Finite Group Databasebeta

← #11868723

Subgroups — #11868723

Order 1152.

564 conjugacy classes of subgroups.

The subgroup lattice has 393 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589830C211yesmaximal, characteristic
2C4×Q8×D9C211yesmaximal, characteristic
3C9×#477C211yesmaximal, characteristic, complemented
4#10588764C211yesmaximal, characteristic, complemented
5#10588702C211yesmaximal, characteristic, complemented
6#10588561C212yesmaximal
7#10588557C212yesmaximal, complemented
8#10588521C211yesmaximal, characteristic
9#10588515C211yesmaximal, characteristic, complemented
10#10588482C212yesmaximal
11#10588479C212yesmaximal, complemented
12#81108—31nomaximal
13C2×Q8×D9C2211yescharacteristic
14C9×C4⋊Q8C2211yescharacteristic
15C4×Q8×C9C2211yescharacteristic
16#63508—21no—
17Q8×Dic9—21no—
18Q8×Dic9C2211yescharacteristic
19C2×#3663C2212yes—
20#63459—21no—
21#63454C2212yes—
22C4⋊C4×D9—21no—
23C4⋊C4×D9C2211yescharacteristic
24#63452C2212yes—
25#63449—21no—
26#63449—21no—
27#63449C2211yescharacteristic
28C42×D9—21no—
29C42×D9C2211yescharacteristic
30#63431C2211yescharacteristic
31C4×Dic18—21no—
32C4×Dic18C2211yescharacteristic
33C9×#107C2212yes—
34C9×C4⋊C8C2211yescharacteristic
35C9×#103C2212yes—
36#63395C2212yes—
37#63377C2212yes—
38#63376C2212yes—
39Dic9⋊C8C2212yes—
40#63368C2212yes—
41#63367C2212yes—
42#63366C2212yes—
43C4⋊(C9⋊C8)C2211yescharacteristic
44#5728—31no—
45C4×D3×Q8—31no—
46C3×#477D311yescharacteristic
47#5091—31no—
48#5020—31no—
49#4881—32no—
50#4877—32no—
51#4851—31no—
52#4837—31no—
53#4802—32no—
54#4799—32no—
55C2×Q8×C9—21no—
56C2×Q8×C9C2311yescharacteristic
57Q8×D9—22no—
58Q8×D9Q814yescomplemented
59C2×C4×D9—21no—
60C2×C4×D9—21no—
61C2×C4×D9D411yescharacteristic
62C2×C4×D9D411yescharacteristic
63C2×C4×D9C2311yescharacteristic
64C2×Dic18—21no—
65C2×Dic18—21no—
66C2×Dic18C2311yescharacteristic
67C2×C8×C9C2312yes—
68C9×C4⋊C4—21no—
69C9×C4⋊C4—21no—
70C9×C4⋊C4C2311yescharacteristic
71C9×C4⋊C4C2312yes—
72C42×C9—21no—
73C42×C9C2311yescharacteristic
74(C2×D9)⋊C4—22no—
75C4⋊Dic9—21no—
76C4⋊Dic9—22no—
77C4⋊Dic9—21no—
78C4⋊Dic9C2311yescharacteristic
79C4⋊Dic9C2312yes—
80Dic9⋊C4—21no—
81Dic9⋊C4—22no—
82Dic9⋊C4—21no—
83Dic9⋊C4—21no—
84C4×Dic9—21no—
85C4×Dic9—22no—
86C4×Dic9—21no—
87C4×Dic9—21no—
88C4×Dic9D411yescharacteristic
89C4×Dic9D411yescharacteristic
90C4×Dic9C2311yescharacteristic
91C2×C9⋊C8C2312yes—
92#3663—24no—
93#3078—91noSylow
94C2×D3×Q8—31no—
95C3×C4⋊Q8C2×D311yescharacteristic
96C3×C4×Q8C2×D311yescharacteristic
97#946—61no—
98Q8×Dic3—31no—
99Q8×Dic3—61no—
100C2×ΓL(1,𝔽25)—32no—
101#897—61no—
102#892—32no—
103D3×C4⋊C4—31no—
104D3×C4⋊C4—61no—
105#890—32no—
106#887—31no—
107#887—61no—
108#887—61no—
109C42×D3—31no—
110C42×D3—61no—
111#869—31no—
112C4×Dic6—31no—
113C4×Dic6—61no—
114C3×#107C2×D312yes—
115C3×C4⋊C8C2×D311yescharacteristic
116C3×#103C2×D312yes—
117#835—32no—
118#817—32no—
119#816—32no—
120Dic3⋊C8—32no—
121#810—32no—
122#808—32no—
123#807—32no—
124C4⋊(C3⋊C8)—31no—
125C22×D9C2×D411yescharacteristic
126Q8×C9—21no—
127Q8×C9—42no—
128Q8×C9C2×Q812yes—
129C2×C4×C9—21no—
130C2×C4×C9—21no—
131C2×C4×C9—22no—
132C2×C4×C9C2×D411yescharacteristic
133C2×C4×C9C2×D411yescharacteristic
134C2×C4×C9C2411yescharacteristic
135C2×Dic9—21no—
136C2×Dic9—21no—
137C2×Dic9—22no—
138C2×Dic9C2×D411yescharacteristic
139C2×Dic9C2×D411yescharacteristic
140C2×Dic9C2×D411yescharacteristic
141C4×D9—24no—
142C4×D9—22no—
143C4×D9—41no—
144C4×D9—42no—
145C4×D9C2×Q812yes—
146C4×D9#4112yes—
147Dic18—21no—
148Dic18—24no—
149Dic18—42no—
150Dic18C2×Q812yes—
151C8×C9—22no—
152C9⋊C8—22no—
153#533—91no—
154C2×C4×Q8—91no—
155#479—92no—
156#479—92no—
157#477—91no—
158#477D911yescharacteristic, complemented
159#475—91no—
160#475—91no—
161#428—92no—
162#423—91no—
163#419—92no—
164C2×C3×Q8—21no—
165C2×C3×Q8C22×D311yescharacteristic
166D3×Q8—34no—
167D3×Q8—62no—
168C2×C4×D3—31no—
169C2×C4×D3—31no—
170C2×C4×D3—31no—
171C2×C4×D3—61no—
172C2×C4×D3—61no—
173C2×Dic6—31no—
174C2×Dic6—61no—
175C2×Dic6—61no—
176C2×C3×C8C22×D312yes—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4C22×D312yes—
180C3×C4⋊C4C22×D311yescharacteristic
181C3×C42—21no—
182C3×C42C22×D311yescharacteristic
183(C2×D3)⋊C4—62no—
184C4⋊Dic3—31no—
185C4⋊Dic3—32no—
186C4⋊Dic3—61no—
187C4⋊Dic3—62no—
188C4⋊Dic3—61no—
189Dic3⋊C4—61no—
190Dic3⋊C4—61no—
191Dic3⋊C4—62no—
192Dic3⋊C4—61no—
193C4×Dic3—31no—
194C4×Dic3—31no—
195C4×Dic3—31no—
196C4×Dic3—61no—
197C4×Dic3—61no—
198C4×Dic3—62no—
199C4×Dic3—61no—
200C2×C3⋊C8—32no—
201ΓL(1,𝔽25)—64no—
202C22×C9C22×D411yescharacteristic
203C2×D9—21no—
204C2×D9—21no—
205C2×D9C22⋊Q812yes—
206C4×C9—22no—
207C4×C9—21no—
208C4×C9—41no—
209C4×C9—42no—
210C4×C9#13712yes—
211C4×C9C22×Q811yescharacteristic
212C4×C9C2×#4111yescharacteristic
213Dic9—22no—
214Dic9—21no—
215Dic9—21no—
216Dic9—42no—
217Dic9—41no—
218Dic9C22⋊Q812yes—
219C22×Q8—91no—
220C2×M16—92no—
221C4⋊Q8—91no—
222C4⋊Q8C2×D911yescharacteristic
223#125—92no—
224C22⋊Q8—181no—
225C22⋊Q8—181no—
226C4×Q8—91no—
227C4×Q8—91no—
228C4×Q8—91no—
229C4×Q8—181no—
230C4×Q8—181no—
231C4×Q8—181no—
232C4×Q8—181no—
233C4×Q8C2×D911yescharacteristic
234#117—92no—
235C2×C4⋊C4—91no—
236C2×C4⋊C4—181no—
237C2×C42—91no—
238C2×C42—181no—
239#107—92no—
240#107C2×D912yes—
241#106—92no—
242#106—92no—
243C4⋊C8—92no—
244C4⋊C8—91no—
245C4⋊C8C2×D911yescharacteristic
246#103—92no—
247#103—92no—
248#103—92no—
249#103C2×D912yes—
250C22×D3—31no—
251C3×Q8—21no—
252C3×Q8—42no—
253C3×Q8D3×Q812yes—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—22no—
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4D3×D411yescharacteristic
259C2×C3×C4C23×D311yescharacteristic
260C2×Dic3—31no—
261C2×Dic3—31no—
262C2×Dic3—31no—
263C2×Dic3—61no—
264C2×Dic3—61no—
265C2×Dic3—62no—
266C4×D3—32no—
267C4×D3—32no—
268C4×D3—64no—
269C4×D3—62no—
270C4×D3—121no—
271C4×D3—122no—
272Dic6—32no—
273Dic6—64no—
274Dic6—61no—
275Dic6—122no—
276C3×C8—22no—
277C3⋊C8—62no—
278C2×C9C2×C22⋊Q811yescharacteristic
279C2×C9C2×#13711yescharacteristic
280C2×C9#57511yescharacteristic
281D9—22no—
282C2×Q8—21no—
283C2×Q8—94no—
284C2×Q8—91no—
285C2×Q8—181no—
286C2×Q8—182no—
287C2×Q8—181no—
288C2×Q8C22×D911yescharacteristic
289C22×C4—91no—
290C22×C4—91no—
291C22×C4—91no—
292C22×C4—181no—
293C22×C4—181no—
294M16—184no—
295C2×C8—92no—
296C2×C8C22×D912yes—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—92no—
300C4⋊C4—91no—
301C4⋊C4—181no—
302C4⋊C4—181no—
303C4⋊C4—181no—
304C4⋊C4—182no—
305C4⋊C4—182no—
306C4⋊C4—181no—
307C4⋊C4—181no—
308C4⋊C4C22×D912yes—
309C4⋊C4C22×D911yescharacteristic
310C22⋊C4—182no—
311C42—21no—
312C42—91no—
313C42—91no—
314C42—91no—
315C42—181no—
316C42—181no—
317C42—182no—
318C42—181no—
319C42C22×D911yescharacteristic
320C22×C3C2×D3×D411yescharacteristic
321C2×D3—32no—
322C2×D3—61no—
323C2×D3—61no—
324C3×C4—21no—
325C3×C4—22no—
326C3×C4—41no—
327C3×C4—42no—
328C3×C4#91812yes—
329C3×C4C2×D3×Q811yescharacteristic
330C3×C4D3×#4111yescharacteristic
331Dic3—32no—
332Dic3—61no—
333Dic3—61no—
334Dic3—62no—
335Dic3—122no—
336Dic3—121no—
337C9#307811yescharacteristic, complemented, Sylow
338C23—91no—
339Q8—21no—
340Q8—42no—
341Q8—92no—
342Q8—184no—
343Q8—181no—
344Q8—362no—
345Q8Q8×D912yes—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—91no—
350C2×C4—92no—
351C2×C4—92no—
352C2×C4—91no—
353C2×C4—91no—
354C2×C4—184no—
355C2×C4—181no—
356C2×C4—182no—
357C2×C4—181no—
358C2×C4—182no—
359C2×C4—361no—
360C2×C4—362no—
361C2×C4D4×D911yescharacteristic
362C2×C4D4×D911yescharacteristic
363C2×C4C23×D911yescharacteristic
364C8—22no—
365C8—182no—
366C2×C3D3×C22⋊Q811yescharacteristic
367C2×C3C2×#91811yescharacteristic
368C2×C3#577311yescharacteristic
369D3—62no—
370C22—92no—
371C22—181no—
372C22—181no—
373C22C2×D4×D911yescharacteristic
374C4—22no—
375C4—21no—
376C4—41no—
377C4—42no—
378C4—92no—
379C4—182no—
380C4—181no—
381C4—181no—
382C4—362no—
383C4—361no—
384C4#6348012yes—
385C4C2×Q8×D911yescharacteristic
386C4#41×D911yescharacteristic
387C3#8110811yescharacteristic
388C2—182no—
389C2D9×C22⋊Q811yescharacteristic
390C2C2×#6348011yescharacteristic
391C2#1058987511yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#477C2
socleC22×C3C2×D3×D4
prime radicalC22×D9C2×D4
hypercenter#477D9
hypocenterC9#3078
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
3. C9×#477C2semidirect
4. #10588764C2semidirect
5. #10588702C2semidirect
7. #10588557C2semidirect
9. #10588515C2semidirect
11. #10588479C2semidirect
58. Q8×D9Q8semidirect
158. #477D9semidirect
337. C9#3078semidirect

Maximal subgroups

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

subgroupindex
#105898302
C4×Q8×D92
C9×#4772
#105887642
#105887022
#105885612
#105885572
#105885212
#105885152
#105884822
#105884792
#811083