Finite Group Databasebeta

← D3×#520⋊C3 #11923223

Subgroups — D3×#520⋊C3 #11923223

Order 1152.

811 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 811 conjugacy classes of subgroups — too many to draw. Only its 119 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
2C3×#520⋊C3C211yesmaximal, characteristic, complemented
3#5827⋊C3C211yesmaximal, characteristic, complemented
4C4×D3×SL(2,𝔽3)C212yesmaximal, complemented
5#5574⋊C3C212yesmaximal, complemented
6D3×#520C311yesmaximal, characteristic, complemented
7C2×#520⋊C3—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9D3×#41⋊C3C414yescomplemented
10C2×D3×SL(2,𝔽3)C2211yescharacteristic
11C2×C3⋊(#41⋊C3)C2211yescharacteristic
12C3×D3×C4⋊C4—41nomaximal
13C3×C4×SL(2,𝔽3)C2212yescomplemented
14Dic3×SL(2,𝔽3)C2212yescomplemented
15C2×D3×#41C2×C311yescharacteristic
16C22×#41⋊C3—31no—
17C3×#520C2×C311yescharacteristic, complemented
18#5827C2×C311yescharacteristic, complemented
19#5574C2×C312yescomplemented
20C4×D3×Q8C2×C312yes—
21#5546—32no—
22C4×D3×D4—32no—
23#5523—31no—
24D3×#117—31no—
25#5504—31no—
26C2×D3×C4⋊C4—31no—
27#520⋊C3—21no—
28#520⋊C3—31no—
29#520⋊C3—32no—
30#520⋊C3D311yescharacteristic, direct product factor
31C2×C4×SL(2,𝔽3)—32no—
32C2×C3×C4×D3—41no—
33C2×C3×C4×D3—42no—
34C3×#41⋊C3C2×C412yescomplemented
35C2×C3×SL(2,𝔽3)C2311yescharacteristic
36D3×SL(2,𝔽3)C2×C412yescomplemented
37C3⋊(#41⋊C3)C2×C412yescomplemented
38C32×C4⋊C4—41no—
39C3×C4⋊Dic3—41no—
40C3×Dic3⋊C4—42no—
41C2×#520—31noSylow
42C2×C3×#41C22×C311yescharacteristic
43D3×#41—34no—
44D3×#41C3×C414yescomplemented
45C2×#239C22×C311yescharacteristic
46C2×D3×Q8C22×C311yescharacteristic
47C2×#237—31no—
48C2×D3×D4—31no—
49C2×#235—31no—
50C22×C4×D3—31no—
51C22×C4×D3—32no—
52C2×#41⋊C3—21no—
53C2×#41⋊C3—34no—
54C2×#41⋊C3—31no—
55C2×#41⋊C3C2×D311yescharacteristic
56C22×SL(2,𝔽3)—31no—
57C3×C4×Q8C22×C312yes—
58C3×C4×D4—32no—
59C3×#117—31no—
60C2×C3×C4⋊C4—31no—
61C2×C3×C4⋊C4—121no—
62Q8×Dic3C22×C312yes—
63D4×Dic3—32no—
64C4×#67—34no—
65#926—31no—
66C2×C4⋊Dic3—31no—
67C2×Dic3⋊C4—32no—
68#893—32no—
69#892—31no—
70#892—31no—
71D3×C4⋊C4—32no—
72D3×C4⋊C4—32no—
73D3×C4⋊C4—31no—
74D3×C4⋊C4—32no—
75D3×C4⋊C4A411yescharacteristic
76#887—32no—
77#67⋊C4—34no—
78D3×C22⋊C4—32no—
79#877—32no—
80C4×D12—32no—
81#872—32no—
82C42×D3—32no—
83C4×Dic6—32no—
84C4×SL(2,𝔽3)—22no—
85C4×SL(2,𝔽3)—32no—
86C4×SL(2,𝔽3)C2×D312yescomplemented
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)C22×C411yescharacteristic, complemented
95C22×#41—31no—
96#520—31no—
97#520—32no—
98#520—91no—
99#520—91no—
100#520—92no—
101#520C3×D311yescharacteristic, complemented
102C2×C4×Q8—32no—
103C2×C4×D4—92no—
104C2×#117—91no—
105C22×C4⋊C4—91no—
106C23×D3—31no—
107C3×#41—32no—
108C3×#41C2×C3×C412yescomplemented
109C2×C3×Q8C23×C311yescharacteristic
110C2×C3×D4—31no—
111C22×C3×C4—31no—
112C22×C3×C4—32no—
113C22×C3×C4—121no—
114C22×C3×C4—122no—
115C2×#67—32no—
116C22×Dic3—31no—
117C22×Dic3—32no—
118#239—32no—
119#239C2×C3×C412yescomplemented
120D3×Q8—32no—
121D3×Q8C2×C3×C412yes—
122#237—34no—
123#237—34no—
124D3×D4—34no—
125D3×D4—34no—
126#235—34no—
127#235—34no—
128C2×D12—31no—
129C2×C4×D3—31no—
130C2×C4×D3—31no—
131C2×C4×D3—31no—
132C2×C4×D3—34no—
133C2×C4×D3—34no—
134C2×C4×D3—32no—
135C2×C4×D3—34no—
136C2×C4×D3—124no—
137C2×C4×D3C2×A412yes—
138C2×C4×D3C2×A411yescharacteristic
139C2×Dic6—31no—
140#41⋊C3—22no—
141#41⋊C3—32no—
142#41⋊C3C4×D312yescomplemented
143C2×SL(2,𝔽3)—21no—
144C2×SL(2,𝔽3)—32no—
145C2×SL(2,𝔽3)C22×D311yescharacteristic
146C3×C4⋊C4—32no—
147C3×C4⋊C4—31no—
148C3×C4⋊C4—41no—
149C3×C4⋊C4—81no—
150C3×C4⋊C4—122no—
151C3×C4⋊C4—121no—
152C3×C4⋊C4C2×A411yescharacteristic
153C3×C22⋊C4—32no—
154C3×C42—32no—
155#217—32no—
156(C2×D3)⋊C4—32no—
157(C2×D3)⋊C4—32no—
158C4⋊Dic3—31no—
159C4⋊Dic3—32no—
160C4⋊Dic3C2×A411yescharacteristic
161Dic3⋊C4—34no—
162Dic3⋊C4—32no—
163Dic3⋊C4C2×A412yes—
164C4×Dic3—32no—
165C4×Dic3—32no—
166C4×Dic3—32no—
167C22×C32—41no—
168C2×C3×D3—42no—
169C2×C3×D3—42no—
170C2×C3×D3—42no—
171C32×C4—42no—
172C32×C4—82no—
173C3×Dic3—42no—
174C3×Dic3—82no—
175C2×#41—34no—
176C2×#41—31no—
177C2×#41—91no—
178C2×#41—91no—
179C2×#41—94no—
180C2×#41C2×C3×D311yescharacteristic
181C22×Q8—31no—
182C22×D4—91no—
183C23×C4—91no—
184C23×C4—92no—
185C4×Q8—32no—
186C4×Q8—92no—
187C4×Q8—92no—
188C4×Q8C2×C3×D312yes—
189C4×D4—32no—
190C4×D4—92no—
191C4×D4—94no—
192C4×D4—94no—
193C4×D4—92no—
194C4×D4—92no—
195#117—31no—
196#117—92no—
197#117—92no—
198#117—91no—
199#117—91no—
200#117—91no—
201C2×C4⋊C4—31no—
202C2×C4⋊C4—31no—
203C2×C4⋊C4—91no—
204C2×C4⋊C4—92no—
205C2×C4⋊C4—92no—
206C2×C4⋊C4—92no—
207C2×C4⋊C4—92no—
208C2×C4⋊C4—91no—
209C2×C22⋊C4—92no—
210C2×C42—92no—
211C23×C3—31no—
212C23×C3—121no—
213C22×D3—31no—
214C22×D3—34no—
215C22×D3—62no—
216C22×D3—62no—
217C22×D3C22×A411yescharacteristic
218C3×Q8—31no—
219C3×Q8C22×C3×C411yescharacteristic
220C3×D4—32no—
221C3×D4—32no—
222C2×C3×C4—31no—
223C2×C3×C4—32no—
224C2×C3×C4—32no—
225C2×C3×C4—32no—
226C2×C3×C4—41no—
227C2×C3×C4—42no—
228C2×C3×C4—81no—
229C2×C3×C4—82no—
230C2×C3×C4—124no—
231C2×C3×C4—121no—
232C2×C3×C4—122no—
233C2×C3×C4—122no—
234C2×C3×C4—244no—
235C2×C3×C4C22×A412yes—
236C2×C3×C4C22×A411yescharacteristic
237#67—38no—
238C2×Dic3—31no—
239C2×Dic3—34no—
240C2×Dic3—32no—
241C2×Dic3—122no—
242C2×Dic3C22×A412yes—
243C2×Dic3C22×A411yescharacteristic
244D12—32no—
245D12—32no—
246C4×D3—24no—
247C4×D3—32no—
248C4×D3—32no—
249C4×D3—34no—
250C4×D3—32no—
251C4×D3—32no—
252C4×D3—64no—
253C4×D3—124no—
254C4×D3C4×A414yes—
255Dic6—32no—
256Dic6—32no—
257SL(2,𝔽3)—21no—
258SL(2,𝔽3)C2×C4×D311yescharacteristic, complemented
259C2×C32—41no—
260C2×C32—41no—
261C2×C32—41no—
262C3×D3—44no—
263C24—91no—
264#41—32no—
265#41—32no—
266#41—94no—
267#41—94no—
268#41—94no—
269#41—94no—
270#41—92no—
271#41C3×C4×D312yescomplemented
272C2×Q8—32no—
273C2×Q8—91no—
274C2×Q8—92no—
275C2×Q8C22×C3×D311yescharacteristic
276C2×D4—31no—
277C2×D4—91no—
278C2×D4—94no—
279C2×D4—94no—
280C2×D4—92no—
281C22×C4—31no—
282C22×C4—31no—
283C22×C4—32no—
284C22×C4—32no—
285C22×C4—91no—
286C22×C4—94no—
287C22×C4—94no—
288C22×C4—91no—
289C22×C4—91no—
290C22×C4—92no—
291C22×C4—94no—
292C22×C4—91no—
293C22×C4—92no—
294C22×C4—364no—
295C4⋊C4—32no—
296C4⋊C4—31no—
297C4⋊C4—32no—
298C4⋊C4—31no—
299C4⋊C4—92no—
300C4⋊C4—92no—
301C4⋊C4—94no—
302C4⋊C4—91no—
303C4⋊C4D3×A411yescharacteristic
304C22⋊C4—32no—
305C22⋊C4—92no—
306C22⋊C4—92no—
307C22⋊C4—92no—
308C42—32no—
309C42—92no—
310C42—92no—
311C42—92no—
312C22×C3—32no—
313C22×C3—41no—
314C22×C3—61no—
315C22×C3—61no—
316C22×C3—81no—
317C22×C3—122no—
318C22×C3—122no—
319C22×C3—122no—
320C22×C3C23×A411yescharacteristic
321C2×D3—32no—
322C2×D3—61no—
323C2×D3—61no—
324C2×D3—68no—
325C2×D3C2×C4×A412yes—
326C2×D3#99412yes—
327C2×D32−1+4⋊C312yes—
328C3×C4—22no—
329C3×C4—31no—
330C3×C4—31no—
331C3×C4—42no—
332C3×C4—62no—
333C3×C4—82no—
334C3×C4—82no—
335C3×C4—122no—
336C3×C4—162no—
337C3×C4—242no—
338C3×C4C2×C4×A412yes—
339Dic3—22no—
340Dic3—32no—
341Dic3—62no—
342Dic3C2×C4×A412yes—
343C32—41noSylow
344C23—31no—
345C23—31no—
346C23—94no—
347C23—91no—
348C23—182no—
349C23—182no—
350Q8—31no—
351Q8—92no—
352Q8—92no—
353Q8C2×C3×C4×D311yescharacteristic
354D4—32no—
355D4—32no—
356D4—92no—
357D4—92no—
358D4—98no—
359C2×C4—31no—
360C2×C4—31no—
361C2×C4—32no—
362C2×C4—32no—
363C2×C4—34no—
364C2×C4—32no—
365C2×C4—32no—
366C2×C4—64no—
367C2×C4—92no—
368C2×C4—92no—
369C2×C4—92no—
370C2×C4—92no—
371C2×C4—94no—
372C2×C4—91no—
373C2×C4—94no—
374C2×C4—92no—
375C2×C4—122no—
376C2×C4—184no—
377C2×C4—364no—
378C2×C4—362no—
379C2×C4C2×D3×A412yes—
380C2×C4C2×D3×A411yescharacteristic
381C2×C3—41no—
382C2×C3—41no—
383C2×C3—41no—
384C2×C3—62no—
385C2×C3—81no—
386C2×C3—81no—
387C2×C3—81no—
388C2×C3—124no—
389C2×C3C22×C4×A411yescharacteristic
390C2×C3C2×#99411yescharacteristic
391C2×C3C2×2−1+4⋊C311yescharacteristic
392D3—62no—
393D3#520⋊C314yesdirect product factor
394C22—32no—
395C22—32no—
396C22—32no—
397C22—32no—
398C22—61no—
399C22—61no—
400C22—92no—
401C22—188no—
402C22—181no—
403C22—181no—
404C22C22×D3×A411yescharacteristic
405C4—22no—
406C4—31no—
407C4—31no—
408C4—32no—
409C4—62no—
410C4—62no—
411C4—92no—
412C4—182no—
413C4C4×D3×A412yes—
414C3—41no—
415C3—81no—
416C3C2×#520⋊C311yescharacteristic, complemented
417C2—34no—
418C2—62no—
419C2—182no—
420C2C2×C4×D3×A411yescharacteristic
421C2D3×#99411yescharacteristic
422C2D3×2−1+4⋊C311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, hypocenterC3×Q8C22×C3×C4
FittingC3×#520C2×C3
socleC22×C3C23×A4
prime radicalC2×D3×#41⋊C3C2
cosocleC2×C3×Q8C23×C3
hypercenterC4⋊C4D3×A4
LCSG ▷ C3×Q8
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#520⋊C3C2semidirect
3. #5827⋊C3C2semidirect
4. C4×D3×SL(2,𝔽3)C2semidirect
5. #5574⋊C3C2semidirect
6. D3×#520C3semidirect
9. D3×#41⋊C3C4semidirect
13. C3×C4×SL(2,𝔽3)C22semidirect
14. Dic3×SL(2,𝔽3)C22semidirect
17. C3×#520C2×C3semidirect
18. #5827C2×C3semidirect
19. #5574C2×C3semidirect
30. #520⋊C3D3direct (N × H)
34. C3×#41⋊C3C2×C4semidirect
36. D3×SL(2,𝔽3)C2×C4semidirect
37. C3⋊(#41⋊C3)C2×C4semidirect
44. D3×#41C3×C4semidirect
86. C4×SL(2,𝔽3)C2×D3semidirect
94. C3×SL(2,𝔽3)C22×C4semidirect
101. #520C3×D3semidirect
108. C3×#41C2×C3×C4semidirect
119. #239C2×C3×C4semidirect
142. #41⋊C3C4×D3semidirect
258. SL(2,𝔽3)C2×C4×D3semidirect
271. #41C3×C4×D3semidirect
393. D3#520⋊C3direct (N × H)
416. C3C2×#520⋊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×#520⋊C32
#5827⋊C32
C4×D3×SL(2,𝔽3)2
#5574⋊C32
D3×#5203
C2×#520⋊C33
C3×D3×C4⋊C44