Finite Group Databasebeta

← #11803554

Subgroups — #11803554

Order 1152.

2004 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#117C211yesmaximal, characteristic, complemented
2C2×#64139C211yesmaximal, characteristic
3C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4#10592911C211yesmaximal, characteristic, complemented
5#10592689C212yesmaximal, complemented
6#10592688C212yesmaximal, complemented
7#10592656C212yesmaximal, complemented
8#10592655C212yesmaximal, complemented
9#10592638C211yesmaximal, characteristic, complemented
10C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
11#10592627C211yesmaximal, characteristic, complemented
12#82236—34nomaximal
13C23×C32×C4C2211yescharacteristic
14C22×#638C2212yes—
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C4×C3⋊D3C2212yes—
17C32×#117—24no—
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×C32×C42C2211yescharacteristic
23C2×C32×C42C2211yescharacteristic
24C2×#3757C2212yes—
25#64139C418yescomplemented
26C2×#3752C2212yes—
27C2×#3752C2212yes—
28C2×#3752C2212yes—
29C2×#3752C2212yes—
30C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
31C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
32C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
33C2×#3750C2212yes—
34C2×C4×C3⋊Dic3C2212yes—
35C4×C4⋊(C3⋊D3)—24no—
36#63658C2212yes—
37#63658C2212yes—
38#63658C2212yes—
39C2×C3×#117D314yescomplemented
40C2×#930—34no—
41C2×C4×D12—34no—
42#5212—34no—
43#4990—38no—
44#4989—38no—
45#4957—38no—
46#4956—38no—
47#4939—34no—
48C4×C4⋊Dic3—34no—
49#4928—34no—
50C24×C32C2311yescharacteristic
51C23×C3⋊D3C2312yes—
52C22×C32×C4—22no—
53C22×C32×C4—22no—
54C22×C32×C4C2×C414yescomplemented
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C22×C32×C4C2311yescharacteristic
61C2×#638—42no—
62C2×#638—42no—
63C2×#638C2×C418yescomplemented
64C22×C3⋊Dic3C2312yes—
65C22×C3⋊Dic3C2312yes—
66C22×C3⋊Dic3C2312yes—
67C2×C4⋊(C3⋊D3)—22no—
68C2×C4⋊(C3⋊D3)—22no—
69C2×C4⋊(C3⋊D3)C2×C414yes—
70C2×C4×C3⋊D3—24no—
71C2×C4×C3⋊D3—42no—
72C2×C4×C3⋊D3—42no—
73C32×C4⋊C4—22no—
74C32×C4⋊C4—22no—
75C32×C22⋊C4—22no—
76C32×C22⋊C4—22no—
77C32×C42—22no—
78C32×C42D414yescomplemented
79#3757—42no—
80#3752—24no—
81#3752—42no—
82#3752—42no—
83#3752C2×C418yescomplemented
84C4⋊(C3⋊Dic3)—22no—
85C4⋊(C3⋊Dic3)—22no—
86C4⋊(C3⋊Dic3)C2×C414yescomplemented
87#3750—42no—
88C4×C3⋊Dic3—42no—
89#2324—91noSylow
90C23×C3×C4C2×D314yes—
91C22×#67—38no—
92C22×D12—34no—
93C22×C4×D3—38no—
94C3×#117—216no—
95C2×C3×C4⋊C4C2×D314yes—
96C2×C3×C4⋊C4C2×D314yes—
97C2×C3×C22⋊C4C2×D314yes—
98C2×C3×C22⋊C4C2×D314yes—
99C2×C3×C42C2×D314yes—
100C2×C3×C42C2×D314yes—
101C2×#217—38no—
102#930—332no—
103C2×(C2×D3)⋊C4—38no—
104C2×(C2×D3)⋊C4—38no—
105C2×(C2×D3)⋊C4—38no—
106C2×(C2×D3)⋊C4—38no—
107C2×C4⋊Dic3—34no—
108C2×C4⋊Dic3—34no—
109C2×C4⋊Dic3—34no—
110C2×Dic3⋊C4—38no—
111C2×C4×Dic3—38no—
112C4×D12—616no—
113C3⋊#95—38no—
114C3⋊#95—38no—
115C3⋊#95—38no—
116C23×C32—21no—
117C23×C32—21no—
118C23×C32—21no—
119C23×C32—21no—
120C23×C32—21no—
121C23×C32—21no—
122C23×C32C22×C412yes—
123C23×C32C2411yescharacteristic
124C22×C3⋊D3—22no—
125C22×C3⋊D3—22no—
126C22×C3⋊D3—22no—
127C22×C3⋊D3—22no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3—22no—
130C22×C3⋊D3C22×C414yes—
131C2×C32×C4—21no—
132C2×C32×C4—21no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4—21no—
136C2×C32×C4—21no—
137C2×C32×C4—28no—
138C2×C32×C4—21no—
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C32×C4—21no—
142C2×C32×C4—21no—
143C2×C32×C4—21no—
144C2×C32×C4C22×C412yes—
145C2×C32×C4C22×C412yes—
146C2×C32×C4C2×D412yes—
147C2×C32×C4C2×D412yes—
148C2×C32×C4C2×D412yes—
149C2×C32×C4#4112yes—
150#638—48no—
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3C22×C414yes—
160C4⋊(C3⋊D3)—28no—
161C4×C3⋊D3—48no—
162C2×#121—91no—
163C2×C4×D4—91no—
164C2×#117C3⋊D311yescharacteristic, complemented
165#390—92no—
166#390—91no—
167#389—91no—
168#388—92no—
169#386—92no—
170#385—92no—
171#380—91no—
172C4×C4⋊C4—91no—
173C24×C3C22×D314yes—
174C23×D3—38no—
175C22×C3×C4—28no—
176C22×C3×C4—28no—
177C22×C3×C4C4×D3116yescomplemented
178C22×C3×C4C22×D314yes—
179C22×C3×C4C22×D314yes—
180C22×C3×C4C22×D314yes—
181C22×C3×C4C22×D314yes—
182C22×C3×C4C22×D314yes—
183C22×C3×C4C22×D314yes—
184C2×#67—332no—
185C2×#67—128no—
186C2×#67—128no—
187C22×Dic3—38no—
188C22×Dic3—38no—
189C22×Dic3—38no—
190C2×D12—316no—
191C2×D12—68no—
192C2×D12—68no—
193C2×C4×D3—616no—
194C2×C4×D3—128no—
195C2×C4×D3—128no—
196C3×C4⋊C4—28no—
197C3×C4⋊C4—28no—
198C3×C22⋊C4—28no—
199C3×C22⋊C4—28no—
200C3×C42—28no—
201C3×C42#67116yescomplemented
202#217—128no—
203(C2×D3)⋊C4—332no—
204(C2×D3)⋊C4—616no—
205(C2×D3)⋊C4—128no—
206(C2×D3)⋊C4—128no—
207C4⋊Dic3—316no—
208C4⋊Dic3—68no—
209C4⋊Dic3—68no—
210Dic3⋊C4—128no—
211C4×Dic3—128no—
212C22×C32—22no—
213C22×C32—22no—
214C22×C32—22no—
215C22×C32—41no—
216C22×C32—41no—
217C22×C32—41no—
218C22×C32—41no—
219C22×C32C23×C411yescharacteristic
220C22×C32C22×D411yescharacteristic
221C22×C32C2×#4111yescharacteristic
222C22×C32H(5,𝔽2)11yescharacteristic
223C22×C32H(5,𝔽2)11yescharacteristic
224C22×C32H(5,𝔽2)11yescharacteristic
225C22×C322−1+411yescharacteristic
226C2×C3⋊D3—24no—
227C2×C3⋊D3—24no—
228C2×C3⋊D3—24no—
229C2×C3⋊D3—42no—
230C2×C3⋊D3—42no—
231C2×C3⋊D3—42no—
232C2×C3⋊D3—42no—
233C32×C4—22no—
234C32×C4—22no—
235C32×C4—22no—
236C32×C4—41no—
237C32×C4—41no—
238C32×C4C4×D414yes—
239C3⋊Dic3—24no—
240C3⋊Dic3—42no—
241C3⋊Dic3—42no—
242C22×D4—92no—
243C22×D4—91no—
244C23×C4—92no—
245C23×C4C2×C3⋊D311yescharacteristic
246#121—98no—
247C4×D4—184no—
248#117—24no—
249C2×C4⋊C4—91no—
250C2×C4⋊C4—91no—
251C2×C4⋊C4—91no—
252C2×C4⋊C4—92no—
253C2×C4⋊C4C2×C3⋊D311yescharacteristic
254C2×C4⋊C4C2×C3⋊D311yescharacteristic
255C2×C22⋊C4—92no—
256C2×C22⋊C4—92no—
257C2×C22⋊C4—92no—
258C2×C22⋊C4—92no—
259C2×C22⋊C4—92no—
260C2×C22⋊C4C2×C3⋊D311yescharacteristic
261C2×C22⋊C4C2×C3⋊D311yescharacteristic
262C2×C42—92no—
263C2×C42C2×C3⋊D311yescharacteristic
264C2×C42C2×C3⋊D311yescharacteristic
265#95—92no—
266#95—92no—
267#95—92no—
268C23×C3—24no—
269C23×C3—24no—
270C23×C3—24no—
271C23×C3—24no—
272C23×C3—24no—
273C23×C3—24no—
274C23×C3C2×C4×D318yes—
275C23×C3C23×D314yes—
276C22×D3—316no—
277C22×D3—68no—
278C22×D3—68no—
279C22×D3—68no—
280C22×D3—68no—
281C22×D3—68no—
282C22×D3—68no—
283C2×C3×C4—24no—
284C2×C3×C4—24no—
285C2×C3×C4—24no—
286C2×C3×C4—24no—
287C2×C3×C4—24no—
288C2×C3×C4—24no—
289C2×C3×C4—232no—
290C2×C3×C4—24no—
291C2×C3×C4—24no—
292C2×C3×C4—24no—
293C2×C3×C4—24no—
294C2×C3×C4—24no—
295C2×C3×C4—24no—
296C2×C3×C4C2×C4×D318yes—
297C2×C3×C4C2×C4×D318yes—
298C2×C3×C4#23518yes—
299C2×C3×C4C2×#6718yes—
300C2×C3×C4C2×#6718yes—
301C2×C3×C4C2×#6718yes—
302#67—1232no—
303C2×Dic3—316no—
304C2×Dic3—68no—
305C2×Dic3—68no—
306C2×Dic3—68no—
307C2×Dic3—68no—
308C2×Dic3—68no—
309C2×Dic3—68no—
310C2×Dic3—68no—
311C2×Dic3—68no—
312D12—632no—
313C4×D3—1232no—
314C2×C32—42no—
315C2×C32C2×C4×D411yescharacteristic
316C2×C32#51811yescharacteristic
317C2×C32#52011yescharacteristic
318C2×C32#53511yescharacteristic
319C2×C32#53711yescharacteristic
320C2×C32#54011yescharacteristic
321C2×C32#54211yescharacteristic
322C3⋊D3—44no—
323C24—92no—
324C24C22×C3⋊D311yescharacteristic
325C2×D4—98no—
326C2×D4—94no—
327C2×D4—182no—
328C2×D4—182no—
329C2×D4—362no—
330C2×D4—362no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—92no—
334C22×C4—92no—
335C22×C4—92no—
336C22×C4—184no—
337C22×C4—362no—
338C22×C4—362no—
339C22×C4C4×C3⋊D314yescomplemented
340C22×C4C22×C3⋊D311yescharacteristic
341C22×C4C22×C3⋊D311yescharacteristic
342C22×C4C22×C3⋊D311yescharacteristic
343C22×C4C22×C3⋊D311yescharacteristic
344C22×C4C22×C3⋊D311yescharacteristic
345C22×C4C22×C3⋊D311yescharacteristic
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—94no—
349C4⋊C4—182no—
350C4⋊C4—182no—
351C4⋊C4—362no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—98no—
355C22⋊C4—184no—
356C22⋊C4—362no—
357C22⋊C4—362no—
358C22⋊C4—362no—
359C42—22no—
360C42—362no—
361C42#63814yescomplemented
362C22×C3—28no—
363C22×C3—28no—
364C22×C3—28no—
365C22×C3—44no—
366C22×C3—44no—
367C22×C3—44no—
368C22×C3—44no—
369C22×C3C22×C4×D314yes—
370C22×C3C2×#23514yes—
371C22×C3#100914yes—
372C22×C3#100914yes—
373C22×C3#100914yes—
374C22×C3#101014yes—
375C22×C3C22×#6714yes—
376C2×D3—616no—
377C2×D3—616no—
378C2×D3—616no—
379C2×D3—128no—
380C2×D3—128no—
381C2×D3—128no—
382C2×D3—128no—
383C3×C4—28no—
384C3×C4—28no—
385C3×C4—28no—
386C3×C4—44no—
387C3×C4—44no—
388C3×C4C4×#67116yes—
389Dic3—616no—
390Dic3—128no—
391Dic3—128no—
392C32#232411yescharacteristic, complemented, Sylow
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—94no—
400C23—182no—
401C23—182no—
402C23—182no—
403C23—182no—
404C23—182no—
405C23—182no—
406C23C2×C4×C3⋊D312yes—
407C23C23×C3⋊D311yescharacteristic
408D4—188no—
409D4—368no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—28no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—94no—
424C2×C4—182no—
425C2×C4—182no—
426C2×C4—182no—
427C2×C4—182no—
428C2×C4—182no—
429C2×C4—182no—
430C2×C4—182no—
431C2×C4—182no—
432C2×C4—368no—
433C2×C4C2×C4×C3⋊D312yes—
434C2×C4C2×C4×C3⋊D312yes—
435C2×C4#382812yes—
436C2×C4C2×#63812yes—
437C2×C4C2×#63812yes—
438C2×C4C2×#63812yes—
439C2×C3—48no—
440C2×C3#552114yes—
441C2×C3#552314yes—
442C2×C3#553414yes—
443C2×C3#553514yes—
444C2×C3C2×C4×#6714yes—
445C2×C3#583014yes—
446C2×C3#583314yes—
447D3—1216no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—184no—
456C22—184no—
457C22—184no—
458C22—362no—
459C22—362no—
460C22—362no—
461C22—362no—
462C22C22×C4×C3⋊D311yescharacteristic
463C22C2×#382811yescharacteristic
464C22#6436611yescharacteristic
465C22#6436611yescharacteristic
466C22#6436611yescharacteristic
467C22#6436711yescharacteristic
468C22C22×#63811yescharacteristic
469C4—22no—
470C4—22no—
471C4—22no—
472C4—41no—
473C4—41no—
474C4—184no—
475C4—362no—
476C4—362no—
477C4C4×#63814yes—
478C3#8223614yescomplemented
479C2—42no—
480C2—364no—
481C2#1059599211yescharacteristic
482C2#1059599411yescharacteristic
483C2#1059600511yescharacteristic
484C2#1059600611yescharacteristic
485C2C2×C4×#63811yescharacteristic
486C2#1059630111yescharacteristic
487C2#1059630411yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC2×C32×#117C2
socle, cosocleC23×C32C24
prime radicalC2×#64139C2
hypercenterC2×#117C3⋊D3
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×C32×#117C2semidirect
3. C2×C4×C4⋊(C3⋊D3)C2semidirect
4. #10592911C2semidirect
5. #10592689C2semidirect
6. #10592688C2semidirect
7. #10592656C2semidirect
8. #10592655C2semidirect
9. #10592638C2semidirect
10. C4×C4⋊(C3⋊Dic3)C2semidirect
11. #10592627C2semidirect
25. #64139C4semidirect
39. C2×C3×#117D3semidirect
54. C22×C32×C4C2×C4semidirect
63. C2×#638C2×C4semidirect
78. C32×C42D4semidirect
83. #3752C2×C4semidirect
86. C4⋊(C3⋊Dic3)C2×C4semidirect
164. C2×#117C3⋊D3semidirect
177. C22×C3×C4C4×D3semidirect
201. C3×C42#67semidirect
339. C22×C4C4×C3⋊D3semidirect
361. C42#638semidirect
392. C32#2324semidirect
478. C3#82236semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1172
C2×#641392
C2×C4×C4⋊(C3⋊D3)2
#105929112
#105926892
#105926882
#105926562
#105926552
#105926382
C4×C4⋊(C3⋊Dic3)2
#105926272
#822363