Finite Group Databasebeta

← #11898410

Subgroups — #11898410

Order 1152.

558 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#10589687C211yesmaximal, characteristic, complemented
2#10589644C211yesmaximal, characteristic, complemented
3C4×C9×SD16C211yesmaximal, characteristic, complemented
4#10588848C212yesmaximal, complemented
5#10588707C211yesmaximal, characteristic, complemented
6#10588698C211yesmaximal, characteristic
7#10588532C212yesmaximal, complemented
8#10588478C212yesmaximal, complemented
9#10588467C212yesmaximal, complemented
10#10588375C211yesmaximal, characteristic, complemented
11C8×Dic18C211yesmaximal, characteristic, complemented
12#79638—31nomaximal
13C2×C9×SD16C2211yescharacteristic
14C4×Q8×C9C2211yescharacteristic
15C4×D4×C9C2211yescharacteristic
16#63509C2212yes—
17C2×#3674C2212yes—
18#63498C2212yes—
19C2×#3673C2212yes—
20#63488—21no—
21#63486—21no—
22C2×#3664C2212yes—
23C2×#3664C2212yes—
24#63456—22no—
25#63455C2212yes—
26#63449C2212yes—
27#63441—22no—
28#63437—21no—
29#63436C2211yescharacteristic
30C4×D36—21no—
31#63431C2211yescharacteristic
32C4×Dic18C2211yescharacteristic
33C9×#106C2211yescharacteristic
34C9×#103C2211yescharacteristic
35C9×#102C2211yescharacteristic
36C4×C8×C9C2211yescharacteristic
37Dic9⋊C8C2212yes—
38C8×Dic9C2212yes—
39#63369C2212yes—
40#63368C2212yes—
41C4⋊(C9⋊C8)C2211yescharacteristic
42#5585—31no—
43#5542—31no—
44C3×C4×SD16D311yescharacteristic
45#5168—32no—
46#5031—31no—
47#5015—31no—
48#4852—32no—
49#4798—32no—
50#4787—32no—
51#4693—31no—
52C8×Dic6—31no—
53C2×Q8×C9C2311yescharacteristic
54C2×D4×C9C2311yescharacteristic
55C22×C4×C9—21no—
56C2×D36—21no—
57C2×D36—21no—
58C2×D36C2312yes—
59C2×C4×D9—22no—
60C2×Dic18D411yescharacteristic
61C2×Dic18C2312yes—
62C9×SD16—22no—
63C2×C8×C9C2311yescharacteristic
64C2×C8×C9C2311yescharacteristic
65C9×C4⋊C4—21no—
66C9×C4⋊C4C2311yescharacteristic
67C9×C4⋊C4C2311yescharacteristic
68C9×C22⋊C4—21no—
69C42×C9—21no—
70C42×C9C2311yescharacteristic
71#3676—22no—
72#3676—22no—
73#3674—42no—
74#3673—42no—
75(C2×D9)⋊C4—22no—
76(C2×D9)⋊C4—22no—
77(C2×D9)⋊C4—22no—
78C4⋊Dic9—21no—
79C4⋊Dic9—21no—
80C4⋊Dic9D411yescharacteristic
81Dic9⋊C4—22no—
82Dic9⋊C4D412yes—
83C4×Dic9—22no—
84C4×Dic9C2312yes—
85C2×C9⋊C8C2312yes—
86#3664—24no—
87#3664—42no—
88#3394—91noSylow
89C2×C3×SD16C2×D311yescharacteristic
90C3×C4×Q8C2×D311yescharacteristic
91C3×C4×D4C2×D311yescharacteristic
92#947—32no—
93C2×#216—32no—
94#936—32no—
95C2×#213—32no—
96#926—61no—
97#924—61no—
98C2×#204—32no—
99C2×#204—32no—
100#894—62no—
101#893—32no—
102#887—32no—
103#879—62no—
104#875—61no—
105#874—31no—
106C4×D12—61no—
107#869—31no—
108C4×Dic6—31no—
109C3×#106C2×D311yescharacteristic
110C3×#103C2×D311yescharacteristic
111C3×#102C2×D311yescharacteristic
112C3×C4×C8C2×D311yescharacteristic
113Dic3⋊C8—32no—
114C8×Dic3—32no—
115#810—32no—
116#809—32no—
117C4⋊(C3⋊C8)—31no—
118C23×C9—21no—
119C22×D9—22no—
120Q8×C9—21no—
121Q8×C9—21no—
122D4×C9—21no—
123D4×C9—21no—
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
131C2×Dic9—22no—
132C2×Dic9C2×D412yes—
133C2×Dic9C2×D412yes—
134D36—22no—
135D36—22no—
136D36—42no—
137D36—81no—
138C4×D9—82no—
139Dic18—22no—
140Dic18—22no—
141Dic18—22no—
142C8×C9—21no—
143C8×C9#4112yes—
144C9⋊C8—22no—
145#559—91no—
146#556—91no—
147#495—92no—
148#492—91no—
149#464—92no—
150#463—92no—
151#462—91no—
152#459—91no—
153C8×Q8—91no—
154C4×SD16—92no—
155C4×SD16D911yescharacteristic, complemented
156C2×C3×Q8C22×D311yescharacteristic
157C2×C3×D4C22×D311yescharacteristic
158C22×C3×C4—21no—
159C2×D12—32no—
160C2×D12—61no—
161C2×D12—61no—
162C2×C4×D3—62no—
163C2×Dic6—31no—
164C2×Dic6—32no—
165C3×SD16—22no—
166C2×C3×C8C22×D311yescharacteristic
167C2×C3×C8C22×D311yescharacteristic
168C3×C4⋊C4—21no—
169C3×C4⋊C4C22×D311yescharacteristic
170C3×C4⋊C4C22×D311yescharacteristic
171C3×C22⋊C4—21no—
172C3×C42—21no—
173C3×C42C22×D311yescharacteristic
174#217—62no—
175#217—62no—
176#216—122no—
177#213—122no—
178(C2×D3)⋊C4—62no—
179(C2×D3)⋊C4—62no—
180(C2×D3)⋊C4—62no—
181C4⋊Dic3—31no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184Dic3⋊C4—32no—
185Dic3⋊C4—62no—
186C4×Dic3—32no—
187C4×Dic3—62no—
188C2×C3⋊C8—32no—
189#204—64no—
190#204—122no—
191C22×C9—41no—
192C22×C9—41no—
193C22×C9—41no—
194C22×C9C22×D411yescharacteristic
195C2×D9—42no—
196C2×D9—42no—
197C2×D9—42no—
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—22no—
207Dic9—42no—
208C2×Q16—92no—
209C2×SD16—92no—
210C2×SD16—92no—
211C2×SD16C2×D911yescharacteristic
212C2×D8—92no—
213C4⋊Q8—91no—
214#127—91no—
215#126—182no—
216#124—92no—
217#124—92no—
218#124—181no—
219#123—182no—
220C22⋊Q8—181no—
221C4×Q8—91no—
222C4×Q8—92no—
223C4×Q8C2×D911yescharacteristic
224C4×D4—92no—
225C4×D4—181no—
226C4×D4C2×D911yescharacteristic
227#117—181no—
228#106C2×D911yescharacteristic
229C4⋊C8—92no—
230C4⋊C8—91no—
231#103—92no—
232#103C2×D911yescharacteristic
233#102—92no—
234#102C2×D911yescharacteristic
235C4×C8—92no—
236C4×C8C2×D911yescharacteristic
237C23×C3—21no—
238C22×D3—62no—
239C3×Q8—21no—
240C3×Q8—21no—
241C3×D4—21no—
242C3×D4—21no—
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
250C2×Dic3—32no—
251C2×Dic3—32no—
252C2×Dic3—62no—
253D12—62no—
254D12—62no—
255D12—122no—
256D12—241no—
257C4×D3—242no—
258Dic6—62no—
259Dic6—62no—
260Dic6—62no—
261C3×C8—21no—
262C3×C8#23512yes—
263C3⋊C8—62no—
264C2×C9—81no—
265C2×C9#55011yescharacteristic
266C2×C9C2×#13511yescharacteristic
267C2×C9#57711yescharacteristic
268D9—82no—
269C2×Q8—91no—
270C2×Q8—92no—
271C2×Q8C22×D911yescharacteristic
272C2×D4—92no—
273C2×D4—181no—
274C2×D4—181no—
275C2×D4C22×D911yescharacteristic
276C22×C4—21no—
277C22×C4—182no—
278Q16—362no—
279SD16—22no—
280SD16—184no—
281SD16—362no—
282D8—362no—
283C2×C8—92no—
284C2×C8C22×D911yescharacteristic
285C2×C8C22×D911yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—91no—
288C4⋊C4—92no—
289C4⋊C4—182no—
290C4⋊C4—181no—
291C4⋊C4—181no—
292C4⋊C4C22×D911yescharacteristic
293C4⋊C4C22×D911yescharacteristic
294C22⋊C4—21no—
295C22⋊C4—182no—
296C22⋊C4—182no—
297C22⋊C4—182no—
298C22⋊C4—182no—
299C22⋊C4—182no—
300C42—21no—
301C42—92no—
302C42—182no—
303C42C22×D911yescharacteristic
304C22×C3—41no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3C2×D3×D411yescharacteristic
308C2×D3—122no—
309C2×D3—122no—
310C2×D3—122no—
311C3×C4—21no—
312C3×C4—41no—
313C3×C4—41no—
314C3×C4—41no—
315C3×C4#91612yes—
316C3×C4C2×#23511yescharacteristic
317C3×C4#100911yescharacteristic
318Dic3—62no—
319Dic3—62no—
320Dic3—122no—
321C9#339411yescharacteristic, complemented, Sylow
322C23—21no—
323C23—182no—
324Q8—21no—
325Q8—21no—
326Q8—182no—
327Q8—182no—
328Q8—182no—
329D4—21no—
330D4—21no—
331D4—182no—
332D4—182no—
333D4—362no—
334D4—721no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—92no—
340C2×C4—92no—
341C2×C4—182no—
342C2×C4—722no—
343C2×C4D4×D911yescharacteristic
344C2×C4D4×D911yescharacteristic
345C2×C4C23×D911yescharacteristic
346C8—21no—
347C8—182no—
348C8#369712yes—
349C2×C3—81no—
350C2×C3#555311yescharacteristic
351C2×C3C2×#91611yescharacteristic
352C2×C3#577011yescharacteristic
353D3—242no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—362no—
358C22—362no—
359C22—362no—
360C22C2×D4×D911yescharacteristic
361C4—21no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—182no—
366C4—182no—
367C4—362no—
368C4#6347812yes—
369C4C2×#369711yescharacteristic
370C4#6371511yescharacteristic
371C3#7963811yescharacteristic
372C2—81no—
373C2—722no—
374C2#1058965511yescharacteristic
375C2C2×#6347811yescharacteristic
376C2#1058987211yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC4×C9×SD16C2
socleC22×C3C2×D3×D4
prime radical#10588698C2
hypercenterC4×SD16D9
hypocenterC9#3394
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. #10589687C2semidirect
2. #10589644C2semidirect
3. C4×C9×SD16C2semidirect
4. #10588848C2semidirect
5. #10588707C2semidirect
7. #10588532C2semidirect
8. #10588478C2semidirect
9. #10588467C2semidirect
10. #10588375C2semidirect
11. C8×Dic18C2semidirect
155. C4×SD16D9semidirect
321. C9#3394semidirect

Maximal subgroups

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

subgroupindex
#105896872
#105896442
C4×C9×SD162
#105888482
#105887072
#105886982
#105885322
#105884782
#105884672
#105883752
C8×Dic182
#796383