×C4—81no—
175C3×Dic3—82no—
176C2×#41—32no—
177C2×#41—64no—
178C2×#41—92no—
179C2×#41—92no—
180C2×#41—184no—
181C2×#41C2×C3×D311yescharacteristic
182C22×Q8—32no—
183C22×D4—91no—
184C22×D4—92no—
185C23×C4—92no—
186C4⋊Q8—91no—
187#127—91no—
188#124—92no—
189#123—94no—
190C22⋊Q8—92no—
191C22⋊Q8—92no—
192#121—92no—
193#121—92no—
194#121—92no—
195#121—92no—
196#120—94no—
197C4×Q8C2×C3×D311yescharacteristic
198C4×Q8C2×C3×D311yescharacteristic
199C4×D4—31no—
200C4×D4—31no—
201C4×D4—31no—
202C4×D4—92no—
203C4×D4—91no—
204C4×D4—92no—
205C4×D4—91no—
206C4×D4—92no—
207C4×D4—91no—
208#117—31no—
209C2×C4⋊C4—91no—
210C2×C22⋊C4—92no—
211C2×C42—31no—
212C23×C3—31no—
213C23×C3—122no—
214C22×D3—32no—
215C22×D3—64no—
216C22×D3—64no—
217C22×D3—122no—
218C22×D3C22×A412yes—
219C3×Q8—31no—
220C3×Q8C2×C3×D411yescharacteristic
221C3×D4—32no—
222C3×D4—32no—
223C3×D4—124no—
224C2×C3×C4—31no—
225C2×C3×C4—32no—
226C2×C3×C4—32no—
227C2×C3×C4—31no—
228C2×C3×C4—31no—
229C2×C3×C4—41no—
230C2×C3×C4—41no—
231C2×C3×C4—41no—
232C2×C3×C4—62no—
233C2×C3×C4—81no—
234C2×C3×C4—81no—
235C2×C3×C4—81no—
236C2×C3×C4—122no—
237C2×C3×C4—121no—
238C2×C3×C4—244no—
239C2×C3×C4C22×A411yescharacteristic
240C2×C3×C4C22×A411yescharacteristic
241C2×C3×C4C22×A411yescharacteristic
242#67—68no—
243C2×Dic3—32no—
244C2×Dic3—64no—
245C2×Dic3C22×A412yes—
246D12—62no—
247D12—62no—
248D12—64no—
249D12—62no—
250D12—122no—
251D12#41⋊C314yesdirect product factor
252C4×D3—24no—
253C4×D3—62no—
254C4×D3—62no—
255C4×D3—62no—
256C4×D3—62no—
257C4×D3—64no—
258Dic6—62no—
259Dic6—62no—
260SL(2,𝔽3)—21no—
261SL(2,𝔽3)C2×D1211yescharacteristic, complemented
262C2×C32—41no—
263C2×C32—41no—
264C2×C32—41no—
265C3×D3—84no—
266C24—92no—
267#41—32no—
268#41—62no—
269#41—184no—
270#41—184no—
271#41—184no—
272#41—184no—
273#41—182no—
274#41C3×D1212yescomplemented
275C2×Q8—62no—
276C2×Q8—92no—
277C2×Q8—182no—
278C2×Q8C22×C3×D311yescharacteristic
279C2×D4—31no—
280C2×D4—31no—
281C2×D4—92no—
282C2×D4—92no—
283C2×D4—92no—
284C2×D4—94no—
285C2×D4—91no—
286C2×D4—184no—
287C2×D4—184no—
288C2×D4—184no—
289C22×C4—31no—
290C22×C4—31no—
291C22×C4—32no—
292C22×C4—31no—
293C22×C4—92no—
294C22×C4—92no—
295C22×C4—92no—
296C22×C4—92no—
297C22×C4—184no—
298C22×C4—184no—
299C4⋊C4—31no—
300C4⋊C4—31no—
301C4⋊C4—31no—
302C4⋊C4—92no—
303C4⋊C4—92no—
304C4⋊C4—91no—
305C22⋊C4—32no—
306C22⋊C4—32no—
307C22⋊C4—92no—
308C22⋊C4—92no—
309C22⋊C4—94no—
310C22⋊C4—92no—
311C42—31no—
312C42—31no—
313C42—31no—
314C42D3×A411yescharacteristic
315C22×C3—32no—
316C22×C3—41no—
317C22×C3—61no—
318C22×C3—61no—
319C22×C3—81no—
320C22×C3—124no—
321C22×C3—242no—
322C22×C3—242no—
323C22×C3C23×A411yescharacteristic
324C2×D3—22no—
325C2×D3—22no—
326C2×D3—62no—
327C2×D3—62no—
328C2×D3—62no—
329C2×D3—128no—
330C2×D3C2×#41⋊C314yescomplemented
331C3×C4—21no—
332C3×C4—31no—
333C3×C4—31no—
334C3×C4—42no—
335C3×C4—42no—
336C3×C4—61no—
337C3×C4—61no—
338C3×C4—81no—
339C3×C4—82no—
340C3×C4—82no—
341C3×C4—82no—
342C3×C4—242no—
343C3×C4D4×A412yes—
344C3×C4C2×#41⋊C312yescomplemented
345Dic3—22no—
346Dic3—62no—
347C32—41noSylow
348C23—31no—
349C23—32no—
350C23—92no—
351C23—184no—
352C23—184no—
353C23—362no—
354Q8—31no—
355Q8—182no—
356Q8—182no—
357Q8C2×C3×D1211yescharacteristic
358D4—32no—
359D4—32no—
360D4—34no—
361D4—182no—
362D4—182no—
363D4—184no—
364D4—188no—
365D4—182no—
366D4—362no—
367C2×C4—31no—
368C2×C4—32no—
369C2×C4—32no—
370C2×C4—31no—
371C2×C4—31no—
372C2×C4—32no—
373C2×C4—64no—
374C2×C4—62no—
375C2×C4—92no—
376C2×C4—121no—
377C2×C4—182no—
378C2×C4—182no—
379C2×C4—182no—
380C2×C4—182no—
381C2×C4—184no—
382C2×C4—184no—
383C2×C4C2×D3×A411yescharacteristic
384C2×C4C2×D3×A411yescharacteristic
385C2×C4C2×D3×A411yescharacteristic
386C2×C3—41no—
387C2×C3—41no—
388C2×C3—41no—
389C2×C3—62no—
390C2×C3—81no—
391C2×C3—81no—
392C2×C3—81no—
393C2×C3—244no—
394C2×C3C2×D4×A411yescharacteristic
395C2×C3C22×#41⋊C311yescharacteristic
396C2×C3#594511yescharacteristic
397D3—24no—
398D3—122no—
399C22—32no—
400C22—34no—
401C22—62no—
402C22—61no—
403C22—61no—
404C22—62no—
405C22—182no—
406C22—182no—
407C22—182no—
408C22—368no—
409C22C22×D3×A411yescharacteristic
410C4—21no—
411C4—31no—
412C4—31no—
413C4—62no—
414C4—61no—
415C4—61no—
416C4—182no—
417C4A4×D1212yes—
418C4D3×#41⋊C312yescomplemented
419C3—41no—
420C3—81no—
421C3D4×#41⋊C311yescharacteristic, complemented
422C2—62no—
423C2—64no—
424C2—362no—
425C2C2×A4×D1211yescharacteristic
426C2C2×D3×#41⋊C311yescharacteristic
427C2#5964⋊C311yescharacteristic
subgroupG/H
centerC2×C4C2×D3×A4
commutator, cosocleC2×C3×Q8C23×C3
FrattiniC22C22×D3×A4
FittingC3×C4×#41C2×C3
socleC22×C3C23×A4
hypercenterC42D3×A4
hypocenterC3×Q8C2×C3×D4
LCSG ▷ C2×C3×Q8 ▷ C3×Q8
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C2×D3×#41⋊C3C2semidirect
2. C3×C4×#41⋊C3C2semidirect
3. #5576⋊C3C2semidirect
4. SL(2,𝔽3)×D12C2semidirect
5. C4⋊(C3⋊(#41⋊C3))C2semidirect
6. #41×D12C3semidirect
10. C2×D3×SL(2,𝔽3)C22semidirect
11. C2×C3⋊(#41⋊C3)C22semidirect
13. C3×C4×SL(2,𝔽3)C22semidirect
14. C3×C4×SL(2,𝔽3)C22semidirect
15. C2×D3×#41C2×C3semidirect
17. C3×C4×#41C2×C3semidirect
18. #5577C2×C3semidirect
19. #5576C2×C3semidirect
31. C4×#41⋊C3D3semidirect
34. C3×#41⋊C3D4semidirect
86. C4×SL(2,𝔽3)C2×D3semidirect
87. C4×SL(2,𝔽3)C2×D3semidirect
95. C3×SL(2,𝔽3)C2×D4semidirect
105. C4×#41C3×D3semidirect
109. C3×#41C3×D4semidirect
144. #41⋊C3D12direct (N × H)
251. D12#41⋊C3direct (N × H)
261. SL(2,𝔽3)C2×D12semidirect
274. #41C3×D12semidirect
330. C2×D3C2×#41⋊C3semidirect
344. C3×C4C2×#41⋊C3semidirect
418. C4D3×#41⋊C3semidirect
421. C3D4×#41⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#41⋊C32
C3×C4×#41⋊C32
#5576⋊C32
SL(2,𝔽3)×D122
C4⋊(C3⋊(#41⋊C3))2
#41×D123
D4×#41⋊C33
C3×C4×D124