Finite Group Databasebeta

← #11868782

Subgroups — #11868782

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×#3832C211yesmaximal, characteristic
3C32×#475C211yesmaximal, characteristic, complemented
4#10592786C211yesmaximal, characteristic, complemented
5#10592719C211yesmaximal, characteristic, complemented
6#10592569C212yesmaximal, complemented
7#10592560C212yesmaximal, complemented
8#10592545C211yesmaximal, characteristic, complemented
9#10592536C211yesmaximal, characteristic, complemented
10#10592502C212yesmaximal
11#10592492C212yesmaximal, complemented
12#81012—34nomaximal
13C2×#3832C2211yescharacteristic
14C2×Q8×C3⋊D3—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17Q8×C3⋊Dic3C2211yescharacteristic
18#64153—21no—
19C2×#3743C2212yes—
20#64102—21no—
21#64102C2211yescharacteristic
22#64101—21no—
23#64101C2211yescharacteristic
24C4⋊C4×C3⋊D3—21no—
25C4⋊C4×C3⋊D3C2212yes—
26#64097—21no—
27#64097C2212yes—
28C4×C4⋊(C3⋊D3)—21no—
29C4×C4⋊(C3⋊D3)C2211yescharacteristic
30C42×C3⋊D3—21no—
31C42×C3⋊D3C2211yescharacteristic
32#64078C2211yescharacteristic
33C32×#106C2212yes—
34C32×C4⋊C8C2211yescharacteristic
35C32×#103C2212yes—
36#63662C2212yes—
37#63648C2212yes—
38#63645C2212yes—
39#63641C2212yes—
40#63636C2212yes—
41#63635C2212yes—
42#63634C2212yes—
43C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
44D3×C4⋊Q8—34no—
45C4×#239—34no—
46C3×#475D314yescomplemented
47#5087—34no—
48#5020—34no—
49#4870—38no—
50#4861—38no—
51#4846—34no—
52#4837—34no—
53#4803—38no—
54#4793—38no—
55C2×C32×Q8—21no—
56C2×C32×Q8C2311yescharacteristic
57#3832—22no—
58#3832Q814yescomplemented
59Q8×C3⋊D3—44no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)C2311yescharacteristic
62C2×C4×C3⋊D3—21no—
63C2×C4×C3⋊D3—22no—
64C2×C4×C3⋊D3—21no—
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3D411yescharacteristic
67C2×C4×C3⋊D3D411yescharacteristic
68C2×C4×C3⋊D3C2311yescharacteristic
69C2×#634—21no—
70C2×#634—22no—
71C2×C32×C8C2312yes—
72C32×C4⋊C4—21no—
73C32×C4⋊C4—21no—
74C32×C4⋊C4C2312yes—
75C32×C4⋊C4C2311yescharacteristic
76C32×C42—21no—
77C32×C42C2311yescharacteristic
78#3752—21no—
79#3752—21no—
80#3752—21no—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)C2312yes—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85#3750—22no—
86#3750—22no—
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×#239—34no—
96C2×D3×Q8—64no—
97C3×C4⋊Q8C2×D314yes—
98C3×C4×Q8C2×D314yes—
99Q8×Dic3—34no—
100#944—64no—
101C2×ΓL(1,𝔽25)—38no—
102#893—34no—
103#893—64no—
104#892—34no—
105#892—64no—
106D3×C4⋊C4—38no—
107D3×C4⋊C4—64no—
108#888—38no—
109#888—64no—
110C4×D12—34no—
111C4×D12—64no—
112C42×D3—34no—
113C42×D3—64no—
114#869—34no—
115C3×#106C2×D318yes—
116C3×C4⋊C8C2×D314yes—
117C3×#103C2×D318yes—
118#835—38no—
119#821—38no—
120#818—38no—
121Dic3⋊C8—38no—
122#809—38no—
123#808—38no—
124#807—38no—
125C4⋊(C3⋊C8)—34no—
126C22×C3⋊D3—21no—
127C22×C3⋊D3C2×D411yescharacteristic
128C32×Q8—21no—
129C32×Q8—42no—
130C32×Q8C2×Q812yescomplemented
131C2×C32×C4—21no—
132C2×C32×C4—21no—
133C2×C32×C4—22no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2411yescharacteristic
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3C2×D411yescharacteristic
140C2×C3⋊Dic3C2×D411yescharacteristic
141C2×C3⋊Dic3C2×D411yescharacteristic
142C4⋊(C3⋊D3)—24no—
143C4⋊(C3⋊D3)—21no—
144C4⋊(C3⋊D3)C2×Q812yescomplemented
145C4×C3⋊D3—22no—
146C4×C3⋊D3—24no—
147C4×C3⋊D3—22no—
148C4×C3⋊D3—44no—
149C4×C3⋊D3—42no—
150C4×C3⋊D3—42no—
151C4×C3⋊D3C2×Q812yes—
152C4×C3⋊D3#4112yes—
153#634—44no—
154#634—42no—
155C32×C8—22no—
156C3⋊(C3⋊C8)—22no—
157C2×C4⋊Q8—91no—
158C4×#41—91no—
159#477—92no—
160#476—92no—
161#475—91no—
162#475C3⋊D311yescharacteristic, complemented
163#474—91no—
164#474—91no—
165#428—92no—
166#423—91no—
167#417—92no—
168C2×C3×Q8—24no—
169C2×C3×Q8C22×D314yes—
170#239—316no—
171#239—68no—
172D3×Q8—1216no—
173C2×D12—34no—
174C2×D12—64no—
175C2×C4×D3—34no—
176C2×C4×D3—34no—
177C2×C4×D3—34no—
178C2×C4×D3—64no—
179C2×C4×D3—64no—
180C2×C4×D3—68no—
181C2×C4×D3—64no—
182C2×Dic6—68no—
183C2×Dic6—64no—
184C2×C3×C8C22×D318yes—
185C3×C4⋊C4—24no—
186C3×C4⋊C4—24no—
187C3×C4⋊C4C22×D318yes—
188C3×C4⋊C4C22×D314yes—
189C3×C42—24no—
190C3×C42C22×D314yes—
191(C2×D3)⋊C4—64no—
192(C2×D3)⋊C4—64no—
193(C2×D3)⋊C4—64no—
194C4⋊Dic3—34no—
195C4⋊Dic3—38no—
196C4⋊Dic3—64no—
197C4⋊Dic3—64no—
198Dic3⋊C4—68no—
199Dic3⋊C4—68no—
200C4×Dic3—34no—
201C4×Dic3—34no—
202C4×Dic3—34no—
203C4×Dic3—64no—
204C4×Dic3—64no—
205C2×C3⋊C8—38no—
206ΓL(1,𝔽25)—616no—
207C22×C32C22×D411yescharacteristic
208C2×C3⋊D3—21no—
209C2×C3⋊D3—21no—
210C2×C3⋊D3—22no—
211C2×C3⋊D3—41no—
212C2×C3⋊D3—41no—
213C2×C3⋊D3C22⋊Q812yes—
214C32×C4—22no—
215C32×C4—21no—
216C32×C4—42no—
217C32×C4—41no—
218C32×C4AGL(1,ℤ/8)12yes—
219C32×C4C22×Q811yescharacteristic
220C32×C4C2×#4111yescharacteristic
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×Q8C2×C3⋊D311yescharacteristic
236C4×D4—91no—
237C4×D4—91no—
238C4×D4—181no—
239C4×D4—181no—
240#117—91no—
241#117—181no—
242C2×C4⋊C4—92no—
243C2×C4⋊C4—181no—
244C2×C42—91no—
245C2×C42—181no—
246#107—92no—
247#107—92no—
248#106—92no—
249#106C2×C3⋊D312yes—
250C4⋊C8—92no—
251C4⋊C8—91no—
252C4⋊C8C2×C3⋊D311yescharacteristic
253#103—92no—
254#103C2×C3⋊D312yes—
255#102—92no—
256#102—92no—
257C22×D3—34no—
258C22×D3—64no—
259C3×Q8—24no—
260C3×Q8—48no—
261C3×Q8D3×Q818yescomplemented
262C2×C3×C4—24no—
263C2×C3×C4—24no—
264C2×C3×C4—28no—
265C2×C3×C4D3×D414yes—
266C2×C3×C4D3×D414yes—
267C2×C3×C4C23×D314yes—
268C2×Dic3—34no—
269C2×Dic3—34no—
270C2×Dic3—34no—
271C2×Dic3—64no—
272C2×Dic3—68no—
273D12—38no—
274D12—616no—
275D12—64no—
276C4×D3—38no—
277C4×D3—38no—
278C4×D3—68no—
279C4×D3—616no—
280C4×D3—68no—
281C4×D3—128no—
282C4×D3—1216no—
283C4×D3—128no—
284Dic6—1216no—
285Dic6—128no—
286C3×C8—28no—
287C3⋊C8—68no—
288C2×C32C2×C22⋊Q811yescharacteristic
289C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
290C2×C32C2×#13711yescharacteristic
291C3⋊D3—22no—
292C3⋊D3—42no—
293#41—94no—
294#41—182no—
295C2×Q8—21no—
296C2×Q8—182no—
297C2×Q8—181no—
298C2×Q8—364no—
299C2×Q8C22×C3⋊D311yescharacteristic
300C2×D4—91no—
301C2×D4—181no—
302C22×C4—91no—
303C22×C4—91no—
304C22×C4—91no—
305C22×C4—181no—
306C22×C4—181no—
307C22×C4—182no—
308C22×C4—181no—
309M16—184no—
310C2×C8—92no—
311C2×C8C22×C3⋊D312yes—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—92no—
315C4⋊C4—91no—
316C4⋊C4—182no—
317C4⋊C4—182no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C4⋊C4C22×C3⋊D312yes—
321C4⋊C4C22×C3⋊D311yescharacteristic
322C22⋊C4—181no—
323C22⋊C4—181no—
324C22⋊C4—181no—
325C42—21no—
326C42—91no—
327C42—91no—
328C42—91no—
329C42—181no—
330C42—181no—
331C42C22×C3⋊D311yescharacteristic
332C22×C3C2×D3×D414yes—
333C2×D3—38no—
334C2×D3—64no—
335C2×D3—64no—
336C2×D3—68no—
337C2×D3—124no—
338C2×D3—124no—
339C3×C4—24no—
340C3×C4—28no—
341C3×C4—48no—
342C3×C4—44no—
343C3×C4#91418yes—
344C3×C4C2×D3×Q814yes—
345C3×C4D3×#4114yes—
346Dic3—38no—
347Dic3—38no—
348Dic3—64no—
349Dic3—128no—
350Dic3—124no—
351C32#307911yescharacteristic, complemented, Sylow
352C23—91no—
353C23—181no—
354Q8—21no—
355Q8—42no—
356Q8—364no—
357Q8—362no—
358Q8Q8×C3⋊D312yescomplemented
359D4—92no—
360D4—184no—
361D4—181no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—91no—
366C2×C4—91no—
367C2×C4—92no—
368C2×C4—92no—
369C2×C4—91no—
370C2×C4—182no—
371C2×C4—184no—
372C2×C4—182no—
373C2×C4—181no—
374C2×C4—182no—
375C2×C4—362no—
376C2×C4—364no—
377C2×C4—362no—
378C2×C4D4×C3⋊D311yescharacteristic
379C2×C4D4×C3⋊D311yescharacteristic
380C2×C4C23×C3⋊D311yescharacteristic
381C8—22no—
382C8—182no—
383C2×C3D3×C22⋊Q814yes—
384C2×C3C2×#91414yes—
385C2×C3D3×#13714yes—
386D3—68no—
387D3—128no—
388C22—92no—
389C22—181no—
390C22—181no—
391C22—182no—
392C22—361no—
393C22—361no—
394C22C2×D4×C3⋊D311yescharacteristic
395C4—22no—
396C4—21no—
397C4—42no—
398C4—41no—
399C4—92no—
400C4—92no—
401C4—181no—
402C4—362no—
403C4—361no—
404C4#6412312yes—
405C4C2×Q8×C3⋊D311yescharacteristic
406C4#41×C3⋊D311yescharacteristic
407C3#8101214yescomplemented
408C2—182no—
409C2—362no—
410C2C3⋊D3×C22⋊Q811yescharacteristic
411C2C2×#6412311yescharacteristic
412C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#475C2
socleC22×C32C22×D4
prime radicalC2×#3832C22
hypercenter#475C3⋊D3
hypocenterC32#3079
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×C4⋊Q8C2semidirect
3. C32×#475C2semidirect
4. #10592786C2semidirect
5. #10592719C2semidirect
6. #10592569C2semidirect
7. #10592560C2semidirect
8. #10592545C2semidirect
9. #10592536C2semidirect
11. #10592492C2semidirect
46. C3×#475D3semidirect
58. #3832Q8semidirect
130. C32×Q8C2×Q8semidirect
144. C4⋊(C3⋊D3)C2×Q8semidirect
162. #475C3⋊D3semidirect
261. C3×Q8D3×Q8semidirect
351. C32#3079semidirect
358. Q8Q8×C3⋊D3semidirect
407. C3#81012semidirect

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×#38322
C32×#4752
#105927862
#105927192
#105925692
#105925602
#105925452
#105925362
#105925022
#105924922
#810123