Finite Group Databasebeta

← #11888022

Subgroups — #11888022

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
1#10589686C211yesmaximal, characteristic, complemented
2#10589657C211yesmaximal, characteristic
3C4×C9×SD16C211yesmaximal, characteristic, complemented
4#10588853C212yesmaximal, complemented
5#10588707C211yesmaximal, characteristic, complemented
6#10588690C211yesmaximal, characteristic, complemented
7#10588548C212yesmaximal, complemented
8#10588493C212yesmaximal, complemented
9#10588452C212yesmaximal, complemented
10C8×D36C211yesmaximal, characteristic, complemented
11#10588361C211yesmaximal, characteristic, complemented
12#79680—31nomaximal
13C2×#3699C2212yes—
14C2×C9×SD16C2211yescharacteristic
15C4×Q8×C9C2211yescharacteristic
16C4×D4×C9C2211yescharacteristic
17#63508C2212yes—
18C2×#3674C2212yes—
19#63492—21no—
20C2×C4⋊Dic9—21no—
21C2×C8×D9C2212yes—
22#63460—22no—
23#63459C2212yes—
24#63454C2212yes—
25#63448—22no—
26#63437—21no—
27C4×D36C2211yescharacteristic
28#63431C2211yescharacteristic
29#63431C2211yescharacteristic
30C4×Dic18—21no—
31C9×#106C2211yescharacteristic
32C9×#103C2211yescharacteristic
33C9×#102C2211yescharacteristic
34C4×C8×C9C2211yescharacteristic
35#63392C2212yes—
36(C2×D9)⋊C8C2212yes—
37#63376C2212yes—
38#63376C2212yes—
39#63368C2212yes—
40#63366C2212yes—
41C4⋊(C9⋊C8)C2211yescharacteristic
42#5584—31no—
43#5555—31no—
44C3×C4×SD16D311yescharacteristic
45#5173—32no—
46#5031—31no—
47#5007—31no—
48#4868—32no—
49#4813—32no—
50#4772—32no—
51C8×D12—31no—
52#4681—31no—
53C2×Q8×C9C2311yescharacteristic
54C2×D4×C9C2311yescharacteristic
55C22×C4×C9—21no—
56C2×#611—22no—
57C22×Dic9—22no—
58#3699—24no—
59#3699—42no—
60C2×D36D411yescharacteristic
61C2×C4×D9C2312yes—
62C2×Dic18—21no—
63C2×Dic18C2312yes—
64C9×SD16—22no—
65C2×C8×C9C2311yescharacteristic
66C2×C8×C9C2311yescharacteristic
67C9×C4⋊C4—21no—
68C9×C4⋊C4C2311yescharacteristic
69C9×C4⋊C4C2311yescharacteristic
70C9×C22⋊C4—21no—
71C42×C9—21no—
72C42×C9C2311yescharacteristic
73#3674—42no—
74(C2×D9)⋊C4—22no—
75(C2×D9)⋊C4—22no—
76(C2×D9)⋊C4—22no—
77(C2×D9)⋊C4D412yes—
78C4⋊Dic9—21no—
79C4⋊Dic9—21no—
80C4⋊Dic9—21no—
81C4⋊Dic9—22no—
82C4⋊Dic9D411yescharacteristic
83C4⋊Dic9C2312yes—
84Dic9⋊C4—22no—
85C4×Dic9—22no—
86C2×C9⋊C8C2312yes—
87C8×D9—42no—
88#3302—91noSylow
89C2×#237—32no—
90C2×C3×SD16C2×D311yescharacteristic
91C3×C4×Q8C2×D311yescharacteristic
92C3×C4×D4C2×D311yescharacteristic
93#946—32no—
94C2×#216—32no—
95#930—61no—
96C2×C4⋊Dic3—61no—
97C2×D3×C8—32no—
98#898—62no—
99#897—32no—
100#892—32no—
101#886—62no—
102#875—61no—
103C4×D12—31no—
104#869—31no—
105#869—31no—
106C4×Dic6—61no—
107C3×#106C2×D311yescharacteristic
108C3×#103C2×D311yescharacteristic
109C3×#102C2×D311yescharacteristic
110C3×C4×C8C2×D311yescharacteristic
111#832—32no—
112(C2×D3)⋊C8—32no—
113#816—32no—
114#816—32no—
115#810—32no—
116#807—32no—
117C4⋊(C3⋊C8)—31no—
118C23×C9—21no—
119C22×D9C2×D412yes—
120Q8×C9—21no—
121Q8×C9—21no—
122D4×C9—21no—
123D4×C9#4112yes—
124C2×C4×C9—21no—
125C2×C4×C9—21no—
126C2×C4×C9—21no—
127C2×C4×C9—42no—
128C2×C4×C9C2×D411yescharacteristic
129C2×C4×C9C2×D411yescharacteristic
130C2×C4×C9C2411yescharacteristic
131#611—44no—
132C2×Dic9—22no—
133C2×Dic9—22no—
134C2×Dic9—44no—
135C2×Dic9C2×D412yes—
136D36—22no—
137C4×D9—22no—
138C4×D9—22no—
139Dic18—22no—
140Dic18—22no—
141Dic18—42no—
142C8×C9—21no—
143C8×C9—21no—
144C9⋊C8—22no—
145#556—91no—
146#547—91no—
147#487—91no—
148#485—92no—
149#474—91no—
150#467—92no—
151#462—91no—
152#452—92no—
153C4×SD16D911yescharacteristic, complemented
154C8×D4—91no—
155#416—92no—
156C2×C3×Q8C22×D311yescharacteristic
157C2×C3×D4C22×D311yescharacteristic
158C22×C3×C4—21no—
159C2×#67—62no—
160C22×Dic3—62no—
161#237—64no—
162#237—122no—
163C2×D12—31no—
164C2×C4×D3—32no—
165C2×Dic6—32no—
166C2×Dic6—61no—
167C3×SD16—22no—
168C2×C3×C8C22×D311yescharacteristic
169C2×C3×C8C22×D311yescharacteristic
170C3×C4⋊C4—21no—
171C3×C4⋊C4C22×D311yescharacteristic
172C3×C4⋊C4C22×D311yescharacteristic
173C3×C22⋊C4—21no—
174C3×C42—21no—
175C3×C42C22×D311yescharacteristic
176#216—122no—
177(C2×D3)⋊C4—32no—
178(C2×D3)⋊C4—62no—
179(C2×D3)⋊C4—62no—
180(C2×D3)⋊C4—62no—
181C4⋊Dic3—31no—
182C4⋊Dic3—32no—
183C4⋊Dic3—62no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186C4⋊Dic3—61no—
187Dic3⋊C4—62no—
188C4×Dic3—62no—
189C2×C3⋊C8—32no—
190D3×C8—122no—
191C22×C9—22no—
192C22×C9—41no—
193C22×C9—41no—
194C22×C9C22×D411yescharacteristic
195C2×D9—22no—
196C2×D9—22no—
197C2×D9—22no—
198C4×C9—21no—
199C4×C9—41no—
200C4×C9—41no—
201C4×C9—41no—
202C4×C9#13512yes—
203C4×C9C2×#4111yescharacteristic
204C4×C9H(5,𝔽2)11yescharacteristic
205Dic9—22no—
206Dic9—42no—
207Dic9—42no—
208C2×#41—92no—
209C2×Q16—92no—
210C2×SD16C2×D911yescharacteristic
211C22×C8—92no—
212C4⋊Q8—91no—
213C4⋊Q8—91no—
214#126—182no—
215#124—181no—
216#123—182no—
217C22⋊Q8—92no—
218C22⋊Q8—92no—
219#121—181no—
220C4×Q8—181no—
221C4×Q8C2×D911yescharacteristic
222C4×D4—91no—
223C4×D4C2×D911yescharacteristic
224#117—92no—
225C2×C4⋊C4—181no—
226#107—92no—
227#106C2×D911yescharacteristic
228C4⋊C8—91no—
229#103—92no—
230#103—92no—
231#103—92no—
232#103C2×D911yescharacteristic
233#102—92no—
234#102C2×D911yescharacteristic
235C22⋊C8—92no—
236C4×C8C2×D911yescharacteristic
237C23×C3—21no—
238C22×D3—32no—
239C3×Q8—21no—
240C3×Q8—21no—
241C3×D4—21no—
242C3×D4#23512yes—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—42no—
247C2×C3×C4D3×D411yescharacteristic
248C2×C3×C4D3×D411yescharacteristic
249C2×C3×C4C23×D311yescharacteristic
250#67—124no—
251C2×Dic3—32no—
252C2×Dic3—62no—
253C2×Dic3—62no—
254C2×Dic3—124no—
255D12—62no—
256C4×D3—62no—
257C4×D3—62no—
258Dic6—62no—
259Dic6—62no—
260Dic6—122no—
261C3×C8—21no—
262C3×C8—21no—
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—92no—
272C2×Q8—181no—
273C2×Q8C22×D911yescharacteristic
274C2×D4—91no—
275C2×D4—182no—
276C2×D4C22×D911yescharacteristic
277C22×C4—21no—
278C22×C4—92no—
279C22×C4—182no—
280Q16—362no—
281SD16—22no—
282C2×C8—92no—
283C2×C8—362no—
284C2×C8C22×D911yescharacteristic
285C2×C8C22×D911yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—91no—
288C4⋊C4—92no—
289C4⋊C4—182no—
290C4⋊C4—182no—
291C4⋊C4—181no—
292C4⋊C4—181no—
293C4⋊C4—181no—
294C4⋊C4C22×D911yescharacteristic
295C4⋊C4C22×D911yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—92no—
298C22⋊C4—182no—
299C22⋊C4—182no—
300C22⋊C4—182no—
301C42—21no—
302C42—182no—
303C42C22×D911yescharacteristic
304C22×C3—22no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3C2×D3×D411yescharacteristic
308C2×D3—62no—
309C2×D3—62no—
310C2×D3—62no—
311C3×C4—21no—
312C3×C4—41no—
313C3×C4—41no—
314C3×C4—41no—
315C3×C4#91612yes—
316C3×C4C2×#23511yescharacteristic
317C3×C4#100911yescharacteristic
318Dic3—62no—
319Dic3—122no—
320Dic3—122no—
321C9#330211yescharacteristic, complemented, Sylow
322C23—21no—
323C23—92no—
324Q8—21no—
325Q8—21no—
326Q8—182no—
327Q8—182no—
328Q8—362no—
329D4—21no—
330D4—182no—
331D4—364no—
332D4#369712yes—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—92no—
338C2×C4—182no—
339C2×C4—182no—
340C2×C4—182no—
341C2×C4—182no—
342C2×C4—364no—
343C2×C4D4×D911yescharacteristic
344C2×C4D4×D911yescharacteristic
345C2×C4C23×D911yescharacteristic
346C8—21no—
347C8—21no—
348C8—182no—
349C2×C3—42no—
350C2×C3#555011yescharacteristic
351C2×C3C2×#91611yescharacteristic
352C2×C3#577111yescharacteristic
353D3—122no—
354C22—22no—
355C22—41no—
356C22—41no—
357C22—182no—
358C22—182no—
359C22—182no—
360C22C2×D4×D911yescharacteristic
361C4—21no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—182no—
366C4—362no—
367C4—362no—
368C4#6347812yes—
369C4C2×#369711yescharacteristic
370C4#6371511yescharacteristic
371C3#7968011yescharacteristic
372C2—42no—
373C2—362no—
374C2#1058965211yescharacteristic
375C2C2×#6347811yescharacteristic
376C2#1058987311yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC4×C9×SD16C2
socleC22×C3C2×D3×D4
prime radical#10589657C2
hypercenterC4×SD16D9
hypocenterC9#3302
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #10589686C2semidirect
3. C4×C9×SD16C2semidirect
4. #10588853C2semidirect
5. #10588707C2semidirect
6. #10588690C2semidirect
7. #10588548C2semidirect
8. #10588493C2semidirect
9. #10588452C2semidirect
10. C8×D36C2semidirect
11. #10588361C2semidirect
153. C4×SD16D9semidirect
321. C9#3302semidirect

Maximal subgroups

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

subgroupindex
#105896862
#105896572
C4×C9×SD162
#105888532
#105887072
#105886902
#105885482
#105884932
#105884522
C8×D362
#105883612
#796803