Finite Group Databasebeta

← #11775101

Subgroups — #11775101

Order 1152.

1002 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 1002 conjugacy classes of subgroups — too many to draw. Only its 133 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#10596077C211yesmaximal, characteristic
2#10592425C211yesmaximal, characteristic, complemented
3C3⋊D3×#95C211yesmaximal, characteristic, complemented
4C32×#327C211yesmaximal, characteristic, complemented
5#10589403C211yesmaximal, characteristic, complemented
6#10589333C211yesmaximal, characteristic, complemented
7#10589318C211yesmaximal, characteristic, complemented
8#68302—34nomaximal
9C2×#3830C411yescharacteristic, complemented
10C22×C4×C3⋊D3—21no—
11C22×C4×C3⋊D3C2211yescharacteristic
12C32×#121C2211yescharacteristic
13#64147C411yescharacteristic, complemented
14#64146—21no—
15D4×C3⋊Dic3—21no—
16#64133C2211yescharacteristic
17C2×#3743—21no—
18#64106C411yescharacteristic, complemented
19#64101C411yescharacteristic, complemented
20#64092—21no—
21#64090—21no—
22C32×C22⋊C8C2211yescharacteristic
23C32×#95C2211yescharacteristic
24#63658—21no—
25#63658C2211yescharacteristic
26#63657C2211yescharacteristic
27#63647—21no—
28#5606—34no—
29#4726—34no—
30D3×#95—34no—
31C3×#327D314yescomplemented
32#4537—34no—
33#4467—34no—
34#4452—34no—
35C23×C3⋊D3D411yescharacteristic
36C2×C32×D4—21no—
37C2×C32×D4C2×C411yescharacteristic, complemented
38C22×C32×C4—21no—
39C22×C32×C4C2311yescharacteristic
40C2×#638—21no—
41C2×#638—21no—
42C22×C3⋊Dic3—21no—
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3D411yescharacteristic
45#3830—42no—
46C2×C4×C3⋊D3—24no—
47C2×C4×C3⋊D3—42no—
48C2×C4×C3⋊D3—42no—
49C2×C4×C3⋊D3—42no—
50C2×C4×C3⋊D3C2×C411yescharacteristic
51C2×C4×C3⋊D3C2×C411yescharacteristic
52C2×C4×C3⋊D3D411yescharacteristic
53C2×C4×C3⋊D3D411yescharacteristic
54C2×#634C2×C411yescharacteristic, complemented
55C2×C32×C8—21no—
56C32×C4⋊C4C2×C411yescharacteristic, complemented
57C32×C22⋊C4—21no—
58#3757—21no—
59#3757—21no—
60#3752—21no—
61#3752—21no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)C2×C411yescharacteristic, complemented
64#3750—21no—
65C4×C3⋊Dic3—21no—
66C2×C3⋊(C3⋊C8)—21no—
67#3743—42no—
68#1504—91noSylow
69C2×#237—34no—
70C22×C4×D3—34no—
71C22×C4×D3—64no—
72C3×#121C2×D314yes—
73#938—34no—
74#937—64no—
75D4×Dic3—64no—
76#924—34no—
77C2×ΓL(1,𝔽25)—64no—
78#897—34no—
79#892—34no—
80#883—64no—
81#67⋊C4—64no—
82C3×C22⋊C8C2×D314yes—
83C3×#95C2×D314yes—
84C3⋊#95—34no—
85C3⋊#95—64no—
86#830—34no—
87(C2×D3)⋊C8—64no—
88C23×C32—21no—
89C23×C32C2×D411yescharacteristic
90C22×C3⋊D3—21no—
91C22×C3⋊D3—21no—
92C22×C3⋊D3—22no—
93C22×C3⋊D3—22no—
94C22×C3⋊D3C22⋊C411yescharacteristic
95C22×C3⋊D3C22⋊C411yescharacteristic
96C32×D4—41no—
97C32×D4—41no—
98C32×D4—41no—
99C2×C32×C4—22no—
100C2×C32×C4—21no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C32×C4—41no—
104C2×C32×C4C22×C411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106#638—42no—
107#638—42no—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—21no—
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—41no—
112C2×C3⋊Dic3—42no—
113C2×C3⋊Dic3—41no—
114C2×C3⋊Dic3—41no—
115C2×C3⋊Dic3C22⋊C411yescharacteristic
116C2×C3⋊Dic3C22⋊C411yescharacteristic
117C4×C3⋊D3—22no—
118C4×C3⋊D3—22no—
119C4×C3⋊D3—41no—
120C4×C3⋊D3—41no—
121C4×C3⋊D3—48no—
122#634—41no—
123C32×C8—41no—
124C3⋊(C3⋊C8)—41no—
125#525—91no—
126#407—91no—
127C2×#95—91no—
128#328—91no—
129#328—91no—
130#327—91no—
131#327C3⋊D311yescharacteristic, complemented
132C23×D3—34no—
133C2×C3×D4—24no—
134C2×C3×D4C4×D314yescomplemented
135C22×C3×C4—24no—
136C22×C3×C4C22×D314yes—
137C2×#67—64no—
138C2×#67—64no—
139C22×Dic3—34no—
140C22×Dic3—64no—
141C22×Dic3—64no—
142#237—128no—
143C2×C4×D3—34no—
144C2×C4×D3—34no—
145C2×C4×D3—34no—
146C2×C4×D3—34no—
147C2×C4×D3—616no—
148C2×C4×D3—128no—
149C2×C4×D3—128no—
150C2×C4×D3—128no—
151C2×Dic6—34no—
152C2×C3×C8—24no—
153C3×C4⋊C4C4×D314yescomplemented
154C3×C22⋊C4—24no—
155#217—64no—
156#217—64no—
157(C2×D3)⋊C4—64no—
158(C2×D3)⋊C4—64no—
159C4⋊Dic3—34no—
160C4⋊Dic3—64no—
161Dic3⋊C4—64no—
162C4×Dic3—64no—
163C2×C3⋊C8—64no—
164ΓL(1,𝔽25)—128no—
165C22×C32—21no—
166C22×C32—21no—
167C22×C32—41no—
168C22×C32—41no—
169C22×C32—41no—
170C22×C32C2×C22⋊C411yescharacteristic
171C22×C32AGL(1,ℤ/8)11yescharacteristic
172C22×C32#13711yescharacteristic
173C2×C3⋊D3—24no—
174C2×C3⋊D3—24no—
175C2×C3⋊D3—21no—
176C2×C3⋊D3—21no—
177C2×C3⋊D3—21no—
178C2×C3⋊D3—21no—
179C2×C3⋊D3#9912yes—
180C2×C3⋊D3#10412yes—
181C32×C4—21no—
182C32×C4—21no—
183C32×C4—42no—
184C32×C4—41no—
185C3⋊Dic3—21no—
186C3⋊Dic3—21no—
187C3⋊Dic3—42no—
188C3⋊Dic3—41no—
189C3⋊Dic3—41no—
190C2×#41—91no—
191C23×C4—91no—
192C23×C4—181no—
193C2×M16—181no—
194#123—181no—
195C22⋊Q8—91no—
196C22⋊Q8—91no—
197#121—91no—
198#121C2×C3⋊D311yescharacteristic
199#120—181no—
200C4×D4—181no—
201C4×D4—181no—
202#117—91no—
203C22⋊C8—91no—
204C22⋊C8—181no—
205C22⋊C8C2×C3⋊D311yescharacteristic
206#95—91no—
207#95—181no—
208#95C2×C3⋊D311yescharacteristic
209C23×C3—24no—
210C23×C3D3×D414yes—
211C22×D3—34no—
212C22×D3—34no—
213C22×D3—68no—
214C22×D3—68no—
215C22×D3—64no—
216C22×D3—64no—
217C3×D4—44no—
218C3×D4—44no—
219C3×D4—44no—
220C2×C3×C4—28no—
221C2×C3×C4—24no—
222C2×C3×C4—44no—
223C2×C3×C4—44no—
224C2×C3×C4—44no—
225C2×C3×C4C2×C4×D314yes—
226C2×C3×C4D3×D414yes—
227#67—128no—
228#67—128no—
229C2×Dic3—34no—
230C2×Dic3—34no—
231C2×Dic3—68no—
232C2×Dic3—64no—
233C2×Dic3—64no—
234C2×Dic3—124no—
235C2×Dic3—128no—
236C2×Dic3—124no—
237C2×Dic3—124no—
238C4×D3—68no—
239C4×D3—68no—
240C4×D3—124no—
241C4×D3—124no—
242C4×D3—1232no—
243Dic6—124no—
244C3×C8—44no—
245C3⋊C8—124no—
246C2×C32—21no—
247C2×C32—21no—
248C2×C32—81no—
249C2×C32C2×#9911yescharacteristic
250C2×C32#41711yescharacteristic
251C2×C32C2×#10411yescharacteristic
252C3⋊D3—22no—
253C3⋊D3—22no—
254C24—91no—
255#41—362no—
256C2×Q8—91no—
257C2×D4—21no—
258C2×D4—181no—
259C2×D4—181no—
260C2×D4C4×C3⋊D311yescharacteristic, complemented
261C22×C4—21no—
262C22×C4—91no—
263C22×C4—91no—
264C22×C4—91no—
265C22×C4—91no—
266C22×C4—91no—
267C22×C4—184no—
268C22×C4—181no—
269C22×C4—181no—
270C22×C4—362no—
271C22×C4—362no—
272C22×C4—362no—
273C22×C4C22×C3⋊D311yescharacteristic
274M16—362no—
275C2×C8—21no—
276C2×C8—181no—
277C4⋊C4—91no—
278C4⋊C4—181no—
279C4⋊C4—181no—
280C4⋊C4C4×C3⋊D311yescharacteristic, complemented
281C22⋊C4—21no—
282C22⋊C4—181no—
283C22⋊C4—181no—
284C22⋊C4—181no—
285C22⋊C4—181no—
286C42—181no—
287C22×C3—24no—
288C22×C3—24no—
289C22×C3—44no—
290C22×C3—44no—
291C22×C3—44no—
292C22×C3D3×C22⋊C414yes—
293C22×C3#91114yes—
294C22×C3#91514yes—
295C2×D3—38no—
296C2×D3—38no—
297C2×D3—616no—
298C2×D3—616no—
299C2×D3—64no—
300C2×D3—64no—
301C2×D3—64no—
302C2×D3—64no—
303C3×C4—24no—
304C3×C4—24no—
305C3×C4—48no—
306C3×C4—44no—
307Dic3—64no—
308Dic3—64no—
309Dic3—128no—
310Dic3—124no—
311Dic3—124no—
312C32#150411yescharacteristic, complemented, Sylow
313C23—21no—
314C23—91no—
315C23—91no—
316C23—182no—
317C23—182no—
318C23—181no—
319C23—181no—
320C23D4×C3⋊D311yescharacteristic
321Q8—361no—
322D4—41no—
323D4—41no—
324D4—41no—
325D4—362no—
326D4—362no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—91no—
333C2×C4—91no—
334C2×C4—182no—
335C2×C4—182no—
336C2×C4—182no—
337C2×C4—181no—
338C2×C4—181no—
339C2×C4—361no—
340C2×C4—361no—
341C2×C4—368no—
342C2×C4—361no—
343C2×C4—362no—
344C2×C4—361no—
345C2×C4—361no—
346C2×C4C2×C4×C3⋊D311yescharacteristic
347C2×C4D4×C3⋊D311yescharacteristic
348C8—41no—
349C8—361no—
350C2×C3—24no—
351C2×C3—24no—
352C2×C3—84no—
353C2×C3D3×#9914yes—
354C2×C3#477114yes—
355C2×C3D3×#10414yes—
356D3—68no—
357D3—68no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—92no—
364C22—92no—
365C22—184no—
366C22—184no—
367C22—181no—
368C22—181no—
369C22—181no—
370C22—181no—
371C22C22⋊C4×C3⋊D311yescharacteristic
372C22#6412011yescharacteristic
373C22#6412411yescharacteristic
374C4—21no—
375C4—21no—
376C4—42no—
377C4—41no—
378C4—181no—
379C4—181no—
380C4—362no—
381C4—361no—
382C4—361no—
383C3#6830214yescomplemented
384C2—21no—
385C2—21no—
386C2—81no—
387C2—182no—
388C2—182no—
389C2C3⋊D3×#9911yescharacteristic
390C2#1059247011yescharacteristic
391C2C3⋊D3×#10411yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#327C2
socleC22×C32C2×C22⋊C4
prime radical#10596077C2
cosocleC22×C32×C4C23
hypercenter#327C3⋊D3
hypocenterC32#1504
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #10592425C2semidirect
3. C3⋊D3×#95C2semidirect
4. C32×#327C2semidirect
5. #10589403C2semidirect
6. #10589333C2semidirect
7. #10589318C2semidirect
9. C2×#3830C4semidirect
13. #64147C4semidirect
18. #64106C4semidirect
19. #64101C4semidirect
31. C3×#327D3semidirect
37. C2×C32×D4C2×C4semidirect
54. C2×#634C2×C4semidirect
56. C32×C4⋊C4C2×C4semidirect
63. C4⋊(C3⋊Dic3)C2×C4semidirect
131. #327C3⋊D3semidirect
134. C2×C3×D4C4×D3semidirect
153. C3×C4⋊C4C4×D3semidirect
260. C2×D4C4×C3⋊D3semidirect
280. C4⋊C4C4×C3⋊D3semidirect
312. C32#1504semidirect
383. C3#68302semidirect

Maximal subgroups

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

subgroupindex
#105960772
#105924252
C3⋊D3×#952
C32×#3272
#105894032
#105893332
#105893182
#683023