Finite Group Databasebeta

← #11807750

Subgroups — #11807750

Order 1152.

1269 conjugacy classes of subgroups.

The subgroup lattice has 533 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63980C211yesmaximal, characteristic
2#10592641C211yesmaximal, characteristic, complemented
3C3×#4956C212yesmaximal, complemented
4#10591707C212yesmaximal, complemented
5#10591697C211yesmaximal, characteristic, complemented
6#10591381C212yesmaximal, complemented
7#10591281C212yesmaximal, complemented
8#10591278C212yesmaximal, complemented
9#10591249C212yesmaximal, complemented
10#74683—32nomaximal
11C23×C3⋊Dic3C2211yescharacteristic
12C22×C3×#67C2212yes—
13C22×C3×C4×D3C2212yes—
14C22×#625C2211yescharacteristic
15C2×C32×C22⋊C4C2211yescharacteristic
16C2×#3757C2211yescharacteristic
17C2×#3750C2212yes—
18C2×C3×#217C2212yes—
19C2×C3×(C2×D3)⋊C4C2212yes—
20#63980C418yescomplemented
21C2×#3724C2211yescharacteristic
22C2×Dic3⋊Dic3C2212yes—
23C2×(C2×D3)⋊Dic3C2212yes—
24C2×(C2×D3)⋊Dic3C2212yes—
25C2×(C2×D3)⋊Dic3C2212yes—
26C2×Dic32C2212yes—
27#63658C2212yes—
28C3×C3⋊#95C2212yes—
29C3×C3⋊#95C2212yes—
30#63579C2212yes—
31#63579C2211yescharacteristic
32#63579C2211yescharacteristic
33C2×#939—32no—
34C3×#386—32no—
35#5221—32no—
36#5213—32no—
37#5210—32no—
38#4957—32no—
39#4956—32no—
40#4956D312yescomplemented
41#4944—32no—
42#4943—32no—
43#4942—32no—
44#4942—61no—
45#4669—32no—
46#4668—32no—
47#4655—32no—
48#4652—32no—
49C24×C32C2311yescharacteristic
50C23×C3×D3C2312yes—
51C22×C32×C4C2312yes—
52C22×C3⋊Dic3—42no—
53C22×C3⋊Dic3C2×C414yescomplemented
54C22×C3⋊Dic3C2312yes—
55C22×C3⋊Dic3C2311yescharacteristic
56C22×C3⋊Dic3C2311yescharacteristic
57C2×C3×#67—42no—
58C2×C3×#67—42no—
59C2×C3×#67C2×C418yescomplemented
60C22×C3×Dic3C2312yes—
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2312yes—
63C2×C3×C4×D3—42no—
64C2×C3×C4×D3—42no—
65C2×C3×C4×D3—42no—
66C2×#625—42no—
67C2×#625C2×C414yes—
68C32×C22⋊C4—41no—
69#3757—41no—
70#3750—42no—
71C3×#217—42no—
72C3×(C2×D3)⋊C4—42no—
73#3724C2×C414yescomplemented
74Dic3⋊Dic3—42no—
75(C2×D3)⋊Dic3—42no—
76(C2×D3)⋊Dic3—42no—
77(C2×D3)⋊Dic3C2×C418yescomplemented
78Dic32—42no—
79#2377—91noSylow
80C22×C3×D4—32no—
81C23×C3×C4—32no—
82C22×#67—32no—
83C22×#67C2×D312yes—
84C23×Dic3—32no—
85C23×Dic3—61no—
86C22×C4×D3C2×D312yes—
87C2×C3×C22⋊C4—21no—
88C2×C3×C22⋊C4—32no—
89C2×C3×C22⋊C4—32no—
90C2×C3×C22⋊C4C2×D312yes—
91C2×#217—32no—
92C2×#217—32no—
93C2×#217—32no—
94C2×#217—32no—
95C2×#217—61no—
96C2×#217C2×D312yes—
97#939—316no—
98C2×(C2×D3)⋊C4—32no—
99C2×(C2×D3)⋊C4—32no—
100C2×(C2×D3)⋊C4—32no—
101C2×(C2×D3)⋊C4C2×D312yes—
102C2×C4⋊Dic3—32no—
103C2×Dic3⋊C4—32no—
104C2×Dic3⋊C4—32no—
105C2×Dic3⋊C4—32no—
106C2×Dic3⋊C4—32no—
107C2×Dic3⋊C4—62no—
108C2×C4×Dic3—32no—
109C2×C4×Dic3—32no—
110C3×#95—32no—
111C3×#95—32no—
112C3⋊#95—32no—
113C3⋊#95—32no—
114C3⋊#95—32no—
115C3⋊#95—32no—
116C3⋊#95—32no—
117C3⋊#95—32no—
118C3⋊#95—62no—
119C3⋊#95C2×D312yes—
120C3⋊#95C2×D312yes—
121C23×C32—21no—
122C23×C32—21no—
123C23×C32—22no—
124C23×C32—22no—
125C23×C32C22×C412yes—
126C23×C32C2411yescharacteristic
127C22×C3×D3—22no—
128C22×C3×D3—22no—
129C22×C3×D3—22no—
130C22×C3×D3—22no—
131C22×C3×D3—22no—
132C22×C3×D3—22no—
133C22×C3×D3C22×C414yes—
134C2×C32×C4—22no—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—44no—
143C2×C3⋊Dic3C22×C412yes—
144C2×C3⋊Dic3C22×C412yes—
145C3×#67—48no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3C22×C414yes—
155C3×C4×D3—48no—
156#625—44no—
157C2×#121—91no—
158#390—92no—
159#388—92no—
160#387—92no—
161#386—32no—
162#386—92no—
163#385—92no—
164#381—91no—
165#380—91no—
166C24×C3—21no—
167C24×C3—32no—
168C24×C3C22×D312yes—
169C23×D3C22×D312yes—
170C2×C3×D4—38no—
171C2×C3×D4—122no—
172C2×C3×D4—122no—
173C22×C3×C4—22no—
174C22×C3×C4—32no—
175C22×C3×C4—32no—
176C22×C3×C4—32no—
177C22×C3×C4—122no—
178C22×C3×C4—122no—
179C22×C3×C4—122no—
180C22×C3×C4C22×D312yes—
181C22×C3×C4C22×D312yes—
182C2×#67—38no—
183C2×#67—42no—
184C2×#67—42no—
185C2×#67—122no—
186C2×#67—122no—
187C2×#67C4×D318yescomplemented
188C22×Dic3—32no—
189C22×Dic3—32no—
190C22×Dic3—38no—
191C22×Dic3—32no—
192C22×Dic3—32no—
193C22×Dic3—61no—
194C22×Dic3—61no—
195C22×Dic3—64no—
196C22×Dic3—62no—
197C22×Dic3—122no—
198C22×Dic3—122no—
199C22×Dic3—124no—
200C22×Dic3C22×D312yes—
201C22×Dic3C22×D312yes—
202C22×Dic3C22×D312yes—
203C2×C4×D3—42no—
204C2×C4×D3—42no—
205C2×C4×D3—42no—
206C3×C22⋊C4—42no—
207C3×C22⋊C4—42no—
208C3×C22⋊C4—122no—
209C3×C22⋊C4—122no—
210#217—38no—
211#217—42no—
212#217—122no—
213#217—122no—
214#217—122no—
215#217—122no—
216(C2×D3)⋊C4—38no—
217(C2×D3)⋊C4—42no—
218(C2×D3)⋊C4—122no—
219(C2×D3)⋊C4—122no—
220C4⋊Dic3—122no—
221Dic3⋊C4—38no—
222Dic3⋊C4—122no—
223Dic3⋊C4—122no—
224Dic3⋊C4—122no—
225Dic3⋊C4—124no—
226C4×Dic3—122no—
227C4×Dic3—122no—
228C22×C32—22no—
229C22×C32—22no—
230C22×C32—22no—
231C22×C32—42no—
232C22×C32—42no—
233C22×C32C23×C411yescharacteristic
234C22×C32H(5,𝔽2)12yes—
235C22×C32H(5,𝔽2)11yescharacteristic
236C22×C32H(5,𝔽2)12yes—
237C22×C322−1+411yescharacteristic
238C2×C3×D3—24no—
239C2×C3×D3—24no—
240C2×C3×D3—24no—
241C2×C3×D3—42no—
242C2×C3×D3—42no—
243C2×C3×D3—42no—
244C2×C3×D3—42no—
245C32×C4—42no—
246C3⋊Dic3—22no—
247C3⋊Dic3—22no—
248C3⋊Dic3—42no—
249C3×Dic3—24no—
250C3×Dic3—42no—
251C3×Dic3—42no—
252C22×D4—32no—
253C22×D4—91no—
254C23×C4—32no—
255C23×C4—91no—
256#121—98no—
257C2×C4⋊C4—91no—
258C2×C4⋊C4—92no—
259C2×C4⋊C4—92no—
260C2×C22⋊C4—32no—
261C2×C22⋊C4—32no—
262C2×C22⋊C4—92no—
263C2×C22⋊C4—92no—
264C2×C22⋊C4—92no—
265C2×C22⋊C4—91no—
266C2×C22⋊C4D3211yescharacteristic
267C2×C42—92no—
268#95—32no—
269#95—32no—
270#95—91no—
271#95—92no—
272#95—91no—
273#95—92no—
274C23×C3—22no—
275C23×C3—22no—
276C23×C3—22no—
277C23×C3—22no—
278C23×C3—22no—
279C23×C3—22no—
280C23×C3—22no—
281C23×C3—22no—
282C23×C3—21no—
283C23×C3—22no—
284C23×C3—34no—
285C23×C3—42no—
286C23×C3—42no—
287C23×C3—62no—
288C23×C3—62no—
289C23×C3—62no—
290C23×C3—62no—
291C23×C3—62no—
292C23×C3—62no—
293C23×C3C2×C4×D314yes—
294C23×C3C23×D312yes—
295C22×D3—22no—
296C22×D3—22no—
297C22×D3—22no—
298C22×D3—22no—
299C22×D3—22no—
300C22×D3—22no—
301C22×D3C2×C4×D314yes—
302C3×D4—128no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—34no—
310C2×C3×C4—42no—
311C2×C3×C4—42no—
312C2×C3×C4—42no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—128no—
322#67—48no—
323#67—128no—
324C2×Dic3—22no—
325C2×Dic3—22no—
326C2×Dic3—22no—
327C2×Dic3—22no—
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—22no—
331C2×Dic3—22no—
332C2×Dic3—34no—
333C2×Dic3—34no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—64no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—62no—
340C2×Dic3—62no—
341C2×Dic3—62no—
342C2×Dic3—62no—
343C2×Dic3—62no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—122no—
348C2×Dic3—122no—
349C2×Dic3—122no—
350C2×Dic3—122no—
351C2×Dic3—128no—
352C2×Dic3—128no—
353C2×Dic3C2×C4×D314yes—
354C4×D3—48no—
355C2×C32—42no—
356C2×C32#51811yescharacteristic
357C2×C32#51811yescharacteristic
358C2×C32#52011yescharacteristic
359C2×C32#56012yes—
360C2×C32#56212yes—
361C3×D3—44no—
362C24—32no—
363C24C2×D3211yescharacteristic
364C2×D4—38no—
365C2×D4—94no—
366C2×D4—122no—
367C2×D4—122no—
368C2×D4—362no—
369C22×C4—32no—
370C22×C4—32no—
371C22×C4—32no—
372C22×C4—91no—
373C22×C4—91no—
374C22×C4—94no—
375C22×C4—92no—
376C22×C4—122no—
377C22×C4—122no—
378C22×C4—122no—
379C22×C4—362no—
380C22×C4C2×D3212yes—
381C4⋊C4—94no—
382C4⋊C4—362no—
383C4⋊C4—362no—
384C22⋊C4—41no—
385C22⋊C4—98no—
386C22⋊C4—122no—
387C22⋊C4—122no—
388C22⋊C4—362no—
389C22⋊C4—362no—
390C22⋊C4—361no—
391C42—362no—
392C22×C3—24no—
393C22×C3—24no—
394C22×C3—24no—
395C22×C3—24no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—22no—
399C22×C3—22no—
400C22×C3—21no—
401C22×C3—42no—
402C22×C3—42no—
403C22×C3—44no—
404C22×C3—44no—
405C22×C3—42no—
406C22×C3—42no—
407C22×C3—42no—
408C22×C3—42no—
409C22×C3—64no—
410C22×C3—64no—
411C22×C3—64no—
412C22×C3—122no—
413C22×C3—122no—
414C22×C3—122no—
415C22×C3—122no—
416C22×C3C22×C4×D312yes—
417C22×C3#100412yes—
418C22×C3#100412yes—
419C22×C3#100412yes—
420C22×C3#100412yes—
421C22×C3#100912yes—
422C22×C3#101012yes—
423C2×D3—24no—
424C2×D3—24no—
425C2×D3—24no—
426C2×D3—42no—
427C2×D3—42no—
428C2×D3—42no—
429C2×D3—42no—
430C3×C4—42no—
431C3×C4—42no—
432C3×C4—64no—
433C3×C4—82no—
434C3×C4—122no—
435C3×C4—122no—
436Dic3—24no—
437Dic3—42no—
438Dic3—42no—
439Dic3—64no—
440Dic3—64no—
441Dic3—64no—
442Dic3—122no—
443Dic3—122no—
444Dic3—122no—
445Dic3—242no—
446C32#237711yescharacteristic, complemented, Sylow
447C23—21no—
448C23—22no—
449C23—22no—
450C23—21no—
451C23—34no—
452C23—62no—
453C23—62no—
454C23—62no—
455C23—62no—
456C23—62no—
457C23—62no—
458C23C4×D3212yes—
459C23C22×D3211yescharacteristic
460D4—128no—
461D4—364no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—34no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—62no—
471C2×C4—62no—
472C2×C4—62no—
473C2×C4—62no—
474C2×C4—92no—
475C2×C4—92no—
476C2×C4—128no—
477C2×C4—182no—
478C2×C4—182no—
479C2×C4—182no—
480C2×C4—182no—
481C2×C4—182no—
482C2×C4—364no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—22no—
486C2×C3—22no—
487C2×C3—21no—
488C2×C3—44no—
489C2×C3—44no—
490C2×C3—124no—
491C2×C3#548612yes—
492C2×C3#554512yes—
493C2×C3#554612yes—
494C2×C3#559512yes—
495C2×C3#562012yes—
496C2×C3#562112yes—
497C2×C3#566712yes—
498D3—44no—
499C22—22no—
500C22—22no—
501C22—22no—
502C22—42no—
503C22—42no—
504C22—64no—
505C22—64no—
506C22—64no—
507C22—122no—
508C22—122no—
509C22—122no—
510C22—122no—
511C22#6429811yescharacteristic
512C22C2×C4×D3211yescharacteristic
513C22#6431312yes—
514C22#6431412yes—
515C22#6433011yescharacteristic
516C4—42no—
517C4—64no—
518C4—122no—
519C4—122no—
520C4—182no—
521C4—182no—
522C4—362no—
523C3—21no—
524C3#7468312yescomplemented
525C2—42no—
526C2—124no—
527C2#1059418111yescharacteristic
528C2#1059423912yes—
529C2#1059425611yescharacteristic
530C2#1059487611yescharacteristic
531C2#1059525712yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63980C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2377
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592641C2semidirect
3. C3×#4956C2semidirect
4. #10591707C2semidirect
5. #10591697C2semidirect
6. #10591381C2semidirect
7. #10591281C2semidirect
8. #10591278C2semidirect
9. #10591249C2semidirect
20. #63980C4semidirect
40. #4956D3semidirect
53. C22×C3⋊Dic3C2×C4semidirect
59. C2×C3×#67C2×C4semidirect
73. #3724C2×C4semidirect
77. (C2×D3)⋊Dic3C2×C4semidirect
187. C2×#67C4×D3semidirect
446. C32#2377semidirect
524. C3#74683semidirect

Maximal subgroups

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

subgroupindex
C2×#639802
#105926412
C3×#49562
#105917072
#105916972
#105913812
#105912812
#105912782
#105912492
#746833