Finite Group Databasebeta

← #11786487

Subgroups — #11786487

Order 1152.

474 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×#63454C211yesmaximal, characteristic
2C2×C9×#106C211yesmaximal, characteristic, complemented
3C2×(C2×D9)⋊C8C211yesmaximal, characteristic
4#10588667C211yesmaximal, characteristic
5C2×#63366C211yesmaximal, characteristic, complemented
6#10588229C211yesmaximal, characteristic, complemented
7#10588206C211yesmaximal, characteristic, complemented
8#70580—31nomaximal
9C22×C4×D9C2211yescharacteristic
10C22×C8×C9C2211yescharacteristic
11C2×C9×C4⋊C4C2211yescharacteristic
12C2×C9×C4⋊C4C2211yescharacteristic
13C2×(C2×D9)⋊C4—21no—
14C2×(C2×D9)⋊C4—21no—
15C2×C4⋊Dic9C2211yescharacteristic
16C2×C4⋊Dic9C2211yescharacteristic
17C2×C4×Dic9—21no—
18C22×C9⋊C8C2211yescharacteristic
19#63454—22no—
20#63454—22no—
21C9×#106—22no—
22C9⋊#95—21no—
23(C2×D9)⋊C8C414yescomplemented
24#63366—22no—
25C2×#892—31no—
26C2×C3×#106D311yescharacteristic
27C2×(C2×D3)⋊C8—31no—
28#4987—31no—
29C2×#807—31no—
30#4551—31no—
31#4529—31no—
32C23×D9D411yescharacteristic
33C22×C4×C9—21no—
34C22×C4×C9—21no—
35C22×C4×C9C2311yescharacteristic
36C22×Dic9—21no—
37C22×Dic9—21no—
38C22×Dic9D411yescharacteristic
39C2×C4×D9—21no—
40C2×C4×D9—21no—
41C2×C4×D9—21no—
42C2×C4×D9—21no—
43C2×C4×D9C2×C412yes—
44C2×C4×D9Q812yes—
45C2×C8×C9—21no—
46C2×C8×C9—21no—
47C2×C8×C9C2×C412yes—
48C9×C4⋊C4—21no—
49C9×C4⋊C4—21no—
50C9×C4⋊C4—21no—
51C9×C4⋊C4D412yes—
52(C2×D9)⋊C4—24no—
53(C2×D9)⋊C4—42no—
54C4⋊Dic9—21no—
55C4⋊Dic9—21no—
56C4⋊Dic9—21no—
57C4⋊Dic9D412yes—
58C4×Dic9—24no—
59C2×C9⋊C8—21no—
60C2×C9⋊C8—21no—
61C2×C9⋊C8C2×C412yes—
62#1854—91noSylow
63C22×C4×D3—31no—
64C22×C3×C8C2×D311yescharacteristic
65C2×C3×C4⋊C4C2×D311yescharacteristic
66C2×C3×C4⋊C4C2×D311yescharacteristic
67C2×(C2×D3)⋊C4—61no—
68C2×(C2×D3)⋊C4—61no—
69C2×C4⋊Dic3—31no—
70C2×C4⋊Dic3—31no—
71C2×C4×Dic3—61no—
72C22×C3⋊C8—31no—
73#892—62no—
74#892—62no—
75C3×#106—22no—
76C3⋊#95—61no—
77(C2×D3)⋊C8—34no—
78#807—62no—
79C23×C9C2×D411yescharacteristic
80C22×D9—21no—
81C22×D9—21no—
82C22×D9—21no—
83C22×D9—21no—
84C22×D9—21no—
85C22×D9—21no—
86C22×D9C4⋊C412yes—
87C2×C4×C9—22no—
88C2×C4×C9—41no—
89C2×C4×C9—41no—
90C2×C4×C9—41no—
91C2×C4×C9—41no—
92C2×C4×C9—41no—
93C2×C4×C9C22×C411yescharacteristic
94C2×C4×C9C2×D411yescharacteristic
95C2×C4×C9C2×D411yescharacteristic
96C2×C4×C9C2×Q811yescharacteristic
97C2×C4×C9#4111yescharacteristic
98C2×C4×C9#4111yescharacteristic
99C2×Dic9—21no—
100C2×Dic9—21no—
101C2×Dic9—22no—
102C2×Dic9—41no—
103C2×Dic9—41no—
104C2×Dic9—41no—
105C2×Dic9—41no—
106C2×Dic9—41no—
107C2×Dic9C4⋊C412yes—
108C4×D9—22no—
109C4×D9—22no—
110C4×D9—22no—
111C4×D9—22no—
112C8×C9—22no—
113C9⋊C8—22no—
114C2×#117—91no—
115C2×#107—91no—
116C2×#106D911yescharacteristic, complemented
117C2×C22⋊C8—91no—
118#380—91no—
119#340—91no—
120#340—91no—
121C23×D3—31no—
122C22×C3×C4—21no—
123C22×C3×C4—21no—
124C22×C3×C4C22×D311yescharacteristic
125C22×Dic3—31no—
126C22×Dic3—61no—
127C22×Dic3—61no—
128C2×C4×D3—32no—
129C2×C4×D3—32no—
130C2×C4×D3—61no—
131C2×C4×D3—61no—
132C2×C4×D3—61no—
133C2×C4×D3—61no—
134C2×C3×C8—21no—
135C2×C3×C8—21no—
136C2×C3×C8C4×D312yes—
137C3×C4⋊C4—21no—
138C3×C4⋊C4—21no—
139C3×C4⋊C4—21no—
140C3×C4⋊C4#6712yes—
141(C2×D3)⋊C4—64no—
142(C2×D3)⋊C4—122no—
143C4⋊Dic3—32no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147C4×Dic3—64no—
148C2×C3⋊C8—32no—
149C2×C3⋊C8—61no—
150C2×C3⋊C8—61no—
151C22×C9C2×C4⋊C411yescharacteristic
152C22×C9#12011yescharacteristic
153C22×C9#12311yescharacteristic
154C22×C9#13511yescharacteristic
155C22×C9#13511yescharacteristic
156C22×C9AGL(1,ℤ/8)11yescharacteristic
157C22×C9#13711yescharacteristic
158C2×D9—22no—
159C2×D9—22no—
160C2×D9—22no—
161C2×D9—41no—
162C2×D9—41no—
163C2×D9—41no—
164C2×D9—41no—
165C4×C9—42no—
166C4×C9—81no—
167C4×C9C4×D411yescharacteristic
168C4×C9C4×D411yescharacteristic
169C4×C9C22⋊Q811yescharacteristic
170C4×C9C22⋊Q811yescharacteristic
171Dic9—22no—
172Dic9—42no—
173Dic9—81no—
174C23×C4—91no—
175C22×C8—91no—
176C22×C8C2×D911yescharacteristic
177#117—182no—
178#117—182no—
179C2×C4⋊C4—91no—
180C2×C4⋊C4—91no—
181C2×C4⋊C4C2×D911yescharacteristic
182C2×C4⋊C4C2×D911yescharacteristic
183C2×C22⋊C4—181no—
184C2×C22⋊C4—181no—
185C2×C42—181no—
186#107—182no—
187#106—22no—
188C22⋊C8—94no—
189#95—181no—
190C23×C3D3×D411yescharacteristic
191C22×D3—32no—
192C22×D3—61no—
193C22×D3—61no—
194C22×D3—61no—
195C22×D3—61no—
196C22×D3—61no—
197C22×D3—61no—
198C2×C3×C4—22no—
199C2×C3×C4—41no—
200C2×C3×C4—41no—
201C2×C3×C4—41no—
202C2×C3×C4—41no—
203C2×C3×C4—41no—
204C2×C3×C4C2×C4×D311yescharacteristic
205C2×C3×C4#23511yescharacteristic
206C2×C3×C4D3×D411yescharacteristic
207C2×C3×C4D3×Q811yescharacteristic
208C2×C3×C4#23911yescharacteristic
209C2×C3×C4C2×#6711yescharacteristic
210C2×Dic3—32no—
211C2×Dic3—61no—
212C2×Dic3—61no—
213C2×Dic3—62no—
214C2×Dic3—121no—
215C2×Dic3—121no—
216C2×Dic3—121no—
217C2×Dic3—121no—
218C2×Dic3—121no—
219C4×D3—62no—
220C4×D3—62no—
221C4×D3—62no—
222C4×D3—62no—
223C3×C8—22no—
224C3⋊C8—62no—
225C2×C9#38511yescharacteristic
226C2×C9#42711yescharacteristic
227C2×C9#42811yescharacteristic
228C2×C9#44911yescharacteristic
229C2×C9#45211yescharacteristic
230C2×C9#48211yescharacteristic
231C2×C9#48511yescharacteristic
232D9—42no—
233C24—91no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—91no—
237C22×C4—92no—
238C22×C4—92no—
239C22×C4—181no—
240C22×C4—181no—
241C22×C4—181no—
242C22×C4—181no—
243C22×C4—181no—
244C22×C4—181no—
245C22×C4C22×D911yescharacteristic
246C2×C8—21no—
247C2×C8—21no—
248C2×C8—92no—
249C2×C8—181no—
250C2×C8—181no—
251C2×C8C4×D912yes—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—92no—
256C4⋊C4—181no—
257C4⋊C4—181no—
258C4⋊C4—181no—
259C4⋊C4#61112yes—
260C22⋊C4—184no—
261C22⋊C4—362no—
262C42—184no—
263C22×C3D3×C4⋊C411yescharacteristic
264C22×C3#89411yescharacteristic
265C22×C3#91411yescharacteristic
266C22×C3#91511yescharacteristic
267C22×C3#91611yescharacteristic
268C22×C3#91611yescharacteristic
269C22×C3#93711yescharacteristic
270C2×D3—62no—
271C2×D3—62no—
272C2×D3—62no—
273C2×D3—121no—
274C2×D3—121no—
275C2×D3—121no—
276C2×D3—121no—
277C3×C4—42no—
278C3×C4—81no—
279C3×C4#89311yescharacteristic
280C3×C4#89611yescharacteristic
281C3×C4C4×#6711yescharacteristic
282C3×C4#94611yescharacteristic
283Dic3—62no—
284Dic3—122no—
285Dic3—241no—
286C9#185411yescharacteristic, complemented, Sylow
287C23—92no—
288C23—181no—
289C23—181no—
290C23—181no—
291C23—181no—
292C23—181no—
293C23—181no—
294C23D4×D911yescharacteristic
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—92no—
302C2×C4—181no—
303C2×C4—181no—
304C2×C4—182no—
305C2×C4—182no—
306C2×C4—182no—
307C2×C4—182no—
308C2×C4—182no—
309C2×C4—361no—
310C2×C4—361no—
311C2×C4—361no—
312C2×C4—361no—
313C2×C4—361no—
314C2×C4C2×C4×D911yescharacteristic
315C2×C4#369711yescharacteristic
316C2×C4D4×D911yescharacteristic
317C2×C4Q8×D911yescharacteristic
318C2×C4#370111yescharacteristic
319C2×C4C2×#61111yescharacteristic
320C8—22no—
321C8—182no—
322C2×C3#486011yescharacteristic
323C2×C3#486111yescharacteristic
324C2×C3#486611yescharacteristic
325C2×C3#486811yescharacteristic
326C2×C3#498911yescharacteristic
327C2×C3#517211yescharacteristic
328C2×C3#517311yescharacteristic
329D3—122no—
330C22—182no—
331C22—182no—
332C22—182no—
333C22—361no—
334C22—361no—
335C22—361no—
336C22—361no—
337C22C4⋊C4×D911yescharacteristic
338C22#6345611yescharacteristic
339C22#6347611yescharacteristic
340C22#6347711yescharacteristic
341C22#6347811yescharacteristic
342C22#6347811yescharacteristic
343C22#6349911yescharacteristic
344C4—42no—
345C4—81no—
346C4—182no—
347C4—362no—
348C4—721no—
349C4#6345511yescharacteristic
350C4#6345811yescharacteristic
351C4C4×#61111yescharacteristic
352C4#6350811yescharacteristic
353C3#7058011yescharacteristic
354C2—362no—
355C2#1058854011yescharacteristic
356C2#1058854111yescharacteristic
357C2#1058854611yescharacteristic
358C2#1058854811yescharacteristic
359C2#1058866911yescharacteristic
360C2#1058885211yescharacteristic
361C2#1058885311yescharacteristic
subgroupG/H
centerC23D4×D9
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC2×C9×#106C2
socleC23×C3D3×D4
prime radicalC23×D9D4
cosocleC22×C4×C9C23
hypercenterC2×#106D9
hypocenterC9#1854
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×C9×#106C2semidirect
5. C2×#63366C2semidirect
6. #10588229C2semidirect
7. #10588206C2semidirect
23. (C2×D9)⋊C8C4semidirect
116. C2×#106D9semidirect
286. C9#1854semidirect

Maximal subgroups

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

subgroupindex
C2×#634542
C2×C9×#1062
C2×(C2×D9)⋊C82
#105886672
C2×#633662
#105882292
#105882062
#705803