Finite Group Databasebeta

← #11898384

Subgroups — #11898384

Order 1152.

787 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593865C212yesmaximal, complemented
2C4×#3745C211yesmaximal, characteristic
3C3×#4699C211yesmaximal, characteristic, complemented
4C3×C8×Dic6C211yesmaximal, characteristic, complemented
5#10590865C212yesmaximal
6Dic3×Dic12C212yesmaximal, complemented
7#10590801C214yesmaximal, complemented
8#10590379C212yesmaximal, complemented
9#81795—31nomaximal
10#79912—31nomaximal
11C2×#3745C2211yescharacteristic
12C4×C4⋊(C3⋊D3)C2212yes—
13C2×C3×Dic12C2212yes—
14C2×C3×Dic12C2212yes—
15C3×#869C2212yes—
16C3×C4×Dic6C2211yescharacteristic
17#63871—22no—
18#63864C2214yes—
19#63849—22no—
20#63848—24no—
21Dic3×Dic6C2214yes—
22C2×#3717C2214yes—
23C32×C4×C8C2211yescharacteristic
24#63648C2212yes—
25#63645C2211yescharacteristic
26C3×Dic3⋊C8C2212yes—
27C3×C8×Dic3C2212yes—
28C3×C4⋊(C3⋊C8)C2211yescharacteristic
29#63566C2214yes—
30#5732—32no—
31#5584—32no—
32C3×#494—31no—
33C3×C8×Q8—31no—
34#5191—32no—
35#5185—34no—
36Dic3×Q16—32no—
37#5083—32no—
38#4845—34no—
39#4841—32no—
40#4699D311yescharacteristic, complemented
41C4×Dic12—32no—
42#4696—32no—
43C4×D24—31no—
44C4×D24—31no—
45C4×D24—61no—
46C8×Dic6D311yescharacteristic, complemented
47C2×C4⋊(C3⋊D3)C2312yes—
48C2×C4×C3⋊D3—22no—
49C2×C3×Dic6D411yescharacteristic
50C2×C3×Dic6C2314yes—
51C2×C32×C8C2311yescharacteristic
52C2×C32×C8C2311yescharacteristic
53C32×C42C2311yescharacteristic
54#3752—22no—
55C4⋊(C3⋊Dic3)C2312yes—
56#3745—22no—
57C3×C4⋊Dic3—22no—
58C3×C4⋊Dic3—22no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4D412yes—
61C3×C4×Dic3C2312yes—
62C2×C3×C3⋊C8C2312yes—
63C3×Dic12—24no—
64C3×Dic12—42no—
65Dic3⋊Dic3—24no—
66#3722—24no—
67#3722—24no—
68Dic32—24no—
69#3717—44no—
70#3393—91noSylow
71C2×C3×Q16—32no—
72C2×C3×Q16—32no—
73C3×C4⋊Q8—32no—
74C3×C4×Q8—31no—
75#947—34no—
76#946—62no—
77Q8×Dic3—34no—
78C2×#215—34no—
79C2×Dic12C2×D312yes—
80C2×Dic12C2×D312yes—
81C2×D24—31no—
82C2×D24—31no—
83C2×D24—61no—
84C2×#204—34no—
85#898—64no—
86#898—64no—
87#897—62no—
88#892—62no—
89#892—62no—
90#875—34no—
91C4×D12—32no—
92C4×D12—32no—
93C4×D12—62no—
94#869C2×D312yes—
95C4×Dic6—34no—
96C4×Dic6C2×D311yescharacteristic
97C3×C4⋊C8—32no—
98C3×C4⋊C8—31no—
99C3×C4×C8—21no—
100C3×C4×C8—32no—
101C3×C4×C8C2×D311yescharacteristic
102C3×C4×C8C2×D311yescharacteristic
103#835—34no—
104#821—32no—
105#821—32no—
106#821—62no—
107#818—31no—
108#818—31no—
109#818—61no—
110#816—34no—
111Dic3⋊C8C2×D312yes—
112C8×Dic3C2×D312yes—
113C4⋊(C3⋊C8)C2×D311yescharacteristic
114C22×C3⋊D3—22no—
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2411yescharacteristic
118C2×C3⋊Dic3—22no—
119C4⋊(C3⋊D3)—22no—
120C4⋊(C3⋊D3)—22no—
121C4×C3⋊D3—44no—
122C2×C3×Dic3—24no—
123C2×C3×Dic3C2×D412yes—
124C2×C3×Dic3C2×D412yes—
125C3×Dic6—22no—
126C3×Dic6—24no—
127C3×Dic6—24no—
128C32×C8—21no—
129C32×C8#4112yes—
130C3×C3⋊C8—22no—
131#556—92no—
132#495—92no—
133#494—31no—
134#464—94no—
135#461—92no—
136C8×Q8—31no—
137C4×Q16—92no—
138C4×D8—91no—
139C2×C3×Q8—31no—
140C2×C3×Q8—34no—
141C2×D12—32no—
142C2×D12—32no—
143C2×D12—62no—
144C2×C4×D3—62no—
145C2×C4×D3—62no—
146C2×C4×D3—122no—
147C2×Dic6D1211yescharacteristic
148C2×Dic6C22×D314yes—
149C3×Q16—64no—
150C3×Q16—122no—
151C2×C3×C8—21no—
152C2×C3×C8—21no—
153C2×C3×C8—32no—
154C2×C3×C8C22×D311yescharacteristic
155C2×C3×C8C22×D311yescharacteristic
156C2×C3×C8C22×D311yescharacteristic
157C2×C3×C8C22×D311yescharacteristic
158C3×C4⋊C4—31no—
159C3×C4⋊C4—32no—
160C3×C4⋊C4—62no—
161C3×C4⋊C4—62no—
162C3×C42—21no—
163C3×C42—32no—
164C3×C42C22×D311yescharacteristic
165C3×C42C22×D311yescharacteristic
166#215—124no—
167(C2×D3)⋊C4—64no—
168(C2×D3)⋊C4—64no—
169(C2×D3)⋊C4—62no—
170(C2×D3)⋊C4—62no—
171(C2×D3)⋊C4—64no—
172(C2×D3)⋊C4—64no—
173(C2×D3)⋊C4—122no—
174C4⋊Dic3—22no—
175C4⋊Dic3—22no—
176C4⋊Dic3—32no—
177C4⋊Dic3—32no—
178C4⋊Dic3—62no—
179C4⋊Dic3—64no—
180C4⋊Dic3D1211yescharacteristic
181Dic3⋊C4—64no—
182Dic3⋊C4D1212yes—
183C4×Dic3—64no—
184C4×Dic3—64no—
185C4×Dic3C22×D312yes—
186C2×C3⋊C8C22×D312yes—
187Dic12—24no—
188Dic12—42no—
189D24—64no—
190D24—62no—
191D24—62no—
192#204—124no—
193C22×C32C22×D411yescharacteristic
194C2×C3⋊D3—42no—
195C2×C3⋊D3—42no—
196C2×C3⋊D3—42no—
197C32×C4—21no—
198C32×C4#13512yes—
199C32×C4C2×#4111yescharacteristic
200C32×C4H(5,𝔽2)11yescharacteristic
201C3⋊Dic3—42no—
202C3×Dic3—22no—
203C3×Dic3—22no—
204C3×Dic3—44no—
205C2×Q16—32no—
206C2×Q16—32no—
207C2×SD16—94no—
208C2×D8—91no—
209C4⋊Q8—32no—
210#126—184no—
211#124—94no—
212C22⋊Q8—182no—
213C4×Q8—31no—
214C4×Q8—94no—
215C4×D4—92no—
216#117—182no—
217#107—91no—
218C4⋊C8—32no—
219C4⋊C8—31no—
220#103—94no—
221#102—92no—
222C4×C8—32no—
223C4×C8D3211yescharacteristic
224C22×D3—62no—
225C22×D3—62no—
226C22×D3—122no—
227C3×Q8—62no—
228C3×Q8—64no—
229C3×Q8—64no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—32no—
234C2×C3×C4—32no—
235C2×C3×C4—64no—
236C2×C3×C4C2×D1211yescharacteristic
237C2×C3×C4C2×D1211yescharacteristic
238C2×C3×C4D3×D411yescharacteristic
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4C23×D311yescharacteristic
241C2×C3×C4C23×D311yescharacteristic
242C2×Dic3—24no—
243C2×Dic3—62no—
244C2×Dic3—62no—
245C2×Dic3—122no—
246C2×Dic3C2×D1212yes—
247C2×Dic3C2×D1212yes—
248D12—64no—
249D12—62no—
250D12—62no—
251D12—62no—
252D12—62no—
253D12—122no—
254C4×D3—124no—
255C4×D3—124no—
256C4×D3—244no—
257Dic6—22no—
258Dic6—24no—
259Dic6—24no—
260C3×C8—21no—
261C3×C8—21no—
262C3×C8—22no—
263C3×C8—41no—
264C3×C8—62no—
265C3×C8#23712yes—
266C3×C8#23912yes—
267C3⋊C8—22no—
268C2×C32#55011yescharacteristic
269C2×C32C2×#13511yescharacteristic
270C2×C32#57811yescharacteristic
271C3⋊D3—82no—
272C2×Q8—31no—
273C2×Q8—34no—
274C2×D4—92no—
275C22×C4—182no—
276Q16—64no—
277Q16—122no—
278SD16—364no—
279D8—182no—
280C2×C8—32no—
281C2×C8C2×D3211yescharacteristic
282C2×C8C2×D3211yescharacteristic
283C4⋊C4—31no—
284C4⋊C4—32no—
285C4⋊C4—62no—
286C4⋊C4—62no—
287C4⋊C4—92no—
288C4⋊C4—184no—
289C22⋊C4—184no—
290C22⋊C4—184no—
291C22⋊C4—182no—
292C42—32no—
293C42—184no—
294C42C2×D3211yescharacteristic
295C22×C3—21no—
296C22×C3C22×D1211yescharacteristic
297C22×C3C2×D3×D411yescharacteristic
298C2×D3—124no—
299C2×D3—122no—
300C2×D3—122no—
301C2×D3—122no—
302C2×D3—122no—
303C2×D3—122no—
304C2×D3—122no—
305C2×D3—242no—
306C2×D3—242no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—22no—
312C3×C4—41no—
313C3×C4—62no—
314C3×C4—62no—
315C3×C4—124no—
316C3×C4#90412yes—
317C3×C4#91912yes—
318C3×C4C2×#23711yescharacteristic
319C3×C4#100411yescharacteristic
320C3×C4C2×#23911yescharacteristic
321C3×C4#100911yescharacteristic
322Dic3—22no—
323Dic3—22no—
324Dic3—44no—
325Dic3—122no—
326Dic3—122no—
327Dic3—242no—
328C32#339311yescharacteristic, complemented, Sylow
329C23—182no—
330Q8—62no—
331Q8—64no—
332Q8—64no—
333D4—182no—
334D4—182no—
335C2×C4—32no—
336C2×C4—32no—
337C2×C4—64no—
338C2×C4—182no—
339C2×C4—364no—
340C2×C4D3×D1211yescharacteristic
341C2×C4D3×D1211yescharacteristic
342C2×C4C22×D3211yescharacteristic
343C8—21no—
344C8—62no—
345C8#379612yes—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3#557711yescharacteristic
350C2×C3#571811yescharacteristic
351C2×C3C2×#90411yescharacteristic
352C2×C3#575311yescharacteristic
353C2×C3C2×#91911yescharacteristic
354C2×C3#576611yescharacteristic
355D3—244no—
356D3—242no—
357D3—242no—
358C22—362no—
359C22—362no—
360C22—362no—
361C22C2×D3×D1211yescharacteristic
362C4—21no—
363C4—62no—
364C4—62no—
365C4—124no—
366C4—362no—
367C4#6380812yes—
368C4C2×#379611yescharacteristic
369C4#6430711yescharacteristic
370C3—21no—
371C3#7991211yescharacteristic, complemented
372C3#8179511yescharacteristic, complemented
373C2—722no—
374C2#1059390011yescharacteristic
375C2#1059469111yescharacteristic
376C2C2×#6380811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×#3745C22
hypercenterC4×C8D32
hypocenterC32#3393
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10593865C2semidirect
3. C3×#4699C2semidirect
4. C3×C8×Dic6C2semidirect
6. Dic3×Dic12C2semidirect
7. #10590801C2semidirect
8. #10590379C2semidirect
40. #4699D3semidirect
46. C8×Dic6D3semidirect
328. C32#3393semidirect
371. C3#79912semidirect
372. C3#81795semidirect

Maximal subgroups

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

subgroupindex
#105938652
C4×#37452
C3×#46992
C3×C8×Dic62
#105908652
Dic3×Dic122
#105908012
#105903792
#817953
#799123