Finite Group Databasebeta

← C32×#2438 #11769487

Subgroups — C32×#2438 #11769487

Order 1152.

1584 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C22⋊Q8C211yesmaximal, characteristic
2C2×C32×#117C211yesmaximal, characteristic
3C32×#400C211yesmaximal, characteristic, complemented
4C32×#398C211yesmaximal, characteristic, complemented
5C32×#398C211yesmaximal, characteristic, complemented
6C32×#395C211yesmaximal, characteristic, complemented
7C32×#391C211yesmaximal, characteristic, complemented
8C32×#389C211yesmaximal, characteristic, complemented
9C32×#387C211yesmaximal, characteristic, complemented
10C32×#387C211yesmaximal, characteristic, complemented
11C32×#385C211yesmaximal, characteristic
12C32×#385C211yesmaximal, characteristic
13C32×#381C211yesmaximal, characteristic
14C32×#380C211yesmaximal, characteristic
15C2×C32×#95C211yesmaximal, characteristic
16C3×#2438C314yesmaximal, direct product factor
17C22×C32×Q8C2211yescharacteristic
18C23×C32×C4C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic
21C32×C22⋊Q8—24no—
22C32×#117—24no—
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×C32×C4⋊C4C2211yescharacteristic
27C2×C32×C4⋊C4C2211yescharacteristic
28C2×C32×C4⋊C4C2211yescharacteristic
29C2×C32×C4⋊C4C2211yescharacteristic
30C2×C32×C4⋊C4C2211yescharacteristic
31C2×C32×C4⋊C4C2211yescharacteristic
32C2×C32×C4⋊C4C2211yescharacteristic
33C2×C32×C4⋊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
52C32×#95C2211yescharacteristic
53C32×#95C2211yescharacteristic
54C2×C3×C22⋊Q8C2×C314yes—
55C2×C3×#117C2×C314yes—
56C3×#400C2×C314yescomplemented
57C3×#398C2×C314yescomplemented
58C3×#398C2×C314yescomplemented
59C3×#395C2×C314yescomplemented
60C3×#391C2×C314yescomplemented
61C3×#389C2×C314yescomplemented
62C3×#387C2×C314yescomplemented
63C3×#387C2×C314yescomplemented
64C3×#385C2×C314yes—
65C3×#385C2×C314yes—
66C3×#381C2×C314yes—
67C3×#380C2×C314yes—
68C2×C3×#95C2×C314yes—
69C24×C32C2311yescharacteristic
70C2×C32×Q8—22no—
71C2×C32×Q8—22no—
72C2×C32×Q8—41no—
73C22×C32×C4—22no—
74C22×C32×C4—22no—
75C22×C32×C4—22no—
76C22×C32×C4—22no—
77C22×C32×C4—22no—
78C22×C32×C4—22no—
79C22×C32×C4—41no—
80C22×C32×C4—41no—
81C22×C32×C4Q814yescomplemented
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
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C32×C4⋊C4—22no—
97C32×C4⋊C4—22no—
98C32×C4⋊C4—22no—
99C32×C4⋊C4—22no—
100C32×C4⋊C4—22no—
101C32×C4⋊C4—22no—
102C32×C4⋊C4—22no—
103C32×C4⋊C4—22no—
104C32×C4⋊C4—41no—
105C32×C4⋊C4—41no—
106C32×C4⋊C4—41no—
107C32×C22⋊C4—22no—
108C32×C22⋊C4—22no—
109C32×C22⋊C4—22no—
110C32×C22⋊C4D414yes—
111C32×C42—22no—
112C32×C42—22no—
113#2438C3211yescharacteristic, direct product factor, Sylow
114C22×C3×Q8C22×C314yes—
115C23×C3×C4C22×C314yes—
116C23×C3×C4C22×C314yes—
117C23×C3×C4C22×C314yes—
118C3×C22⋊Q8—216no—
119C3×#117—216no—
120C2×C3×C4⋊C4C22×C314yes—
121C2×C3×C4⋊C4C22×C314yes—
122C2×C3×C4⋊C4C22×C314yes—
123C2×C3×C4⋊C4C22×C314yes—
124C2×C3×C4⋊C4C22×C314yes—
125C2×C3×C4⋊C4C22×C314yes—
126C2×C3×C4⋊C4C22×C314yes—
127C2×C3×C4⋊C4C22×C314yes—
128C2×C3×C4⋊C4C22×C314yes—
129C2×C3×C4⋊C4C22×C314yes—
130C2×C3×C4⋊C4C22×C314yes—
131C2×C3×C22⋊C4C22×C314yes—
132C2×C3×C22⋊C4C22×C314yes—
133C2×C3×C22⋊C4C22×C314yes—
134C2×C3×C22⋊C4C22×C314yes—
135C2×C3×C42C22×C314yes—
136C2×C3×C42C22×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—
145C3×#95C22×C314yes—
146C3×#95C22×C314yes—
147C3×#95C22×C314yes—
148C3×#95C22×C314yes—
149C3×#95C22×C314yes—
150C3×#95C22×C314yes—
151C23×C32—21no—
152C23×C32—21no—
153C23×C32—21no—
154C23×C32—21no—
155C23×C32C2×D412yes—
156C23×C32C2×Q812yes—
157C23×C32#4112yes—
158C23×C32C2411yescharacteristic
159C32×Q8—44no—
160C2×C32×C4—28no—
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—44no—
198C2×C32×C4—44no—
199C2×C32×C4C2×D412yes—
200C2×C32×C4C2×D412yes—
201C2×C32×C4C2×Q812yes—
202C2×C32×C4C2×Q812yes—
203C2×C32×C4#4112yes—
204C2×C32×C4#4112yes—
205C2×C22⋊Q8C2×C3211yescharacteristic
206C2×#117C2×C3211yescharacteristic
207#400C2×C3211yescharacteristic, complemented
208#398C2×C3211yescharacteristic, complemented
209#398C2×C3211yescharacteristic, complemented
210#395C2×C3211yescharacteristic, complemented
211#391C2×C3211yescharacteristic, complemented
212#389C2×C3211yescharacteristic, complemented
213#387C2×C3211yescharacteristic, complemented
214#387C2×C3211yescharacteristic, complemented
215#385C2×C3211yescharacteristic
216#385C2×C3211yescharacteristic
217#381C2×C3211yescharacteristic
218#380C2×C3211yescharacteristic
219C2×#95C2×C3211yescharacteristic
220C24×C3C23×C314yes—
221C2×C3×Q8—28no—
222C2×C3×Q8—28no—
223C2×C3×Q8—44no—
224C22×C3×C4—28no—
225C22×C3×C4—28no—
226C22×C3×C4—28no—
227C22×C3×C4—28no—
228C22×C3×C4—28no—
229C22×C3×C4—28no—
230C22×C3×C4—44no—
231C22×C3×C4—44no—
232C22×C3×C4C3×Q8116yescomplemented
233C22×C3×C4C23×C314yes—
234C22×C3×C4C23×C314yes—
235C22×C3×C4C23×C314yes—
236C22×C3×C4C23×C314yes—
237C22×C3×C4C23×C314yes—
238C22×C3×C4C23×C314yes—
239C22×C3×C4C23×C314yes—
240C22×C3×C4C23×C314yes—
241C22×C3×C4C23×C314yes—
242C22×C3×C4C23×C314yes—
243C22×C3×C4C23×C314yes—
244C22×C3×C4C23×C314yes—
245C22×C3×C4C23×C314yes—
246C22×C3×C4C23×C314yes—
247C3×C4⋊C4—28no—
248C3×C4⋊C4—28no—
249C3×C4⋊C4—28no—
250C3×C4⋊C4—28no—
251C3×C4⋊C4—28no—
252C3×C4⋊C4—28no—
253C3×C4⋊C4—28no—
254C3×C4⋊C4—28no—
255C3×C4⋊C4—44no—
256C3×C4⋊C4—44no—
257C3×C4⋊C4—44no—
258C3×C22⋊C4—28no—
259C3×C22⋊C4—28no—
260C3×C22⋊C4—28no—
261C3×C22⋊C4C3×D4116yes—
262C3×C42—28no—
263C3×C42—28no—
264C22×C32—22no—
265C22×C32—22no—
266C22×C32—22no—
267C22×C32—22no—
268C22×C32—22no—
269C22×C32—22no—
270C22×C32C22⋊Q814yes—
271C22×C32C22×D411yescharacteristic
272C22×C32C22×Q811yescharacteristic
273C22×C32C2×#4111yescharacteristic
274C22×C32C2×#4111yescharacteristic
275C22×C32C2×#4111yescharacteristic
276C22×C32H(5,𝔽2)11yescharacteristic
277C22×C322−1+411yescharacteristic
278C32×C4—22no—
279C32×C4—22no—
280C32×C4—22no—
281C32×C4—22no—
282C32×C4—22no—
283C32×C4—22no—
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×Q8C22×C3211yescharacteristic
293C23×C4C22×C3211yescharacteristic
294C23×C4C22×C3211yescharacteristic
295C23×C4C22×C3211yescharacteristic
296C22⋊Q8—24no—
297#117—24no—
298C2×C4⋊C4C22×C3211yescharacteristic
299C2×C4⋊C4C22×C3211yescharacteristic
300C2×C4⋊C4C22×C3211yescharacteristic
301C2×C4⋊C4C22×C3211yescharacteristic
302C2×C4⋊C4C22×C3211yescharacteristic
303C2×C4⋊C4C22×C3211yescharacteristic
304C2×C4⋊C4C22×C3211yescharacteristic
305C2×C4⋊C4C22×C3211yescharacteristic
306C2×C4⋊C4C22×C3211yescharacteristic
307C2×C4⋊C4C22×C3211yescharacteristic
308C2×C4⋊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
327#95C22×C3211yescharacteristic
328#95C22×C3211yescharacteristic
329C23×C3—24no—
330C23×C3—24no—
331C23×C3—24no—
332C23×C3—24no—
333C23×C3C2×C3×D418yes—
334C23×C3C2×C3×Q818yes—
335C23×C3C3×#4118yes—
336C23×C3C24×C314yes—
337C3×Q8—416no—
338C2×C3×C4—232no—
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—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—416no—
376C2×C3×C4—416no—
377C2×C3×C4C2×C3×D418yes—
378C2×C3×C4C2×C3×D418yes—
379C2×C3×C4C2×C3×Q818yes—
380C2×C3×C4C2×C3×Q818yes—
381C2×C3×C4C3×#4118yes—
382C2×C3×C4C3×#4118yes—
383C2×C32—24no—
384C2×C32C2×C22⋊Q811yescharacteristic
385C2×C32#53311yescharacteristic
386C2×C32#54411yescharacteristic
387C2×C32#54611yescharacteristic
388C2×C32#54711yescharacteristic
389C2×C32#55111yescharacteristic
390C2×C32#55211yescharacteristic
391C24C23×C3211yescharacteristic
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—41no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4C32×Q814yescomplemented
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
413C22×C4C23×C3211yescharacteristic
414C22×C4C23×C3211yescharacteristic
415C22×C4C23×C3211yescharacteristic
416C22×C4C23×C3211yescharacteristic
417C22×C4C23×C3211yescharacteristic
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4C32×D414yes—
433C42—22no—
434C42—22no—
435C22×C3—28no—
436C22×C3—28no—
437C22×C3—28no—
438C22×C3—28no—
439C22×C3—28no—
440C22×C3—28no—
441C22×C3C3×C22⋊Q8116yes—
442C22×C3C22×C3×D414yes—
443C22×C3C22×C3×Q814yes—
444C22×C3C2×C3×#4114yes—
445C22×C3C2×C3×#4114yes—
446C22×C3C2×C3×#4114yes—
447C22×C3C3×H(5,𝔽2)14yes—
448C22×C3C3×2−1+414yes—
449C3×C4—28no—
450C3×C4—28no—
451C3×C4—28no—
452C3×C4—28no—
453C3×C4—28no—
454C3×C4—28no—
455C3×C4—44no—
456C3×C4—44no—
457C3×C4—44no—
458C3×C4—44no—
459C3×C4—44no—
460C3×C4—44no—
461C3×C4—44no—
462C3×C4—44no—
463C32#243811yescharacteristic, direct product factor, Sylow
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23C2×C32×D412yes—
469C23C2×C32×Q812yes—
470C23C32×#4112yes—
471C23C24×C3211yescharacteristic
472Q8—44no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—28no—
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—44no—
511C2×C4—44no—
512C2×C4C2×C32×D412yes—
513C2×C4C2×C32×D412yes—
514C2×C4C2×C32×Q812yes—
515C2×C4C2×C32×Q812yes—
516C2×C4C32×#4112yes—
517C2×C4C32×#4112yes—
518C2×C3—216no—
519C2×C3C2×C3×C22⋊Q814yes—
520C2×C3C3×#53314yes—
521C2×C3C3×#54414yes—
522C2×C3C3×#54614yes—
523C2×C3C3×#54714yes—
524C2×C3C3×#55114yes—
525C2×C3C3×#55214yes—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22C32×C22⋊Q814yes—
533C22C22×C32×D411yescharacteristic
534C22C22×C32×Q811yescharacteristic
535C22C2×C32×#4111yescharacteristic
536C22C2×C32×#4111yescharacteristic
537C22C2×C32×#4111yescharacteristic
538C22C32×H(5,𝔽2)11yescharacteristic
539C22C32×2−1+411yescharacteristic
540C4—22no—
541C4—22no—
542C4—22no—
543C4—22no—
544C4—22no—
545C4—22no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C3C3×#243814yesdirect product factor
555C2—24no—
556C2C2×C32×C22⋊Q811yescharacteristic
557C2C32×#53311yescharacteristic
558C2C32×#54411yescharacteristic
559C2C32×#54611yescharacteristic
560C2C32×#54711yescharacteristic
561C2C32×#55111yescharacteristic
562C2C32×#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
3. C32×#400C2semidirect
4. C32×#398C2semidirect
5. C32×#398C2semidirect
6. C32×#395C2semidirect
7. C32×#391C2semidirect
8. C32×#389C2semidirect
9. C32×#387C2semidirect
10. C32×#387C2semidirect
16. C3×#2438C3direct (N × H)
56. C3×#400C2×C3semidirect
57. C3×#398C2×C3semidirect
58. C3×#398C2×C3semidirect
59. C3×#395C2×C3semidirect
60. C3×#391C2×C3semidirect
61. C3×#389C2×C3semidirect
62. C3×#387C2×C3semidirect
63. C3×#387C2×C3semidirect
81. C22×C32×C4Q8semidirect
113. #2438C32direct (N × H)
207. #400C2×C32semidirect
208. #398C2×C32semidirect
209. #398C2×C32semidirect
210. #395C2×C32semidirect
211. #391C2×C32semidirect
212. #389C2×C32semidirect
213. #387C2×C32semidirect
214. #387C2×C32semidirect
232. C22×C3×C4C3×Q8semidirect
403. C22×C4C32×Q8semidirect
463. C32#2438direct (N × H)
554. C3C3×#2438direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C22⋊Q82
C2×C32×#1172
C32×#4002
C32×#3982
C32×#3952
C32×#3912
C32×#3892
C32×#3872
C32×#3852
C32×#3812
C32×#3802
C2×C32×#952
C3×#24383