Finite Group Databasebeta

← #11775907

Subgroups — #11775907

Order 1152.

454 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5688C211yesmaximal, characteristic
2D3×#803C211yesmaximal, characteristic
3#10590262C211yesmaximal, characteristic
4#10589409C211yesmaximal, characteristic, complemented
5C3×#4543C211yesmaximal, characteristic, complemented
6#10589088C211yesmaximal, characteristic, complemented
7#10589088C211yesmaximal, characteristic, complemented
8#71822—31nomaximal
9#68365—31nomaximal
10C32×#125C2211yescharacteristic
11C3×#896—21no—
12C3×#896—21no—
13C3×#892C411yescharacteristic
14C3×#892C411yescharacteristic
15C3×#888C411yescharacteristic
16C3×#888C411yescharacteristic
17C3×#887—21no—
18C3×#887—21no—
19C3×C42×D3C2211yescharacteristic
20C3×#870C2211yescharacteristic
21C2×D3×C3⋊C8—21no—
22#63630C2211yescharacteristic
23#63630C2211yescharacteristic
24C3×#803C2211yescharacteristic
25C3×#803C2211yescharacteristic
26Dic3⋊(C3⋊C8)—21no—
27(C2×D3)⋊(C3⋊C8)—21no—
28#63554—21no—
29C3×#533—31no—
30#5688D311yescharacteristic
31#4926—31no—
32C2×#803—31no—
33#4705—31no—
34D3×#97—31no—
35C3×#330—31no—
36#4543—31no—
37#4543—31no—
38#4543—31no—
39#4543—31no—
40#4543—61no—
41#4543D311yescharacteristic, complemented
42#4465—31no—
43#4465—31no—
44C2×C3×C4×D3C2×C411yescharacteristic
45C2×C3×C4×D3D411yescharacteristic
46C2×C3×C4×D3D411yescharacteristic
47C2×C3×Dic6—21no—
48C2×C3×Dic6—21no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4—21no—
51C32×C4⋊C4C2×C411yescharacteristic
52C32×C4⋊C4C2×C411yescharacteristic
53C32×C42C2311yescharacteristic
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×(C2×D3)⋊C4—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3C2×C411yescharacteristic
59C3×C4⋊Dic3C2×C411yescharacteristic
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×C4×Dic3—21no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3C2×C411yescharacteristic
67C3×C4×Dic3D411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71D3×C3⋊C8—24no—
72#1531—91noSylow
73C3×C4⋊Q8—31no—
74C3×C4⋊Q8—31no—
75C3×#125—21no—
76C3×#125—31no—
77C3×#125C2×D311yescharacteristic
78C3×#125C2×D311yescharacteristic
79C3×C22⋊Q8—61no—
80C3×C22⋊Q8—61no—
81C3×C4×Q8—61no—
82C3×C4×Q8—61no—
83C3×#117—31no—
84C3×#117—31no—
85C2×C3×C42—31no—
86C22×C3⋊C8—61no—
87C2×D3×C8—61no—
88#896—21no—
89#896—21no—
90#892Dic311yescharacteristic
91#892Dic311yescharacteristic
92#888Dic311yescharacteristic
93#888Dic311yescharacteristic
94#887—21no—
95#887—21no—
96C42×D3C2×D311yescharacteristic
97#870C2×D311yescharacteristic
98C3×#97—31no—
99C3×#97—31no—
100#830—61no—
101(C2×D3)⋊C8—61no—
102#815—61no—
103Dic3⋊C8—61no—
104C4⋊(C3⋊C8)—61no—
105#803—31no—
106#803—31no—
107#803—31no—
108#803—31no—
109#803—61no—
110#803—61no—
111#803—61no—
112#803C2×D311yescharacteristic
113#803C2×D311yescharacteristic
114C22×C3×D3C22⋊C411yescharacteristic
115C2×C32×C4—21no—
116C2×C32×C4—21no—
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3C22⋊C411yescharacteristic
123C2×C3×Dic3C22⋊C411yescharacteristic
124C2×C3×Dic3C22⋊C411yescharacteristic
125C3×C4×D3—22no—
126C3×C4×D3—22no—
127C3×C4×D3—41no—
128C3×Dic6—42no—
129C3×Dic6—42no—
130C3⋊(C3⋊C8)—22no—
131C3⋊(C3⋊C8)—41no—
132C3×C3⋊C8—22no—
133C3×C3⋊C8—41no—
134#533—31no—
135#432—91no—
136C2×#97—91no—
137#330—31no—
138#330—91no—
139#330—91no—
140#330—91no—
141C2×C3×Q8—61no—
142C2×C3×Q8—61no—
143C22×C3×C4—31no—
144C22×C3×C4—31no—
145C22×C3×C4—31no—
146C2×C4×D3C2×Dic311yescharacteristic
147C2×C4×D3#6711yescharacteristic
148C2×C4×D3#6711yescharacteristic
149C2×Dic6—21no—
150C2×Dic6—21no—
151C2×C3×C8—61no—
152C2×C3×C8—61no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4—31no—
160C3×C4⋊C4—31no—
161C3×C4⋊C4—41no—
162C3×C4⋊C4—41no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4—61no—
165C3×C4⋊C4—61no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4C4×D311yescharacteristic
168C3×C4⋊C4C4×D311yescharacteristic
169C3×C4⋊C4C2×Dic311yescharacteristic
170C3×C4⋊C4C2×Dic311yescharacteristic
171C3×C22⋊C4—61no—
172C3×C22⋊C4—61no—
173C3×C42—21no—
174C3×C42—31no—
175C3×C42—31no—
176C3×C42—31no—
177C3×C42—61no—
178C3×C42—61no—
179C3×C42C22×D311yescharacteristic
180C3×C42C22×D311yescharacteristic
181(C2×D3)⋊C4—21no—
182(C2×D3)⋊C4—21no—
183C4⋊Dic3C2×Dic311yescharacteristic
184C4⋊Dic3C2×Dic311yescharacteristic
185Dic3⋊C4—21no—
186Dic3⋊C4—21no—
187Dic3⋊C4—21no—
188Dic3⋊C4—21no—
189C4×Dic3—21no—
190C4×Dic3—21no—
191C4×Dic3C2×Dic311yescharacteristic
192C4×Dic3#6711yescharacteristic
193C4×Dic3#6711yescharacteristic
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—64no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—61no—
199C2×C3⋊C8—61no—
200C2×C3⋊C8—61no—
201C2×C3⋊C8—121no—
202C2×C3⋊C8—121no—
203D3×C8—64no—
204C22×C32C2×C22⋊C411yescharacteristic
205C2×C3×D3—21no—
206C2×C3×D3—21no—
207C2×C3×D3#10112yes—
208C32×C4—21no—
209C32×C4—21no—
210C32×C4—21no—
211C32×C4—41no—
212C32×C4—41no—
213C3×Dic3—21no—
214C3×Dic3—21no—
215C3×Dic3—41no—
216C3×Dic3—41no—
217C3×Dic3#10412yes—
218C22×C8—181no—
219C4⋊Q8—31no—
220C4⋊Q8—31no—
221#125—31no—
222#125D3211yescharacteristic
223C22⋊Q8—61no—
224C22⋊Q8—61no—
225C4×Q8—61no—
226C4×Q8—61no—
227#117—31no—
228#117—31no—
229C2×C42—31no—
230C4⋊C8—181no—
231C22⋊C8—181no—
232#97—31no—
233#97—31no—
234#97—91no—
235#97—91no—
236#97—181no—
237C23×C3—31no—
238C22×D3#21711yescharacteristic
239C3×Q8—122no—
240C3×Q8—122no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—31no—
249C2×C3×C4—31no—
250C2×C3×C4—31no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—62no—
254C2×C3×C4—62no—
255C2×C3×C4—61no—
256C2×C3×C4—61no—
257C2×C3×C4—121no—
258C2×C3×C4C2×C4×D311yescharacteristic
259C2×C3×C4D3×D411yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4C22×Dic311yescharacteristic
262C2×C3×C4C2×#6711yescharacteristic
263C2×C3×C4C2×#6711yescharacteristic
264C2×Dic3—21no—
265C2×Dic3—21no—
266C2×Dic3#21711yescharacteristic
267C2×Dic3#21711yescharacteristic
268C2×Dic3#21711yescharacteristic
269C4×D3—22no—
270C4×D3—22no—
271C4×D3—41no—
272Dic6—42no—
273Dic6—42no—
274C3×C8—62no—
275C3×C8—121no—
276C3⋊C8—22no—
277C3⋊C8—41no—
278C3⋊C8—62no—
279C3⋊C8—62no—
280C3⋊C8—122no—
281C3⋊C8—121no—
282C3⋊C8—121no—
283C3⋊C8—122no—
284C2×C32C2×#10111yescharacteristic
285C2×C32C2×#10411yescharacteristic
286C2×C32#42111yescharacteristic
287C3×D3—22no—
288C2×Q8—61no—
289C2×Q8—61no—
290C22×C4—31no—
291C22×C4—31no—
292C22×C4—31no—
293C2×C8—61no—
294C2×C8—61no—
295C2×C8—184no—
296C2×C8—181no—
297C2×C8—181no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—31no—
301C4⋊C4—31no—
302C4⋊C4—61no—
303C4⋊C4—61no—
304C4⋊C4—61no—
305C4⋊C4—61no—
306C4⋊C4D3×Dic311yescharacteristic
307C4⋊C4D3×Dic311yescharacteristic
308C22⋊C4—61no—
309C22⋊C4—61no—
310C42—31no—
311C42—31no—
312C42—31no—
313C42—61no—
314C42—61no—
315C42C2×D3211yescharacteristic
316C22×C3—21no—
317C22×C3—32no—
318C22×C3—61no—
319C22×C3—61no—
320C22×C3D3×C22⋊C411yescharacteristic
321C22×C3C2×#21711yescharacteristic
322C2×D3—21no—
323C2×D3—21no—
324C2×D3#83612yes—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—32no—
332C3×C4—41no—
333C3×C4—41no—
334C3×C4—41no—
335C3×C4—41no—
336C3×C4—41no—
337C3×C4—41no—
338C3×C4—41no—
339C3×C4—61no—
340C3×C4—61no—
341C3×C4—81no—
342C3×C4—81no—
343C3×C4—121no—
344C3×C4—121no—
345Dic3—21no—
346Dic3—21no—
347Dic3—41no—
348Dic3—41no—
349Dic3#83712yes—
350C32#153111yescharacteristic, complemented, Sylow
351C23—31no—
352Q8—122no—
353Q8—122no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—31no—
357C2×C4—31no—
358C2×C4—31no—
359C2×C4—62no—
360C2×C4—62no—
361C2×C4—61no—
362C2×C4—61no—
363C2×C4—121no—
364C2×C4C2×D3×Dic311yescharacteristic
365C2×C4D3×#6711yescharacteristic
366C2×C4D3×#6711yescharacteristic
367C8—62no—
368C8—121no—
369C8—182no—
370C8—361no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—62no—
375C2×C3D3×#10111yescharacteristic
376C2×C3D3×#10411yescharacteristic
377C2×C3#482111yescharacteristic
378C2×C3C2×#83611yescharacteristic
379C2×C3C2×#83711yescharacteristic
380C2×C3#523611yescharacteristic
381D3—22no—
382C22—32no—
383C22—61no—
384C22—61no—
385C22D3×#21711yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—32no—
390C4—41no—
391C4—41no—
392C4—61no—
393C4—61no—
394C4—121no—
395C4—121no—
396C3—21no—
397C3#6836511yescharacteristic, complemented
398C3#7182211yescharacteristic, complemented
399C2—62no—
400C2D3×#83611yescharacteristic
401C2D3×#83711yescharacteristic
402C2#1059167011yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×#125C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D3C22⋊C4
cosocleC32×C42C23
hypercenter#125D32
hypocenterC32#1531
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
4. #10589409C2semidirect
5. C3×#4543C2semidirect
6. #10589088C2semidirect
7. #10589088C2semidirect
41. #4543D3semidirect
350. C32#1531semidirect
397. C3#68365semidirect
398. C3#71822semidirect

Maximal subgroups

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

subgroupindex
C3×#56882
D3×#8032
#105902622
#105894092
C3×#45432
#105890882
#718223
#683653