Finite Group Databasebeta

← #11774719

Subgroups — #11774719

Order 1152.

575 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×Dic6C211yesmaximal, characteristic
2C4×#3748C211yesmaximal, characteristic
3C3×#4926C211yesmaximal, characteristic
4#10589083C214yesmaximal, complemented
5#71623—31nomaximal
6#70802—31nomaximal
7C22×C3×Dic6C411yescharacteristic
8C2×C32×C42C2211yescharacteristic
9C2×#3748—21no—
10C2×C3×C4⋊Dic3C411yescharacteristic
11C2×C3×Dic3⋊C4—21no—
12C2×C3×C4×Dic3—21no—
13C3×C4×Dic6—21no—
14C3×C4×Dic6—21no—
15C3×C4×Dic6C412yes—
16C3×C4×Dic6C2212yes—
17#63630—21no—
18C4×C3⋊(C3⋊C8)C2212yes—
19C3×#830—21no—
20C3×C4⋊(C3⋊C8)C2212yes—
21C3×#803—21no—
22C2×C3×C4×Q8—31no—
23C2×C4×Dic6D311yescharacteristic
24C3×#432—31no—
25#4926D311yescharacteristic
26C4×#208—31no—
27C4×#208—31no—
28C4×#208—61no—
29#4535—34no—
30#4484—34no—
31C22×C32×C4C2×C411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C3×Dic3—21no—
35C22×C3×Dic3—21no—
36C2×C3×Dic6—21no—
37C2×C3×Dic6—24no—
38C2×C3×Dic6C2×C412yes—
39C32×C42C2×C411yescharacteristic
40C32×C42D411yescharacteristic
41C32×C42D411yescharacteristic
42C32×C42C2311yescharacteristic
43#3748—24no—
44C2×C3⋊(C3⋊C8)—22no—
45C3×C4⋊Dic3—21no—
46C3×C4⋊Dic3C2×C412yes—
47C3×Dic3⋊C4—22no—
48C3×Dic3⋊C4—22no—
49C3×C4×Dic3—22no—
50C3×C4×Dic3—22no—
51C2×C3×C3⋊C8—22no—
52#1491—91noSylow
53C22×C3×Q8—31no—
54C22×Dic6Dic311yescharacteristic
55C3×C4×Q8—32no—
56C3×C4×Q8—32no—
57C3×C4×Q8—61no—
58C3×C4×Q8—61no—
59C2×C3×C4⋊C4—31no—
60C2×C3×C4⋊C4—61no—
61C2×C3×C42—21no—
62C2×C3×C42—61no—
63C2×C3×C42C2×D311yescharacteristic
64C2×C3×C42C2×D311yescharacteristic
65C2×C4⋊Dic3Dic311yescharacteristic
66C2×Dic3⋊C4—21no—
67C2×C4×Dic3—21no—
68C2×#208—62no—
69C2×#208—61no—
70C2×#208—61no—
71C4×Dic6—21no—
72C4×Dic6—21no—
73C4×Dic6Dic312yes—
74C4×Dic6C2×D312yes—
75C3×C4⋊C8—32no—
76C3×C22⋊C8—61no—
77C3×#97—61no—
78#830—21no—
79C4⋊(C3⋊C8)C2×D312yes—
80#803—21no—
81#803—62no—
82#803—61no—
83#803—61no—
84C4×C3⋊C8—32no—
85C4×C3⋊C8—32no—
86C4×C3⋊C8—62no—
87C23×C32C22⋊C411yescharacteristic
88C2×C32×C4—22no—
89C2×C32×C4—22no—
90C2×C32×C4—22no—
91C2×C32×C4C22⋊C411yescharacteristic
92C2×C32×C4C22⋊C411yescharacteristic
93C2×C32×C4C22⋊C411yescharacteristic
94C2×C32×C4C22×C411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C3×Dic3—24no—
98C2×C3×Dic3—22no—
99C2×C3×Dic3—22no—
100C2×C3×Dic3—42no—
101C3×Dic6—24no—
102C3×Dic6—22no—
103C3×Dic6M1614yescomplemented
104C3⋊(C3⋊C8)—24no—
105C3×C3⋊C8—42no—
106C2×C4×Q8—31no—
107#432—31no—
108C4×M16—91no—
109Q8⋊C8—94no—
110C2×C3×Q8—32no—
111C2×C3×Q8—64no—
112C2×C3×Q8—61no—
113C22×C3×C4—21no—
114C22×C3×C4—21no—
115C22×C3×C4—21no—
116C22×C3×C4—61no—
117C22×C3×C4—61no—
118C22×C3×C4C4×D311yescharacteristic
119C22×C3×C4D1211yescharacteristic
120C22×C3×C4C2×Dic311yescharacteristic
121C22×C3×C4#6711yescharacteristic
122C22×C3×C4#6711yescharacteristic
123C22×C3×C4#6711yescharacteristic
124C22×Dic3—21no—
125C22×Dic3—21no—
126C2×Dic6—21no—
127C2×Dic6—24no—
128C2×Dic6C2×Dic312yes—
129C2×C3×C8—62no—
130C3×C4⋊C4—32no—
131C3×C4⋊C4—62no—
132C3×C4⋊C4—61no—
133C3×C4⋊C4—62no—
134C3×C42—21no—
135C3×C42—21no—
136C3×C42—21no—
137C3×C42—21no—
138C3×C42—62no—
139C3×C42—62no—
140C3×C42C4×D311yescharacteristic
141C3×C42D1211yescharacteristic
142C3×C42C2×Dic311yescharacteristic
143C3×C42#6711yescharacteristic
144C3×C42#6711yescharacteristic
145C3×C42#6711yescharacteristic
146C3×C42C22×D311yescharacteristic
147C3×C42C22×D311yescharacteristic
148C4⋊Dic3—21no—
149C4⋊Dic3C2×Dic312yes—
150Dic3⋊C4—22no—
151Dic3⋊C4—22no—
152C4×Dic3—22no—
153C4×Dic3—22no—
154#208—68no—
155#208—64no—
156#208—64no—
157C2×C3⋊C8—22no—
158C2×C3⋊C8—64no—
159C2×C3⋊C8—62no—
160C2×C3⋊C8—62no—
161C22×C32—21no—
162C22×C32—21no—
163C22×C32#10412yes—
164C22×C32C2×C22⋊C411yescharacteristic
165C32×C4—21no—
166C32×C4—21no—
167C32×C4—21no—
168C32×C4—21no—
169C32×C4C2×M1612yes—
170C32×C4#13712yes—
171C3×Dic3—24no—
172C3×Dic3—42no—
173C22×Q8—31no—
174C2×M16—181no—
175C4×Q8—32no—
176C4×Q8—32no—
177C4×Q8—61no—
178C4×Q8—61no—
179C2×C4⋊C4—31no—
180C2×C4⋊C4—61no—
181C2×C42—61no—
182C2×C42D3211yescharacteristic
183C4⋊C8—32no—
184C22⋊C8—61no—
185#97—61no—
186#97—181no—
187C4×C8—92no—
188C23×C3—21no—
189C23×C3(C2×D3)⋊C411yescharacteristic
190C23×C3#21711yescharacteristic
191C3×Q8—34no—
192C3×Q8—64no—
193C3×Q8—62no—
194C2×C3×C4—24no—
195C2×C3×C4—22no—
196C2×C3×C4—22no—
197C2×C3×C4—22no—
198C2×C3×C4—22no—
199C2×C3×C4—22no—
200C2×C3×C4—22no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—42no—
208C2×C3×C4—42no—
209C2×C3×C4—64no—
210C2×C3×C4—62no—
211C2×C3×C4—62no—
212C2×C3×C4—122no—
213C2×C3×C4(C2×D3)⋊C411yescharacteristic
214C2×C3×C4(C2×D3)⋊C411yescharacteristic
215C2×C3×C4(C2×D3)⋊C411yescharacteristic
216C2×C3×C4#21711yescharacteristic
217C2×C3×C4#21711yescharacteristic
218C2×C3×C4#21711yescharacteristic
219C2×C3×C4C2×C4×D311yescharacteristic
220C2×C3×C4C2×D1211yescharacteristic
221C2×C3×C4C22×Dic311yescharacteristic
222C2×C3×C4C2×#6711yescharacteristic
223C2×C3×C4C2×#6711yescharacteristic
224C2×C3×C4C2×#6711yescharacteristic
225C2×Dic3—24no—
226C2×Dic3—22no—
227C2×Dic3—22no—
228C2×Dic3—42no—
229Dic6—24no—
230Dic6—22no—
231Dic6#20814yescomplemented
232C3×C8—122no—
233C3⋊C8—42no—
234C3⋊C8—68no—
235C3⋊C8—64no—
236C3⋊C8—64no—
237C2×C32—22no—
238C2×C32#40711yescharacteristic
239C2×C32#41911yescharacteristic
240C2×C32C2×#10411yescharacteristic
241C2×Q8—32no—
242C2×Q8—64no—
243C2×Q8—61no—
244C22×C4—61no—
245C22×C4—61no—
246C22×C4D3×Dic311yescharacteristic
247C22×C4#62511yescharacteristic
248C22×C4#62611yescharacteristic
249M16—184no—
250C2×C8—62no—
251C2×C8—182no—
252C4⋊C4—32no—
253C4⋊C4—61no—
254C4⋊C4—62no—
255C4⋊C4—62no—
256C42—62no—
257C42—62no—
258C42D3×Dic311yescharacteristic
259C42#62511yescharacteristic
260C42#62611yescharacteristic
261C42C2×D3211yescharacteristic
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—22no—
267C22×C3—21no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3#82512yes—
271C22×C3#83712yes—
272C22×C3C2×(C2×D3)⋊C411yescharacteristic
273C22×C3C2×#21711yescharacteristic
274C3×C4—22no—
275C3×C4—22no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—22no—
285C3×C4—22no—
286C3×C4—41no—
287C3×C4—41no—
288C3×C4—64no—
289C3×C4—122no—
290C3×C4D3×M1612yes—
291C3×C4C2×#20812yes—
292C3×C4#94212yes—
293C3×C4#95112yes—
294Dic3—24no—
295Dic3—42no—
296C32#149111yescharacteristic, complemented, Sylow
297C23(C2×D3)⋊Dic311yescharacteristic
298Q8—34no—
299Q8—64no—
300Q8—62no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—64no—
305C2×C4—62no—
306C2×C4—62no—
307C2×C4—122no—
308C2×C4(C2×D3)⋊Dic311yescharacteristic
309C2×C4(C2×D3)⋊Dic311yescharacteristic
310C2×C4(C2×D3)⋊Dic311yescharacteristic
311C2×C4C2×D3×Dic311yescharacteristic
312C2×C4C2×#62511yescharacteristic
313C2×C4C2×#62611yescharacteristic
314C8—122no—
315C8—184no—
316C2×C3—22no—
317C2×C3—22no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—42no—
322C2×C3#500411yescharacteristic
323C2×C3#512611yescharacteristic
324C2×C3C2×#82511yescharacteristic
325C2×C3#520711yescharacteristic
326C2×C3#522511yescharacteristic
327C2×C3C2×#83711yescharacteristic
328C22—21no—
329C22—21no—
330C22#6356812yes—
331C22C2×(C2×D3)⋊Dic311yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—64no—
337C4—122no—
338C4D3×#20812yes—
339C4#6382712yes—
340C3—21no—
341C3#7080211yescharacteristic, complemented
342C3#7162311yescharacteristic, complemented
343C2—22no—
344C2#1059106911yescharacteristic
345C2#1059109911yescharacteristic
346C2C2×#6356811yescharacteristic
subgroupG/H
centerC2×C4C2×#625
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC32×C42C23
hypercenterC2×C42D32
hypocenterC32#1491
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. #10589083C2semidirect
103. C3×Dic6M16semidirect
231. Dic6#208semidirect
296. C32#1491semidirect
341. C3#70802semidirect
342. C3#71623semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×Dic62
C4×#37482
C3×#49262
#105890832
#716233
#708023