Finite Group Databasebeta

← #11887998

Subgroups — #11887998

Order 1152.

579 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#556C211yesmaximal, characteristic, complemented
2#10589653C211yesmaximal, characteristic
3#10588772C211yesmaximal, characteristic, complemented
4#10588766C211yesmaximal, characteristic, complemented
5#10588730C212yesmaximal, complemented
6#10588727C212yesmaximal, complemented
7C4×#3675C211yesmaximal, characteristic, complemented
8#10588707C211yesmaximal, characteristic, complemented
9D4×C9⋊C8C211yesmaximal, characteristic, complemented
10#10588683C212yesmaximal, complemented
11#10588680C212yesmaximal, complemented
12#83664—31nomaximal
13C2×#3697C2212yes—
14C9×C4⋊Q8C2211yescharacteristic
15C9×#126—22no—
16C9×#124—21no—
17C9×C22⋊Q8C2212yes—
18C4×Q8×C9—21no—
19C4×Q8×C9C2211yescharacteristic
20C4×D4×C9C2211yescharacteristic
21C9×#117C2212yes—
22C2×#3675C2211yescharacteristic
23C2×#3674C2212yes—
24#63500—21no—
25#63486C2212yes—
26C22×C9⋊C8C2212yes—
27C4⋊C4×D9—21no—
28#63445—22no—
29C4×D36C2211yescharacteristic
30#63431C2211yescharacteristic
31#63395C2211yescharacteristic
32#63389C2212yes—
33#63369C2211yescharacteristic
34#63369C2212yes—
35#63368C2212yes—
36#63368C2212yes—
37#63368C2212yes—
38#63367C2211yescharacteristic
39#63366C2212yes—
40C4⋊(C9⋊C8)C2211yescharacteristic
41C4×C9⋊C8C2211yescharacteristic
42C3×#556D311yescharacteristic
43#5551—31no—
44#5093—31no—
45#5087—31no—
46#5051—32no—
47#5047—32no—
48#5031—31no—
49C4×#215—31no—
50D4×C3⋊C8—31no—
51#5002—32no—
52#4996—32no—
53C2×Q8×C9—21no—
54C2×Q8×C9C2311yescharacteristic
55C2×D4×C9D411yescharacteristic
56C22×C4×C9C2312yes—
57C2×#611—22no—
58#3697—24no—
59#3697—42no—
60C2×D36C2311yescharacteristic
61C2×C4×D9—21no—
62C2×C4×D9—22no—
63C2×Dic18C2312yes—
64C9×C4⋊C4—22no—
65C9×C4⋊C4—21no—
66C9×C4⋊C4—21no—
67C9×C4⋊C4D411yescharacteristic
68C9×C4⋊C4C2311yescharacteristic
69C9×C4⋊C4C2312yes—
70C9×C22⋊C4—22no—
71C9×C22⋊C4—22no—
72C9×C22⋊C4D412yes—
73C42×C9—22no—
74C42×C9—21no—
75C42×C9C2311yescharacteristic
76#3676—22no—
77#3675—22no—
78#3674—42no—
79(C2×D9)⋊C4—21no—
80C4⋊Dic9—21no—
81C4⋊Dic9—21no—
82C4⋊Dic9C2311yescharacteristic
83Dic9⋊C4—22no—
84C2×C9⋊C8—42no—
85C2×C9⋊C8C2312yes—
86C2×C9⋊C8C2311yescharacteristic
87C2×C9⋊C8C2311yescharacteristic
88#3302—91noSylow
89C2×#235—32no—
90C3×C4⋊Q8C2×D311yescharacteristic
91C3×#126—22no—
92C3×#124—21no—
93C3×C22⋊Q8C2×D312yes—
94C3×C4×Q8—21no—
95C3×C4×Q8C2×D311yescharacteristic
96C3×C4×D4C2×D311yescharacteristic
97C3×#117C2×D312yes—
98C2×#216—32no—
99C2×#215—31no—
100#938—61no—
101#924—32no—
102C22×C3⋊C8—32no—
103D3×C4⋊C4—61no—
104#883—62no—
105C4×D12—31no—
106#869—31no—
107#835—31no—
108#830—32no—
109#810—32no—
110#810—32no—
111#810—32no—
112#809—31no—
113#809—32no—
114#808—31no—
115#807—32no—
116C4⋊(C3⋊C8)—31no—
117C4×C3⋊C8—31no—
118C23×C9C2×D412yes—
119C22×D9—21no—
120Q8×C9—21no—
121Q8×C9—21no—
122Q8×C9—42no—
123D4×C9—22no—
124C2×C4×C9—22no—
125C2×C4×C9—22no—
126C2×C4×C9—21no—
127C2×C4×C9—21no—
128C2×C4×C9—22no—
129C2×C4×C9C2×D412yes—
130C2×C4×C9C2×D411yescharacteristic
131C2×C4×C9C2×D411yescharacteristic
132C2×C4×C9C2411yescharacteristic
133#611—44no—
134C2×Dic9—21no—
135C2×Dic9—22no—
136D36—21no—
137D36#4112yes—
138C4×D9—44no—
139C4×D9—42no—
140Dic18—22no—
141Dic18—22no—
142C9⋊C8—21no—
143C9⋊C8—21no—
144C9⋊C8—22no—
145#556D911yescharacteristic, complemented
146#547—91no—
147#487—91no—
148#485—92no—
149#474—91no—
150#467—92no—
151#462—91no—
152#452—92no—
153C4×SD16—91no—
154C8×D4—91no—
155#416—92no—
156C2×C3×Q8—21no—
157C2×C3×Q8C22×D311yescharacteristic
158C2×C3×D4#6711yescharacteristic
159C22×C3×C4C22×D312yes—
160C2×#67—62no—
161#235—64no—
162#235—122no—
163C2×D12—31no—
164C2×C4×D3—61no—
165C2×C4×D3—62no—
166C2×Dic6—32no—
167C3×C4⋊C4—22no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4#6711yescharacteristic
171C3×C4⋊C4C22×D312yes—
172C3×C4⋊C4C22×D311yescharacteristic
173C3×C22⋊C4—22no—
174C3×C22⋊C4—22no—
175C3×C22⋊C4#6712yes—
176C3×C42—22no—
177C3×C42—21no—
178C3×C42C22×D311yescharacteristic
179#217—62no—
180#216—122no—
181#215—62no—
182(C2×D3)⋊C4—61no—
183C4⋊Dic3—31no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186Dic3⋊C4—62no—
187C2×C3⋊C8—31no—
188C2×C3⋊C8—31no—
189C2×C3⋊C8—32no—
190C2×C3⋊C8—122no—
191C22×C9—22no—
192C22×C9—22no—
193C22×C9—22no—
194C22×C9C22×D411yescharacteristic
195C2×D9—22no—
196C2×D9—41no—
197C2×D9—41no—
198C4×C9—22no—
199C4×C9—21no—
200C4×C9—41no—
201C4×C9—42no—
202C4×C9—41no—
203C4×C9#13512yes—
204C4×C9C2×#4111yescharacteristic
205C4×C9H(5,𝔽2)11yescharacteristic
206Dic9—42no—
207Dic9—41no—
208C2×#41—92no—
209C2×Q16—92no—
210C2×SD16—91no—
211C22×C8—92no—
212C4⋊Q8—91no—
213C4⋊Q8C2×D911yescharacteristic
214#126—22no—
215#124—21no—
216#123—182no—
217C22⋊Q8—92no—
218C22⋊Q8C2×D912yes—
219#121—181no—
220C4×Q8—21no—
221C4×Q8C2×D911yescharacteristic
222C4×D4—91no—
223C4×D4C2×D911yescharacteristic
224#117C2×D912yes—
225C2×C4⋊C4—181no—
226#107—92no—
227#106—91no—
228C4⋊C8—91no—
229#103—91no—
230#103—92no—
231#103—92no—
232#103—92no—
233#102—91no—
234#102—92no—
235C22⋊C8—92no—
236C4×C8—91no—
237C23×C3C2×#6712yes—
238C22×D3—61no—
239C3×Q8—21no—
240C3×Q8—21no—
241C3×Q8—42no—
242C3×D4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—22no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—22no—
248C2×C3×C4C2×#6712yes—
249C2×C3×C4C2×#6711yescharacteristic
250C2×C3×C4C2×#6711yescharacteristic
251C2×C3×C4C23×D311yescharacteristic
252#67—124no—
253C2×Dic3—61no—
254C2×Dic3—62no—
255D12—32no—
256D12—61no—
257C4×D3—124no—
258C4×D3—122no—
259Dic6—62no—
260Dic6—62no—
261C3⋊C8—61no—
262C3⋊C8—61no—
263C3⋊C8—62no—
264C2×C9—42no—
265C2×C9#54611yescharacteristic
266C2×C9C2×#13511yescharacteristic
267C2×C9#57811yescharacteristic
268D9—42no—
269#41—184no—
270#41—362no—
271C2×Q8—21no—
272C2×Q8—92no—
273C2×Q8C22×D911yescharacteristic
274C2×D4—91no—
275C2×D4—182no—
276C2×D4#61111yescharacteristic
277C22×C4—181no—
278C22×C4—182no—
279C22×C4C22×D912yes—
280Q16—362no—
281SD16—182no—
282C2×C8—91no—
283C2×C8—91no—
284C2×C8—92no—
285C2×C8—362no—
286C4⋊C4—22no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—91no—
290C4⋊C4—181no—
291C4⋊C4—182no—
292C4⋊C4—181no—
293C4⋊C4#61111yescharacteristic
294C4⋊C4C22×D911yescharacteristic
295C4⋊C4C22×D912yes—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C22⋊C4—182no—
299C22⋊C4—181no—
300C22⋊C4#61112yes—
301C42—22no—
302C42—21no—
303C42C22×D911yescharacteristic
304C22×C3—22no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3C22×#6711yescharacteristic
308C2×D3—62no—
309C2×D3—121no—
310C2×D3—121no—
311C3×C4—22no—
312C3×C4—21no—
313C3×C4—42no—
314C3×C4—41no—
315C3×C4—41no—
316C3×C4#95012yes—
317C3×C4D3×#4111yescharacteristic
318C3×C4#100911yescharacteristic
319Dic3—121no—
320Dic3—122no—
321C9#330211yescharacteristic, complemented, Sylow
322C23—181no—
323C23C2×#61112yes—
324Q8—21no—
325Q8—21no—
326Q8—42no—
327Q8—182no—
328Q8—182no—
329D4—22no—
330D4—92no—
331D4—181no—
332D4—364no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—181no—
339C2×C4—182no—
340C2×C4—364no—
341C2×C4—362no—
342C2×C4C2×#61112yes—
343C2×C4C2×#61111yescharacteristic
344C2×C4C2×#61111yescharacteristic
345C2×C4C23×D911yescharacteristic
346C8—181no—
347C8—181no—
348C8—182no—
349C2×C3—42no—
350C2×C3C2×#95011yescharacteristic
351C2×C3#582911yescharacteristic
352C2×C3#583811yescharacteristic
353D3—122no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—182no—
358C22—361no—
359C22—361no—
360C22C22×#61111yescharacteristic
361C4—22no—
362C4—21no—
363C4—42no—
364C4—41no—
365C4—41no—
366C4—361no—
367C4—362no—
368C4#6351312yes—
369C4#41×D911yescharacteristic
370C4#6371511yescharacteristic
371C3#8366411yescharacteristic
372C2—42no—
373C2—362no—
374C2C2×#6351311yescharacteristic
375C2#1058993111yescharacteristic
376C2#1058994011yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#556C2
socleC22×C3C22×#67
prime radical#10589653C2
hypercenter#556D9
hypocenterC9#3302
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
1. C9×#556C2semidirect
3. #10588772C2semidirect
4. #10588766C2semidirect
5. #10588730C2semidirect
6. #10588727C2semidirect
7. C4×#3675C2semidirect
8. #10588707C2semidirect
9. D4×C9⋊C8C2semidirect
10. #10588683C2semidirect
11. #10588680C2semidirect
145. #556D9semidirect
321. C9#3302semidirect

Maximal subgroups

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

subgroupindex
C9×#5562
#105896532
#105887722
#105887662
#105887302
#105887272
C4×#36752
#105887072
D4×C9⋊C82
#105886832
#105886802
#836643