Finite Group Databasebeta

← (C2×D3)⋊(#131⋊C3) #11921338

Subgroups — (C2×D3)⋊(#131⋊C3) #11921338

Order 1152.

417 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 417 conjugacy classes of subgroups — too many to draw. Only its 59 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
4#83793C311yesmaximal, characteristic, complemented
5#2880⋊C3—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7D3×#41⋊C3—21no—
8D3×#41⋊C3—21no—
9C2×D3×SL(2,𝔽3)C411yescharacteristic
10C2×C3⋊(#41⋊C3)C411yescharacteristic
11C3×#131⋊C3—21no—
12C3⋊(#131⋊C3)—21no—
13C3×(C2×D3)⋊C8—41nomaximal
14C2×D3×#41C2×C311yescharacteristic
15C22×#41⋊C3—31no—
16C2×C3×#131C2×C311yescharacteristic, complemented
17C2×#948C2×C311yescharacteristic, complemented
18C2×#131⋊C3—21no—
19C2×#131⋊C3—31no—
20C2×#131⋊C3D311yescharacteristic, complemented
21#5129—31no—
22#5126—31no—
23#5110—31no—
24C2×(C2×D3)⋊C8—31no—
25C2×C3×C4×D3—41no—
26C3×#41⋊C3D411yescharacteristic
27C3×#41⋊C3D411yescharacteristic
28C2×C3×SL(2,𝔽3)C2×C411yescharacteristic
29D3×SL(2,𝔽3)—21no—
30C3⋊(#41⋊C3)—21no—
31C2×C32×C8—41no—
32C2×C3×C3⋊C8—41no—
33#2880—31noSylow
34C2×C3×#41C22×C311yescharacteristic
35D3×#41—21no—
36D3×#41—21no—
37D3×#41—61no—
38D3×#41—61no—
39C2×#239C3×C411yescharacteristic
40C2×D3×Q8C3×C411yescharacteristic
41C2×#237—31no—
42C2×D3×D4—31no—
43C2×#235—31no—
44C22×C4×D3—31no—
45C2×#41⋊C3—21no—
46C2×#41⋊C3—31no—
47C2×#41⋊C3—61no—
48C2×#41⋊C3—61no—
49C2×#41⋊C3C2×D311yescharacteristic
50C22×SL(2,𝔽3)—31no—
51C3×#131—21no—
52C3×#131—61no—
53C2×C3×M16—31no—
54C22×C3×C8—31no—
55#948—21no—
56#948—61no—
57C2×#208—31no—
58C22×C3⋊C8—31no—
59#131⋊C3—22no—
60#131⋊C3—21no—
61#131⋊C3—61no—
62C3×C22⋊C8—121no—
63(C2×D3)⋊C8—32no—
64(C2×D3)⋊C8—31no—
65(C2×D3)⋊C8—31no—
66(C2×D3)⋊C8—31no—
67(C2×D3)⋊C8A411yescharacteristic
68C22×C3×D3—41no—
69C2×C32×C4—41no—
70C2×C3×Dic3—41no—
71C3×C4×D3—81no—
72C3×C4×D3—81no—
73C3×SL(2,𝔽3)C22⋊C411yescharacteristic
74C32×C8—81no—
75C3×C3⋊C8—81no—
76C22×#41—31no—
77C2×#131—31no—
78C2×#131C3×D311yescharacteristic, complemented
79#408—91no—
80#408—91no—
81#407—91no—
82C2×C22⋊C8—91no—
83C23×D3—31no—
84C3×#41—31no—
85C3×#41—31no—
86C3×#41C3×D411yescharacteristic
87C3×#41C3×D411yescharacteristic
88C2×C3×Q8C2×C3×C411yescharacteristic
89C2×C3×D4—31no—
90C22×C3×C4—31no—
91C22×C3×C4—121no—
92C2×#67—32no—
93C22×Dic3—31no—
94#239—21no—
95#239—61no—
96D3×Q8—21no—
97D3×Q8—61no—
98#237—62no—
99#237—61no—
100#237—61no—
101D3×D4—61no—
102D3×D4—61no—
103D3×D4—62no—
104#235—61no—
105#235—61no—
106#235—61no—
107#235—61no—
108C2×D12—31no—
109C2×C4×D3—31no—
110C2×C4×D3—31no—
111C2×C4×D3—31no—
112C2×C4×D3—61no—
113C2×C4×D3—61no—
114C2×C4×D3—61no—
115C2×C4×D3—61no—
116C2×C4×D3C2×A411yescharacteristic
117C2×Dic6—31no—
118#41⋊C3—21no—
119#41⋊C3—21no—
120#41⋊C3—61no—
121#41⋊C3D1211yescharacteristic
122#41⋊C3#6711yescharacteristic
123C2×SL(2,𝔽3)—21no—
124C2×SL(2,𝔽3)—61no—
125C2×SL(2,𝔽3)C4×D311yescharacteristic
126C3×M16—61no—
127C3×M16—61no—
128C2×C3×C8—31no—
129C2×C3×C8—41no—
130C2×C3×C8—61no—
131C2×C3×C8—61no—
132C2×C3×C8—81no—
133C2×C3×C8—121no—
134C2×C3×C8C2×A411yescharacteristic
135#208—61no—
136#208—61no—
137C2×C3⋊C8—31no—
138C2×C3⋊C8—61no—
139C2×C3⋊C8—61no—
140C2×C3⋊C8C2×A411yescharacteristic
141C22×C32—41no—
142C2×C3×D3—42no—
143C2×C3×D3—81no—
144C2×C3×D3—81no—
145C32×C4—41no—
146C32×C4—41no—
147C3×Dic3—81no—
148C2×#41—31no—
149C2×#41—61no—
150C2×#41—61no—
151C2×#41—91no—
152C2×#41—91no—
153C2×#41—181no—
154C2×#41—181no—
155C2×#41C2×C3×D311yescharacteristic
156C22×Q8—31no—
157C22×D4—91no—
158C23×C4—91no—
159#131—21no—
160#131—61no—
161#131—61no—
162#131—181no—
163C2×M16—31no—
164C2×M16—91no—
165C22×C8—31no—
166C22×C8—91no—
167C22⋊C8—31no—
168C22⋊C8—91no—
169C22⋊C8—91no—
170C22⋊C8—92no—
171C22⋊C8—91no—
172C23×C3—31no—
173C23×C3—121no—
174C22×D3—31no—
175C22×D3—61no—
176C22×D3—61no—
177C22×D3—62no—
178C22×D3—121no—
179C22×D3C4×A411yescharacteristic
180C3×Q8—31no—
181C3×Q8C3×C22⋊C411yescharacteristic
182C3×D4—31no—
183C3×D4—31no—
184C3×D4—32no—
185C2×C3×C4—31no—
186C2×C3×C4—31no—
187C2×C3×C4—31no—
188C2×C3×C4—31no—
189C2×C3×C4—31no—
190C2×C3×C4—41no—
191C2×C3×C4—81no—
192C2×C3×C4—121no—
193C2×C3×C4—241no—
194C2×C3×C4—241no—
195C2×C3×C4C22×A411yescharacteristic
196#67—62no—
197#67—62no—
198C2×Dic3—31no—
199C2×Dic3—61no—
200C2×Dic3—61no—
201C2×Dic3C4×A411yescharacteristic
202D12—61no—
203D12—61no—
204C4×D3—21no—
205C4×D3—21no—
206C4×D3—61no—
207C4×D3—61no—
208C4×D3—61no—
209C4×D3—61no—
210C4×D3—61no—
211C4×D3—61no—
212Dic6—61no—
213Dic6—61no—
214SL(2,𝔽3)—21no—
215SL(2,𝔽3)(C2×D3)⋊C411yescharacteristic
216C3×C8—21no—
217C3×C8—61no—
218C3×C8—81no—
219C3×C8—82no—
220C3×C8—241no—
221C3⋊C8—21no—
222C3⋊C8—61no—
223C2×C32—41no—
224C2×C32—41no—
225C2×C32—41no—
226C3×D3—82no—
227C24—91no—
228#41—31no—
229#41—31no—
230#41—61no—
231#41—181no—
232#41—181no—
233#41—181no—
234#41—181no—
235#41—182no—
236#41—181no—
237#41—181no—
238#41—181no—
239#41C3×D1211yescharacteristic
240#41C3×#6711yescharacteristic
241C2×Q8—61no—
242C2×Q8—91no—
243C2×Q8—181no—
244C2×Q8C3×C4×D311yescharacteristic
245C2×D4—31no—
246C2×D4—91no—
247C2×D4—92no—
248C2×D4—181no—
249C2×D4—181no—
250C2×D4—182no—
251C22×C4—31no—
252C22×C4—31no—
253C22×C4—91no—
254C22×C4—91no—
255C22×C4—91no—
256C22×C4—91no—
257C22×C4—181no—
258C22×C4—181no—
259C22×C4—181no—
260C22×C4—181no—
261M16—61no—
262M16—61no—
263M16—181no—
264M16—181no—
265C2×C8—31no—
266C2×C8—31no—
267C2×C8—61no—
268C2×C8—61no—
269C2×C8—91no—
270C2×C8—181no—
271C2×C8—181no—
272C2×C8D3×A411yescharacteristic
273C22×C3—31no—
274C22×C3—31no—
275C22×C3—41no—
276C22×C3—61no—
277C22×C3—61no—
278C22×C3—81no—
279C22×C3—122no—
280C22×C3—241no—
281C22×C3—241no—
282C22×C3C2×C4×A411yescharacteristic
283C2×D3—21no—
284C2×D3—21no—
285C2×D3—61no—
286C2×D3—61no—
287C2×D3—61no—
288C2×D3—122no—
289C2×D3—122no—
290C2×D3#131⋊C312yescomplemented
291C3×C4—31no—
292C3×C4—31no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4—81no—
296C3×C4—81no—
297C3×C4—241no—
298C3×C4D4×A411yescharacteristic
299C3×C4D4×A411yescharacteristic
300Dic3—21no—
301Dic3—61no—
302C32—41noSylow
303C23—31no—
304C23—31no—
305C23—91no—
306C23—181no—
307C23—181no—
308C23—182no—
309C23—361no—
310Q8—31no—
311Q8—181no—
312Q8—181no—
313Q8C3×(C2×D3)⋊C411yescharacteristic
314D4—31no—
315D4—31no—
316D4—32no—
317D4—181no—
318D4—181no—
319D4—182no—
320D4—182no—
321C2×C4—31no—
322C2×C4—31no—
323C2×C4—31no—
324C2×C4—31no—
325C2×C4—31no—
326C2×C4—31no—
327C2×C4—61no—
328C2×C4—61no—
329C2×C4—91no—
330C2×C4—181no—
331C2×C4—181no—
332C2×C4—181no—
333C2×C4—181no—
334C2×C4—181no—
335C2×C4—181no—
336C2×C4—181no—
337C2×C4—181no—
338C2×C4C2×D3×A411yescharacteristic
339C8—21no—
340C8—61no—
341C8—61no—
342C8—181no—
343C2×C3—41no—
344C2×C3—41no—
345C2×C3—41no—
346C2×C3—61no—
347C2×C3—61no—
348C2×C3—81no—
349C2×C3—81no—
350C2×C3—81no—
351C2×C3—242no—
352C2×C3A4×C22⋊C411yescharacteristic
353C2×C3C2×#131⋊C311yescharacteristic
354C2×C3#568⋊C311yescharacteristic
355D3—22no—
356D3—121no—
357C22—32no—
358C22—31no—
359C22—31no—
360C22—61no—
361C22—61no—
362C22—61no—
363C22—61no—
364C22—181no—
365C22—181no—
366C22—181no—
367C22—362no—
368C22—362no—
369C22C4×D3×A411yescharacteristic
370C4—31no—
371C4—31no—
372C4—61no—
373C4—181no—
374C4A4×D1211yescharacteristic
375C4A4×#6711yescharacteristic
376C3—41no—
377C3—81no—
378C3#2880⋊C311yescharacteristic, complemented
379C2—62no—
380C2—61no—
381C2—61no—
382C2—361no—
383C2D3×#131⋊C311yescharacteristic
384C2#5750⋊C311yescharacteristic
385C2A4×(C2×D3)⋊C411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×D3×A4
commutatorC2×C3×Q8C2×C3×C4
FittingC2×C3×#131C2×C3
socleC22×C3C2×C4×A4
prime radicalC2×D3×#41⋊C3C2
cosocleC2×C3×#41C22×C3
hypercenterC2×C8D3×A4
hypocenterC3×Q8C3×C22⋊C4
LCSG ▷ C2×C3×Q8 ▷ C3×Q8
UCSC1 ◁ C2×C4 ◁ 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. #83793C3semidirect
16. C2×C3×#131C2×C3semidirect
17. C2×#948C2×C3semidirect
20. C2×#131⋊C3D3semidirect
78. C2×#131C3×D3semidirect
290. C2×D3#131⋊C3semidirect
378. C3#2880⋊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
C2×C3×#131⋊C32
C2×C3⋊(#131⋊C3)2
#837933
#2880⋊C33
C3×(C2×D3)⋊C84