Finite Group Databasebeta

← C22×D3×#1094 #72252759

Subgroups — C22×D3×#1094 #72252759

Order 2592.

2142 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 2142 conjugacy classes of subgroups — too many to draw. Only its 210 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
1C22×C3×#1094C211yesmaximal, characteristic, complemented
2C2×D3×#1094C216yesmaximal, direct product factor
3C24×C32×D3C311yesmaximal, characteristic
4C23×#1094—31nomaximal
5C22×D3×C22⋊C9C313yesmaximal, complemented
6C22×D3×3−1+2—41nomaximal
7C2×C3×#1094C2213yescomplemented
8D3×#1094C2214yesdirect product factor
9C24×C33C2×C311yescharacteristic
10C23×C32×D3—31no—
11C23×C32×D3—31no—
12C23×C32×D3—36no—
13C23×C32×D3C2×C316yes—
14C22×#1094—23no—
15C22×#1094—21no—
16C22×#1094—36no—
17C22×#1094D311yescharacteristic, direct product factor
18C22×C3×C22⋊C9C2×C313yescomplemented
19C2×D3×C22⋊C9C2×C3118yescomplemented
20C22×C3×3−1+2—41no—
21C2×D3×3−1+2—46no—
22C3×#1094C2311yescharacteristic, complemented
23C25×C32—31no—
24C24×C3×D3—31no—
25C24×C3×D3C3211yescharacteristic
26C23×C22⋊C9—33no—
27C23×C33—31no—
28C23×C33—33no—
29C23×C33C22×C313yes—
30C22×C32×D3—36no—
31C22×C32×D3—38no—
32C22×C32×D3—31no—
33C22×C32×D3—36no—
34C22×C32×D3—36no—
35C22×C32×D3—36no—
36C22×C32×D3—312no—
37C22×C32×D3A411yescharacteristic
38C22×C32×D3C22×C314yes—
39C23×3−1+2—121no—
40C22×D3×C9—43no—
41C2×#1094—23no—
42C2×#1094—29no—
43C2×#1094—34no—
44C2×#1094C2×D313yesdirect product factor
45C2×C3×C22⋊C9C22×C319yescomplemented
46D3×C22⋊C9C22×C3112yescomplemented
47C2×C3×3−1+2—43no—
48D3×3−1+2—44no—
49C24×C32—21no—
50C24×C32—31no—
51C24×C32—36no—
52C24×C32—61no—
53C24×C32—91no—
54C24×C32—96no—
55C24×C32—91no—
56C24×C32C3×D311yescharacteristic
57C24×C32C2×C3211yescharacteristic
58C23×C3×D3—33no—
59C23×C3×D3—318no—
60C23×C3×D3—33no—
61C23×C3×D3—36no—
62C23×C3×D3—31no—
63C23×C3×D3—31no—
64C23×C3×D3—36no—
65C23×C3×D3C2×C3216yes—
66C22×C22⋊C9—23no—
67C22×C22⋊C9—318no—
68C22×C22⋊C9C3×D313yescomplemented
69C22×C33—32no—
70C22×C33—33no—
71C22×C33—33no—
72C22×C33—33no—
73C22×C33C2×A411yescharacteristic
74C22×C33C23×C311yescharacteristic
75C2×C32×D3—312no—
76C2×C32×D3—36no—
77C2×C32×D3—312no—
78C2×C32×D3—34no—
79C2×C32×D3—34no—
80C2×C32×D3C2×A416yes—
81C22×3−1+2—41no—
82C22×3−1+2—83no—
83C22×3−1+2—81no—
84C22×3−1+2—126no—
85C22×C3×C9—43no—
86C2×D3×C9—418no—
87#1094—21no—
88#1094—23no—
89#1094C22×D311yescharacteristic, direct product factor
90C3×C22⋊C9C23×C313yescomplemented
91C25×C3—31no—
92C25×C3—91no—
93C24×D33−1+211yescharacteristic, complemented
94C3×3−1+2—41noSylow
95C23×C32—23no—
96C23×C32—33no—
97C23×C32—31no—
98C23×C32—33no—
99C23×C32—39no—
100C23×C32—33no—
101C23×C32—31no—
102C23×C32—33no—
103C23×C32—31no—
104C23×C32—34no—
105C23×C32—63no—
106C23×C32—61no—
107C23×C32—63no—
108C23×C32—63no—
109C23×C32—69no—
110C23×C32—96no—
111C23×C32—96no—
112C23×C32—912no—
113C23×C32—96no—
114C23×C32—98no—
115C23×C32—96no—
116C23×C32—91no—
117C23×C32C2×C3×D313yes—
118C23×C32C22×C3213yes—
119C22×C3×D3—318no—
120C22×C3×D3—324no—
121C22×C3×D3—36no—
122C22×C3×D3—38no—
123C22×C3×D3—33no—
124C22×C3×D3—318no—
125C22×C3×D3—318no—
126C22×C3×D3—318no—
127C22×C3×D3—336no—
128C22×C3×D3—31no—
129C22×C3×D3—36no—
130C22×C3×D3—36no—
131C22×C3×D3—36no—
132C22×C3×D3—312no—
133C22×C3×D3—31no—
134C22×C3×D3—34no—
135C22×C3×D3C3×A411yescharacteristic
136C22×C3×D3C22×C3214yes—
137C23×C9—123no—
138C2×C22⋊C9—29no—
139C2×C22⋊C9—312no—
140C2×C22⋊C9C2×C3×D319yescomplemented
141C2×C33—33no—
142C2×C33—31no—
143C2×C33C22×A413yes—
144C32×D3—34no—
145C32×D3C22×A414yes—
146C2×3−1+2—43no—
147C2×3−1+2—89no—
148C2×3−1+2—83no—
149C2×3−1+2—124no—
150C2×C3×C9—49no—
151D3×C9—412no—
152C24×C3—21no—
153C24×C3—36no—
154C24×C3—31no—
155C24×C3—61no—
156C24×C3—96no—
157C24×C3—91no—
158C24×C3—96no—
159C24×C3—91no—
160C24×C3—93no—
161C24×C3—918no—
162C24×C3—93no—
163C24×C3C2×3−1+211yescharacteristic, complemented
164C24×C3C32×D311yescharacteristic
165C23×D3—31no—
166C23×D3—31no—
167C23×D3—36no—
168C23×D3C2×3−1+216yescomplemented
169C22×C32—21no—
170C22×C32—21no—
171C22×C32—33no—
172C22×C32—32no—
173C22×C32—33no—
174C22×C32—33no—
175C22×C32—33no—
176C22×C32—39no—
177C22×C32—36no—
178C22×C32—32no—
179C22×C32—39no—
180C22×C32—39no—
181C22×C32—33no—
182C22×C32—33no—
183C22×C32—31no—
184C22×C32—31no—
185C22×C32—36no—
186C22×C32—61no—
187C22×C32—61no—
188C22×C32—63no—
189C22×C32—63no—
190C22×C32—63no—
191C22×C32—69no—
192C22×C32—69no—
193C22×C32—69no—
194C22×C32—62no—
195C22×C32—66no—
196C22×C32—94no—
197C22×C32—912no—
198C22×C32—94no—
199C22×C32—912no—
200C22×C32—96no—
201C22×C32D3×A411yescharacteristic
202C22×C32C2×C3×A411yescharacteristic
203C22×C32C22×C3×D311yescharacteristic
204C22×C32C23×C3211yescharacteristic
205C2×C3×D3—336no—
206C2×C3×D3—312no—
207C2×C3×D3—318no—
208C2×C3×D3—312no—
209C2×C3×D3—336no—
210C2×C3×D3—312no—
211C2×C3×D3—36no—
212C2×C3×D3—312no—
213C2×C3×D3—34no—
214C2×C3×D3—34no—
215C2×C3×D3—36no—
216C2×C3×D3C2×C3×A416yes—
217C22×C9—43no—
218C22×C9—83no—
219C22×C9—1218no—
220C22⋊C9—23no—
221C22⋊C9C22×C3×D313yescomplemented
222C25—31noSylow
223C33C23×A411yescharacteristic
2243−1+2—41no—
2253−1+2—83no—
2263−1+2—81no—
227C3×C9—43no—
228C23×C3—23no—
229C23×C3—33no—
230C23×C3—33no—
231C23×C3—39no—
232C23×C3—33no—
233C23×C3—31no—
234C23×C3—31no—
235C23×C3—31no—
236C23×C3—34no—
237C23×C3—33no—
238C23×C3—61no—
239C23×C3—63no—
240C23×C3—69no—
241C23×C3—63no—
242C23×C3—63no—
243C23×C3—91no—
244C23×C3—94no—
245C23×C3—96no—
246C23×C3—96no—
247C23×C3—912no—
248C23×C3—96no—
249C23×C3—918no—
250C23×C3—918no—
251C23×C3—936no—
252C23×C3—918no—
253C23×C3—98no—
254C23×C3—924no—
255C23×C3—918no—
256C23×C3—96no—
257C23×C3—93no—
258C23×C3—91no—
259C23×C3C22×3−1+213yescomplemented
260C23×C3C2×C32×D313yes—
261C22×D3—36no—
262C22×D3—38no—
263C22×D3—31no—
264C22×D3—36no—
265C22×D3—36no—
266C22×D3—36no—
267C22×D3—312no—
268C22×D3#109411yescharacteristic, direct product factor
269C22×D3C22×3−1+214yescomplemented
270C2×C32—23no—
271C2×C32—33no—
272C2×C32—31no—
273C2×C32—33no—
274C2×C32—39no—
275C2×C32—33no—
276C2×C32—31no—
277C2×C32—33no—
278C2×C32—34no—
279C2×C32—63no—
280C2×C32—61no—
281C2×C32—63no—
282C2×C32—63no—
283C2×C32—69no—
284C2×C32—94no—
285C2×C32C2×D3×A413yes—
286C2×C32C22×C3×A413yes—
287C3×D3—312no—
288C3×D3—34no—
289C3×D3—34no—
290C3×D3C22×C3×A414yes—
291C2×C9—49no—
292C2×C9—89no—
293C2×C9—1212no—
294C24—36no—
295C24—91no—
296C24—96no—
297C24—91no—
298C24D3×3−1+211yescharacteristic, complemented
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—33no—
302C22×C3—33no—
303C22×C3—32no—
304C22×C3—39no—
305C22×C3—36no—
306C22×C3—32no—
307C22×C3—39no—
308C22×C3—39no—
309C22×C3—33no—
310C22×C3—33no—
311C22×C3—36no—
312C22×C3—33no—
313C22×C3—33no—
314C22×C3—31no—
315C22×C3—31no—
316C22×C3—63no—
317C22×C3—63no—
318C22×C3—63no—
319C22×C3—69no—
320C22×C3—62no—
321C22×C3—66no—
322C22×C3—69no—
323C22×C3—69no—
324C22×C3—61no—
325C22×C3—61no—
326C22×C3—96no—
327C22×C3—94no—
328C22×C3—912no—
329C22×C3—94no—
330C22×C3—912no—
331C22×C3—936no—
332C22×C3—912no—
333C22×C3—936no—
334C22×C3—912no—
335C22×C3—918no—
336C22×C3—96no—
337C22×C3C2×#109411yescharacteristic, complemented
338C22×C3C23×3−1+211yescharacteristic, complemented
339C22×C3C3×D3×A411yescharacteristic
340C22×C3C22×C32×D311yescharacteristic
341C2×D3—312no—
342C2×D3—36no—
343C2×D3—34no—
344C2×D3—312no—
345C2×D3—34no—
346C2×D3C2×#109416yesdirect product factor
347C32—21no—
348C32—31no—
349C32—61no—
350C32C22×D3×A411yescharacteristic
351C32C23×C3×A411yescharacteristic
352C9—43no—
353C9—83no—
354C23—33no—
355C23—31no—
356C23—31no—
357C23—34no—
358C23—96no—
359C23—96no—
360C23—912no—
361C23—96no—
362C23—98no—
363C23—96no—
364C23—91no—
365C23C2×D3×3−1+213yescomplemented
366C2×C3—23no—
367C2×C3—33no—
368C2×C3—39no—
369C2×C3—31no—
370C2×C3—33no—
371C2×C3—31no—
372C2×C3—33no—
373C2×C3—34no—
374C2×C3—33no—
375C2×C3—61no—
376C2×C3—63no—
377C2×C3—63no—
378C2×C3—69no—
379C2×C3—63no—
380C2×C3—94no—
381C2×C3—912no—
382C2×C3—94no—
383C2×C3C22×#109413yescomplemented
384C2×C3C2×C3×D3×A413yes—
385D3—34no—
386D3C22×#109414yesdirect product factor
387C22—33no—
388C22—32no—
389C22—33no—
390C22—33no—
391C22—36no—
392C22—94no—
393C22—912no—
394C22—94no—
395C22—912no—
396C22—96no—
397C22D3×#109411yescharacteristic, direct product factor
398C22C22×D3×3−1+211yescharacteristic, complemented
399C3—21no—
400C3—31no—
401C3—61no—
402C3C23×#109411yescharacteristic, complemented
403C3C22×C3×D3×A411yescharacteristic
404C2—31no—
405C2—33no—
406C2—34no—
407C2—94no—
408C2C2×D3×#109413yesdirect product factor
subgroupG/H
centerC22×C3C3×D3×A4
commutator, cosocleC22×C32C23×C32
FrattiniC3C22×C3×D3×A4
FittingC24×C33C2×C3
socleC24×C32C2×C32
prime radicalC24×C32×D3C3
hypercenterC22×C32D3×A4
hypocenterC22×C3C23×3−1+2
LCSG ▷ C22×C32 ▷ C22×C3
UCSC1 ◁ C22×C3 ◁ C22×C32

Complements

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

NH ≅ G/Ntype
1. C22×C3×#1094C2semidirect
2. C2×D3×#1094C2direct (N × H)
5. C22×D3×C22⋊C9C3semidirect
7. C2×C3×#1094C22semidirect
8. D3×#1094C22direct (N × H)
17. C22×#1094D3direct (N × H)
18. C22×C3×C22⋊C9C2×C3semidirect
19. C2×D3×C22⋊C9C2×C3semidirect
22. C3×#1094C23semidirect
44. C2×#1094C2×D3direct (N × H)
45. C2×C3×C22⋊C9C22×C3semidirect
46. D3×C22⋊C9C22×C3semidirect
68. C22×C22⋊C9C3×D3semidirect
89. #1094C22×D3direct (N × H)
90. C3×C22⋊C9C23×C3semidirect
93. C24×D33−1+2semidirect
140. C2×C22⋊C9C2×C3×D3semidirect
163. C24×C3C2×3−1+2semidirect
168. C23×D3C2×3−1+2semidirect
221. C22⋊C9C22×C3×D3semidirect
259. C23×C3C22×3−1+2semidirect
268. C22×D3#1094direct (N × H)
269. C22×D3C22×3−1+2semidirect
298. C24D3×3−1+2semidirect
337. C22×C3C2×#1094semidirect
338. C22×C3C23×3−1+2semidirect
346. C2×D3C2×#1094direct (N × H)
365. C23C2×D3×3−1+2semidirect
383. C2×C3C22×#1094semidirect
386. D3C22×#1094direct (N × H)
397. C22D3×#1094direct (N × H)
398. C22C22×D3×3−1+2semidirect
402. C3C23×#1094semidirect
408. C2C2×D3×#1094direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#10942
C2×D3×#10942
C24×C32×D33
C23×#10943
C22×D3×C22⋊C93
C22×D3×3−1+24