Finite Group Databasebeta

← #11858879

Subgroups — #11858879

Order 1152.

855 conjugacy classes of subgroups.

The subgroup lattice has 421 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63855C211yesmaximal, characteristic
2M16×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C3×#5126C211yesmaximal, characteristic
4C3×#5118C211yesmaximal, characteristic, complemented
5#10591115C211yesmaximal, characteristic, complemented
6#10591069C211yesmaximal, characteristic
7#10591060C211yesmaximal, characteristic, complemented
8#10590699C214yesmaximal, complemented
9#10590698C214yesmaximal, complemented
10#79039—31nomaximal
11#78620—31nomaximal
12C22×C3×C4×D3C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C2×Dic3⋊Dic3C412yes—
20C2×(C2×D3)⋊Dic3C412yes—
21#63855C414yes—
22#63855C2212yes—
23#63855C2212yes—
24#63642C2212yescomplemented
25C8×C3⋊Dic3C2212yescomplemented
26C3×(C2×D3)⋊C8C2214yes—
27C3×Dic3⋊C8C2214yescomplemented
28Dic3⋊(C3⋊C8)C2214yescomplemented
29(C2×D3)⋊(C3⋊C8)C2214yes—
30#63555C2212yescomplemented
31#63553C2212yescomplemented
32C2×#926—31no—
33C2×#872—31no—
34C3×#423—31no—
35C3×#407—31no—
36#5207—31no—
37#5126—31no—
38#5126D311yescharacteristic
39#5118—31no—
40#5118D311yescharacteristic, complemented
41Dic3×M16—31no—
42Dic3×M16—31no—
43Dic3×M16—31no—
44Dic3×M16—31no—
45Dic3×M16—61no—
46#4924—31no—
47#4840—34no—
48#4840—34no—
49#4720—34no—
50#4720—34no—
51C23×C3×D3C2×C411yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3C2×C412yes—
54C22×C3×Dic3C2×C411yescharacteristic
55C22×C3×Dic3C2×C412yes—
56C2×C3×C4×D3—22no—
57C2×C3×C4×D3—22no—
58C2×C3×C4×D3C2×C412yes—
59C2×C3×C4×D3C2312yes—
60C32×M16—22no—
61C2×C32×C8C2312yes—
62C4×C3⋊Dic3C2×C412yes—
63C4×C3⋊Dic3C2311yescharacteristic
64C4×C3⋊Dic3C2311yescharacteristic
65#3748—22no—
66C2×C3⋊(C3⋊C8)C2312yes—
67C3×C4×Dic3C2×C412yes—
68C3×C4×Dic3C2312yes—
69C3×#208—22no—
70C3×#208—22no—
71C2×C3×C3⋊C8C2312yes—
72C2×C3×C3⋊C8C2312yes—
73Dic3⋊Dic3C2×C414yes—
74Dic3⋊Dic3C2×C414yes—
75(C2×D3)⋊Dic3C2×C414yes—
76(C2×D3)⋊Dic3C2×C414yes—
77#2921—91noSylow
78C23×C3×C4—31no—
79C22×C4×D3C2×D311yescharacteristic
80C2×C3×M16—21no—
81C2×C3×M16—31no—
82C2×C3×M16—31no—
83C2×C3×M16C2×D311yescharacteristic
84C2×C3×M16C2×D311yescharacteristic
85C2×C3×C42—31no—
86C2×#217—32no—
87C2×(C2×D3)⋊C4—32no—
88#926—34no—
89#926—32no—
90#926—32no—
91C2×C4⋊Dic3—32no—
92C2×Dic3⋊C4—32no—
93C2×C4×Dic3—31no—
94C2×C4×Dic3—31no—
95C2×C4×Dic3—61no—
96C2×C4×Dic3C2×D311yescharacteristic
97C2×#208—31no—
98C2×#208—31no—
99C2×#208—61no—
100C2×#208C2×D311yescharacteristic
101C2×#208C2×D311yescharacteristic
102#872—34no—
103#872—32no—
104#872—32no—
105C3×C4⋊C8—34no—
106C3×C22⋊C8—34no—
107#830—34no—
108(C2×D3)⋊C8—34no—
109(C2×D3)⋊C8C2×D314yes—
110#815—32no—
111#815—32no—
112#815—32no—
113#815—32no—
114#815—62no—
115Dic3⋊C8—34no—
116Dic3⋊C8C2×D314yescomplemented
117C8×Dic3—32no—
118C8×Dic3—32no—
119C8×Dic3—32no—
120C8×Dic3—32no—
121C8×Dic3—62no—
122C4⋊(C3⋊C8)—34no—
123C23×C32C22×C411yescharacteristic
124C22×C3×D3—22no—
125C22×C3×D3—42no—
126C22×C3×D3C22×C412yes—
127C2×C32×C4C22×C411yescharacteristic
128C2×C32×C4#4112yes—
129C2×C32×C4#4112yes—
130C2×C32×C4C2411yescharacteristic
131C2×C3⋊Dic3—42no—
132C2×C3⋊Dic3C22×C412yes—
133C2×C3⋊Dic3C22×C412yes—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—42no—
136C2×C3×Dic3C22×C414yes—
137C2×C3×Dic3C22×C412yes—
138C3×C4×D3—24no—
139C3×C4×D3—22no—
140C3×C4×D3—22no—
141C32×C8—22no—
142C3⋊(C3⋊C8)—22no—
143C3×C3⋊C8—22no—
144C3×C3⋊C8—22no—
145C2×#117—91no—
146#433—94no—
147#433—94no—
148#423—31no—
149#423—91no—
150#407—31no—
151#407—91no—
152C4×M16—91no—
153C4×M16—91no—
154C24×C3—31no—
155C23×D3C4×D311yescharacteristic
156C22×C3×C4—21no—
157C22×C3×C4—31no—
158C22×C3×C4—32no—
159C22×C3×C4—32no—
160C22×C3×C4—32no—
161C22×C3×C4—62no—
162C22×C3×C4—62no—
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C22×D311yescharacteristic
165C22×Dic3—32no—
166C22×Dic3—32no—
167C22×Dic3—62no—
168C22×Dic3C4×D311yescharacteristic
169C22×Dic3C4×D312yes—
170C2×C4×D3—22no—
171C2×C4×D3—22no—
172C2×C4×D3C4×D312yes—
173C2×C4×D3C22×D312yes—
174C3×M16—24no—
175C3×M16—22no—
176C3×M16—22no—
177C3×M16—62no—
178C3×M16—62no—
179C2×C3×C8—22no—
180C2×C3×C8—32no—
181C2×C3×C8—32no—
182C2×C3×C8C22×D312yes—
183C2×C3×C8C22×D312yes—
184C3×C42—32no—
185C3×C42—32no—
186#217—34no—
187#217—34no—
188(C2×D3)⋊C4—34no—
189(C2×D3)⋊C4—34no—
190C4⋊Dic3—34no—
191C4⋊Dic3—34no—
192Dic3⋊C4—34no—
193Dic3⋊C4—34no—
194C4×Dic3—32no—
195C4×Dic3—32no—
196C4×Dic3—31no—
197C4×Dic3—31no—
198C4×Dic3—31no—
199C4×Dic3—31no—
200C4×Dic3—61no—
201C4×Dic3—61no—
202C4×Dic3—62no—
203C4×Dic3C4×D312yes—
204C4×Dic3C22×D312yes—
205#208—22no—
206#208—22no—
207#208—64no—
208#208—62no—
209#208—62no—
210C2×C3⋊C8—32no—
211C2×C3⋊C8—32no—
212C2×C3⋊C8—62no—
213C2×C3⋊C8C22×D312yes—
214C2×C3⋊C8C22×D312yes—
215C22×C32—22no—
216C22×C32#11712yes—
217C22×C32C23×C411yescharacteristic
218C2×C3×D3—22no—
219C2×C3×D3—24no—
220C2×C3×D3—44no—
221C32×C4#11712yes—
222C32×C4C2×#4111yescharacteristic
223C32×C4C2×#4111yescharacteristic
224C3⋊Dic3—22no—
225C3⋊Dic3—22no—
226C3×Dic3—22no—
227C3×Dic3—24no—
228C23×C4—31no—
229C2×M16—31no—
230C2×M16—31no—
231C2×M16—91no—
232C2×M16D3211yescharacteristic
233#117—94no—
234#117—92no—
235#117—92no—
236C2×C4⋊C4—92no—
237C2×C22⋊C4—92no—
238C2×C42—31no—
239C2×C42—91no—
240C4⋊C8—34no—
241C4⋊C8—94no—
242C22⋊C8—34no—
243C22⋊C8—94no—
244#97—92no—
245#97—92no—
246C4×C8—92no—
247C4×C8—92no—
248C23×C3—21no—
249C23×C3—32no—
250C23×C3—62no—
251C23×C3—122no—
252C23×C3C2×C4×D311yescharacteristic
253C23×C3C2×C4×D311yescharacteristic
254C22×D3—22no—
255C22×D3—42no—
256C22×D3C2×C4×D312yes—
257C2×C3×C4—21no—
258C2×C3×C4—22no—
259C2×C3×C4—21no—
260C2×C3×C4—22no—
261C2×C3×C4—34no—
262C2×C3×C4—32no—
263C2×C3×C4—62no—
264C2×C3×C4—64no—
265C2×C3×C4—62no—
266C2×C3×C4—62no—
267C2×C3×C4—122no—
268C2×C3×C4C2×C4×D311yescharacteristic
269C2×C3×C4C2×C4×D311yescharacteristic
270C2×C3×C4#23712yes—
271C2×C3×C4#23712yes—
272C2×C3×C4#23712yes—
273C2×C3×C4#23912yes—
274C2×C3×C4C23×D311yescharacteristic
275C2×C3×C4C23×D311yescharacteristic
276C2×Dic3—22no—
277C2×Dic3—32no—
278C2×Dic3—32no—
279C2×Dic3—32no—
280C2×Dic3—32no—
281C2×Dic3—42no—
282C2×Dic3—62no—
283C2×Dic3—62no—
284C2×Dic3—122no—
285C2×Dic3—122no—
286C2×Dic3—124no—
287C2×Dic3C2×C4×D314yes—
288C2×Dic3C2×C4×D312yes—
289C4×D3—24no—
290C4×D3—22no—
291C4×D3—22no—
292C3×C8—24no—
293C3×C8—22no—
294C3×C8—22no—
295C3×C8—62no—
296C3×C8—62no—
297C3⋊C8—22no—
298C3⋊C8—22no—
299C3⋊C8—64no—
300C3⋊C8—62no—
301C3⋊C8—62no—
302C2×C32—22no—
303C2×C32C2×#11711yescharacteristic
304C2×C32#56812yes—
305C3×D3—42no—
306C24—31no—
307C22×C4—31no—
308C22×C4—32no—
309C22×C4—32no—
310C22×C4—32no—
311C22×C4—62no—
312C22×C4—62no—
313C22×C4—92no—
314C22×C4C2×D3211yescharacteristic
315M16—22no—
316M16—62no—
317M16—62no—
318M16—182no—
319C2×C8—32no—
320C2×C8—32no—
321C2×C8—92no—
322C2×C8C2×D3212yes—
323C4⋊C4—94no—
324C4⋊C4—94no—
325C22⋊C4—94no—
326C22⋊C4—94no—
327C42—32no—
328C42—32no—
329C42—91no—
330C42—91no—
331C42—92no—
332C22×C3—22no—
333C22×C3—22no—
334C22×C3—21no—
335C22×C3—22no—
336C22×C3—42no—
337C22×C3—64no—
338C22×C3—62no—
339C22×C3—124no—
340C22×C3#87712yes—
341C22×C3#89212yes—
342C22×C3C22×C4×D311yescharacteristic
343C22×C3C22×C4×D311yescharacteristic
344C2×D3—22no—
345C2×D3—24no—
346C2×D3—44no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—22no—
350C3×C4—64no—
351C3×C4—62no—
352C3×C4#87712yes—
353C3×C4#89212yes—
354C3×C4C2×#23711yescharacteristic
355C3×C4C2×#23711yescharacteristic
356C3×C4C2×#23711yescharacteristic
357C3×C4C2×#23911yescharacteristic
358Dic3—22no—
359Dic3—24no—
360Dic3—64no—
361Dic3—62no—
362Dic3—62no—
363Dic3—62no—
364Dic3—62no—
365Dic3—122no—
366C32#292111yescharacteristic, complemented, Sylow
367C23—32no—
368C23—62no—
369C23—122no—
370C23C4×D3211yescharacteristic
371C2×C4—34no—
372C2×C4—32no—
373C2×C4—62no—
374C2×C4—62no—
375C2×C4—62no—
376C2×C4—64no—
377C2×C4—92no—
378C2×C4—92no—
379C2×C4—122no—
380C2×C4—362no—
381C2×C4#379612yes—
382C2×C4C4×D3211yescharacteristic
383C2×C4#380512yes—
384C2×C4C22×D3211yescharacteristic
385C8—22no—
386C8—62no—
387C8—62no—
388C8—182no—
389C2×C3—22no—
390C2×C3—22no—
391C2×C3—21no—
392C2×C3—22no—
393C2×C3—42no—
394C2×C3—122no—
395C2×C3C2×#87711yescharacteristic
396C2×C3C2×#89211yescharacteristic
397C2×C3#574512yes—
398C2×C3#574512yes—
399D3—42no—
400C22—22no—
401C22—62no—
402C22—64no—
403C22—124no—
404C22#6387812yes—
405C22C2×C4×D3211yescharacteristic
406C4—62no—
407C4—64no—
408C4—182no—
409C4—182no—
410C4#6387812yes—
411C4C2×#379611yescharacteristic
412C4C2×#380511yescharacteristic
413C3—21no—
414C3#7862011yescharacteristic, complemented
415C3#7903911yescharacteristic, complemented
416C2—22no—
417C2—122no—
418C2#1059472212yes—
419C2C2×#6387811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×M16C22
prime radicalC23×C3×D3C2×C4
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2921
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. M16×C3⋊Dic3C2semidirect
4. C3×#5118C2semidirect
5. #10591115C2semidirect
7. #10591060C2semidirect
8. #10590699C2semidirect
9. #10590698C2semidirect
24. #63642C22semidirect
25. C8×C3⋊Dic3C22semidirect
27. C3×Dic3⋊C8C22semidirect
28. Dic3⋊(C3⋊C8)C22semidirect
30. #63555C22semidirect
31. #63553C22semidirect
40. #5118D3semidirect
116. Dic3⋊C8C2×D3semidirect
366. C32#2921semidirect
414. C3#78620semidirect
415. C3#79039semidirect

Maximal subgroups

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

subgroupindex
C2×#638552
M16×C3⋊Dic32
C3×#51262
C3×#51182
#105911152
#105910692
#105910602
#105906992
#105906982
#790393
#786203