Finite Group Databasebeta

← C2×D3×#131⋊C3 #11923309

Subgroups — C2×D3×#131⋊C3 #11923309

Order 1152.

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

normal subgroups only

This group has 737 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
2C2×C3×#131⋊C3C211yesmaximal, characteristic, complemented
3C2×C3⋊(#131⋊C3)C211yesmaximal, characteristic, complemented
4D3×#131⋊C3C214yesmaximal, direct product factor
5C2×D3×#131C311yesmaximal, characteristic, complemented
6C22×#131⋊C3—31nomaximal
7C2×C3×#41⋊C3C2211yescharacteristic
8D3×#41⋊C3C412yes—
9D3×#41⋊C3C2212yes—
10C2×D3×SL(2,𝔽3)C411yescharacteristic
11C2×C3⋊(#41⋊C3)C411yescharacteristic
12C2×C3×D3×C8—41nomaximal
13C3×#131⋊C3C2212yescomplemented
14C3⋊(#131⋊C3)C2212yescomplemented
15C2×D3×#41C2×C311yescharacteristic
16C22×#41⋊C3—31no—
17C2×C3×#131C2×C311yescharacteristic, complemented
18C2×#948C2×C311yescharacteristic, complemented
19D3×#131—34no—
20D3×#131C2×C314yescomplemented
21C2×#907—31no—
22C2×D3×M16—31no—
23C2×#901—31no—
24C22×D3×C8—31no—
25C2×#131⋊C3—21no—
26C2×#131⋊C3—31no—
27C2×#131⋊C3—34no—
28C2×#131⋊C3D311yescharacteristic, direct product factor
29C2×C3×C4×D3—41no—
30C3×#41⋊C3C2×C411yescharacteristic
31C3×#41⋊C3C2311yescharacteristic
32C2×C3×SL(2,𝔽3)C2×C411yescharacteristic
33D3×SL(2,𝔽3)C2×C412yes—
34C3⋊(#41⋊C3)C2×C412yes—
35C2×C32×C8—41no—
36C2×C3×C3⋊C8—41no—
37C3×D3×C8—44no—
38C22×#131—31noSylow
39C2×C3×#41C22×C311yescharacteristic
40D3×#41—32no—
41D3×#41—32no—
42D3×#41C3×C412yes—
43D3×#41C22×C312yes—
44C2×#239C3×C411yescharacteristic
45C2×D3×Q8C3×C411yescharacteristic
46C2×#237—31no—
47C2×D3×D4—31no—
48C2×#235—31no—
49C22×C4×D3—31no—
50C2×#41⋊C3—21no—
51C2×#41⋊C3—32no—
52C2×#41⋊C3—32no—
53C2×#41⋊C3—31no—
54C2×#41⋊C3C2×D311yescharacteristic
55C22×SL(2,𝔽3)—31no—
56C3×#131—32no—
57C3×#131C22×C312yescomplemented
58C2×C3×M16—31no—
59C22×C3×C8—31no—
60C22×C3×C8—121no—
61#948—32no—
62#948C22×C312yescomplemented
63C2×#208—31no—
64C22×C3⋊C8—31no—
65#907—34no—
66#907—34no—
67D3×M16—34no—
68D3×M16—34no—
69#901—34no—
70#901—34no—
71C2×ΓL(1,𝔽25)—32no—
72C2×D3×C8—31no—
73C2×D3×C8—31no—
74C2×D3×C8—31no—
75C2×D3×C8—34no—
76C2×D3×C8—34no—
77C2×D3×C8A411yescharacteristic
78#131⋊C3—22no—
79#131⋊C3—32no—
80#131⋊C3C2×D312yesdirect product factor
81C22×C3×D3—41no—
82C2×C32×C4—41no—
83C2×C3×Dic3—41no—
84C3×C4×D3—42no—
85C3×C4×D3—42no—
86C3×SL(2,𝔽3)C22×C411yescharacteristic
87C32×C8—42no—
88C3×C3⋊C8—42no—
89C22×#41—31no—
90C2×#131—31no—
91C2×#131—34no—
92C2×#131—91no—
93C2×#131—91no—
94C2×#131—94no—
95C2×#131C3×D311yescharacteristic, complemented
96C22×M16—91no—
97C23×C8—91no—
98C23×D3—31no—
99C3×#41—31no—
100C3×#41—31no—
101C3×#41C2×C3×C411yescharacteristic
102C3×#41C23×C311yescharacteristic
103C2×C3×Q8C2×C3×C411yescharacteristic
104C2×C3×D4—31no—
105C22×C3×C4—31no—
106C22×C3×C4—121no—
107C2×#67—32no—
108C22×Dic3—31no—
109#239—32no—
110#239C2×C3×C412yes—
111D3×Q8—32no—
112D3×Q8C2×C3×C412yes—
113#237—34no—
114#237—32no—
115#237—32no—
116D3×D4—32no—
117D3×D4—32no—
118D3×D4—34no—
119#235—32no—
120#235—32no—
121#235—32no—
122#235—32no—
123C2×D12—31no—
124C2×C4×D3—31no—
125C2×C4×D3—31no—
126C2×C4×D3—31no—
127C2×C4×D3—32no—
128C2×C4×D3—32no—
129C2×C4×D3—32no—
130C2×C4×D3—32no—
131C2×C4×D3C2×A411yescharacteristic
132C2×Dic6—31no—
133#41⋊C3—21no—
134#41⋊C3—21no—
135#41⋊C3—32no—
136#41⋊C3C4×D311yescharacteristic
137#41⋊C3C22×D311yescharacteristic
138C2×SL(2,𝔽3)—21no—
139C2×SL(2,𝔽3)—32no—
140C2×SL(2,𝔽3)C4×D311yescharacteristic
141C3×M16—32no—
142C3×M16—32no—
143C2×C3×C8—31no—
144C2×C3×C8—32no—
145C2×C3×C8—32no—
146C2×C3×C8—41no—
147C2×C3×C8—81no—
148C2×C3×C8—124no—
149C2×C3×C8—121no—
150C2×C3×C8C2×A411yescharacteristic
151#208—32no—
152#208—32no—
153C2×C3⋊C8—31no—
154C2×C3⋊C8—32no—
155C2×C3⋊C8—32no—
156C2×C3⋊C8C2×A411yescharacteristic
157ΓL(1,𝔽25)—38no—
158D3×C8—34no—
159D3×C8—34no—
160D3×C8—34no—
161D3×C8C2×A414yes—
162C22×C32—41no—
163C2×C3×D3—44no—
164C2×C3×D3—42no—
165C32×C4—41no—
166C32×C4—41no—
167C3×Dic3—42no—
168C2×#41—32no—
169C2×#41—32no—
170C2×#41—31no—
171C2×#41—91no—
172C2×#41—91no—
173C2×#41—92no—
174C2×#41—92no—
175C2×#41C2×C3×D311yescharacteristic
176C22×Q8—31no—
177C22×D4—91no—
178C23×C4—91no—
179#131—32no—
180#131—32no—
181#131—94no—
182#131—94no—
183#131—94no—
184#131—94no—
185#131—92no—
186#131C2×C3×D312yescomplemented
187C2×M16—31no—
188C2×M16—92no—
189C2×M16—94no—
190C2×M16—94no—
191C2×M16—91no—
192C22×C8—31no—
193C22×C8—31no—
194C22×C8—94no—
195C22×C8—91no—
196C22×C8—94no—
197C22×C8—91no—
198C22×C8—91no—
199C22×C8—91no—
200C23×C3—31no—
201C23×C3—121no—
202C22×D3—31no—
203C22×D3—32no—
204C22×D3—32no—
205C22×D3—64no—
206C22×D3C4×A411yescharacteristic
207C3×Q8—31no—
208C3×Q8C22×C3×C411yescharacteristic
209C3×D4—31no—
210C3×D4—31no—
211C3×D4—32no—
212C2×C3×C4—31no—
213C2×C3×C4—31no—
214C2×C3×C4—31no—
215C2×C3×C4—31no—
216C2×C3×C4—31no—
217C2×C3×C4—41no—
218C2×C3×C4—81no—
219C2×C3×C4—122no—
220C2×C3×C4—122no—
221C2×C3×C4—121no—
222C2×C3×C4C22×A411yescharacteristic
223#67—34no—
224#67—34no—
225C2×Dic3—31no—
226C2×Dic3—32no—
227C2×Dic3—32no—
228C2×Dic3C4×A411yescharacteristic
229D12—32no—
230D12—32no—
231C4×D3—32no—
232C4×D3—32no—
233C4×D3—32no—
234C4×D3—32no—
235C4×D3—32no—
236C4×D3—32no—
237C4×D3C4×A412yes—
238C4×D3C22×A412yes—
239Dic6—32no—
240Dic6—32no—
241SL(2,𝔽3)—21no—
242SL(2,𝔽3)C2×C4×D311yescharacteristic
243C3×C8—32no—
244C3×C8—42no—
245C3×C8—82no—
246C3×C8—122no—
247C3×C8C22×A412yes—
248C3⋊C8—32no—
249C3⋊C8C22×A412yes—
250C2×C32—41no—
251C2×C32—42no—
252C3×D3—44no—
253C24—91no—
254#41—31no—
255#41—31no—
256#41—32no—
257#41—92no—
258#41—92no—
259#41—92no—
260#41—92no—
261#41—94no—
262#41—92no—
263#41—92no—
264#41—92no—
265#41C3×C4×D311yescharacteristic
266#41C22×C3×D311yescharacteristic
267C2×Q8—32no—
268C2×Q8—91no—
269C2×Q8—92no—
270C2×Q8C3×C4×D311yescharacteristic
271C2×D4—31no—
272C2×D4—91no—
273C2×D4—92no—
274C2×D4—92no—
275C2×D4—94no—
276C2×D4—92no—
277C22×C4—31no—
278C22×C4—31no—
279C22×C4—92no—
280C22×C4—92no—
281C22×C4—91no—
282C22×C4—92no—
283C22×C4—92no—
284C22×C4—91no—
285C22×C4—91no—
286C22×C4—91no—
287M16—32no—
288M16—32no—
289M16—98no—
290M16—92no—
291M16—92no—
292C2×C8—31no—
293C2×C8—31no—
294C2×C8—32no—
295C2×C8—32no—
296C2×C8—34no—
297C2×C8—94no—
298C2×C8—94no—
299C2×C8—92no—
300C2×C8—92no—
301C2×C8—91no—
302C2×C8—94no—
303C2×C8D3×A411yescharacteristic
304C22×C3—31no—
305C22×C3—31no—
306C22×C3—41no—
307C22×C3—62no—
308C22×C3—81no—
309C22×C3—122no—
310C22×C3—124no—
311C22×C3C2×C4×A411yescharacteristic
312C2×D3—32no—
313C2×D3—62no—
314C2×D3—64no—
315C2×D3—64no—
316C2×D3#131⋊C314yesdirect product factor
317C2×D3C2×C4×A412yes—
318C3×C4—31no—
319C3×C4—31no—
320C3×C4—41no—
321C3×C4—41no—
322C3×C4—81no—
323C3×C4—81no—
324C3×C4—122no—
325C3×C4C2×C4×A411yescharacteristic
326C3×C4C23×A411yescharacteristic
327Dic3—32no—
328Dic3C2×C4×A412yes—
329C32—41noSylow
330C23—31no—
331C23—31no—
332C23—92no—
333C23—92no—
334C23—91no—
335C23—184no—
336Q8—31no—
337Q8—92no—
338Q8—92no—
339Q8C2×C3×C4×D311yescharacteristic
340D4—31no—
341D4—31no—
342D4—32no—
343D4—92no—
344D4—92no—
345D4—94no—
346D4—94no—
347C2×C4—31no—
348C2×C4—31no—
349C2×C4—31no—
350C2×C4—31no—
351C2×C4—32no—
352C2×C4—31no—
353C2×C4—31no—
354C2×C4—32no—
355C2×C4—92no—
356C2×C4—92no—
357C2×C4—92no—
358C2×C4—92no—
359C2×C4—92no—
360C2×C4—92no—
361C2×C4—91no—
362C2×C4—92no—
363C2×C4—92no—
364C2×C4C2×D3×A411yescharacteristic
365C8—32no—
366C8—32no—
367C8—92no—
368C8C2×D3×A412yes—
369C2×C3—41no—
370C2×C3—42no—
371C2×C3—61no—
372C2×C3—61no—
373C2×C3—81no—
374C2×C3—82no—
375C2×C3—124no—
376C2×C3C2×#131⋊C312yescomplemented
377C2×C3C22×C4×A411yescharacteristic
378D3—62no—
379D3C2×#131⋊C314yesdirect product factor
380C22—32no—
381C22—34no—
382C22—31no—
383C22—31no—
384C22—62no—
385C22—92no—
386C22—184no—
387C22—184no—
388C22—182no—
389C22C4×D3×A411yescharacteristic
390C4—31no—
391C4—31no—
392C4—32no—
393C4—92no—
394C4C4×D3×A411yescharacteristic
395C4C22×D3×A411yescharacteristic
396C3—41no—
397C3—81no—
398C3C22×#131⋊C311yescharacteristic, complemented
399C2—34no—
400C2—61no—
401C2—61no—
402C2—182no—
403C2D3×#131⋊C312yesdirect product factor
404C2C2×C4×D3×A411yescharacteristic
subgroupG/H
center, hypercenterC2×C8D3×A4
commutator, hypocenterC3×Q8C22×C3×C4
FrattiniC4C22×D3×A4
FittingC2×C3×#131C2×C3
socleC22×C3C2×C4×A4
prime radicalC2×D3×#41⋊C3C2
cosocleC3×#41C23×C3
LCSG ▷ C3×Q8
UCSC1 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#131⋊C3C2semidirect
3. C2×C3⋊(#131⋊C3)C2semidirect
4. D3×#131⋊C3C2direct (N × H)
5. C2×D3×#131C3semidirect
13. C3×#131⋊C3C22semidirect
14. C3⋊(#131⋊C3)C22semidirect
17. C2×C3×#131C2×C3semidirect
18. C2×#948C2×C3semidirect
20. D3×#131C2×C3semidirect
28. C2×#131⋊C3D3direct (N × H)
57. C3×#131C22×C3semidirect
62. #948C22×C3semidirect
80. #131⋊C3C2×D3direct (N × H)
95. C2×#131C3×D3semidirect
186. #131C2×C3×D3semidirect
316. C2×D3#131⋊C3direct (N × H)
376. C2×C3C2×#131⋊C3semidirect
379. D3C2×#131⋊C3direct (N × H)
398. C3C22×#131⋊C3semidirect
403. C2D3×#131⋊C3direct (N × H)

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×C3×#131⋊C32
C2×C3⋊(#131⋊C3)2
D3×#131⋊C32
C2×D3×#1313
C22×#131⋊C33
C2×C3×D3×C84