Finite Group Databasebeta

← #11808020

Subgroups — #11808020

Order 1152.

1368 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64088C211yesmaximal, characteristic
2C32×#388C211yesmaximal, characteristic
3#10592675C211yesmaximal, characteristic, complemented
4#10592674C211yesmaximal, characteristic, complemented
5#10592649C211yesmaximal, characteristic
6#10592645C211yesmaximal, characteristic
7#10592645C211yesmaximal, characteristic
8#10592644C211yesmaximal, characteristic
9#10592643C211yesmaximal, characteristic
10#10592632C211yesmaximal, characteristic, complemented
11#10592627C211yesmaximal, characteristic, complemented
12#10592354C211yesmaximal, characteristic, complemented
13#10592352C211yesmaximal, characteristic, complemented
14#10592350C211yesmaximal, characteristic, complemented
15#10592346C211yesmaximal, characteristic, complemented
16#75494—34nomaximal
17C23×C3⋊Dic3C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C32×C22⋊C4C2211yescharacteristic
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×C32×C42C2211yescharacteristic
23C2×#3757C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C2×#3750C2211yescharacteristic
33C2×#3750C2211yescharacteristic
34C2×#3750C2211yescharacteristic
35C2×#3750C2211yescharacteristic
36C2×#3750C2211yescharacteristic
37C2×C4×C3⋊Dic3C2211yescharacteristic
38C2×C4×C3⋊Dic3C2211yescharacteristic
39C2×C4×C3⋊Dic3C2211yescharacteristic
40#64088C418yescomplemented
41C32×#95C2211yescharacteristic
42C32×#95C2211yescharacteristic
43#63658C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52#63658C2211yescharacteristic
53C2×#879—34no—
54C3×#388D314yes—
55#4976—34no—
56#4975—34no—
57#4950—34no—
58#4946—34no—
59#4946—34no—
60#4945—34no—
61#4944—34no—
62#4933—34no—
63#4928—34no—
64#4655—34no—
65#4653—34no—
66#4651—34no—
67#4647—34no—
68C24×C32C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C3⋊Dic3—41no—
76C22×C3⋊Dic3—41no—
77C22×C3⋊Dic3—41no—
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2311yescharacteristic
82C22×C3⋊Dic3C2311yescharacteristic
83C22×C3⋊Dic3C2311yescharacteristic
84C22×C3⋊Dic3C2311yescharacteristic
85C22×C3⋊Dic3C2311yescharacteristic
86C32×C4⋊C4—41no—
87C32×C22⋊C4—41no—
88C32×C22⋊C4—41no—
89C32×C22⋊C4C2×C414yes—
90C32×C42—41no—
91#3757—41no—
92#3757C2×C414yes—
93#3757C2×C414yes—
94C4⋊(C3⋊Dic3)—41no—
95C4⋊(C3⋊Dic3)—41no—
96C4⋊(C3⋊Dic3)C2×C414yescomplemented
97#3750—41no—
98#3750—41no—
99#3750—41no—
100#3750—41no—
101#3750—41no—
102#3750—41no—
103#3750C2×C414yescomplemented
104#3750C2×C414yescomplemented
105C4×C3⋊Dic3—41no—
106C4×C3⋊Dic3—41no—
107C4×C3⋊Dic3C2×C414yescomplemented
108#2383—91noSylow
109C23×Dic3—34no—
110C2×C3×C4⋊C4C2×D314yes—
111C2×C3×C22⋊C4C2×D314yes—
112C2×C3×C22⋊C4C2×D314yes—
113C2×C3×C22⋊C4C2×D314yes—
114C2×C3×C42C2×D314yes—
115C2×#217—34no—
116C2×#217—34no—
117C2×#217—34no—
118C2×C4⋊Dic3—34no—
119C2×C4⋊Dic3—34no—
120C2×C4⋊Dic3—34no—
121C2×Dic3⋊C4—34no—
122C2×Dic3⋊C4—34no—
123C2×Dic3⋊C4—34no—
124C2×Dic3⋊C4—34no—
125C2×Dic3⋊C4—34no—
126C2×Dic3⋊C4—34no—
127C2×Dic3⋊C4—34no—
128C2×Dic3⋊C4—34no—
129C2×C4×Dic3—34no—
130C2×C4×Dic3—34no—
131C2×C4×Dic3—34no—
132#879—332no—
133C3×#95C2×D314yes—
134C3×#95C2×D314yes—
135C3⋊#95—34no—
136C3⋊#95—34no—
137C3⋊#95—34no—
138C3⋊#95—34no—
139C3⋊#95—34no—
140C3⋊#95—34no—
141C3⋊#95—34no—
142C3⋊#95—34no—
143C3⋊#95—34no—
144C3⋊#95—34no—
145C23×C32—21no—
146C23×C32—21no—
147C23×C32—21no—
148C23×C32—21no—
149C23×C32—21no—
150C23×C32—21no—
151C23×C32C22×C412yes—
152C23×C32C2411yescharacteristic
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4C22×C412yes—
170C2×C32×C4C22×C412yes—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—44no—
192C2×C3⋊Dic3C22×C412yes—
193C2×C3⋊Dic3C22×C412yes—
194C2×C3⋊Dic3C22×C412yes—
195C2×C3⋊Dic3C22×C412yes—
196C2×#126—91no—
197#389—91no—
198#389—91no—
199#389—91no—
200#388—91no—
201#388—91no—
202#388C3⋊D311yescharacteristic
203#387—91no—
204#387—91no—
205#387—91no—
206#385—91no—
207#385—91no—
208#385—91no—
209#384—91no—
210#383—91no—
211C24×C3C22×D314yes—
212C22×C3×C4C22×D314yes—
213C22×C3×C4C22×D314yes—
214C22×C3×C4C22×D314yes—
215C22×C3×C4C22×D314yes—
216C22×C3×C4C22×D314yes—
217C22×C3×C4C22×D314yes—
218C22×Dic3—34no—
219C22×Dic3—34no—
220C22×Dic3—34no—
221C22×Dic3—34no—
222C22×Dic3—34no—
223C22×Dic3—34no—
224C22×Dic3—34no—
225C22×Dic3—34no—
226C22×Dic3—124no—
227C22×Dic3—124no—
228C22×Dic3—124no—
229C3×C4⋊C4—44no—
230C3×C22⋊C4—44no—
231C3×C22⋊C4—44no—
232C3×C22⋊C4C4×D3116yes—
233C3×C42—44no—
234#217—316no—
235#217—316no—
236#217—124no—
237C4⋊Dic3—316no—
238C4⋊Dic3—124no—
239C4⋊Dic3—124no—
240Dic3⋊C4—316no—
241Dic3⋊C4—316no—
242Dic3⋊C4—124no—
243Dic3⋊C4—124no—
244Dic3⋊C4—124no—
245Dic3⋊C4—124no—
246Dic3⋊C4—124no—
247Dic3⋊C4—124no—
248C4×Dic3—316no—
249C4×Dic3—124no—
250C4×Dic3—124no—
251C22×C32—22no—
252C22×C32—22no—
253C22×C32—22no—
254C22×C32—41no—
255C22×C32—41no—
256C22×C32—41no—
257C22×C32—41no—
258C22×C32C23×C411yescharacteristic
259C22×C32H(5,𝔽2)11yescharacteristic
260C22×C32H(5,𝔽2)11yescharacteristic
261C22×C32H(5,𝔽2)11yescharacteristic
262C22×C322−1+411yescharacteristic
263C22×C322−1+411yescharacteristic
264C22×C322−1+411yescharacteristic
265C32×C4—22no—
266C32×C4—22no—
267C32×C4—41no—
268C32×C4—41no—
269C32×C4—41no—
270C32×C4—41no—
271C3⋊Dic3—22no—
272C3⋊Dic3—22no—
273C3⋊Dic3—22no—
274C3⋊Dic3—22no—
275C3⋊Dic3—41no—
276C3⋊Dic3—41no—
277C3⋊Dic3—41no—
278C3⋊Dic3—41no—
279C23×C4—91no—
280#126—98no—
281C2×C4⋊C4—91no—
282C2×C4⋊C4—91no—
283C2×C4⋊C4—91no—
284C2×C4⋊C4—91no—
285C2×C4⋊C4—91no—
286C2×C4⋊C4—91no—
287C2×C4⋊C4—91no—
288C2×C4⋊C4—91no—
289C2×C4⋊C4—91no—
290C2×C4⋊C4—91no—
291C2×C4⋊C4—91no—
292C2×C4⋊C4C2×C3⋊D311yescharacteristic
293C2×C22⋊C4—91no—
294C2×C22⋊C4—91no—
295C2×C22⋊C4—91no—
296C2×C22⋊C4C2×C3⋊D311yescharacteristic
297C2×C22⋊C4C2×C3⋊D311yescharacteristic
298C2×C22⋊C4C2×C3⋊D311yescharacteristic
299C2×C42—91no—
300C2×C42—91no—
301C2×C42—91no—
302C2×C42C2×C3⋊D311yescharacteristic
303#95—91no—
304#95—91no—
305#95—91no—
306#95—91no—
307#95—91no—
308#95—91no—
309#95—91no—
310#95—91no—
311#95—91no—
312#95—91no—
313#95C2×C3⋊D311yescharacteristic
314#95C2×C3⋊D311yescharacteristic
315C23×C3—24no—
316C23×C3—24no—
317C23×C3—24no—
318C23×C3—24no—
319C23×C3—24no—
320C23×C3—24no—
321C23×C3C2×C4×D318yes—
322C23×C3C23×D314yes—
323C2×C3×C4—24no—
324C2×C3×C4—24no—
325C2×C3×C4—24no—
326C2×C3×C4—24no—
327C2×C3×C4—24no—
328C2×C3×C4—24no—
329C2×C3×C4—24no—
330C2×C3×C4—24no—
331C2×C3×C4—24no—
332C2×C3×C4—24no—
333C2×C3×C4—24no—
334C2×C3×C4—24no—
335C2×C3×C4—24no—
336C2×C3×C4—24no—
337C2×C3×C4—24no—
338C2×C3×C4—24no—
339C2×C3×C4C2×C4×D318yes—
340C2×C3×C4C2×C4×D318yes—
341C2×Dic3—38no—
342C2×Dic3—38no—
343C2×Dic3—38no—
344C2×Dic3—38no—
345C2×Dic3—64no—
346C2×Dic3—64no—
347C2×Dic3—64no—
348C2×Dic3—64no—
349C2×Dic3—64no—
350C2×Dic3—64no—
351C2×Dic3—64no—
352C2×Dic3—64no—
353C2×Dic3—64no—
354C2×Dic3—64no—
355C2×Dic3—64no—
356C2×Dic3—64no—
357C2×Dic3—64no—
358C2×Dic3—64no—
359C2×Dic3—64no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362C2×Dic3—64no—
363C2×Dic3—64no—
364C2×Dic3—64no—
365C2×Dic3—1216no—
366C2×C32—42no—
367C2×C32#52011yescharacteristic
368C2×C32#52011yescharacteristic
369C2×C32#52011yescharacteristic
370C2×C32#56011yescharacteristic
371C2×C32#56311yescharacteristic
372C2×C32#56311yescharacteristic
373C2×C32#56311yescharacteristic
374C24C22×C3⋊D311yescharacteristic
375C22×C4—91no—
376C22×C4—91no—
377C22×C4—91no—
378C22×C4—91no—
379C22×C4—91no—
380C22×C4—91no—
381C22×C4—91no—
382C22×C4—91no—
383C22×C4—361no—
384C22×C4—361no—
385C22×C4—361no—
386C22×C4C22×C3⋊D311yescharacteristic
387C22×C4C22×C3⋊D311yescharacteristic
388C22×C4C22×C3⋊D311yescharacteristic
389C22×C4C22×C3⋊D311yescharacteristic
390C22×C4C22×C3⋊D311yescharacteristic
391C22×C4C22×C3⋊D311yescharacteristic
392C4⋊C4—41no—
393C4⋊C4—94no—
394C4⋊C4—94no—
395C4⋊C4—94no—
396C4⋊C4—361no—
397C4⋊C4—361no—
398C4⋊C4—361no—
399C4⋊C4—361no—
400C4⋊C4—361no—
401C4⋊C4—361no—
402C4⋊C4—361no—
403C4⋊C4—361no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—94no—
407C22⋊C4—94no—
408C22⋊C4—361no—
409C22⋊C4C4×C3⋊D314yes—
410C42—41no—
411C42—94no—
412C42—361no—
413C42—361no—
414C22×C3—28no—
415C22×C3—28no—
416C22×C3—28no—
417C22×C3—44no—
418C22×C3—44no—
419C22×C3—44no—
420C22×C3—44no—
421C22×C3C22×C4×D314yes—
422C22×C3#100414yes—
423C22×C3#100414yes—
424C22×C3#100914yes—
425C22×C3#101014yes—
426C22×C3#101014yes—
427C22×C3#101014yes—
428C3×C4—28no—
429C3×C4—28no—
430C3×C4—44no—
431C3×C4—44no—
432C3×C4—44no—
433C3×C4—44no—
434Dic3—68no—
435Dic3—68no—
436Dic3—68no—
437Dic3—68no—
438Dic3—124no—
439Dic3—124no—
440Dic3—124no—
441Dic3—124no—
442C32#238311yescharacteristic, complemented, Sylow
443C23—21no—
444C23—21no—
445C23—21no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23C2×C4×C3⋊D312yes—
450C23C23×C3⋊D311yescharacteristic
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—92no—
468C2×C4—92no—
469C2×C4—92no—
470C2×C4—92no—
471C2×C4—181no—
472C2×C4—181no—
473C2×C4—181no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—181no—
481C2×C4—181no—
482C2×C4—181no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—364no—
492C2×C4C2×C4×C3⋊D312yes—
493C2×C4C2×C4×C3⋊D312yes—
494C2×C3—48no—
495C2×C3#552314yes—
496C2×C3#554614yes—
497C2×C3#554614yes—
498C2×C3#562014yes—
499C2×C3#565114yes—
500C2×C3#567214yes—
501C2×C3#571214yes—
502C22—22no—
503C22—22no—
504C22—22no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22C22×C4×C3⋊D311yescharacteristic
510C22#6436111yescharacteristic
511C22#6436111yescharacteristic
512C22#6436611yescharacteristic
513C22#6436711yescharacteristic
514C22#6436711yescharacteristic
515C22#6436711yescharacteristic
516C4—22no—
517C4—22no—
518C4—41no—
519C4—41no—
520C4—41no—
521C4—41no—
522C4—182no—
523C4—182no—
524C4—182no—
525C4—182no—
526C4—361no—
527C4—361no—
528C4—361no—
529C4—361no—
530C3#7549414yescomplemented
531C2—42no—
532C2#1059599411yescharacteristic
533C2#1059601711yescharacteristic
534C2#1059601711yescharacteristic
535C2#1059609111yescharacteristic
536C2#1059612211yescharacteristic
537C2#1059614311yescharacteristic
538C2#1059618311yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#388C2
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenter#388C3⋊D3
hypocenterC32#2383
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
3. #10592675C2semidirect
4. #10592674C2semidirect
10. #10592632C2semidirect
11. #10592627C2semidirect
12. #10592354C2semidirect
13. #10592352C2semidirect
14. #10592350C2semidirect
15. #10592346C2semidirect
40. #64088C4semidirect
96. C4⋊(C3⋊Dic3)C2×C4semidirect
103. #3750C2×C4semidirect
104. #3750C2×C4semidirect
107. C4×C3⋊Dic3C2×C4semidirect
442. C32#2383semidirect
530. C3#75494semidirect

Maximal subgroups

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

subgroupindex
C2×#640882
C32×#3882
#105926752
#105926742
#105926492
#105926452
#105926442
#105926432
#105926322
#105926272
#105923542
#105923522
#105923502
#105923462
#754943