Finite Group Databasebeta

← #11824511

Subgroups — #11824511

Order 1152.

1449 conjugacy classes of subgroups.

The subgroup lattice has 493 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63919C211yesmaximal, characteristic, complemented
2C2×#63899C214yesmaximal, complemented
3C2×#63898C211yesmaximal, characteristic
4C4×#3750C211yesmaximal, characteristic, complemented
5C3×#4939C211yesmaximal, characteristic
6C3×#4935C211yesmaximal, characteristic, complemented
7#10591359C211yesmaximal, characteristic, complemented
8#10591324C214yesmaximal, complemented
9#10591323C211yesmaximal, characteristic
10#76349—31nomaximal
11#74334—31nomaximal
12C22×C3×D12C2211yescharacteristic
13C22×#627C2212yes—
14C22×D3×Dic3C2212yes—
15C2×C32×C42C2211yescharacteristic
16C2×#3750C2212yes—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4C2214yes—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2214yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×#3724C2212yes—
25C2×#3724C2214yes—
26C2×(C2×D3)⋊Dic3C2214yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28#63919—24no—
29#63899—216no—
30#63898—24no—
31#63658C2212yes—
32C2×D4×Dic3—31no—
33C2×#896—34no—
34C2×#893—31no—
35C2×#888—31no—
36C2×#888—31no—
37C2×#878—34no—
38C3×#390—31no—
39C3×#384—31no—
40#5221—31no—
41#4993—34no—
42#4988—31no—
43#4975—31no—
44#4975—31no—
45#4949—34no—
46#4939D311yescharacteristic
47#4935D311yescharacteristic, complemented
48C4×Dic3⋊C4—31no—
49C4×Dic3⋊C4—31no—
50C4×Dic3⋊C4—61no—
51C23×C3×D3C2312yes—
52C22×C32×C4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3C2312yes—
55C22×C3⋊Dic3C2311yescharacteristic
56C22×C3⋊Dic3C2311yescharacteristic
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2312yes—
60C2×C3×D12—22no—
61C2×C3×D12—22no—
62C2×C3×D12Q814yescomplemented
63C2×#627—28no—
64C2×#627—24no—
65C2×D3×Dic3—24no—
66C2×D3×Dic3—28no—
67C32×C42—22no—
68#3750D418yescomplemented
69C4×C3⋊Dic3—22no—
70C4×C3⋊Dic3D414yes—
71C3×(C2×D3)⋊C4—28no—
72C3×C4⋊Dic3—22no—
73C3×C4⋊Dic3—28no—
74C3×C4⋊Dic3—22no—
75C3×C4⋊Dic3—22no—
76#3724—28no—
77#3724—24no—
78(C2×D3)⋊Dic3—24no—
79(C2×D3)⋊Dic3—28no—
80#2542—91noSylow
81C22×C3×D4—31no—
82C23×Dic3—32no—
83C22×D12C2×D311yescharacteristic
84C22×C4×D3—32no—
85C22×Dic6—32no—
86C22×Dic6—32no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4—34no—
91C2×C3×C22⋊C4—34no—
92C2×C3×C42—21no—
93C2×C3×C42C2×D311yescharacteristic
94C2×C3×C42C2×D311yescharacteristic
95C2×#217—32no—
96C2×#217—34no—
97D4×Dic3—64no—
98C2×(C2×D3)⋊C4—34no—
99C2×(C2×D3)⋊C4—32no—
100C2×(C2×D3)⋊C4C2×D314yes—
101C2×C4⋊Dic3C2×D314yes—
102C2×C4⋊Dic3C2×D311yescharacteristic
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×Dic3⋊C4—32no—
106C2×Dic3⋊C4—32no—
107C2×Dic3⋊C4—32no—
108C2×Dic3⋊C4—34no—
109C2×Dic3⋊C4—34no—
110C2×Dic3⋊C4—32no—
111C2×Dic3⋊C4—62no—
112C2×C4×Dic3—31no—
113C2×C4×Dic3—31no—
114C2×C4×Dic3—31no—
115C2×C4×Dic3—31no—
116C2×C4×Dic3—61no—
117C2×C4×Dic3—61no—
118#896—616no—
119#893—64no—
120#888—64no—
121#888—64no—
122#878—616no—
123C3⋊#95—32no—
124C3⋊#95—32no—
125C3⋊#95—62no—
126C23×C32C2411yescharacteristic
127C22×C3×D3—24no—
128C22×C3×D3—22no—
129C22×C3×D3—22no—
130C22×C3×D3—24no—
131C22×C3×D3C2×Q814yes—
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4C2×D414yes—
135C2×C32×C4C2×D412yes—
136C2×C32×C4C2×Q812yes—
137C2×C32×C4#4112yes—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3C2×D412yes—
142C2×C3⋊Dic3C2×D414yes—
143C2×C3⋊Dic3C2×D412yes—
144C2×C3⋊Dic3C2×D414yes—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—24no—
147C2×C3×Dic3—24no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—24no—
151C3×D12—28no—
152#627—48no—
153D3×Dic3—48no—
154C2×C4⋊Q8—91no—
155C2×C22⋊Q8—94no—
156C2×C4×D4—91no—
157#399—94no—
158#390—31no—
159#390—91no—
160#384—31no—
161#384—91no—
162C4×C4⋊C4—91no—
163C24×C3—32no—
164C23×D3C22×D312yes—
165C2×C3×D4—34no—
166C2×C3×D4—62no—
167C2×C3×D4—62no—
168C22×C3×C4—21no—
169C22×C3×C4—22no—
170C22×C3×C4—32no—
171C22×C3×C4—32no—
172C22×C3×C4—32no—
173C22×C3×C4C22×D312yes—
174C22×C3×C4C22×D312yes—
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C22×Dic3—31no—
178C22×Dic3—31no—
179C22×Dic3—31no—
180C22×Dic3—31no—
181C22×Dic3—32no—
182C22×Dic3—32no—
183C22×Dic3—61no—
184C22×Dic3—61no—
185C22×Dic3—62no—
186C22×Dic3—68no—
187C22×Dic3—64no—
188C22×Dic3C22×D312yes—
189C22×Dic3C22×D312yes—
190C22×Dic3C22×D312yes—
191C2×D12—22no—
192C2×D12—22no—
193C2×D12Dic614yescomplemented
194C2×C4×D3—64no—
195C2×C4×D3—68no—
196C2×Dic6—68no—
197C2×Dic6—64no—
198C2×Dic6—64no—
199C2×Dic6—68no—
200C3×C4⋊C4—62no—
201C3×C4⋊C4—62no—
202C3×C4⋊C4—62no—
203C3×C4⋊C4—68no—
204C3×C22⋊C4—68no—
205C3×C42—22no—
206C3×C42—22no—
207C3×C42—42no—
208#217—68no—
209#217—64no—
210(C2×D3)⋊C4—28no—
211(C2×D3)⋊C4—64no—
212(C2×D3)⋊C4—68no—
213C4⋊Dic3—28no—
214C4⋊Dic3—22no—
215C4⋊Dic3—22no—
216C4⋊Dic3—22no—
217Dic3⋊C4—38no—
218Dic3⋊C4—38no—
219Dic3⋊C4—68no—
220Dic3⋊C4—68no—
221Dic3⋊C4—64no—
222Dic3⋊C4—64no—
223Dic3⋊C4—68no—
224C4×Dic3—34no—
225C4×Dic3—34no—
226C4×Dic3—64no—
227C4×Dic3—62no—
228C4×Dic3—62no—
229C4×Dic3—122no—
230C22×C32C22×D411yescharacteristic
231C22×C32C22×D412yes—
232C22×C32C22×Q811yescharacteristic
233C22×C32C2×#4111yescharacteristic
234C22×C322−1+412yes—
235C2×C3×D3—24no—
236C2×C3×D3—28no—
237C2×C3×D3—42no—
238C2×C3×D3—42no—
239C2×C3×D3—44no—
240C32×C4—24no—
241C32×C4C22⋊Q814yescomplemented
242C3⋊Dic3—22no—
243C3⋊Dic3—24no—
244C3⋊Dic3#12714yes—
245C3×Dic3—42no—
246C3×Dic3—42no—
247C3×Dic3—42no—
248C22×Q8—92no—
249C22×D4—31no—
250C23×C4—92no—
251C4⋊Q8—184no—
252C22⋊Q8—1816no—
253C4×D4—184no—
254C2×C4⋊C4—31no—
255C2×C4⋊C4—34no—
256C2×C4⋊C4—31no—
257C2×C4⋊C4—31no—
258C2×C4⋊C4—92no—
259C2×C4⋊C4—94no—
260C2×C4⋊C4—92no—
261C2×C22⋊C4—34no—
262C2×C22⋊C4—92no—
263C2×C22⋊C4—94no—
264C2×C42—91no—
265C2×C42—91no—
266C2×C42D3211yescharacteristic
267#95—92no—
268C23×C3—21no—
269C23×C3—34no—
270C23×C3—62no—
271C23×C3—64no—
272C23×C3—62no—
273C23×C3—64no—
274C23×C3C23×D311yescharacteristic
275C23×C3C23×D311yescharacteristic
276C22×D3—24no—
277C22×D3—22no—
278C22×D3—22no—
279C22×D3—24no—
280C22×D3C2×Dic614yes—
281C3×D4—68no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—24no—
289C2×C3×C4—22no—
290C2×C3×C4—42no—
291C2×C3×C4—42no—
292C2×C3×C4—64no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—64no—
296C2×C3×C4—64no—
297C2×C3×C4—62no—
298C2×C3×C4C2×Dic612yes—
299C2×C3×C4#23512yes—
300C2×C3×C4D3×D414yes—
301C2×C3×C4D3×D414yes—
302C2×C3×C4D3×D412yes—
303C2×C3×C4D3×D412yes—
304C2×C3×C4#23712yes—
305C2×C3×C4D3×Q812yes—
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—24no—
309C2×Dic3—24no—
310C2×Dic3—24no—
311C2×Dic3—22no—
312C2×Dic3—32no—
313C2×Dic3—32no—
314C2×Dic3—34no—
315C2×Dic3—34no—
316C2×Dic3—32no—
317C2×Dic3—32no—
318C2×Dic3—34no—
319C2×Dic3—34no—
320C2×Dic3—62no—
321C2×Dic3—64no—
322C2×Dic3—62no—
323C2×Dic3—64no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327C2×Dic3—62no—
328C2×Dic3—62no—
329C2×Dic3—62no—
330C2×Dic3—122no—
331C2×Dic3—122no—
332C2×Dic3—122no—
333C2×Dic3—128no—
334D12—28no—
335C4×D3—128no—
336Dic6—128no—
337Dic6—128no—
338C2×C32C2×C22⋊Q811yescharacteristic
339C2×C32C2×#12711yescharacteristic
340C2×C32#53611yescharacteristic
341C2×C32#54712yes—
342C2×C32D4×Q812yes—
343C3×D3—44no—
344C24—32no—
345C2×Q8—188no—
346C2×Q8—184no—
347C2×D4—34no—
348C2×D4—62no—
349C2×D4—62no—
350C22×C4—32no—
351C22×C4—32no—
352C22×C4—32no—
353C22×C4—91no—
354C22×C4—91no—
355C22×C4—92no—
356C22×C4—184no—
357C22×C4—188no—
358C22×C4C2×D3212yes—
359C22×C4C2×D3211yescharacteristic
360C4⋊C4—62no—
361C4⋊C4—68no—
362C4⋊C4—62no—
363C4⋊C4—62no—
364C4⋊C4—98no—
365C4⋊C4—188no—
366C4⋊C4—184no—
367C22⋊C4—68no—
368C22⋊C4—184no—
369C22⋊C4—188no—
370C42—22no—
371C42—94no—
372C42—182no—
373C22×C3—21no—
374C22×C3—22no—
375C22×C3—21no—
376C22×C3—22no—
377C22×C3—21no—
378C22×C3—68no—
379C22×C3—64no—
380C22×C3—122no—
381C22×C3—122no—
382C22×C3—124no—
383C22×C3C22×Dic611yescharacteristic
384C22×C3C2×#23511yescharacteristic
385C22×C3C2×D3×D411yescharacteristic
386C22×C3C2×D3×D411yescharacteristic
387C22×C3C2×D3×D412yes—
388C22×C3C2×D3×D412yes—
389C22×C3C2×#23711yescharacteristic
390C22×C3C2×D3×Q811yescharacteristic
391C22×C3#100712yes—
392C22×C3#101012yes—
393C2×D3—24no—
394C2×D3—28no—
395C2×D3—42no—
396C2×D3—42no—
397C2×D3—44no—
398C3×C4—24no—
399C3×C4—24no—
400C3×C4—24no—
401C3×C4—44no—
402C3×C4—122no—
403C3×C4—122no—
404C3×C4—122no—
405C3×C4#87814yescomplemented
406C3×C4#89614yescomplemented
407Dic3—34no—
408Dic3—34no—
409Dic3—42no—
410Dic3—42no—
411Dic3—42no—
412Dic3—64no—
413Dic3—62no—
414Dic3—62no—
415Dic3—64no—
416Dic3—64no—
417Dic3—124no—
418Dic3—122no—
419C32#254211yescharacteristic, complemented, Sylow
420C23—34no—
421C23—64no—
422C23—64no—
423C23—62no—
424C23—62no—
425C23C22×D3211yescharacteristic
426Q8—368no—
427D4—68no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—64no—
431C2×C4—62no—
432C2×C4—64no—
433C2×C4—64no—
434C2×C4—62no—
435C2×C4—62no—
436C2×C4—92no—
437C2×C4—94no—
438C2×C4—92no—
439C2×C4—94no—
440C2×C4—182no—
441C2×C4—182no—
442C2×C4—182no—
443C2×C4—368no—
444C2×C4D3×Dic612yes—
445C2×C4#380214yes—
446C2×C4#380212yes—
447C2×C4#380412yes—
448C2×C3—21no—
449C2×C3—22no—
450C2×C3—22no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—124no—
454C2×C3C2×#87811yescharacteristic
455C2×C3#550712yes—
456C2×C3C2×#89611yescharacteristic
457C2×C3D4×Dic612yes—
458C2×C3#561112yes—
459C2×C3#567511yescharacteristic
460C2×C3D3×#12711yescharacteristic
461C2×C3D3×#12711yescharacteristic
462C2×C3#572411yescharacteristic
463C2×C3#572712yes—
464D3—44no—
465C22—64no—
466C22—68no—
467C22—124no—
468C22—122no—
469C22—122no—
470C22C2×D3×Dic611yescharacteristic
471C22#6429712yes—
472C22C2×#380211yescharacteristic
473C22C2×#380212yes—
474C22C2×#380411yescharacteristic
475C4—24no—
476C4—94no—
477C4—122no—
478C4—122no—
479C4—122no—
480C4—184no—
481C4—182no—
482C4#6389914yescomplemented
483C3—21no—
484C3#7433411yescharacteristic, complemented
485C3#7634911yescharacteristic, complemented
486C2—124no—
487C2#1059390412yes—
488C2#1059390811yescharacteristic
489C2#1059400811yescharacteristic
490C2C2×#6389911yescharacteristic
491C2#1059492812yes—
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C42C22
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32#2542
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#63919C2semidirect
2. C2×#63899C2semidirect
4. C4×#3750C2semidirect
6. C3×#4935C2semidirect
7. #10591359C2semidirect
8. #10591324C2semidirect
47. #4935D3semidirect
62. C2×C3×D12Q8semidirect
68. #3750D4semidirect
193. C2×D12Dic6semidirect
241. C32×C4C22⋊Q8semidirect
405. C3×C4#878semidirect
406. C3×C4#896semidirect
419. C32#2542semidirect
482. C4#63899semidirect
484. C3#74334semidirect
485. C3#76349semidirect

Maximal subgroups

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

subgroupindex
C2×#639192
C2×#638992
C2×#638982
C4×#37502
C3×#49392
C3×#49352
#105913592
#105913242
#105913232
#763493
#743343