Finite Group Databasebeta

← #11775312

Subgroups — #11775312

Order 1152.

411 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 411 conjugacy classes of subgroups — too many to draw. Only its 80 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
1D9×C22⋊Q8C211yesmaximal, characteristic
2#10588408C211yesmaximal, characteristic
3#10588344C211yesmaximal, characteristic
4C9×#328C211yesmaximal, characteristic, complemented
5#10588215C211yesmaximal, characteristic, complemented
6#10588144C211yesmaximal, characteristic, complemented
7#10588128C211yesmaximal, characteristic, complemented
8#68336—31nomaximal
9C2×Q8×D9C411yescharacteristic, complemented
10C22×C4×D9C2211yescharacteristic
11C9×C22⋊Q8C2211yescharacteristic
12#63508C411yescharacteristic, complemented
13C2×(C2×D9)⋊C4—21no—
14#63486C2211yescharacteristic
15C2×#3663—21no—
16#63459C411yescharacteristic, complemented
17#63458—21no—
18C4⋊C4×D9—21no—
19C4⋊C4×D9C411yescharacteristic, complemented
20C22⋊C4×D9—21no—
21#63440—21no—
22C9×C22⋊C8C2211yescharacteristic
23C9×#95C2211yescharacteristic
24C9⋊#95—21no—
25C9⋊#95C2211yescharacteristic
26#63389C2211yescharacteristic
27(C2×D9)⋊C8—21no—
28D3×C22⋊Q8—31no—
29#4726—31no—
30#4664—31no—
31C3×#328D311yescharacteristic
32#4538—31no—
33#4467—31no—
34#4452—31no—
35C23×D9D411yescharacteristic
36C2×Q8×C9C2×C411yescharacteristic
37C22×C4×C9—21no—
38C22×C4×C9C2311yescharacteristic
39C22×Dic9—21no—
40C22×Dic9D411yescharacteristic
41Q8×D9—42no—
42C2×C4×D9—21no—
43C2×C4×D9—21no—
44C2×C4×D9—42no—
45C2×C4×D9C2×C411yescharacteristic
46C2×C4×D9C2×C411yescharacteristic
47C2×C4×D9D411yescharacteristic
48C2×C4×D9D411yescharacteristic
49C2×Dic18—21no—
50C2×Dic18C2×C411yescharacteristic
51C2×C8×C9—21no—
52C9×C4⋊C4—21no—
53C9×C4⋊C4C2×C411yescharacteristic
54C9×C22⋊C4—21no—
55#3676—21no—
56(C2×D9)⋊C4—21no—
57(C2×D9)⋊C4—21no—
58(C2×D9)⋊C4—42no—
59C4⋊Dic9—21no—
60C4⋊Dic9C2×C411yescharacteristic
61Dic9⋊C4—21no—
62Dic9⋊C4—21no—
63Dic9⋊C4—21no—
64C2×C9⋊C8—21no—
65#3663—42no—
66#1511—91noSylow
67C2×D3×Q8—31no—
68C22×C4×D3—31no—
69C3×C22⋊Q8C2×D311yescharacteristic
70#946—31no—
71C2×(C2×D3)⋊C4—61no—
72#924—31no—
73C2×ΓL(1,𝔽25)—61no—
74#897—31no—
75#896—61no—
76D3×C4⋊C4—31no—
77D3×C4⋊C4—61no—
78D3×C22⋊C4—61no—
79#878—61no—
80C3×C22⋊C8C2×D311yescharacteristic
81C3×#95C2×D311yescharacteristic
82C3⋊#95—31no—
83C3⋊#95—61no—
84#830—31no—
85(C2×D3)⋊C8—61no—
86C23×C9C2×D411yescharacteristic
87C22×D9—21no—
88C22×D9—21no—
89C22×D9—22no—
90C22×D9—41no—
91C22×D9C22⋊C411yescharacteristic
92C22×D9C22⋊C411yescharacteristic
93Q8×C9—41no—
94C2×C4×C9—21no—
95C2×C4×C9—21no—
96C2×C4×C9—41no—
97C2×C4×C9—41no—
98C2×C4×C9—41no—
99C2×C4×C9—41no—
100C2×C4×C9C22×C411yescharacteristic
101C2×C4×C9C2×D411yescharacteristic
102C2×Dic9—21no—
103C2×Dic9—21no—
104C2×Dic9—41no—
105C2×Dic9—41no—
106C2×Dic9—41no—
107C2×Dic9—41no—
108C2×Dic9C22⋊C411yescharacteristic
109C2×Dic9C22⋊C411yescharacteristic
110C4×D9—22no—
111C4×D9—22no—
112C4×D9—41no—
113C4×D9—41no—
114C4×D9—42no—
115C4×D9—42no—
116Dic18—42no—
117Dic18—41no—
118C8×C9—41no—
119C9⋊C8—41no—
120C2×C22⋊Q8—91no—
121#407—91no—
122#381—91no—
123#328—91no—
124#328—91no—
125#328—91no—
126#328D911yescharacteristic, complemented
127C23×D3—31no—
128C2×C3×Q8C4×D311yescharacteristic
129C22×C3×C4—21no—
130C22×C3×C4C22×D311yescharacteristic
131C22×Dic3—31no—
132C22×Dic3—61no—
133D3×Q8—122no—
134C2×C4×D3—31no—
135C2×C4×D3—31no—
136C2×C4×D3—31no—
137C2×C4×D3—31no—
138C2×C4×D3—61no—
139C2×C4×D3—61no—
140C2×C4×D3—122no—
141C2×Dic6—31no—
142C2×Dic6—61no—
143C2×C3×C8—21no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4C4×D311yescharacteristic
146C3×C22⋊C4—21no—
147#217—61no—
148(C2×D3)⋊C4—61no—
149(C2×D3)⋊C4—61no—
150(C2×D3)⋊C4—122no—
151C4⋊Dic3—31no—
152C4⋊Dic3—61no—
153Dic3⋊C4—61no—
154Dic3⋊C4—61no—
155Dic3⋊C4—61no—
156C2×C3⋊C8—61no—
157ΓL(1,𝔽25)—122no—
158C22×C9—21no—
159C22×C9—21no—
160C22×C9C2×C22⋊C411yescharacteristic
161C22×C9#13711yescharacteristic
162C22×C9#13711yescharacteristic
163C2×D9—21no—
164C2×D9—21no—
165C2×D9—21no—
166C2×D9—21no—
167C2×D9—21no—
168C2×D9—42no—
169C2×D9—42no—
170C2×D9#9912yes—
171C4×C9—21no—
172C4×C9—21no—
173C4×C9—41no—
174C4×C9—41no—
175C4×C9—81no—
176Dic9—21no—
177Dic9—21no—
178Dic9—41no—
179Dic9—41no—
180Dic9—81no—
181C22×Q8—91no—
182C23×C4—91no—
183C2×M16—181no—
184C22⋊Q8—91no—
185C22⋊Q8—91no—
186C22⋊Q8—91no—
187C22⋊Q8—181no—
188C22⋊Q8—181no—
189C22⋊Q8C2×D911yescharacteristic
190C2×C4⋊C4—91no—
191C2×C4⋊C4—181no—
192C2×C22⋊C4—181no—
193C2×C22⋊C4—181no—
194C22⋊C8—91no—
195C22⋊C8—181no—
196C22⋊C8C2×D911yescharacteristic
197#95—91no—
198#95—181no—
199#95C2×D911yescharacteristic
200C23×C3D3×D411yescharacteristic
201C22×D3—31no—
202C22×D3—31no—
203C22×D3—62no—
204C22×D3—61no—
205C22×D3—61no—
206C22×D3—121no—
207C3×Q8—41no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—41no—
211C2×C3×C4—41no—
212C2×C3×C4—41no—
213C2×C3×C4—41no—
214C2×C3×C4C2×C4×D311yescharacteristic
215C2×C3×C4D3×D411yescharacteristic
216C2×Dic3—31no—
217C2×Dic3—31no—
218C2×Dic3—61no—
219C2×Dic3—61no—
220C2×Dic3—121no—
221C2×Dic3—121no—
222C2×Dic3—121no—
223C2×Dic3—121no—
224C4×D3—62no—
225C4×D3—62no—
226C4×D3—121no—
227C4×D3—121no—
228C4×D3—122no—
229C4×D3—122no—
230Dic6—122no—
231Dic6—121no—
232C3×C8—41no—
233C3⋊C8—121no—
234C2×C9—21no—
235C2×C9—21no—
236C2×C9C2×#9911yescharacteristic
237C2×C9#41911yescharacteristic
238C2×C9#42111yescharacteristic
239D9—22no—
240D9—41no—
241C24—91no—
242C2×Q8—91no—
243C2×Q8—181no—
244C2×Q8—362no—
245C2×Q8C4×D911yescharacteristic
246C22×C4—21no—
247C22×C4—91no—
248C22×C4—91no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4—91no—
252C22×C4—181no—
253C22×C4—181no—
254C22×C4—181no—
255C22×C4—362no—
256C22×C4C22×D911yescharacteristic
257M16—362no—
258C2×C8—21no—
259C2×C8—181no—
260C4⋊C4—21no—
261C4⋊C4—91no—
262C4⋊C4—181no—
263C4⋊C4—181no—
264C4⋊C4—181no—
265C4⋊C4—181no—
266C4⋊C4C4×D911yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—181no—
269C22⋊C4—181no—
270C22⋊C4—181no—
271C22⋊C4—362no—
272C22×C3—21no—
273C22×C3—21no—
274C22×C3D3×C22⋊C411yescharacteristic
275C22×C3#91511yescharacteristic
276C22×C3#91811yescharacteristic
277C2×D3—32no—
278C2×D3—61no—
279C2×D3—61no—
280C2×D3—61no—
281C2×D3—61no—
282C2×D3—61no—
283C2×D3—122no—
284C2×D3—122no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4—81no—
290Dic3—61no—
291Dic3—61no—
292Dic3—121no—
293Dic3—121no—
294Dic3—241no—
295C9#151111yescharacteristic, complemented, Sylow
296C23—91no—
297C23—91no—
298C23—182no—
299C23—181no—
300C23—181no—
301C23—361no—
302C23D4×D911yescharacteristic
303Q8—41no—
304Q8—361no—
305Q8—362no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—91no—
313C2×C4—91no—
314C2×C4—182no—
315C2×C4—182no—
316C2×C4—181no—
317C2×C4—181no—
318C2×C4—361no—
319C2×C4—361no—
320C2×C4—362no—
321C2×C4—362no—
322C2×C4—361no—
323C2×C4—361no—
324C2×C4—361no—
325C2×C4—361no—
326C2×C4C2×C4×D911yescharacteristic
327C2×C4D4×D911yescharacteristic
328C8—41no—
329C8—361no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3D3×#9911yescharacteristic
333C2×C3#480211yescharacteristic
334C2×C3#482111yescharacteristic
335D3—62no—
336D3—121no—
337C22—21no—
338C22—21no—
339C22—92no—
340C22—181no—
341C22—181no—
342C22—181no—
343C22—181no—
344C22—181no—
345C22—362no—
346C22—362no—
347C22C22⋊C4×D911yescharacteristic
348C22#6347711yescharacteristic
349C22#6348011yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—81no—
355C4—181no—
356C4—181no—
357C4—361no—
358C4—361no—
359C4—721no—
360C3#6833611yescharacteristic
361C2—21no—
362C2—21no—
363C2—182no—
364C2—361no—
365C2D9×#9911yescharacteristic
366C2#1058848211yescharacteristic
367C2#1058850111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D9
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#328C2
socleC22×C3D3×C22⋊C4
prime radicalC23×D9D4
cosocleC22×C4×C9C23
hypercenter#328D9
hypocenterC9#1511
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
4. C9×#328C2semidirect
5. #10588215C2semidirect
6. #10588144C2semidirect
7. #10588128C2semidirect
9. C2×Q8×D9C4semidirect
12. #63508C4semidirect
16. #63459C4semidirect
19. C4⋊C4×D9C4semidirect
126. #328D9semidirect
295. C9#1511semidirect

Maximal subgroups

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

subgroupindex
D9×C22⋊Q82
#105884082
#105883442
C9×#3282
#105882152
#105881442
#105881282
#683363