Finite Group Databasebeta

← #11803353

Subgroups — #11803353

Order 1152.

948 conjugacy classes of subgroups.

The subgroup lattice has 435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#611C211yesmaximal, characteristic
2C22×Dic9⋊C4C211yesmaximal, characteristic, complemented
3C2×#63448C211yesmaximal, characteristic
4C4×C9×C22⋊C4C211yesmaximal, characteristic, complemented
5#10588638C211yesmaximal, characteristic
6#10588630C211yesmaximal, characteristic, complemented
7#10588623C211yesmaximal, characteristic, complemented
8#10588620C212yesmaximal, complemented
9#10588608C212yesmaximal, complemented
10#10588348C212yesmaximal, complemented
11#10588333C212yesmaximal, complemented
12#73446—31nomaximal
13C23×C4×C9C2211yescharacteristic
14C22×#611C2211yescharacteristic
15C23×Dic9C2211yescharacteristic
16C23×Dic9C2211yescharacteristic
17C22×C4×D9C2211yescharacteristic
18C2×C9×C22⋊C4C2211yescharacteristic
19C2×C9×C22⋊C4C2211yescharacteristic
20C2×C42×C9C2212yes—
21C2×#3676C2211yescharacteristic
22C4×#611—24no—
23C2×(C2×D9)⋊C4C2211yescharacteristic
24C2×(C2×D9)⋊C4C2212yes—
25C2×(C2×D9)⋊C4C2212yes—
26C2×C4⋊Dic9C2212yes—
27C2×C4⋊Dic9C2212yes—
28C2×Dic9⋊C4—24no—
29C2×Dic9⋊C4C2212yes—
30C2×Dic9⋊C4C2212yes—
31C2×Dic9⋊C4C2211yescharacteristic
32C2×C4×Dic9C2211yescharacteristic
33#63448C418yescomplemented
34C9×#95C2212yes—
35C9⋊#95C2212yes—
36C9⋊#95C2212yes—
37C9⋊#95C2212yes—
38C9⋊#95C2212yes—
39C2×C4×#67—31no—
40C22×Dic3⋊C4—31no—
41C2×#886—31no—
42C3×C4×C22⋊C4D311yescharacteristic
43#4958—31no—
44#4950—31no—
45#4943—31no—
46#4940—32no—
47#4928—32no—
48#4668—32no—
49#4653—32no—
50C24×C9C2311yescharacteristic
51C23×D9C2311yescharacteristic
52C22×C4×C9—42no—
53C22×C4×C9D414yes—
54C22×C4×C9C2312yes—
55C22×C4×C9C2312yes—
56C22×C4×C9C2311yescharacteristic
57C22×C4×C9C2311yescharacteristic
58C2×#611—22no—
59C2×#611—22no—
60C2×#611C2×C414yes—
61C22×Dic9—22no—
62C22×Dic9—22no—
63C22×Dic9—22no—
64C22×Dic9—42no—
65C22×Dic9C2×C414yescomplemented
66C22×Dic9C2311yescharacteristic
67C22×Dic9C2312yes—
68C22×Dic9C2311yescharacteristic
69C22×Dic9C2312yes—
70C22×Dic9C2311yescharacteristic
71C2×C4×D9—22no—
72C2×C4×D9—42no—
73C9×C22⋊C4—22no—
74C9×C22⋊C4C2×C414yescomplemented
75C42×C9—42no—
76#3676—22no—
77(C2×D9)⋊C4—22no—
78(C2×D9)⋊C4—42no—
79(C2×D9)⋊C4C2×C418yescomplemented
80C4⋊Dic9—42no—
81C4⋊Dic9C2×C418yescomplemented
82Dic9⋊C4—22no—
83Dic9⋊C4—24no—
84Dic9⋊C4—24no—
85C4×Dic9—22no—
86#2322—91noSylow
87C23×C3×C4C2×D311yescharacteristic
88C22×#67—31no—
89C23×Dic3—31no—
90C23×Dic3—31no—
91C22×C4×D3—31no—
92C2×C3×C22⋊C4C2×D311yescharacteristic
93C2×C3×C22⋊C4C2×D311yescharacteristic
94C2×C3×C42C2×D312yes—
95C2×#217—31no—
96C4×#67—64no—
97C2×(C2×D3)⋊C4—32no—
98C2×(C2×D3)⋊C4—31no—
99C2×(C2×D3)⋊C4—32no—
100C2×C4⋊Dic3—32no—
101C2×C4⋊Dic3—32no—
102C2×Dic3⋊C4—32no—
103C2×Dic3⋊C4—31no—
104C2×Dic3⋊C4—32no—
105C2×Dic3⋊C4—64no—
106C2×C4×Dic3—31no—
107#886—38no—
108C3×#95C2×D312yes—
109C3⋊#95—32no—
110C3⋊#95—32no—
111C3⋊#95—32no—
112C3⋊#95—32no—
113C23×C9—22no—
114C23×C9—22no—
115C23×C9C22×C412yes—
116C23×C9C2×D412yes—
117C23×C9#4112yes—
118C23×C9C2411yescharacteristic
119C22×D9—21no—
120C22×D9—21no—
121C22×D9—22no—
122C22×D9—22no—
123C22×D9C22×C412yes—
124C2×C4×C9—22no—
125C2×C4×C9—22no—
126C2×C4×C9—22no—
127C2×C4×C9—22no—
128C2×C4×C9—22no—
129C2×C4×C9—22no—
130C2×C4×C9—22no—
131C2×C4×C9—44no—
132C2×C4×C9C22×C414yes—
133C2×C4×C9C2×D412yes—
134C2×C4×C9C2×D412yes—
135#611—28no—
136C2×Dic9—28no—
137C2×Dic9—21no—
138C2×Dic9—22no—
139C2×Dic9—22no—
140C2×Dic9—21no—
141C2×Dic9—21no—
142C2×Dic9—22no—
143C2×Dic9—21no—
144C2×Dic9—22no—
145C2×Dic9—22no—
146C2×Dic9—22no—
147C2×Dic9—22no—
148C2×Dic9—44no—
149C2×Dic9C22×C412yes—
150C2×Dic9C22×C414yes—
151C4×D9—44no—
152C2×#123—91no—
153C2×C4×D4—91no—
154C22×C4⋊C4—91no—
155#389—92no—
156#388—92no—
157#387—92no—
158#386—91no—
159#385—91no—
160#385—92no—
161#381—91no—
162C4×C22⋊C4D911yescharacteristic, complemented
163C24×C3C22×D311yescharacteristic
164C23×D3—31no—
165C22×C3×C4—42no—
166C22×C3×C4D1214yes—
167C22×C3×C4C22×D312yes—
168C22×C3×C4C22×D312yes—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C2×#67—34no—
172C2×#67—62no—
173C2×#67—62no—
174C22×Dic3—34no—
175C22×Dic3—31no—
176C22×Dic3—32no—
177C22×Dic3—31no—
178C22×Dic3—32no—
179C22×Dic3—31no—
180C22×Dic3—62no—
181C22×Dic3—62no—
182C22×Dic3—62no—
183C22×Dic3—122no—
184C2×C4×D3—62no—
185C2×C4×D3—122no—
186C3×C22⋊C4—22no—
187C3×C22⋊C4C4×D314yes—
188C3×C42—42no—
189#217—62no—
190(C2×D3)⋊C4—38no—
191(C2×D3)⋊C4—62no—
192(C2×D3)⋊C4—122no—
193C4⋊Dic3—38no—
194C4⋊Dic3—122no—
195Dic3⋊C4—64no—
196Dic3⋊C4—64no—
197Dic3⋊C4—62no—
198C4×Dic3—62no—
199C22×C9—24no—
200C22×C9—22no—
201C22×C9—22no—
202C22×C9—24no—
203C22×C9C4×D414yes—
204C22×C9C23×C411yescharacteristic
205C22×C9C22×D411yescharacteristic
206C22×C9C2×#4111yescharacteristic
207C22×C9H(5,𝔽2)12yes—
208C22×C92−1+412yes—
209C2×D9—22no—
210C2×D9—24no—
211C2×D9—41no—
212C2×D9—41no—
213C2×D9—42no—
214C4×C9—24no—
215C4×C9—22no—
216C4×C9—22no—
217C4×C9—42no—
218Dic9—24no—
219Dic9—22no—
220Dic9—41no—
221Dic9—42no—
222Dic9—41no—
223C22×D4—91no—
224C23×C4—91no—
225C23×C4—91no—
226C23×C4—91no—
227C23×C4C2×D911yescharacteristic
228#123—98no—
229C4×D4—184no—
230C2×C4⋊C4—92no—
231C2×C4⋊C4—92no—
232C2×C4⋊C4—92no—
233C2×C4⋊C4—91no—
234C2×C4⋊C4—92no—
235C2×C4⋊C4—184no—
236C2×C22⋊C4—92no—
237C2×C22⋊C4—91no—
238C2×C22⋊C4—91no—
239C2×C22⋊C4—92no—
240C2×C22⋊C4C2×D911yescharacteristic
241C2×C22⋊C4C2×D911yescharacteristic
242C2×C42—91no—
243C2×C42C2×D912yes—
244#95—92no—
245#95—92no—
246#95—92no—
247#95—92no—
248#95C2×D912yes—
249C23×C3—22no—
250C23×C3—22no—
251C23×C3C2×C4×D312yes—
252C23×C3C2×D1212yes—
253C23×C3#23512yes—
254C23×C3C23×D311yescharacteristic
255C22×D3—32no—
256C22×D3—61no—
257C22×D3—61no—
258C22×D3—62no—
259C22×D3—62no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—22no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—44no—
268C2×C3×C4C2×C4×D314yes—
269C2×C3×C4C2×D1212yes—
270C2×C3×C4C2×D1212yes—
271#67—68no—
272C2×Dic3—32no—
273C2×Dic3—34no—
274C2×Dic3—68no—
275C2×Dic3—61no—
276C2×Dic3—62no—
277C2×Dic3—62no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—62no—
281C2×Dic3—61no—
282C2×Dic3—62no—
283C2×Dic3—62no—
284C2×Dic3—62no—
285C2×Dic3—62no—
286C2×Dic3—124no—
287C4×D3—124no—
288C2×C9—24no—
289C2×C9C2×C4×D411yescharacteristic
290C2×C9#52012yes—
291C2×C9#53411yescharacteristic
292C2×C9#53611yescharacteristic
293C2×C9#53912yes—
294D9—42no—
295C24—91no—
296C24C22×D911yescharacteristic
297C2×D4—94no—
298C2×D4—182no—
299C2×D4—182no—
300C22×C4—42no—
301C22×C4—94no—
302C22×C4—91no—
303C22×C4—92no—
304C22×C4—91no—
305C22×C4—91no—
306C22×C4—92no—
307C22×C4—182no—
308C22×C4—182no—
309C22×C4—182no—
310C22×C4—182no—
311C22×C4—362no—
312C22×C4—362no—
313C22×C4D3614yes—
314C22×C4C22×D912yes—
315C22×C4C22×D912yes—
316C22×C4C22×D911yescharacteristic
317C22×C4C22×D911yescharacteristic
318C4⋊C4—98no—
319C4⋊C4—184no—
320C4⋊C4—184no—
321C4⋊C4—182no—
322C4⋊C4—362no—
323C22⋊C4—22no—
324C22⋊C4—98no—
325C22⋊C4—182no—
326C22⋊C4—182no—
327C22⋊C4—362no—
328C22⋊C4C4×D914yescomplemented
329C42—42no—
330C42—182no—
331C22×C3—22no—
332C22×C3—22no—
333C22×C3—24no—
334C22×C3—24no—
335C22×C3C4×D1214yes—
336C22×C3C22×C4×D311yescharacteristic
337C22×C3C22×D1211yescharacteristic
338C22×C3C2×#23511yescharacteristic
339C22×C3#100412yes—
340C22×C3#101012yes—
341C2×D3—62no—
342C2×D3—64no—
343C2×D3—121no—
344C2×D3—121no—
345C2×D3—122no—
346C3×C4—22no—
347C3×C4—22no—
348C3×C4—24no—
349C3×C4—42no—
350Dic3—64no—
351Dic3—62no—
352Dic3—121no—
353Dic3—122no—
354Dic3—121no—
355C9#232211yescharacteristic, complemented, Sylow
356C23—22no—
357C23—22no—
358C23—92no—
359C23—181no—
360C23—181no—
361C23—182no—
362C23—182no—
363C23C2×C4×D912yes—
364C23C2×D3612yes—
365C23#369712yes—
366C23C23×D911yescharacteristic
367D4—188no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—44no—
376C2×C4—94no—
377C2×C4—92no—
378C2×C4—188no—
379C2×C4—181no—
380C2×C4—182no—
381C2×C4—182no—
382C2×C4—181no—
383C2×C4—181no—
384C2×C4—181no—
385C2×C4—182no—
386C2×C4—182no—
387C2×C4—182no—
388C2×C4—182no—
389C2×C4—182no—
390C2×C4—364no—
391C2×C4—364no—
392C2×C4C2×C4×D914yes—
393C2×C4C2×D3612yes—
394C2×C4C2×D3612yes—
395C2×C3—24no—
396C2×C3C2×C4×D1211yescharacteristic
397C2×C3#549311yescharacteristic
398C2×C3#552611yescharacteristic
399C2×C3#554612yes—
400C2×C3#556412yes—
401D3—122no—
402C22—22no—
403C22—22no—
404C22—24no—
405C22—24no—
406C22—182no—
407C22—184no—
408C22—361no—
409C22—361no—
410C22—362no—
411C22C4×D3614yes—
412C22C22×C4×D911yescharacteristic
413C22C22×D3611yescharacteristic
414C22C2×#369711yescharacteristic
415C22#6371012yes—
416C22#6371612yes—
417C4—22no—
418C4—22no—
419C4—24no—
420C4—42no—
421C4—184no—
422C4—182no—
423C4—361no—
424C4—362no—
425C4—361no—
426C3#7344611yescharacteristic
427C2—24no—
428C2—362no—
429C2C2×C4×D3611yescharacteristic
430C2#1058959511yescharacteristic
431C2#1058962811yescharacteristic
432C2#1058964812yes—
433C2#1058966612yes—
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC4×C9×C22⋊C4C2
prime radicalC22×#611C22
cosocleC23×C9C24
hypercenterC4×C22⋊C4D9
hypocenterC9#2322
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×Dic9⋊C4C2semidirect
4. C4×C9×C22⋊C4C2semidirect
6. #10588630C2semidirect
7. #10588623C2semidirect
8. #10588620C2semidirect
9. #10588608C2semidirect
10. #10588348C2semidirect
11. #10588333C2semidirect
33. #63448C4semidirect
65. C22×Dic9C2×C4semidirect
74. C9×C22⋊C4C2×C4semidirect
79. (C2×D9)⋊C4C2×C4semidirect
81. C4⋊Dic9C2×C4semidirect
162. C4×C22⋊C4D9semidirect
328. C22⋊C4C4×D9semidirect
355. C9#2322semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6112
C22×Dic9⋊C42
C2×#634482
C4×C9×C22⋊C42
#105886382
#105886302
#105886232
#105886202
#105886082
#105883482
#105883332
#734463