Finite Group Databasebeta

← #11801812

Subgroups — #11801812

Order 1152.

1968 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic
2C2×#64081C211yesmaximal, characteristic
3C2×C42×C3⋊D3C211yesmaximal, characteristic
4C32×C4×C4⋊C4C211yesmaximal, characteristic, complemented
5#10592688C212yesmaximal
6#10592675C212yesmaximal, complemented
7C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
8C4×#3750C211yesmaximal, characteristic, complemented
9C4×#3750C211yesmaximal, characteristic, complemented
10#10592367C212yesmaximal
11#10592346C212yesmaximal, complemented
12#73755—34nomaximal
13C22×C4×C3⋊D3C2212yes—
14C22×C4×C3⋊D3C2211yescharacteristic
15C2×C32×C4⋊C4C2212yes—
16C2×C32×C42C2211yescharacteristic
17C2×C32×C42C2211yescharacteristic
18C2×C32×C42C2211yescharacteristic
19C2×#3752C2212yes—
20C2×#3752C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2212yes—
23C2×#3750C2212yes—
24C2×#3750C2212yes—
25C2×#3750C2212yes—
26C2×#3750C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×C4×C3⋊Dic3C2212yes—
29C2×C4×C3⋊Dic3C2211yescharacteristic
30C2×C4×C3⋊Dic3C2211yescharacteristic
31C2×C4×C3⋊Dic3C2211yescharacteristic
32#64081—24no—
33#64081C418yescomplemented
34C42×C3⋊D3—24no—
35C32×#95C2212yes—
36#63658C2212yes—
37#63658C2212yes—
38#63658C2212yes—
39C2×#872—34no—
40C2×#872—34no—
41C2×C42×D3—34no—
42C3×C4×C4⋊C4D314yescomplemented
43#4989—38no—
44#4976—38no—
45C4×C4⋊Dic3—34no—
46C4×Dic3⋊C4—34no—
47C4×Dic3⋊C4—34no—
48#4668—38no—
49#4647—38no—
50C23×C3⋊D3C2311yescharacteristic
51C22×C32×C4C2312yes—
52C22×C32×C4C2311yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C22×C32×C4C2312yes—
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3C2312yes—
57C22×C3⋊Dic3C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3⋊Dic3C2312yes—
60C22×C3⋊Dic3C2311yescharacteristic
61C2×C4×C3⋊D3—24no—
62C2×C4×C3⋊D3—24no—
63C2×C4×C3⋊D3—24no—
64C2×C4×C3⋊D3C2×C414yes—
65C2×C4×C3⋊D3D414yes—
66C2×C4×C3⋊D3Q814yes—
67C32×C4⋊C4—24no—
68C32×C42—22no—
69C32×C42—22no—
70C32×C42C2×C414yescomplemented
71#3752—24no—
72#3752C2×C414yes—
73#3752C2×C414yes—
74C4⋊(C3⋊Dic3)—24no—
75#3750—24no—
76#3750—24no—
77#3750—24no—
78#3750C2×C414yescomplemented
79#3750C2×C414yescomplemented
80C4×C3⋊Dic3—22no—
81C4×C3⋊Dic3—22no—
82C4×C3⋊Dic3—24no—
83C4×C3⋊Dic3C2×C414yescomplemented
84#2296—91noSylow
85C22×C4×D3—34no—
86C22×C4×D3—38no—
87C2×C3×C4⋊C4C2×D318yes—
88C2×C3×C42C2×D314yes—
89C2×C3×C42C2×D314yes—
90C2×C3×C42C2×D314yes—
91C2×(C2×D3)⋊C4—34no—
92C2×(C2×D3)⋊C4—34no—
93C2×(C2×D3)⋊C4—38no—
94C2×C4⋊Dic3—38no—
95C2×Dic3⋊C4—34no—
96C2×Dic3⋊C4—34no—
97C2×Dic3⋊C4—38no—
98C2×Dic3⋊C4—38no—
99C2×Dic3⋊C4—38no—
100C2×C4×Dic3—34no—
101C2×C4×Dic3—38no—
102C2×C4×Dic3—34no—
103C2×C4×Dic3—34no—
104#872—332no—
105#872—616no—
106C42×D3—616no—
107C3×#95C2×D318yes—
108C3⋊#95—38no—
109C3⋊#95—38no—
110C3⋊#95—38no—
111C23×C32C2411yescharacteristic
112C22×C3⋊D3—22no—
113C22×C3⋊D3—22no—
114C22×C3⋊D3C22×C412yes—
115C22×C3⋊D3C2×D412yes—
116C22×C3⋊D3C2×Q812yes—
117C2×C32×C4—22no—
118C2×C32×C4—22no—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4C22×C412yes—
125C2×C32×C4C22×C412yes—
126C2×C32×C4C22×C412yes—
127C2×C32×C4C2×D412yes—
128C2×C32×C4C2×Q812yes—
129C2×C32×C4#4114yes—
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3C22×C412yes—
138C2×C3⋊Dic3C22×C412yes—
139C2×C3⋊Dic3C22×C412yes—
140C2×C3⋊Dic3C2×D412yes—
141C2×C3⋊Dic3C2×Q812yes—
142C2×C3⋊Dic3#4114yes—
143C4×C3⋊D3—216no—
144C4×C3⋊D3C4⋊C4116yescomplemented
145C2×#117—91no—
146C2×#117—91no—
147C22×C42—91no—
148#389—92no—
149#389—92no—
150#385—92no—
151#385—92no—
152C4×C4⋊C4—91no—
153C4×C4⋊C4—91no—
154C4×C4⋊C4—91no—
155C4×C4⋊C4C3⋊D311yescharacteristic, complemented
156C23×D3—34no—
157C22×C3×C4C22×D318yes—
158C22×C3×C4C22×D314yes—
159C22×C3×C4C22×D314yes—
160C22×C3×C4C22×D318yes—
161C22×C3×C4C22×D314yes—
162C22×Dic3—34no—
163C22×Dic3—38no—
164C22×Dic3—34no—
165C22×Dic3—34no—
166C22×Dic3—38no—
167C2×C4×D3—316no—
168C2×C4×D3—316no—
169C2×C4×D3—316no—
170C2×C4×D3—616no—
171C2×C4×D3—616no—
172C2×C4×D3—616no—
173C3×C4⋊C4—216no—
174C3×C42—28no—
175C3×C42—28no—
176C3×C42C4×D3116yescomplemented
177(C2×D3)⋊C4—316no—
178(C2×D3)⋊C4—316no—
179(C2×D3)⋊C4—616no—
180C4⋊Dic3—616no—
181Dic3⋊C4—316no—
182Dic3⋊C4—316no—
183Dic3⋊C4—616no—
184Dic3⋊C4—616no—
185Dic3⋊C4—616no—
186C4×Dic3—316no—
187C4×Dic3—616no—
188C4×Dic3—68no—
189C4×Dic3—68no—
190C22×C32C23×C411yescharacteristic
191C22×C32C22×D411yescharacteristic
192C22×C32C22×Q811yescharacteristic
193C22×C32C2×#4112yes—
194C22×C32C2×#4112yes—
195C2×C3⋊D3—22no—
196C2×C3⋊D3—22no—
197C2×C3⋊D3—24no—
198C2×C3⋊D3—24no—
199C2×C3⋊D3C2×C4⋊C414yes—
200C32×C4—22no—
201C32×C4—22no—
202C32×C4—24no—
203C32×C4—42no—
204C32×C4C2×C4⋊C414yes—
205C3⋊Dic3—22no—
206C3⋊Dic3—22no—
207C3⋊Dic3—24no—
208C3⋊Dic3—42no—
209C3⋊Dic3C2×C4⋊C414yes—
210C23×C4—91no—
211C23×C4—92no—
212#117—98no—
213#117—184no—
214C2×C4⋊C4—91no—
215C2×C4⋊C4—91no—
216C2×C4⋊C4—92no—
217C2×C4⋊C4—92no—
218C2×C4⋊C4—92no—
219C2×C4⋊C4—92no—
220C2×C4⋊C4C2×C3⋊D312yes—
221C2×C22⋊C4—91no—
222C2×C22⋊C4—91no—
223C2×C22⋊C4—92no—
224C2×C42—91no—
225C2×C42—92no—
226C2×C42—91no—
227C2×C42—91no—
228C2×C42—184no—
229C2×C42C2×C3⋊D311yescharacteristic
230C2×C42C2×C3⋊D311yescharacteristic
231C2×C42C2×C3⋊D311yescharacteristic
232#95—92no—
233#95—92no—
234#95—92no—
235#95C2×C3⋊D312yes—
236C23×C3C23×D314yes—
237C22×D3—38no—
238C22×D3—38no—
239C22×D3—38no—
240C22×D3—68no—
241C22×D3—68no—
242C2×C3×C4—28no—
243C2×C3×C4—28no—
244C2×C3×C4—28no—
245C2×C3×C4—28no—
246C2×C3×C4—28no—
247C2×C3×C4—28no—
248C2×C3×C4—28no—
249C2×C3×C4C2×C4×D318yes—
250C2×C3×C4C2×C4×D318yes—
251C2×C3×C4C2×C4×D318yes—
252C2×C3×C4#235116yes—
253C2×C3×C4D3×D418yes—
254C2×C3×C4D3×Q818yes—
255C2×Dic3—38no—
256C2×Dic3—38no—
257C2×Dic3—38no—
258C2×Dic3—38no—
259C2×Dic3—38no—
260C2×Dic3—316no—
261C2×Dic3—68no—
262C2×Dic3—68no—
263C2×Dic3—68no—
264C2×Dic3—68no—
265C2×Dic3—68no—
266C2×Dic3—68no—
267C2×Dic3—68no—
268C4×D3—364no—
269C4×D3—664no—
270C2×C32C22×C4⋊C411yescharacteristic
271C2×C32C4×#4111yescharacteristic
272C2×C32C4×#4111yescharacteristic
273C2×C32#52512yes—
274C2×C32#53312yes—
275C3⋊D3—24no—
276C24—91no—
277C22×C4—91no—
278C22×C4—94no—
279C22×C4—94no—
280C22×C4—94no—
281C22×C4—92no—
282C22×C4—91no—
283C22×C4—91no—
284C22×C4—92no—
285C22×C4—184no—
286C22×C4—184no—
287C22×C4—184no—
288C22×C4C22×C3⋊D312yes—
289C22×C4C22×C3⋊D311yescharacteristic
290C22×C4C22×C3⋊D311yescharacteristic
291C22×C4C22×C3⋊D312yes—
292C22×C4C22×C3⋊D311yescharacteristic
293C4⋊C4—24no—
294C4⋊C4—94no—
295C4⋊C4—94no—
296C4⋊C4—184no—
297C4⋊C4—184no—
298C4⋊C4—184no—
299C4⋊C4—184no—
300C22⋊C4—94no—
301C22⋊C4—94no—
302C22⋊C4—184no—
303C42—22no—
304C42—22no—
305C42—94no—
306C42—184no—
307C42—182no—
308C42—182no—
309C42C4×C3⋊D314yescomplemented
310C22×C3C22×C4×D314yes—
311C22×C3C2×#23518yes—
312C22×C3C2×D3×D414yes—
313C22×C3C2×D3×Q814yes—
314C22×C3D3×#4118yes—
315C2×D3—316no—
316C2×D3—68no—
317C2×D3—68no—
318C2×D3—616no—
319C2×D3—616no—
320C3×C4—28no—
321C3×C4—28no—
322C3×C4—216no—
323C3×C4—48no—
324C3×C4D3×C4⋊C4116yes—
325Dic3—316no—
326Dic3—68no—
327Dic3—68no—
328Dic3—616no—
329Dic3—128no—
330C32#229611yescharacteristic, complemented, Sylow
331C23—92no—
332C23—92no—
333C23—92no—
334C23—182no—
335C23—182no—
336C23C23×C3⋊D311yescharacteristic
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—92no—
345C2×C4—92no—
346C2×C4—92no—
347C2×C4—916no—
348C2×C4—92no—
349C2×C4—92no—
350C2×C4—94no—
351C2×C4—1816no—
352C2×C4—182no—
353C2×C4—182no—
354C2×C4—182no—
355C2×C4—182no—
356C2×C4—182no—
357C2×C4—182no—
358C2×C4—182no—
359C2×C4C2×C4×C3⋊D312yes—
360C2×C4C2×C4×C3⋊D312yes—
361C2×C4C2×C4×C3⋊D312yes—
362C2×C4#382814yes—
363C2×C4D4×C3⋊D312yes—
364C2×C4Q8×C3⋊D312yes—
365C2×C3C4×#23514yes—
366C2×C3C2×D3×C4⋊C414yes—
367C2×C3#552214yes—
368C2×C3#554718yes—
369C2×C3#557818yes—
370D3—616no—
371C22—94no—
372C22—182no—
373C22—182no—
374C22—184no—
375C22—184no—
376C22C22×C4×C3⋊D311yescharacteristic
377C22C2×#382812yes—
378C22C2×D4×C3⋊D311yescharacteristic
379C22C2×Q8×C3⋊D311yescharacteristic
380C22#41×C3⋊D312yes—
381C4—22no—
382C4—22no—
383C4—24no—
384C4—42no—
385C4—94no—
386C4—182no—
387C4—182no—
388C4—184no—
389C4—362no—
390C4C4⋊C4×C3⋊D314yes—
391C3#7375514yescomplemented
392C2—184no—
393C2C4×#382811yescharacteristic
394C2C2×C4⋊C4×C3⋊D311yescharacteristic
395C2#1059599311yescharacteristic
396C2#1059601812yes—
397C2#1059604912yes—
subgroupG/H
centerC22×C4C22×C3⋊D3
commutatorC22×C32C23×C4
FrattiniC23C23×C3⋊D3
FittingC32×C4×C4⋊C4C2
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC4×C4⋊C4C3⋊D3
hypocenterC32#2296
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C32×C4×C4⋊C4C2semidirect
6. #10592675C2semidirect
7. C4×C4⋊(C3⋊Dic3)C2semidirect
8. C4×#3750C2semidirect
9. C4×#3750C2semidirect
11. #10592346C2semidirect
33. #64081C4semidirect
42. C3×C4×C4⋊C4D3semidirect
70. C32×C42C2×C4semidirect
78. #3750C2×C4semidirect
79. #3750C2×C4semidirect
83. C4×C3⋊Dic3C2×C4semidirect
144. C4×C3⋊D3C4⋊C4semidirect
155. C4×C4⋊C4C3⋊D3semidirect
176. C3×C42C4×D3semidirect
309. C42C4×C3⋊D3semidirect
330. C32#2296semidirect
391. C3#73755semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C2×C42×C3⋊D32
C32×C4×C4⋊C42
#105926882
#105926752
C4×C4⋊(C3⋊Dic3)2
C4×#37502
#105923672
#105923462
#737553