Finite Group Databasebeta

← #11808155

Subgroups — #11808155

Order 1152.

2713 conjugacy classes of subgroups.

The subgroup lattice has 551 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3802C211yesmaximal, characteristic
2C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×#63921C212yesmaximal, complemented
4C2×#63921C212yesmaximal, complemented
5C3×#4991C212yesmaximal, complemented
6#10591394C212yesmaximal, complemented
7#10591388C212yesmaximal, complemented
8#10591370C211yesmaximal, characteristic, complemented
9#10591302C212yesmaximal, complemented
10D3×#394—32nomaximal
11C23×D32C2212yes—
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×D12C2212yes—
16C22×#625C2212yes—
17C22×#624C2212yes—
18C2×#3802—24no—
19C2×#3802—28no—
20C2×C32×C4⋊C4C2211yescharacteristic, complemented
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C2×#3750C2211yescharacteristic, complemented
23C2×#3750C2211yescharacteristic, complemented
24C4⋊C4×C3⋊D3—24no—
25C2×C3×(C2×D3)⋊C4C2214yescomplemented
26C2×C3×(C2×D3)⋊C4C2214yescomplemented
27C2×(C2×D3)⋊Dic3C2214yescomplemented
28C2×(C2×D3)⋊Dic3C2214yescomplemented
29#63921—28no—
30#63921—28no—
31C3×C3⋊#95C2212yescomplemented
32#63579C2212yescomplemented
33C22×D3×D4—32no—
34C2×D3×C4⋊C4—32no—
35C2×D3×C4⋊C4—61no—
36C2×D3×C22⋊C4—34no—
37C2×D3×C22⋊C4—34no—
38C3×#394—32no—
39#5222—32no—
40#4991D312yescomplemented
41#4961—34no—
42#4959—34no—
43#4672—32no—
44D3×#95—32no—
45C23×C3⋊D3C2311yescharacteristic
46C23×C3×D3C2314yes—
47C22×D32—24no—
48C22×D32—24no—
49C22×D32—24no—
50C22×D32—24no—
51C22×D32—24no—
52C22×D32—24no—
53C22×D32D418yes—
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3⋊Dic3C2311yescharacteristic
60C2×C4×C3⋊D3—22no—
61C2×C4×C3⋊D3—24no—
62C2×C4×C3⋊D3—22no—
63C2×C4×C3⋊D3—22no—
64C2×C4×C3⋊D3—24no—
65C2×C4×C3⋊D3D414yes—
66C2×C4×C3⋊D3D414yescomplemented
67C22×C3×Dic3C2314yes—
68C2×C3×D12—28no—
69C2×C3×D12—24no—
70C2×#625—28no—
71C2×#625—24no—
72C2×#624—24no—
73C2×#624—24no—
74C2×#624—24no—
75#3802—232no—
76C32×C4⋊C4—22no—
77C4⋊(C3⋊Dic3)—22no—
78#3750—22no—
79#3750—22no—
80C3×(C2×D3)⋊C4—28no—
81C3×(C2×D3)⋊C4—28no—
82(C2×D3)⋊Dic3—28no—
83(C2×D3)⋊Dic3—28no—
84C2×#394—91noSylow
85C24×D3—34no—
86C22×C3×D4—32no—
87C22×#67—34no—
88C2×D3×D4—68no—
89C2×D3×D4—616no—
90C22×D12C2×D312yes—
91C22×C4×D3—32no—
92C22×C4×D3—32no—
93C22×C4×D3—32no—
94C22×C4×D3—34no—
95C22×C4×D3—61no—
96C22×C4×D3—61no—
97C22×C4×D3—61no—
98C2×C3×C4⋊C4—21no—
99C2×C3×C4⋊C4C2×D312yescomplemented
100C2×C3×C22⋊C4—34no—
101C2×C3×C22⋊C4—34no—
102C2×#217—34no—
103C2×#217—34no—
104C2×(C2×D3)⋊C4—34no—
105C2×(C2×D3)⋊C4—34no—
106C2×(C2×D3)⋊C4C2×D314yescomplemented
107C2×(C2×D3)⋊C4C2×D314yescomplemented
108C2×C4⋊Dic3—32no—
109C2×C4⋊Dic3—61no—
110C2×Dic3⋊C4—32no—
111C2×Dic3⋊C4—32no—
112C2×Dic3⋊C4—61no—
113C2×Dic3⋊C4—61no—
114D3×C4⋊C4—68no—
115D3×C4⋊C4—68no—
116D3×C22⋊C4—616no—
117D3×C22⋊C4—616no—
118C3×#95—32no—
119C3⋊#95—34no—
120C3⋊#95C2×D312yescomplemented
121C23×C32C2411yescharacteristic
122C22×C3⋊D3C2×D414yes—
123C22×C3⋊D3C2×D412yes—
124C22×C3⋊D3C2×D412yes—
125C22×C3⋊D3#4112yes—
126C22×C3⋊D3#4114yes—
127C22×C3×D3—24no—
128C22×C3×D3—24no—
129C22×C3×D3—24no—
130C22×C3×D3—24no—
131C22×C3×D3—24no—
132C22×C3×D3—24no—
133C22×C3×D3C2×D418yes—
134C2×D32—216no—
135C2×D32—216no—
136C2×D32—216no—
137C2×D32—48no—
138C2×D32—48no—
139C2×D32—48no—
140C2×D32—48no—
141C2×C32×C4—21no—
142C2×C32×C4—21no—
143C2×C32×C4—21no—
144C2×C32×C4—22no—
145C2×C32×C4—22no—
146C2×C32×C4C2×D412yes—
147C2×C32×C4C2×D412yescomplemented
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3C2×D412yes—
154C2×C3⋊Dic3C2×D412yescomplemented
155C4×C3⋊D3—28no—
156C4×C3⋊D3—28no—
157C4×C3⋊D3—44no—
158C2×C3×Dic3—24no—
159C2×C3×Dic3—24no—
160C2×C3×Dic3—24no—
161C3×D12—216no—
162#625—216no—
163#624—48no—
164C23×D4—91no—
165C22×C4⋊C4—91no—
166C22×C22⋊C4—92no—
167C22×C22⋊C4—92no—
168#394—32no—
169#394—92no—
170#394—92no—
171#394—92no—
172C2×#95—91no—
173C24×C3—34no—
174C23×D3—32no—
175C23×D3—316no—
176C23×D3—61no—
177C23×D3—68no—
178C23×D3—68no—
179C23×D3—68no—
180C23×D3—68no—
181C23×D3—68no—
182C23×D3—68no—
183C23×D3C22×D314yes—
184C2×C3×D4—68no—
185C2×C3×D4—64no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—34no—
190C22×C3×C4C22×D312yes—
191C22×C3×C4C22×D312yes—
192C22×C3×C4C22×D312yes—
193C2×#67—68no—
194C2×#67—68no—
195C2×#67—68no—
196C22×Dic3—32no—
197C22×Dic3—32no—
198C22×Dic3—32no—
199C22×Dic3—61no—
200C22×Dic3—61no—
201C22×Dic3—61no—
202C22×Dic3C22×D314yes—
203D3×D4—664no—
204C2×D12—28no—
205C2×D12—24no—
206C2×C4×D3—38no—
207C2×C4×D3—38no—
208C2×C4×D3—64no—
209C2×C4×D3—64no—
210C2×C4×D3—64no—
211C2×C4×D3—68no—
212C2×C4×D3—64no—
213C2×C4×D3—64no—
214C2×C4×D3—64no—
215C2×C4×D3—68no—
216C2×C4×D3—68no—
217C2×C4×D3—68no—
218C2×C4×D3—68no—
219C2×C4×D3—64no—
220C2×C4×D3—64no—
221C2×C4×D3—124no—
222C2×C4×D3—124no—
223C3×C4⋊C4—24no—
224C3×C4⋊C4—24no—
225C3×C22⋊C4—68no—
226C3×C22⋊C4—68no—
227#217—68no—
228#217—68no—
229(C2×D3)⋊C4—28no—
230(C2×D3)⋊C4—28no—
231(C2×D3)⋊C4—68no—
232(C2×D3)⋊C4—68no—
233C4⋊Dic3—64no—
234C4⋊Dic3—64no—
235Dic3⋊C4—64no—
236Dic3⋊C4—64no—
237Dic3⋊C4—64no—
238Dic3⋊C4—64no—
239C22×C32C22×D412yes—
240C22×C32C22×D411yescharacteristic
241C22×C32C22×D411yescharacteristic
242C22×C32C2×#4111yescharacteristic
243C22×C32C2×#4112yes—
244C2×C3⋊D3#12014yes—
245C2×C3⋊D3#12118yes—
246C2×C3⋊D3#12114yes—
247C2×C3⋊D3#12318yes—
248C2×C3⋊D3#12414yes—
249C2×C3×D3—28no—
250C2×C3×D3—28no—
251C2×C3×D3—28no—
252C2×C3×D3—44no—
253C2×C3×D3—44no—
254C2×C3×D3—44no—
255C2×C3×D3—44no—
256D32—432no—
257C32×C4—22no—
258C32×C4—22no—
259C32×C4—41no—
260C3⋊Dic3—22no—
261C3⋊Dic3—22no—
262C3⋊Dic3—41no—
263C3×Dic3—44no—
264C25—92no—
265C22×D4—32no—
266C22×D4—92no—
267C22×D4—184no—
268C22×D4—188no—
269C23×C4—92no—
270C23×C4—91no—
271C23×C4—91no—
272C23×C4—91no—
273C2×C4⋊C4—91no—
274C2×C4⋊C4—91no—
275C2×C4⋊C4—91no—
276C2×C4⋊C4—184no—
277C2×C4⋊C4D3211yescharacteristic, complemented
278C2×C22⋊C4—34no—
279C2×C22⋊C4—34no—
280C2×C22⋊C4—94no—
281C2×C22⋊C4—94no—
282C2×C22⋊C4—188no—
283C2×C22⋊C4—188no—
284#95—32no—
285#95—92no—
286C23×C3—21no—
287C23×C3—38no—
288C23×C3—64no—
289C23×C3—64no—
290C23×C3—64no—
291C23×C3—64no—
292C23×C3—64no—
293C23×C3—64no—
294C23×C3C23×D312yes—
295C22×D3—24no—
296C22×D3—24no—
297C22×D3—24no—
298C22×D3—24no—
299C22×D3—24no—
300C22×D3—24no—
301C22×D3—34no—
302C22×D3—34no—
303C22×D3—38no—
304C22×D3—34no—
305C22×D3—38no—
306C22×D3—62no—
307C22×D3—62no—
308C22×D3—64no—
309C22×D3—62no—
310C22×D3—64no—
311C22×D3—632no—
312C22×D3—632no—
313C22×D3—632no—
314C22×D3—1216no—
315C22×D3—1216no—
316C22×D3—1216no—
317C22×D3—1216no—
318C22×D3D3×D418yes—
319C3×D4—616no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—24no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—24no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—42no—
331C2×C3×C4—42no—
332C2×C3×C4—64no—
333C2×C3×C4—64no—
334C2×C3×C4—64no—
335C2×C3×C4D3×D414yes—
336C2×C3×C4D3×D414yescomplemented
337#67—632no—
338C2×Dic3—24no—
339C2×Dic3—24no—
340C2×Dic3—24no—
341C2×Dic3—34no—
342C2×Dic3—34no—
343C2×Dic3—62no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—64no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—64no—
353C2×Dic3—122no—
354C2×Dic3—122no—
355D12—216no—
356C4×D3—616no—
357C4×D3—616no—
358C4×D3—616no—
359C4×D3—128no—
360C4×D3—1216no—
361C4×D3—128no—
362C4×D3—128no—
363C2×C32C2×#12011yescharacteristic
364C2×C32C2×#12112yes—
365C2×C32C2×#12111yescharacteristic
366C2×C32C2×#12312yes—
367C2×C32C2×#12411yescharacteristic
368C3⋊D3#39418yescomplemented
369C3×D3—48no—
370C24—34no—
371C24—98no—
372C24—91no—
373C24—184no—
374C24—184no—
375C24—184no—
376C24—184no—
377C24—184no—
378C24—184no—
379C2×D4—68no—
380C2×D4—64no—
381C2×D4—184no—
382C2×D4—1832no—
383C2×D4—188no—
384C22×C4—34no—
385C22×C4—91no—
386C22×C4—91no—
387C22×C4—94no—
388C22×C4—94no—
389C22×C4—91no—
390C22×C4—182no—
391C22×C4—184no—
392C22×C4—182no—
393C22×C4—184no—
394C22×C4—182no—
395C22×C4—184no—
396C22×C4—184no—
397C22×C4—184no—
398C22×C4C2×D3211yescharacteristic
399C22×C4C2×D3211yescharacteristic
400C22×C4C2×D3211yescharacteristic
401C4⋊C4—22no—
402C4⋊C4—182no—
403C4⋊C4—182no—
404C4⋊C4—182no—
405C22⋊C4—68no—
406C22⋊C4—68no—
407C22⋊C4—188no—
408C22⋊C4—188no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—22no—
412C22×C3—22no—
413C22×C3—21no—
414C22×C3—68no—
415C22×C3—68no—
416C22×C3—68no—
417C22×C3—124no—
418C22×C3—124no—
419C22×C3—124no—
420C22×C3—124no—
421C22×C3C2×D3×D412yes—
422C22×C3C2×D3×D414yes—
423C22×C3C2×D3×D412yes—
424C22×C3D3×#4112yes—
425C22×C3D3×#4114yes—
426C2×D3—28no—
427C2×D3—28no—
428C2×D3—28no—
429C2×D3—316no—
430C2×D3—38no—
431C2×D3—38no—
432C2×D3—38no—
433C2×D3—316no—
434C2×D3—44no—
435C2×D3—44no—
436C2×D3—44no—
437C2×D3—44no—
438C2×D3—64no—
439C2×D3—64no—
440C2×D3—68no—
441C2×D3—68no—
442C2×D3—64no—
443C2×D3—1264no—
444C3×C4—24no—
445C3×C4—24no—
446C3×C4—24no—
447C3×C4—42no—
448C3×C4—42no—
449C3×C4—42no—
450C3×C4—124no—
451Dic3—44no—
452Dic3—64no—
453Dic3—64no—
454Dic3—64no—
455Dic3—122no—
456Dic3—122no—
457Dic3—122no—
458C32C2×#39411yescharacteristic, complemented, Sylow
459C23—38no—
460C23—64no—
461C23—64no—
462C23—64no—
463C23—64no—
464C23—64no—
465C23—64no—
466C23—92no—
467C23—92no—
468C23—94no—
469C23—94no—
470C23—92no—
471C23—1816no—
472C23—1816no—
473C23—1816no—
474C23—368no—
475C23—368no—
476C23—368no—
477C23—368no—
478C23C22×D3211yescharacteristic
479D4—616no—
480D4—1816no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—64no—
487C2×C4—64no—
488C2×C4—64no—
489C2×C4—92no—
490C2×C4—92no—
491C2×C4—188no—
492C2×C4—188no—
493C2×C4—181no—
494C2×C4—182no—
495C2×C4—181no—
496C2×C4—182no—
497C2×C4—181no—
498C2×C4—364no—
499C2×C4—368no—
500C2×C4#380212yescomplemented
501C2×C4#381112yes—
502C2×C3—21no—
503C2×C3—22no—
504C2×C3—22no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—128no—
508C2×C3D3×#12012yes—
509C2×C3D3×#12112yes—
510C2×C3D3×#12114yes—
511C2×C3D3×#12314yes—
512C2×C3D3×#12412yes—
513D3—316no—
514D3—48no—
515D3—68no—
516C22—68no—
517C22—68no—
518C22—68no—
519C22—94no—
520C22—98no—
521C22—98no—
522C22—94no—
523C22—94no—
524C22—124no—
525C22—124no—
526C22—124no—
527C22—124no—
528C22—3632no—
529C22C2×#380211yescharacteristic
530C22#6430611yescharacteristic
531C22D32×D412yes—
532C22#6431912yes—
533C22C2×#381111yescharacteristic
534C4—22no—
535C4—22no—
536C4—41no—
537C4—124no—
538C4—182no—
539C4—182no—
540C4—361no—
541C3—21no—
542C3D3×#39412yescomplemented
543C2—98no—
544C2—128no—
545C2#1059460812yes—
546C2#1059461212yes—
547C2#1059508111yescharacteristic
548C2#1059527811yescharacteristic
549C2#1059543211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC22×#3802C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#394
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×C3⋊D3C2semidirect
3. C2×#63921C2semidirect
4. C2×#63921C2semidirect
5. C3×#4991C2semidirect
6. #10591394C2semidirect
7. #10591388C2semidirect
8. #10591370C2semidirect
9. #10591302C2semidirect
20. C2×C32×C4⋊C4C22semidirect
21. C2×C4⋊(C3⋊Dic3)C22semidirect
22. C2×#3750C22semidirect
23. C2×#3750C22semidirect
25. C2×C3×(C2×D3)⋊C4C22semidirect
26. C2×C3×(C2×D3)⋊C4C22semidirect
27. C2×(C2×D3)⋊Dic3C22semidirect
28. C2×(C2×D3)⋊Dic3C22semidirect
31. C3×C3⋊#95C22semidirect
32. #63579C22semidirect
40. #4991D3semidirect
66. C2×C4×C3⋊D3D4semidirect
99. C2×C3×C4⋊C4C2×D3semidirect
106. C2×(C2×D3)⋊C4C2×D3semidirect
107. C2×(C2×D3)⋊C4C2×D3semidirect
120. C3⋊#95C2×D3semidirect
147. C2×C32×C4C2×D4semidirect
154. C2×C3⋊Dic3C2×D4semidirect
277. C2×C4⋊C4D32semidirect
336. C2×C3×C4D3×D4semidirect
368. C3⋊D3#394semidirect
458. C32C2×#394semidirect
500. C2×C4#3802semidirect
542. C3D3×#394semidirect

Maximal subgroups

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

subgroupindex
C22×#38022
C2×C4⋊C4×C3⋊D32
C2×#639212
C3×#49912
#105913942
#105913882
#105913702
#105913022
D3×#3943