Finite Group Databasebeta

← #11808827

Subgroups — #11808827

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×Q8×Dic9C211yesmaximal, characteristic
2C2×#63449C211yesmaximal, characteristic
3C9×#395C211yesmaximal, characteristic
4#10588910C211yesmaximal, characteristic
5#10588662C212yesmaximal
6#10588661C211yesmaximal, characteristic
7C4⋊C4×Dic9C212yesmaximal
8#10588341C211yesmaximal, characteristic
9#10588336C212yesmaximal
10#10588329C212yesmaximal
11#10588328C211yesmaximal, characteristic
12#77171—31nomaximal
13C22×Q8×C9C2211yescharacteristic
14C22×Dic18C2211yescharacteristic
15C2×C9×C4⋊C4C2211yescharacteristic
16C2×C9×C4⋊C4C2212yes—
17Q8×Dic9—24no—
18C2×C4⋊Dic9C2212yes—
19C2×C4⋊Dic9C2212yes—
20C2×C4⋊Dic9C2211yescharacteristic
21C2×Dic9⋊C4C2211yescharacteristic
22C2×Dic9⋊C4C2211yescharacteristic
23C2×Dic9⋊C4C2212yes—
24C2×Dic9⋊C4C2212yes—
25C2×C4×Dic9C2211yescharacteristic
26C2×C4×Dic9C2211yescharacteristic
27C2×C4×Dic9C2212yes—
28C2×C4×Dic9C2211yescharacteristic
29C2×C4×Dic9C2212yes—
30#63449—24no—
31C9×#95C2211yescharacteristic
32C9×#95C2212yes—
33C9⋊#95C2212yes—
34C9⋊#95C2211yescharacteristic
35C9⋊#95C2212yes—
36C9⋊#95C2212yes—
37C9⋊#95C2212yes—
38C2×Q8×Dic3—31no—
39C2×#887—31no—
40C3×#395D311yescharacteristic
41#5230—31no—
42#4982—32no—
43#4981—31no—
44Dic3×C4⋊C4—32no—
45#4661—31no—
46#4656—32no—
47#4649—32no—
48#4648—31no—
49C2×Q8×C9—22no—
50C2×Q8×C9—24no—
51C22×C4×C9C2311yescharacteristic
52C22×C4×C9C2311yescharacteristic
53C22×C4×C9C2312yes—
54C22×C4×C9C2312yes—
55C22×C4×C9C2311yescharacteristic
56C22×Dic9C2311yescharacteristic
57C22×Dic9C2312yes—
58C22×Dic9C2311yescharacteristic
59C22×Dic9C2312yes—
60C22×Dic9C2311yescharacteristic
61C22×Dic9C2311yescharacteristic
62C2×Dic18—22no—
63C2×Dic18—22no—
64C2×Dic18—22no—
65C9×C4⋊C4—22no—
66C9×C4⋊C4—24no—
67C4⋊Dic9—22no—
68C4⋊Dic9—24no—
69C4⋊Dic9—24no—
70Dic9⋊C4—22no—
71Dic9⋊C4—24no—
72Dic9⋊C4—24no—
73Dic9⋊C4—22no—
74C4×Dic9—24no—
75C4×Dic9—22no—
76C4×Dic9—22no—
77C4×Dic9D414yes—
78C4×Dic9Q818yescomplemented
79#2399—91noSylow
80C22×C3×Q8C2×D311yescharacteristic
81C22×Dic6—31no—
82C2×C3×C4⋊C4C2×D312yes—
83C2×C3×C4⋊C4C2×D311yescharacteristic
84Q8×Dic3—64no—
85C2×C4⋊Dic3—32no—
86C2×C4⋊Dic3—32no—
87C2×C4⋊Dic3—31no—
88C2×Dic3⋊C4—32no—
89C2×Dic3⋊C4—32no—
90C2×Dic3⋊C4—31no—
91C2×Dic3⋊C4—31no—
92C2×C4×Dic3—32no—
93C2×C4×Dic3—31no—
94C2×C4×Dic3—31no—
95C2×C4×Dic3—32no—
96C2×C4×Dic3—31no—
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
106Q8×C9—28no—
107C2×C4×C9—22no—
108C2×C4×C9—21no—
109C2×C4×C9—22no—
110C2×C4×C9—22no—
111C2×C4×C9—21no—
112C2×C4×C9—22no—
113C2×C4×C9—22no—
114C2×C4×C9—21no—
115C2×C4×C9—22no—
116C2×C4×C9C2×D412yes—
117C2×C4×C9C2×Q814yes—
118C2×C4×C9#4114yes—
119C2×C4×C9#4112yes—
120C2×Dic9—21no—
121C2×Dic9—22no—
122C2×Dic9—22no—
123C2×Dic9—21no—
124C2×Dic9—21no—
125C2×Dic9—21no—
126C2×Dic9—21no—
127C2×Dic9—22no—
128C2×Dic9—22no—
129C2×Dic9—22no—
130C2×Dic9—22no—
131C2×Dic9C2×D412yes—
132C2×Dic9C2×D412yes—
133C2×Dic9C2×Q814yes—
134C2×Dic9C2×Q814yes—
135C2×Dic9#4112yes—
136Dic18—28no—
137C2×C4×Q8—91no—
138C2×C4×Q8—91no—
139#398—91no—
140#398—92no—
141#398—91no—
142#395—91no—
143#395—92no—
144#395D911yescharacteristic
145C4×C4⋊C4—92no—
146C4×C4⋊C4—92no—
147#376—91no—
148C2×C3×Q8—22no—
149C2×C3×Q8—24no—
150C22×C3×C4C22×D311yescharacteristic
151C22×C3×C4C22×D311yescharacteristic
152C22×C3×C4C22×D312yes—
153C22×C3×C4C22×D312yes—
154C22×C3×C4C22×D311yescharacteristic
155C22×Dic3—31no—
156C22×Dic3—32no—
157C22×Dic3—31no—
158C22×Dic3—31no—
159C22×Dic3—31no—
160C22×Dic3—32no—
161C2×Dic6—62no—
162C2×Dic6—62no—
163C2×Dic6—62no—
164C3×C4⋊C4—22no—
165C3×C4⋊C4—24no—
166C4⋊Dic3—64no—
167C4⋊Dic3—64no—
168C4⋊Dic3—62no—
169Dic3⋊C4—62no—
170Dic3⋊C4—62no—
171Dic3⋊C4—64no—
172Dic3⋊C4—64no—
173C4×Dic3—34no—
174C4×Dic3—38no—
175C4×Dic3—62no—
176C4×Dic3—62no—
177C4×Dic3—64no—
178C22×C9C22×D411yescharacteristic
179C22×C9C22×Q812yes—
180C22×C9C2×#4112yes—
181C22×C9C2×#4111yescharacteristic
182C22×C9C2×#4111yescharacteristic
183C4×C9—22no—
184C4×C9—22no—
185C4×C9—24no—
186C4×C9—24no—
187C4×C9—41no—
188Dic9—22no—
189Dic9—22no—
190Dic9—24no—
191Dic9—41no—
192Dic9—42no—
193Dic9C4⋊Q814yes—
194C22×Q8—91no—
195C22×Q8C2×D911yescharacteristic
196C4×Q8—184no—
197C4×Q8—184no—
198C2×C4⋊C4—91no—
199C2×C4⋊C4—92no—
200C2×C4⋊C4—91no—
201C2×C4⋊C4—91no—
202C2×C4⋊C4—92no—
203C2×C4⋊C4—92no—
204C2×C4⋊C4—92no—
205C2×C4⋊C4C2×D911yescharacteristic
206C2×C4⋊C4C2×D912yes—
207C2×C42—91no—
208C2×C42—92no—
209C2×C42—91no—
210C2×C42—92no—
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
220C3×Q8—28no—
221C2×C3×C4—22no—
222C2×C3×C4—21no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—22no—
230C2×C3×C4D3×D412yes—
231C2×C3×C4#23714yes—
232C2×C3×C4D3×Q814yes—
233C2×C3×C4#23912yes—
234C2×Dic3—32no—
235C2×Dic3—34no—
236C2×Dic3—32no—
237C2×Dic3—34no—
238C2×Dic3—32no—
239C2×Dic3—61no—
240C2×Dic3—62no—
241C2×Dic3—62no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3—61no—
245C2×Dic3—61no—
246C2×Dic3—62no—
247C2×Dic3—62no—
248C2×Dic3—62no—
249C2×Dic3—62no—
250Dic6—68no—
251C2×C9#52511yescharacteristic
252C2×C9#52511yescharacteristic
253C2×C9C2×C4⋊Q811yescharacteristic
254C2×C9#53312yes—
255C2×C9#53312yes—
256C2×Q8—22no—
257C2×Q8—24no—
258C2×Q8—182no—
259C2×Q8—182no—
260C2×Q8—182no—
261C22×C4—91no—
262C22×C4—92no—
263C22×C4—91no—
264C22×C4—91no—
265C22×C4—91no—
266C22×C4—92no—
267C22×C4C22×D911yescharacteristic
268C22×C4C22×D911yescharacteristic
269C22×C4C22×D912yes—
270C22×C4C22×D912yes—
271C22×C4C22×D911yescharacteristic
272C4⋊C4—22no—
273C4⋊C4—24no—
274C4⋊C4—182no—
275C4⋊C4—184no—
276C4⋊C4—184no—
277C4⋊C4—182no—
278C4⋊C4—182no—
279C4⋊C4—184no—
280C4⋊C4—184no—
281C42—94no—
282C42—98no—
283C42—182no—
284C42—184no—
285C42—182no—
286C22×C3C2×D3×D411yescharacteristic
287C22×C3C2×#23712yes—
288C22×C3C2×D3×Q812yes—
289C22×C3C2×#23911yescharacteristic
290C22×C3D3×#4111yescharacteristic
291C3×C4—22no—
292C3×C4—24no—
293C3×C4—24no—
294C3×C4—22no—
295C3×C4—41no—
296Dic3—34no—
297Dic3—64no—
298Dic3—62no—
299Dic3—62no—
300Dic3—121no—
301Dic3—122no—
302C9#239911yescharacteristic, complemented, Sylow
303C23C23×D911yescharacteristic
304Q8—28no—
305Q8—188no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—22no—
315C2×C4—92no—
316C2×C4—94no—
317C2×C4—92no—
318C2×C4—94no—
319C2×C4—92no—
320C2×C4—181no—
321C2×C4—182no—
322C2×C4—182no—
323C2×C4—181no—
324C2×C4—181no—
325C2×C4—181no—
326C2×C4—182no—
327C2×C4—181no—
328C2×C4—182no—
329C2×C4—182no—
330C2×C4—182no—
331C2×C4D4×D912yes—
332C2×C4#369914yes—
333C2×C4Q8×D914yes—
334C2×C4#370112yes—
335C2×C3#558611yescharacteristic
336C2×C3#562212yes—
337C2×C3#562711yescharacteristic
338C2×C3D3×C4⋊Q811yescharacteristic
339C2×C3#572812yes—
340C22C2×D4×D911yescharacteristic
341C22C2×#369912yes—
342C22C2×Q8×D912yes—
343C22C2×#370111yescharacteristic
344C22#41×D911yescharacteristic
345C4—24no—
346C4—22no—
347C4—22no—
348C4—24no—
349C4—41no—
350C4—94no—
351C4—182no—
352C4—182no—
353C4—184no—
354C4—362no—
355C4—361no—
356C3#7717111yescharacteristic
357C2#1058968811yescharacteristic
358C2#1058972412yes—
359C2#1058972911yescharacteristic
360C2D9×C4⋊Q811yescharacteristic
361C2#1058983012yes—
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socle, prime radicalC23×C3C23×D3
FittingC9×#395C2
hypercenter#395D9
hypocenterC9#2399
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ #395

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×Q8×Dic92
C2×#634492
C9×#3952
#105889102
#105886622
#105886612
C4⋊C4×Dic92
#105883412
#105883362
#105883292
#105883282
#771713