Finite Group Databasebeta

← C2×#14517984 #72252762

Subgroups — C2×#14517984 #72252762

Order 3888.

584 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 75 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×#11757845C211yesmaximal, characteristic, complemented
2#14517984C212yesmaximal, direct product factor
3C2×C3×((C22⋊C9)⋊C2)⋊C3C311yesmaximal, characteristic
4C2×#67×3−1+2—31nomaximal
5C2×((C22⋊C9)⋊C2)⋊C9C312yesmaximal, complemented
6C2×C9×(C22⋊C9)⋊C2C311yesmaximal, characteristic, complemented
7C2×#92265—41nomaximal
8#11757845C2211yescharacteristic, complemented
9C23×C3×3−1+2D311yescharacteristic
10C22×D3×3−1+2—31no—
11C2×C3×#1094—21no—
12C2×C3×#1094C2×C311yescharacteristic
13C3×((C22⋊C9)⋊C2)⋊C3C2×C312yes—
14#67×3−1+2—32no—
15#67×3−1+2—32no—
16C2×Dic3×3−1+2—31no—
17C2×C9⋊(C22⋊C9)—21no—
18C2×(C22⋊C9)⋊C9—22no—
19C2×(C22⋊C9)⋊C9C2×C312yescomplemented
20C2×C9×C22⋊C9C2×C311yescharacteristic, complemented
21C9×(C22⋊C9)⋊C2C2×C312yescomplemented
22((C22⋊C9)⋊C2)⋊C9C2×C314yescomplemented
23C2×#6900—41no—
24#92265—42no—
25C2×C32×#67—31no—
26C2×C3×(C22⋊C9)⋊C2C3211yescharacteristic
27C2×((C22⋊C9)⋊C2)⋊C3—31no—
28C2×D4×3−1+2—91no—
29C2×C9×#67—31no—
30C2×C9×#67—32no—
31C22×C3×3−1+2—31no—
32C22×C3×3−1+2—31no—
33C22×C3×3−1+2C2×D311yescharacteristic
34C2×D3×3−1+2—32no—
35C2×D3×3−1+2—61no—
36C2×D3×3−1+2—61no—
37C2×C3×AGL(1,ℤ/9)—41no—
38C3×#1094—21no—
39C3×#1094C22×C311yescharacteristic
40Dic3×3−1+2—32no—
41C2×D9⋊C9—42no—
42C2×C9×D9—41no—
43C9⋊(C22⋊C9)—21no—
44(C22⋊C9)⋊C9—22no—
45(C22⋊C9)⋊C9C22×C312yescomplemented
46C9×C22⋊C9C22×C311yescharacteristic, complemented
47#6900—41noSylow
48C23×C33C3×D311yescharacteristic
49C22×C32×D3—31no—
50C32×#67—32no—
51C32×#67—32no—
52C2×C32×Dic3—31no—
53C23×3−1+2—31no—
54C23×3−1+2—61no—
55C23×3−1+2—91no—
56C23×C3×C9C3×D311yescharacteristic
57C23×C3×C9C3×D312yes—
58C22×D3×C9—31no—
59C22×D3×C9—32no—
60C2×#1094—31no—
61C2×#1094—63no—
62C2×#1094—61no—
63C2×C3×C22⋊C9—21no—
64C2×C3×C22⋊C9—21no—
65C2×C3×C22⋊C9—22no—
66C2×C3×C22⋊C9C2×C3211yescharacteristic
67C3×(C22⋊C9)⋊C2C2×C3212yes—
68((C22⋊C9)⋊C2)⋊C3—32no—
69D4×3−1+2—92no—
70D4×3−1+2—92no—
71C2×C4×3−1+2—91no—
72C9×#67—32no—
73C9×#67—34no—
74C9×#67—34no—
75C9×#67—32no—
76C2×C9×Dic3—31no—
77C2×C9×Dic3—32no—
78C2×C3×3−1+2—31no—
79C2×C3×3−1+2—31no—
80C2×C3×3−1+2—41no—
81C2×C3×3−1+2—81no—
82C2×C3×3−1+2S411yescharacteristic
83D3×3−1+2—62no—
84C3×AGL(1,ℤ/9)—42no—
85C2×C9⋊C9—42no—
86C2×C9⋊C9—82no—
87C2×C9⋊C9—81no—
88C2×C92—41no—
89D9⋊C9—44no—
90C9×D9—42no—
91C2×C32×D4—91no—
92C2×C3×#67—31no—
93C2×C3×#67—91no—
94C2×(C22⋊C9)⋊C23−1+211yescharacteristic, complemented
95C2×D4×C9—92no—
96C2×D4×C9—91no—
97C22×C33—31no—
98C22×C33—31no—
99C22×C33C2×C3×D311yescharacteristic
100C2×C32×D3—32no—
101C2×C32×D3—61no—
102C2×C32×D3—61no—
103C32×Dic3—32no—
104C22×3−1+2—31no—
105C22×3−1+2—31no—
106C22×3−1+2—31no—
107C22×3−1+2—61no—
108C22×3−1+2—61no—
109C22×3−1+2—61no—
110C22×3−1+2—62no—
111C22×3−1+2—62no—
112C22×3−1+2—61no—
113C22×3−1+2—61no—
114C22×3−1+2—92no—
115C22×3−1+2—181no—
116C22×3−1+2—181no—
117C22×C3×C9—31no—
118C22×C3×C9—32no—
119C22×C3×C9—31no—
120C22×C3×C9—32no—
121C22×C3×C9C2×C3×D311yescharacteristic
122C22×C3×C9C2×C3×D312yes—
123C2×AGL(1,ℤ/9)—121no—
124C2×D3×C9—32no—
125C2×D3×C9—34no—
126C2×D3×C9—61no—
127C2×D3×C9—62no—
128C2×D3×C9—61no—
129C2×D3×C9—62no—
130C2×C3×D9—41no—
131#1094—31no—
132#1094—63no—
133#1094—61no—
134C3×C22⋊C9—21no—
135C3×C22⋊C9—21no—
136C3×C22⋊C9—22no—
137C3×C22⋊C9C22×C3211yescharacteristic
138C4×3−1+2—92no—
139C9×Dic3—34no—
140C9×Dic3—32no—
141C3×3−1+2—41no—
142C3×3−1+2—81no—
143C3×3−1+2C2×S411yescharacteristic
144C9⋊C9—42no—
145C9⋊C9—82no—
146C9⋊C9—81no—
147C92—41no—
148C23×C32—31no—
149C23×C32—31no—
150C23×C32—61no—
151C23×C32—91no—
152C23×C32C32×D311yescharacteristic
153C22×C3×D3—31no—
154C22×C3×D3—91no—
155C32×D4—92no—
156C32×D4—92no—
157C2×C32×C4—91no—
158C3×#67—32no—
159C3×#67—32no—
160C3×#67—92no—
161C3×#67—92no—
162C2×C3×Dic3—31no—
163C2×C3×Dic3—91no—
164C23×C9—21no—
165C23×C9—32no—
166C23×C9—92no—
167C23×C9—91no—
168C23×C9AGL(1,ℤ/9)11yescharacteristic, complemented
169C2×C22⋊C9—23no—
170C2×C22⋊C9—21no—
171C2×C22⋊C9—62no—
172C2×C22⋊C9—61no—
173C2×C22⋊C9C2×3−1+211yescharacteristic, complemented
174(C22⋊C9)⋊C2C2×3−1+212yescomplemented
175D4×C9—92no—
176D4×C9—94no—
177D4×C9—94no—
178D4×C9—92no—
179C2×C4×C9—92no—
180C2×C4×C9—91no—
181C2×C33—31no—
182C2×C33—31no—
183C2×C33C3×S411yescharacteristic
184C32×D3—62no—
185C2×3−1+2—31no—
186C2×3−1+2—31no—
187C2×3−1+2—31no—
188C2×3−1+2—61no—
189C2×3−1+2—61no—
190C2×3−1+2—61no—
191C2×3−1+2—62no—
192C2×3−1+2—62no—
193C2×3−1+2—61no—
194C2×3−1+2—61no—
195C2×3−1+2—121no—
196C2×3−1+2—182no—
197C2×3−1+2—243no—
198C2×3−1+2—241no—
199C2×C3×C9—32no—
200C2×C3×C9—31no—
201C2×C3×C9—32no—
202C2×C3×C9—31no—
203C2×C3×C9—41no—
204C2×C3×C9—81no—
205C2×C3×C9—82no—
206C2×C3×C9—81no—
207C2×C3×C9C3×S411yescharacteristic
208C2×C3×C9C3×S412yes—
209AGL(1,ℤ/9)—122no—
210D3×C9—62no—
211D3×C9—64no—
212C3×D9—42no—
213C2×C3×D4—91no—
214C2×C3×D4—271no—
215C2×#67—31no—
216C22×C32—31no—
217C22×C32—31no—
218C22×C32—31no—
219C22×C32—31no—
220C22×C32—31no—
221C22×C32—31no—
222C22×C32—61no—
223C22×C32—61no—
224C22×C32—61no—
225C22×C32—91no—
226C22×C32—91no—
227C22×C32—92no—
228C22×C32—181no—
229C22×C32—181no—
230C22×C32—181no—
231C22×C32—181no—
232C22×C32C2×C32×D311yescharacteristic
233C2×C3×D3—32no—
234C2×C3×D3—61no—
235C2×C3×D3—61no—
236C2×C3×D3—92no—
237C2×C3×D3—181no—
238C2×C3×D3—181no—
239C32×C4—92no—
240C3×Dic3—32no—
241C3×Dic3—92no—
242C22×C9—21no—
243C22×C9—31no—
244C22×C9—32no—
245C22×C9—31no—
246C22×C9—32no—
247C22×C9—32no—
248C22×C9—61no—
249C22×C9—62no—
250C22×C9—62no—
251C22×C9—61no—
252C22×C9—94no—
253C22×C9—92no—
254C22×C9—182no—
255C22×C9—181no—
256C22×C9—182no—
257C22×C9—181no—
258C22×C9C2×AGL(1,ℤ/9)11yescharacteristic, complemented
259C2×D9—41no—
260C22⋊C9—23no—
261C22⋊C9—21no—
262C22⋊C9—62no—
263C22⋊C9—61no—
264C22⋊C9C22×3−1+211yescharacteristic, complemented
265C4×C9—94no—
266C4×C9—92no—
267C33C2×C3×S411yescharacteristic
2683−1+2—31no—
2693−1+2—61no—
2703−1+2—121no—
2713−1+2—243no—
2723−1+2—241no—
273C3×C9—41no—
274C3×C9—81no—
275C3×C9—82no—
276C3×C9—81no—
277C3×C9C2×C3×S411yescharacteristic
278C3×C9C2×C3×S412yes—
279C23×C3—21no—
280C23×C3—91no—
281C23×C3—91no—
282C23×C3—271no—
283C23×C3C3×AGL(1,ℤ/9)11yescharacteristic
284C23×C3D3×3−1+211yescharacteristic
285C22×D3—31no—
286C3×D4—92no—
287C3×D4—92no—
288C3×D4—272no—
289C3×D4—272no—
290C2×C3×C4—91no—
291C2×C3×C4—271no—
292#67—32no—
293#67—32no—
294C2×Dic3—31no—
295C2×C32—31no—
296C2×C32—31no—
297C2×C32—31no—
298C2×C32—31no—
299C2×C32—31no—
300C2×C32—31no—
301C2×C32—61no—
302C2×C32—61no—
303C2×C32—61no—
304C2×C32—91no—
305C2×C32—91no—
306C2×C32—181no—
307C2×C32—181no—
308C2×C32—182no—
309C2×C32C32×S411yescharacteristic
310C3×D3—62no—
311C3×D3—182no—
312C2×C9—21no—
313C2×C9—32no—
314C2×C9—32no—
315C2×C9—31no—
316C2×C9—31no—
317C2×C9—32no—
318C2×C9—41no—
319C2×C9—61no—
320C2×C9—61no—
321C2×C9—62no—
322C2×C9—62no—
323C2×C9—83no—
324C2×C9—81no—
325C2×C9—184no—
326C2×C9—182no—
327C2×C9—242no—
328C2×C9—241no—
329C2×C9((C22⋊C9)⋊C2)⋊C311yescharacteristic, complemented
330D9—42no—
331C2×D4—91noSylow
332C22×C3—21no—
333C22×C3—31no—
334C22×C3—31no—
335C22×C3—31no—
336C22×C3—31no—
337C22×C3—61no—
338C22×C3—61no—
339C22×C3—91no—
340C22×C3—91no—
341C22×C3—92no—
342C22×C3—91no—
343C22×C3—181no—
344C22×C3—181no—
345C22×C3—181no—
346C22×C3—181no—
347C22×C3—272no—
348C22×C3—541no—
349C22×C3—541no—
350C22×C3C2×C3×AGL(1,ℤ/9)11yescharacteristic
351C22×C3C2×D3×3−1+211yescharacteristic
352C2×D3—32no—
353C2×D3—61no—
354C2×D3—61no—
355C3×C4—92no—
356C3×C4—272no—
357Dic3—32no—
358C32—31no—
359C32—31no—
360C32—61no—
361C32C2×C32×S411yescharacteristic
362C9—21no—
363C9—32no—
364C9—41no—
365C9—83no—
366C9—81no—
367C9—242no—
368C9—241no—
369C9C2×((C22⋊C9)⋊C2)⋊C311yescharacteristic, complemented
370C23—91no—
371C23#9226511yescharacteristic, complemented
372D4—92no—
373D4—92no—
374C2×C4—91no—
375C2×C3—21no—
376C2×C3—31no—
377C2×C3—31no—
378C2×C3—31no—
379C2×C3—31no—
380C2×C3—61no—
381C2×C3—61no—
382C2×C3—91no—
383C2×C3—91no—
384C2×C3—91no—
385C2×C3—181no—
386C2×C3—181no—
387C2×C3—182no—
388C2×C3—542no—
389C2×C3S4×3−1+211yescharacteristic
390C2×C3C3×((C22⋊C9)⋊C2)⋊C311yescharacteristic
391D3—62no—
392C22—31no—
393C22—31no—
394C22—92no—
395C22—181no—
396C22—181no—
397C22C2×#9226511yescharacteristic, complemented
398C4—92no—
399C3—21no—
400C3—91no—
401C3C2×S4×3−1+211yescharacteristic
402C3C2×C3×((C22⋊C9)⋊C2)⋊C311yescharacteristic
403C2—31no—
404C2—31no—
405C2—182no—
406C2#1451798411yescharacteristic, direct product factor
subgroupG/H
centerC2×C3C3×((C22⋊C9)⋊C2)⋊C3
commutator, cosocleC3×C22⋊C9C22×C32
FrattiniC32C2×C32×S4
FittingC23×C3×3−1+2D3
socleC23×C32C32×D3
prime radicalC2×C3×((C22⋊C9)⋊C2)⋊C3C3
hypercenterC2×C9((C22⋊C9)⋊C2)⋊C3
hypocenterC22⋊C9C22×3−1+2
LCSG ▷ C3×C22⋊C9 ▷ C22⋊C9
UCSC1 ◁ C2×C3 ◁ C2×C9

Complements

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

NH ≅ G/Ntype
1. C2×#11757845C2semidirect
2. #14517984C2direct (N × H)
5. C2×((C22⋊C9)⋊C2)⋊C9C3semidirect
6. C2×C9×(C22⋊C9)⋊C2C3semidirect
8. #11757845C22semidirect
19. C2×(C22⋊C9)⋊C9C2×C3semidirect
20. C2×C9×C22⋊C9C2×C3semidirect
21. C9×(C22⋊C9)⋊C2C2×C3semidirect
22. ((C22⋊C9)⋊C2)⋊C9C2×C3semidirect
45. (C22⋊C9)⋊C9C22×C3semidirect
46. C9×C22⋊C9C22×C3semidirect
94. C2×(C22⋊C9)⋊C23−1+2semidirect
168. C23×C9AGL(1,ℤ/9)semidirect
173. C2×C22⋊C9C2×3−1+2semidirect
174. (C22⋊C9)⋊C2C2×3−1+2semidirect
258. C22×C9C2×AGL(1,ℤ/9)semidirect
264. C22⋊C9C22×3−1+2semidirect
329. C2×C9((C22⋊C9)⋊C2)⋊C3semidirect
369. C9C2×((C22⋊C9)⋊C2)⋊C3semidirect
371. C23#92265semidirect
397. C22C2×#92265semidirect
406. C2#14517984direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117578452
#145179842
C2×C3×((C22⋊C9)⋊C2)⋊C33
C2×#67×3−1+23
C2×((C22⋊C9)⋊C2)⋊C93
C2×C9×(C22⋊C9)⋊C23
C2×#922654