Finite Group Databasebeta

← #11857049

Subgroups — #11857049

Order 1152.

1254 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#387C211yesmaximal, characteristic, complemented
2#10592689C211yesmaximal, characteristic
3#10592689C211yesmaximal, characteristic
4#10592679C211yesmaximal, characteristic, complemented
5#10592677C211yesmaximal, characteristic, complemented
6#10592639C211yesmaximal, characteristic
7C42×C3⋊Dic3C211yesmaximal, characteristic, complemented
8#10592369C211yesmaximal, characteristic
9#10592369C211yesmaximal, characteristic
10#10592368C211yesmaximal, characteristic
11#10592368C211yesmaximal, characteristic
12#10592354C211yesmaximal, characteristic, complemented
13#10592353C211yesmaximal, characteristic, complemented
14#10592352C211yesmaximal, characteristic, complemented
15#10592351C211yesmaximal, characteristic, complemented
16#75294—34nomaximal
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C32×C42C2211yescharacteristic
20C2×#3752C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C2×C4×C3⋊Dic3C2211yescharacteristic
33C2×C4×C3⋊Dic3C2211yescharacteristic
34C2×C4×C3⋊Dic3C2211yescharacteristic
35C2×C4×C3⋊Dic3C2211yescharacteristic
36C2×C4×C3⋊Dic3C2211yescharacteristic
37C2×C4×C3⋊Dic3C2211yescharacteristic
38C32×#95C2211yescharacteristic
39C32×#95C2211yescharacteristic
40C32×#95C2211yescharacteristic
41C32×#95C2211yescharacteristic
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52C3×#387D314yescomplemented
53#4990—34no—
54#4990—34no—
55#4980—34no—
56#4978—34no—
57#4940—34no—
58C42×Dic3—34no—
59#4670—34no—
60#4670—34no—
61#4669—34no—
62#4669—34no—
63#4655—34no—
64#4654—34no—
65#4653—34no—
66#4652—34no—
67C23×C3⋊D3C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C3⋊Dic3C2311yescharacteristic
76C22×C3⋊Dic3C2311yescharacteristic
77C22×C3⋊Dic3C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2311yescharacteristic
82C32×C4⋊C4—22no—
83C32×C4⋊C4—22no—
84C32×C42—22no—
85#3752—22no—
86#3752—22no—
87#3752—22no—
88#3752—22no—
89#3752—22no—
90#3752—22no—
91#3752—22no—
92C4⋊(C3⋊Dic3)—22no—
93C4⋊(C3⋊Dic3)—22no—
94#3750—22no—
95#3750—22no—
96#3750—22no—
97C4×C3⋊Dic3—22no—
98C4×C3⋊Dic3—22no—
99C4×C3⋊Dic3—22no—
100C4×C3⋊Dic3—22no—
101C4×C3⋊Dic3—22no—
102C4×C3⋊Dic3—22no—
103#2866—91noSylow
104C2×C3×C4⋊C4C2×D314yes—
105C2×C3×C4⋊C4C2×D314yes—
106C2×C3×C42C2×D314yes—
107C2×(C2×D3)⋊C4—34no—
108C2×(C2×D3)⋊C4—34no—
109C2×(C2×D3)⋊C4—34no—
110C2×(C2×D3)⋊C4—34no—
111C2×(C2×D3)⋊C4—34no—
112C2×(C2×D3)⋊C4—34no—
113C2×(C2×D3)⋊C4—34no—
114C2×C4⋊Dic3—34no—
115C2×C4⋊Dic3—34no—
116C2×Dic3⋊C4—34no—
117C2×Dic3⋊C4—34no—
118C2×Dic3⋊C4—34no—
119C2×C4×Dic3—34no—
120C2×C4×Dic3—34no—
121C2×C4×Dic3—34no—
122C2×C4×Dic3—34no—
123C2×C4×Dic3—34no—
124C2×C4×Dic3—34no—
125C3×#95C2×D314yes—
126C3×#95C2×D314yes—
127C3×#95C2×D314yes—
128C3×#95C2×D314yes—
129C3⋊#95—34no—
130C3⋊#95—34no—
131C3⋊#95—34no—
132C3⋊#95—34no—
133C3⋊#95—34no—
134C3⋊#95—34no—
135C3⋊#95—34no—
136C3⋊#95—34no—
137C3⋊#95—34no—
138C3⋊#95—34no—
139C23×C32C2411yescharacteristic
140C22×C3⋊D3—21no—
141C22×C3⋊D3—21no—
142C22×C3⋊D3—21no—
143C22×C3⋊D3—21no—
144C22×C3⋊D3—21no—
145C22×C3⋊D3—21no—
146C22×C3⋊D3—21no—
147C2×C32×C4—21no—
148C2×C32×C4—21no—
149C2×C32×C4—21no—
150C2×C32×C4—21no—
151C2×C32×C4—21no—
152C2×C32×C4—21no—
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#4112yes—
166C2×C32×C4#4112yes—
167C2×C32×C4#4112yes—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
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#4112yes—
186C2×C3⋊Dic3#4112yes—
187C2×C3⋊Dic3#4112yes—
188C2×C3⋊Dic3#4112yes—
189#388—91no—
190#388—91no—
191#388—91no—
192#388—91no—
193#388—91no—
194#388—91no—
195#388—91no—
196#387—91no—
197#387—91no—
198#387—91no—
199#387—91no—
200#387—91no—
201#387—91no—
202#387C3⋊D311yescharacteristic, complemented
203C43—91no—
204C23×D3—34no—
205C22×C3×C4C22×D314yes—
206C22×C3×C4C22×D314yes—
207C22×C3×C4C22×D314yes—
208C22×C3×C4C22×D314yes—
209C22×C3×C4C22×D314yes—
210C22×C3×C4C22×D314yes—
211C22×C3×C4C22×D314yes—
212C22×Dic3—34no—
213C22×Dic3—34no—
214C22×Dic3—34no—
215C22×Dic3—34no—
216C22×Dic3—34no—
217C22×Dic3—34no—
218C22×Dic3—34no—
219C3×C4⋊C4—28no—
220C3×C4⋊C4—28no—
221C3×C42—28no—
222(C2×D3)⋊C4—68no—
223(C2×D3)⋊C4—68no—
224(C2×D3)⋊C4—68no—
225(C2×D3)⋊C4—68no—
226(C2×D3)⋊C4—68no—
227(C2×D3)⋊C4—68no—
228(C2×D3)⋊C4—68no—
229C4⋊Dic3—68no—
230C4⋊Dic3—68no—
231Dic3⋊C4—68no—
232Dic3⋊C4—68no—
233Dic3⋊C4—68no—
234C4×Dic3—68no—
235C4×Dic3—68no—
236C4×Dic3—68no—
237C4×Dic3—68no—
238C4×Dic3—68no—
239C4×Dic3—68no—
240C22×C32C2×#4111yescharacteristic
241C22×C32C2×#4111yescharacteristic
242C22×C32C2×#4111yescharacteristic
243C22×C32C2×#4111yescharacteristic
244C22×C32C2×#4111yescharacteristic
245C22×C32C2×#4111yescharacteristic
246C22×C32C2×#4111yescharacteristic
247C2×C3⋊D3—41no—
248C2×C3⋊D3—41no—
249C2×C3⋊D3—41no—
250C2×C3⋊D3—41no—
251C2×C3⋊D3—41no—
252C2×C3⋊D3—41no—
253C2×C3⋊D3—41no—
254C32×C4—22no—
255C32×C4—22no—
256C32×C4—22no—
257C32×C4—41no—
258C32×C4—41no—
259C32×C4—41no—
260C32×C4—41no—
261C3⋊Dic3—22no—
262C3⋊Dic3—22no—
263C3⋊Dic3—22no—
264C3⋊Dic3—22no—
265C3⋊Dic3—41no—
266C3⋊Dic3—41no—
267C3⋊Dic3—41no—
268C2×C4⋊C4—91no—
269C2×C4⋊C4—91no—
270C2×C4⋊C4—91no—
271C2×C4⋊C4—91no—
272C2×C4⋊C4—91no—
273C2×C4⋊C4C2×C3⋊D311yescharacteristic
274C2×C4⋊C4C2×C3⋊D311yescharacteristic
275C2×C22⋊C4—91no—
276C2×C22⋊C4—91no—
277C2×C22⋊C4—91no—
278C2×C22⋊C4—91no—
279C2×C22⋊C4—91no—
280C2×C22⋊C4—91no—
281C2×C22⋊C4—91no—
282C2×C42—91no—
283C2×C42—91no—
284C2×C42—91no—
285C2×C42—91no—
286C2×C42—91no—
287C2×C42—91no—
288C2×C42C2×C3⋊D311yescharacteristic
289#95—91no—
290#95—91no—
291#95—91no—
292#95—91no—
293#95—91no—
294#95—91no—
295#95—91no—
296#95—91no—
297#95—91no—
298#95—91no—
299#95C2×C3⋊D311yescharacteristic
300#95C2×C3⋊D311yescharacteristic
301#95C2×C3⋊D311yescharacteristic
302#95C2×C3⋊D311yescharacteristic
303C23×C3C23×D314yes—
304C22×D3—64no—
305C22×D3—64no—
306C22×D3—64no—
307C22×D3—64no—
308C22×D3—64no—
309C22×D3—64no—
310C22×D3—64no—
311C2×C3×C4—24no—
312C2×C3×C4—24no—
313C2×C3×C4—24no—
314C2×C3×C4—24no—
315C2×C3×C4—24no—
316C2×C3×C4—24no—
317C2×C3×C4—24no—
318C2×C3×C4—24no—
319C2×C3×C4—24no—
320C2×C3×C4—24no—
321C2×C3×C4—24no—
322C2×C3×C4—24no—
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#23518yes—
330C2×C3×C4#23718yes—
331C2×C3×C4#23918yes—
332C2×Dic3—38no—
333C2×Dic3—38no—
334C2×Dic3—38no—
335C2×Dic3—38no—
336C2×Dic3—64no—
337C2×Dic3—64no—
338C2×Dic3—64no—
339C2×Dic3—64no—
340C2×Dic3—64no—
341C2×Dic3—64no—
342C2×Dic3—64no—
343C2×Dic3—64no—
344C2×Dic3—64no—
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×C32#52911yescharacteristic
354C2×C32#52911yescharacteristic
355C2×C32#52911yescharacteristic
356C2×C32#52911yescharacteristic
357C2×C32#52911yescharacteristic
358C2×C32#52911yescharacteristic
359C2×C32#52911yescharacteristic
360C3⋊D3—81no—
361C24—91no—
362C22×C4—91no—
363C22×C4—91no—
364C22×C4—91no—
365C22×C4—91no—
366C22×C4—91no—
367C22×C4—91no—
368C22×C4—91no—
369C22×C4C22×C3⋊D311yescharacteristic
370C22×C4C22×C3⋊D311yescharacteristic
371C22×C4C22×C3⋊D311yescharacteristic
372C22×C4C22×C3⋊D311yescharacteristic
373C22×C4C22×C3⋊D311yescharacteristic
374C22×C4C22×C3⋊D311yescharacteristic
375C22×C4C22×C3⋊D311yescharacteristic
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—182no—
379C4⋊C4—182no—
380C4⋊C4—182no—
381C4⋊C4—182no—
382C4⋊C4—182no—
383C22⋊C4—182no—
384C22⋊C4—182no—
385C22⋊C4—182no—
386C22⋊C4—182no—
387C22⋊C4—182no—
388C22⋊C4—182no—
389C22⋊C4—182no—
390C42—22no—
391C42—182no—
392C42—182no—
393C42—182no—
394C42—182no—
395C42—182no—
396C42—182no—
397C22×C3C2×#23514yes—
398C22×C3C2×#23714yes—
399C22×C3C2×#23914yes—
400C22×C3D3×#4114yes—
401C22×C3D3×#4114yes—
402C22×C3D3×#4114yes—
403C22×C3D3×#4114yes—
404C2×D3—124no—
405C2×D3—124no—
406C2×D3—124no—
407C2×D3—124no—
408C2×D3—124no—
409C2×D3—124no—
410C2×D3—124no—
411C3×C4—28no—
412C3×C4—28no—
413C3×C4—28no—
414C3×C4—44no—
415C3×C4—44no—
416C3×C4—44no—
417C3×C4—44no—
418Dic3—68no—
419Dic3—68no—
420Dic3—68no—
421Dic3—68no—
422Dic3—124no—
423Dic3—124no—
424Dic3—124no—
425C32#286611yescharacteristic, complemented, Sylow
426C23—181no—
427C23—181no—
428C23—181no—
429C23—181no—
430C23—181no—
431C23—181no—
432C23—181no—
433C23C23×C3⋊D311yescharacteristic
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—92no—
453C2×C4—92no—
454C2×C4—92no—
455C2×C4—92no—
456C2×C4—181no—
457C2×C4—181no—
458C2×C4—181no—
459C2×C4—181no—
460C2×C4—181no—
461C2×C4—181no—
462C2×C4—181no—
463C2×C4—181no—
464C2×C4—181no—
465C2×C4—181no—
466C2×C4—181no—
467C2×C4—181no—
468C2×C4—181no—
469C2×C4—181no—
470C2×C4—181no—
471C2×C4—181no—
472C2×C4—181no—
473C2×C4#382812yes—
474C2×C4#383012yes—
475C2×C4#383212yes—
476C2×C3#552814yes—
477C2×C3#553814yes—
478C2×C3#558014yes—
479C2×C3#562414yes—
480C2×C3#564914yes—
481C2×C3#569114yes—
482C2×C3#570614yes—
483D3—244no—
484C22—361no—
485C22—361no—
486C22—361no—
487C22—361no—
488C22—361no—
489C22—361no—
490C22—361no—
491C22C2×#382811yescharacteristic
492C22C2×#383011yescharacteristic
493C22C2×#383211yescharacteristic
494C22#41×C3⋊D311yescharacteristic
495C22#41×C3⋊D311yescharacteristic
496C22#41×C3⋊D311yescharacteristic
497C22#41×C3⋊D311yescharacteristic
498C4—22no—
499C4—22no—
500C4—22no—
501C4—41no—
502C4—41no—
503C4—41no—
504C4—41no—
505C4—182no—
506C4—182no—
507C4—182no—
508C4—182no—
509C4—361no—
510C4—361no—
511C4—361no—
512C3#7529414yescomplemented
513C2—721no—
514C2#1059599911yescharacteristic
515C2#1059600911yescharacteristic
516C2#1059605111yescharacteristic
517C2#1059609511yescharacteristic
518C2#1059612011yescharacteristic
519C2#1059616211yescharacteristic
520C2#1059617711yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#387C2
prime radicalC23×C3⋊D3C23
hypercenter#387C3⋊D3
hypocenterC32#2866
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. C32×#387C2semidirect
4. #10592679C2semidirect
5. #10592677C2semidirect
7. C42×C3⋊Dic3C2semidirect
12. #10592354C2semidirect
13. #10592353C2semidirect
14. #10592352C2semidirect
15. #10592351C2semidirect
52. C3×#387D3semidirect
202. #387C3⋊D3semidirect
425. C32#2866semidirect
512. C3#75294semidirect

Maximal subgroups

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

subgroupindex
C32×#3872
#105926892
#105926792
#105926772
#105926392
C42×C3⋊Dic32
#105923692
#105923682
#105923542
#105923532
#105923522
#105923512
#752943