Finite Group Databasebeta

← #11896012

Subgroups — #11896012

Order 1152.

507 conjugacy classes of subgroups.

The subgroup lattice has 351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#556C211yesmaximal, characteristic
2Q8×Dic18C211yesmaximal, characteristic, complemented
3#10588763C211yesmaximal, characteristic, complemented
4#10588759C211yesmaximal, characteristic, complemented
5#10588736C212yesmaximal
6#10588734C212yesmaximal
7#10588706C212yesmaximal, complemented
8#10588702C212yesmaximal, complemented
9#10588701C211yesmaximal, characteristic, complemented
10C4×#3672C211yesmaximal, characteristic
11#10588691C211yesmaximal, characteristic
12#83677—31nomaximal
13C9×C4⋊Q8C2211yescharacteristic
14C9×#126—22no—
15C9×#124C2212yes—
16C9×C22⋊Q8—21no—
17C4×Q8×C9C2212yes—
18C4×Q8×C9C2211yescharacteristic
19C4×D4×C9C2211yescharacteristic
20C9×#117—21no—
21Q8×Dic9—21no—
22C2×#3674C2212yes—
23C2×#3672C2211yescharacteristic
24#63450—21no—
25#63450—22no—
26#63431C2211yescharacteristic
27#63431C2212yes—
28C4×Dic18C2211yescharacteristic
29C4×Dic18C2212yes—
30#63395C2212yes—
31#63395C2212yes—
32#63395C2212yes—
33#63392C2212yes—
34#63392C2211yescharacteristic
35#63368C2211yescharacteristic
36#63367C2212yes—
37#63367C2211yescharacteristic
38C4⋊(C9⋊C8)C2211yescharacteristic
39C4⋊(C9⋊C8)C2212yes—
40#63362C2212yes—
41C4×C9⋊C8C2211yescharacteristic
42C3×#556D311yescharacteristic
43Q8×Dic6—31no—
44#5090—31no—
45#5079—31no—
46#5055—32no—
47#5054—32no—
48#5030—32no—
49#5024—31no—
50#5020—32no—
51C4×#214—31no—
52#5008—31no—
53C2×Q8×C9D411yescharacteristic
54C2×Q8×C9C2312yes—
55C2×D4×C9C2311yescharacteristic
56C22×C4×C9—21no—
57C2×Dic18—22no—
58C2×Dic18—21no—
59C2×Dic18C2311yescharacteristic
60C9×C4⋊C4—21no—
61C9×C4⋊C4—22no—
62C9×C4⋊C4—21no—
63C9×C4⋊C4D411yescharacteristic
64C9×C4⋊C4D412yes—
65C9×C4⋊C4C2311yescharacteristic
66C9×C22⋊C4—22no—
67C9×C22⋊C4—21no—
68C9×C22⋊C4—22no—
69C42×C9—22no—
70C42×C9C2311yescharacteristic
71C42×C9C2312yes—
72#3674—24no—
73#3672—22no—
74C4⋊Dic9—22no—
75C4⋊Dic9—21no—
76C4⋊Dic9C2312yes—
77C4⋊Dic9C2311yescharacteristic
78Dic9⋊C4—22no—
79Dic9⋊C4—21no—
80C4×Dic9—22no—
81C4×Dic9—21no—
82C2×C9⋊C8C2311yescharacteristic
83C2×C9⋊C8C2312yes—
84C2×C9⋊C8C2311yescharacteristic
85#3369—91noSylow
86C3×C4⋊Q8C2×D311yescharacteristic
87C3×#126—22no—
88C3×#124C2×D312yes—
89C3×C22⋊Q8—21no—
90C3×C4×Q8C2×D312yes—
91C3×C4×Q8C2×D311yescharacteristic
92C3×C4×D4C2×D311yescharacteristic
93C3×#117—21no—
94Q8×Dic3—61no—
95C2×#216—32no—
96C2×#214—31no—
97#888—61no—
98#888—62no—
99#869—31no—
100#869—32no—
101C4×Dic6—31no—
102C4×Dic6—32no—
103#835—32no—
104#835—32no—
105#835—32no—
106#832—32no—
107#832—31no—
108#810—31no—
109#808—32no—
110#808—31no—
111C4⋊(C3⋊C8)—31no—
112C4⋊(C3⋊C8)—32no—
113#803—32no—
114C4×C3⋊C8—31no—
115C23×C9—21no—
116Q8×C9—22no—
117Q8×C9—22no—
118Q8×C9—22no—
119D4×C9—21no—
120D4×C9—21no—
121C2×C4×C9—21no—
122C2×C4×C9—22no—
123C2×C4×C9—42no—
124C2×C4×C9C2×D412yes—
125C2×C4×C9C2×D412yes—
126C2×C4×C9C2×D411yescharacteristic
127C2×C4×C9C2×D411yescharacteristic
128C2×C4×C9C2411yescharacteristic
129C2×Dic9—21no—
130C2×Dic9—22no—
131C2×Dic9—21no—
132Dic18—21no—
133Dic18—82no—
134Dic18—81no—
135Dic18#4112yes—
136C9⋊C8—21no—
137C9⋊C8—22no—
138C9⋊C8—21no—
139Q82—91no—
140#556D911yescharacteristic
141#489—92no—
142#487—91no—
143#476—91no—
144#475—92no—
145#464—92no—
146#462—91no—
147#446—91no—
148#441—92no—
149C4×SD16—91no—
150C2×C3×Q8#6711yescharacteristic
151C2×C3×Q8C22×D312yes—
152C2×C3×D4C22×D311yescharacteristic
153C22×C3×C4—21no—
154C2×Dic6—31no—
155C2×Dic6—62no—
156C2×Dic6—61no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4—22no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4#6711yescharacteristic
161C3×C4⋊C4#6712yes—
162C3×C4⋊C4C22×D311yescharacteristic
163C3×C22⋊C4—22no—
164C3×C22⋊C4—21no—
165C3×C22⋊C4—22no—
166C3×C42—22no—
167C3×C42C22×D311yescharacteristic
168C3×C42C22×D312yes—
169#216—64no—
170#214—62no—
171C4⋊Dic3—32no—
172C4⋊Dic3—31no—
173C4⋊Dic3—62no—
174C4⋊Dic3—61no—
175Dic3⋊C4—62no—
176Dic3⋊C4—61no—
177C4×Dic3—62no—
178C4×Dic3—61no—
179C2×C3⋊C8—31no—
180C2×C3⋊C8—31no—
181C2×C3⋊C8—32no—
182C22×C9—41no—
183C22×C9—41no—
184C22×C9—41no—
185C22×C9C22×D411yescharacteristic
186C4×C9—22no—
187C4×C9—22no—
188C4×C9—21no—
189C4×C9—42no—
190C4×C9—41no—
191C4×C9#13712yes—
192C4×C9C2×#4111yescharacteristic
193C4×C92−1+411yescharacteristic
194Dic9—22no—
195Dic9—41no—
196Dic9—42no—
197C2×Q16—92no—
198C2×SD16—91no—
199C4⋊Q8—92no—
200C4⋊Q8—91no—
201C4⋊Q8—181no—
202C4⋊Q8—182no—
203C4⋊Q8C2×D911yescharacteristic
204#126—22no—
205#124C2×D912yes—
206C22⋊Q8—21no—
207C4×Q8—91no—
208C4×Q8—92no—
209C4×Q8—181no—
210C4×Q8C2×D912yes—
211C4×Q8C2×D911yescharacteristic
212C4×D4C2×D911yescharacteristic
213#117—21no—
214#106—91no—
215#106—92no—
216C4⋊C8—91no—
217C4⋊C8—92no—
218#103—92no—
219#103—92no—
220#103—92no—
221#103—91no—
222#102—91no—
223#102—92no—
224#97—92no—
225C4×C8—91no—
226C23×C3—21no—
227C3×Q8—22no—
228C3×Q8—22no—
229C3×Q8—22no—
230C3×D4—21no—
231C3×D4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—22no—
234C2×C3×C4—42no—
235C2×C3×C4C2×#6712yes—
236C2×C3×C4C2×#6712yes—
237C2×C3×C4C2×#6711yescharacteristic
238C2×C3×C4C2×#6711yescharacteristic
239C2×C3×C4C23×D311yescharacteristic
240C2×Dic3—61no—
241C2×Dic3—62no—
242C2×Dic3—61no—
243Dic6—32no—
244Dic6—61no—
245Dic6—242no—
246Dic6—241no—
247C3⋊C8—61no—
248C3⋊C8—62no—
249C3⋊C8—61no—
250C2×C9—81no—
251C2×C9#54811yescharacteristic
252C2×C9C2×#13711yescharacteristic
253C2×C9#57711yescharacteristic
254C2×Q8—91no—
255C2×Q8—182no—
256C2×Q8—181no—
257C2×Q8#61111yescharacteristic
258C2×Q8C22×D912yes—
259C2×D4C22×D911yescharacteristic
260C22×C4—21no—
261Q16—184no—
262SD16—182no—
263C2×C8—91no—
264C2×C8—91no—
265C2×C8—92no—
266C4⋊C4—21no—
267C4⋊C4—22no—
268C4⋊C4—21no—
269C4⋊C4—91no—
270C4⋊C4—92no—
271C4⋊C4—182no—
272C4⋊C4—181no—
273C4⋊C4—182no—
274C4⋊C4—181no—
275C4⋊C4#61111yescharacteristic
276C4⋊C4#61112yes—
277C4⋊C4C22×D911yescharacteristic
278C22⋊C4—22no—
279C22⋊C4—21no—
280C22⋊C4—22no—
281C42—22no—
282C42—182no—
283C42—181no—
284C42C22×D911yescharacteristic
285C42C22×D912yes—
286C22×C3—41no—
287C22×C3—41no—
288C22×C3—41no—
289C22×C3C22×#6711yescharacteristic
290C3×C4—22no—
291C3×C4—22no—
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—42no—
295C3×C4#95112yes—
296C3×C4D3×#4111yescharacteristic
297C3×C4#101011yescharacteristic
298Dic3—62no—
299Dic3—121no—
300Dic3—122no—
301C9#336911yescharacteristic, complemented, Sylow
302C23—21no—
303Q8—22no—
304Q8—22no—
305Q8—22no—
306Q8—92no—
307Q8—181no—
308Q8—722no—
309Q8—721no—
310D4—21no—
311D4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—42no—
315C2×C4—181no—
316C2×C4—182no—
317C2×C4—181no—
318C2×C4C2×#61112yes—
319C2×C4C2×#61112yes—
320C2×C4C2×#61111yescharacteristic
321C2×C4C2×#61111yescharacteristic
322C2×C4C23×D911yescharacteristic
323C8—181no—
324C8—182no—
325C8—181no—
326C2×C3—81no—
327C2×C3C2×#95111yescharacteristic
328C2×C3#583111yescharacteristic
329C2×C3#583711yescharacteristic
330C22—41no—
331C22—41no—
332C22—41no—
333C22C22×#61111yescharacteristic
334C4—22no—
335C4—22no—
336C4—21no—
337C4—41no—
338C4—42no—
339C4—182no—
340C4—362no—
341C4—361no—
342C4#6351112yes—
343C4#41×D911yescharacteristic
344C4#6371611yescharacteristic
345C3#8367711yescharacteristic
346C2—81no—
347C2C2×#6351111yescharacteristic
348C2#1058993311yescharacteristic
349C2#1058993911yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#556C2
socleC22×C3C22×#67
prime radicalC2×C3×D4C22×D3
hypercenter#556D9
hypocenterC9#3369
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
2. Q8×Dic18C2semidirect
3. #10588763C2semidirect
4. #10588759C2semidirect
7. #10588706C2semidirect
8. #10588702C2semidirect
9. #10588701C2semidirect
301. C9#3369semidirect

Maximal subgroups

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

subgroupindex
C9×#5562
Q8×Dic182
#105887632
#105887592
#105887362
#105887342
#105887062
#105887022
#105887012
C4×#36722
#105886912
#836773