Finite Group Databasebeta

← #11808807

Subgroups — #11808807

Order 1152.

1285 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×C4×#634C211yesmaximal, characteristic, complemented
2C2×C4×#625C211yesmaximal, characteristic
3C3×C4×(C2×D3)⋊C4C212yesmaximal, complemented
4#10591394C211yesmaximal, characteristic
5#10591388C211yesmaximal, characteristic
6#10591322C212yesmaximal, complemented
7#10591298C212yesmaximal, complemented
8C4×(C2×D3)⋊Dic3C212yesmaximal, complemented
9#10591222C211yesmaximal, characteristic, complemented
10#10591218C211yesmaximal, characteristic, complemented
11#10591217C211yesmaximal, characteristic, complemented
12#73481—32nomaximal
13C22×#634C2211yescharacteristic
14C22×C3×C4×D3C2212yes—
15C22×#625C2211yescharacteristic
16C2×C32×C42C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×#3750C2211yescharacteristic
19C2×#3750C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C4×#634—24no—
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×C4×Dic3C2212yes—
26C2×#3724C2211yescharacteristic
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×(C2×D3)⋊Dic3C2212yes—
30C4×#625—24no—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33#63579C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2211yescharacteristic
37#63579C2211yescharacteristic
38C2×C4×#67—32no—
39C2×C4×Dic6—32no—
40C2×C4×Dic6—61no—
41C3×C4×C22⋊C4—32no—
42C4×#217—32no—
43#4961—32no—
44#4959—32no—
45#4952—32no—
46#4947—32no—
47C4×(C2×D3)⋊C4—32no—
48C4×(C2×D3)⋊C4D312yescomplemented
49#4932—32no—
50#4675—32no—
51#4673—32no—
52#4660—32no—
53#4658—32no—
54C23×C3×D3C2312yes—
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3⋊Dic3C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3⋊Dic3C2311yescharacteristic
62C2×#634—22no—
63C2×#634—22no—
64C2×#634—22no—
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C2×C3×C4×D3—24no—
69C2×C3×C4×D3—24no—
70C2×C3×C4×D3—24no—
71C2×#625—24no—
72C2×#625—22no—
73C32×C42—22no—
74C4⋊(C3⋊Dic3)—22no—
75#3750—22no—
76#3750—22no—
77C4×C3⋊Dic3—22no—
78C4×C3⋊Dic3D414yes—
79C3×(C2×D3)⋊C4—24no—
80C3×(C2×D3)⋊C4—24no—
81C3×C4×Dic3—24no—
82#3724—22no—
83(C2×D3)⋊Dic3—24no—
84(C2×D3)⋊Dic3—24no—
85(C2×D3)⋊Dic3—24no—
86#2398—91noSylow
87C23×C3×C4—32no—
88C22×#67—32no—
89C22×C4×D3C2×D312yes—
90C22×Dic6—32no—
91C22×Dic6—61no—
92C2×C3×C22⋊C4—32no—
93C2×C3×C22⋊C4—32no—
94C2×C3×C42—21no—
95C2×C3×C42—32no—
96C2×C3×C42C2×D312yes—
97C2×#217—32no—
98C2×#217—32no—
99C2×#217—32no—
100C4×#67—68no—
101C2×(C2×D3)⋊C4—32no—
102C2×(C2×D3)⋊C4—32no—
103C2×(C2×D3)⋊C4—32no—
104C2×(C2×D3)⋊C4C2×D312yes—
105C2×(C2×D3)⋊C4C2×D312yes—
106C2×C4⋊Dic3—32no—
107C2×C4⋊Dic3—61no—
108C2×Dic3⋊C4—32no—
109C2×Dic3⋊C4—32no—
110C2×Dic3⋊C4—32no—
111C2×Dic3⋊C4—61no—
112C2×Dic3⋊C4—61no—
113C2×C4×Dic3—32no—
114C2×C4×Dic3—32no—
115C2×C4×Dic3—61no—
116C2×C4×Dic3—61no—
117C2×C4×Dic3C2×D312yes—
118C4×Dic6—68no—
119C4×Dic6—68no—
120C3×#95—32no—
121C3×#95—32no—
122C3⋊#95—32no—
123C3⋊#95—32no—
124C3⋊#95—32no—
125C3⋊#95—32no—
126C3⋊#95—32no—
127C3⋊#95—32no—
128C3⋊#95—32no—
129C3⋊#95—32no—
130C3⋊#95C2×D312yes—
131C3⋊#95C2×D312yes—
132C23×C32C2411yescharacteristic
133C22×C3×D3—22no—
134C22×C3×D3—22no—
135C22×C3×D3—22no—
136C22×C3×D3—22no—
137C22×C3×D3—22no—
138C22×C3×D3—22no—
139C22×C3×D3#4114yes—
140C2×C32×C4—21no—
141C2×C32×C4—21no—
142C2×C32×C4—21no—
143C2×C32×C4—22no—
144C2×C32×C4C2×D412yes—
145C2×C32×C4#4112yes—
146C2×C32×C4#4114yes—
147C2×C3⋊Dic3—21no—
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3—21no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3C2×D412yes—
155C2×C3⋊Dic3C2×D412yes—
156C2×C3⋊Dic3#4112yes—
157#634—28no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C3×C4×D3—48no—
168#625—28no—
169C2×C4×Q8—91no—
170C2×C4×D4—91no—
171#400—91no—
172#400—91no—
173#397—92no—
174#394—91no—
175#394—91no—
176#393—92no—
177C4×C22⋊C4—32no—
178C4×C22⋊C4—92no—
179#376—91no—
180C24×C3—32no—
181C23×D3C22×D312yes—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—32no—
186C22×C3×C4—32no—
187C22×C3×C4—32no—
188C22×C3×C4—64no—
189C22×C3×C4—64no—
190C22×C3×C4—64no—
191C22×C3×C4C22×D312yes—
192C22×C3×C4C22×D312yes—
193C22×C3×C4C22×D312yes—
194C2×#67—64no—
195C2×#67—64no—
196C2×#67—64no—
197C22×Dic3—32no—
198C22×Dic3—32no—
199C22×Dic3—32no—
200C22×Dic3—32no—
201C22×Dic3—61no—
202C22×Dic3—61no—
203C22×Dic3—61no—
204C22×Dic3—61no—
205C22×Dic3C22×D312yes—
206C22×Dic3C22×D312yes—
207C22×Dic3C22×D312yes—
208C2×C4×D3—24no—
209C2×C4×D3—24no—
210C2×C4×D3—24no—
211C2×Dic6—64no—
212C2×Dic6—64no—
213C2×Dic6—64no—
214C2×Dic6—64no—
215C2×Dic6—64no—
216C2×Dic6—64no—
217C3×C22⋊C4—64no—
218C3×C22⋊C4—64no—
219C3×C42—24no—
220C3×C42—24no—
221C3×C42—64no—
222#217—64no—
223#217—64no—
224#217—64no—
225(C2×D3)⋊C4—24no—
226(C2×D3)⋊C4—24no—
227(C2×D3)⋊C4—64no—
228(C2×D3)⋊C4—64no—
229(C2×D3)⋊C4—64no—
230C4⋊Dic3—64no—
231C4⋊Dic3—64no—
232Dic3⋊C4—64no—
233Dic3⋊C4—64no—
234Dic3⋊C4—64no—
235Dic3⋊C4—64no—
236Dic3⋊C4—64no—
237C4×Dic3—24no—
238C4×Dic3—38no—
239C4×Dic3—64no—
240C4×Dic3—64no—
241C4×Dic3—64no—
242C22×C32C22×D411yescharacteristic
243C22×C32C2×#4111yescharacteristic
244C22×C32C2×#4112yes—
245C22×C32C2×#4112yes—
246C22×C32C2×#4111yescharacteristic
247C2×C3×D3—24no—
248C2×C3×D3—24no—
249C2×C3×D3—24no—
250C2×C3×D3—42no—
251C2×C3×D3—42no—
252C2×C3×D3—42no—
253C2×C3×D3—42no—
254C32×C4—22no—
255C32×C4—41no—
256C32×C4#12414yes—
257C3⋊Dic3—22no—
258C3⋊Dic3—22no—
259C3⋊Dic3—22no—
260C3⋊Dic3—41no—
261C3×Dic3—42no—
262C3×Dic3—42no—
263C3×Dic3—42no—
264C22×Q8—91no—
265C22×D4—91no—
266C23×C4—32no—
267C4×Q8—184no—
268C4×D4—184no—
269C2×C4⋊C4—91no—
270C2×C4⋊C4—91no—
271C2×C4⋊C4—91no—
272C2×C4⋊C4—91no—
273C2×C22⋊C4—32no—
274C2×C22⋊C4—32no—
275C2×C22⋊C4—92no—
276C2×C22⋊C4—92no—
277C2×C22⋊C4—92no—
278C2×C42—32no—
279C2×C42—91no—
280C2×C42—91no—
281C2×C42D3211yescharacteristic
282#95—32no—
283#95—32no—
284#95—92no—
285#95—91no—
286#95—91no—
287#95—92no—
288#95—92no—
289C23×C3—21no—
290C23×C3—34no—
291C23×C3—62no—
292C23×C3—62no—
293C23×C3—62no—
294C23×C3—62no—
295C23×C3—62no—
296C23×C3—62no—
297C23×C3C23×D312yes—
298C22×D3—22no—
299C22×D3—22no—
300C22×D3—22no—
301C22×D3—22no—
302C22×D3—22no—
303C22×D3—22no—
304C22×D3#23514yes—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—24no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—42no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—128no—
327C2×C3×C4#23514yes—
328C2×C3×C4#23514yes—
329C2×C3×C4D3×D414yes—
330C2×C3×C4#23714yes—
331#67—616no—
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—34no—
342C2×Dic3—34no—
343C2×Dic3—34no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—122no—
362C2×Dic3—122no—
363C4×D3—48no—
364Dic6—616no—
365Dic6—616no—
366C2×C32#52511yescharacteristic
367C2×C32#52511yescharacteristic
368C2×C32C2×#12411yescharacteristic
369C2×C32#52912yes—
370C2×C32#52912yes—
371C3×D3—44no—
372C24—32no—
373C2×Q8—182no—
374C2×Q8—182no—
375C2×Q8—182no—
376C2×D4—182no—
377C2×D4—184no—
378C22×C4—32no—
379C22×C4—32no—
380C22×C4—32no—
381C22×C4—64no—
382C22×C4—64no—
383C22×C4—64no—
384C22×C4—91no—
385C22×C4—91no—
386C22×C4—91no—
387C22×C4—91no—
388C22×C4C2×D3211yescharacteristic
389C22×C4C2×D3211yescharacteristic
390C22×C4C2×D3211yescharacteristic
391C4⋊C4—182no—
392C4⋊C4—182no—
393C4⋊C4—182no—
394C4⋊C4—182no—
395C22⋊C4—64no—
396C22⋊C4—64no—
397C22⋊C4—184no—
398C22⋊C4—184no—
399C22⋊C4—184no—
400C42—22no—
401C42—64no—
402C42—94no—
403C42—182no—
404C22×C3—22no—
405C22×C3—21no—
406C22×C3—22no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—64no—
410C22×C3—64no—
411C22×C3—64no—
412C22×C3—122no—
413C22×C3—122no—
414C22×C3—122no—
415C22×C3—122no—
416C22×C3C2×#23512yes—
417C22×C3C2×#23512yes—
418C22×C3C2×#23512yes—
419C22×C3C2×D3×D412yes—
420C22×C3C2×#23712yes—
421C22×C3D3×#4112yes—
422C22×C3D3×#4112yes—
423C2×D3—24no—
424C2×D3—24no—
425C2×D3—24no—
426C2×D3—42no—
427C2×D3—42no—
428C2×D3—42no—
429C2×D3—42no—
430C3×C4—24no—
431C3×C4—24no—
432C3×C4—24no—
433C3×C4—42no—
434C3×C4—42no—
435C3×C4—122no—
436C3×C4—122no—
437C3×C4—122no—
438C3×C4#88518yes—
439Dic3—42no—
440Dic3—42no—
441Dic3—42no—
442Dic3—64no—
443Dic3—64no—
444Dic3—64no—
445Dic3—64no—
446Dic3—64no—
447Dic3—122no—
448Dic3—122no—
449Dic3—122no—
450C32#239811yescharacteristic, complemented, Sylow
451C23—34no—
452C23—62no—
453C23—62no—
454C23—62no—
455C23—62no—
456C23—62no—
457C23—62no—
458C23C22×D3211yescharacteristic
459Q8—188no—
460D4—188no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—21no—
465C2×C4—62no—
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—92no—
477C2×C4—128no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—182no—
481C2×C4—181no—
482C2×C4—181no—
483C2×C4—182no—
484C2×C4—181no—
485C2×C4#379514yes—
486C2×C4#379812yes—
487C2×C4#381112yes—
488C2×C3—21no—
489C2×C3—22no—
490C2×C3—22no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—124no—
494C2×C3#547912yes—
495C2×C3C2×#88512yes—
496C2×C3#552812yes—
497C2×C3#553812yes—
498C2×C3#554712yes—
499C2×C3#554712yes—
500C2×C3#555712yes—
501D3—44no—
502C22—64no—
503C22—64no—
504C22—64no—
505C22—122no—
506C22—122no—
507C22—122no—
508C22—122no—
509C22C2×#379512yes—
510C22C2×#379811yescharacteristic
511C22D3×#23512yes—
512C22#6430611yescharacteristic
513C22C2×#381111yescharacteristic
514C4—22no—
515C4—41no—
516C4—122no—
517C4—122no—
518C4—122no—
519C4—182no—
520C4—182no—
521C4—182no—
522C4—361no—
523C4#6391314yes—
524C3—21no—
525C3#7348112yescomplemented
526C2—124no—
527C2#1059391012yes—
528C2#1059397412yes—
529C2C2×#6391311yescharacteristic
530C2#1059501611yescharacteristic
531C2#1059507611yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×C42C22
prime radicalC22×#625C22
hypercenterC2×C42D32
hypocenterC32#2398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×#634C2semidirect
3. C3×C4×(C2×D3)⋊C4C2semidirect
6. #10591322C2semidirect
7. #10591298C2semidirect
8. C4×(C2×D3)⋊Dic3C2semidirect
9. #10591222C2semidirect
10. #10591218C2semidirect
11. #10591217C2semidirect
48. C4×(C2×D3)⋊C4D3semidirect
450. C32#2398semidirect
525. C3#73481semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C2×C4×#6252
C3×C4×(C2×D3)⋊C42
#105913942
#105913882
#105913222
#105912982
C4×(C2×D3)⋊Dic32
#105912222
#105912182
#105912172
#734813