Finite Group Databasebeta

← #11808647

Subgroups — #11808647

Order 1152.

792 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic9C211yesmaximal, characteristic, complemented
2C2×#63454C211yesmaximal, characteristic
3C9×#395C211yesmaximal, characteristic, complemented
4#10588911C211yesmaximal, characteristic
5#10588674C212yesmaximal
6#10588666C211yesmaximal, characteristic, complemented
7C4⋊C4×Dic9C212yesmaximal, complemented
8#10588357C211yesmaximal, characteristic
9#10588346C212yesmaximal
10#10588341C212yesmaximal, complemented
11#10588329C211yesmaximal, characteristic, complemented
12#77170—31nomaximal
13C22×Q8×C9C2211yescharacteristic
14C22×C4×D9C2211yescharacteristic
15C2×C9×C4⋊C4C2212yes—
16C2×C9×C4⋊C4C2211yescharacteristic
17Q8×Dic9—24no—
18C2×(C2×D9)⋊C4C2211yescharacteristic
19C2×(C2×D9)⋊C4C2212yes—
20C2×(C2×D9)⋊C4C2212yes—
21C2×(C2×D9)⋊C4C2211yescharacteristic
22C2×C4⋊Dic9C2212yes—
23C2×C4⋊Dic9C2211yescharacteristic
24C2×C4⋊Dic9C2212yes—
25C2×C4⋊Dic9C2211yescharacteristic
26C2×Dic9⋊C4C2212yes—
27C2×C4×Dic9C2211yescharacteristic
28C2×C4×Dic9C2212yes—
29C2×C4×Dic9C2212yes—
30C2×C4×Dic9C2211yescharacteristic
31#63454—24no—
32C9×#95C2211yescharacteristic
33C9×#95C2212yes—
34C9⋊#95C2212yes—
35C9⋊#95C2211yescharacteristic
36C9⋊#95C2212yes—
37C9⋊#95C2212yes—
38C2×Q8×Dic3—31no—
39C2×#892—31no—
40C3×#395D311yescharacteristic
41#5231—31no—
42#4994—32no—
43#4986—31no—
44Dic3×C4⋊C4—32no—
45#4677—31no—
46#4666—32no—
47#4661—32no—
48#4649—31no—
49C23×D9C2311yescharacteristic
50C2×Q8×C9—22no—
51C2×Q8×C9—24no—
52C22×C4×C9C2311yescharacteristic
53C22×C4×C9C2311yescharacteristic
54C22×C4×C9C2311yescharacteristic
55C22×C4×C9C2312yes—
56C22×C4×C9C2312yes—
57C22×Dic9C2312yes—
58C22×Dic9C2312yes—
59C22×Dic9C2311yescharacteristic
60C22×Dic9C2311yescharacteristic
61C22×Dic9C2311yescharacteristic
62C2×C4×D9—22no—
63C2×C4×D9—22no—
64C2×C4×D9Q814yescomplemented
65C9×C4⋊C4—22no—
66C9×C4⋊C4—24no—
67(C2×D9)⋊C4—22no—
68(C2×D9)⋊C4—24no—
69(C2×D9)⋊C4—24no—
70(C2×D9)⋊C4—22no—
71C4⋊Dic9—22no—
72C4⋊Dic9—24no—
73C4⋊Dic9—24no—
74C4⋊Dic9—22no—
75Dic9⋊C4—24no—
76C4×Dic9—24no—
77C4×Dic9—22no—
78C4×Dic9—24no—
79C4×Dic9D414yes—
80#2396—91noSylow
81C22×C3×Q8C2×D311yescharacteristic
82C22×C4×D3—31no—
83C2×C3×C4⋊C4C2×D312yes—
84C2×C3×C4⋊C4C2×D311yescharacteristic
85Q8×Dic3—64no—
86C2×(C2×D3)⋊C4—32no—
87C2×(C2×D3)⋊C4—32no—
88C2×(C2×D3)⋊C4—31no—
89C2×(C2×D3)⋊C4—31no—
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—32no—
92C2×C4⋊Dic3—32no—
93C2×C4⋊Dic3—31no—
94C2×Dic3⋊C4—32no—
95C2×C4×Dic3—31no—
96C2×C4×Dic3—32no—
97C2×C4×Dic3—32no—
98C2×C4×Dic3—31no—
99#892—64no—
100C3×#95C2×D311yescharacteristic
101C3×#95C2×D312yes—
102C3⋊#95—31no—
103C3⋊#95—32no—
104C3⋊#95—32no—
105C3⋊#95—32no—
106C23×C9C2411yescharacteristic
107C22×D9—21no—
108C22×D9—22no—
109C22×D9—22no—
110C22×D9—21no—
111C22×D9C2×Q812yes—
112Q8×C9—28no—
113C2×C4×C9—22no—
114C2×C4×C9—21no—
115C2×C4×C9—22no—
116C2×C4×C9—22no—
117C2×C4×C9—21no—
118C2×C4×C9—22no—
119C2×C4×C9—22no—
120C2×C4×C9—21no—
121C2×C4×C9—22no—
122C2×C4×C9C2×D412yes—
123C2×C4×C9C2×Q812yes—
124C2×C4×C9#4114yes—
125C2×C4×C9#4114yes—
126C2×Dic9—22no—
127C2×Dic9—22no—
128C2×Dic9—21no—
129C2×Dic9—22no—
130C2×Dic9—22no—
131C2×Dic9—22no—
132C2×Dic9—22no—
133C2×Dic9—22no—
134C2×Dic9—22no—
135C2×Dic9C2×D412yes—
136C2×Dic9C2×D412yes—
137C2×Dic9C2×Q812yes—
138C2×Dic9#4112yes—
139C4×D9—28no—
140C2×C4×Q8—91no—
141C2×#117—91no—
142#400—91no—
143#399—91no—
144#398—92no—
145#396—92no—
146#395D911yescharacteristic, complemented
147#393—91no—
148C4×C4⋊C4—92no—
149C4×C4⋊C4—91no—
150C4×C22⋊C4—92no—
151C23×D3—31no—
152C2×C3×Q8—22no—
153C2×C3×Q8—24no—
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C22×D312yes—
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C22×D312yes—
159C22×Dic3—31no—
160C22×Dic3—31no—
161C22×Dic3—32no—
162C22×Dic3—32no—
163C22×Dic3—31no—
164C2×C4×D3—34no—
165C2×C4×D3—62no—
166C2×C4×D3—62no—
167C3×C4⋊C4—22no—
168C3×C4⋊C4—24no—
169(C2×D3)⋊C4—62no—
170(C2×D3)⋊C4—62no—
171(C2×D3)⋊C4—64no—
172(C2×D3)⋊C4—64no—
173C4⋊Dic3—62no—
174C4⋊Dic3—64no—
175C4⋊Dic3—62no—
176C4⋊Dic3—64no—
177Dic3⋊C4—64no—
178C4×Dic3—34no—
179C4×Dic3—62no—
180C4×Dic3—64no—
181C4×Dic3—64no—
182C22×C9C22×D411yescharacteristic
183C22×C9C22×Q811yescharacteristic
184C22×C9C2×#4112yes—
185C22×C9C2×#4112yes—
186C22×C9C2×#4111yescharacteristic
187C2×D9—22no—
188C2×D9—24no—
189C2×D9—41no—
190C2×D9—42no—
191C2×D9—41no—
192C4×C9—22no—
193C4×C9—22no—
194C4×C9—24no—
195C4×C9—24no—
196C4×C9—41no—
197Dic9—22no—
198Dic9—42no—
199Dic9—42no—
200Dic9—41no—
201Dic9C22⋊Q814yes—
202C22×Q8C2×D911yescharacteristic
203C23×C4—91no—
204C4×Q8—184no—
205#117—184no—
206C2×C4⋊C4—91no—
207C2×C4⋊C4—92no—
208C2×C4⋊C4—91no—
209C2×C4⋊C4—92no—
210C2×C4⋊C4—92no—
211C2×C4⋊C4C2×D911yescharacteristic
212C2×C4⋊C4C2×D912yes—
213C2×C22⋊C4—91no—
214C2×C22⋊C4—91no—
215C2×C22⋊C4—92no—
216C2×C22⋊C4—92no—
217C2×C42—91no—
218C2×C42—91no—
219C2×C42—92no—
220C2×C42—92no—
221#95—92no—
222#95—92no—
223#95—91no—
224#95—92no—
225#95C2×D912yes—
226#95C2×D911yescharacteristic
227C23×C3C23×D311yescharacteristic
228C22×D3—32no—
229C22×D3—61no—
230C22×D3—62no—
231C22×D3—62no—
232C22×D3—61no—
233C3×Q8—28no—
234C2×C3×C4—22no—
235C2×C3×C4—21no—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—22no—
239C2×C3×C4—22no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—22no—
243C2×C3×C4D3×D412yes—
244C2×C3×C4#23714yes—
245C2×C3×C4D3×Q812yes—
246C2×C3×C4#23914yes—
247C2×Dic3—32no—
248C2×Dic3—32no—
249C2×Dic3—32no—
250C2×Dic3—32no—
251C2×Dic3—62no—
252C2×Dic3—62no—
253C2×Dic3—61no—
254C2×Dic3—62no—
255C2×Dic3—62no—
256C2×Dic3—62no—
257C2×Dic3—62no—
258C2×Dic3—62no—
259C2×Dic3—62no—
260C4×D3—68no—
261C2×C9C2×C22⋊Q811yescharacteristic
262C2×C9#52511yescharacteristic
263C2×C9#52912yes—
264C2×C9#53211yescharacteristic
265C2×C9#53312yes—
266D9—42no—
267C24—91no—
268C2×Q8—22no—
269C2×Q8—24no—
270C22×C4—91no—
271C22×C4—91no—
272C22×C4—94no—
273C22×C4—92no—
274C22×C4—91no—
275C22×C4—92no—
276C22×C4—182no—
277C22×C4—182no—
278C22×C4C22×D911yescharacteristic
279C22×C4C22×D911yescharacteristic
280C22×C4C22×D912yes—
281C22×C4C22×D911yescharacteristic
282C22×C4C22×D912yes—
283C4⋊C4—22no—
284C4⋊C4—24no—
285C4⋊C4—182no—
286C4⋊C4—184no—
287C4⋊C4—182no—
288C4⋊C4—184no—
289C4⋊C4—184no—
290C22⋊C4—182no—
291C22⋊C4—182no—
292C22⋊C4—184no—
293C22⋊C4—184no—
294C42—94no—
295C42—182no—
296C42—184no—
297C42—184no—
298C22×C3C2×D3×D411yescharacteristic
299C22×C3C2×#23712yes—
300C22×C3C2×D3×Q811yescharacteristic
301C22×C3C2×#23912yes—
302C22×C3D3×#4111yescharacteristic
303C2×D3—64no—
304C2×D3—62no—
305C2×D3—121no—
306C2×D3—121no—
307C2×D3—122no—
308C3×C4—22no—
309C3×C4—24no—
310C3×C4—24no—
311C3×C4—22no—
312C3×C4—41no—
313Dic3—34no—
314Dic3—62no—
315Dic3—122no—
316Dic3—121no—
317Dic3—122no—
318C9#239611yescharacteristic, complemented, Sylow
319C23—92no—
320C23—181no—
321C23—182no—
322C23—182no—
323C23—181no—
324C23C23×D911yescharacteristic
325Q8—28no—
326C2×C4—22no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—92no—
336C2×C4—92no—
337C2×C4—92no—
338C2×C4—92no—
339C2×C4—188no—
340C2×C4—182no—
341C2×C4—181no—
342C2×C4—182no—
343C2×C4—182no—
344C2×C4—182no—
345C2×C4—182no—
346C2×C4—182no—
347C2×C4—182no—
348C2×C4—182no—
349C2×C4D4×D912yes—
350C2×C4#369914yes—
351C2×C4Q8×D912yes—
352C2×C4#370114yes—
353C2×C3#558611yescharacteristic
354C2×C3#562412yes—
355C2×C3D3×C22⋊Q811yescharacteristic
356C2×C3#572511yescharacteristic
357C2×C3#572812yes—
358D3—122no—
359C22—182no—
360C22—184no—
361C22—362no—
362C22—361no—
363C22—361no—
364C22C2×D4×D911yescharacteristic
365C22C2×#369912yes—
366C22C2×Q8×D911yescharacteristic
367C22C2×#370112yes—
368C22#41×D911yescharacteristic
369C4—24no—
370C4—22no—
371C4—22no—
372C4—24no—
373C4—41no—
374C4—94no—
375C4—182no—
376C4—362no—
377C4—361no—
378C4—362no—
379C3#7717011yescharacteristic
380C2—362no—
381C2#1058968811yescharacteristic
382C2#1058972612yes—
383C2D9×C22⋊Q811yescharacteristic
384C2#1058982711yescharacteristic
385C2#1058983012yes—
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC9×#395C2
prime radicalC23×D9C23
hypercenter#395D9
hypocenterC9#2396
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic9C2semidirect
3. C9×#395C2semidirect
6. #10588666C2semidirect
7. C4⋊C4×Dic9C2semidirect
10. #10588341C2semidirect
11. #10588329C2semidirect
64. C2×C4×D9Q8semidirect
146. #395D9semidirect
318. C9#2396semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic92
C2×#634542
C9×#3952
#105889112
#105886742
#105886662
C4⋊C4×Dic92
#105883572
#105883462
#105883412
#105883292
#771703