Finite Group Databasebeta

← #11775106

Subgroups — #11775106

Order 1152.

501 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 501 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589729C211yesmaximal, characteristic
2#10588408C211yesmaximal, characteristic, complemented
3D9×#95C211yesmaximal, characteristic, complemented
4C9×#328C211yesmaximal, characteristic, complemented
5#10588215C211yesmaximal, characteristic, complemented
6#10588147C211yesmaximal, characteristic, complemented
7#10588129C211yesmaximal, characteristic, complemented
8#68334—31nomaximal
9C2×#3701C411yescharacteristic, complemented
10C22×C4×D9—21no—
11C22×C4×D9C2211yescharacteristic
12C9×C22⋊Q8C2211yescharacteristic
13#63508C411yescharacteristic, complemented
14#63492C2211yescharacteristic
15C2×#3663—21no—
16#63457C411yescharacteristic, complemented
17#63456—21no—
18#63455—21no—
19#63454C411yescharacteristic, complemented
20#63444—21no—
21#611⋊C4—21no—
22C9×C22⋊C8C2211yescharacteristic
23C9×#95C2211yescharacteristic
24C9⋊#95—21no—
25C9⋊#95C2211yescharacteristic
26#63389C2211yescharacteristic
27(C2×D9)⋊C8—21no—
28#5627—31no—
29#4726—31no—
30D3×#95—31no—
31C3×#328D311yescharacteristic
32#4538—31no—
33#4470—31no—
34#4451—31no—
35C23×D9D411yescharacteristic
36C2×Q8×C9C2×C411yescharacteristic, complemented
37C22×C4×C9—21no—
38C22×C4×C9C2311yescharacteristic
39C2×#611—21no—
40C22×Dic9—21no—
41C22×Dic9D411yescharacteristic
42#3701—42no—
43C2×D36—21no—
44C2×D36—21no—
45C2×D36C2×C411yescharacteristic, complemented
46C2×C4×D9—24no—
47C2×C4×D9—21no—
48C2×C4×D9—42no—
49C2×C4×D9—42no—
50C2×C4×D9—42no—
51C2×C4×D9C2×C411yescharacteristic
52C2×C4×D9C2×C411yescharacteristic
53C2×C4×D9D411yescharacteristic
54C2×C4×D9D411yescharacteristic
55C2×C8×C9—21no—
56C9×C4⋊C4—21no—
57C9×C4⋊C4C2×C411yescharacteristic, complemented
58C9×C22⋊C4—21no—
59(C2×D9)⋊C4—21no—
60(C2×D9)⋊C4—21no—
61(C2×D9)⋊C4—21no—
62(C2×D9)⋊C4—21no—
63C4⋊Dic9C2×C411yescharacteristic, complemented
64Dic9⋊C4—21no—
65C4×Dic9—21no—
66C2×C9⋊C8—21no—
67#3663—42no—
68#1504—91noSylow
69C2×#239—31no—
70C22×C4×D3—31no—
71C22×C4×D3—61no—
72C3×C22⋊Q8C2×D311yescharacteristic
73#946—31no—
74#930—31no—
75C2×ΓL(1,𝔽25)—61no—
76#895—31no—
77#894—61no—
78#893—61no—
79#892—31no—
80#882—61no—
81#67⋊C4—61no—
82C3×C22⋊C8C2×D311yescharacteristic
83C3×#95C2×D311yescharacteristic
84C3⋊#95—31no—
85C3⋊#95—61no—
86#830—31no—
87(C2×D3)⋊C8—61no—
88C23×C9C2×D411yescharacteristic
89C22×D9—21no—
90C22×D9—21no—
91C22×D9—22no—
92C22×D9—22no—
93C22×D9—21no—
94C22×D9C22⋊C411yescharacteristic
95C22×D9C22⋊C411yescharacteristic
96Q8×C9—41no—
97C2×C4×C9—22no—
98C2×C4×C9—21no—
99C2×C4×C9—21no—
100C2×C4×C9—41no—
101C2×C4×C9—41no—
102C2×C4×C9—41no—
103C2×C4×C9C22×C411yescharacteristic
104C2×C4×C9C2×D411yescharacteristic
105#611—41no—
106#611—41no—
107C2×Dic9—22no—
108C2×Dic9—21no—
109C2×Dic9—41no—
110C2×Dic9—41no—
111C2×Dic9—41no—
112C2×Dic9C22⋊C411yescharacteristic
113C2×Dic9C22⋊C411yescharacteristic
114D36—41no—
115D36—42no—
116D36—42no—
117C4×D9—22no—
118C4×D9—22no—
119C4×D9—41no—
120C4×D9—41no—
121C4×D9—42no—
122C4×D9—48no—
123C8×C9—41no—
124C9⋊C8—41no—
125#525—91no—
126#407—91no—
127C2×#95—91no—
128#328—91no—
129#328D911yescharacteristic, complemented
130#327—91no—
131#327—91no—
132C23×D3—31no—
133C2×C3×Q8C4×D311yescharacteristic
134C22×C3×C4—21no—
135C22×C3×C4C22×D311yescharacteristic
136C2×#67—61no—
137C22×Dic3—31no—
138C22×Dic3—61no—
139#239—122no—
140C2×D12—31no—
141C2×D12—61no—
142C2×D12—61no—
143C2×C4×D3—31no—
144C2×C4×D3—31no—
145C2×C4×D3—31no—
146C2×C4×D3—31no—
147C2×C4×D3—61no—
148C2×C4×D3—64no—
149C2×C4×D3—122no—
150C2×C4×D3—122no—
151C2×C4×D3—122no—
152C2×C3×C8—21no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4C4×D311yescharacteristic
155C3×C22⋊C4—21no—
156(C2×D3)⋊C4—61no—
157(C2×D3)⋊C4—61no—
158(C2×D3)⋊C4—61no—
159(C2×D3)⋊C4—61no—
160C4⋊Dic3—31no—
161Dic3⋊C4—61no—
162C4×Dic3—61no—
163C2×C3⋊C8—61no—
164ΓL(1,𝔽25)—122no—
165C22×C9—21no—
166C22×C9—21no—
167C22×C9C2×C22⋊C411yescharacteristic
168C22×C9AGL(1,ℤ/8)11yescharacteristic
169C22×C9#13711yescharacteristic
170C2×D9—24no—
171C2×D9—24no—
172C2×D9—21no—
173C2×D9—21no—
174C2×D9—21no—
175C2×D9—21no—
176C2×D9—41no—
177C2×D9—41no—
178C2×D9—41no—
179C2×D9#9912yes—
180C2×D9#10412yes—
181C4×C9—21no—
182C4×C9—21no—
183C4×C9—42no—
184C4×C9—41no—
185C4×C9—41no—
186Dic9—21no—
187Dic9—21no—
188Dic9—42no—
189Dic9—41no—
190C2×#41—91no—
191C23×C4—91no—
192C23×C4—181no—
193C2×M16—181no—
194#123—181no—
195C22⋊Q8—91no—
196C22⋊Q8C2×D911yescharacteristic
197#121—91no—
198#121—91no—
199#120—181no—
200C4×D4—181no—
201C4×D4—181no—
202#117—91no—
203C22⋊C8—91no—
204C22⋊C8—181no—
205C22⋊C8C2×D911yescharacteristic
206#95—91no—
207#95—181no—
208#95C2×D911yescharacteristic
209C23×C3D3×D411yescharacteristic
210C22×D3—31no—
211C22×D3—31no—
212C22×D3—62no—
213C22×D3—62no—
214C22×D3—61no—
215C22×D3—61no—
216C22×D3—61no—
217C3×Q8—41no—
218C2×C3×C4—22no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—41no—
222C2×C3×C4—41no—
223C2×C3×C4—41no—
224C2×C3×C4C2×C4×D311yescharacteristic
225C2×C3×C4D3×D411yescharacteristic
226#67—121no—
227#67—121no—
228C2×Dic3—31no—
229C2×Dic3—31no—
230C2×Dic3—62no—
231C2×Dic3—61no—
232C2×Dic3—121no—
233C2×Dic3—121no—
234C2×Dic3—121no—
235D12—121no—
236D12—122no—
237D12—122no—
238C4×D3—62no—
239C4×D3—62no—
240C4×D3—121no—
241C4×D3—121no—
242C4×D3—122no—
243C4×D3—128no—
244C3×C8—41no—
245C3⋊C8—121no—
246C2×C9—21no—
247C2×C9—21no—
248C2×C9C2×#9911yescharacteristic
249C2×C9#41711yescharacteristic
250C2×C9C2×#10411yescharacteristic
251D9—22no—
252D9—22no—
253D9—81no—
254C24—91no—
255#41—362no—
256C2×Q8C4×D911yescharacteristic, complemented
257C2×D4—91no—
258C2×D4—181no—
259C2×D4—181no—
260C2×D4—181no—
261C22×C4—21no—
262C22×C4—91no—
263C22×C4—91no—
264C22×C4—91no—
265C22×C4—91no—
266C22×C4—91no—
267C22×C4—181no—
268C22×C4—184no—
269C22×C4—181no—
270C22×C4—362no—
271C22×C4—362no—
272C22×C4—362no—
273C22×C4C22×D911yescharacteristic
274M16—362no—
275C2×C8—21no—
276C2×C8—181no—
277C4⋊C4—21no—
278C4⋊C4—91no—
279C4⋊C4—181no—
280C4⋊C4C4×D911yescharacteristic, complemented
281C22⋊C4—21no—
282C22⋊C4—181no—
283C22⋊C4—181no—
284C22⋊C4—181no—
285C22⋊C4—181no—
286C42—181no—
287C22×C3—21no—
288C22×C3—21no—
289C22×C3D3×C22⋊C411yescharacteristic
290C22×C3#91411yescharacteristic
291C22×C3#91811yescharacteristic
292C2×D3—32no—
293C2×D3—32no—
294C2×D3—64no—
295C2×D3—64no—
296C2×D3—61no—
297C2×D3—61no—
298C2×D3—61no—
299C2×D3—61no—
300C2×D3—121no—
301C2×D3—121no—
302C2×D3—121no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—42no—
306C3×C4—41no—
307C3×C4—41no—
308Dic3—61no—
309Dic3—61no—
310Dic3—122no—
311Dic3—121no—
312C9#150411yescharacteristic, complemented, Sylow
313C23—91no—
314C23—91no—
315C23—182no—
316C23—182no—
317C23—181no—
318C23—181no—
319C23—181no—
320C23D4×D911yescharacteristic
321Q8—41no—
322D4—361no—
323D4—362no—
324D4—362no—
325D4—361no—
326D4—361no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—91no—
334C2×C4—91no—
335C2×C4—182no—
336C2×C4—182no—
337C2×C4—182no—
338C2×C4—181no—
339C2×C4—361no—
340C2×C4—361no—
341C2×C4—362no—
342C2×C4—368no—
343C2×C4—361no—
344C2×C4—361no—
345C2×C4—361no—
346C2×C4C2×C4×D911yescharacteristic
347C2×C4D4×D911yescharacteristic
348C8—41no—
349C8—361no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3D3×#9911yescharacteristic
353C2×C3#480311yescharacteristic
354C2×C3D3×#10411yescharacteristic
355D3—62no—
356D3—62no—
357D3—241no—
358C22—21no—
359C22—21no—
360C22—92no—
361C22—92no—
362C22—184no—
363C22—184no—
364C22—181no—
365C22—181no—
366C22—181no—
367C22—181no—
368C22—361no—
369C22—361no—
370C22—361no—
371C22C22⋊C4×D911yescharacteristic
372C22#6347611yescharacteristic
373C22#6348011yescharacteristic
374C4—21no—
375C4—21no—
376C4—42no—
377C4—41no—
378C4—41no—
379C4—181no—
380C4—181no—
381C4—362no—
382C4—361no—
383C3#6833411yescharacteristic
384C2—21no—
385C2—21no—
386C2—182no—
387C2—182no—
388C2—721no—
389C2D9×#9911yescharacteristic
390C2#1058848311yescharacteristic
391C2D9×#10411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D9
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#328C2
socleC22×C3D3×C22⋊C4
prime radical#10589729C2
cosocleC22×C4×C9C23
hypercenter#328D9
hypocenterC9#1504
LCSG ▷ C2×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #10588408C2semidirect
3. D9×#95C2semidirect
4. C9×#328C2semidirect
5. #10588215C2semidirect
6. #10588147C2semidirect
7. #10588129C2semidirect
9. C2×#3701C4semidirect
13. #63508C4semidirect
16. #63457C4semidirect
19. #63454C4semidirect
36. C2×Q8×C9C2×C4semidirect
45. C2×D36C2×C4semidirect
57. C9×C4⋊C4C2×C4semidirect
63. C4⋊Dic9C2×C4semidirect
129. #328D9semidirect
256. C2×Q8C4×D9semidirect
280. C4⋊C4C4×D9semidirect
312. C9#1504semidirect

Maximal subgroups

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

subgroupindex
#105897292
#105884082
D9×#952
C9×#3282
#105882152
#105881472
#105881292
#683343