Finite Group Databasebeta

← #11808833

Subgroups — #11808833

Order 1152.

756 conjugacy classes of subgroups.

The subgroup lattice has 363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63449C211yesmaximal, characteristic
2C2×#63449C211yesmaximal, characteristic
3C9×#398C211yesmaximal, characteristic
4#10588663C211yesmaximal, characteristic
5#10588659C211yesmaximal, characteristic
6#10588659C212yesmaximal
7C4⋊C4×Dic9C212yesmaximal
8#10588337C212yesmaximal
9#10588336C211yesmaximal, characteristic
10#10588329C212yesmaximal
11#10588328C211yesmaximal, characteristic
12#77740—31nomaximal
13C22×Dic18C2211yescharacteristic
14C22×Dic18C2211yescharacteristic
15C2×C9×C4⋊C4C2211yescharacteristic
16C2×C9×C4⋊C4C2211yescharacteristic
17C2×C9×C4⋊C4C2212yes—
18C2×C4⋊Dic9C2212yes—
19C2×Dic9⋊C4C2211yescharacteristic
20C2×Dic9⋊C4C2211yescharacteristic
21C2×Dic9⋊C4C2212yes—
22C2×Dic9⋊C4C2212yes—
23C2×Dic9⋊C4C2212yes—
24C2×C4×Dic9C2211yescharacteristic
25C2×C4×Dic9C2212yes—
26C2×C4×Dic9C2211yescharacteristic
27C2×C4×Dic9C2211yescharacteristic
28C2×C4×Dic9C2212yes—
29#63449—24no—
30#63449—24no—
31C9×#95C2211yescharacteristic
32C9×#95C2212yes—
33C9⋊#95C2212yes—
34C9⋊#95C2211yescharacteristic
35C9⋊#95C2212yes—
36C9⋊#95C2212yes—
37C9⋊#95C2212yes—
38C2×#887—31no—
39C2×#887—31no—
40C3×#398D311yescharacteristic
41#4983—31no—
42#4979—32no—
43#4979—31no—
44Dic3×C4⋊C4—32no—
45#4657—32no—
46#4656—31no—
47#4649—32no—
48#4648—31no—
49C22×C4×C9C2312yes—
50C22×C4×C9C2311yescharacteristic
51C22×C4×C9C2311yescharacteristic
52C22×C4×C9C2312yes—
53C22×C4×C9C2311yescharacteristic
54C22×Dic9C2311yescharacteristic
55C22×Dic9C2311yescharacteristic
56C22×Dic9C2312yes—
57C22×Dic9C2311yescharacteristic
58C22×Dic9C2312yes—
59C22×Dic9C2311yescharacteristic
60C2×Dic18—22no—
61C2×Dic18—22no—
62C2×Dic18—22no—
63C2×Dic18—22no—
64C2×Dic18—24no—
65C9×C4⋊C4—22no—
66C9×C4⋊C4—22no—
67C9×C4⋊C4—24no—
68C4⋊Dic9—24no—
69Dic9⋊C4—22no—
70Dic9⋊C4—24no—
71Dic9⋊C4—22no—
72Dic9⋊C4—24no—
73Dic9⋊C4—24no—
74C4×Dic9—22no—
75C4×Dic9—24no—
76C4×Dic9—22no—
77C4×Dic9D414yes—
78C4×Dic9Q818yescomplemented
79#2399—91noSylow
80C22×Dic6—31no—
81C22×Dic6—31no—
82C2×C3×C4⋊C4C2×D312yes—
83C2×C3×C4⋊C4C2×D311yescharacteristic
84C2×C3×C4⋊C4C2×D311yescharacteristic
85C2×C4⋊Dic3—32no—
86C2×Dic3⋊C4—32no—
87C2×Dic3⋊C4—32no—
88C2×Dic3⋊C4—31no—
89C2×Dic3⋊C4—31no—
90C2×Dic3⋊C4—32no—
91C2×C4×Dic3—32no—
92C2×C4×Dic3—31no—
93C2×C4×Dic3—31no—
94C2×C4×Dic3—32no—
95C2×C4×Dic3—31no—
96#887—64no—
97#887—64no—
98C3×#95C2×D311yescharacteristic
99C3×#95C2×D312yes—
100C3⋊#95—32no—
101C3⋊#95—31no—
102C3⋊#95—32no—
103C3⋊#95—32no—
104C3⋊#95—32no—
105C23×C9C2411yescharacteristic
106C2×C4×C9—21no—
107C2×C4×C9—22no—
108C2×C4×C9—22no—
109C2×C4×C9—22no—
110C2×C4×C9—21no—
111C2×C4×C9—22no—
112C2×C4×C9—21no—
113C2×C4×C9—22no—
114C2×C4×C9—22no—
115C2×C4×C9—22no—
116C2×C4×C9C2×D412yes—
117C2×C4×C9C2×Q814yes—
118C2×C4×C9#4112yes—
119C2×Dic9—21no—
120C2×Dic9—22no—
121C2×Dic9—22no—
122C2×Dic9—22no—
123C2×Dic9—21no—
124C2×Dic9—21no—
125C2×Dic9—21no—
126C2×Dic9—22no—
127C2×Dic9—21no—
128C2×Dic9—22no—
129C2×Dic9C2×D412yes—
130C2×Dic9C2×D412yes—
131C2×Dic9C2×Q814yes—
132C2×Dic9C2×Q814yes—
133C2×Dic9#4112yes—
134C2×Dic9#4114yes—
135Dic18—28no—
136Dic18—28no—
137C2×C4×Q8—91no—
138C2×C4×Q8—91no—
139#398—91no—
140#398—92no—
141#398D911yescharacteristic
142#395—92no—
143#395—91no—
144#395—91no—
145C4×C4⋊C4—92no—
146C4×C4⋊C4—92no—
147#376—91no—
148C22×C3×C4C22×D312yes—
149C22×C3×C4C22×D311yescharacteristic
150C22×C3×C4C22×D311yescharacteristic
151C22×C3×C4C22×D311yescharacteristic
152C22×C3×C4C22×D312yes—
153C22×Dic3—31no—
154C22×Dic3—32no—
155C22×Dic3—31no—
156C22×Dic3—31no—
157C22×Dic3—32no—
158C22×Dic3—31no—
159C2×Dic6—62no—
160C2×Dic6—62no—
161C2×Dic6—64no—
162C2×Dic6—62no—
163C2×Dic6—62no—
164C3×C4⋊C4—22no—
165C3×C4⋊C4—22no—
166C3×C4⋊C4—24no—
167C4⋊Dic3—64no—
168Dic3⋊C4—64no—
169Dic3⋊C4—62no—
170Dic3⋊C4—64no—
171Dic3⋊C4—64no—
172Dic3⋊C4—62no—
173C4×Dic3—34no—
174C4×Dic3—38no—
175C4×Dic3—62no—
176C4×Dic3—64no—
177C4×Dic3—62no—
178C22×C9C22×D411yescharacteristic
179C22×C9C22×Q812yes—
180C22×C9C2×#4111yescharacteristic
181C22×C9C2×#4112yes—
182C22×C9C2×#4111yescharacteristic
183C4×C9—22no—
184C4×C9—22no—
185C4×C9—24no—
186C4×C9—41no—
187C4×C9—42no—
188Dic9—22no—
189Dic9—24no—
190Dic9—22no—
191Dic9—24no—
192Dic9—41no—
193Dic9C4⋊Q814yes—
194C22×Q8—91no—
195C22×Q8—91no—
196C4×Q8—184no—
197C4×Q8—184no—
198C2×C4⋊C4—92no—
199C2×C4⋊C4—91no—
200C2×C4⋊C4—91no—
201C2×C4⋊C4—92no—
202C2×C4⋊C4—92no—
203C2×C4⋊C4—92no—
204C2×C4⋊C4C2×D911yescharacteristic
205C2×C4⋊C4C2×D911yescharacteristic
206C2×C4⋊C4C2×D912yes—
207C2×C42—91no—
208C2×C42—92no—
209C2×C42—92no—
210C2×C42—91no—
211C2×C42—91no—
212#95—91no—
213#95—92no—
214#95—92no—
215#95—92no—
216#95—92no—
217#95C2×D911yescharacteristic
218#95C2×D912yes—
219C23×C3C23×D311yescharacteristic
220C2×C3×C4—21no—
221C2×C3×C4—22no—
222C2×C3×C4—22no—
223C2×C3×C4—22no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—22no—
227C2×C3×C4—22no—
228C2×C3×C4—22no—
229C2×C3×C4—22no—
230C2×C3×C4D3×D412yes—
231C2×C3×C4#23712yes—
232C2×C3×C4D3×Q814yes—
233C2×Dic3—32no—
234C2×Dic3—34no—
235C2×Dic3—32no—
236C2×Dic3—34no—
237C2×Dic3—32no—
238C2×Dic3—34no—
239C2×Dic3—62no—
240C2×Dic3—61no—
241C2×Dic3—61no—
242C2×Dic3—61no—
243C2×Dic3—62no—
244C2×Dic3—62no—
245C2×Dic3—62no—
246C2×Dic3—61no—
247C2×Dic3—61no—
248C2×Dic3—62no—
249Dic6—68no—
250Dic6—68no—
251C2×C9#52511yescharacteristic
252C2×C9#52511yescharacteristic
253C2×C9C2×C4⋊Q811yescharacteristic
254C2×C9#53312yes—
255C2×C9#53312yes—
256C2×Q8—182no—
257C2×Q8—182no—
258C2×Q8—184no—
259C2×Q8—182no—
260C2×Q8—182no—
261C22×C4—91no—
262C22×C4—92no—
263C22×C4—91no—
264C22×C4—91no—
265C22×C4—92no—
266C22×C4—91no—
267C22×C4C22×D912yes—
268C22×C4C22×D911yescharacteristic
269C22×C4C22×D911yescharacteristic
270C22×C4C22×D911yescharacteristic
271C22×C4C22×D912yes—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—24no—
275C4⋊C4—184no—
276C4⋊C4—182no—
277C4⋊C4—184no—
278C4⋊C4—184no—
279C4⋊C4—184no—
280C4⋊C4—182no—
281C42—94no—
282C42—98no—
283C42—182no—
284C42—184no—
285C42—182no—
286C22×C3C2×D3×D411yescharacteristic
287C22×C3C2×#23711yescharacteristic
288C22×C3C2×D3×Q812yes—
289C22×C3D3×#4112yes—
290C22×C3D3×#4111yescharacteristic
291C3×C4—22no—
292C3×C4—22no—
293C3×C4—24no—
294C3×C4—41no—
295C3×C4—42no—
296Dic3—34no—
297Dic3—64no—
298Dic3—64no—
299Dic3—62no—
300Dic3—62no—
301Dic3—121no—
302C9#239911yescharacteristic, complemented, Sylow
303C23C23×D911yescharacteristic
304Q8—188no—
305Q8—188no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—92no—
317C2×C4—94no—
318C2×C4—92no—
319C2×C4—94no—
320C2×C4—92no—
321C2×C4—94no—
322C2×C4—181no—
323C2×C4—182no—
324C2×C4—181no—
325C2×C4—181no—
326C2×C4—182no—
327C2×C4—182no—
328C2×C4—181no—
329C2×C4—182no—
330C2×C4—181no—
331C2×C4—182no—
332C2×C4D4×D912yes—
333C2×C4#369912yes—
334C2×C4Q8×D914yes—
335C2×C3#560611yescharacteristic
336C2×C3#562212yes—
337C2×C3#565611yescharacteristic
338C2×C3#568812yes—
339C2×C3D3×C4⋊Q811yescharacteristic
340C22C2×D4×D911yescharacteristic
341C22C2×#369911yescharacteristic
342C22C2×Q8×D912yes—
343C22#41×D911yescharacteristic
344C22#41×D912yes—
345C4—22no—
346C4—24no—
347C4—22no—
348C4—42no—
349C4—41no—
350C4—94no—
351C4—182no—
352C4—182no—
353C4—184no—
354C4—184no—
355C4—361no—
356C3#7774011yescharacteristic
357C2#1058970811yescharacteristic
358C2#1058972412yes—
359C2#1058975811yescharacteristic
360C2#1058979012yes—
361C2D9×C4⋊Q811yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socle, prime radicalC23×C3C23×D3
FittingC9×#398C2
hypercenter#398D9
hypocenterC9#2399
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
78. C4×Dic9Q8semidirect
302. C9#2399semidirect

Maximal subgroups

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

subgroupindex
C2×#634492
C9×#3982
#105886632
#105886592
C4⋊C4×Dic92
#105883372
#105883362
#105883292
#105883282
#777403