Finite Group Databasebeta

← #11895206

Subgroups — #11895206

Order 1152.

1050 conjugacy classes of subgroups.

The subgroup lattice has 363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596201C211yesmaximal, characteristic, complemented
2#10596013C211yesmaximal, characteristic, complemented
3C32×#476C211yesmaximal, characteristic, complemented
4#10592792C211yesmaximal, characteristic, complemented
5C4×#3753C211yesmaximal, characteristic
6#10592556C212yesmaximal, complemented
7#10592551C212yesmaximal, complemented
8#10592540C211yesmaximal, characteristic, complemented
9#10592529C211yesmaximal, characteristic, complemented
10#10592486C212yesmaximal
11#10592467C212yesmaximal, complemented
12#81087—34nomaximal
13C32×C4⋊Q8C2211yescharacteristic
14C32×C4×D4C2211yescharacteristic
15#64155—22no—
16#64145C2212yes—
17C2×#3753C2211yescharacteristic
18#64135—21no—
19#64133—21no—
20C2×#3744C2212yes—
21#64106—21no—
22#64102C2212yes—
23C4⋊C4×C3⋊D3—21no—
24#64099C2212yes—
25#64096C2212yes—
26#64088—22no—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28#64078C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C32×#106C2212yes—
31C32×C4⋊C8C2211yescharacteristic
32C32×#102C2212yes—
33#63659C2211yescharacteristic
34#63643C2212yes—
35#63641C2212yes—
36C8×C3⋊Dic3C2212yes—
37#63637C2212yes—
38#63637C2212yes—
39#63636C2211yescharacteristic
40#63634C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42#5730—34no—
43#5542—34no—
44C3×#476D314yescomplemented
45#5093—34no—
46C4×#213—34no—
47#4857—38no—
48#4852—38no—
49#4841—34no—
50#4830—34no—
51#4787—38no—
52#4768—38no—
53C2×C32×Q8—21no—
54C2×C32×D4C2311yescharacteristic
55C22×C32×C4—21no—
56C2×C4⋊(C3⋊D3)C2311yescharacteristic
57C2×C4×C3⋊D3—21no—
58C2×C4×C3⋊D3—22no—
59C2×#634D411yescharacteristic
60C2×#634C2312yes—
61C2×C32×C8C2312yes—
62C32×C4⋊C4—21no—
63C32×C4⋊C4C2311yescharacteristic
64C32×C4⋊C4C2312yes—
65C32×C22⋊C4—21no—
66C32×C42C2311yescharacteristic
67#3757—22no—
68#3757—22no—
69#3753—22no—
70#3752—21no—
71#3752—22no—
72C4⋊(C3⋊Dic3)—21no—
73C4⋊(C3⋊Dic3)—21no—
74C4⋊(C3⋊Dic3)—22no—
75C4⋊(C3⋊Dic3)D411yescharacteristic
76C4⋊(C3⋊Dic3)C2311yescharacteristic
77#3750—22no—
78#3750—22no—
79#3750D412yes—
80C4×C3⋊Dic3—22no—
81C4×C3⋊Dic3C2312yes—
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84#3744—24no—
85#3360—91noSylow
86C3×C4⋊Q8C2×D314yes—
87C3×C4×D4C2×D314yes—
88#946—68no—
89#936—38no—
90C2×#213—34no—
91#926—64no—
92#924—64no—
93C2×#204—38no—
94#897—64no—
95#893—38no—
96D3×C4⋊C4—64no—
97#890—38no—
98#887—38no—
99#879—68no—
100C4×D12—34no—
101#869—34no—
102C4×Dic6—34no—
103C3×#106C2×D318yes—
104C3×C4⋊C8C2×D314yes—
105C3×#102C2×D318yes—
106#832—34no—
107#816—38no—
108Dic3⋊C8—38no—
109C8×Dic3—38no—
110#810—38no—
111#810—38no—
112#809—34no—
113#807—34no—
114C4×C3⋊C8—34no—
115C23×C32—21no—
116C22×C3⋊D3—21no—
117C32×Q8—81no—
118C32×D4—21no—
119C32×D4—21no—
120C2×C32×C4—21no—
121C2×C32×C4—22no—
122C2×C32×C4—42no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2411yescharacteristic
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3C2×D412yes—
129C2×C3⋊Dic3C2×D412yes—
130C4⋊(C3⋊D3)—21no—
131C4⋊(C3⋊D3)#4112yes—
132C4×C3⋊D3—42no—
133C4×C3⋊D3—82no—
134#634—22no—
135#634—22no—
136#634—22no—
137C32×C8—22no—
138C3⋊(C3⋊C8)—21no—
139C3⋊(C3⋊C8)—21no—
140#556—91no—
141#554—91no—
142#488—92no—
143#487—91no—
144#479—92no—
145#476C3⋊D311yescharacteristic, complemented
146#463—92no—
147#461—91no—
148C8×Q8—91no—
149C4×SD16—92no—
150C4×D8—91no—
151C2×C3×Q8—24no—
152C2×C3×D4C22×D314yes—
153C22×C3×C4—24no—
154C2×D12—34no—
155C2×C4×D3—64no—
156C2×C4×D3—68no—
157C2×Dic6—34no—
158C2×Dic6—38no—
159C2×C3×C8C22×D318yes—
160C3×C4⋊C4—24no—
161C3×C4⋊C4C22×D314yes—
162C3×C4⋊C4C22×D318yes—
163C3×C22⋊C4—24no—
164C3×C42C22×D314yes—
165#217—68no—
166#217—68no—
167#213—68no—
168(C2×D3)⋊C4—68no—
169(C2×D3)⋊C4—64no—
170C4⋊Dic3—34no—
171C4⋊Dic3—34no—
172C4⋊Dic3—68no—
173C4⋊Dic3—64no—
174C4⋊Dic3—64no—
175Dic3⋊C4—38no—
176Dic3⋊C4—68no—
177Dic3⋊C4—68no—
178C4×Dic3—38no—
179C4×Dic3—68no—
180C2×C3⋊C8—34no—
181C2×C3⋊C8—34no—
182#204—616no—
183C22×C32—41no—
184C22×C32—41no—
185C22×C32—41no—
186C22×C32C22×D411yescharacteristic
187C2×C3⋊D3—22no—
188C2×C3⋊D3—41no—
189C2×C3⋊D3—41no—
190C32×C4—21no—
191C32×C4—41no—
192C32×C4—42no—
193C32×C4#13512yes—
194C32×C4C2×#4111yescharacteristic
195C32×C42−1+411yescharacteristic
196C3⋊Dic3—22no—
197C3⋊Dic3—22no—
198C3⋊Dic3—42no—
199C3⋊Dic3—41no—
200C2×SD16—92no—
201C2×D8—91no—
202C4⋊Q8—91no—
203C4⋊Q8C2×C3⋊D311yescharacteristic
204#126—182no—
205#125—92no—
206#124—92no—
207C22⋊Q8—181no—
208C22⋊Q8—182no—
209C22⋊Q8—181no—
210C4×Q8—91no—
211C4×Q8—92no—
212C4×D4—92no—
213C4×D4—91no—
214C4×D4C2×C3⋊D311yescharacteristic
215#117—181no—
216C2×C4⋊C4—181no—
217#107—91no—
218#106C2×C3⋊D312yes—
219C4⋊C8—92no—
220C4⋊C8C2×C3⋊D311yescharacteristic
221#103—92no—
222#103—92no—
223#103—92no—
224#102—91no—
225#102—91no—
226#102C2×C3⋊D312yes—
227C4×C8—92no—
228C4×C8—91no—
229C23×C3—24no—
230C22×D3—64no—
231C3×Q8—84no—
232C3×D4—24no—
233C3×D4—24no—
234C2×C3×C4—24no—
235C2×C3×C4—28no—
236C2×C3×C4—48no—
237C2×C3×C4D3×D414yes—
238C2×C3×C4D3×D414yes—
239C2×C3×C4C23×D314yes—
240C2×Dic3—38no—
241C2×Dic3—38no—
242C2×Dic3—68no—
243C2×Dic3—64no—
244D12—38no—
245D12—64no—
246C4×D3—128no—
247C4×D3—248no—
248Dic6—68no—
249Dic6—68no—
250Dic6—68no—
251C3×C8—28no—
252C3⋊C8—64no—
253C3⋊C8—64no—
254C2×C32—81no—
255C2×C32#54811yescharacteristic
256C2×C32C2×#13511yescharacteristic
257C2×C32#57711yescharacteristic
258C3⋊D3—42no—
259C2×Q8—21no—
260C2×Q8—91no—
261C2×Q8—92no—
262C2×D4—91no—
263C2×D4C22×C3⋊D311yescharacteristic
264C22×C4—21no—
265C22×C4—182no—
266C22×C4—181no—
267SD16—184no—
268D8—182no—
269C2×C8—91no—
270C2×C8—91no—
271C2×C8C22×C3⋊D312yes—
272C4⋊C4—21no—
273C4⋊C4—91no—
274C4⋊C4—92no—
275C4⋊C4—91no—
276C4⋊C4—182no—
277C4⋊C4—182no—
278C4⋊C4—182no—
279C4⋊C4—181no—
280C4⋊C4—181no—
281C4⋊C4C22×C3⋊D311yescharacteristic
282C4⋊C4C22×C3⋊D312yes—
283C22⋊C4—21no—
284C22⋊C4—182no—
285C22⋊C4—182no—
286C22⋊C4—182no—
287C22⋊C4—181no—
288C42—92no—
289C42—182no—
290C42C22×C3⋊D311yescharacteristic
291C22×C3—44no—
292C22×C3—44no—
293C22×C3—44no—
294C22×C3C2×D3×D414yes—
295C2×D3—68no—
296C2×D3—124no—
297C2×D3—124no—
298C3×C4—24no—
299C3×C4—44no—
300C3×C4—48no—
301C3×C4#91618yes—
302C3×C4#100714yes—
303C3×C4D3×#4114yes—
304Dic3—68no—
305Dic3—68no—
306Dic3—128no—
307Dic3—124no—
308C32#336011yescharacteristic, complemented, Sylow
309C23—21no—
310C23—181no—
311Q8—81no—
312Q8—182no—
313Q8—182no—
314Q8—182no—
315D4—21no—
316D4—21no—
317D4—92no—
318D4—181no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—42no—
322C2×C4—92no—
323C2×C4—92no—
324C2×C4—182no—
325C2×C4—181no—
326C2×C4—362no—
327C2×C4—722no—
328C2×C4D4×C3⋊D311yescharacteristic
329C2×C4D4×C3⋊D311yescharacteristic
330C2×C4C23×C3⋊D311yescharacteristic
331C8—22no—
332C8—181no—
333C8—181no—
334C2×C3—84no—
335C2×C3#563314yes—
336C2×C3C2×#91614yes—
337C2×C3#577514yes—
338D3—128no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—182no—
343C22—361no—
344C22—361no—
345C22C2×D4×C3⋊D311yescharacteristic
346C4—21no—
347C4—41no—
348C4—42no—
349C4—182no—
350C4—182no—
351C4—362no—
352C4—361no—
353C4#6412512yes—
354C4#6436411yescharacteristic
355C4#41×C3⋊D311yescharacteristic
356C3#8108714yescomplemented
357C2—81no—
358C2—362no—
359C2#1059610411yescharacteristic
360C2C2×#6412511yescharacteristic
361C2#1059624611yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#476C2
socleC22×C32C22×D4
prime radicalC2×#3753C22
hypercenter#476C3⋊D3
hypocenterC32#3360
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #10596201C2semidirect
2. #10596013C2semidirect
3. C32×#476C2semidirect
4. #10592792C2semidirect
6. #10592556C2semidirect
7. #10592551C2semidirect
8. #10592540C2semidirect
9. #10592529C2semidirect
11. #10592467C2semidirect
44. C3×#476D3semidirect
145. #476C3⋊D3semidirect
308. C32#3360semidirect
356. C3#81087semidirect

Maximal subgroups

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

subgroupindex
#105962012
#105960132
C32×#4762
#105927922
C4×#37532
#105925562
#105925512
#105925402
#105925292
#105924862
#105924672
#810873