Finite Group Databasebeta

← D3×C4⋊(#41⋊C3) #11923269

Subgroups — D3×C4⋊(#41⋊C3) #11923269

Order 1152.

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

normal subgroups only

This group has 843 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⋊C3)C211yesmaximal, characteristic, complemented
3#5834⋊C3C212yesmaximal, complemented
4C4×D3×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
5C4⋊(C3⋊(#41⋊C3))C211yesmaximal, characteristic, complemented
6D3×#550C311yesmaximal, characteristic, complemented
7C2×C4⋊(#41⋊C3)—31nomaximal
8C2×C3×#41⋊C3C2212yescomplemented
9D3×#41⋊C3—24no—
10C2×D3×SL(2,𝔽3)C2211yescharacteristic
11C2×C3⋊(#41⋊C3)C2212yescomplemented
12C3×D3×C4⋊C4—41nomaximal
13C3×C4×SL(2,𝔽3)C2211yescharacteristic, complemented
14Dic3×SL(2,𝔽3)C2211yescharacteristic, complemented
15C2×D3×#41C2×C312yes—
16C22×#41⋊C3—32no—
17C3×#550C2×C311yescharacteristic, complemented
18#5834C2×C312yescomplemented
19#5718—31no—
20D3×#127—31no—
21D3×#121—32no—
22#5599—32no—
23#5577C2×C311yescharacteristic, complemented
24C4×D3×Q8C2×C311yescharacteristic
25#5553—31no—
26C4×D3×D4—31no—
27C4⋊(#41⋊C3)—21no—
28C4⋊(#41⋊C3)—32no—
29C4⋊(#41⋊C3)—31no—
30C4⋊(#41⋊C3)D311yescharacteristic, direct product factor
31C2×C4×SL(2,𝔽3)—31no—
32C2×C3×C4×D3—41no—
33C2×C3×C4×D3—42no—
34C3×#41⋊C3—22no—
35C2×C3×SL(2,𝔽3)C2311yescharacteristic
36D3×SL(2,𝔽3)D412yescomplemented
37C3⋊(#41⋊C3)—22no—
38C32×C4⋊C4—41no—
39C3×C4⋊Dic3—41no—
40C3×Dic3⋊C4—42no—
41C2×#550—31noSylow
42C2×C3×#41C22×C312yes—
43D3×#41—24no—
44D3×#41—64no—
45C2×#239C22×C312yes—
46C2×D3×Q8C22×C311yescharacteristic
47C2×#237—32no—
48C2×D3×D4—32no—
49C2×D3×D4—32no—
50C2×D3×D4—31no—
51C2×#235—32no—
52C22×C4×D3—32no—
53C2×#41⋊C3—22no—
54C2×#41⋊C3—32no—
55C2×#41⋊C3—64no—
56C2×#41⋊C3C2×D312yescomplemented
57C22×SL(2,𝔽3)—31no—
58C3×#127—31no—
59C3×#121—32no—
60C3×C4×Q8C22×C311yescharacteristic
61C3×C4×D4—31no—
62C2×C3×C4⋊C4—121no—
63Q8×Dic3C22×C311yescharacteristic
64#940—32no—
65#940—32no—
66#940—32no—
67#939—34no—
68#938—32no—
69D4×Dic3—31no—
70#930—32no—
71C4×#67—32no—
72#895—32no—
73#893—31no—
74D3×C4⋊C4—31no—
75D3×C4⋊C4A411yescharacteristic
76#887—31no—
77#884—34no—
78#67⋊C4—32no—
79D3×C22⋊C4—32no—
80#874—31no—
81C4×D12—31no—
82C42×D3—31no—
83C4×Dic6—31no—
84C4×SL(2,𝔽3)—21no—
85C4×SL(2,𝔽3)—31no—
86C4×SL(2,𝔽3)C2×D311yescharacteristic, complemented
87C22×C3×D3—41no—
88C2×C32×C4—41no—
89C2×C32×C4—42no—
90C2×C3×Dic3—41no—
91C2×C3×Dic3—42no—
92C3×C4×D3—44no—
93C3×C4×D3—84no—
94C3×SL(2,𝔽3)C2×D411yescharacteristic, complemented
95C22×#41—32no—
96#550—32no—
97#550—31no—
98#550—91no—
99#550—92no—
100#550—91no—
101#550C3×D311yescharacteristic, complemented
102C2×#127—91no—
103C2×#121—92no—
104C2×C4×Q8—31no—
105C2×C4×D4—91no—
106C23×D3—32no—
107C3×#41—22no—
108C3×#41—62no—
109C2×C3×Q8C23×C311yescharacteristic
110C2×C3×D4—32no—
111C2×C3×D4—32no—
112C2×C3×D4—31no—
113C22×C3×C4—32no—
114C22×C3×C4—121no—
115C22×C3×C4—122no—
116C2×#67—34no—
117C2×#67—34no—
118C2×#67—32no—
119C22×Dic3—32no—
120#239—22no—
121#239—62no—
122D3×Q8—32no—
123D3×Q8C3×D412yes—
124#237—64no—
125#237—64no—
126D3×D4—64no—
127D3×D4—64no—
128D3×D4—64no—
129D3×D4—124no—
130#235—64no—
131#235—64no—
132C2×D12—32no—
133C2×D12—31no—
134C2×D12—32no—
135C2×C4×D3—31no—
136C2×C4×D3—31no—
137C2×C4×D3—32no—
138C2×C4×D3—32no—
139C2×C4×D3—64no—
140C2×C4×D3—64no—
141C2×C4×D3C2×A412yes—
142C2×C4×D3C2×A411yescharacteristic
143C2×Dic6—31no—
144#41⋊C3—22no—
145#41⋊C3—42no—
146#41⋊C3—62no—
147C2×SL(2,𝔽3)—21no—
148C2×SL(2,𝔽3)—32no—
149C2×SL(2,𝔽3)C22×D311yescharacteristic
150C3×C4⋊C4—31no—
151C3×C4⋊C4—41no—
152C3×C4⋊C4—81no—
153C3×C4⋊C4—122no—
154C3×C4⋊C4—121no—
155C3×C4⋊C4C2×A411yescharacteristic
156C3×C22⋊C4—32no—
157C3×C42—31no—
158#217—32no—
159(C2×D3)⋊C4—32no—
160(C2×D3)⋊C4—32no—
161C4⋊Dic3—31no—
162C4⋊Dic3C2×A411yescharacteristic
163Dic3⋊C4—32no—
164Dic3⋊C4C2×A412yes—
165C4×Dic3—31no—
166C4×Dic3—31no—
167C4×Dic3—31no—
168C22×C32—41no—
169C2×C3×D3—42no—
170C2×C3×D3—42no—
171C2×C3×D3—42no—
172C32×C4—42no—
173C32×C4—82no—
174C3×Dic3—42no—
175C3×Dic3—82no—
176C2×#41—32no—
177C2×#41—64no—
178C2×#41—92no—
179C2×#41—92no—
180C2×#41—184no—
181C2×#41C2×C3×D312yes—
182C22×Q8—31no—
183C22×D4—91no—
184C22×D4—92no—
185C22×D4—92no—
186C23×C4—92no—
187#127—31no—
188#127—91no—
189#127—92no—
190#127—92no—
191#127—92no—
192#121—32no—
193#121—94no—
194#121—94no—
195#121—92no—
196#121—92no—
197#121—92no—
198C4×Q8—31no—
199C4×Q8—91no—
200C4×Q8—91no—
201C4×Q8C2×C3×D311yescharacteristic
202C4×D4—31no—
203C4×D4—91no—
204C4×D4—92no—
205C4×D4—92no—
206C4×D4—91no—
207C4×D4—91no—
208C2×C4⋊C4—31no—
209C2×C4⋊C4—91no—
210C2×C22⋊C4—92no—
211C2×C42—91no—
212C23×C3—32no—
213C23×C3—121no—
214C22×D3—32no—
215C22×D3—64no—
216C22×D3—64no—
217C22×D3—64no—
218C22×D3C22×A411yescharacteristic
219C3×Q8—31no—
220C3×Q8C2×C3×D411yescharacteristic
221C3×D4—62no—
222C3×D4—62no—
223C3×D4—62no—
224C3×D4—122no—
225C2×C3×C4—31no—
226C2×C3×C4—31no—
227C2×C3×C4—41no—
228C2×C3×C4—42no—
229C2×C3×C4—62no—
230C2×C3×C4—62no—
231C2×C3×C4—81no—
232C2×C3×C4—82no—
233C2×C3×C4—124no—
234C2×C3×C4—121no—
235C2×C3×C4—122no—
236C2×C3×C4—244no—
237C2×C3×C4C22×A412yes—
238C2×C3×C4C22×A411yescharacteristic
239#67—68no—
240#67—64no—
241#67—124no—
242C2×Dic3—31no—
243C2×Dic3—31no—
244C2×Dic3—64no—
245C2×Dic3C22×A412yes—
246C2×Dic3C22×A411yescharacteristic
247D12—62no—
248D12—62no—
249D12—62no—
250D12—122no—
251C4×D3—24no—
252C4×D3—32no—
253C4×D3—32no—
254C4×D3—62no—
255C4×D3—62no—
256C4×D3—64no—
257C4×D3—62no—
258C4×D3#41⋊C314yescomplemented
259Dic6—32no—
260Dic6—32no—
261SL(2,𝔽3)—21no—
262SL(2,𝔽3)D3×D411yescharacteristic, complemented
263C2×C32—41no—
264C2×C32—41no—
265C2×C32—41no—
266C3×D3—44no—
267C24—92no—
268#41—22no—
269#41—62no—
270#41—62no—
271#41—184no—
272#41—184no—
273#41—184no—
274#41—184no—
275#41—182no—
276C2×Q8—32no—
277C2×Q8—91no—
278C2×Q8—92no—
279C2×Q8C22×C3×D311yescharacteristic
280C2×D4—32no—
281C2×D4—32no—
282C2×D4—31no—
283C2×D4—92no—
284C2×D4—92no—
285C2×D4—92no—
286C2×D4—94no—
287C2×D4—94no—
288C2×D4—91no—
289C2×D4—184no—
290C2×D4—184no—
291C2×D4—184no—
292C2×D4—364no—
293C22×C4—31no—
294C22×C4—32no—
295C22×C4—32no—
296C22×C4—92no—
297C22×C4—91no—
298C22×C4—91no—
299C22×C4—92no—
300C22×C4—92no—
301C22×C4—184no—
302C22×C4—184no—
303C4⋊C4—31no—
304C4⋊C4—32no—
305C4⋊C4—31no—
306C4⋊C4—91no—
307C4⋊C4—92no—
308C4⋊C4D3×A411yescharacteristic
309C22⋊C4—32no—
310C22⋊C4—92no—
311C22⋊C4—92no—
312C22⋊C4—92no—
313C42—31no—
314C42—91no—
315C42—91no—
316C42—91no—
317C22×C3—41no—
318C22×C3—62no—
319C22×C3—62no—
320C22×C3—62no—
321C22×C3—81no—
322C22×C3—122no—
323C22×C3—122no—
324C22×C3—122no—
325C22×C3C23×A411yescharacteristic
326C2×D3—62no—
327C2×D3—62no—
328C2×D3—62no—
329C2×D3—128no—
330C2×D3D4×A412yes—
331C2×D3C2×#41⋊C312yes—
332C2×D3#99412yes—
333C3×C4—22no—
334C3×C4—31no—
335C3×C4—31no—
336C3×C4—42no—
337C3×C4—61no—
338C3×C4—82no—
339C3×C4—82no—
340C3×C4—122no—
341C3×C4—162no—
342C3×C4—242no—
343C3×C4C2×#41⋊C312yescomplemented
344Dic3—22no—
345Dic3—32no—
346Dic3—61no—
347Dic3C2×#41⋊C312yescomplemented
348C32—41noSylow
349C23—31no—
350C23—32no—
351C23—92no—
352C23—184no—
353C23—184no—
354C23—184no—
355Q8—31no—
356Q8—92no—
357Q8—92no—
358Q8C3×D3×D411yescharacteristic
359D4—62no—
360D4—62no—
361D4—62no—
362D4—122no—
363D4—184no—
364D4—182no—
365D4—182no—
366D4—188no—
367D4—182no—
368D4—362no—
369D4—364no—
370C2×C4—31no—
371C2×C4—31no—
372C2×C4—34no—
373C2×C4—31no—
374C2×C4—32no—
375C2×C4—62no—
376C2×C4—62no—
377C2×C4—64no—
378C2×C4—92no—
379C2×C4—92no—
380C2×C4—91no—
381C2×C4—91no—
382C2×C4—184no—
383C2×C4—182no—
384C2×C4—182no—
385C2×C4—184no—
386C2×C4—182no—
387C2×C4C2×D3×A412yes—
388C2×C4C2×D3×A411yescharacteristic
389C2×C3—41no—
390C2×C3—41no—
391C2×C3—41no—
392C2×C3—81no—
393C2×C3—81no—
394C2×C3—81no—
395C2×C3—124no—
396C2×C3—122no—
397C2×C3C2×D4×A411yescharacteristic
398C2×C3C22×#41⋊C311yescharacteristic
399C2×C3C2×#99411yescharacteristic
400D3—122no—
401D3C4⋊(#41⋊C3)14yesdirect product factor
402C22—32no—
403C22—32no—
404C22—32no—
405C22—62no—
406C22—62no—
407C22—62no—
408C22—182no—
409C22—182no—
410C22—182no—
411C22—368no—
412C22C22×D3×A411yescharacteristic
413C4—22no—
414C4—31no—
415C4—31no—
416C4—32no—
417C4—62no—
418C4—61no—
419C4—92no—
420C4—181no—
421C4D3×#41⋊C312yescomplemented
422C3—41no—
423C3—81no—
424C3C2×C4⋊(#41⋊C3)11yescharacteristic, complemented
425C2—34no—
426C2—122no—
427C2—362no—
428C2D3×D4×A411yescharacteristic
429C2C2×D3×#41⋊C311yescharacteristic
430C2D3×#99411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, cosocleC2×C3×Q8C23×C3
FittingC3×#550C2×C3
socleC22×C3C23×A4
hypercenterC4⋊C4D3×A4
hypocenterC3×Q8C2×C3×D4
LCSG ▷ C2×C3×Q8 ▷ C3×Q8
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D3×#41⋊C3C2semidirect
2. C3×C4⋊(#41⋊C3)C2semidirect
3. #5834⋊C3C2semidirect
4. C4×D3×SL(2,𝔽3)C2semidirect
5. C4⋊(C3⋊(#41⋊C3))C2semidirect
6. D3×#550C3semidirect
8. C2×C3×#41⋊C3C22semidirect
11. C2×C3⋊(#41⋊C3)C22semidirect
13. C3×C4×SL(2,𝔽3)C22semidirect
14. Dic3×SL(2,𝔽3)C22semidirect
17. C3×#550C2×C3semidirect
18. #5834C2×C3semidirect
23. #5577C2×C3semidirect
30. C4⋊(#41⋊C3)D3direct (N × H)
36. D3×SL(2,𝔽3)D4semidirect
56. C2×#41⋊C3C2×D3semidirect
86. C4×SL(2,𝔽3)C2×D3semidirect
94. C3×SL(2,𝔽3)C2×D4semidirect
101. #550C3×D3semidirect
258. C4×D3#41⋊C3semidirect
262. SL(2,𝔽3)D3×D4semidirect
343. C3×C4C2×#41⋊C3semidirect
347. Dic3C2×#41⋊C3semidirect
401. D3C4⋊(#41⋊C3)direct (N × H)
421. C4D3×#41⋊C3semidirect
424. C3C2×C4⋊(#41⋊C3)semidirect

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⋊C3)2
#5834⋊C32
C4×D3×SL(2,𝔽3)2
C4⋊(C3⋊(#41⋊C3))2
D3×#5503
C2×C4⋊(#41⋊C3)3
C3×D3×C4⋊C44