Finite Group Databasebeta

← #11808299

Subgroups — #11808299

Order 1152.

1977 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic
2C2×#63974C212yesmaximal
3C2×#63900C211yesmaximal, characteristic, complemented
4C3×#4953C212yesmaximal, complemented
5#10591694C212yesmaximal, complemented
6#10591370C212yesmaximal, complemented
7#10591370C211yesmaximal, characteristic, complemented
8#10591326C212yesmaximal, complemented
9#10591216C212yesmaximal, complemented
10D3×#397—32nomaximal
11C24×C3⋊D3C2211yescharacteristic
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×#624C2212yes—
15C22×#624C2212yes—
16C2×C32×C22⋊C4C2211yescharacteristic
17C2×#3757C2211yescharacteristic
18C2×#3752C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C22⋊C4×C3⋊D3—24no—
21C2×C3×#217C2214yes—
22C2×C3×C4⋊Dic3C2212yescomplemented
23#63974—28no—
24C2×#3724C2212yescomplemented
25C2×#3722C2214yes—
26#63900—24no—
27C3×C3⋊#95C2212yescomplemented
28C3×C3⋊#95C2214yescomplemented
29#63579C2214yescomplemented
30#63579C2212yescomplemented
31C2×D3×C4⋊C4—32no—
32C2×D3×C22⋊C4—32no—
33C2×D3×C22⋊C4—34no—
34C2×D3×C22⋊C4—61no—
35C3×#397—32no—
36#4992—32no—
37#4953D312yescomplemented
38#4952—34no—
39#4675—34no—
40#4674—32no—
41D3×#95—34no—
42D3×#95—32no—
43C24×C32C2311yescharacteristic
44C23×C3⋊D3—22no—
45C23×C3⋊D3—22no—
46C23×C3⋊D3—24no—
47C23×C3⋊D3—24no—
48C23×C3⋊D3D414yes—
49C23×C3⋊D3C2311yescharacteristic
50C23×C3⋊D3C2311yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3C2311yescharacteristic
54C22×C3⋊Dic3C2311yescharacteristic
55C2×C4×C3⋊D3—24no—
56C2×C4×C3⋊D3—22no—
57C2×C4×C3⋊D3—24no—
58C2×C4×C3⋊D3D414yes—
59C22×C3×Dic3C2314yes—
60C22×C3×Dic3C2314yes—
61C2×#624—24no—
62C2×#624—24no—
63C2×#624—24no—
64C2×#624—24no—
65C2×#624—24no—
66C2×#624—24no—
67C32×C22⋊C4—22no—
68#3757—22no—
69#3752—22no—
70#3752—22no—
71C3×#217—28no—
72C3×C4⋊Dic3—24no—
73#3724—24no—
74#3722—28no—
75C2×#397—91noSylow
76C24×D3—32no—
77C24×D3—61no—
78C22×C4×D3—32no—
79C22×C4×D3—32no—
80C22×C4×D3—34no—
81C22×C4×D3—34no—
82C22×C4×D3—61no—
83C22×C4×D3—61no—
84C2×C3×C4⋊C4—32no—
85C2×C3×C22⋊C4—21no—
86C2×C3×C22⋊C4—34no—
87C2×C3×C22⋊C4C2×D312yes—
88C2×#217—32no—
89C2×#217—61no—
90C2×#217C2×D314yes—
91C2×(C2×D3)⋊C4—32no—
92C2×(C2×D3)⋊C4—32no—
93C2×(C2×D3)⋊C4—34no—
94C2×(C2×D3)⋊C4—34no—
95C2×(C2×D3)⋊C4—61no—
96C2×(C2×D3)⋊C4—61no—
97C2×C4⋊Dic3C2×D312yescomplemented
98C2×Dic3⋊C4—34no—
99D3×C4⋊C4—68no—
100D3×C22⋊C4—616no—
101D3×C22⋊C4—68no—
102D3×C22⋊C4—68no—
103C3×#95—32no—
104C3×#95—34no—
105C3⋊#95—34no—
106C3⋊#95—34no—
107C3⋊#95—34no—
108C3⋊#95C2×D314yescomplemented
109C3⋊#95C2×D312yescomplemented
110C23×C32—21no—
111C23×C32—21no—
112C23×C32—22no—
113C23×C32—22no—
114C23×C32C2×D412yes—
115C23×C32C2411yescharacteristic
116C22×C3⋊D3—21no—
117C22×C3⋊D3—21no—
118C22×C3⋊D3—28no—
119C22×C3⋊D3—22no—
120C22×C3⋊D3—22no—
121C22×C3⋊D3—216no—
122C22×C3⋊D3—44no—
123C22×C3⋊D3—44no—
124C22×C3⋊D3—48no—
125C22×C3⋊D3C2×D412yes—
126C22×C3⋊D3C2×D412yes—
127C22×C3⋊D3C2×D412yes—
128C22×C3⋊D3#4112yes—
129C22×C3⋊D3#4114yes—
130C22×C3⋊D3#4114yes—
131C2×C32×C4—21no—
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4C2×D412yes—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3C2×D412yes—
139C4×C3⋊D3—28no—
140C4×C3⋊D3—44no—
141C2×C3×Dic3—24no—
142C2×C3×Dic3—24no—
143C2×C3×Dic3—24no—
144C2×C3×Dic3—24no—
145C2×C3×Dic3—24no—
146C2×C3×Dic3—24no—
147#624—48no—
148#624—48no—
149C22×C4⋊C4—91no—
150C22×C22⋊C4—92no—
151C22×C22⋊C4—91no—
152#397—32no—
153#397—92no—
154#397—92no—
155#397—92no—
156C2×#95—92no—
157C2×#95—91no—
158C24×C3—21no—
159C24×C3C22×D312yes—
160C23×D3—32no—
161C23×D3—38no—
162C23×D3—32no—
163C23×D3—61no—
164C23×D3—64no—
165C23×D3—61no—
166C23×D3—64no—
167C23×D3—64no—
168C23×D3—68no—
169C23×D3—68no—
170C23×D3—64no—
171C23×D3—64no—
172C23×D3—124no—
173C23×D3—124no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—34no—
177C22×C3×C4—34no—
178C22×C3×C4C22×D312yes—
179C22×C3×C4C22×D312yes—
180C22×Dic3—32no—
181C22×Dic3—32no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C22×Dic3C22×D314yes—
185C22×Dic3C22×D314yes—
186C2×C4×D3—38no—
187C2×C4×D3—64no—
188C2×C4×D3—68no—
189C2×C4×D3—68no—
190C2×C4×D3—68no—
191C2×C4×D3—68no—
192C2×C4×D3—68no—
193C2×C4×D3—68no—
194C2×C4×D3—68no—
195C2×C4×D3—64no—
196C2×C4×D3—68no—
197C2×C4×D3—64no—
198C2×C4×D3—124no—
199C2×C4×D3—124no—
200C3×C4⋊C4—64no—
201C3×C22⋊C4—24no—
202C3×C22⋊C4—24no—
203C3×C22⋊C4—68no—
204#217—28no—
205#217—64no—
206#217—64no—
207(C2×D3)⋊C4—68no—
208(C2×D3)⋊C4—68no—
209(C2×D3)⋊C4—64no—
210(C2×D3)⋊C4—64no—
211(C2×D3)⋊C4—64no—
212(C2×D3)⋊C4—64no—
213C4⋊Dic3—24no—
214Dic3⋊C4—68no—
215C22×C32—22no—
216C22×C32—24no—
217C22×C32—41no—
218C22×C32—41no—
219C22×C32—42no—
220C22×C32C22×D411yescharacteristic
221C22×C32C22×D411yescharacteristic
222C22×C32C2×#4111yescharacteristic
223C22×C32C2×#4112yes—
224C22×C32C2×#4112yes—
225C2×C3⋊D3—22no—
226C2×C3⋊D3—24no—
227C2×C3⋊D3—41no—
228C2×C3⋊D3—41no—
229C2×C3⋊D3—42no—
230C2×C3⋊D3—416no—
231C2×C3⋊D3#12114yes—
232C2×C3⋊D3#12318yes—
233C2×C3⋊D3#12314yes—
234C2×C3⋊D3#12414yes—
235C2×C3⋊D3#12618yes—
236C32×C4—22no—
237C32×C4—41no—
238C3⋊Dic3—22no—
239C3⋊Dic3—41no—
240C3×Dic3—44no—
241C3×Dic3—44no—
242C25—91no—
243C23×C4—92no—
244C23×C4—92no—
245C23×C4—91no—
246C23×C4—91no—
247C2×C4⋊C4—32no—
248C2×C4⋊C4—92no—
249C2×C4⋊C4—184no—
250C2×C22⋊C4—34no—
251C2×C22⋊C4—94no—
252C2×C22⋊C4—91no—
253C2×C22⋊C4—91no—
254C2×C22⋊C4—91no—
255C2×C22⋊C4—184no—
256C2×C22⋊C4—188no—
257C2×C22⋊C4D3211yescharacteristic
258#95—32no—
259#95—34no—
260#95—92no—
261#95—94no—
262C23×C3—22no—
263C23×C3—22no—
264C23×C3—22no—
265C23×C3—22no—
266C23×C3—24no—
267C23×C3—24no—
268C23×C3—21no—
269C23×C3—22no—
270C23×C3—42no—
271C23×C3—42no—
272C23×C3D3×D414yes—
273C23×C3C23×D312yes—
274C22×D3—34no—
275C22×D3—34no—
276C22×D3—34no—
277C22×D3—38no—
278C22×D3—38no—
279C22×D3—34no—
280C22×D3—62no—
281C22×D3—62no—
282C22×D3—64no—
283C22×D3—64no—
284C22×D3—62no—
285C22×D3—62no—
286C22×D3—616no—
287C22×D3—632no—
288C22×D3—62no—
289C22×D3—616no—
290C22×D3—62no—
291C22×D3—62no—
292C22×D3—62no—
293C22×D3—64no—
294C22×D3—64no—
295C22×D3—1216no—
296C22×D3—122no—
297C22×D3—122no—
298C22×D3—128no—
299C22×D3—128no—
300C22×D3—1216no—
301C22×D3—128no—
302C22×D3—128no—
303C22×D3—1216no—
304C2×C3×C4—24no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—24no—
308C2×C3×C4—22no—
309C2×C3×C4—42no—
310C2×C3×C4—42no—
311C2×C3×C4—64no—
312C2×C3×C4—64no—
313C2×C3×C4—64no—
314C2×C3×C4—64no—
315C2×C3×C4—64no—
316C2×C3×C4—64no—
317C2×C3×C4D3×D414yes—
318C2×Dic3—24no—
319C2×Dic3—24no—
320C2×Dic3—24no—
321C2×Dic3—24no—
322C2×Dic3—24no—
323C2×Dic3—24no—
324C2×Dic3—34no—
325C2×Dic3—62no—
326C2×Dic3—64no—
327C2×Dic3—62no—
328C2×Dic3—62no—
329C2×Dic3—64no—
330C2×Dic3—122no—
331C2×Dic3—122no—
332C4×D3—616no—
333C4×D3—128no—
334C4×D3—1216no—
335C4×D3—1216no—
336C4×D3—128no—
337C4×D3—128no—
338C2×C32—42no—
339C2×C32C2×#12111yescharacteristic
340C2×C32C2×#12312yes—
341C2×C32C2×#12311yescharacteristic
342C2×C32C2×#12411yescharacteristic
343C2×C32C2×#12612yes—
344C3⋊D3—42no—
345C3⋊D3#39718yescomplemented
346C24—91no—
347C24—91no—
348C24—94no—
349C24—182no—
350C24—182no—
351C24—184no—
352C24—184no—
353C24C2×D3211yescharacteristic
354C22×C4—34no—
355C22×C4—34no—
356C22×C4—91no—
357C22×C4—94no—
358C22×C4—91no—
359C22×C4—184no—
360C22×C4—182no—
361C22×C4—184no—
362C22×C4—184no—
363C22×C4—184no—
364C22×C4—184no—
365C22×C4—184no—
366C22×C4—184no—
367C22×C4—184no—
368C22×C4C2×D3211yescharacteristic
369C22×C4C2×D3211yescharacteristic
370C4⋊C4—64no—
371C4⋊C4—184no—
372C22⋊C4—22no—
373C22⋊C4—68no—
374C22⋊C4—182no—
375C22⋊C4—188no—
376C22⋊C4—182no—
377C22⋊C4—182no—
378C22×C3—24no—
379C22×C3—28no—
380C22×C3—24no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—22no—
384C22×C3—22no—
385C22×C3—21no—
386C22×C3—44no—
387C22×C3—42no—
388C22×C3—42no—
389C22×C3—44no—
390C22×C3—42no—
391C22×C3—42no—
392C22×C3—44no—
393C22×C3C2×D3×D412yes—
394C22×C3C2×D3×D412yes—
395C22×C3D3×#4112yes—
396C22×C3D3×#4114yes—
397C22×C3D3×#4114yes—
398C2×D3—38no—
399C2×D3—316no—
400C2×D3—38no—
401C2×D3—316no—
402C2×D3—38no—
403C2×D3—64no—
404C2×D3—64no—
405C2×D3—64no—
406C2×D3—68no—
407C2×D3—68no—
408C2×D3—64no—
409C2×D3—68no—
410C2×D3—64no—
411C2×D3—124no—
412C2×D3—1232no—
413C2×D3—1232no—
414C2×D3—122no—
415C2×D3—122no—
416C2×D3—124no—
417C2×D3—122no—
418C2×D3—122no—
419C2×D3—124no—
420C3×C4—24no—
421C3×C4—42no—
422C3×C4—42no—
423C3×C4—42no—
424C3×C4—124no—
425C3×C4—124no—
426Dic3—44no—
427Dic3—44no—
428Dic3—64no—
429Dic3—122no—
430Dic3—122no—
431Dic3—122no—
432C32C2×#39711yescharacteristic, complemented, Sylow
433C23—21no—
434C23—22no—
435C23—22no—
436C23—21no—
437C23—92no—
438C23—92no—
439C23—94no—
440C23—94no—
441C23—92no—
442C23—92no—
443C23—188no—
444C23—1816no—
445C23—181no—
446C23—182no—
447C23—182no—
448C23—181no—
449C23—364no—
450C23—364no—
451C23—368no—
452C23#380212yes—
453C23C22×D3211yescharacteristic
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—21no—
457C2×C4—64no—
458C2×C4—64no—
459C2×C4—64no—
460C2×C4—64no—
461C2×C4—64no—
462C2×C4—64no—
463C2×C4—92no—
464C2×C4—188no—
465C2×C4—182no—
466C2×C4—182no—
467C2×C4—181no—
468C2×C4—364no—
469C2×C4—368no—
470C2×C4—368no—
471C2×C4#381112yes—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—22no—
476C2×C3—22no—
477C2×C3—44no—
478C2×C3—44no—
479C2×C3D3×#12112yes—
480C2×C3D3×#12312yes—
481C2×C3D3×#12314yes—
482C2×C3D3×#12412yes—
483C2×C3D3×#12614yes—
484D3—316no—
485D3—68no—
486D3—124no—
487D3—124no—
488C22—22no—
489C22—24no—
490C22—41no—
491C22—41no—
492C22—42no—
493C22—94no—
494C22—94no—
495C22—94no—
496C22—98no—
497C22—98no—
498C22—182no—
499C22—184no—
500C22—3616no—
501C22—361no—
502C22—361no—
503C22—362no—
504C22C2×#380211yescharacteristic
505C22#6430611yescharacteristic
506C22#6431212yes—
507C22#6431212yes—
508C22C2×#381111yescharacteristic
509C4—22no—
510C4—41no—
511C4—124no—
512C4—124no—
513C4—182no—
514C4—361no—
515C3—21no—
516C3D3×#39712yescomplemented
517C2—42no—
518C2—98no—
519C2—362no—
520C2#1059415412yes—
521C2#1059429512yes—
522C2#1059508111yescharacteristic
523C2#1059516911yescharacteristic
524C2#1059517011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC24×C3⋊D3C22
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#397
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#63900C2semidirect
4. C3×#4953C2semidirect
5. #10591694C2semidirect
6. #10591370C2semidirect
7. #10591370C2semidirect
8. #10591326C2semidirect
9. #10591216C2semidirect
22. C2×C3×C4⋊Dic3C22semidirect
24. C2×#3724C22semidirect
27. C3×C3⋊#95C22semidirect
28. C3×C3⋊#95C22semidirect
29. #63579C22semidirect
30. #63579C22semidirect
37. #4953D3semidirect
97. C2×C4⋊Dic3C2×D3semidirect
108. C3⋊#95C2×D3semidirect
109. C3⋊#95C2×D3semidirect
345. C3⋊D3#397semidirect
432. C32C2×#397semidirect
516. C3D3×#397semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×C3⋊D32
C2×#639742
C2×#639002
C3×#49532
#105916942
#105913702
#105913262
#105912162
D3×#3973