Finite Group Databasebeta

← #72252811

Subgroups — #72252811

Order 5184.

895 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 895 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C3×A4×C22⋊A4C311yesmaximal, characteristic
2#13180074C312yesmaximal, complemented
3#13180070C312yesmaximal, complemented
4#13180069C314yesmaximal, complemented
5#13180067C311yesmaximal, characteristic, complemented
6C22×#88880C312yesmaximal, complemented
7C22×(C22⋊A4)⋊C9C311yesmaximal, characteristic, complemented
8#13049240—41nomaximal
9A4×C9⋊A4—42nomaximal
10C2×#88880—32no—
11C2×(C22⋊A4)⋊C9—31no—
12C3×C22⋊(C22⋊A4)C3212yes—
13C22×C3×C22⋊A4C3211yescharacteristic
14C24×C3×A4C3211yescharacteristic
15A4×C22⋊A4—33no—
16C22⋊(C22⋊(C22⋊C9))C3212yescomplemented
17C22×C22⋊(C22⋊C9)C3211yescharacteristic, complemented
18C22×C22⋊(C22⋊C9)C3214yescomplemented
19C24×C22⋊C9C3212yescomplemented
20C32×C22⋊A4—41no—
21C3×A42—42no—
22C3×A42—121no—
23#88907—41no—
24C9⋊(C22⋊A4)—44no—
25C22×#1094—42no—
26C22×C9⋊A4—42no—
27C22×C9×A4—42no—
28#88881—44no—
29#88881—42no—
30#88881—44no—
31#88881—44no—
32#88881—124no—
33#88880—42no—
34#88880—121no—
35#88880A412yescomplemented
36(C22⋊A4)⋊C9—42no—
37(C22⋊A4)⋊C9A411yescharacteristic, complemented
38A4×C22⋊C9—44no—
39A4×3−1+2—162no—
40C3×C9⋊A4—161no—
41C2×C3×C22⋊A4—31no—
42C23×C3×A4—32no—
43C23×C3×A4—91no—
44C2×C22⋊(C22⋊C9)—31no—
45C2×C22⋊(C22⋊C9)—34no—
46C23×C22⋊C9—32no—
47C23×C22⋊C9—32no—
48C23×C22⋊C9—92no—
49C2×#1094—122no—
50C2×C9⋊A4—122no—
51C2×C9×A4—122no—
52C26×C3C3311yescharacteristic
53C22⋊(C22⋊A4)—32no—
54C22×C22⋊A43−1+213yescomplemented
55C24×A4—31no—
56C24×C32—41no—
57C3×C22⋊A4—44no—
58C3×C22⋊A4—42no—
59C3×C22⋊A4—122no—
60C3×C22⋊A4—124no—
61C3×C22⋊A4—123no—
62C3×C22⋊A4—362no—
63C3×C22⋊A4C3×A411yescharacteristic
64C22×C3×A4—31no—
65C22×C3×A4—31no—
66C22×C3×A4—42no—
67C22×C3×A4—91no—
68C22×C3×A4—92no—
69C22×C3×A4—121no—
70C22×C3×A4C3×A412yes—
71A42—126no—
72A42—129no—
73C24×C9—42no—
74C22⋊(C22⋊C9)—44no—
75C22⋊(C22⋊C9)—42no—
76C22⋊(C22⋊C9)—122no—
77C22⋊(C22⋊C9)—124no—
78C22⋊(C22⋊C9)—362no—
79C22⋊(C22⋊C9)C3×A414yescomplemented
80C22⋊(C22⋊C9)C3×A411yescharacteristic, complemented
81C22×C22⋊C9—34no—
82C22×C22⋊C9—44no—
83C22×C22⋊C9—44no—
84C22×C22⋊C9—42no—
85C22×C22⋊C9—92no—
86C22×C22⋊C9—92no—
87C22×C22⋊C9—92no—
88C22×C22⋊C9—121no—
89C22×C22⋊C9—124no—
90C22×C22⋊C9C3×A412yescomplemented
91C22×C22⋊C9C3×A412yescomplemented
92C32×A4—162no—
93C32×A4—161no—
94C32×A4—481no—
95C22×3−1+2—162no—
96C22×C3×C9—161no—
97#1094—42no—
98#1094—162no—
99#1094—481no—
100C3×C22⋊C9—162no—
101C9⋊A4—42no—
102C9⋊A4—162no—
103C9⋊A4—164no—
104C9⋊A4—164no—
105C9⋊A4—164no—
106C9⋊A4—161no—
107C9⋊A4—164no—
108C9⋊A4—484no—
109C9×A4—42no—
110C9×A4—164no—
111C25×C3—32no—
112C25×C3—31no—
113C25×C3—91no—
114C25×C3—92no—
115C25×C3—271no—
116C2×C22⋊A4—33no—
117C23×A4—92no—
118C23×A4—93no—
119C3×3−1+2—641noSylow
120C23×C32—122no—
121C23×C32—361no—
122C2×C3×A4—32no—
123C2×C3×A4—91no—
124C2×C3×A4—122no—
125C2×C3×A4—361no—
126C23×C9—122no—
127C23×C9—122no—
128C23×C9—362no—
129C2×C22⋊C9—32no—
130C2×C22⋊C9—32no—
131C2×C22⋊C9—92no—
132C2×C22⋊C9—122no—
133C2×C22⋊C9—124no—
134C2×C22⋊C9—124no—
135C2×C22⋊C9—361no—
136C2×C22⋊C9—364no—
137C26C3×3−1+211yescharacteristic, complemented, Sylow
138C2×3−1+2—482no—
139C2×C3×C9—481no—
140C24×C3—31no—
141C24×C3—31no—
142C24×C3—34no—
143C24×C3—91no—
144C24×C3—92no—
145C24×C3—92no—
146C24×C3—92no—
147C24×C3—92no—
148C24×C3—92no—
149C24×C3—92no—
150C24×C3—121no—
151C24×C3—272no—
152C24×C3—271no—
153C24×C3—272no—
154C24×C3—271no—
155C24×C3—271no—
156C24×C3—274no—
157C24×C3—271no—
158C24×C3—271no—
159C24×C3—274no—
160C24×C3—272no—
161C24×C3C32×A411yescharacteristic
162C24×C3C32×A412yes—
163C22⋊A4—122no—
164C22⋊A4—126no—
165C22⋊A4—124no—
166C22⋊A4—364no—
167C22⋊A4—366no—
168C22⋊A4C9⋊A413yescomplemented
169C22×A4—33no—
170C22×A4—32no—
171C22×A4—46no—
172C22×A4—91no—
173C22×A4—93no—
174C22×A4—96no—
175C22×A4—123no—
176C22×C32—42no—
177C22×C32—121no—
178C22×C32—121no—
179C22×C32—161no—
180C22×C32—361no—
181C22×C32—362no—
182C3×A4—42no—
183C3×A4—121no—
184C3×A4—164no—
185C3×A4—162no—
186C3×A4—482no—
187C3×A4—484no—
188C3×A4—483no—
189C3×A4—486no—
190C3×A4—489no—
191C3×A4—1442no—
192C3×A4A4211yescharacteristic
193C22×C9—42no—
194C22×C9—42no—
195C22×C9—124no—
196C22×C9—164no—
197C22×C9—161no—
198C22×C9—362no—
199C22×C9—362no—
200C22×C9—362no—
201C22⋊C9—42no—
202C22⋊C9—44no—
203C22⋊C9—44no—
204C22⋊C9—124no—
205C22⋊C9—121no—
206C22⋊C9—164no—
207C22⋊C9—162no—
208C22⋊C9—484no—
209C22⋊C9—482no—
210C22⋊C9—1442no—
211C22⋊C9A4212yescomplemented
212C25—31no—
213C25—32no—
214C25—92no—
215C25—91no—
216C25—271no—
217C33—641no—
2183−1+2—162no—
2193−1+2—644no—
2203−1+2—642no—
2213−1+2—641no—
222C3×C9—161no—
223C3×C9—642no—
224C23×C3—32no—
225C23×C3—32no—
226C23×C3—32no—
227C23×C3—92no—
228C23×C3—91no—
229C23×C3—91no—
230C23×C3—94no—
231C23×C3—91no—
232C23×C3—92no—
233C23×C3—91no—
234C23×C3—271no—
235C23×C3—274no—
236C23×C3—271no—
237C23×C3—271no—
238C23×C3—271no—
239C23×C3—274no—
240C23×C3—271no—
241C23×C3—272no—
242C23×C3—272no—
243C23×C3—272no—
244C23×C3—271no—
245C23×C3—272no—
246C23×C3—272no—
247C23×C3—271no—
248C23×C3—274no—
249C23×C3—274no—
250C23×C3—274no—
251C23×C3—274no—
252C23×C3—274no—
253C23×C3—272no—
254C23×C3—362no—
255C23×C3—363no—
256C2×A4—92no—
257C2×A4—93no—
258C2×A4—126no—
259C2×A4—363no—
260C2×C32—122no—
261C2×C32—361no—
262C2×C32—481no—
263C2×C9—122no—
264C2×C9—122no—
265C2×C9—362no—
266C2×C9—481no—
267C2×C9—484no—
268C24—31no—
269C24—31no—
270C24—34no—
271C24—91no—
272C24—92no—
273C24—92no—
274C24—92no—
275C24—92no—
276C24—92no—
277C24—92no—
278C24—271no—
279C24—272no—
280C24—271no—
281C24—272no—
282C24—271no—
283C24—274no—
284C24—271no—
285C24—271no—
286C24—272no—
287C24—274no—
288C24C3×C9⋊A411yescharacteristic, complemented
289C24A4×3−1+212yescomplemented
290C22×C3—31no—
291C22×C3—34no—
292C22×C3—31no—
293C22×C3—92no—
294C22×C3—91no—
295C22×C3—92no—
296C22×C3—92no—
297C22×C3—92no—
298C22×C3—92no—
299C22×C3—92no—
300C22×C3—123no—
301C22×C3—122no—
302C22×C3—163no—
303C22×C3—271no—
304C22×C3—272no—
305C22×C3—271no—
306C22×C3—272no—
307C22×C3—271no—
308C22×C3—272no—
309C22×C3—274no—
310C22×C3—274no—
311C22×C3—271no—
312C22×C3—271no—
313C22×C3—361no—
314C22×C3—363no—
315C22×C3—366no—
316C22×C3C3×A4212yes—
317C22×C3C3×A4211yescharacteristic
318A4—31no—
319A4—46no—
320A4—123no—
321A4—486no—
322A4—484no—
323A4—482no—
324A4—1444no—
325A4—1446no—
326C32—41no—
327C32—161no—
328C32—642no—
329C32—1923no—
330C9—42no—
331C9—161no—
332C9—164no—
333C9—642no—
334C23—32no—
335C23—32no—
336C23—32no—
337C23—91no—
338C23—92no—
339C23—91no—
340C23—94no—
341C23—91no—
342C23—92no—
343C23—91no—
344C23—271no—
345C23—274no—
346C23—271no—
347C23—271no—
348C23—271no—
349C23—274no—
350C23—271no—
351C23—272no—
352C23—272no—
353C23—272no—
354C23—271no—
355C23—272no—
356C23—272no—
357C23—271no—
358C23—274no—
359C23—274no—
360C23—274no—
361C23—274no—
362C23—274no—
363C23—272no—
364C2×C3—31no—
365C2×C3—32no—
366C2×C3—92no—
367C2×C3—91no—
368C2×C3—271no—
369C2×C3—362no—
370C2×C3—363no—
371C2×C3—483no—
372C22—31no—
373C22—34no—
374C22—31no—
375C22—92no—
376C22—91no—
377C22—92no—
378C22—92no—
379C22—92no—
380C22—92no—
381C22—92no—
382C22—272no—
383C22—271no—
384C22—272no—
385C22—271no—
386C22—271no—
387C22—272no—
388C22—274no—
389C22—274no—
390C22—271no—
391C22—271no—
392C22A4×C9⋊A412yescomplemented
393C22#1304924011yescharacteristic, complemented
394C3—121no—
395C3—163no—
396C3—1922no—
397C3A4311yescharacteristic
398C2—32no—
399C2—31no—
400C2—92no—
401C2—91no—
402C2—271no—
subgroupG/H
center, Frattini, hypercenterC3A43
commutator, Fitting, socle, cosocleC26×C3C33
prime radicalC3×A4×C22⋊A4C3
hypocenterC26C3×3−1+2
LCSG ▷ C26×C3 ▷ C26
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
2. #13180074C3semidirect
3. #13180070C3semidirect
4. #13180069C3semidirect
5. #13180067C3semidirect
6. C22×#88880C3semidirect
7. C22×(C22⋊A4)⋊C9C3semidirect
16. C22⋊(C22⋊(C22⋊C9))C32semidirect
17. C22×C22⋊(C22⋊C9)C32semidirect
18. C22×C22⋊(C22⋊C9)C32semidirect
19. C24×C22⋊C9C32semidirect
35. #88880A4semidirect
37. (C22⋊A4)⋊C9A4semidirect
54. C22×C22⋊A43−1+2semidirect
79. C22⋊(C22⋊C9)C3×A4semidirect
80. C22⋊(C22⋊C9)C3×A4semidirect
90. C22×C22⋊C9C3×A4semidirect
91. C22×C22⋊C9C3×A4semidirect
137. C26C3×3−1+2semidirect
168. C22⋊A4C9⋊A4semidirect
211. C22⋊C9A42semidirect
288. C24C3×C9⋊A4semidirect
289. C24A4×3−1+2semidirect
392. C22A4×C9⋊A4semidirect
393. C22#13049240semidirect

Maximal subgroups

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

subgroupindex
C3×A4×C22⋊A43
#131800743
#131800703
#131800693
#131800673
C22×#888803
C22×(C22⋊A4)⋊C93
#130492404
A4×C9⋊A44