Finite Group Databasebeta

← #11808883

Subgroups — #11808883

Order 1152.

1296 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#400C211yesmaximal, characteristic, complemented
2#10592693C211yesmaximal, characteristic
3#10592691C211yesmaximal, characteristic
4C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
6#10592374C211yesmaximal, characteristic
7#10592373C211yesmaximal, characteristic
8#10592365C211yesmaximal, characteristic
9#10592365C211yesmaximal, characteristic
10#10592365C211yesmaximal, characteristic
11#10592361C211yesmaximal, characteristic, complemented
12#10592359C211yesmaximal, characteristic, complemented
13#10592358C211yesmaximal, characteristic, complemented
14#10592348C211yesmaximal, characteristic, complemented
15#10592347C211yesmaximal, characteristic, complemented
16#78132—34nomaximal
17C22×C4×C3⋊D3C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×#3752C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30C2×C4×C3⋊Dic3C2211yescharacteristic
31C2×C4×C3⋊Dic3C2211yescharacteristic
32C2×C4×C3⋊Dic3C2211yescharacteristic
33C2×C4×C3⋊Dic3C2211yescharacteristic
34C2×C4×C3⋊Dic3C2211yescharacteristic
35C2×C4×C3⋊Dic3C2211yescharacteristic
36C32×#95C2211yescharacteristic
37C32×#95C2211yescharacteristic
38C32×#95C2211yescharacteristic
39C32×#95C2211yescharacteristic
40C32×#95C2211yescharacteristic
41#63658C2211yescharacteristic
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52C3×#400D314yescomplemented
53#4994—34no—
54#4992—34no—
55Dic3×C4⋊C4—34no—
56Dic3×C4⋊C4—34no—
57#4675—34no—
58#4674—34no—
59#4666—34no—
60#4666—34no—
61#4666—34no—
62C3⋊#401—34no—
63#4660—34no—
64#4659—34no—
65#4649—34no—
66#4648—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
82C2×C4×C3⋊D3—22no—
83C2×C4×C3⋊D3—22no—
84C2×C4×C3⋊D3—22no—
85C32×C4⋊C4—22no—
86C32×C4⋊C4—22no—
87#3752—22no—
88#3752—22no—
89#3752—22no—
90#3752—22no—
91#3752—22no—
92#3752—22no—
93C4⋊(C3⋊Dic3)—22no—
94C4⋊(C3⋊Dic3)—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#2401—91noSylow
104C22×C4×D3—34no—
105C2×C3×C4⋊C4C2×D314yes—
106C2×C3×C4⋊C4C2×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×C4⋊Dic3—34no—
114C2×C4⋊Dic3—34no—
115C2×Dic3⋊C4—34no—
116C2×Dic3⋊C4—34no—
117C2×C4×Dic3—34no—
118C2×C4×Dic3—34no—
119C2×C4×Dic3—34no—
120C2×C4×Dic3—34no—
121C2×C4×Dic3—34no—
122C2×C4×Dic3—34no—
123C3×#95C2×D314yes—
124C3×#95C2×D314yes—
125C3×#95C2×D314yes—
126C3×#95C2×D314yes—
127C3×#95C2×D314yes—
128C3⋊#95—34no—
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#4112yes—
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—21no—
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—
189C4×C3⋊D3—44no—
190#401—91no—
191#400—91no—
192#400—91no—
193#400C3⋊D311yescharacteristic, complemented
194#397—91no—
195#397—91no—
196#397—91no—
197#396—91no—
198C4×C4⋊C4—91no—
199C4×C4⋊C4—91no—
200C4×C4⋊C4—91no—
201C4×C22⋊C4—91no—
202C4×C22⋊C4—91no—
203C4×C22⋊C4—91no—
204#376—91no—
205C23×D3—34no—
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×C3×C4C22×D314yes—
213C22×Dic3—34no—
214C22×Dic3—34no—
215C22×Dic3—34no—
216C22×Dic3—34no—
217C22×Dic3—34no—
218C22×Dic3—34no—
219C22×Dic3—34no—
220C2×C4×D3—68no—
221C2×C4×D3—68no—
222C2×C4×D3—68no—
223C3×C4⋊C4—28no—
224C3×C4⋊C4—28no—
225(C2×D3)⋊C4—68no—
226(C2×D3)⋊C4—68no—
227(C2×D3)⋊C4—68no—
228(C2×D3)⋊C4—68no—
229(C2×D3)⋊C4—68no—
230(C2×D3)⋊C4—68no—
231C4⋊Dic3—68no—
232C4⋊Dic3—68no—
233Dic3⋊C4—68no—
234Dic3⋊C4—68no—
235C4×Dic3—68no—
236C4×Dic3—68no—
237C4×Dic3—68no—
238C4×Dic3—68no—
239C4×Dic3—68no—
240C4×Dic3—68no—
241C22×C32C2×#4111yescharacteristic
242C22×C32C2×#4111yescharacteristic
243C22×C32C2×#4111yescharacteristic
244C22×C32C2×#4111yescharacteristic
245C22×C32C2×#4111yescharacteristic
246C22×C32C2×#4111yescharacteristic
247C22×C32C2×#4111yescharacteristic
248C2×C3⋊D3—22no—
249C2×C3⋊D3—22no—
250C2×C3⋊D3—22no—
251C2×C3⋊D3—41no—
252C2×C3⋊D3—41no—
253C2×C3⋊D3—41no—
254C2×C3⋊D3—41no—
255C32×C4—22no—
256C32×C4—22no—
257C32×C4—41no—
258C32×C4—41no—
259C32×C4—41no—
260C32×C4—41no—
261C32×C4—41no—
262C3⋊Dic3—22no—
263C3⋊Dic3—41no—
264C3⋊Dic3—41no—
265C3⋊Dic3—41no—
266C3⋊Dic3—41no—
267C3⋊Dic3—41no—
268C3⋊Dic3#12614yes—
269C23×C4—91no—
270C2×C4⋊C4—91no—
271C2×C4⋊C4—91no—
272C2×C4⋊C4—91no—
273C2×C4⋊C4—91no—
274C2×C4⋊C4C2×C3⋊D311yescharacteristic
275C2×C4⋊C4C2×C3⋊D311yescharacteristic
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—
288#95—91no—
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
303#95C2×C3⋊D311yescharacteristic
304C23×C3C23×D314yes—
305C22×D3—38no—
306C22×D3—64no—
307C22×D3—64no—
308C22×D3—64no—
309C22×D3—64no—
310C22×D3—64no—
311C22×D3—64no—
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—24no—
330C2×C3×C4—24no—
331C2×C3×C4#23718yes—
332C2×C3×C4#23918yes—
333C2×Dic3—38no—
334C2×Dic3—38no—
335C2×Dic3—38no—
336C2×Dic3—38no—
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×Dic3—64no—
354C4×D3—1216no—
355C2×C32C2×#12611yescharacteristic
356C2×C32#52911yescharacteristic
357C2×C32#52911yescharacteristic
358C2×C32#52911yescharacteristic
359C2×C32#52911yescharacteristic
360C2×C32#52911yescharacteristic
361C2×C32#52911yescharacteristic
362C3⋊D3—42no—
363C24—91no—
364C22×C4—91no—
365C22×C4—91no—
366C22×C4—91no—
367C22×C4—91no—
368C22×C4—91no—
369C22×C4—91no—
370C22×C4—91no—
371C22×C4—182no—
372C22×C4—182no—
373C22×C4—182no—
374C22×C4C22×C3⋊D311yescharacteristic
375C22×C4C22×C3⋊D311yescharacteristic
376C22×C4C22×C3⋊D311yescharacteristic
377C22×C4C22×C3⋊D311yescharacteristic
378C22×C4C22×C3⋊D311yescharacteristic
379C22×C4C22×C3⋊D311yescharacteristic
380C22×C4C22×C3⋊D311yescharacteristic
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—182no—
384C4⋊C4—182no—
385C4⋊C4—182no—
386C4⋊C4—182no—
387C22⋊C4—182no—
388C22⋊C4—182no—
389C22⋊C4—182no—
390C22⋊C4—182no—
391C22⋊C4—182no—
392C22⋊C4—182no—
393C42—182no—
394C42—182no—
395C42—182no—
396C42—182no—
397C42—182no—
398C42—182no—
399C22×C3C2×#23714yes—
400C22×C3C2×#23914yes—
401C22×C3D3×#4114yes—
402C22×C3D3×#4114yes—
403C22×C3D3×#4114yes—
404C22×C3D3×#4114yes—
405C22×C3D3×#4114yes—
406C2×D3—68no—
407C2×D3—68no—
408C2×D3—68no—
409C2×D3—124no—
410C2×D3—124no—
411C2×D3—124no—
412C2×D3—124no—
413C3×C4—28no—
414C3×C4—28no—
415C3×C4—44no—
416C3×C4—44no—
417C3×C4—44no—
418C3×C4—44no—
419C3×C4—44no—
420Dic3—316no—
421Dic3—68no—
422Dic3—124no—
423Dic3—124no—
424Dic3—124no—
425Dic3—124no—
426Dic3—124no—
427C32#240111yescharacteristic, complemented, Sylow
428C23—92no—
429C23—181no—
430C23—181no—
431C23—181no—
432C23—181no—
433C23—181no—
434C23—181no—
435C23C23×C3⋊D311yescharacteristic
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—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—92no—
456C2×C4—92no—
457C2×C4—92no—
458C2×C4—92no—
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—181no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—364no—
477C2×C4#383012yes—
478C2×C4#383212yes—
479C2×C3#562414yes—
480C2×C3#564914yes—
481C2×C3#568014yes—
482C2×C3#569114yes—
483C2×C3#569114yes—
484C2×C3D3×#12614yes—
485C2×C3#570614yes—
486D3—128no—
487C22—182no—
488C22—182no—
489C22—182no—
490C22—361no—
491C22—361no—
492C22—361no—
493C22—361no—
494C22C2×#383011yescharacteristic
495C22C2×#383211yescharacteristic
496C22#41×C3⋊D311yescharacteristic
497C22#41×C3⋊D311yescharacteristic
498C22#41×C3⋊D311yescharacteristic
499C22#41×C3⋊D311yescharacteristic
500C22#41×C3⋊D311yescharacteristic
501C4—22no—
502C4—22no—
503C4—41no—
504C4—41no—
505C4—41no—
506C4—41no—
507C4—41no—
508C4—94no—
509C4—182no—
510C4—361no—
511C4—361no—
512C4—361no—
513C4—361no—
514C4—361no—
515C3#7813214yescomplemented
516C2—362no—
517C2#1059609511yescharacteristic
518C2#1059612011yescharacteristic
519C2#1059615111yescharacteristic
520C2#1059616211yescharacteristic
521C2#1059616211yescharacteristic
522C2C3⋊D3×#12611yescharacteristic
523C2#1059617711yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#400C2
prime radicalC23×C3⋊D3C23
hypercenter#400C3⋊D3
hypocenterC32#2401
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C32×#400C2semidirect
4. C4⋊C4×C3⋊Dic3C2semidirect
5. C4⋊C4×C3⋊Dic3C2semidirect
11. #10592361C2semidirect
12. #10592359C2semidirect
13. #10592358C2semidirect
14. #10592348C2semidirect
15. #10592347C2semidirect
52. C3×#400D3semidirect
193. #400C3⋊D3semidirect
427. C32#2401semidirect
515. C3#78132semidirect

Maximal subgroups

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

subgroupindex
C32×#4002
#105926932
#105926912
C4⋊C4×C3⋊Dic32
#105923742
#105923732
#105923652
#105923612
#105923592
#105923582
#105923482
#105923472
#781323