Finite Group Databasebeta

← C32×#2493 #11769542

Subgroups — C32×#2493 #11769542

Order 1152.

1320 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#401C211yesmaximal, characteristic, complemented
2C32×#400C211yesmaximal, characteristic, complemented
3C32×#400C211yesmaximal, characteristic, complemented
4C32×#400C211yesmaximal, characteristic, complemented
5C32×#387C211yesmaximal, characteristic, complemented
6C32×#387C211yesmaximal, characteristic, complemented
7C32×#387C211yesmaximal, characteristic, complemented
8C32×#385C211yesmaximal, characteristic
9C32×#385C211yesmaximal, characteristic
10C32×#383C211yesmaximal, characteristic, complemented
11C32×#381C211yesmaximal, characteristic
12C32×#381C211yesmaximal, characteristic
13C32×#380C211yesmaximal, characteristic
14C32×C4×C22⋊C4C211yesmaximal, characteristic
15C2×C32×#95C211yesmaximal, characteristic
16C3×#2493C314yesmaximal, direct product factor
17C23×C32×C4C2211yescharacteristic
18C23×C32×C4C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×C32×C42C2211yescharacteristic
31C2×C32×C42C2211yescharacteristic
32C32×#95C2211yescharacteristic
33C32×#95C2211yescharacteristic
34C32×#95C2211yescharacteristic
35C32×#95C2211yescharacteristic
36C32×#95C2211yescharacteristic
37C32×#95C2211yescharacteristic
38C32×#95C2211yescharacteristic
39C32×#95C2211yescharacteristic
40C32×#95C2211yescharacteristic
41C32×#95C2211yescharacteristic
42C32×#95C2211yescharacteristic
43C32×#95C2211yescharacteristic
44C32×#95C2211yescharacteristic
45C32×#95C2211yescharacteristic
46C32×#95C2211yescharacteristic
47C32×#95C2211yescharacteristic
48C32×#95C2211yescharacteristic
49C32×#95C2211yescharacteristic
50C32×#95C2211yescharacteristic
51C32×#95C2211yescharacteristic
52C3×#401C2×C314yescomplemented
53C3×#400C2×C314yescomplemented
54C3×#400C2×C314yescomplemented
55C3×#400C2×C314yescomplemented
56C3×#387C2×C314yescomplemented
57C3×#387C2×C314yescomplemented
58C3×#387C2×C314yescomplemented
59C3×#385C2×C314yes—
60C3×#385C2×C314yes—
61C3×#383C2×C314yescomplemented
62C3×#381C2×C314yes—
63C3×#381C2×C314yes—
64C3×#380C2×C314yes—
65C3×C4×C22⋊C4C2×C314yes—
66C2×C3×#95C2×C314yes—
67C24×C32C2311yescharacteristic
68C22×C32×C4—22no—
69C22×C32×C4—22no—
70C22×C32×C4—22no—
71C22×C32×C4—22no—
72C22×C32×C4—22no—
73C22×C32×C4—22no—
74C22×C32×C4—22no—
75C22×C32×C4—41no—
76C22×C32×C4—41no—
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2311yescharacteristic
82C22×C32×C4C2311yescharacteristic
83C22×C32×C4C2311yescharacteristic
84C22×C32×C4C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C32×C4⋊C4—22no—
92C32×C4⋊C4—22no—
93C32×C4⋊C4—22no—
94C32×C4⋊C4—41no—
95C32×C4⋊C4—41no—
96C32×C4⋊C4—41no—
97C32×C22⋊C4—22no—
98C32×C22⋊C4—22no—
99C32×C22⋊C4—22no—
100C32×C22⋊C4—22no—
101C32×C42—22no—
102C32×C42—41no—
103#2493C3211yescharacteristic, direct product factor, Sylow
104C23×C3×C4C22×C314yes—
105C23×C3×C4C22×C314yes—
106C23×C3×C4C22×C314yes—
107C2×C3×C4⋊C4C22×C314yes—
108C2×C3×C4⋊C4C22×C314yes—
109C2×C3×C4⋊C4C22×C314yes—
110C2×C3×C4⋊C4C22×C314yes—
111C2×C3×C4⋊C4C22×C314yes—
112C2×C3×C4⋊C4C22×C314yes—
113C2×C3×C22⋊C4C22×C314yes—
114C2×C3×C22⋊C4C22×C314yes—
115C2×C3×C22⋊C4C22×C314yes—
116C2×C3×C22⋊C4C22×C314yes—
117C2×C3×C42C22×C314yes—
118C2×C3×C42C22×C314yes—
119C3×#95C22×C314yes—
120C3×#95C22×C314yes—
121C3×#95C22×C314yes—
122C3×#95C22×C314yes—
123C3×#95C22×C314yes—
124C3×#95C22×C314yes—
125C3×#95C22×C314yes—
126C3×#95C22×C314yes—
127C3×#95C22×C314yes—
128C3×#95C22×C314yes—
129C3×#95C22×C314yes—
130C3×#95C22×C314yes—
131C3×#95C22×C314yes—
132C3×#95C22×C314yes—
133C3×#95C22×C314yes—
134C3×#95C22×C314yes—
135C3×#95C22×C314yes—
136C3×#95C22×C314yes—
137C3×#95C22×C314yes—
138C3×#95C22×C314yes—
139C23×C32—21no—
140C23×C32—21no—
141C23×C32—21no—
142C23×C32—21no—
143C23×C32#4112yes—
144C23×C32#4112yes—
145C23×C32#4112yes—
146C23×C32C2411yescharacteristic
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—21no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—44no—
188C2×C32×C4—44no—
189C2×C32×C4—44no—
190C2×C32×C4#4112yes—
191C2×C32×C4#4112yes—
192#401C2×C3211yescharacteristic, complemented
193#400C2×C3211yescharacteristic, complemented
194#400C2×C3211yescharacteristic, complemented
195#400C2×C3211yescharacteristic, complemented
196#387C2×C3211yescharacteristic, complemented
197#387C2×C3211yescharacteristic, complemented
198#387C2×C3211yescharacteristic, complemented
199#385C2×C3211yescharacteristic
200#385C2×C3211yescharacteristic
201#383C2×C3211yescharacteristic, complemented
202#381C2×C3211yescharacteristic
203#381C2×C3211yescharacteristic
204#380C2×C3211yescharacteristic
205C4×C22⋊C4C2×C3211yescharacteristic
206C2×#95C2×C3211yescharacteristic
207C24×C3C23×C314yes—
208C22×C3×C4—28no—
209C22×C3×C4—28no—
210C22×C3×C4—28no—
211C22×C3×C4—28no—
212C22×C3×C4—28no—
213C22×C3×C4—28no—
214C22×C3×C4—28no—
215C22×C3×C4—44no—
216C22×C3×C4—44no—
217C22×C3×C4C23×C314yes—
218C22×C3×C4C23×C314yes—
219C22×C3×C4C23×C314yes—
220C22×C3×C4C23×C314yes—
221C22×C3×C4C23×C314yes—
222C22×C3×C4C23×C314yes—
223C22×C3×C4C23×C314yes—
224C22×C3×C4C23×C314yes—
225C22×C3×C4C23×C314yes—
226C22×C3×C4C23×C314yes—
227C22×C3×C4C23×C314yes—
228C22×C3×C4C23×C314yes—
229C22×C3×C4C23×C314yes—
230C22×C3×C4C23×C314yes—
231C3×C4⋊C4—28no—
232C3×C4⋊C4—28no—
233C3×C4⋊C4—28no—
234C3×C4⋊C4—44no—
235C3×C4⋊C4—44no—
236C3×C4⋊C4—44no—
237C3×C22⋊C4—28no—
238C3×C22⋊C4—28no—
239C3×C22⋊C4—28no—
240C3×C22⋊C4—28no—
241C3×C42—28no—
242C3×C42—44no—
243C22×C32—22no—
244C22×C32—22no—
245C22×C32—22no—
246C22×C32—22no—
247C22×C32—22no—
248C22×C32—22no—
249C22×C32#12614yes—
250C22×C32C2×#4111yescharacteristic
251C22×C32C2×#4111yescharacteristic
252C22×C32C2×#4111yescharacteristic
253C22×C32C2×#4111yescharacteristic
254C22×C32C2×#4111yescharacteristic
255C22×C32H(5,𝔽2)11yescharacteristic
256C22×C322−1+411yescharacteristic
257C32×C4—22no—
258C32×C4—22no—
259C32×C4—41no—
260C32×C4—41no—
261C32×C4—41no—
262C32×C4—41no—
263C32×C4—41no—
264C32×C4—41no—
265C32×C4—41no—
266C32×C4—41no—
267C32×C4—41no—
268C32×C4—41no—
269C32×C4—41no—
270C32×C4—41no—
271C23×C4C22×C3211yescharacteristic
272C23×C4C22×C3211yescharacteristic
273C23×C4C22×C3211yescharacteristic
274C2×C4⋊C4C22×C3211yescharacteristic
275C2×C4⋊C4C22×C3211yescharacteristic
276C2×C4⋊C4C22×C3211yescharacteristic
277C2×C4⋊C4C22×C3211yescharacteristic
278C2×C4⋊C4C22×C3211yescharacteristic
279C2×C4⋊C4C22×C3211yescharacteristic
280C2×C22⋊C4C22×C3211yescharacteristic
281C2×C22⋊C4C22×C3211yescharacteristic
282C2×C22⋊C4C22×C3211yescharacteristic
283C2×C22⋊C4C22×C3211yescharacteristic
284C2×C42C22×C3211yescharacteristic
285C2×C42C22×C3211yescharacteristic
286#95C22×C3211yescharacteristic
287#95C22×C3211yescharacteristic
288#95C22×C3211yescharacteristic
289#95C22×C3211yescharacteristic
290#95C22×C3211yescharacteristic
291#95C22×C3211yescharacteristic
292#95C22×C3211yescharacteristic
293#95C22×C3211yescharacteristic
294#95C22×C3211yescharacteristic
295#95C22×C3211yescharacteristic
296#95C22×C3211yescharacteristic
297#95C22×C3211yescharacteristic
298#95C22×C3211yescharacteristic
299#95C22×C3211yescharacteristic
300#95C22×C3211yescharacteristic
301#95C22×C3211yescharacteristic
302#95C22×C3211yescharacteristic
303#95C22×C3211yescharacteristic
304#95C22×C3211yescharacteristic
305#95C22×C3211yescharacteristic
306C23×C3—24no—
307C23×C3—24no—
308C23×C3—24no—
309C23×C3—24no—
310C23×C3C3×#4118yes—
311C23×C3C3×#4118yes—
312C23×C3C3×#4118yes—
313C23×C3C24×C314yes—
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—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×C4—24no—
340C2×C3×C4—24no—
341C2×C3×C4—24no—
342C2×C3×C4—24no—
343C2×C3×C4—24no—
344C2×C3×C4—24no—
345C2×C3×C4—24no—
346C2×C3×C4—24no—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—24no—
353C2×C3×C4—24no—
354C2×C3×C4—416no—
355C2×C3×C4—416no—
356C2×C3×C4—416no—
357C2×C3×C4C3×#4118yes—
358C2×C3×C4C3×#4118yes—
359C2×C32—24no—
360C2×C32C2×#12611yescharacteristic
361C2×C32#52911yescharacteristic
362C2×C32#53911yescharacteristic
363C2×C32#55111yescharacteristic
364C2×C32#55111yescharacteristic
365C2×C32#55211yescharacteristic
366C2×C32#55211yescharacteristic
367C24C23×C3211yescharacteristic
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4C23×C3211yescharacteristic
378C22×C4C23×C3211yescharacteristic
379C22×C4C23×C3211yescharacteristic
380C22×C4C23×C3211yescharacteristic
381C22×C4C23×C3211yescharacteristic
382C22×C4C23×C3211yescharacteristic
383C22×C4C23×C3211yescharacteristic
384C22×C4C23×C3211yescharacteristic
385C22×C4C23×C3211yescharacteristic
386C22×C4C23×C3211yescharacteristic
387C22×C4C23×C3211yescharacteristic
388C22×C4C23×C3211yescharacteristic
389C22×C4C23×C3211yescharacteristic
390C22×C4C23×C3211yescharacteristic
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C22⋊C4—22no—
401C42—22no—
402C42—41no—
403C22×C3—28no—
404C22×C3—28no—
405C22×C3—28no—
406C22×C3—28no—
407C22×C3—28no—
408C22×C3—28no—
409C22×C3C3×#126116yes—
410C22×C3C2×C3×#4114yes—
411C22×C3C2×C3×#4114yes—
412C22×C3C2×C3×#4114yes—
413C22×C3C2×C3×#4114yes—
414C22×C3C2×C3×#4114yes—
415C22×C3C3×H(5,𝔽2)14yes—
416C22×C3C3×2−1+414yes—
417C3×C4—28no—
418C3×C4—28no—
419C3×C4—44no—
420C3×C4—44no—
421C3×C4—44no—
422C3×C4—44no—
423C3×C4—44no—
424C3×C4—44no—
425C3×C4—44no—
426C3×C4—44no—
427C3×C4—44no—
428C3×C4—44no—
429C3×C4—44no—
430C3×C4—44no—
431C32#249311yescharacteristic, direct product factor, Sylow
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23C32×#4112yes—
437C23C32×#4112yes—
438C23C32×#4112yes—
439C23C24×C3211yescharacteristic
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—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—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—44no—
481C2×C4—44no—
482C2×C4—44no—
483C2×C4C32×#4112yes—
484C2×C4C32×#4112yes—
485C2×C3—216no—
486C2×C3C2×C3×#12614yes—
487C2×C3C3×#52914yes—
488C2×C3C3×#53914yes—
489C2×C3C3×#55114yes—
490C2×C3C3×#55114yes—
491C2×C3C3×#55214yes—
492C2×C3C3×#55214yes—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22C32×#12614yes—
500C22C2×C32×#4111yescharacteristic
501C22C2×C32×#4111yescharacteristic
502C22C2×C32×#4111yescharacteristic
503C22C2×C32×#4111yescharacteristic
504C22C2×C32×#4111yescharacteristic
505C22C32×H(5,𝔽2)11yescharacteristic
506C22C32×2−1+411yescharacteristic
507C4—22no—
508C4—22no—
509C4—41no—
510C4—41no—
511C4—41no—
512C4—41no—
513C4—41no—
514C4—41no—
515C4—41no—
516C4—41no—
517C4—41no—
518C4—41no—
519C4—41no—
520C4—41no—
521C3C3×#249314yesdirect product factor
522C2—24no—
523C2C2×C32×#12611yescharacteristic
524C2C32×#52911yescharacteristic
525C2C32×#53911yescharacteristic
526C2C32×#55111yescharacteristic
527C2C32×#55111yescharacteristic
528C2C32×#55211yescharacteristic
529C2C32×#55211yescharacteristic
subgroupG/H
center, socleC23×C32C24
commutator, Frattini, cosocleC23C24×C32
prime radicalC24×C32C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C32 ◁ G

Complements

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

NH ≅ G/Ntype
1. C32×#401C2semidirect
2. C32×#400C2semidirect
3. C32×#400C2semidirect
4. C32×#400C2semidirect
5. C32×#387C2semidirect
6. C32×#387C2semidirect
7. C32×#387C2semidirect
10. C32×#383C2semidirect
16. C3×#2493C3direct (N × H)
52. C3×#401C2×C3semidirect
53. C3×#400C2×C3semidirect
54. C3×#400C2×C3semidirect
55. C3×#400C2×C3semidirect
56. C3×#387C2×C3semidirect
57. C3×#387C2×C3semidirect
58. C3×#387C2×C3semidirect
61. C3×#383C2×C3semidirect
103. #2493C32direct (N × H)
192. #401C2×C32semidirect
193. #400C2×C32semidirect
194. #400C2×C32semidirect
195. #400C2×C32semidirect
196. #387C2×C32semidirect
197. #387C2×C32semidirect
198. #387C2×C32semidirect
201. #383C2×C32semidirect
431. C32#2493direct (N × H)
521. C3C3×#2493direct (N × H)

Maximal subgroups

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

subgroupindex
C32×#4012
C32×#4002
C32×#3872
C32×#3852
C32×#3832
C32×#3812
C32×#3802
C32×C4×C22⋊C42
C2×C32×#952
C3×#24933