Finite Group Databasebeta

← #11788315

Subgroups — #11788315

Order 1152.

993 conjugacy classes of subgroups.

The subgroup lattice has 547 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64139C211yesmaximal, characteristic
2C22×C3×#208C211yesmaximal, characteristic, complemented
3C3×#5207C211yesmaximal, characteristic, complemented
4C2×#63559C212yesmaximal, complemented
5#10589168C212yesmaximal, complemented
6#72002—31nomaximal
7#69985—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C22×#638C412yes—
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11#64139—21no—
12#64139—21no—
13#64139—21no—
14#64139—21no—
15C2×#3752C412yes—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C3×#208—21no—
18C2×C3×#208—24no—
19C2×C3×#208C2212yes—
20C2×C3×#208C2212yes—
21C22×C3×C3⋊C8—21no—
22C3×#830—21no—
23C3×#830—21no—
24#63559—24no—
25C22×C3×M16—31no—
26C2×#930—31no—
27C2×#930—31no—
28C2×#930—61no—
29C22×#208D311yescharacteristic, complemented
30C3×#407—31no—
31#5207D311yescharacteristic, complemented
32C2×#823—32no—
33C2×#823—32no—
34#4554—32no—
35#4554—32no—
36C24×C32C2×C411yescharacteristic
37C23×C3⋊D3C2×C412yes—
38C22×C32×C4—22no—
39C22×C32×C4—22no—
40C22×C32×C4C2×C411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D411yescharacteristic
43C22×C32×C4D411yescharacteristic
44C22×C32×C4D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C2×#638—22no—
47C2×#638—22no—
48C2×#638—44no—
49C22×C3⋊Dic3C2×C412yes—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—22no—
53C2×C4⋊(C3⋊D3)—22no—
54#3752—22no—
55#3752—22no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—21no—
58C3×#208—24no—
59C3×#208—22no—
60C3×#208—22no—
61C3×#208—22no—
62C3×#208D414yescomplemented
63C2×C3×C3⋊C8—24no—
64C2×C3×C3⋊C8—22no—
65C2×C3×C3⋊C8—22no—
66#1900—91noSylow
67C23×C3×C4—21no—
68C23×C3×C4C2×D311yescharacteristic
69C23×C3×C4C2×D311yescharacteristic
70C22×#67—32no—
71C22×#67—32no—
72C22×#67—62no—
73C22×D12—31no—
74C22×D12—31no—
75C22×D12—61no—
76C2×C3×M16—32no—
77C2×C3×M16—32no—
78C2×C3×M16—64no—
79C2×C3×M16—61no—
80C22×C3×C8—61no—
81#930—62no—
82#930—62no—
83#930—62no—
84#930—62no—
85#930—61no—
86#930—61no—
87#930—61no—
88#930—61no—
89#930—61no—
90#930—61no—
91#930—61no—
92#930—61no—
93C2×(C2×D3)⋊C4—32no—
94C2×(C2×D3)⋊C4—32no—
95C2×(C2×D3)⋊C4—62no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—61no—
99C2×#208—21no—
100C2×#208—24no—
101C2×#208C2×D312yes—
102C2×#208C2×D312yes—
103C22×C3⋊C8—21no—
104C3×C22⋊C8—61no—
105C3×C22⋊C8—61no—
106#830—21no—
107#830—21no—
108#823—64no—
109#823—64no—
110C23×C32—22no—
111C23×C32—22no—
112C23×C32—41no—
113C23×C32C22⋊C411yescharacteristic
114C23×C32C22⋊C411yescharacteristic
115C23×C32C22×C411yescharacteristic
116C22×C3⋊D3—22no—
117C22×C3⋊D3—24no—
118C22×C3⋊D3—42no—
119C22×C3⋊D3—42no—
120C2×C32×C4—22no—
121C2×C32×C4—21no—
122C2×C32×C4—21no—
123C2×C32×C4—22no—
124C2×C32×C4—22no—
125C2×C32×C4—21no—
126C2×C32×C4—21no—
127C2×C32×C4C22⋊C411yescharacteristic
128C2×C32×C4C22⋊C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D412yes—
132C2×C32×C4#4112yes—
133#638—44no—
134#638—44no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—42no—
137C4⋊(C3⋊D3)—41no—
138C4⋊(C3⋊D3)—42no—
139C4⋊(C3⋊D3)—41no—
140C3×C3⋊C8—24no—
141C3×C3⋊C8—42no—
142C22×M16—31no—
143C2×#121—91no—
144C2×#100—92no—
145#407—31no—
146#343—92no—
147C24×C3—21no—
148C24×C3C4×D311yescharacteristic
149C24×C3C4×D311yescharacteristic
150C23×D3—32no—
151C23×D3—32no—
152C23×D3—62no—
153C22×C3×C4—22no—
154C22×C3×C4—22no—
155C22×C3×C4—22no—
156C22×C3×C4—22no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—42no—
164C22×C3×C4—42no—
165C22×C3×C4C4×D311yescharacteristic
166C22×C3×C4C4×D311yescharacteristic
167C22×C3×C4D1211yescharacteristic
168C22×C3×C4D1211yescharacteristic
169C22×C3×C4D1211yescharacteristic
170C22×C3×C4D1211yescharacteristic
171C22×C3×C4#6711yescharacteristic
172C22×C3×C4#6711yescharacteristic
173C22×C3×C4#6711yescharacteristic
174C22×C3×C4#6711yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C2×#67—64no—
178C2×#67—64no—
179C2×#67—62no—
180C2×#67—62no—
181C2×#67—62no—
182C2×#67—62no—
183C2×#67—128no—
184C2×#67—124no—
185C2×#67—124no—
186C22×Dic3—32no—
187C22×Dic3—32no—
188C22×Dic3—62no—
189C2×D12—62no—
190C2×D12—62no—
191C2×D12—61no—
192C2×D12—61no—
193C2×D12—62no—
194C2×D12—62no—
195C2×D12—62no—
196C2×D12—62no—
197C2×D12—61no—
198C2×D12—61no—
199C2×D12—122no—
200C2×D12—122no—
201C3×M16—34no—
202C3×M16—64no—
203C3×M16—62no—
204C3×M16—62no—
205C3×M16—62no—
206C2×C3×C8—64no—
207C2×C3×C8—62no—
208C2×C3×C8—62no—
209(C2×D3)⋊C4—64no—
210(C2×D3)⋊C4—64no—
211(C2×D3)⋊C4—62no—
212(C2×D3)⋊C4—62no—
213(C2×D3)⋊C4—62no—
214(C2×D3)⋊C4—62no—
215C4⋊Dic3—62no—
216C4⋊Dic3—62no—
217C4⋊Dic3—61no—
218C4⋊Dic3—61no—
219C4⋊Dic3—61no—
220C4⋊Dic3—61no—
221#208—24no—
222#208—22no—
223#208—22no—
224#208—22no—
225#208#6714yescomplemented
226C2×C3⋊C8—24no—
227C2×C3⋊C8—22no—
228C2×C3⋊C8—22no—
229C22×C32—21no—
230C22×C32—21no—
231C22×C32—21no—
232C22×C32—21no—
233C22×C32—21no—
234C22×C32—21no—
235C22×C32—21no—
236C22×C32—44no—
237C22×C32#10012yescomplemented
238C22×C32C2×C22⋊C411yescharacteristic
239C22×C32C4×D412yes—
240C2×C3⋊D3—42no—
241C2×C3⋊D3—42no—
242C2×C3⋊D3—42no—
243C2×C3⋊D3—84no—
244C32×C4—21no—
245C32×C4—21no—
246C32×C4#12011yescharacteristic
247C32×C4#12112yes—
248C32×C4#12311yescharacteristic
249C3⋊Dic3—42no—
250C22×D4—92no—
251C22×D4—91no—
252C23×C4D3211yescharacteristic
253C2×M16—32no—
254C2×M16—32no—
255C2×M16—64no—
256C2×M16—61no—
257C22×C8—61no—
258#121—181no—
259#121—181no—
260#121—181no—
261#121—181no—
262C2×C4⋊C4—91no—
263C2×C22⋊C4—92no—
264#100—184no—
265C22⋊C8—61no—
266C22⋊C8—61no—
267C23×C3—24no—
268C23×C3—22no—
269C23×C3—22no—
270C23×C3—22no—
271C23×C3—22no—
272C23×C3—21no—
273C23×C3—21no—
274C23×C3—21no—
275C23×C3—42no—
276C23×C3—41no—
277C23×C3—41no—
278C23×C3—42no—
279C23×C3(C2×D3)⋊C411yescharacteristic
280C23×C3(C2×D3)⋊C411yescharacteristic
281C23×C3(C2×D3)⋊C411yescharacteristic
282C23×C3(C2×D3)⋊C411yescharacteristic
283C23×C3C2×C4×D311yescharacteristic
284C23×C3C2×C4×D311yescharacteristic
285C22×D3—64no—
286C22×D3—62no—
287C22×D3—62no—
288C22×D3—64no—
289C22×D3—64no—
290C22×D3—124no—
291C22×D3—124no—
292C22×D3—124no—
293C22×D3—122no—
294C22×D3—122no—
295C22×D3—122no—
296C22×D3—122no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—22no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—22no—
317C2×C3×C4—41no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—42no—
322C2×C3×C4—42no—
323C2×C3×C4—42no—
324C2×C3×C4(C2×D3)⋊C411yescharacteristic
325C2×C3×C4(C2×D3)⋊C411yescharacteristic
326C2×C3×C4(C2×D3)⋊C411yescharacteristic
327C2×C3×C4(C2×D3)⋊C411yescharacteristic
328C2×C3×C4C2×D1211yescharacteristic
329C2×C3×C4C2×D1211yescharacteristic
330C2×C3×C4#23512yes—
331C2×C3×C4D3×D412yes—
332C2×C3×C4#23712yes—
333C2×C3×C4C2×#6711yescharacteristic
334C2×C3×C4C2×#6711yescharacteristic
335C2×C3×C4C2×#6712yes—
336#67—128no—
337#67—124no—
338#67—124no—
339#67—128no—
340#67—124no—
341#67—124no—
342C2×Dic3—64no—
343C2×Dic3—62no—
344C2×Dic3—62no—
345C2×Dic3—124no—
346C2×Dic3—122no—
347C2×Dic3—122no—
348D12—122no—
349D12—122no—
350D12—124no—
351D12—121no—
352D12—121no—
353D12—121no—
354D12—122no—
355D12—122no—
356D12—121no—
357C3×C8—64no—
358C3×C8—122no—
359C3⋊C8—24no—
360C3⋊C8—42no—
361C2×C32—22no—
362C2×C32—22no—
363C2×C32—41no—
364C2×C32#38611yescharacteristic
365C2×C32C2×#10011yescharacteristic
366C2×C32#41311yescharacteristic
367C3⋊D3—82no—
368C24—92no—
369C24#62411yescharacteristic
370C2×D4—182no—
371C2×D4—182no—
372C2×D4—182no—
373C2×D4—181no—
374C2×D4—181no—
375C2×D4—182no—
376C2×D4—364no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—92no—
380C22×C4#62411yescharacteristic
381C22×C4#62611yescharacteristic
382C22×C4#62611yescharacteristic
383C22×C4#62611yescharacteristic
384C22×C4#62611yescharacteristic
385C22×C4C2×D3211yescharacteristic
386M16—34no—
387M16—64no—
388M16—62no—
389M16—62no—
390M16—62no—
391C2×C8—64no—
392C2×C8—62no—
393C2×C8—62no—
394C4⋊C4—181no—
395C4⋊C4—181no—
396C22⋊C4—182no—
397C22⋊C4—182no—
398C22×C3—22no—
399C22×C3—22no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—22no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—22no—
416C22×C3—22no—
417C22×C3—21no—
418C22×C3—41no—
419C22×C3—41no—
420C22×C3—41no—
421C22×C3—41no—
422C22×C3—44no—
423C22×C3—44no—
424C22×C3—48no—
425C22×C3#82312yescomplemented
426C22×C3#82312yescomplemented
427C22×C3#67⋊C412yes—
428C22×C3C2×(C2×D3)⋊C411yescharacteristic
429C22×C3C2×(C2×D3)⋊C411yescharacteristic
430C22×C3C4×#6712yes—
431C2×D3—124no—
432C2×D3—124no—
433C2×D3—124no—
434C2×D3—122no—
435C2×D3—122no—
436C2×D3—122no—
437C2×D3—122no—
438C2×D3—122no—
439C2×D3—122no—
440C2×D3—248no—
441C2×D3—244no—
442C2×D3—244no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—22no—
450C3×C4—41no—
451C3×C4—41no—
452C3×C4#88211yescharacteristic
453C3×C4#88611yescharacteristic
454C3×C4#92911yescharacteristic
455C3×C4#93012yes—
456C3×C4#93912yes—
457C3×C4#95311yescharacteristic
458Dic3—124no—
459Dic3—122no—
460Dic3—122no—
461C32#190011yescharacteristic, complemented, Sylow
462C23—22no—
463C23—22no—
464C23—41no—
465C23—182no—
466C23—184no—
467C23—362no—
468C23—362no—
469C23#372211yescharacteristic
470C23#372211yescharacteristic
471C23C2×#62411yescharacteristic
472D4—364no—
473D4—364no—
474D4—361no—
475D4—361no—
476D4—362no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—182no—
485C2×C4—362no—
486C2×C4#372211yescharacteristic
487C2×C4#372211yescharacteristic
488C2×C4#380412yes—
489C2×C4C2×#62611yescharacteristic
490C2×C4C2×#62611yescharacteristic
491C2×C4D3×#6712yes—
492C8—64no—
493C8—122no—
494C2×C3—24no—
495C2×C3—22no—
496C2×C3—22no—
497C2×C3—22no—
498C2×C3—22no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—42no—
503C2×C3—42no—
504C2×C3—41no—
505C2×C3—41no—
506C2×C3#495811yescharacteristic
507C2×C3C2×#82311yescharacteristic
508C2×C3C2×#82311yescharacteristic
509C2×C3#513211yescharacteristic
510C2×C3#513211yescharacteristic
511C2×C3#521311yescharacteristic
512D3—244no—
513D3—242no—
514D3—242no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—44no—
523C22—362no—
524C22—362no—
525C22—362no—
526C22—724no—
527C22#6355912yescomplemented
528C22#6395212yes—
529C22C2×#372211yescharacteristic
530C4—21no—
531C4—21no—
532C4—362no—
533C4#6396611yescharacteristic
534C4#6397711yescharacteristic
535C4#6397812yes—
536C3—21no—
537C3#6998511yescharacteristic, complemented
538C3#7200211yescharacteristic, complemented
539C2—22no—
540C2—22no—
541C2—41no—
542C2—722no—
543C2C2×#6355911yescharacteristic
544C2#1059107811yescharacteristic
545C2#1059171111yescharacteristic
subgroupG/H
centerC22C2×#3722
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#64139C2
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1900
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×#208C2semidirect
3. C3×#5207C2semidirect
4. C2×#63559C2semidirect
5. #10589168C2semidirect
29. C22×#208D3semidirect
31. #5207D3semidirect
62. C3×#208D4semidirect
225. #208#67semidirect
237. C22×C32#100semidirect
425. C22×C3#823semidirect
426. C22×C3#823semidirect
461. C32#1900semidirect
527. C22#63559semidirect
537. C3#69985semidirect
538. C3#72002semidirect

Maximal subgroups

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

subgroupindex
C2×#641392
C22×C3×#2082
C3×#52072
C2×#635592
#105891682
#720023
#699853