Finite Group Databasebeta

← #11868776

Subgroups — #11868776

Order 1152.

1248 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic, complemented
2C4×#3830C211yesmaximal, characteristic
3C32×#474C211yesmaximal, characteristic, complemented
4#10592793C211yesmaximal, characteristic, complemented
5#10592706C211yesmaximal, characteristic, complemented
6#10592580C212yesmaximal, complemented
7#10592574C212yesmaximal, complemented
8#10592550C211yesmaximal, characteristic, complemented
9#10592536C211yesmaximal, characteristic, complemented
10#10592470C212yesmaximal
11#10592460C212yesmaximal, complemented
12#80966—34nomaximal
13C2×Q8×C3⋊D3—21no—
14C2×#3830C2211yescharacteristic
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17#64153—21no—
18D4×C3⋊Dic3C2211yescharacteristic
19C4×#638—21no—
20C2×C4×C3⋊Dic3—21no—
21C2×#3743C2212yes—
22#64101C2211yescharacteristic
23C4⋊C4×C3⋊D3—21no—
24C4⋊C4×C3⋊D3C2212yes—
25#64097—21no—
26#64097C2212yes—
27#64096C2211yescharacteristic
28#64090—21no—
29#64086—21no—
30C42×C3⋊D3C2211yescharacteristic
31#64078C2211yescharacteristic
32C4×#634C2211yescharacteristic
33C32×#107C2212yes—
34C32×C4⋊C8C2211yescharacteristic
35C32×#102C2212yes—
36#63659C2212yes—
37#63644C2212yes—
38#63643C2212yes—
39#63641C2212yes—
40#63637C2212yes—
41#63635C2212yes—
42#63634C2212yes—
43C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
44D3×C4⋊Q8—34no—
45C4×#237—34no—
46C3×#474D314yescomplemented
47#5094—34no—
48#5007—34no—
49#4881—38no—
50#4875—38no—
51#4851—34no—
52#4837—34no—
53#4771—38no—
54#4761—38no—
55C2×C32×Q8—21no—
56C2×C32×D4C2311yescharacteristic
57C22×C32×C4—21no—
58C2×#638—21no—
59C22×C3⋊Dic3—21no—
60C22×C3⋊Dic3—21no—
61Q8×C3⋊D3—44no—
62#3830—22no—
63#3830Q814yescomplemented
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3D411yescharacteristic
66C2×C4×C3⋊D3D411yescharacteristic
67C2×C4×C3⋊D3C2311yescharacteristic
68C2×#634—21no—
69C2×#634—22no—
70C2×#634C2311yescharacteristic
71C2×C32×C8C2312yes—
72C32×C4⋊C4—21no—
73C32×C4⋊C4C2311yescharacteristic
74C32×C4⋊C4C2312yes—
75C32×C22⋊C4—21no—
76C32×C42C2311yescharacteristic
77#3757—21no—
78#3752—21no—
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81C4⋊(C3⋊Dic3)C2312yes—
82#3750—21no—
83#3750—21no—
84#3750—22no—
85#3750—22no—
86C4×C3⋊Dic3—21no—
87C4×C3⋊Dic3—21no—
88C4×C3⋊Dic3—21no—
89C4×C3⋊Dic3D411yescharacteristic
90C4×C3⋊Dic3D411yescharacteristic
91C4×C3⋊Dic3C2311yescharacteristic
92C2×C3⋊(C3⋊C8)C2312yes—
93#3743—24no—
94#3079—91noSylow
95C2×D3×Q8—64no—
96C2×#237—34no—
97C3×C4⋊Q8C2×D314yes—
98C3×C4×D4C2×D314yes—
99#944—64no—
100D4×Dic3—34no—
101C4×#67—64no—
102C2×C4×Dic3—64no—
103C2×ΓL(1,𝔽25)—38no—
104#892—34no—
105D3×C4⋊C4—38no—
106D3×C4⋊C4—64no—
107#888—38no—
108#888—64no—
109#887—34no—
110#67⋊C4—64no—
111#877—64no—
112C42×D3—34no—
113#869—34no—
114C4×Dic6—34no—
115C3×#107C2×D318yes—
116C3×C4⋊C8C2×D314yes—
117C3×#102C2×D318yes—
118#832—38no—
119#817—38no—
120#816—38no—
121Dic3⋊C8—38no—
122#810—38no—
123#808—38no—
124#807—38no—
125C4⋊(C3⋊C8)—34no—
126C23×C32—21no—
127C22×C3⋊D3C2×D411yescharacteristic
128C32×Q8—42no—
129C32×D4—21no—
130C32×D4C2×Q812yescomplemented
131C2×C32×C4—21no—
132C2×C32×C4—22no—
133C2×C32×C4—42no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2411yescharacteristic
137#638—24no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—24no—
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—42no—
143C2×C3⋊Dic3C2×D411yescharacteristic
144C2×C3⋊Dic3C2×D411yescharacteristic
145C2×C3⋊Dic3C2×D411yescharacteristic
146C4×C3⋊D3—22no—
147C4×C3⋊D3—22no—
148C4×C3⋊D3—44no—
149C4×C3⋊D3C2×Q812yes—
150C4×C3⋊D3#4112yes—
151#634—21no—
152#634—44no—
153#634—42no—
154#634C2×Q812yescomplemented
155C32×C8—22no—
156C3⋊(C3⋊C8)—22no—
157C2×C4⋊Q8—91no—
158C4×#41—91no—
159#477—92no—
160#476—92no—
161#475—91no—
162#475—91no—
163#474—91no—
164#474C3⋊D311yescharacteristic, complemented
165#428—92no—
166#423—91no—
167#417—92no—
168C2×C3×Q8—24no—
169C2×C3×D4C22×D314yes—
170C22×C3×C4—24no—
171C2×#67—64no—
172C22×Dic3—64no—
173C22×Dic3—64no—
174D3×Q8—1216no—
175#237—316no—
176#237—68no—
177C2×C4×D3—34no—
178C2×C4×D3—34no—
179C2×C4×D3—34no—
180C2×C4×D3—68no—
181C2×Dic6—34no—
182C2×Dic6—68no—
183C2×Dic6—64no—
184C2×C3×C8C22×D318yes—
185C3×C4⋊C4—24no—
186C3×C4⋊C4C22×D314yes—
187C3×C4⋊C4C22×D318yes—
188C3×C22⋊C4—24no—
189C3×C42C22×D314yes—
190#217—64no—
191(C2×D3)⋊C4—64no—
192C4⋊Dic3—38no—
193C4⋊Dic3—34no—
194C4⋊Dic3—64no—
195Dic3⋊C4—64no—
196Dic3⋊C4—68no—
197Dic3⋊C4—68no—
198Dic3⋊C4—64no—
199C4×Dic3—34no—
200C4×Dic3—34no—
201C4×Dic3—34no—
202C4×Dic3—64no—
203C4×Dic3—64no—
204C4×Dic3—64no—
205C2×C3⋊C8—38no—
206ΓL(1,𝔽25)—616no—
207C22×C32—22no—
208C22×C32—41no—
209C22×C32—41no—
210C22×C32C22×D411yescharacteristic
211C2×C3⋊D3—21no—
212C2×C3⋊D3—21no—
213C2×C3⋊D3C22⋊Q812yes—
214C32×C4—21no—
215C32×C4—42no—
216C32×C4—41no—
217C32×C4AGL(1,ℤ/8)12yes—
218C32×C4C22×Q811yescharacteristic
219C32×C4C2×#4111yescharacteristic
220C3⋊Dic3—22no—
221C3⋊Dic3—21no—
222C3⋊Dic3—42no—
223C3⋊Dic3—41no—
224C3⋊Dic3C22⋊Q812yes—
225C3⋊Dic3#13712yes—
226C2×#41—91no—
227C22×Q8—181no—
228C2×M16—92no—
229C4⋊Q8—92no—
230C4⋊Q8—91no—
231C4⋊Q8—181no—
232C4⋊Q8—181no—
233C4⋊Q8C2×C3⋊D311yescharacteristic
234C4×Q8—91no—
235C4×Q8—91no—
236C4×D4—91no—
237C4×D4—181no—
238C4×D4—181no—
239C4×D4C2×C3⋊D311yescharacteristic
240#117—91no—
241#117—181no—
242C2×C4⋊C4—92no—
243C2×C4⋊C4—181no—
244C2×C42—91no—
245C2×C42—181no—
246#107—92no—
247#107C2×C3⋊D312yes—
248#106—92no—
249#106—92no—
250C4⋊C8—92no—
251C4⋊C8—91no—
252C4⋊C8C2×C3⋊D311yescharacteristic
253#103—92no—
254#103—92no—
255#102—92no—
256#102C2×C3⋊D312yes—
257C23×C3—24no—
258C22×D3—34no—
259C3×Q8—48no—
260C3×D4—24no—
261C3×D4D3×Q818yescomplemented
262C2×C3×C4—24no—
263C2×C3×C4—28no—
264C2×C3×C4—48no—
265C2×C3×C4D3×D414yes—
266C2×C3×C4D3×D414yes—
267C2×C3×C4C23×D314yes—
268#67—616no—
269C2×Dic3—34no—
270C2×Dic3—34no—
271C2×Dic3—34no—
272C2×Dic3—616no—
273C2×Dic3—64no—
274C2×Dic3—64no—
275C2×Dic3—68no—
276C2×Dic3—128no—
277C4×D3—38no—
278C4×D3—38no—
279C4×D3—68no—
280C4×D3—68no—
281C4×D3—1216no—
282Dic6—38no—
283Dic6—64no—
284Dic6—1216no—
285Dic6—128no—
286C3×C8—28no—
287C3⋊C8—68no—
288C2×C32—42no—
289C2×C32C2×C22⋊Q811yescharacteristic
290C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
291C2×C32C2×#13711yescharacteristic
292C3⋊D3—22no—
293#41—94no—
294#41—182no—
295C2×Q8—21no—
296C2×Q8—91no—
297C2×Q8—182no—
298C2×Q8—181no—
299C2×Q8—364no—
300C2×D4—181no—
301C2×D4C22×C3⋊D311yescharacteristic
302C22×C4—21no—
303C22×C4—91no—
304C22×C4—91no—
305C22×C4—91no—
306C22×C4—182no—
307C22×C4—181no—
308C22×C4—181no—
309M16—184no—
310C2×C8—92no—
311C2×C8C22×C3⋊D312yes—
312C4⋊C4—21no—
313C4⋊C4—92no—
314C4⋊C4—91no—
315C4⋊C4—182no—
316C4⋊C4—182no—
317C4⋊C4—181no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C4⋊C4C22×C3⋊D312yes—
321C4⋊C4C22×C3⋊D311yescharacteristic
322C22⋊C4—21no—
323C22⋊C4—181no—
324C22⋊C4—181no—
325C42—91no—
326C42—91no—
327C42—91no—
328C42—181no—
329C42—181no—
330C42—181no—
331C42C22×C3⋊D311yescharacteristic
332C22×C3—28no—
333C22×C3—44no—
334C22×C3—44no—
335C22×C3C2×D3×D414yes—
336C2×D3—38no—
337C2×D3—64no—
338C2×D3—64no—
339C3×C4—24no—
340C3×C4—48no—
341C3×C4—44no—
342C3×C4#91118yes—
343C3×C4C2×D3×Q814yes—
344C3×C4D3×#4114yes—
345Dic3—38no—
346Dic3—38no—
347Dic3—64no—
348Dic3—68no—
349Dic3—128no—
350Dic3—124no—
351C32#307911yescharacteristic, complemented, Sylow
352C23—21no—
353C23—91no—
354Q8—42no—
355Q8—92no—
356Q8—181no—
357Q8—364no—
358Q8—362no—
359D4—21no—
360D4—184no—
361D4Q8×C3⋊D312yescomplemented
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—42no—
365C2×C4—91no—
366C2×C4—91no—
367C2×C4—92no—
368C2×C4—92no—
369C2×C4—91no—
370C2×C4—182no—
371C2×C4—184no—
372C2×C4—181no—
373C2×C4—182no—
374C2×C4—181no—
375C2×C4—182no—
376C2×C4—364no—
377C2×C4—362no—
378C2×C4D4×C3⋊D311yescharacteristic
379C2×C4D4×C3⋊D311yescharacteristic
380C2×C4C23×C3⋊D311yescharacteristic
381C8—22no—
382C8—182no—
383C2×C3—48no—
384C2×C3D3×C22⋊Q814yes—
385C2×C3C2×#91114yes—
386C2×C3D3×#13714yes—
387D3—68no—
388C22—22no—
389C22—41no—
390C22—41no—
391C22—92no—
392C22—181no—
393C22—181no—
394C22C2×D4×C3⋊D311yescharacteristic
395C4—21no—
396C4—41no—
397C4—42no—
398C4—92no—
399C4—92no—
400C4—182no—
401C4—181no—
402C4—362no—
403C4—361no—
404C4#6412012yes—
405C4C2×Q8×C3⋊D311yescharacteristic
406C4#41×C3⋊D311yescharacteristic
407C3#8096614yescomplemented
408C2—42no—
409C2—182no—
410C2C3⋊D3×C22⋊Q811yescharacteristic
411C2C2×#6412011yescharacteristic
412C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#474C2
socleC22×C32C22×D4
prime radicalC2×#3830C22
hypercenter#474C3⋊D3
hypocenterC32#3079
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×C4⋊Q8C2semidirect
3. C32×#474C2semidirect
4. #10592793C2semidirect
5. #10592706C2semidirect
6. #10592580C2semidirect
7. #10592574C2semidirect
8. #10592550C2semidirect
9. #10592536C2semidirect
11. #10592460C2semidirect
46. C3×#474D3semidirect
63. #3830Q8semidirect
130. C32×D4C2×Q8semidirect
154. #634C2×Q8semidirect
164. #474C3⋊D3semidirect
261. C3×D4D3×Q8semidirect
351. C32#3079semidirect
361. D4Q8×C3⋊D3semidirect
407. C3#80966semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
C4×#38302
C32×#4742
#105927932
#105927062
#105925802
#105925742
#105925502
#105925362
#105924702
#105924602
#809663