Finite Group Databasebeta

← #11788194

Subgroups — #11788194

Order 1152.

537 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 537 conjugacy classes of subgroups — too many to draw. Only its 110 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#10589626C211yesmaximal, characteristic
2C2×#63434C211yesmaximal, characteristic, complemented
3C2×#63384C211yesmaximal, characteristic, complemented
4#10588808C211yesmaximal, characteristic, complemented
5C2×#63364C211yesmaximal, characteristic, complemented
6C9×#339C211yesmaximal, characteristic, complemented
7#10588208C211yesmaximal, characteristic, complemented
8#68757—31nomaximal
9C2×#3697C2211yescharacteristic
10C22×C4×D9C2211yescharacteristic
11C2×C9×M16C2211yescharacteristic
12C9×#117C2211yescharacteristic
13C2×C42×C9C2211yescharacteristic
14C2×(C2×D9)⋊C4—21no—
15C2×Dic9⋊C4—21no—
16C2×C4×Dic9C2211yescharacteristic
17C2×#3667C2211yescharacteristic
18#63459C412yescomplemented
19#63457C412yescomplemented
20#63448—21no—
21#63444—21no—
22C4×D36—22no—
23#63434—22no—
24#63434—22no—
25#63384—22no—
26(C2×D9)⋊C8—22no—
27#63364—22no—
28#5524—31no—
29C2×#872—31no—
30C2×#825—31no—
31#5126—31no—
32C2×#805—31no—
33C3×#339D311yescharacteristic
34#4532—31no—
35C23×D9D411yescharacteristic
36C22×C4×C9—21no—
37C22×C4×C9C2311yescharacteristic
38C2×#611—21no—
39C22×Dic9—21no—
40C22×Dic9D411yescharacteristic
41#3697—21no—
42#3697—21no—
43#3697—21no—
44#3697—21no—
45C2×D36—22no—
46C2×D36C2×C411yescharacteristic
47C2×C4×D9—21no—
48C2×C4×D9—21no—
49C2×C4×D9—21no—
50C2×C4×D9—21no—
51C2×C4×D9—21no—
52C2×C4×D9C2×C412yes—
53C2×C4×D9D412yes—
54C2×Dic18C2×C411yescharacteristic
55C9×M16—21no—
56C9×M16—21no—
57C2×C8×C9—21no—
58C9×C4⋊C4C2×C412yes—
59C9×C22⋊C4—21no—
60C42×C9—21no—
61C42×C9—21no—
62C42×C9D412yescomplemented
63(C2×D9)⋊C4—24no—
64(C2×D9)⋊C4—22no—
65(C2×D9)⋊C4—22no—
66C4⋊Dic9—22no—
67Dic9⋊C4—24no—
68C4×Dic9—21no—
69C4×Dic9D412yescomplemented
70#3667—21no—
71#3667—21no—
72C2×C9⋊C8—21no—
73#1897—91noSylow
74C2×#235—31no—
75C22×C4×D3—31no—
76C2×C3×M16C2×D311yescharacteristic
77C3×#117C2×D311yescharacteristic
78C2×C3×C42C2×D311yescharacteristic
79C2×(C2×D3)⋊C4—61no—
80C2×Dic3⋊C4—61no—
81C2×C4×Dic3—31no—
82C2×#208—31no—
83#897—32no—
84#895—32no—
85#886—61no—
86#882—61no—
87C4×D12—62no—
88#872—62no—
89#872—62no—
90#825—62no—
91(C2×D3)⋊C8—62no—
92#805—62no—
93C23×C9C2×D411yescharacteristic
94C22×D9—21no—
95C22×D9—21no—
96C22×D9—21no—
97C22×D9—42no—
98C22×D9C22⋊C412yes—
99C2×C4×C9—22no—
100C2×C4×C9—22no—
101C2×C4×C9—42no—
102C2×C4×C9C22×C411yescharacteristic
103C2×C4×C9C2×D411yescharacteristic
104C2×C4×C9C2×D411yescharacteristic
105C2×C4×C9C2×D411yescharacteristic
106C2×C4×C9#4111yescharacteristic
107C2×C4×C9#4111yescharacteristic
108#611—41no—
109#611—41no—
110C2×Dic9—21no—
111C2×Dic9—21no—
112C2×Dic9—21no—
113C2×Dic9—22no—
114C2×Dic9—42no—
115C2×Dic9C22⋊C412yes—
116D36—21no—
117D36—21no—
118D36—44no—
119C4×D9—22no—
120C4×D9—22no—
121C4×D9—22no—
122C4×D9—22no—
123C4×D9—41no—
124C4×D9—41no—
125Dic18—21no—
126Dic18—21no—
127C8×C9—41no—
128C9⋊C8—41no—
129#525—91no—
130C2×#117—91no—
131C2×#104—91no—
132C2×#104—91no—
133#407—91no—
134#339—91no—
135#339D911yescharacteristic, complemented
136C23×D3—31no—
137C22×C3×C4—21no—
138C22×C3×C4C22×D311yescharacteristic
139C2×#67—61no—
140C22×Dic3—31no—
141C22×Dic3—61no—
142#235—61no—
143#235—61no—
144#235—61no—
145#235—61no—
146C2×D12—31no—
147C2×D12—62no—
148C2×C4×D3—32no—
149C2×C4×D3—32no—
150C2×C4×D3—61no—
151C2×C4×D3—61no—
152C2×C4×D3—61no—
153C2×C4×D3—61no—
154C2×C4×D3—61no—
155C2×Dic6—31no—
156C3×M16—21no—
157C3×M16—21no—
158C2×C3×C8—21no—
159C3×C4⋊C4C4×D312yes—
160C3×C22⋊C4—21no—
161C3×C42—21no—
162C3×C42—21no—
163C3×C42D1212yes—
164(C2×D3)⋊C4—62no—
165(C2×D3)⋊C4—62no—
166(C2×D3)⋊C4—64no—
167C4⋊Dic3—62no—
168Dic3⋊C4—64no—
169C4×Dic3—32no—
170C4×Dic3—61no—
171#208—61no—
172#208—61no—
173C2×C3⋊C8—61no—
174C22×C9—22no—
175C22×C9C2×C22⋊C411yescharacteristic
176C22×C9#12011yescharacteristic
177C22×C9#12311yescharacteristic
178C2×D9—22no—
179C2×D9—22no—
180C2×D9—22no—
181C2×D9—42no—
182C2×D9—42no—
183C2×D9—41no—
184C2×D9—42no—
185C4×C9—42no—
186C4×C9—42no—
187C4×C9C4×D411yescharacteristic
188C4×C9C4×D411yescharacteristic
189C4×C9#12111yescharacteristic
190C4×C9#12111yescharacteristic
191Dic9—22no—
192Dic9—42no—
193Dic9—41no—
194C2×#41—91no—
195C23×C4—91no—
196C2×M16—91no—
197C2×M16C2×D911yescharacteristic
198#123—181no—
199C22⋊Q8—92no—
200#121—92no—
201#120—181no—
202C4×D4—182no—
203#117—182no—
204#117—182no—
205#117C2×D911yescharacteristic
206C2×C4⋊C4—181no—
207C2×C22⋊C4—181no—
208C2×C42—91no—
209C2×C42C2×D911yescharacteristic
210#104—182no—
211#104—182no—
212C22⋊C8—182no—
213C23×C3D3×D411yescharacteristic
214C22×D3—32no—
215C22×D3—61no—
216C22×D3—61no—
217C22×D3—61no—
218C22×D3—122no—
219C2×C3×C4—22no—
220C2×C3×C4—22no—
221C2×C3×C4—42no—
222C2×C3×C4C2×C4×D311yescharacteristic
223C2×C3×C4C2×D1211yescharacteristic
224C2×C3×C4#23511yescharacteristic
225C2×C3×C4D3×D411yescharacteristic
226C2×C3×C4D3×D411yescharacteristic
227C2×C3×C4#23911yescharacteristic
228#67—121no—
229#67—121no—
230C2×Dic3—32no—
231C2×Dic3—61no—
232C2×Dic3—61no—
233C2×Dic3—61no—
234C2×Dic3—62no—
235C2×Dic3—122no—
236D12—61no—
237D12—61no—
238D12—124no—
239C4×D3—62no—
240C4×D3—62no—
241C4×D3—62no—
242C4×D3—62no—
243C4×D3—121no—
244C4×D3—121no—
245Dic6—61no—
246Dic6—61no—
247C3×C8—41no—
248C3⋊C8—121no—
249C2×C9—21no—
250C2×C9—21no—
251C2×C9#38611yescharacteristic
252C2×C9#42112yes—
253D9—42no—
254D9—81no—
255C24—91no—
256#41—181no—
257#41—181no—
258#41—181no—
259#41—181no—
260C2×Q8—91no—
261C2×D4—91no—
262C2×D4—182no—
263C2×D4—181no—
264C22×C4—21no—
265C22×C4—91no—
266C22×C4—92no—
267C22×C4—92no—
268C22×C4—181no—
269C22×C4—181no—
270C22×C4—181no—
271C22×C4—181no—
272C22×C4—181no—
273C22×C4—181no—
274C22×C4C22×D911yescharacteristic
275M16—21no—
276M16—21no—
277M16—181no—
278M16—181no—
279C2×C8—21no—
280C2×C8—181no—
281C4⋊C4—182no—
282C4⋊C4—184no—
283C4⋊C4C4×D912yes—
284C22⋊C4—21no—
285C22⋊C4—182no—
286C22⋊C4—182no—
287C22⋊C4—184no—
288C42—21no—
289C42—21no—
290C42—92no—
291C42—181no—
292C42D3612yescomplemented
293C22×C3—22no—
294C22×C3D3×C22⋊C411yescharacteristic
295C22×C3#88211yescharacteristic
296C22×C3#89411yescharacteristic
297C2×D3—62no—
298C2×D3—62no—
299C2×D3—62no—
300C2×D3—122no—
301C2×D3—122no—
302C2×D3—121no—
303C2×D3—122no—
304C3×C4—42no—
305C3×C4—42no—
306C3×C4C4×D1211yescharacteristic
307C3×C4#88411yescharacteristic
308C3×C4#89311yescharacteristic
309C3×C4#89511yescharacteristic
310Dic3—62no—
311Dic3—122no—
312Dic3—121no—
313C9#189711yescharacteristic, complemented, Sylow
314C23—92no—
315C23—181no—
316C23—181no—
317C23—181no—
318C23—362no—
319C23D4×D911yescharacteristic
320Q8—181no—
321Q8—181no—
322D4—181no—
323D4—181no—
324D4—364no—
325D4—361no—
326D4—361no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—42no—
330C2×C4—92no—
331C2×C4—181no—
332C2×C4—181no—
333C2×C4—182no—
334C2×C4—182no—
335C2×C4—182no—
336C2×C4—182no—
337C2×C4—181no—
338C2×C4—182no—
339C2×C4—362no—
340C2×C4—361no—
341C2×C4—361no—
342C2×C4C2×C4×D911yescharacteristic
343C2×C4C2×D3611yescharacteristic
344C2×C4#369711yescharacteristic
345C2×C4D4×D911yescharacteristic
346C2×C4D4×D911yescharacteristic
347C2×C4#370111yescharacteristic
348C8—41no—
349C8—361no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3#466511yescharacteristic
353C2×C3#482112yes—
354D3—122no—
355D3—241no—
356C22—22no—
357C22—182no—
358C22—182no—
359C22—182no—
360C22—362no—
361C22—362no—
362C22—362no—
363C22—361no—
364C22C22⋊C4×D911yescharacteristic
365C22#6344411yescharacteristic
366C22#6345611yescharacteristic
367C4—42no—
368C4—42no—
369C4—182no—
370C4—362no—
371C4—361no—
372C4C4×D3611yescharacteristic
373C4#6344611yescharacteristic
374C4#6345511yescharacteristic
375C4#6345711yescharacteristic
376C3#6875711yescharacteristic
377C2—21no—
378C2—21no—
379C2—362no—
380C2—721no—
381C2#1058834511yescharacteristic
382C2#1058850112yes—
subgroupG/H
centerC2×C4D4×D9
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#339C2
socleC22×C3D3×C22⋊C4
prime radical#10589626C2
cosocleC22×C4×C9C23
hypercenter#339D9
hypocenterC9#1897
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. C2×#63434C2semidirect
3. C2×#63384C2semidirect
4. #10588808C2semidirect
5. C2×#63364C2semidirect
6. C9×#339C2semidirect
7. #10588208C2semidirect
18. #63459C4semidirect
19. #63457C4semidirect
62. C42×C9D4semidirect
69. C4×Dic9D4semidirect
135. #339D9semidirect
292. C42D36semidirect
313. C9#1897semidirect

Maximal subgroups

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

subgroupindex
#105896262
C2×#634342
C2×#633842
#105888082
C2×#633642
C9×#3392
#105882082
#687573