Finite Group Databasebeta

← #11803560

Subgroups — #11803560

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×#121C211yesmaximal, characteristic
2C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×#64135C211yesmaximal, characteristic, complemented
4#10592920C211yesmaximal, characteristic, complemented
5#10592920C212yesmaximal, complemented
6#10592919C212yesmaximal, complemented
7#10592911C211yesmaximal, characteristic, complemented
8#10592683C211yesmaximal, characteristic, complemented
9C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
10#10592650C212yesmaximal, complemented
11#10592649C212yesmaximal, complemented
12#82633—34nomaximal
13C22×C32×D4C2211yescharacteristic
14C22×C32×D4C2212yes—
15C23×C32×C4C2211yescharacteristic
16C23×C3⋊Dic3C2212yes—
17C32×#121C418yescomplemented
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C32×C22⋊C4C2212yes—
20C2×#3757C2212yes—
21C2×#3757C2211yescharacteristic
22C2×#3757C2211yescharacteristic
23C2×#3757C2212yes—
24C2×#3757C2212yes—
25C2×#3757C2212yes—
26D4×C3⋊Dic3—24no—
27#64135—24no—
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
31C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
32C2×C4⋊(C3⋊Dic3)C2212yes—
33C2×C4×C3⋊Dic3C2211yescharacteristic
34C2×C4×C3⋊Dic3C2212yes—
35C2×C4×C3⋊Dic3C2211yescharacteristic
36#63658C2212yes—
37#63658C2212yes—
38#63658C2212yes—
39C2×C3×#121D314yes—
40C2×D4×Dic3—34no—
41C2×#926—34no—
42#5221—34no—
43#5221—38no—
44#5220—38no—
45#5212—34no—
46#4984—34no—
47Dic3×C4⋊C4—34no—
48#4951—38no—
49#4950—38no—
50C24×C32C2312yes—
51C24×C32C2311yescharacteristic
52C2×C32×D4—22no—
53C2×C32×D4—22no—
54C2×C32×D4—42no—
55C2×C32×D4—42no—
56C2×C32×D4C2×C414yes—
57C2×C32×D4C2×C418yescomplemented
58C22×C32×C4—22no—
59C22×C32×C4—22no—
60C22×C32×C4C2×C414yescomplemented
61C22×C32×C4C2311yescharacteristic
62C22×C32×C4C2312yes—
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3—24no—
65C22×C3⋊Dic3—42no—
66C22×C3⋊Dic3—42no—
67C22×C3⋊Dic3C2312yes—
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2312yes—
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C32×C4⋊C4C2×C414yescomplemented
74C32×C22⋊C4C2×C418yescomplemented
75#3757—22no—
76#3757—22no—
77#3757—24no—
78#3757—42no—
79#3757—42no—
80#3757—42no—
81C4⋊(C3⋊Dic3)—22no—
82C4⋊(C3⋊Dic3)—22no—
83C4⋊(C3⋊Dic3)—22no—
84C4⋊(C3⋊Dic3)—22no—
85C4⋊(C3⋊Dic3)—42no—
86C4×C3⋊Dic3—22no—
87C4×C3⋊Dic3—42no—
88C4×C3⋊Dic3D414yescomplemented
89#2324—91noSylow
90C22×C3×D4C2×D314yes—
91C22×C3×D4C2×D318yes—
92C23×C3×C4C2×D314yes—
93C23×Dic3—38no—
94C3×#121Dic3132yescomplemented
95C2×C3×C4⋊C4C2×D314yes—
96C2×C3×C22⋊C4C2×D318yes—
97C2×#217—38no—
98C2×#217—34no—
99C2×#217—34no—
100C2×#217—38no—
101C2×#217—38no—
102C2×#217—38no—
103D4×Dic3—616no—
104#926—616no—
105C2×C4⋊Dic3—34no—
106C2×C4⋊Dic3—34no—
107C2×C4⋊Dic3—34no—
108C2×C4⋊Dic3—34no—
109C2×C4⋊Dic3—38no—
110C2×C4×Dic3—34no—
111C2×C4×Dic3—34no—
112C2×C4×Dic3—38no—
113C3⋊#95—38no—
114C3⋊#95—38no—
115C3⋊#95—38no—
116C23×C32—21no—
117C23×C32—22no—
118C23×C32—21no—
119C23×C32—22no—
120C23×C32—21no—
121C23×C32—22no—
122C23×C32—22no—
123C23×C32—22no—
124C23×C32—21no—
125C23×C32—21no—
126C23×C32—22no—
127C23×C32—21no—
128C23×C32C22×C414yes—
129C23×C32C22×C412yes—
130C23×C32C2411yescharacteristic
131C32×D4—28no—
132C32×D4—48no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4—28no—
138C2×C32×C4C22×C412yes—
139C2×C32×C4C22×C414yes—
140C2×C32×C4C22×C412yes—
141C2×C32×C4C2×D412yes—
142C2×C32×C4#4112yes—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3—21no—
147C2×C3⋊Dic3—21no—
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—21no—
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3—48no—
160C2×C3⋊Dic3C2×D412yes—
161C2×C3⋊Dic3C2×D412yes—
162C2×#121C3⋊D311yescharacteristic
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⋊C4—91no—
173C24×C3C22×D314yes—
174C24×C3C22×D318yes—
175C2×C3×D4—28no—
176C2×C3×D4—28no—
177C2×C3×D4—48no—
178C2×C3×D4—48no—
179C2×C3×D4C2×Dic3116yes—
180C2×C3×D4C2×Dic3132yescomplemented
181C22×C3×C4—28no—
182C22×C3×C4—28no—
183C22×C3×C4C2×Dic3116yescomplemented
184C22×C3×C4C22×D318yes—
185C22×C3×C4C22×D314yes—
186C22×C3×C4C22×D314yes—
187C22×Dic3—34no—
188C22×Dic3—34no—
189C22×Dic3—34no—
190C22×Dic3—38no—
191C22×Dic3—38no—
192C22×Dic3—34no—
193C22×Dic3—616no—
194C22×Dic3—128no—
195C22×Dic3—128no—
196C3×C4⋊C4C2×Dic3116yescomplemented
197C3×C22⋊C4C2×Dic3132yescomplemented
198#217—68no—
199#217—68no—
200#217—616no—
201#217—128no—
202#217—128no—
203#217—128no—
204C4⋊Dic3—68no—
205C4⋊Dic3—68no—
206C4⋊Dic3—68no—
207C4⋊Dic3—68no—
208C4⋊Dic3—128no—
209C4×Dic3—316no—
210C4×Dic3—68no—
211C4×Dic3—128no—
212C22×C32—22no—
213C22×C32—24no—
214C22×C32—22no—
215C22×C32—24no—
216C22×C32—22no—
217C22×C32—24no—
218C22×C32—42no—
219C22×C32—41no—
220C22×C32—41no—
221C22×C32—42no—
222C22×C32—41no—
223C22×C32—42no—
224C22×C32—41no—
225C22×C32—42no—
226C22×C32C23×C411yescharacteristic
227C22×C32C22×D411yescharacteristic
228C22×C32C2×#4111yescharacteristic
229C22×C32H(5,𝔽2)11yescharacteristic
230C22×C32H(5,𝔽2)11yescharacteristic
231C22×C32H(5,𝔽2)11yescharacteristic
232C22×C322−1+411yescharacteristic
233C32×C4—22no—
234C32×C4—24no—
235C32×C4C4×D414yes—
236C3⋊Dic3—22no—
237C3⋊Dic3—22no—
238C3⋊Dic3—41no—
239C3⋊Dic3—42no—
240C3⋊Dic3—41no—
241C3⋊Dic3—42no—
242C22×D4C2×C3⋊D311yescharacteristic
243C22×D4C2×C3⋊D312yes—
244C23×C4—92no—
245C23×C4C2×C3⋊D311yescharacteristic
246#121C3⋊Dic318yescomplemented
247C4×D4—184no—
248#117—184no—
249C2×C4⋊C4—91no—
250C2×C4⋊C4—91no—
251C2×C4⋊C4—91no—
252C2×C4⋊C4—91no—
253C2×C4⋊C4—92no—
254C2×C4⋊C4C2×C3⋊D311yescharacteristic
255C2×C22⋊C4—91no—
256C2×C22⋊C4—91no—
257C2×C22⋊C4—92no—
258C2×C22⋊C4—92no—
259C2×C22⋊C4—92no—
260C2×C22⋊C4—92no—
261C2×C22⋊C4C2×C3⋊D312yes—
262C2×C42—91no—
263C2×C42—91no—
264C2×C42—92no—
265#95—92no—
266#95—92no—
267#95—92no—
268C23×C3—24no—
269C23×C3—28no—
270C23×C3—24no—
271C23×C3—28no—
272C23×C3—28no—
273C23×C3—28no—
274C23×C3—24no—
275C23×C3—24no—
276C23×C3—24no—
277C23×C3—28no—
278C23×C3—24no—
279C23×C3—28no—
280C23×C3C22×Dic3116yes—
281C23×C3C22×Dic318yes—
282C23×C3C23×D314yes—
283C3×D4—232no—
284C3×D4—432no—
285C2×C3×C4—24no—
286C2×C3×C4—24no—
287C2×C3×C4—28no—
288C2×C3×C4—28no—
289C2×C3×C4—232no—
290C2×C3×C4D3×D418yes—
291C2×C3×C4#23718yes—
292C2×C3×C4C22×Dic318yes—
293C2×C3×C4C22×Dic3116yes—
294C2×C3×C4C22×Dic318yes—
295C2×Dic3—38no—
296C2×Dic3—38no—
297C2×Dic3—64no—
298C2×Dic3—64no—
299C2×Dic3—64no—
300C2×Dic3—64no—
301C2×Dic3—64no—
302C2×Dic3—64no—
303C2×Dic3—68no—
304C2×Dic3—68no—
305C2×Dic3—68no—
306C2×Dic3—64no—
307C2×Dic3—68no—
308C2×Dic3—64no—
309C2×Dic3—64no—
310C2×Dic3—68no—
311C2×Dic3—68no—
312C2×Dic3—64no—
313C2×Dic3—1232no—
314C2×C32—42no—
315C2×C32—44no—
316C2×C32C2×C4×D411yescharacteristic
317C2×C32#51811yescharacteristic
318C2×C32#52011yescharacteristic
319C2×C32#53511yescharacteristic
320C2×C32#53711yescharacteristic
321C2×C32#54011yescharacteristic
322C2×C32#54211yescharacteristic
323C24C22×C3⋊D311yescharacteristic
324C24C22×C3⋊D312yes—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—42no—
328C2×D4—42no—
329C2×D4C2×C3⋊Dic314yes—
330C2×D4C2×C3⋊Dic318yescomplemented
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—91no—
334C22×C4—91no—
335C22×C4—91no—
336C22×C4—92no—
337C22×C4—92no—
338C22×C4—91no—
339C22×C4—184no—
340C22×C4—362no—
341C22×C4—362no—
342C22×C4C2×C3⋊Dic314yescomplemented
343C22×C4C22×C3⋊D312yes—
344C22×C4C22×C3⋊D311yescharacteristic
345C22×C4C22×C3⋊D311yescharacteristic
346C4⋊C4—182no—
347C4⋊C4—182no—
348C4⋊C4—182no—
349C4⋊C4—182no—
350C4⋊C4—362no—
351C4⋊C4C2×C3⋊Dic314yescomplemented
352C22⋊C4—182no—
353C22⋊C4—182no—
354C22⋊C4—184no—
355C22⋊C4—362no—
356C22⋊C4—362no—
357C22⋊C4—362no—
358C22⋊C4C2×C3⋊Dic318yescomplemented
359C42—94no—
360C42—182no—
361C42—362no—
362C22×C3—28no—
363C22×C3—216no—
364C22×C3—28no—
365C22×C3—216no—
366C22×C3—28no—
367C22×C3—216no—
368C22×C3—44no—
369C22×C3—48no—
370C22×C3—48no—
371C22×C3—44no—
372C22×C3—44no—
373C22×C3—48no—
374C22×C3—44no—
375C22×C3—48no—
376C22×C3C2×D3×D414yes—
377C22×C3C2×#23714yes—
378C22×C3#100414yes—
379C22×C3#100414yes—
380C22×C3#100914yes—
381C22×C3#101014yes—
382C22×C3C23×Dic314yes—
383C3×C4—28no—
384C3×C4—216no—
385C3×C4D4×Dic3116yes—
386Dic3—68no—
387Dic3—68no—
388Dic3—128no—
389Dic3—124no—
390Dic3—124no—
391Dic3—128no—
392C32#232411yescharacteristic, complemented, Sylow
393C23—21no—
394C23—22no—
395C23—21no—
396C23—22no—
397C23—22no—
398C23—22no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—22no—
403C23—21no—
404C23—22no—
405C23C22×C3⋊Dic314yes—
406C23C22×C3⋊Dic312yes—
407C23C23×C3⋊D311yescharacteristic
408D4—28no—
409D4—48no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—28no—
415C2×C4—92no—
416C2×C4—92no—
417C2×C4—181no—
418C2×C4—181no—
419C2×C4—181no—
420C2×C4—181no—
421C2×C4—181no—
422C2×C4—181no—
423C2×C4—182no—
424C2×C4—182no—
425C2×C4—182no—
426C2×C4—181no—
427C2×C4—181no—
428C2×C4—182no—
429C2×C4—181no—
430C2×C4—182no—
431C2×C4—182no—
432C2×C4—181no—
433C2×C4—368no—
434C2×C4D4×C3⋊D312yes—
435C2×C4#383012yes—
436C2×C4C22×C3⋊Dic312yes—
437C2×C4C22×C3⋊Dic314yes—
438C2×C4C22×C3⋊Dic312yes—
439C2×C3—48no—
440C2×C3—416no—
441C2×C3#560314yes—
442C2×C3#560714yes—
443C2×C3#560814yes—
444C2×C3#561914yes—
445C2×C3C2×D4×Dic314yes—
446C2×C3#579814yes—
447C2×C3#582714yes—
448C22—22no—
449C22—24no—
450C22—22no—
451C22—24no—
452C22—22no—
453C22—24no—
454C22—41no—
455C22—42no—
456C22—42no—
457C22—41no—
458C22—41no—
459C22—42no—
460C22—41no—
461C22—42no—
462C22C2×D4×C3⋊D311yescharacteristic
463C22C2×#383011yescharacteristic
464C22#6436111yescharacteristic
465C22#6436111yescharacteristic
466C22#6436611yescharacteristic
467C22#6436711yescharacteristic
468C22C23×C3⋊Dic311yescharacteristic
469C4—22no—
470C4—24no—
471C4—182no—
472C4—182no—
473C4—362no—
474C4—361no—
475C4—361no—
476C4—362no—
477C4D4×C3⋊Dic314yes—
478C3#8263314yescomplemented
479C2—42no—
480C2—44no—
481C2#1059607411yescharacteristic
482C2#1059607811yescharacteristic
483C2#1059607911yescharacteristic
484C2#1059609011yescharacteristic
485C2C2×D4×C3⋊Dic311yescharacteristic
486C2#1059626911yescharacteristic
487C2#1059629811yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
Fitting, prime radicalC2×C32×#121C2
socle, cosocleC23×C32C24
hypercenterC2×#121C3⋊D3
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×D4×C3⋊Dic3C2semidirect
3. C2×#64135C2semidirect
4. #10592920C2semidirect
5. #10592920C2semidirect
6. #10592919C2semidirect
7. #10592911C2semidirect
8. #10592683C2semidirect
9. C4⋊C4×C3⋊Dic3C2semidirect
10. #10592650C2semidirect
11. #10592649C2semidirect
17. C32×#121C4semidirect
57. C2×C32×D4C2×C4semidirect
60. C22×C32×C4C2×C4semidirect
73. C32×C4⋊C4C2×C4semidirect
74. C32×C22⋊C4C2×C4semidirect
88. C4×C3⋊Dic3D4semidirect
94. C3×#121Dic3semidirect
180. C2×C3×D4C2×Dic3semidirect
183. C22×C3×C4C2×Dic3semidirect
196. C3×C4⋊C4C2×Dic3semidirect
197. C3×C22⋊C4C2×Dic3semidirect
246. #121C3⋊Dic3semidirect
330. C2×D4C2×C3⋊Dic3semidirect
342. C22×C4C2×C3⋊Dic3semidirect
351. C4⋊C4C2×C3⋊Dic3semidirect
358. C22⋊C4C2×C3⋊Dic3semidirect
392. C32#2324semidirect
478. C3#82633semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1212
C2×D4×C3⋊Dic32
C2×#641352
#105929202
#105929192
#105929112
#105926832
C4⋊C4×C3⋊Dic32
#105926502
#105926492
#826333