Finite Group Databasebeta

← #11800885

Subgroups — #11800885

Order 1152.

1557 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic
3C2×#63849C211yesmaximal, characteristic
4C3×C4×C4⋊Dic3C212yesmaximal, complemented
5#10591274C212yesmaximal, complemented
6#10591243C214yesmaximal, complemented
7#10591233C214yesmaximal
8#73750—32nomaximal
9C22×C4×C3⋊D3C2211yescharacteristic
10C22×#624C2212yes—
11C2×C32×C42C2211yescharacteristic
12C2×#3752C2212yes—
13C2×#3750C2212yes—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15#64081C418yescomplemented
16C2×C3×C4⋊Dic3C2212yes—
17C2×C3×C4⋊Dic3C2212yes—
18C2×C3×C4×Dic3C2214yes—
19C2×#3724C2212yes—
20C2×#3722C2212yes—
21C2×Dic32C2214yes—
22C2×Dic32C2212yes—
23#63900C418yescomplemented
24#63849C418yescomplemented
25C3×C3⋊#95C2214yes—
26#63579C2214yes—
27C2×#892—32no—
28C2×D3×C4⋊C4—32no—
29C2×#872—32no—
30C2×#872—61no—
31C3×C4×C4⋊C4—32no—
32Dic3×C4⋊C4—32no—
33Dic3×C4⋊C4—32no—
34C4×(C2×D3)⋊C4—34no—
35C4×C4⋊Dic3D312yescomplemented
36C4×Dic3⋊C4—34no—
37#4666—34no—
38#4649—34no—
39C23×C3⋊D3C2311yescharacteristic
40C22×C32×C4C2312yes—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3C2312yes—
43C22×C3⋊Dic3C2311yescharacteristic
44C2×C4×C3⋊D3C2×C414yes—
45C2×C4×C3⋊D3C2×C414yes—
46C2×C4×C3⋊D3C2×C414yes—
47C22×C3×Dic3C2314yes—
48C22×C3×Dic3C2314yes—
49C2×#624—44no—
50C2×#624C2×C418yes—
51C32×C42C2×C414yescomplemented
52#3752C2×C418yes—
53#3750C2×C418yescomplemented
54C4×C3⋊Dic3C2×C414yescomplemented
55C3×C4⋊Dic3C2×C418yes—
56C3×C4⋊Dic3C2×C418yescomplemented
57C3×C4×Dic3—44no—
58#3724C2×C418yes—
59#3722C2×C418yes—
60Dic32—44no—
61Dic32C2×C418yescomplemented
62#2274—91noSylow
63C22×C4×D3—32no—
64C22×C4×D3—34no—
65C22×C4×D3—61no—
66C2×C3×C4⋊C4—32no—
67C2×C3×C4⋊C4—32no—
68C2×C3×C42—21no—
69C2×C3×C42—34no—
70C2×C3×C42C2×D312yes—
71C2×(C2×D3)⋊C4—32no—
72C2×(C2×D3)⋊C4—32no—
73C2×(C2×D3)⋊C4—34no—
74C2×(C2×D3)⋊C4—62no—
75C2×C4⋊Dic3C2×D312yes—
76C2×C4⋊Dic3C2×D312yes—
77C2×Dic3⋊C4—32no—
78C2×Dic3⋊C4—32no—
79C2×Dic3⋊C4—34no—
80C2×Dic3⋊C4—62no—
81C2×C4×Dic3—32no—
82C2×C4×Dic3—34no—
83C2×C4×Dic3—34no—
84C2×C4×Dic3—34no—
85C2×C4×Dic3—61no—
86C2×C4×Dic3C2×D314yes—
87#892—316no—
88D3×C4⋊C4—316no—
89#872—316no—
90#872—68no—
91C3×#95—34no—
92C3⋊#95—34no—
93C3⋊#95—34no—
94C3⋊#95C2×D314yes—
95C23×C32C2411yescharacteristic
96C22×C3⋊D3—22no—
97C22×C3⋊D3—22no—
98C22×C3⋊D3C22×C412yes—
99C22×C3⋊D3C22×C412yes—
100C22×C3⋊D3C22×C412yes—
101C2×C32×C4—22no—
102C2×C32×C4—22no—
103C2×C32×C4C22×C414yes—
104C2×C32×C4C22×C412yes—
105C2×C32×C4C22×C412yes—
106C2×C32×C4C22×C412yes—
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3C22×C414yes—
110C2×C3⋊Dic3C22×C412yes—
111C2×C3⋊Dic3C22×C412yes—
112C2×C3⋊Dic3C22×C412yes—
113C4×C3⋊D3C42116yescomplemented
114C2×C3×Dic3—24no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3C22×C418yes—
119C2×C3×Dic3C22×C418yes—
120#624—48no—
121C2×#117—91no—
122C2×#117—91no—
123C22×C4⋊C4—91no—
124C4×C4⋊C4—32no—
125C4×C4⋊C4—94no—
126C4×C4⋊C4—92no—
127C4×C22⋊C4—94no—
128C23×D3—32no—
129C23×D3—61no—
130C22×C3×C4—21no—
131C22×C3×C4—22no—
132C22×C3×C4—34no—
133C22×C3×C4—34no—
134C22×C3×C4C22×D312yes—
135C22×C3×C4C22×D312yes—
136C22×C3×C4C22×D312yes—
137C22×Dic3—32no—
138C22×Dic3—32no—
139C22×Dic3—32no—
140C22×Dic3—61no—
141C22×Dic3—62no—
142C22×Dic3C22×D314yes—
143C22×Dic3C22×D314yes—
144C2×C4×D3—38no—
145C2×C4×D3—38no—
146C2×C4×D3—38no—
147C2×C4×D3—316no—
148C2×C4×D3—64no—
149C2×C4×D3—64no—
150C2×C4×D3—64no—
151C2×C4×D3—124no—
152C2×C4×D3—124no—
153C3×C4⋊C4—38no—
154C3×C4⋊C4—38no—
155C3×C42—24no—
156C3×C42—124no—
157C3×C42C4×D318yescomplemented
158(C2×D3)⋊C4—38no—
159(C2×D3)⋊C4—38no—
160(C2×D3)⋊C4—316no—
161(C2×D3)⋊C4—68no—
162C4⋊Dic3C4×D318yes—
163C4⋊Dic3C4×D318yescomplemented
164Dic3⋊C4—38no—
165Dic3⋊C4—38no—
166Dic3⋊C4—316no—
167Dic3⋊C4—68no—
168C4×Dic3—38no—
169C4×Dic3—316no—
170C4×Dic3—44no—
171C4×Dic3—64no—
172C4×Dic3—124no—
173C4×Dic3—124no—
174C22×C32C23×C411yescharacteristic
175C22×C32C23×C411yescharacteristic
176C22×C32C23×C411yescharacteristic
177C22×C32H(5,𝔽2)12yes—
178C22×C322−1+412yes—
179C2×C3⋊D3—22no—
180C2×C3⋊D3—22no—
181C2×C3⋊D3—24no—
182C2×C3⋊D3—24no—
183C2×C3⋊D3C2×C4214yes—
184C32×C4—24no—
185C32×C4C2×C4214yes—
186C3⋊Dic3—24no—
187C3⋊Dic3C2×C4214yes—
188C3×Dic3—28no—
189C3×Dic3—28no—
190C23×C4—92no—
191C23×C4—91no—
192#117—98no—
193#117—98no—
194C2×C4⋊C4—32no—
195C2×C4⋊C4—32no—
196C2×C4⋊C4—98no—
197C2×C4⋊C4—92no—
198C2×C4⋊C4—92no—
199C2×C22⋊C4—92no—
200C2×C22⋊C4—92no—
201C2×C42—34no—
202C2×C42—92no—
203C2×C42—91no—
204C2×C42—94no—
205C2×C42D3211yescharacteristic
206#95—34no—
207#95—94no—
208C23×C3—21no—
209C23×C3C23×D312yes—
210C22×D3—34no—
211C22×D3—34no—
212C22×D3—34no—
213C22×D3—62no—
214C22×D3—62no—
215C22×D3—62no—
216C22×D3—62no—
217C22×D3—62no—
218C22×D3—62no—
219C22×D3—62no—
220C22×D3—122no—
221C22×D3—122no—
222C2×C3×C4—22no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—22no—
228C2×C3×C4—22no—
229C2×C3×C4—24no—
230C2×C3×C4—38no—
231C2×C3×C4—38no—
232C2×C3×C4—42no—
233C2×C3×C4—42no—
234C2×C3×C4—64no—
235C2×C3×C4—64no—
236C2×C3×C4—64no—
237C2×C3×C4—64no—
238C2×C3×C4C2×C4×D314yes—
239C2×C3×C4C2×C4×D314yes—
240C2×C3×C4C2×C4×D314yes—
241C2×C3×C4C2×C4×D314yes—
242C2×C3×C4C2×C4×D314yes—
243C2×Dic3—24no—
244C2×Dic3—24no—
245C2×Dic3—24no—
246C2×Dic3—24no—
247C2×Dic3—34no—
248C2×Dic3—34no—
249C2×Dic3—34no—
250C2×Dic3—34no—
251C2×Dic3—34no—
252C2×Dic3—62no—
253C2×Dic3—62no—
254C2×Dic3—62no—
255C2×Dic3—64no—
256C2×Dic3—62no—
257C2×Dic3—62no—
258C2×Dic3—62no—
259C2×Dic3—62no—
260C2×Dic3—122no—
261C2×Dic3—122no—
262C2×Dic3C2×C4×D318yes—
263C2×Dic3C2×C4×D318yes—
264C4×D3—332no—
265C4×D3—616no—
266C4×D3—1216no—
267C2×C32C22×C4211yescharacteristic
268C2×C32#51811yescharacteristic
269C2×C32#51911yescharacteristic
270C2×C32#52012yes—
271C2×C32#52012yes—
272C3⋊D3—24no—
273C24—91no—
274C22×C4—34no—
275C22×C4—34no—
276C22×C4—98no—
277C22×C4—91no—
278C22×C4—94no—
279C22×C4—94no—
280C22×C4—94no—
281C22×C4—92no—
282C22×C4—364no—
283C22×C4C2×D3212yes—
284C22×C4C2×D3211yescharacteristic
285C4⋊C4—38no—
286C4⋊C4—38no—
287C4⋊C4—98no—
288C4⋊C4—98no—
289C22⋊C4—98no—
290C22⋊C4—98no—
291C42—98no—
292C42—94no—
293C42—124no—
294C42—364no—
295C42#62414yescomplemented
296C22×C3—22no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—22no—
300C22×C3—21no—
301C22×C3C22×C4×D312yes—
302C22×C3C22×C4×D312yes—
303C22×C3C22×C4×D312yes—
304C22×C3#100412yes—
305C22×C3#100712yes—
306C22×C3#100912yes—
307C22×C3#101012yes—
308C2×D3—38no—
309C2×D3—64no—
310C2×D3—64no—
311C2×D3—64no—
312C2×D3—64no—
313C2×D3—64no—
314C2×D3—64no—
315C2×D3—64no—
316C2×D3—122no—
317C2×D3—124no—
318C2×D3—124no—
319C2×D3—122no—
320C3×C4—24no—
321C3×C4—24no—
322C3×C4—24no—
323C3×C4—44no—
324C3×C4—68no—
325C3×C4—68no—
326C3×C4C42×D318yes—
327Dic3—28no—
328Dic3—28no—
329Dic3—38no—
330Dic3—64no—
331Dic3—64no—
332Dic3—64no—
333Dic3—124no—
334C32#227411yescharacteristic, complemented, Sylow
335C23—92no—
336C23—92no—
337C23—92no—
338C23—182no—
339C23—182no—
340C23C22×D3211yescharacteristic
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—38no—
344C2×C4—38no—
345C2×C4—64no—
346C2×C4—64no—
347C2×C4—64no—
348C2×C4—64no—
349C2×C4—92no—
350C2×C4—92no—
351C2×C4—92no—
352C2×C4—916no—
353C2×C4—94no—
354C2×C4—182no—
355C2×C4—182no—
356C2×C4—368no—
357C2×C4C4×D3212yes—
358C2×C4C4×D3212yes—
359C2×C4C2×#62414yes—
360C2×C4C2×#62412yes—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—22no—
364C2×C3—22no—
365C2×C3—21no—
366C2×C3C2×C42×D312yes—
367C2×C3#550412yes—
368C2×C3#552312yes—
369C2×C3#554512yes—
370C2×C3#554612yes—
371C2×C3#557212yes—
372C2×C3#557412yes—
373D3—68no—
374D3—124no—
375C22—94no—
376C22—182no—
377C22—184no—
378C22—184no—
379C22—182no—
380C22#6429712yes—
381C22C2×C4×D3211yescharacteristic
382C22C2×C4×D3211yescharacteristic
383C22#6430712yes—
384C22C22×#62411yescharacteristic
385C4—24no—
386C4—68no—
387C4—68no—
388C4—94no—
389C4—184no—
390C4C4×#62414yes—
391C3—21no—
392C3#7375012yescomplemented
393C2—184no—
394C2#1059384811yescharacteristic
395C2#1059388912yes—
396C2#1059399611yescharacteristic
397C2C2×C4×#62411yescharacteristic
398C2#1059499012yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC2×C32C22×C42
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32#2274
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. C3×C4×C4⋊Dic3C2semidirect
5. #10591274C2semidirect
6. #10591243C2semidirect
15. #64081C4semidirect
23. #63900C4semidirect
24. #63849C4semidirect
35. C4×C4⋊Dic3D3semidirect
51. C32×C42C2×C4semidirect
53. #3750C2×C4semidirect
54. C4×C3⋊Dic3C2×C4semidirect
56. C3×C4⋊Dic3C2×C4semidirect
61. Dic32C2×C4semidirect
113. C4×C3⋊D3C42semidirect
157. C3×C42C4×D3semidirect
163. C4⋊Dic3C4×D3semidirect
295. C42#624semidirect
334. C32#2274semidirect
392. C3#73750semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C2×#639002
C2×#638492
C3×C4×C4⋊Dic32
#105912742
#105912432
#105912332
#737503