Finite Group Databasebeta

← C32×#2649 #11769698

Subgroups — C32×#2649 #11769698

Order 1152.

1302 conjugacy classes of subgroups.

The subgroup lattice has 579 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#400C211yesmaximal, characteristic, complemented
2C32×#400C211yesmaximal, characteristic, complemented
3C32×#399C211yesmaximal, characteristic, complemented
4C32×#397C211yesmaximal, characteristic, complemented
5C32×#397C211yesmaximal, characteristic, complemented
6C32×#396C211yesmaximal, characteristic, complemented
7C32×#394C211yesmaximal, characteristic
8C32×#394C211yesmaximal, characteristic
9C32×#389C211yesmaximal, characteristic, complemented
10C32×#388C211yesmaximal, characteristic, complemented
11C32×#388C211yesmaximal, characteristic, complemented
12C32×#387C211yesmaximal, characteristic, complemented
13C32×#386C211yesmaximal, characteristic
14C32×#385C211yesmaximal, characteristic, complemented
15C32×C4×C22⋊C4C211yesmaximal, characteristic, complemented
16C3×#2649C314yesmaximal, direct product factor
17C22×C32×D4C2211yescharacteristic
18C23×C32×C4C2211yescharacteristic
19C2×C32×C4⋊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×C4⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×C32×C22⋊C4C2211yescharacteristic
31C2×C32×C22⋊C4C2211yescharacteristic
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×C32×C22⋊C4C2211yescharacteristic
34C2×C32×C22⋊C4C2211yescharacteristic
35C2×C32×C22⋊C4C2211yescharacteristic
36C2×C32×C22⋊C4C2211yescharacteristic
37C2×C32×C22⋊C4C2211yescharacteristic
38C2×C32×C42C2211yescharacteristic
39C2×C32×C42C2211yescharacteristic
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×#400C2×C314yescomplemented
53C3×#400C2×C314yescomplemented
54C3×#399C2×C314yescomplemented
55C3×#397C2×C314yescomplemented
56C3×#397C2×C314yescomplemented
57C3×#396C2×C314yescomplemented
58C3×#394C2×C314yes—
59C3×#394C2×C314yes—
60C3×#389C2×C314yescomplemented
61C3×#388C2×C314yescomplemented
62C3×#388C2×C314yescomplemented
63C3×#387C2×C314yescomplemented
64C3×#386C2×C314yes—
65C3×#385C2×C314yescomplemented
66C3×C4×C22⋊C4C2×C314yescomplemented
67C24×C32C2311yescharacteristic
68C24×C32C2311yescharacteristic
69C2×C32×D4—22no—
70C2×C32×D4—41no—
71C2×C32×D4—41no—
72C22×C32×C4—22no—
73C22×C32×C4—41no—
74C22×C32×C4—41no—
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
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
88C32×C4⋊C4—22no—
89C32×C4⋊C4—22no—
90C32×C4⋊C4—41no—
91C32×C4⋊C4—41no—
92C32×C4⋊C4—41no—
93C32×C4⋊C4—41no—
94C32×C4⋊C4—41no—
95C32×C4⋊C4—41no—
96C32×C22⋊C4—22no—
97C32×C22⋊C4—22no—
98C32×C22⋊C4—22no—
99C32×C22⋊C4—22no—
100C32×C22⋊C4—22no—
101C32×C22⋊C4—41no—
102C32×C22⋊C4—41no—
103C32×C22⋊C4—41no—
104C32×C22⋊C4—41no—
105C32×C22⋊C4—41no—
106C32×C22⋊C4—41no—
107C32×C42—41no—
108C32×C42—41no—
109#2649C3211yescharacteristic, direct product factor, Sylow
110C22×C3×D4C22×C314yes—
111C23×C3×C4C22×C314yes—
112C2×C3×C4⋊C4C22×C314yes—
113C2×C3×C4⋊C4C22×C314yes—
114C2×C3×C4⋊C4C22×C314yes—
115C2×C3×C4⋊C4C22×C314yes—
116C2×C3×C4⋊C4C22×C314yes—
117C2×C3×C4⋊C4C22×C314yes—
118C2×C3×C4⋊C4C22×C314yes—
119C2×C3×C4⋊C4C22×C314yes—
120C2×C3×C22⋊C4C22×C314yes—
121C2×C3×C22⋊C4C22×C314yes—
122C2×C3×C22⋊C4C22×C314yes—
123C2×C3×C22⋊C4C22×C314yes—
124C2×C3×C22⋊C4C22×C314yes—
125C2×C3×C22⋊C4C22×C314yes—
126C2×C3×C22⋊C4C22×C314yes—
127C2×C3×C22⋊C4C22×C314yes—
128C2×C3×C22⋊C4C22×C314yes—
129C2×C3×C22⋊C4C22×C314yes—
130C2×C3×C22⋊C4C22×C314yes—
131C2×C3×C42C22×C314yes—
132C2×C3×C42C22×C314yes—
133C3×#95C22×C314yes—
134C3×#95C22×C314yes—
135C3×#95C22×C314yes—
136C3×#95C22×C314yes—
137C3×#95C22×C314yes—
138C3×#95C22×C314yes—
139C3×#95C22×C314yes—
140C3×#95C22×C314yes—
141C3×#95C22×C314yes—
142C3×#95C22×C314yes—
143C3×#95C22×C314yes—
144C3×#95C22×C314yes—
145C23×C32—21no—
146C23×C32—21no—
147C23×C32—21no—
148C23×C32—21no—
149C23×C32—21no—
150C23×C32—21no—
151C23×C32—21no—
152C23×C32—21no—
153C23×C32—21no—
154C23×C32—21no—
155C23×C32—21no—
156C23×C32—21no—
157C23×C32—21no—
158C23×C32#4112yes—
159C23×C32C2411yescharacteristic
160C32×D4—44no—
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—21no—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4—21no—
191C2×C32×C4—21no—
192C2×C32×C4—21no—
193C2×C32×C4—21no—
194C2×C32×C4—21no—
195C2×C32×C4—21no—
196C2×C32×C4—21no—
197C2×C32×C4—21no—
198C2×C32×C4—44no—
199C2×C32×C4#4112yes—
200C2×C32×C4#4112yes—
201#400C2×C3211yescharacteristic, complemented
202#400C2×C3211yescharacteristic, complemented
203#399C2×C3211yescharacteristic, complemented
204#397C2×C3211yescharacteristic, complemented
205#397C2×C3211yescharacteristic, complemented
206#396C2×C3211yescharacteristic, complemented
207#394C2×C3211yescharacteristic
208#394C2×C3211yescharacteristic
209#389C2×C3211yescharacteristic, complemented
210#388C2×C3211yescharacteristic, complemented
211#388C2×C3211yescharacteristic, complemented
212#387C2×C3211yescharacteristic, complemented
213#386C2×C3211yescharacteristic
214#385C2×C3211yescharacteristic, complemented
215C4×C22⋊C4C2×C3211yescharacteristic, complemented
216C24×C3C23×C314yes—
217C24×C3C23×C314yes—
218C2×C3×D4—28no—
219C2×C3×D4—44no—
220C2×C3×D4—44no—
221C22×C3×C4—28no—
222C22×C3×C4—44no—
223C22×C3×C4—44no—
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—
231C22×C3×C4C23×C314yes—
232C22×C3×C4C23×C314yes—
233C22×C3×C4C23×C314yes—
234C22×C3×C4C23×C314yes—
235C22×C3×C4C23×C314yes—
236C22×C3×C4C23×C314yes—
237C3×C4⋊C4—28no—
238C3×C4⋊C4—28no—
239C3×C4⋊C4—44no—
240C3×C4⋊C4—44no—
241C3×C4⋊C4—44no—
242C3×C4⋊C4—44no—
243C3×C4⋊C4—44no—
244C3×C4⋊C4—44no—
245C3×C22⋊C4—28no—
246C3×C22⋊C4—28no—
247C3×C22⋊C4—28no—
248C3×C22⋊C4—28no—
249C3×C22⋊C4—28no—
250C3×C22⋊C4—44no—
251C3×C22⋊C4—44no—
252C3×C22⋊C4—44no—
253C3×C22⋊C4—44no—
254C3×C22⋊C4—44no—
255C3×C22⋊C4—44no—
256C3×C42—44no—
257C3×C42—44no—
258C22×C32—22no—
259C22×C32—22no—
260C22×C32—22no—
261C22×C32—41no—
262C22×C32—41no—
263C22×C32—41no—
264C22×C32—41no—
265C22×C32—41no—
266C22×C32—41no—
267C22×C32—41no—
268C22×C32—41no—
269C22×C32—41no—
270C22×C32—41no—
271C22×C32—41no—
272C22×C32C2×#4111yescharacteristic
273C22×C32C2×#4111yescharacteristic
274C22×C32C2×#4111yescharacteristic
275C22×C32H(5,𝔽2)11yescharacteristic
276C22×C32H(5,𝔽2)11yescharacteristic
277C22×C32H(5,𝔽2)11yescharacteristic
278C22×C322−1+411yescharacteristic
279C32×C4—22no—
280C32×C4—22no—
281C32×C4—41no—
282C32×C4—41no—
283C32×C4—41no—
284C32×C4—41no—
285C32×C4—41no—
286C32×C4—41no—
287C32×C4—41no—
288C32×C4—41no—
289C32×C4—41no—
290C32×C4—41no—
291C32×C4—41no—
292C22×D4C22×C3211yescharacteristic
293C23×C4C22×C3211yescharacteristic
294C2×C4⋊C4C22×C3211yescharacteristic
295C2×C4⋊C4C22×C3211yescharacteristic
296C2×C4⋊C4C22×C3211yescharacteristic
297C2×C4⋊C4C22×C3211yescharacteristic
298C2×C4⋊C4C22×C3211yescharacteristic
299C2×C4⋊C4C22×C3211yescharacteristic
300C2×C4⋊C4C22×C3211yescharacteristic
301C2×C4⋊C4C22×C3211yescharacteristic
302C2×C22⋊C4C22×C3211yescharacteristic
303C2×C22⋊C4C22×C3211yescharacteristic
304C2×C22⋊C4C22×C3211yescharacteristic
305C2×C22⋊C4C22×C3211yescharacteristic
306C2×C22⋊C4C22×C3211yescharacteristic
307C2×C22⋊C4C22×C3211yescharacteristic
308C2×C22⋊C4C22×C3211yescharacteristic
309C2×C22⋊C4C22×C3211yescharacteristic
310C2×C22⋊C4C22×C3211yescharacteristic
311C2×C22⋊C4C22×C3211yescharacteristic
312C2×C22⋊C4C22×C3211yescharacteristic
313C2×C42C22×C3211yescharacteristic
314C2×C42C22×C3211yescharacteristic
315#95C22×C3211yescharacteristic
316#95C22×C3211yescharacteristic
317#95C22×C3211yescharacteristic
318#95C22×C3211yescharacteristic
319#95C22×C3211yescharacteristic
320#95C22×C3211yescharacteristic
321#95C22×C3211yescharacteristic
322#95C22×C3211yescharacteristic
323#95C22×C3211yescharacteristic
324#95C22×C3211yescharacteristic
325#95C22×C3211yescharacteristic
326#95C22×C3211yescharacteristic
327C23×C3—24no—
328C23×C3—24no—
329C23×C3—24no—
330C23×C3—24no—
331C23×C3—24no—
332C23×C3—24no—
333C23×C3—24no—
334C23×C3—24no—
335C23×C3—24no—
336C23×C3—24no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—24no—
340C23×C3C3×#4118yes—
341C23×C3C24×C314yes—
342C3×D4—416no—
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—24no—
355C2×C3×C4—24no—
356C2×C3×C4—24no—
357C2×C3×C4—24no—
358C2×C3×C4—24no—
359C2×C3×C4—24no—
360C2×C3×C4—24no—
361C2×C3×C4—24no—
362C2×C3×C4—24no—
363C2×C3×C4—24no—
364C2×C3×C4—24no—
365C2×C3×C4—24no—
366C2×C3×C4—24no—
367C2×C3×C4—24no—
368C2×C3×C4—24no—
369C2×C3×C4—24no—
370C2×C3×C4—24no—
371C2×C3×C4—24no—
372C2×C3×C4—24no—
373C2×C3×C4—24no—
374C2×C3×C4—24no—
375C2×C3×C4—24no—
376C2×C3×C4—24no—
377C2×C3×C4—24no—
378C2×C3×C4—24no—
379C2×C3×C4—24no—
380C2×C3×C4—416no—
381C2×C3×C4C3×#4118yes—
382C2×C3×C4C3×#4118yes—
383C2×C32—42no—
384C2×C32—81no—
385C2×C32#52911yescharacteristic
386C2×C32#53811yescharacteristic
387C2×C32#53811yescharacteristic
388C2×C32#53911yescharacteristic
389C2×C32#53911yescharacteristic
390C2×C32#54011yescharacteristic
391C2×C32#54211yescharacteristic
392C24C23×C3211yescharacteristic
393C24C23×C3211yescharacteristic
394C2×D4—22no—
395C2×D4—41no—
396C2×D4—41no—
397C22×C4—22no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4C23×C3211yescharacteristic
401C22×C4C23×C3211yescharacteristic
402C22×C4C23×C3211yescharacteristic
403C22×C4C23×C3211yescharacteristic
404C22×C4C23×C3211yescharacteristic
405C22×C4C23×C3211yescharacteristic
406C22×C4C23×C3211yescharacteristic
407C22×C4C23×C3211yescharacteristic
408C22×C4C23×C3211yescharacteristic
409C22×C4C23×C3211yescharacteristic
410C22×C4C23×C3211yescharacteristic
411C22×C4C23×C3211yescharacteristic
412C22×C4C23×C3211yescharacteristic
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C42—41no—
433C42—41no—
434C22×C3—28no—
435C22×C3—28no—
436C22×C3—28no—
437C22×C3—44no—
438C22×C3—44no—
439C22×C3—44no—
440C22×C3—44no—
441C22×C3—44no—
442C22×C3—44no—
443C22×C3—44no—
444C22×C3—44no—
445C22×C3—44no—
446C22×C3—44no—
447C22×C3—44no—
448C22×C3C2×C3×#4114yes—
449C22×C3C2×C3×#4114yes—
450C22×C3C2×C3×#4114yes—
451C22×C3C3×H(5,𝔽2)14yes—
452C22×C3C3×H(5,𝔽2)14yes—
453C22×C3C3×H(5,𝔽2)14yes—
454C22×C3C3×2−1+414yes—
455C3×C4—28no—
456C3×C4—28no—
457C3×C4—44no—
458C3×C4—44no—
459C3×C4—44no—
460C3×C4—44no—
461C3×C4—44no—
462C3×C4—44no—
463C3×C4—44no—
464C3×C4—44no—
465C3×C4—44no—
466C3×C4—44no—
467C3×C4—44no—
468C32#264911yescharacteristic, direct product factor, Sylow
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—21no—
479C23—21no—
480C23—21no—
481C23—21no—
482C23C32×#4112yes—
483C23C24×C3211yescharacteristic
484D4—44no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—44no—
523C2×C4C32×#4112yes—
524C2×C4C32×#4112yes—
525C2×C3—48no—
526C2×C3—84no—
527C2×C3C3×#52914yes—
528C2×C3C3×#53814yes—
529C2×C3C3×#53814yes—
530C2×C3C3×#53914yes—
531C2×C3C3×#53914yes—
532C2×C3C3×#54014yes—
533C2×C3C3×#54214yes—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22C2×C32×#4111yescharacteristic
549C22C2×C32×#4111yescharacteristic
550C22C2×C32×#4111yescharacteristic
551C22C32×H(5,𝔽2)11yescharacteristic
552C22C32×H(5,𝔽2)11yescharacteristic
553C22C32×H(5,𝔽2)11yescharacteristic
554C22C32×2−1+411yescharacteristic
555C4—22no—
556C4—22no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C3C3×#264914yesdirect product factor
569C2—42no—
570C2—81no—
571C2C32×#52911yescharacteristic
572C2C32×#53811yescharacteristic
573C2C32×#53811yescharacteristic
574C2C32×#53911yescharacteristic
575C2C32×#53911yescharacteristic
576C2C32×#54011yescharacteristic
577C2C32×#54211yescharacteristic
subgroupG/H
center, socleC23×C32C24
commutator, Frattini, cosocleC23C24×C32
prime radicalC22×C32×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C32 ◁ G

Complements

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

NH ≅ G/Ntype
1. C32×#400C2semidirect
2. C32×#400C2semidirect
3. C32×#399C2semidirect
4. C32×#397C2semidirect
5. C32×#397C2semidirect
6. C32×#396C2semidirect
9. C32×#389C2semidirect
10. C32×#388C2semidirect
11. C32×#388C2semidirect
12. C32×#387C2semidirect
14. C32×#385C2semidirect
15. C32×C4×C22⋊C4C2semidirect
16. C3×#2649C3direct (N × H)
52. C3×#400C2×C3semidirect
53. C3×#400C2×C3semidirect
54. C3×#399C2×C3semidirect
55. C3×#397C2×C3semidirect
56. C3×#397C2×C3semidirect
57. C3×#396C2×C3semidirect
60. C3×#389C2×C3semidirect
61. C3×#388C2×C3semidirect
62. C3×#388C2×C3semidirect
63. C3×#387C2×C3semidirect
65. C3×#385C2×C3semidirect
66. C3×C4×C22⋊C4C2×C3semidirect
109. #2649C32direct (N × H)
201. #400C2×C32semidirect
202. #400C2×C32semidirect
203. #399C2×C32semidirect
204. #397C2×C32semidirect
205. #397C2×C32semidirect
206. #396C2×C32semidirect
209. #389C2×C32semidirect
210. #388C2×C32semidirect
211. #388C2×C32semidirect
212. #387C2×C32semidirect
214. #385C2×C32semidirect
215. C4×C22⋊C4C2×C32semidirect
468. C32#2649direct (N × H)
568. C3C3×#2649direct (N × H)

Maximal subgroups

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

subgroupindex
C32×#4002
C32×#3992
C32×#3972
C32×#3962
C32×#3942
C32×#3892
C32×#3882
C32×#3872
C32×#3862
C32×#3852
C32×C4×C22⋊C42
C3×#26493