Finite Group Databasebeta

← #11801809

Subgroups — #11801809

Order 1152.

1968 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C3⋊Dic3C211yesmaximal, characteristic
2C2×#64086C211yesmaximal, characteristic
3C2×#64086C211yesmaximal, characteristic
4C32×#385C211yesmaximal, characteristic
5#10592909C211yesmaximal, characteristic
6#10592675C212yesmaximal, complemented
7C4⋊C4×C3⋊Dic3C212yesmaximal, complemented
8#10592649C211yesmaximal, characteristic
9#10592645C211yesmaximal, characteristic
10#10592348C212yesmaximal, complemented
11#10592346C212yesmaximal, complemented
12#74378—34nomaximal
13C23×C32×C4C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C2×C32×C4⋊C4C2212yes—
17C2×C32×C22⋊C4C2211yescharacteristic
18C2×C32×C22⋊C4C2211yescharacteristic
19C2×#3757C2211yescharacteristic
20C2×#3757C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2212yes—
22C2×#3750C2211yescharacteristic
23C2×#3750C2212yes—
24C2×#3750C2212yes—
25C2×#3750C2211yescharacteristic
26C2×#3750C2212yes—
27C2×C4×C3⋊Dic3—24no—
28C2×C4×C3⋊Dic3C2212yes—
29C2×C4×C3⋊Dic3C2211yescharacteristic
30C2×C4×C3⋊Dic3C2212yes—
31C2×C4×C3⋊Dic3C2211yescharacteristic
32C2×C4×C3⋊Dic3C2212yes—
33#64086—24no—
34#64086C418yescomplemented
35C32×#95C2212yes—
36#63658C2212yes—
37#63658C2212yes—
38#63658C2212yes—
39C22×C4×Dic3—34no—
40C2×#877—34no—
41C2×#877—34no—
42C3×#385D314yes—
43#5210—34no—
44#4976—38no—
45Dic3×C4⋊C4—38no—
46#4950—34no—
47#4946—34no—
48#4649—38no—
49#4647—38no—
50C24×C32C2311yescharacteristic
51C22×C32×C4—22no—
52C22×C32×C4—24no—
53C22×C32×C4C2311yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2312yes—
56C22×C32×C4C2312yes—
57C22×C3⋊Dic3—22no—
58C22×C3⋊Dic3—24no—
59C22×C3⋊Dic3C2×C414yes—
60C22×C3⋊Dic3D414yes—
61C22×C3⋊Dic3Q814yes—
62C22×C3⋊Dic3C2311yescharacteristic
63C22×C3⋊Dic3C2311yescharacteristic
64C22×C3⋊Dic3C2312yes—
65C22×C3⋊Dic3C2312yes—
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C32×C4⋊C4—24no—
69C32×C22⋊C4—22no—
70C32×C22⋊C4C2×C414yes—
71#3757—22no—
72#3757C2×C414yes—
73C4⋊(C3⋊Dic3)—24no—
74#3750—24no—
75#3750—22no—
76#3750—22no—
77#3750—24no—
78#3750C2×C418yescomplemented
79C4×C3⋊Dic3—22no—
80C4×C3⋊Dic3—22no—
81C4×C3⋊Dic3—24no—
82C4×C3⋊Dic3—24no—
83C4×C3⋊Dic3C2×C418yescomplemented
84#2296—91noSylow
85C23×C3×C4C2×D314yes—
86C23×Dic3—34no—
87C23×Dic3—34no—
88C2×C3×C4⋊C4C2×D318yes—
89C2×C3×C22⋊C4C2×D314yes—
90C2×C3×C22⋊C4C2×D314yes—
91C2×#217—34no—
92C2×#217—34no—
93C2×C4⋊Dic3—38no—
94C2×Dic3⋊C4—38no—
95C2×Dic3⋊C4—34no—
96C2×Dic3⋊C4—38no—
97C2×Dic3⋊C4—38no—
98C2×Dic3⋊C4—34no—
99C2×C4×Dic3—38no—
100C2×C4×Dic3—38no—
101C2×C4×Dic3—34no—
102C2×C4×Dic3—38no—
103C2×C4×Dic3—34no—
104C2×C4×Dic3—616no—
105#877—332no—
106#877—616no—
107C3×#95C2×D318yes—
108C3⋊#95—38no—
109C3⋊#95—38no—
110C3⋊#95—38no—
111C23×C32—22no—
112C23×C32—22no—
113C23×C32C22×C412yes—
114C23×C32C2×D412yes—
115C23×C32C2×Q812yes—
116C23×C32C2411yescharacteristic
117C2×C32×C4—28no—
118C2×C32×C4—22no—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4C22×C414yes—
127C2×C32×C4#4114yes—
128C2×C3⋊Dic3—28no—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3C4⋊C4116yescomplemented
138C2×C3⋊Dic3C22×C414yes—
139C2×C3⋊Dic3C22×C412yes—
140C2×C3⋊Dic3C22×C412yes—
141C2×C3⋊Dic3C2×D412yes—
142C2×C3⋊Dic3C2×D412yes—
143C2×C3⋊Dic3C2×Q812yes—
144C2×C3⋊Dic3C2×Q812yes—
145C2×C3⋊Dic3#4114yes—
146C2×#117—91no—
147C2×#117—91no—
148C22×C42—91no—
149#389—92no—
150#389—92no—
151#385—91no—
152#385—91no—
153#385—91no—
154#385C3⋊D311yescharacteristic
155C4×C4⋊C4—92no—
156C4×C4⋊C4—92no—
157C24×C3C22×D314yes—
158C22×C3×C4—28no—
159C22×C3×C4—216no—
160C22×C3×C4C22×D314yes—
161C22×C3×C4C22×D314yes—
162C22×C3×C4C22×D318yes—
163C22×C3×C4C22×D318yes—
164C22×Dic3—316no—
165C22×Dic3—316no—
166C22×Dic3—316no—
167C22×Dic3—34no—
168C22×Dic3—34no—
169C22×Dic3—38no—
170C22×Dic3—38no—
171C22×Dic3—34no—
172C22×Dic3—34no—
173C22×Dic3—616no—
174C22×Dic3—68no—
175C3×C4⋊C4—216no—
176C3×C22⋊C4—28no—
177C3×C22⋊C4C4×D3116yes—
178#217—316no—
179#217—68no—
180C4⋊Dic3—616no—
181Dic3⋊C4—332no—
182Dic3⋊C4—68no—
183Dic3⋊C4—68no—
184Dic3⋊C4—616no—
185Dic3⋊C4—616no—
186C4×Dic3—332no—
187C4×Dic3—68no—
188C4×Dic3—68no—
189C4×Dic3—616no—
190C4×Dic3—616no—
191C22×C32—24no—
192C22×C32—22no—
193C22×C32—22no—
194C22×C32—24no—
195C22×C32C2×C4⋊C414yes—
196C22×C32C23×C411yescharacteristic
197C22×C32C22×D411yescharacteristic
198C22×C32C22×Q811yescharacteristic
199C22×C32C2×#4112yes—
200C22×C32C2×#4112yes—
201C32×C4—24no—
202C32×C4—24no—
203C32×C4—41no—
204C32×C4—41no—
205C3⋊Dic3—24no—
206C3⋊Dic3—24no—
207C3⋊Dic3—41no—
208C3⋊Dic3—41no—
209C3⋊Dic3C2×C4⋊C414yes—
210C3⋊Dic3C2×C4⋊C414yes—
211C23×C4—91no—
212C23×C4—91no—
213C23×C4C2×C3⋊D311yescharacteristic
214#117—98no—
215#117—184no—
216C2×C4⋊C4—92no—
217C2×C4⋊C4—91no—
218C2×C4⋊C4—91no—
219C2×C4⋊C4—92no—
220C2×C4⋊C4—92no—
221C2×C4⋊C4—92no—
222C2×C4⋊C4C2×C3⋊D312yes—
223C2×C22⋊C4—91no—
224C2×C22⋊C4—91no—
225C2×C22⋊C4C2×C3⋊D311yescharacteristic
226C2×C22⋊C4C2×C3⋊D311yescharacteristic
227C2×C42—92no—
228C2×C42—91no—
229C2×C42—91no—
230C2×C42—92no—
231C2×C42—92no—
232C2×C42—184no—
233#95—92no—
234#95—92no—
235#95—92no—
236#95C2×C3⋊D312yes—
237C23×C3—28no—
238C23×C3—28no—
239C23×C3C2×C4×D318yes—
240C23×C3D3×D418yes—
241C23×C3D3×Q818yes—
242C23×C3C23×D314yes—
243C2×C3×C4—232no—
244C2×C3×C4—28no—
245C2×C3×C4—28no—
246C2×C3×C4—28no—
247C2×C3×C4—28no—
248C2×C3×C4—24no—
249C2×C3×C4—24no—
250C2×C3×C4—28no—
251C2×C3×C4—28no—
252C2×C3×C4C2×C4×D3116yes—
253C2×C3×C4#237116yes—
254C2×Dic3—364no—
255C2×Dic3—38no—
256C2×Dic3—38no—
257C2×Dic3—38no—
258C2×Dic3—38no—
259C2×Dic3—38no—
260C2×Dic3—38no—
261C2×Dic3—316no—
262C2×Dic3—316no—
263C2×Dic3—632no—
264C2×Dic3—68no—
265C2×Dic3—68no—
266C2×Dic3—68no—
267C2×Dic3—68no—
268C2×Dic3—64no—
269C2×Dic3—64no—
270C2×Dic3—68no—
271C2×Dic3—68no—
272C2×C32—24no—
273C2×C32C22×C4⋊C411yescharacteristic
274C2×C32C4×#4112yes—
275C2×C32#52511yescharacteristic
276C2×C32#52511yescharacteristic
277C2×C32#53312yes—
278C24C22×C3⋊D311yescharacteristic
279C22×C4—22no—
280C22×C4—24no—
281C22×C4—91no—
282C22×C4—91no—
283C22×C4—94no—
284C22×C4—94no—
285C22×C4—94no—
286C22×C4—92no—
287C22×C4—92no—
288C22×C4—91no—
289C22×C4—91no—
290C22×C4—184no—
291C22×C4—182no—
292C22×C4C22×C3⋊D311yescharacteristic
293C22×C4C22×C3⋊D311yescharacteristic
294C22×C4C22×C3⋊D312yes—
295C22×C4C22×C3⋊D312yes—
296C4⋊C4—24no—
297C4⋊C4—98no—
298C4⋊C4—182no—
299C4⋊C4—182no—
300C4⋊C4—184no—
301C4⋊C4—184no—
302C4⋊C4—184no—
303C22⋊C4—22no—
304C22⋊C4—94no—
305C22⋊C4—182no—
306C22⋊C4C4×C3⋊D314yes—
307C42—98no—
308C42—184no—
309C42—184no—
310C42—182no—
311C42—182no—
312C22×C3—28no—
313C22×C3—216no—
314C22×C3—28no—
315C22×C3—216no—
316C22×C3D3×C4⋊C4116yes—
317C22×C3C22×C4×D314yes—
318C22×C3C2×D3×D414yes—
319C22×C3C2×#23718yes—
320C22×C3C2×D3×Q814yes—
321C22×C3D3×#4118yes—
322C3×C4—216no—
323C3×C4—216no—
324C3×C4—44no—
325C3×C4—44no—
326Dic3—316no—
327Dic3—316no—
328Dic3—616no—
329Dic3—616no—
330Dic3—124no—
331Dic3—124no—
332C32#229611yescharacteristic, complemented, Sylow
333C23—22no—
334C23—22no—
335C23C2×C4×C3⋊D312yes—
336C23D4×C3⋊D312yes—
337C23Q8×C3⋊D312yes—
338C23C23×C3⋊D311yescharacteristic
339C2×C4—28no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—916no—
349C2×C4—92no—
350C2×C4—92no—
351C2×C4—92no—
352C2×C4—92no—
353C2×C4—92no—
354C2×C4—92no—
355C2×C4—94no—
356C2×C4—94no—
357C2×C4—188no—
358C2×C4—182no—
359C2×C4—182no—
360C2×C4—182no—
361C2×C4—182no—
362C2×C4—181no—
363C2×C4—181no—
364C2×C4—182no—
365C2×C4—182no—
366C2×C4C2×C4×C3⋊D314yes—
367C2×C4#383014yes—
368C2×C3—216no—
369C2×C3C2×D3×C4⋊C414yes—
370C2×C3C4×#23718yes—
371C2×C3#558614yes—
372C2×C3#562218yes—
373C2×C3#565614yes—
374C22—22no—
375C22—24no—
376C22—22no—
377C22—24no—
378C22C4⋊C4×C3⋊D314yes—
379C22C22×C4×C3⋊D311yescharacteristic
380C22C2×D4×C3⋊D311yescharacteristic
381C22C2×#383012yes—
382C22C2×Q8×C3⋊D311yescharacteristic
383C22#41×C3⋊D312yes—
384C4—24no—
385C4—24no—
386C4—41no—
387C4—41no—
388C4—94no—
389C4—94no—
390C4—184no—
391C4—184no—
392C4—361no—
393C4—361no—
394C3#7437814yescomplemented
395C2—24no—
396C2C2×C4⋊C4×C3⋊D311yescharacteristic
397C2C4×#383012yes—
398C2#1059605711yescharacteristic
399C2#1059609312yes—
400C2#1059612711yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#385C2
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenter#385C3⋊D3
hypocenterC32#2296
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
6. #10592675C2semidirect
7. C4⋊C4×C3⋊Dic3C2semidirect
10. #10592348C2semidirect
11. #10592346C2semidirect
34. #64086C4semidirect
78. #3750C2×C4semidirect
83. C4×C3⋊Dic3C2×C4semidirect
137. C2×C3⋊Dic3C4⋊C4semidirect
332. C32#2296semidirect
394. C3#74378semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊Dic32
C2×#640862
C32×#3852
#105929092
#105926752
C4⋊C4×C3⋊Dic32
#105926492
#105926452
#105923482
#105923462
#743783