Finite Group Databasebeta

← #11775285

Subgroups — #11775285

Order 1152.

978 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 978 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C3⋊D3×#121C211yesmaximal, characteristic
2#10592425C211yesmaximal, characteristic, complemented
3#10592363C211yesmaximal, characteristic, complemented
4C32×#327C211yesmaximal, characteristic, complemented
5#10589403C211yesmaximal, characteristic, complemented
6#10589336C211yesmaximal, characteristic, complemented
7#10589317C211yesmaximal, characteristic, complemented
8#68304—34nomaximal
9C2×D4×C3⋊D3—21no—
10C2×D4×C3⋊D3C411yescharacteristic, complemented
11C22×C4×C3⋊D3C2211yescharacteristic
12C32×#121C2211yescharacteristic
13#64148—21no—
14#64147C411yescharacteristic, complemented
15#64139C2211yescharacteristic
16C2×#3752—21no—
17C2×#3743—21no—
18#64104C411yescharacteristic, complemented
19C4⋊C4×C3⋊D3C411yescharacteristic, complemented
20#64093—21no—
21C22⋊C4×C3⋊D3—21no—
22C32×C22⋊C8C2211yescharacteristic, complemented
23C32×#95C2211yescharacteristic, complemented
24#63658—21no—
25#63658C2211yescharacteristic, complemented
26#63657C2211yescharacteristic, complemented
27#63647—21no—
28D3×#121—34no—
29#4726—34no—
30#4664—34no—
31C3×#327D314yescomplemented
32#4537—34no—
33#4470—34no—
34#4451—34no—
35C23×C3⋊D3—21no—
36C23×C3⋊D3D411yescharacteristic
37C2×C32×D4—21no—
38C2×C32×D4C2×C411yescharacteristic
39C22×C32×C4—21no—
40C22×C32×C4C2311yescharacteristic
41C2×#638—21no—
42C2×#638—21no—
43C2×#638—21no—
44C22×C3⋊Dic3—21no—
45C22×C3⋊Dic3D411yescharacteristic
46D4×C3⋊D3—42no—
47D4×C3⋊D3—42no—
48D4×C3⋊D3—42no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—42no—
53C2×C4×C3⋊D3C2×C411yescharacteristic
54C2×C4×C3⋊D3C2×C411yescharacteristic
55C2×C4×C3⋊D3D411yescharacteristic
56C2×C4×C3⋊D3D411yescharacteristic
57C2×C32×C8—21no—
58C32×C4⋊C4C2×C411yescharacteristic
59C32×C22⋊C4—21no—
60#3757—21no—
61#3752—21no—
62#3752—21no—
63#3752—42no—
64C4⋊(C3⋊Dic3)C2×C411yescharacteristic
65#3750—21no—
66C2×C3⋊(C3⋊C8)—21no—
67#3743—42no—
68#1510—91noSylow
69C2×D3×D4—34no—
70C2×D3×D4—64no—
71C22×C4×D3—34no—
72C3×#121C2×D314yes—
73#939—64no—
74#938—34no—
75#930—34no—
76C2×(C2×D3)⋊C4—64no—
77C2×ΓL(1,𝔽25)—64no—
78#895—34no—
79D3×C4⋊C4—34no—
80#884—64no—
81D3×C22⋊C4—64no—
82C3×C22⋊C8C2×D314yescomplemented
83C3×#95C2×D314yescomplemented
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—21no—
94C22×C3⋊D3—41no—
95C22×C3⋊D3—42no—
96C22×C3⋊D3—42no—
97C22×C3⋊D3—42no—
98C22×C3⋊D3C22⋊C411yescharacteristic
99C22×C3⋊D3C22⋊C411yescharacteristic
100C32×D4—41no—
101C32×D4—41no—
102C32×D4—41no—
103C2×C32×C4—21no—
104C2×C32×C4—41no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C32×C4—41no—
108C2×C32×C4C22×C411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110#638—42no—
111#638—42no—
112#638—41no—
113#638—41no—
114C2×C3⋊Dic3—21no—
115C2×C3⋊Dic3—41no—
116C2×C3⋊Dic3—41no—
117C2×C3⋊Dic3—41no—
118C2×C3⋊Dic3—41no—
119C2×C3⋊Dic3C22⋊C411yescharacteristic
120C2×C3⋊Dic3C22⋊C411yescharacteristic
121C4⋊(C3⋊D3)—41no—
122C4⋊(C3⋊D3)—42no—
123C4×C3⋊D3—22no—
124C4×C3⋊D3—22no—
125C4×C3⋊D3—41no—
126C4×C3⋊D3—41no—
127C4×C3⋊D3—42no—
128C32×C8—41no—
129C3⋊(C3⋊C8)—41no—
130C2×#121—91no—
131#407—91no—
132#381—91no—
133#327—91no—
134#327—91no—
135#327—91no—
136#327C3⋊D311yescharacteristic, complemented
137C23×D3—34no—
138C23×D3—64no—
139C2×C3×D4—24no—
140C2×C3×D4C4×D314yes—
141C22×C3×C4—24no—
142C22×C3×C4C22×D314yes—
143C2×#67—64no—
144C2×#67—64no—
145C2×#67—64no—
146C22×Dic3—34no—
147C22×Dic3—64no—
148D3×D4—128no—
149D3×D4—128no—
150D3×D4—128no—
151C2×D12—34no—
152C2×D12—64no—
153C2×C4×D3—34no—
154C2×C4×D3—34no—
155C2×C4×D3—34no—
156C2×C4×D3—34no—
157C2×C4×D3—64no—
158C2×C4×D3—128no—
159C2×C3×C8—24no—
160C3×C4⋊C4C4×D314yes—
161C3×C22⋊C4—24no—
162#217—64no—
163(C2×D3)⋊C4—64no—
164(C2×D3)⋊C4—64no—
165(C2×D3)⋊C4—128no—
166C4⋊Dic3—34no—
167Dic3⋊C4—64no—
168C2×C3⋊C8—64no—
169ΓL(1,𝔽25)—128no—
170C22×C32—21no—
171C22×C32—21no—
172C22×C32—41no—
173C22×C32—41no—
174C22×C32—41no—
175C22×C32C2×C22⋊C411yescharacteristic
176C22×C32AGL(1,ℤ/8)11yescharacteristic
177C22×C32AGL(1,ℤ/8)11yescharacteristic
178C2×C3⋊D3—21no—
179C2×C3⋊D3—21no—
180C2×C3⋊D3—21no—
181C2×C3⋊D3—21no—
182C2×C3⋊D3—21no—
183C2×C3⋊D3—42no—
184C2×C3⋊D3—42no—
185C2×C3⋊D3—41no—
186C2×C3⋊D3—41no—
187C2×C3⋊D3—41no—
188C2×C3⋊D3—84no—
189C2×C3⋊D3#9912yes—
190C32×C4—21no—
191C32×C4—21no—
192C32×C4—41no—
193C32×C4—81no—
194C3⋊Dic3—21no—
195C3⋊Dic3—21no—
196C3⋊Dic3—41no—
197C3⋊Dic3—81no—
198C22×D4—91no—
199C22×D4—181no—
200C23×C4—91no—
201C2×M16—181no—
202#121—91no—
203#121—91no—
204#121—91no—
205#121—181no—
206#121—181no—
207#121C2×C3⋊D311yescharacteristic
208C2×C4⋊C4—91no—
209C2×C22⋊C4—181no—
210C2×C22⋊C4—181no—
211C22⋊C8—91no—
212C22⋊C8—181no—
213C22⋊C8C2×C3⋊D311yescharacteristic, complemented
214#95—91no—
215#95—181no—
216#95C2×C3⋊D311yescharacteristic, complemented
217C23×C3—24no—
218C23×C3D3×D414yes—
219C22×D3—34no—
220C22×D3—34no—
221C22×D3—68no—
222C22×D3—64no—
223C22×D3—64no—
224C22×D3—64no—
225C22×D3—128no—
226C22×D3—124no—
227C22×D3—128no—
228C22×D3—128no—
229C3×D4—44no—
230C3×D4—44no—
231C3×D4—44no—
232C2×C3×C4—24no—
233C2×C3×C4—44no—
234C2×C3×C4—44no—
235C2×C3×C4—44no—
236C2×C3×C4—44no—
237C2×C3×C4C2×C4×D314yes—
238C2×C3×C4D3×D414yes—
239#67—128no—
240#67—128no—
241#67—124no—
242#67—124no—
243C2×Dic3—34no—
244C2×Dic3—34no—
245C2×Dic3—64no—
246C2×Dic3—124no—
247C2×Dic3—124no—
248C2×Dic3—124no—
249C2×Dic3—124no—
250D12—124no—
251D12—128no—
252C4×D3—68no—
253C4×D3—68no—
254C4×D3—124no—
255C4×D3—124no—
256C4×D3—128no—
257C3×C8—44no—
258C3⋊C8—124no—
259C2×C32—21no—
260C2×C32—21no—
261C2×C32—81no—
262C2×C32C2×#9911yescharacteristic
263C2×C32#41811yescharacteristic
264C2×C32#42111yescharacteristic
265C3⋊D3—22no—
266C3⋊D3—41no—
267C3⋊D3—81no—
268C24—91no—
269C24—181no—
270C2×D4—21no—
271C2×D4—91no—
272C2×D4—181no—
273C2×D4—181no—
274C2×D4—181no—
275C2×D4—181no—
276C2×D4—362no—
277C2×D4—362no—
278C2×D4—362no—
279C2×D4C4×C3⋊D311yescharacteristic
280C22×C4—21no—
281C22×C4—91no—
282C22×C4—91no—
283C22×C4—91no—
284C22×C4—91no—
285C22×C4—91no—
286C22×C4—181no—
287C22×C4—181no—
288C22×C4—362no—
289C22×C4C22×C3⋊D311yescharacteristic
290M16—362no—
291C2×C8—21no—
292C2×C8—181no—
293C4⋊C4—91no—
294C4⋊C4—181no—
295C4⋊C4C4×C3⋊D311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—181no—
298C22⋊C4—181no—
299C22⋊C4—181no—
300C22⋊C4—362no—
301C22×C3—24no—
302C22×C3—24no—
303C22×C3—44no—
304C22×C3—44no—
305C22×C3—44no—
306C22×C3D3×C22⋊C414yes—
307C22×C3#91114yes—
308C22×C3#91414yes—
309C2×D3—38no—
310C2×D3—64no—
311C2×D3—64no—
312C2×D3—64no—
313C2×D3—64no—
314C2×D3—64no—
315C2×D3—128no—
316C2×D3—128no—
317C2×D3—124no—
318C2×D3—124no—
319C2×D3—124no—
320C2×D3—2416no—
321C3×C4—24no—
322C3×C4—24no—
323C3×C4—44no—
324C3×C4—84no—
325Dic3—64no—
326Dic3—64no—
327Dic3—124no—
328Dic3—244no—
329C32#151011yescharacteristic, complemented, Sylow
330C23—21no—
331C23—91no—
332C23—91no—
333C23—182no—
334C23—181no—
335C23—181no—
336C23—181no—
337C23—361no—
338C23—362no—
339C23—362no—
340C23—362no—
341C23D4×C3⋊D311yescharacteristic
342D4—41no—
343D4—41no—
344D4—41no—
345D4—361no—
346D4—362no—
347D4—362no—
348D4—362no—
349D4—361no—
350D4—361no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—91no—
357C2×C4—91no—
358C2×C4—182no—
359C2×C4—182no—
360C2×C4—181no—
361C2×C4—361no—
362C2×C4—361no—
363C2×C4—362no—
364C2×C4—361no—
365C2×C4—361no—
366C2×C4—361no—
367C2×C4—361no—
368C2×C4C2×C4×C3⋊D311yescharacteristic
369C2×C4D4×C3⋊D311yescharacteristic
370C8—41no—
371C8—361no—
372C2×C3—24no—
373C2×C3—24no—
374C2×C3—84no—
375C2×C3D3×#9914yes—
376C2×C3#477014yes—
377C2×C3#482114yes—
378D3—68no—
379D3—124no—
380D3—244no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—92no—
387C22—181no—
388C22—181no—
389C22—181no—
390C22—181no—
391C22—181no—
392C22—362no—
393C22—362no—
394C22—361no—
395C22—361no—
396C22—361no—
397C22—724no—
398C22C22⋊C4×C3⋊D311yescharacteristic
399C22#6412011yescharacteristic
400C22#6412311yescharacteristic
401C4—21no—
402C4—21no—
403C4—41no—
404C4—81no—
405C4—181no—
406C4—181no—
407C4—361no—
408C4—721no—
409C3#6830414yescomplemented
410C2—21no—
411C2—21no—
412C2—81no—
413C2—182no—
414C2—361no—
415C2—721no—
416C2C3⋊D3×#9911yescharacteristic
417C2#1059246911yescharacteristic
418C2#1059252011yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#327C2
socleC22×C32C2×C22⋊C4
prime radicalC3⋊D3×#121C2
cosocleC22×C32×C4C23
hypercenter#327C3⋊D3
hypocenterC32#1510
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. #10592363C2semidirect
4. C32×#327C2semidirect
5. #10589403C2semidirect
6. #10589336C2semidirect
7. #10589317C2semidirect
10. C2×D4×C3⋊D3C4semidirect
14. #64147C4semidirect
18. #64104C4semidirect
19. C4⋊C4×C3⋊D3C4semidirect
22. C32×C22⋊C8C22semidirect
23. C32×#95C22semidirect
25. #63658C22semidirect
26. #63657C22semidirect
31. C3×#327D3semidirect
82. C3×C22⋊C8C2×D3semidirect
83. C3×#95C2×D3semidirect
136. #327C3⋊D3semidirect
213. C22⋊C8C2×C3⋊D3semidirect
216. #95C2×C3⋊D3semidirect
329. C32#1510semidirect
409. C3#68304semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1212
#105924252
#105923632
C32×#3272
#105894032
#105893362
#105893172
#683043