Finite Group Databasebeta

← #11805475

Subgroups — #11805475

Order 1152.

2112 conjugacy classes of subgroups.

The subgroup lattice has 429 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic
2C2×#64090C212yesmaximal
3C32×#380C211yesmaximal, characteristic, complemented
4C2×#63658C211yesmaximal, characteristic, complemented
5#10592688C212yesmaximal, complemented
6#10592675C212yesmaximal, complemented
7#10592645C212yesmaximal, complemented
8#10592366C211yesmaximal, characteristic, complemented
9C3⋊D3×#95C211yesmaximal, characteristic, complemented
10#10592349C211yesmaximal, characteristic, complemented
11#10592348C211yesmaximal, characteristic, complemented
12#74011—34nomaximal
13C23×C32×C4C2211yescharacteristic
14C22×#638C2211yescharacteristic
15C23×C3⋊Dic3C2212yes—
16C22×C4×C3⋊D3C2212yes—
17C22×C4×C3⋊D3C2211yescharacteristic
18C2×C32×C4⋊C4C2212yes—
19C2×C32×C22⋊C4C2212yes—
20C2×#3757C2211yescharacteristic
21C4×#638C418yescomplemented
22C2×#3752C2212yes—
23C2×#3752C2211yescharacteristic
24C2×#3750C2212yes—
25C2×#3750C2212yes—
26C2×#3750C2212yes—
27C2×#3750C2211yescharacteristic
28C2×C4×C3⋊Dic3C2212yes—
29C2×C4×C3⋊Dic3C2211yescharacteristic
30#64090—28no—
31C32×#95C2211yescharacteristic
32C32×#95C2211yescharacteristic
33#63658C2211yescharacteristic
34#63658C2211yescharacteristic
35#63658C2212yes—
36#63658C2212yes—
37#63658C2212yes—
38C2×C4×#67—34no—
39C2×#67⋊C4—38no—
40C3×#380D314yescomplemented
41C2×C3⋊#95—34no—
42#4989—38no—
43#4976—38no—
44#4946—38no—
45#4667—34no—
46D3×#95—34no—
47#4650—34no—
48#4649—34no—
49C24×C32C2311yescharacteristic
50C23×C3⋊D3C2311yescharacteristic
51C22×C32×C4—42no—
52C22×C32×C4C2×C414yescomplemented
53C22×C32×C4C2312yes—
54C22×C32×C4C2312yes—
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C2×#638C2×C414yes—
58C2×#638D414yes—
59C2×#638Q814yes—
60C22×C3⋊Dic3—24no—
61C22×C3⋊Dic3—24no—
62C22×C3⋊Dic3—42no—
63C22×C3⋊Dic3C2312yes—
64C22×C3⋊Dic3C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2311yescharacteristic
68C2×C4×C3⋊D3—24no—
69C2×C4×C3⋊D3—24no—
70C2×C4×C3⋊D3—42no—
71C2×C4×C3⋊D3—42no—
72C2×C4×C3⋊D3C2×C414yescomplemented
73C32×C4⋊C4—42no—
74C32×C22⋊C4—24no—
75#3757C2×C414yescomplemented
76#3752—24no—
77#3752C2×C414yescomplemented
78#3750—24no—
79#3750—24no—
80#3750—42no—
81#3750C2×C414yescomplemented
82C4×C3⋊Dic3—24no—
83C4×C3⋊Dic3C2×C414yescomplemented
84#2349—91noSylow
85C23×C3×C4C2×D314yes—
86C22×#67—34no—
87C23×Dic3—38no—
88C22×C4×D3—34no—
89C22×C4×D3—38no—
90C2×C3×C4⋊C4C2×D318yes—
91C2×C3×C22⋊C4C2×D318yes—
92C2×#217—34no—
93C4×#67—332no—
94C2×(C2×D3)⋊C4—34no—
95C2×(C2×D3)⋊C4—38no—
96C2×Dic3⋊C4—34no—
97C2×Dic3⋊C4—38no—
98C2×Dic3⋊C4—38no—
99C2×Dic3⋊C4—38no—
100C2×C4×Dic3—34no—
101C2×C4×Dic3—38no—
102#67⋊C4—632no—
103C3×#95C2×D314yes—
104C3×#95C2×D314yes—
105C3⋊#95—34no—
106C3⋊#95—34no—
107C3⋊#95—38no—
108C3⋊#95—38no—
109C3⋊#95—38no—
110C23×C32—22no—
111C23×C32—22no—
112C23×C32C22×C412yes—
113C23×C32C2×D412yes—
114C23×C32C2×Q812yes—
115C23×C32C2411yescharacteristic
116C22×C3⋊D3—22no—
117C22×C3⋊D3—22no—
118C22×C3⋊D3C22×C412yes—
119C22×C3⋊D3C2×D412yes—
120C22×C3⋊D3C2×Q812yes—
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4—22no—
127C2×C32×C4—22no—
128C2×C32×C4—22no—
129C2×C32×C4—44no—
130C2×C32×C4C22×C412yes—
131C2×C32×C4C22×C412yes—
132#638C4⋊C4116yescomplemented
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—48no—
141C2×C3⋊Dic3C22×C412yes—
142C2×C3⋊Dic3C22×C412yes—
143C2×C3⋊Dic3C22×C412yes—
144C2×C3⋊Dic3C2×D412yes—
145C2×C3⋊Dic3C2×Q812yes—
146C2×C3⋊Dic3#4114yes—
147C4×C3⋊D3—44no—
148C4×C3⋊D3—48no—
149C2×C4×D4—91no—
150C2×C4×D4—92no—
151#389—92no—
152#385—92no—
153#385—92no—
154#382—91no—
155#380—91no—
156#380C3⋊D311yescharacteristic, complemented
157C4×C4⋊C4—91no—
158C2×#95—91no—
159C2×#95—91no—
160C24×C3C22×D314yes—
161C23×D3—34no—
162C22×C3×C4—48no—
163C22×C3×C4C4×D3116yescomplemented
164C22×C3×C4C22×D318yes—
165C22×C3×C4C22×D318yes—
166C22×C3×C4C22×D314yes—
167C22×C3×C4C22×D314yes—
168C2×#67—316no—
169C2×#67—316no—
170C2×#67—316no—
171C22×Dic3—34no—
172C22×Dic3—38no—
173C22×Dic3—34no—
174C22×Dic3—34no—
175C22×Dic3—38no—
176C22×Dic3—616no—
177C22×Dic3—616no—
178C22×Dic3—128no—
179C2×C4×D3—316no—
180C2×C4×D3—616no—
181C2×C4×D3—616no—
182C2×C4×D3—128no—
183C2×C4×D3—128no—
184C3×C4⋊C4—48no—
185C3×C22⋊C4—216no—
186#217—316no—
187(C2×D3)⋊C4—316no—
188(C2×D3)⋊C4—616no—
189Dic3⋊C4—316no—
190Dic3⋊C4—616no—
191Dic3⋊C4—616no—
192Dic3⋊C4—128no—
193C4×Dic3—316no—
194C4×Dic3—616no—
195C22×C32—22no—
196C22×C32—22no—
197C22×C32—24no—
198C22×C32—24no—
199C22×C32C2×C4⋊C414yes—
200C22×C32C23×C411yescharacteristic
201C22×C32C22×D411yescharacteristic
202C22×C32C22×Q811yescharacteristic
203C22×C32C2×#4112yes—
204C22×C32H(5,𝔽2)12yes—
205C2×C3⋊D3—22no—
206C2×C3⋊D3—22no—
207C2×C3⋊D3—24no—
208C2×C3⋊D3—24no—
209C2×C3⋊D3C2×C4⋊C414yes—
210C32×C4—22no—
211C32×C4—22no—
212C32×C4—42no—
213C32×C4—42no—
214C3⋊Dic3—22no—
215C3⋊Dic3—22no—
216C3⋊Dic3—24no—
217C3⋊Dic3—42no—
218C3⋊Dic3C2×C4⋊C414yes—
219C22×D4—91no—
220C23×C4—91no—
221C23×C4—92no—
222C23×C4—92no—
223C23×C4C2×C3⋊D311yescharacteristic
224C4×D4—98no—
225C4×D4—188no—
226C2×C4⋊C4—91no—
227C2×C4⋊C4—92no—
228C2×C4⋊C4—92no—
229C2×C4⋊C4—92no—
230C2×C4⋊C4C2×C3⋊D312yes—
231C2×C22⋊C4—91no—
232C2×C22⋊C4—91no—
233C2×C22⋊C4—92no—
234C2×C22⋊C4C2×C3⋊D312yes—
235C2×C42—91no—
236C2×C42—92no—
237#95—91no—
238#95—91no—
239#95—92no—
240#95—92no—
241#95—92no—
242#95C2×C3⋊D311yescharacteristic
243#95C2×C3⋊D311yescharacteristic
244C23×C3—28no—
245C23×C3—28no—
246C23×C3C2×C4×D318yes—
247C23×C3D3×D418yes—
248C23×C3D3×Q818yes—
249C23×C3C23×D314yes—
250C22×D3—38no—
251C22×D3—38no—
252C22×D3—38no—
253C22×D3—68no—
254C22×D3—68no—
255C2×C3×C4—28no—
256C2×C3×C4—28no—
257C2×C3×C4—28no—
258C2×C3×C4—28no—
259C2×C3×C4—28no—
260C2×C3×C4—28no—
261C2×C3×C4—28no—
262C2×C3×C4—28no—
263C2×C3×C4—416no—
264C2×C3×C4C2×C4×D318yes—
265C2×C3×C4C2×C4×D318yes—
266#67—364no—
267C2×Dic3—38no—
268C2×Dic3—38no—
269C2×Dic3—38no—
270C2×Dic3—38no—
271C2×Dic3—38no—
272C2×Dic3—316no—
273C2×Dic3—68no—
274C2×Dic3—68no—
275C2×Dic3—68no—
276C2×Dic3—68no—
277C2×Dic3—68no—
278C2×Dic3—68no—
279C2×Dic3—68no—
280C2×Dic3—1232no—
281C4×D3—1216no—
282C4×D3—1232no—
283C2×C32—24no—
284C2×C32C22×C4⋊C411yescharacteristic
285C2×C32C4×#4111yescharacteristic
286C2×C32#51811yescharacteristic
287C2×C32#54612yes—
288C2×C32#55412yes—
289C3⋊D3—24no—
290C24—91no—
291C24C22×C3⋊D311yescharacteristic
292C2×D4—94no—
293C2×D4—94no—
294C2×D4—94no—
295C22×C4—42no—
296C22×C4—91no—
297C22×C4—92no—
298C22×C4—91no—
299C22×C4—91no—
300C22×C4—94no—
301C22×C4—92no—
302C22×C4—184no—
303C22×C4—184no—
304C22×C4—184no—
305C22×C4—184no—
306C22×C4—362no—
307C22×C4—362no—
308C22×C4—362no—
309C22×C4C4×C3⋊D314yescomplemented
310C22×C4C22×C3⋊D312yes—
311C22×C4C22×C3⋊D312yes—
312C22×C4C22×C3⋊D311yescharacteristic
313C22×C4C22×C3⋊D311yescharacteristic
314C4⋊C4—42no—
315C4⋊C4—94no—
316C4⋊C4—184no—
317C4⋊C4—184no—
318C4⋊C4—362no—
319C22⋊C4—24no—
320C22⋊C4—94no—
321C22⋊C4—94no—
322C22⋊C4—184no—
323C42—94no—
324C42—184no—
325C22×C3—216no—
326C22×C3—28no—
327C22×C3—28no—
328C22×C3—216no—
329C22×C3D3×C4⋊C4116yes—
330C22×C3C22×C4×D314yes—
331C22×C3C2×D3×D414yes—
332C22×C3#100418yes—
333C22×C3C2×D3×Q814yes—
334C22×C3D3×#4118yes—
335C2×D3—316no—
336C2×D3—616no—
337C2×D3—68no—
338C2×D3—68no—
339C2×D3—616no—
340C3×C4—28no—
341C3×C4—28no—
342C3×C4—48no—
343C3×C4—48no—
344Dic3—316no—
345Dic3—68no—
346Dic3—68no—
347Dic3—616no—
348Dic3—128no—
349C32#234911yescharacteristic, complemented, Sylow
350C23—22no—
351C23—22no—
352C23—92no—
353C23—92no—
354C23—92no—
355C23—182no—
356C23—182no—
357C23C2×C4×C3⋊D312yes—
358C23D4×C3⋊D312yes—
359C23Q8×C3⋊D312yes—
360C23C23×C3⋊D311yescharacteristic
361D4—916no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—44no—
371C2×C4—92no—
372C2×C4—92no—
373C2×C4—92no—
374C2×C4—92no—
375C2×C4—92no—
376C2×C4—94no—
377C2×C4—182no—
378C2×C4—182no—
379C2×C4—182no—
380C2×C4—182no—
381C2×C4—182no—
382C2×C4—182no—
383C2×C4—182no—
384C2×C4—364no—
385C2×C4—368no—
386C2×C4—368no—
387C2×C4C2×C4×C3⋊D312yes—
388C2×C4C2×C4×C3⋊D312yes—
389C2×C3—216no—
390C2×C3#548614yes—
391C2×C3C2×D3×C4⋊C414yes—
392C2×C3#552214yes—
393C2×C3#561018yes—
394C2×C3#563618yes—
395D3—616no—
396C22—24no—
397C22—22no—
398C22—22no—
399C22—24no—
400C22—94no—
401C22—184no—
402C22—182no—
403C22—182no—
404C22—184no—
405C22C4⋊C4×C3⋊D314yes—
406C22C22×C4×C3⋊D311yescharacteristic
407C22C2×D4×C3⋊D311yescharacteristic
408C22#6436112yes—
409C22C2×Q8×C3⋊D311yescharacteristic
410C22#41×C3⋊D312yes—
411C4—22no—
412C4—22no—
413C4—42no—
414C4—42no—
415C4—94no—
416C4—182no—
417C4—182no—
418C4—184no—
419C4—362no—
420C3#7401114yescomplemented
421C2—24no—
422C2—184no—
423C2#1059595711yescharacteristic
424C2C2×C4⋊C4×C3⋊D311yescharacteristic
425C2#1059599311yescharacteristic
426C2#1059608112yes—
427C2#1059610712yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#380C2
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenter#380C3⋊D3
hypocenterC32#2349
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
3. C32×#380C2semidirect
4. C2×#63658C2semidirect
5. #10592688C2semidirect
6. #10592675C2semidirect
7. #10592645C2semidirect
8. #10592366C2semidirect
9. C3⋊D3×#95C2semidirect
10. #10592349C2semidirect
11. #10592348C2semidirect
21. C4×#638C4semidirect
40. C3×#380D3semidirect
52. C22×C32×C4C2×C4semidirect
72. C2×C4×C3⋊D3C2×C4semidirect
75. #3757C2×C4semidirect
77. #3752C2×C4semidirect
81. #3750C2×C4semidirect
83. C4×C3⋊Dic3C2×C4semidirect
132. #638C4⋊C4semidirect
156. #380C3⋊D3semidirect
163. C22×C3×C4C4×D3semidirect
309. C22×C4C4×C3⋊D3semidirect
349. C32#2349semidirect
420. C3#74011semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C2×#640902
C32×#3802
C2×#636582
#105926882
#105926752
#105926452
#105923662
C3⋊D3×#952
#105923492
#105923482
#740113