Finite Group Databasebeta

← #11787478

Subgroups — #11787478

Order 1152.

1014 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3746C211yesmaximal, characteristic
2C2×#64096C211yesmaximal, characteristic
3#10592672C211yesmaximal, characteristic
4C2×#63637C211yesmaximal, characteristic
5C2×#63637C211yesmaximal, characteristic
6C32×#340C211yesmaximal, characteristic
7#10589416C211yesmaximal, characteristic
8#68908—34nomaximal
9C22×#634C2211yescharacteristic
10C22×#634C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3750—21no—
15C2×C4×C3⋊Dic3—21no—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×#3746—22no—
19C2×#3746—22no—
20C2×#3746C414yescomplemented
21#64096—22no—
22#64096—22no—
23#63658—21no—
24#63658—21no—
25#63637—22no—
26#63637—22no—
27C22×Dic12—34no—
28C2×#887—34no—
29#4973—34no—
30C2×#810—34no—
31C2×#810—34no—
32C3×#340D314yes—
33#4550—34no—
34C22×C32×C4—21no—
35C22×C32×C4—21no—
36C22×C32×C4C2311yescharacteristic
37C22×C3⋊Dic3—21no—
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3D411yescharacteristic
40C22×C3⋊Dic3D411yescharacteristic
41C2×#634—21no—
42C2×#634—21no—
43C2×#634—21no—
44C2×#634—21no—
45C2×#634—21no—
46C2×#634—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634C2×C412yes—
50C2×#634C2×C412yes—
51C2×#634D412yes—
52C2×#634D412yes—
53C2×C32×C8—21no—
54C2×C32×C8—21no—
55C2×C32×C8C2×C412yes—
56C32×C4⋊C4—21no—
57C32×C4⋊C4—21no—
58C32×C4⋊C4—21no—
59C32×C4⋊C4D412yes—
60#3750—24no—
61C4×C3⋊Dic3—24no—
62C4×C3⋊Dic3—21no—
63C4×C3⋊Dic3—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67#3746—28no—
68#1878—91noSylow
69C22×Dic6—34no—
70C22×Dic6—34no—
71C22×C3×C8C2×D314yes—
72C2×C3×C4⋊C4C2×D314yes—
73C2×C3×C4⋊C4C2×D314yes—
74C2×Dic3⋊C4—64no—
75C2×C4×Dic3—34no—
76C2×C4×Dic3—64no—
77C22×C3⋊C8—34no—
78C2×Dic12—316no—
79C2×Dic12—68no—
80C2×Dic12—68no—
81#887—68no—
82#887—68no—
83C3⋊#95—64no—
84C3⋊#95—64no—
85#810—68no—
86#810—68no—
87C23×C32C2×D411yescharacteristic
88C2×C32×C4—22no—
89C2×C32×C4—41no—
90C2×C32×C4—41no—
91C2×C32×C4—41no—
92C2×C32×C4—41no—
93C2×C32×C4—41no—
94C2×C32×C4C22×C411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—22no—
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—21no—
105C2×C3⋊Dic3—22no—
106C2×C3⋊Dic3—21no—
107C2×C3⋊Dic3—21no—
108C2×C3⋊Dic3—21no—
109C2×C3⋊Dic3—41no—
110C2×C3⋊Dic3—41no—
111C2×C3⋊Dic3Q1612yescomplemented
112#634—22no—
113#634—22no—
114#634—22no—
115#634—22no—
116#634—22no—
117#634—41no—
118#634—41no—
119#634C22⋊C414yes—
120C32×C8—22no—
121C3⋊(C3⋊C8)—41no—
122C22×Q16—91no—
123C2×C4×Q8—91no—
124C2×#103—91no—
125C2×#103—91no—
126#391—91no—
127#340C3⋊D311yescharacteristic
128#336—91no—
129C22×C3×C4—24no—
130C22×C3×C4—24no—
131C22×C3×C4C22×D314yes—
132C22×Dic3—34no—
133C22×Dic3—34no—
134C22×Dic3—64no—
135C22×Dic3—64no—
136C2×Dic6—38no—
137C2×Dic6—38no—
138C2×Dic6—38no—
139C2×Dic6—38no—
140C2×Dic6—64no—
141C2×Dic6—64no—
142C2×Dic6—64no—
143C2×Dic6—64no—
144C2×Dic6—64no—
145C2×Dic6—64no—
146C2×Dic6—64no—
147C2×Dic6—64no—
148C2×C3×C8—24no—
149C2×C3×C8—24no—
150C2×C3×C8C4×D318yes—
151C3×C4⋊C4—24no—
152C3×C4⋊C4—24no—
153C3×C4⋊C4—24no—
154C3×C4⋊C4D1218yes—
155Dic3⋊C4—616no—
156C4×Dic3—616no—
157C4×Dic3—64no—
158C4×Dic3—64no—
159C2×C3⋊C8—64no—
160C2×C3⋊C8—64no—
161C2×C3⋊C8—64no—
162Dic12—632no—
163C22×C32C4×D411yescharacteristic
164C22×C32#12011yescharacteristic
165C22×C32#12111yescharacteristic
166C22×C32C2×Q1611yescharacteristic
167C22×C32#13511yescharacteristic
168C22×C32#13711yescharacteristic
169C22×C32#13711yescharacteristic
170C32×C4—42no—
171C32×C4—81no—
172C32×C4C2×C22⋊C411yescharacteristic
173C32×C4C4×D411yescharacteristic
174C32×C4#12111yescharacteristic
175C32×C4#12311yescharacteristic
176C3⋊Dic3—24no—
177C3⋊Dic3—22no—
178C3⋊Dic3—42no—
179C3⋊Dic3—41no—
180C22×Q8—91no—
181C22×Q8—91no—
182C2×Q16—94no—
183C2×Q16—182no—
184C2×Q16—182no—
185C22×C8—91no—
186C22×C8C2×C3⋊D311yescharacteristic
187C4×Q8—182no—
188C4×Q8—182no—
189C2×C4⋊C4—181no—
190C2×C4⋊C4C2×C3⋊D311yescharacteristic
191C2×C4⋊C4C2×C3⋊D311yescharacteristic
192C2×C42—91no—
193C2×C42—181no—
194#103—182no—
195#103—182no—
196#95—181no—
197#95—181no—
198C23×C3D3×D414yes—
199C2×C3×C4—28no—
200C2×C3×C4—44no—
201C2×C3×C4—44no—
202C2×C3×C4—44no—
203C2×C3×C4—44no—
204C2×C3×C4—44no—
205C2×C3×C4C2×C4×D314yes—
206C2×C3×C4C2×D1214yes—
207C2×C3×C4#23514yes—
208C2×C3×C4D3×D414yes—
209C2×C3×C4D3×D414yes—
210C2×C3×C4#23914yes—
211C2×Dic3—38no—
212C2×Dic3—64no—
213C2×Dic3—68no—
214C2×Dic3—68no—
215C2×Dic3—68no—
216C2×Dic3—64no—
217C2×Dic3—64no—
218C2×Dic3—68no—
219C2×Dic3—64no—
220C2×Dic3—64no—
221C2×Dic3—124no—
222C2×Dic3—124no—
223Dic6—316no—
224Dic6—68no—
225Dic6—68no—
226Dic6—68no—
227Dic6—68no—
228Dic6—68no—
229Dic6—124no—
230Dic6—124no—
231C3×C8—28no—
232C3⋊C8—124no—
233C2×C32#38611yescharacteristic
234C2×C32C4×Q1611yescharacteristic
235C2×C32#44111yescharacteristic
236C2×C32#45111yescharacteristic
237C2×C32#45211yescharacteristic
238C2×C32#46211yescharacteristic
239C2×C32#46411yescharacteristic
240C2×Q8—92no—
241C2×Q8—92no—
242C2×Q8—92no—
243C2×Q8—92no—
244C2×Q8—181no—
245C2×Q8—181no—
246C2×Q8—181no—
247C2×Q8—181no—
248C2×Q8—181no—
249C2×Q8—181no—
250C2×Q8—181no—
251C2×Q8—181no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—91no—
255C22×C4—91no—
256C22×C4—181no—
257C22×C4—181no—
258C22×C4C22×C3⋊D311yescharacteristic
259Q16—188no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—181no—
263C2×C8—181no—
264C2×C8—181no—
265C2×C8C4×C3⋊D312yes—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—184no—
270C4⋊C4C4⋊(C3⋊D3)12yes—
271C42—184no—
272C42—181no—
273C42—181no—
274C22×C3#88214yes—
275C22×C3#88414yes—
276C22×C3#89314yes—
277C22×C3#91214yes—
278C22×C3#91514yes—
279C22×C3#91514yes—
280C22×C3D3×Q1614yes—
281C3×C4—48no—
282C3×C4—84no—
283C3×C4C4×D1214yes—
284C3×C4D3×C22⋊C414yes—
285C3×C4#89414yes—
286C3×C4#89514yes—
287Dic3—616no—
288Dic3—68no—
289Dic3—128no—
290Dic3—124no—
291C32#187811yescharacteristic, complemented, Sylow
292C23D4×C3⋊D311yescharacteristic
293Q8—94no—
294Q8—182no—
295Q8—182no—
296Q8—182no—
297Q8—182no—
298Q8—182no—
299Q8—361no—
300Q8—361no—
301C2×C4—22no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—92no—
308C2×C4—181no—
309C2×C4—182no—
310C2×C4—182no—
311C2×C4—182no—
312C2×C4—181no—
313C2×C4—181no—
314C2×C4—182no—
315C2×C4—181no—
316C2×C4—181no—
317C2×C4—361no—
318C2×C4—361no—
319C2×C4C2×C4×C3⋊D311yescharacteristic
320C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
321C2×C4#382811yescharacteristic
322C2×C4D4×C3⋊D311yescharacteristic
323C2×C4D4×C3⋊D311yescharacteristic
324C2×C4#383211yescharacteristic
325C8—22no—
326C8—361no—
327C2×C3#466514yes—
328C2×C3#476714yes—
329C2×C3#478314yes—
330C2×C3#479514yes—
331C2×C3#480914yes—
332C2×C3#485314yes—
333C2×C3#487314yes—
334C22#6409111yescharacteristic
335C22#6409311yescharacteristic
336C22#6410211yescharacteristic
337C22#6412111yescharacteristic
338C22#6412411yescharacteristic
339C22#6412411yescharacteristic
340C22Q16×C3⋊D311yescharacteristic
341C4—42no—
342C4—81no—
343C4—184no—
344C4—182no—
345C4—362no—
346C4—361no—
347C4C4×C4⋊(C3⋊D3)11yescharacteristic
348C4C22⋊C4×C3⋊D311yescharacteristic
349C4#6410311yescharacteristic
350C4#6410411yescharacteristic
351C3#6890814yescomplemented
352C2#1059236411yescharacteristic
353C2#1059246611yescharacteristic
354C2#1059248211yescharacteristic
355C2#1059249411yescharacteristic
356C2#1059250811yescharacteristic
357C2#1059255211yescharacteristic
358C2#1059257211yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#340C2
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenter#340C3⋊D3
hypocenterC32#1878
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
20. C2×#3746C4semidirect
111. C2×C3⋊Dic3Q16semidirect
291. C32#1878semidirect
351. C3#68908semidirect

Maximal subgroups

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

subgroupindex
C22×#37462
C2×#640962
#105926722
C2×#636372
C32×#3402
#105894162
#689083