Finite Group Databasebeta

← #11802470

Subgroups — #11802470

Order 1152.

1452 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64099C211yesmaximal, characteristic
2C32×#389C211yesmaximal, characteristic
3#10592677C212yesmaximal
4#10592676C211yesmaximal, characteristic
5C4⋊C4×C3⋊Dic3C212yesmaximal
6C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic
7C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic
8C42×C3⋊Dic3C211yesmaximal, characteristic
9#10592627C211yesmaximal, characteristic
10#10592352C212yesmaximal
11#10592348C212yesmaximal
12#75966—34nomaximal
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C32×C4⋊C4C2212yes—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C42C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2212yes—
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×#3750C2212yes—
21C2×#3750C2212yes—
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C4×C3⋊Dic3C2212yes—
24C2×C4×C3⋊Dic3C2212yes—
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C2×C4×C3⋊Dic3C2211yescharacteristic
28C2×C4×C3⋊Dic3C2211yescharacteristic
29C2×C4×C3⋊Dic3C2211yescharacteristic
30#64099C418yescomplemented
31C32×#95C2212yes—
32#63658C2212yes—
33#63658C2212yes—
34#63658C2212yes—
35#63658C2212yes—
36#63658C2212yes—
37C2×#890—34no—
38C3×#389D314yes—
39#4978—38no—
40#4977—34no—
41Dic3×C4⋊C4—38no—
42Dic3×C4⋊C4—34no—
43Dic3×C4⋊C4—34no—
44C42×Dic3—34no—
45#4928—34no—
46#4653—38no—
47#4649—38no—
48C22×C32×C4C2312yes—
49C22×C32×C4C2312yes—
50C22×C32×C4C2311yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3C2312yes—
54C22×C3⋊Dic3C2311yescharacteristic
55C22×C3⋊Dic3C2311yescharacteristic
56C22×C3⋊Dic3C2312yes—
57C22×C3⋊Dic3C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C32×C4⋊C4—24no—
60C32×C4⋊C4—22no—
61C32×C4⋊C4C2×C414yes—
62C32×C42—22no—
63C4⋊(C3⋊Dic3)—22no—
64C4⋊(C3⋊Dic3)C2×C418yes—
65C4⋊(C3⋊Dic3)C2×C414yes—
66#3750—24no—
67#3750C2×C418yes—
68C4×C3⋊Dic3—22no—
69C4×C3⋊Dic3—22no—
70C4×C3⋊Dic3—22no—
71C4×C3⋊Dic3—22no—
72C4×C3⋊Dic3—24no—
73C4×C3⋊Dic3—24no—
74C4×C3⋊Dic3C2×C414yes—
75C4×C3⋊Dic3Q814yes—
76C4×#125—91noSylow
77C2×C3×C4⋊C4C2×D314yes—
78C2×C3×C4⋊C4C2×D318yes—
79C2×C3×C4⋊C4C2×D314yes—
80C2×C3×C42C2×D314yes—
81C2×C4⋊Dic3—38no—
82C2×C4⋊Dic3—34no—
83C2×C4⋊Dic3—34no—
84C2×Dic3⋊C4—38no—
85C2×Dic3⋊C4—38no—
86C2×C4×Dic3—34no—
87C2×C4×Dic3—34no—
88C2×C4×Dic3—34no—
89C2×C4×Dic3—38no—
90C2×C4×Dic3—38no—
91C2×C4×Dic3—34no—
92C2×C4×Dic3—34no—
93C2×C4×Dic3—34no—
94#890—332no—
95C3×#95C2×D318yes—
96C3⋊#95—38no—
97C3⋊#95—38no—
98C3⋊#95—38no—
99C3⋊#95—38no—
100C3⋊#95—38no—
101C23×C32C2411yescharacteristic
102C2×C32×C4—22no—
103C2×C32×C4—21no—
104C2×C32×C4—21no—
105C2×C32×C4—21no—
106C2×C32×C4—21no—
107C2×C32×C4—22no—
108C2×C32×C4—22no—
109C2×C32×C4—22no—
110C2×C32×C4—22no—
111C2×C32×C4C22×C414yes—
112C2×C32×C4C22×C412yes—
113C2×C32×C4C2×Q812yes—
114C2×C32×C4#4112yes—
115C2×C32×C4#4112yes—
116C2×C32×C4#4112yes—
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3C22×C412yes—
129C2×C3⋊Dic3C22×C412yes—
130C2×C3⋊Dic3C22×C414yes—
131C2×C3⋊Dic3C2×Q812yes—
132C2×C3⋊Dic3C2×Q812yes—
133C2×C3⋊Dic3#4112yes—
134C2×C3⋊Dic3#4112yes—
135C2×#125—91no—
136#389—91no—
137#389C3⋊D311yescharacteristic
138#387—92no—
139#387—92no—
140#382—91no—
141C4×C4⋊C4—92no—
142C4×C4⋊C4—91no—
143C4×C4⋊C4—91no—
144C4×C4⋊C4—92no—
145C43—91no—
146C22×C3×C4C22×D318yes—
147C22×C3×C4C22×D318yes—
148C22×C3×C4C22×D314yes—
149C22×C3×C4C22×D314yes—
150C22×C3×C4C22×D314yes—
151C22×Dic3—34no—
152C22×Dic3—34no—
153C22×Dic3—34no—
154C22×Dic3—34no—
155C22×Dic3—38no—
156C22×Dic3—38no—
157C3×C4⋊C4—216no—
158C3×C4⋊C4—28no—
159C3×C4⋊C4C4×D3116yes—
160C3×C42—28no—
161C4⋊Dic3—332no—
162C4⋊Dic3—316no—
163C4⋊Dic3—68no—
164Dic3⋊C4—332no—
165Dic3⋊C4—616no—
166C4×Dic3—316no—
167C4×Dic3—316no—
168C4×Dic3—68no—
169C4×Dic3—68no—
170C4×Dic3—616no—
171C4×Dic3—616no—
172C4×Dic3—68no—
173C4×Dic3—68no—
174C22×C32C23×C411yescharacteristic
175C22×C32C22×Q811yescharacteristic
176C22×C32C2×#4111yescharacteristic
177C22×C32C2×#4111yescharacteristic
178C22×C32C2×#4111yescharacteristic
179C22×C32C2×#4111yescharacteristic
180C22×C32C2×#4111yescharacteristic
181C32×C4—24no—
182C32×C4—22no—
183C32×C4—22no—
184C32×C4—42no—
185C32×C4C4×Q814yes—
186C3⋊Dic3—22no—
187C3⋊Dic3—22no—
188C3⋊Dic3—24no—
189C3⋊Dic3—22no—
190C3⋊Dic3—42no—
191C3⋊Dic3#12514yescomplemented
192#125—98no—
193C2×C4⋊C4—92no—
194C2×C4⋊C4—92no—
195C2×C4⋊C4—91no—
196C2×C4⋊C4—91no—
197C2×C4⋊C4—92no—
198C2×C4⋊C4C2×C3⋊D311yescharacteristic
199C2×C4⋊C4C2×C3⋊D312yes—
200C2×C4⋊C4C2×C3⋊D311yescharacteristic
201C2×C42—91no—
202C2×C42—91no—
203C2×C42—91no—
204C2×C42—91no—
205C2×C42—91no—
206C2×C42—91no—
207C2×C42—92no—
208C2×C42—92no—
209C2×C42C2×C3⋊D311yescharacteristic
210#95—92no—
211#95—92no—
212#95—92no—
213#95—92no—
214#95—92no—
215#95C2×C3⋊D312yes—
216C23×C3C23×D314yes—
217C2×C3×C4—24no—
218C2×C3×C4—24no—
219C2×C3×C4—28no—
220C2×C3×C4—28no—
221C2×C3×C4—24no—
222C2×C3×C4—24no—
223C2×C3×C4—28no—
224C2×C3×C4—28no—
225C2×C3×C4—28no—
226C2×C3×C4C2×C4×D3116yes—
227C2×C3×C4C2×C4×D318yes—
228C2×C3×C4#23718yes—
229C2×C3×C4#23718yes—
230C2×C3×C4D3×Q818yes—
231C2×C3×C4#23918yes—
232C2×Dic3—38no—
233C2×Dic3—38no—
234C2×Dic3—38no—
235C2×Dic3—38no—
236C2×Dic3—38no—
237C2×Dic3—316no—
238C2×Dic3—38no—
239C2×Dic3—64no—
240C2×Dic3—64no—
241C2×Dic3—64no—
242C2×Dic3—64no—
243C2×Dic3—68no—
244C2×Dic3—64no—
245C2×Dic3—64no—
246C2×Dic3—68no—
247C2×Dic3—68no—
248C2×Dic3—68no—
249C2×Dic3—68no—
250C2×C32C2×C4×Q811yescharacteristic
251C2×C32C4×#4111yescharacteristic
252C2×C32C4×#4111yescharacteristic
253C2×C32C2×#12511yescharacteristic
254C2×C32#52911yescharacteristic
255C2×C32#52911yescharacteristic
256C2×C32#53311yescharacteristic
257C22×C4—91no—
258C22×C4—91no—
259C22×C4—91no—
260C22×C4—91no—
261C22×C4—92no—
262C22×C4—92no—
263C22×C4C22×C3⋊D312yes—
264C22×C4C22×C3⋊D312yes—
265C22×C4C22×C3⋊D311yescharacteristic
266C22×C4C22×C3⋊D311yescharacteristic
267C22×C4C22×C3⋊D311yescharacteristic
268C4⋊C4—24no—
269C4⋊C4—22no—
270C4⋊C4—98no—
271C4⋊C4—98no—
272C4⋊C4—94no—
273C4⋊C4—182no—
274C4⋊C4—184no—
275C4⋊C4C4×C3⋊D314yes—
276C42—22no—
277C42—94no—
278C42—94no—
279C42—182no—
280C42—182no—
281C42—184no—
282C42—184no—
283C42—182no—
284C42—182no—
285C22×C3C22×C4×D314yes—
286C22×C3C2×#23714yes—
287C22×C3C2×#23714yes—
288C22×C3C2×D3×Q814yes—
289C22×C3C2×#23914yes—
290C22×C3D3×#4114yes—
291C22×C3D3×#4114yes—
292C3×C4—216no—
293C3×C4—28no—
294C3×C4—28no—
295C3×C4—48no—
296C3×C4#887116yes—
297Dic3—316no—
298Dic3—68no—
299Dic3—68no—
300Dic3—68no—
301Dic3—616no—
302Dic3—128no—
303C32C4×#12511yescharacteristic, complemented, Sylow
304C23C23×C3⋊D311yescharacteristic
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—92no—
315C2×C4—92no—
316C2×C4—92no—
317C2×C4—92no—
318C2×C4—92no—
319C2×C4—94no—
320C2×C4—92no—
321C2×C4—181no—
322C2×C4—181no—
323C2×C4—181no—
324C2×C4—181no—
325C2×C4—182no—
326C2×C4—181no—
327C2×C4—181no—
328C2×C4—182no—
329C2×C4—182no—
330C2×C4—182no—
331C2×C4—182no—
332C2×C4C2×C4×C3⋊D314yes—
333C2×C4C2×C4×C3⋊D312yes—
334C2×C4#383012yes—
335C2×C4#383012yes—
336C2×C4Q8×C3⋊D312yes—
337C2×C4#383212yes—
338C2×C3C2×#88714yes—
339C2×C3C4×#23714yes—
340C2×C3C4×#23914yes—
341C2×C3#560014yes—
342C2×C3#562414yes—
343C2×C3D3×#12514yes—
344C2×C3#572814yes—
345C22C22×C4×C3⋊D311yescharacteristic
346C22C2×#383011yescharacteristic
347C22C2×#383011yescharacteristic
348C22C2×Q8×C3⋊D311yescharacteristic
349C22C2×#383211yescharacteristic
350C22#41×C3⋊D311yescharacteristic
351C22#41×C3⋊D311yescharacteristic
352C4—24no—
353C4—22no—
354C4—22no—
355C4—42no—
356C4—94no—
357C4—182no—
358C4—182no—
359C4—182no—
360C4—184no—
361C4—362no—
362C4#6409614yes—
363C3#7596614yescomplemented
364C2C2×#6409611yescharacteristic
365C2C4×#383011yescharacteristic
366C2C4×#383211yescharacteristic
367C2#1059607111yescharacteristic
368C2#1059609511yescharacteristic
369C2C3⋊D3×#12511yescharacteristic
370C2#1059619911yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#389C2
socle, prime radical, cosocleC23×C32C24
hypercenter#389C3⋊D3
hypocenterC32C4×#125
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
30. #64099C4semidirect
191. C3⋊Dic3#125semidirect
303. C32C4×#125semidirect
363. C3#75966semidirect

Maximal subgroups

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

subgroupindex
C2×#640992
C32×#3892
#105926772
#105926762
C4⋊C4×C3⋊Dic32
C42×C3⋊Dic32
#105926272
#105923522
#105923482
#759663