Finite Group Databasebeta

← #11803557

Subgroups — #11803557

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×#64104C211yesmaximal, characteristic
2C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C2×#64081C211yesmaximal, characteristic, complemented
4C32×C4×C4⋊C4C211yesmaximal, characteristic, complemented
5#10592687C211yesmaximal, characteristic, complemented
6#10592686C211yesmaximal, characteristic, complemented
7#10592683C211yesmaximal, characteristic, complemented
8#10592639C212yesmaximal, complemented
9#10592638C212yesmaximal, complemented
10#10592367C212yesmaximal, complemented
11#10592364C212yesmaximal, complemented
12#73763—34nomaximal
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C4⋊(C3⋊D3)C2212yes—
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C4×C3⋊D3C2212yes—
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C32×C42C2212yes—
20C2×C32×C42C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3752C2212yes—
24C2×#3752C2212yes—
25C2×#3752C2212yes—
26C2×#3752C2212yes—
27C2×#3752C2212yes—
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×C4⋊(C3⋊Dic3)C2212yes—
30C2×#3750C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C2×C4×C3⋊Dic3C2211yescharacteristic
33#64104C418yescomplemented
34C4×C4⋊(C3⋊D3)—24no—
35#64081—24no—
36C32×#95C2212yes—
37#63658C2212yes—
38#63658C2212yes—
39C2×#895—34no—
40C2×C4×D12—34no—
41C2×#872—34no—
42C3×C4×C4⋊C4D314yescomplemented
43#4988—34no—
44#4987—34no—
45#4984—34no—
46#4940—38no—
47#4939—38no—
48#4668—38no—
49#4665—38no—
50C23×C3⋊D3C2311yescharacteristic
51C23×C3⋊D3C2312yes—
52C22×C32×C4C2312yes—
53C22×C32×C4C2312yes—
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3C2312yes—
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3⋊Dic3C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C2×C4⋊(C3⋊D3)—22no—
62C2×C4⋊(C3⋊D3)—22no—
63C2×C4⋊(C3⋊D3)—42no—
64C2×C4⋊(C3⋊D3)—42no—
65C2×C4⋊(C3⋊D3)C2×C414yes—
66C2×C4⋊(C3⋊D3)C2×C418yescomplemented
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3—24no—
70C2×C4×C3⋊D3—42no—
71C2×C4×C3⋊D3—42no—
72C2×C4×C3⋊D3C2×C414yescomplemented
73C32×C4⋊C4—22no—
74C32×C4⋊C4C2×C414yescomplemented
75C32×C42—42no—
76C32×C42D414yescomplemented
77#3752—22no—
78#3752—22no—
79#3752—24no—
80#3752—42no—
81#3752—42no—
82#3752—42no—
83#3752C2×C418yescomplemented
84C4⋊(C3⋊Dic3)—22no—
85C4⋊(C3⋊Dic3)—42no—
86#3750—22no—
87#3750—22no—
88C4×C3⋊Dic3—22no—
89#2324—91noSylow
90C22×D12—34no—
91C22×D12—38no—
92C22×C4×D3—34no—
93C22×C4×D3—38no—
94C2×C3×C4⋊C4C2×D314yes—
95C2×C3×C4⋊C4C2×D314yes—
96C2×C3×C42C2×D318yes—
97C2×C3×C42C2×D314yes—
98C2×(C2×D3)⋊C4—38no—
99C2×(C2×D3)⋊C4—34no—
100C2×(C2×D3)⋊C4—34no—
101C2×(C2×D3)⋊C4—38no—
102C2×(C2×D3)⋊C4—38no—
103C2×(C2×D3)⋊C4—38no—
104C2×(C2×D3)⋊C4—38no—
105C2×C4⋊Dic3—34no—
106C2×C4⋊Dic3—38no—
107C2×Dic3⋊C4—34no—
108C2×Dic3⋊C4—34no—
109C2×C4×Dic3—34no—
110#895—332no—
111C4×D12—616no—
112#872—616no—
113C3×#95C2×D318yes—
114C3⋊#95—38no—
115C3⋊#95—38no—
116C23×C32C2411yescharacteristic
117C22×C3⋊D3—21no—
118C22×C3⋊D3—22no—
119C22×C3⋊D3—21no—
120C22×C3⋊D3—22no—
121C22×C3⋊D3—21no—
122C22×C3⋊D3—22no—
123C22×C3⋊D3—22no—
124C22×C3⋊D3—22no—
125C22×C3⋊D3—21no—
126C22×C3⋊D3—21no—
127C22×C3⋊D3—21no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3C22×C414yes—
130C22×C3⋊D3C22×C412yes—
131C2×C32×C4—22no—
132C2×C32×C4—21no—
133C2×C32×C4—22no—
134C2×C32×C4—21no—
135C2×C32×C4—21no—
136C2×C32×C4—21no—
137C2×C32×C4—22no—
138C2×C32×C4—22no—
139C2×C32×C4—22no—
140C2×C32×C4C22×C414yes—
141C2×C32×C4C22×C412yes—
142C2×C32×C4C2×D412yes—
143C2×C32×C4C2×D412yes—
144C2×C32×C4C2×D412yes—
145C2×C32×C4#4112yes—
146C2×C3⋊Dic3—21no—
147C2×C3⋊Dic3—21no—
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—21no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—21no—
154C2×C3⋊Dic3—21no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3C22×C412yes—
158C4⋊(C3⋊D3)—28no—
159C4⋊(C3⋊D3)—48no—
160C4×C3⋊D3—28no—
161C4×C3⋊D3—48no—
162C2×#121—91no—
163C2×C4×D4—91no—
164C2×#117—91no—
165#390—91no—
166#390—92no—
167#389—91no—
168#388—92no—
169#386—92no—
170#385—92no—
171#380—91no—
172C4×C4⋊C4C3⋊D311yescharacteristic, complemented
173C23×D3—38no—
174C23×D3—34no—
175C22×C3×C4C22×D318yes—
176C22×C3×C4C22×D318yes—
177C22×C3×C4C22×D314yes—
178C22×C3×C4C22×D314yes—
179C22×C3×C4C22×D314yes—
180C22×Dic3—34no—
181C22×Dic3—34no—
182C22×Dic3—38no—
183C22×Dic3—34no—
184C2×D12—316no—
185C2×D12—332no—
186C2×D12—68no—
187C2×D12—68no—
188C2×D12—128no—
189C2×D12—128no—
190C2×C4×D3—316no—
191C2×C4×D3—68no—
192C2×C4×D3—68no—
193C2×C4×D3—616no—
194C2×C4×D3—128no—
195C2×C4×D3—128no—
196C3×C4⋊C4—28no—
197C3×C4⋊C4C4×D3116yescomplemented
198C3×C42—48no—
199C3×C42D12116yescomplemented
200(C2×D3)⋊C4—332no—
201(C2×D3)⋊C4—68no—
202(C2×D3)⋊C4—68no—
203(C2×D3)⋊C4—616no—
204(C2×D3)⋊C4—128no—
205(C2×D3)⋊C4—128no—
206(C2×D3)⋊C4—128no—
207C4⋊Dic3—68no—
208C4⋊Dic3—128no—
209Dic3⋊C4—68no—
210Dic3⋊C4—68no—
211C4×Dic3—68no—
212C22×C32C23×C411yescharacteristic
213C22×C32C22×D411yescharacteristic
214C22×C32C2×#4111yescharacteristic
215C22×C32H(5,𝔽2)11yescharacteristic
216C22×C32H(5,𝔽2)11yescharacteristic
217C22×C32H(5,𝔽2)11yescharacteristic
218C22×C322−1+411yescharacteristic
219C2×C3⋊D3—22no—
220C2×C3⋊D3—24no—
221C2×C3⋊D3—22no—
222C2×C3⋊D3—24no—
223C2×C3⋊D3—22no—
224C2×C3⋊D3—24no—
225C2×C3⋊D3—42no—
226C2×C3⋊D3—41no—
227C2×C3⋊D3—41no—
228C2×C3⋊D3—42no—
229C2×C3⋊D3—41no—
230C2×C3⋊D3—42no—
231C2×C3⋊D3—41no—
232C2×C3⋊D3—42no—
233C32×C4—24no—
234C32×C4—22no—
235C32×C4—22no—
236C32×C4—42no—
237C32×C4C4×D414yes—
238C3⋊Dic3—22no—
239C3⋊Dic3—42no—
240C3⋊Dic3—41no—
241C3⋊Dic3—41no—
242C22×D4—91no—
243C22×D4—92no—
244C23×C4—91no—
245C23×C4—92no—
246#121—98no—
247C4×D4—184no—
248#117—184no—
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—91no—
257C2×C22⋊C4—91no—
258C2×C22⋊C4—92no—
259C2×C22⋊C4—92no—
260C2×C22⋊C4—92no—
261C2×C22⋊C4—92no—
262C2×C42—91no—
263C2×C42C2×C3⋊D312yes—
264C2×C42C2×C3⋊D311yescharacteristic
265#95—92no—
266#95—92no—
267#95C2×C3⋊D312yes—
268C23×C3C23×D314yes—
269C22×D3—316no—
270C22×D3—38no—
271C22×D3—64no—
272C22×D3—68no—
273C22×D3—64no—
274C22×D3—68no—
275C22×D3—68no—
276C22×D3—64no—
277C22×D3—68no—
278C22×D3—64no—
279C22×D3—64no—
280C22×D3—68no—
281C22×D3—68no—
282C22×D3—64no—
283C2×C3×C4—24no—
284C2×C3×C4—28no—
285C2×C3×C4—24no—
286C2×C3×C4—28no—
287C2×C3×C4—24no—
288C2×C3×C4—24no—
289C2×C3×C4—28no—
290C2×C3×C4—28no—
291C2×C3×C4—28no—
292C2×C3×C4C2×C4×D3116yes—
293C2×C3×C4C2×C4×D318yes—
294C2×C3×C4C2×D1218yes—
295C2×C3×C4C2×D1218yes—
296C2×C3×C4C2×D1218yes—
297C2×C3×C4#23518yes—
298C2×Dic3—38no—
299C2×Dic3—64no—
300C2×Dic3—64no—
301C2×Dic3—64no—
302C2×Dic3—64no—
303C2×Dic3—68no—
304C2×Dic3—64no—
305C2×Dic3—64no—
306C2×Dic3—64no—
307C2×Dic3—68no—
308C2×Dic3—64no—
309C2×Dic3—68no—
310D12—632no—
311D12—1232no—
312C4×D3—632no—
313C4×D3—1232no—
314C2×C32C2×C4×D411yescharacteristic
315C2×C32#51811yescharacteristic
316C2×C32#52011yescharacteristic
317C2×C32#53511yescharacteristic
318C2×C32#53711yescharacteristic
319C2×C32#54011yescharacteristic
320C2×C32#54211yescharacteristic
321C3⋊D3—42no—
322C3⋊D3—44no—
323C24—92no—
324C24—91no—
325C2×D4—94no—
326C2×D4—98no—
327C2×D4—182no—
328C2×D4—182no—
329C2×D4—362no—
330C2×D4—362no—
331C22×C4—91no—
332C22×C4—94no—
333C22×C4—91no—
334C22×C4—92no—
335C22×C4—91no—
336C22×C4—182no—
337C22×C4—182no—
338C22×C4—184no—
339C22×C4—362no—
340C22×C4—362no—
341C22×C4C22×C3⋊D312yes—
342C22×C4C22×C3⋊D312yes—
343C22×C4C22×C3⋊D311yescharacteristic
344C22×C4C22×C3⋊D311yescharacteristic
345C22×C4C22×C3⋊D311yescharacteristic
346C4⋊C4—22no—
347C4⋊C4—182no—
348C4⋊C4—182no—
349C4⋊C4—182no—
350C4⋊C4—362no—
351C4⋊C4C4×C3⋊D314yescomplemented
352C22⋊C4—98no—
353C22⋊C4—182no—
354C22⋊C4—182no—
355C22⋊C4—184no—
356C22⋊C4—362no—
357C22⋊C4—362no—
358C22⋊C4—362no—
359C42—42no—
360C42—182no—
361C42C4⋊(C3⋊D3)14yescomplemented
362C22×C3C22×C4×D314yes—
363C22×C3C22×D1214yes—
364C22×C3C2×#23514yes—
365C22×C3#100414yes—
366C22×C3#100714yes—
367C22×C3#100914yes—
368C22×C3#100914yes—
369C2×D3—68no—
370C2×D3—616no—
371C2×D3—68no—
372C2×D3—616no—
373C2×D3—616no—
374C2×D3—68no—
375C2×D3—124no—
376C2×D3—128no—
377C2×D3—128no—
378C2×D3—124no—
379C2×D3—124no—
380C2×D3—128no—
381C2×D3—124no—
382C2×D3—128no—
383C3×C4—28no—
384C3×C4—28no—
385C3×C4—216no—
386C3×C4—48no—
387C3×C4C4×D12116yes—
388Dic3—68no—
389Dic3—124no—
390Dic3—128no—
391Dic3—124no—
392C32#232411yescharacteristic, complemented, Sylow
393C23—94no—
394C23—92no—
395C23—181no—
396C23—182no—
397C23—181no—
398C23—182no—
399C23—182no—
400C23—181no—
401C23—182no—
402C23—181no—
403C23—181no—
404C23—182no—
405C23—182no—
406C23—181no—
407C23C23×C3⋊D311yescharacteristic
408D4—188no—
409D4—368no—
410C2×C4—21no—
411C2×C4—22no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—92no—
420C2×C4—181no—
421C2×C4—181no—
422C2×C4—188no—
423C2×C4—181no—
424C2×C4—181no—
425C2×C4—182no—
426C2×C4—181no—
427C2×C4—181no—
428C2×C4—181no—
429C2×C4—182no—
430C2×C4—181no—
431C2×C4—182no—
432C2×C4—368no—
433C2×C4C2×C4×C3⋊D314yes—
434C2×C4C2×C4×C3⋊D312yes—
435C2×C4C2×C4⋊(C3⋊D3)12yes—
436C2×C4C2×C4⋊(C3⋊D3)12yes—
437C2×C4C2×C4⋊(C3⋊D3)12yes—
438C2×C4#382812yes—
439C2×C3C2×C4×D1214yes—
440C2×C3#551014yes—
441C2×C3#552514yes—
442C2×C3#554514yes—
443C2×C3#556214yes—
444C2×C3#557414yes—
445C2×C3#558214yes—
446D3—128no—
447D3—1216no—
448C22—182no—
449C22—184no—
450C22—182no—
451C22—184no—
452C22—184no—
453C22—182no—
454C22—361no—
455C22—362no—
456C22—362no—
457C22—361no—
458C22—361no—
459C22—362no—
460C22—361no—
461C22—362no—
462C22C22×C4×C3⋊D311yescharacteristic
463C22C22×C4⋊(C3⋊D3)11yescharacteristic
464C22C2×#382811yescharacteristic
465C22#6436111yescharacteristic
466C22#6436411yescharacteristic
467C22#6436611yescharacteristic
468C22#6436611yescharacteristic
469C4—22no—
470C4—22no—
471C4—24no—
472C4—42no—
473C4—182no—
474C4—361no—
475C4—362no—
476C4—361no—
477C4C4×C4⋊(C3⋊D3)14yes—
478C3#7376314yescomplemented
479C2—362no—
480C2—364no—
481C2C2×C4×C4⋊(C3⋊D3)11yescharacteristic
482C2#1059598111yescharacteristic
483C2#1059599611yescharacteristic
484C2#1059601611yescharacteristic
485C2#1059603311yescharacteristic
486C2#1059604511yescharacteristic
487C2#1059605311yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×C4×C4⋊C4C2
socle, cosocleC23×C32C24
prime radicalC2×#64104C2
hypercenterC4×C4⋊C4C3⋊D3
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊(C3⋊D3)C2semidirect
3. C2×#64081C2semidirect
4. C32×C4×C4⋊C4C2semidirect
5. #10592687C2semidirect
6. #10592686C2semidirect
7. #10592683C2semidirect
8. #10592639C2semidirect
9. #10592638C2semidirect
10. #10592367C2semidirect
11. #10592364C2semidirect
33. #64104C4semidirect
42. C3×C4×C4⋊C4D3semidirect
66. C2×C4⋊(C3⋊D3)C2×C4semidirect
72. C2×C4×C3⋊D3C2×C4semidirect
74. C32×C4⋊C4C2×C4semidirect
76. C32×C42D4semidirect
83. #3752C2×C4semidirect
172. C4×C4⋊C4C3⋊D3semidirect
197. C3×C4⋊C4C4×D3semidirect
199. C3×C42D12semidirect
351. C4⋊C4C4×C3⋊D3semidirect
361. C42C4⋊(C3⋊D3)semidirect
392. C32#2324semidirect
478. C3#73763semidirect

Maximal subgroups

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

subgroupindex
C2×#641042
C2×C4×C4⋊(C3⋊D3)2
C2×#640812
C32×C4×C4⋊C42
#105926872
#105926862
#105926832
#105926392
#105926382
#105923672
#105923642
#737633