Finite Group Databasebeta

← C32×#2480 #11769529

Subgroups — C32×#2480 #11769529

Order 1152.

1992 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#126C211yesmaximal, characteristic, complemented
2C22×C32×C22⋊C4C211yesmaximal, characteristic
3C32×#397C211yesmaximal, characteristic, complemented
4C32×#397C211yesmaximal, characteristic, complemented
5C32×#397C211yesmaximal, characteristic, complemented
6C32×#396C211yesmaximal, characteristic, complemented
7C32×#388C211yesmaximal, characteristic, complemented
8C32×#388C211yesmaximal, characteristic, complemented
9C32×#388C211yesmaximal, characteristic, complemented
10C32×#385C211yesmaximal, characteristic, complemented
11C32×#385C211yesmaximal, characteristic, complemented
12C32×#380C211yesmaximal, characteristic, complemented
13C32×#379C211yesmaximal, characteristic
14C32×#379C211yesmaximal, characteristic
15C32×C4×C22⋊C4C211yesmaximal, characteristic, complemented
16C3×#2480C314yesmaximal, direct product factor
17C25×C32C2211yescharacteristic
18C23×C32×C4C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C32×#126—24no—
21C2×C32×C4⋊C4C2211yescharacteristic, complemented
22C2×C32×C4⋊C4C2211yescharacteristic, complemented
23C2×C32×C4⋊C4C2211yescharacteristic, complemented
24C2×C32×C4⋊C4C2211yescharacteristic, complemented
25C2×C32×C4⋊C4C2211yescharacteristic, complemented
26C2×C32×C4⋊C4C2211yescharacteristic, complemented
27C2×C32×C22⋊C4—24no—
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×C22⋊C4C2211yescharacteristic
39C2×C32×C22⋊C4C2211yescharacteristic
40C2×C32×C22⋊C4C2211yescharacteristic
41C2×C32×C22⋊C4C2211yescharacteristic
42C2×C32×C22⋊C4C2211yescharacteristic
43C2×C32×C22⋊C4C2211yescharacteristic
44C2×C32×C42C2211yescharacteristic, complemented
45C2×C32×C42C2211yescharacteristic, complemented
46C32×#95C2211yescharacteristic, complemented
47C32×#95C2211yescharacteristic, complemented
48C32×#95C2211yescharacteristic, complemented
49C32×#95C2211yescharacteristic, complemented
50C32×#95C2211yescharacteristic, complemented
51C32×#95C2211yescharacteristic, complemented
52C32×#95C2211yescharacteristic, complemented
53C32×#95C2211yescharacteristic, complemented
54C2×C3×#126C2×C314yescomplemented
55C22×C3×C22⋊C4C2×C314yes—
56C3×#397C2×C314yescomplemented
57C3×#397C2×C314yescomplemented
58C3×#397C2×C314yescomplemented
59C3×#396C2×C314yescomplemented
60C3×#388C2×C314yescomplemented
61C3×#388C2×C314yescomplemented
62C3×#388C2×C314yescomplemented
63C3×#385C2×C314yescomplemented
64C3×#385C2×C314yescomplemented
65C3×#380C2×C314yescomplemented
66C3×#379C2×C314yes—
67C3×#379C2×C314yes—
68C3×C4×C22⋊C4C2×C314yescomplemented
69C24×C32—22no—
70C24×C32—22no—
71C24×C32—22no—
72C24×C32—22no—
73C24×C32—22no—
74C24×C32—41no—
75C24×C32—41no—
76C24×C32C2311yescharacteristic
77C24×C32C2311yescharacteristic
78C24×C32C2311yescharacteristic
79C22×C32×C4—22no—
80C22×C32×C4—22no—
81C22×C32×C4—22no—
82C22×C32×C4—22no—
83C22×C32×C4—41no—
84C22×C32×C4—41no—
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
96C22×C32×C4C2311yescharacteristic
97C32×C4⋊C4—22no—
98C32×C4⋊C4—22no—
99C32×C4⋊C4—22no—
100C32×C4⋊C4—41no—
101C32×C4⋊C4—41no—
102C32×C4⋊C4—41no—
103C32×C22⋊C4—22no—
104C32×C22⋊C4—22no—
105C32×C22⋊C4—22no—
106C32×C22⋊C4—22no—
107C32×C22⋊C4—22no—
108C32×C22⋊C4—22no—
109C32×C22⋊C4—22no—
110C32×C22⋊C4—22no—
111C32×C22⋊C4—22no—
112C32×C22⋊C4—22no—
113C32×C22⋊C4—22no—
114C32×C22⋊C4—41no—
115C32×C22⋊C4—41no—
116C32×C22⋊C4—41no—
117C32×C22⋊C4—41no—
118C32×C22⋊C4D414yes—
119C32×C42—22no—
120C32×C42—41no—
121#2480C3211yescharacteristic, direct product factor, Sylow
122C25×C3C22×C314yes—
123C23×C3×C4C22×C314yes—
124C23×C3×C4C22×C314yes—
125C3×#126—216no—
126C2×C3×C4⋊C4C22×C314yescomplemented
127C2×C3×C4⋊C4C22×C314yescomplemented
128C2×C3×C4⋊C4C22×C314yescomplemented
129C2×C3×C4⋊C4C22×C314yescomplemented
130C2×C3×C4⋊C4C22×C314yescomplemented
131C2×C3×C4⋊C4C22×C314yescomplemented
132C2×C3×C22⋊C4—216no—
133C2×C3×C22⋊C4C22×C314yes—
134C2×C3×C22⋊C4C22×C314yes—
135C2×C3×C22⋊C4C22×C314yes—
136C2×C3×C22⋊C4C22×C314yes—
137C2×C3×C22⋊C4C22×C314yes—
138C2×C3×C22⋊C4C22×C314yes—
139C2×C3×C22⋊C4C22×C314yes—
140C2×C3×C22⋊C4C22×C314yes—
141C2×C3×C22⋊C4C22×C314yes—
142C2×C3×C22⋊C4C22×C314yes—
143C2×C3×C22⋊C4C22×C314yes—
144C2×C3×C22⋊C4C22×C314yes—
145C2×C3×C22⋊C4C22×C314yes—
146C2×C3×C22⋊C4C22×C314yes—
147C2×C3×C22⋊C4C22×C314yes—
148C2×C3×C22⋊C4C22×C314yes—
149C2×C3×C42C22×C314yescomplemented
150C2×C3×C42C22×C314yescomplemented
151C3×#95C22×C314yescomplemented
152C3×#95C22×C314yescomplemented
153C3×#95C22×C314yescomplemented
154C3×#95C22×C314yescomplemented
155C3×#95C22×C314yescomplemented
156C3×#95C22×C314yescomplemented
157C3×#95C22×C314yescomplemented
158C3×#95C22×C314yescomplemented
159C23×C32—21no—
160C23×C32—21no—
161C23×C32—21no—
162C23×C32—21no—
163C23×C32—28no—
164C23×C32—21no—
165C23×C32—21no—
166C23×C32—21no—
167C23×C32—21no—
168C23×C32—21no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32—21no—
172C23×C32—21no—
173C23×C32—21no—
174C23×C32—21no—
175C23×C32—21no—
176C23×C32—44no—
177C23×C32—44no—
178C23×C32—44no—
179C23×C32—44no—
180C23×C32—44no—
181C23×C32—44no—
182C23×C32C2×D412yes—
183C23×C32#4112yes—
184C23×C32#4112yes—
185C23×C32#4112yes—
186C23×C32#4112yes—
187C23×C32C2411yescharacteristic
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—21no—
199C2×C32×C4—21no—
200C2×C32×C4—21no—
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—44no—
223C2×C32×C4—44no—
224C2×C32×C4C2×D412yes—
225C2×C32×C4C2×D412yes—
226C2×#126C2×C3211yescharacteristic, complemented
227C22×C22⋊C4C2×C3211yescharacteristic
228#397C2×C3211yescharacteristic, complemented
229#397C2×C3211yescharacteristic, complemented
230#397C2×C3211yescharacteristic, complemented
231#396C2×C3211yescharacteristic, complemented
232#388C2×C3211yescharacteristic, complemented
233#388C2×C3211yescharacteristic, complemented
234#388C2×C3211yescharacteristic, complemented
235#385C2×C3211yescharacteristic, complemented
236#385C2×C3211yescharacteristic, complemented
237#380C2×C3211yescharacteristic, complemented
238#379C2×C3211yescharacteristic
239#379C2×C3211yescharacteristic
240C4×C22⋊C4C2×C3211yescharacteristic, complemented
241C24×C3—28no—
242C24×C3—28no—
243C24×C3—28no—
244C24×C3—28no—
245C24×C3—28no—
246C24×C3—44no—
247C24×C3—44no—
248C24×C3C23×C314yes—
249C24×C3C23×C314yes—
250C24×C3C23×C314yes—
251C22×C3×C4—28no—
252C22×C3×C4—28no—
253C22×C3×C4—28no—
254C22×C3×C4—28no—
255C22×C3×C4—44no—
256C22×C3×C4—44no—
257C22×C3×C4C23×C314yes—
258C22×C3×C4C23×C314yes—
259C22×C3×C4C23×C314yes—
260C22×C3×C4C23×C314yes—
261C22×C3×C4C23×C314yes—
262C22×C3×C4C23×C314yes—
263C22×C3×C4C23×C314yes—
264C22×C3×C4C23×C314yes—
265C22×C3×C4C23×C314yes—
266C22×C3×C4C23×C314yes—
267C22×C3×C4C23×C314yes—
268C22×C3×C4C23×C314yes—
269C3×C4⋊C4—28no—
270C3×C4⋊C4—28no—
271C3×C4⋊C4—28no—
272C3×C4⋊C4—44no—
273C3×C4⋊C4—44no—
274C3×C4⋊C4—44no—
275C3×C22⋊C4—28no—
276C3×C22⋊C4—28no—
277C3×C22⋊C4—28no—
278C3×C22⋊C4—28no—
279C3×C22⋊C4—28no—
280C3×C22⋊C4—28no—
281C3×C22⋊C4—28no—
282C3×C22⋊C4—28no—
283C3×C22⋊C4—28no—
284C3×C22⋊C4—28no—
285C3×C22⋊C4—28no—
286C3×C22⋊C4—44no—
287C3×C22⋊C4—44no—
288C3×C22⋊C4—44no—
289C3×C22⋊C4—44no—
290C3×C22⋊C4C3×D4116yes—
291C3×C42—28no—
292C3×C42—44no—
293C22×C32—22no—
294C22×C32—22no—
295C22×C32—22no—
296C22×C32—22no—
297C22×C32—22no—
298C22×C32—22no—
299C22×C32—22no—
300C22×C32—22no—
301C22×C32—22no—
302C22×C32—22no—
303C22×C32—22no—
304C22×C32—22no—
305C22×C32—416no—
306C22×C32—41no—
307C22×C32—41no—
308C22×C32—41no—
309C22×C32—41no—
310C22×C32—41no—
311C22×C32—41no—
312C22×C32—41no—
313C22×C32—41no—
314C22×C32#12614yescomplemented
315C22×C32C22×D411yescharacteristic
316C22×C32C2×#4111yescharacteristic
317C22×C32C2×#4111yescharacteristic
318C22×C32C2×#4111yescharacteristic
319C22×C32C2×#4111yescharacteristic
320C22×C32H(5,𝔽2)11yescharacteristic
321C22×C32H(5,𝔽2)11yescharacteristic
322C32×C4—22no—
323C32×C4—22no—
324C32×C4—41no—
325C32×C4—41no—
326C32×C4—41no—
327C32×C4—41no—
328C32×C4—41no—
329C32×C4—41no—
330C32×C4—41no—
331C32×C4—41no—
332C32×C4—41no—
333C32×C4—41no—
334C25C22×C3211yescharacteristic
335C23×C4C22×C3211yescharacteristic
336C23×C4C22×C3211yescharacteristic
337#126—24no—
338C2×C4⋊C4C22×C3211yescharacteristic, complemented
339C2×C4⋊C4C22×C3211yescharacteristic, complemented
340C2×C4⋊C4C22×C3211yescharacteristic, complemented
341C2×C4⋊C4C22×C3211yescharacteristic, complemented
342C2×C4⋊C4C22×C3211yescharacteristic, complemented
343C2×C4⋊C4C22×C3211yescharacteristic, complemented
344C2×C22⋊C4—24no—
345C2×C22⋊C4C22×C3211yescharacteristic
346C2×C22⋊C4C22×C3211yescharacteristic
347C2×C22⋊C4C22×C3211yescharacteristic
348C2×C22⋊C4C22×C3211yescharacteristic
349C2×C22⋊C4C22×C3211yescharacteristic
350C2×C22⋊C4C22×C3211yescharacteristic
351C2×C22⋊C4C22×C3211yescharacteristic
352C2×C22⋊C4C22×C3211yescharacteristic
353C2×C22⋊C4C22×C3211yescharacteristic
354C2×C22⋊C4C22×C3211yescharacteristic
355C2×C22⋊C4C22×C3211yescharacteristic
356C2×C22⋊C4C22×C3211yescharacteristic
357C2×C22⋊C4C22×C3211yescharacteristic
358C2×C22⋊C4C22×C3211yescharacteristic
359C2×C22⋊C4C22×C3211yescharacteristic
360C2×C22⋊C4C22×C3211yescharacteristic
361C2×C42C22×C3211yescharacteristic, complemented
362C2×C42C22×C3211yescharacteristic, complemented
363#95C22×C3211yescharacteristic, complemented
364#95C22×C3211yescharacteristic, complemented
365#95C22×C3211yescharacteristic, complemented
366#95C22×C3211yescharacteristic, complemented
367#95C22×C3211yescharacteristic, complemented
368#95C22×C3211yescharacteristic, complemented
369#95C22×C3211yescharacteristic, complemented
370#95C22×C3211yescharacteristic, complemented
371C23×C3—24no—
372C23×C3—24no—
373C23×C3—24no—
374C23×C3—24no—
375C23×C3—232no—
376C23×C3—24no—
377C23×C3—24no—
378C23×C3—24no—
379C23×C3—24no—
380C23×C3—24no—
381C23×C3—24no—
382C23×C3—24no—
383C23×C3—24no—
384C23×C3—24no—
385C23×C3—24no—
386C23×C3—24no—
387C23×C3—24no—
388C23×C3—416no—
389C23×C3—416no—
390C23×C3—416no—
391C23×C3—416no—
392C23×C3—416no—
393C23×C3—416no—
394C23×C3C2×C3×D418yes—
395C23×C3C3×#4118yes—
396C23×C3C3×#4118yes—
397C23×C3C3×#4118yes—
398C23×C3C3×#4118yes—
399C23×C3C24×C314yes—
400C2×C3×C4—24no—
401C2×C3×C4—24no—
402C2×C3×C4—24no—
403C2×C3×C4—24no—
404C2×C3×C4—24no—
405C2×C3×C4—24no—
406C2×C3×C4—24no—
407C2×C3×C4—24no—
408C2×C3×C4—24no—
409C2×C3×C4—24no—
410C2×C3×C4—24no—
411C2×C3×C4—24no—
412C2×C3×C4—24no—
413C2×C3×C4—24no—
414C2×C3×C4—24no—
415C2×C3×C4—24no—
416C2×C3×C4—24no—
417C2×C3×C4—24no—
418C2×C3×C4—24no—
419C2×C3×C4—24no—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—24no—
425C2×C3×C4—24no—
426C2×C3×C4—24no—
427C2×C3×C4—24no—
428C2×C3×C4—24no—
429C2×C3×C4—24no—
430C2×C3×C4—24no—
431C2×C3×C4—24no—
432C2×C3×C4—24no—
433C2×C3×C4—24no—
434C2×C3×C4—416no—
435C2×C3×C4—416no—
436C2×C3×C4C2×C3×D418yes—
437C2×C3×C4C2×C3×D418yes—
438C2×C32—24no—
439C2×C32—42no—
440C2×C32—42no—
441C2×C32#52511yescharacteristic
442C2×C32C2×#12611yescharacteristic
443C2×C32#53811yescharacteristic
444C2×C32#54611yescharacteristic
445C2×C32#54611yescharacteristic
446C2×C32#55111yescharacteristic
447C2×C32#55111yescharacteristic
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—41no—
454C24—41no—
455C24C23×C3211yescharacteristic
456C24C23×C3211yescharacteristic
457C24C23×C3211yescharacteristic
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4C23×C3211yescharacteristic
465C22×C4C23×C3211yescharacteristic
466C22×C4C23×C3211yescharacteristic
467C22×C4C23×C3211yescharacteristic
468C22×C4C23×C3211yescharacteristic
469C22×C4C23×C3211yescharacteristic
470C22×C4C23×C3211yescharacteristic
471C22×C4C23×C3211yescharacteristic
472C22×C4C23×C3211yescharacteristic
473C22×C4C23×C3211yescharacteristic
474C22×C4C23×C3211yescharacteristic
475C22×C4C23×C3211yescharacteristic
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4C32×D414yes—
498C42—22no—
499C42—41no—
500C22×C3—28no—
501C22×C3—28no—
502C22×C3—28no—
503C22×C3—28no—
504C22×C3—28no—
505C22×C3—28no—
506C22×C3—28no—
507C22×C3—28no—
508C22×C3—28no—
509C22×C3—28no—
510C22×C3—28no—
511C22×C3—28no—
512C22×C3—464no—
513C22×C3—44no—
514C22×C3—44no—
515C22×C3—44no—
516C22×C3—44no—
517C22×C3—44no—
518C22×C3—44no—
519C22×C3—44no—
520C22×C3—44no—
521C22×C3C3×#126116yescomplemented
522C22×C3C22×C3×D414yes—
523C22×C3C2×C3×#4114yes—
524C22×C3C2×C3×#4114yes—
525C22×C3C2×C3×#4114yes—
526C22×C3C2×C3×#4114yes—
527C22×C3C3×H(5,𝔽2)14yes—
528C22×C3C3×H(5,𝔽2)14yes—
529C3×C4—28no—
530C3×C4—28no—
531C3×C4—44no—
532C3×C4—44no—
533C3×C4—44no—
534C3×C4—44no—
535C3×C4—44no—
536C3×C4—44no—
537C3×C4—44no—
538C3×C4—44no—
539C3×C4—44no—
540C3×C4—44no—
541C32#248011yescharacteristic, direct product factor, Sylow
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—28no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—44no—
560C23—44no—
561C23—44no—
562C23—44no—
563C23—44no—
564C23—44no—
565C23C2×C32×D412yes—
566C23C32×#4112yes—
567C23C32×#4112yes—
568C23C32×#4112yes—
569C23C32×#4112yes—
570C23C24×C3211yescharacteristic
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—44no—
606C2×C4—44no—
607C2×C4C2×C32×D412yes—
608C2×C4C2×C32×D412yes—
609C2×C3—216no—
610C2×C3—48no—
611C2×C3—48no—
612C2×C3C3×#52514yes—
613C2×C3C2×C3×#12614yes—
614C2×C3C3×#53814yes—
615C2×C3C3×#54614yes—
616C2×C3C3×#54614yes—
617C2×C3C3×#55114yes—
618C2×C3C3×#55114yes—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—416no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22C32×#12614yescomplemented
641C22C22×C32×D411yescharacteristic
642C22C2×C32×#4111yescharacteristic
643C22C2×C32×#4111yescharacteristic
644C22C2×C32×#4111yescharacteristic
645C22C2×C32×#4111yescharacteristic
646C22C32×H(5,𝔽2)11yescharacteristic
647C22C32×H(5,𝔽2)11yescharacteristic
648C4—22no—
649C4—22no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—41no—
660C3C3×#248014yesdirect product factor
661C2—24no—
662C2—42no—
663C2—42no—
664C2C32×#52511yescharacteristic
665C2C2×C32×#12611yescharacteristic
666C2C32×#53811yescharacteristic
667C2C32×#54611yescharacteristic
668C2C32×#54611yescharacteristic
669C2C32×#55111yescharacteristic
670C2C32×#55111yescharacteristic
subgroupG/H
center, socleC23×C32C24
commutator, Frattini, cosocleC23C24×C32
prime radicalC25×C32C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C32 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C32×#126C2semidirect
3. C32×#397C2semidirect
4. C32×#397C2semidirect
5. C32×#397C2semidirect
6. C32×#396C2semidirect
7. C32×#388C2semidirect
8. C32×#388C2semidirect
9. C32×#388C2semidirect
10. C32×#385C2semidirect
11. C32×#385C2semidirect
12. C32×#380C2semidirect
15. C32×C4×C22⋊C4C2semidirect
16. C3×#2480C3direct (N × H)
21. C2×C32×C4⋊C4C22semidirect
22. C2×C32×C4⋊C4C22semidirect
23. C2×C32×C4⋊C4C22semidirect
24. C2×C32×C4⋊C4C22semidirect
25. C2×C32×C4⋊C4C22semidirect
26. C2×C32×C4⋊C4C22semidirect
44. C2×C32×C42C22semidirect
45. C2×C32×C42C22semidirect
46. C32×#95C22semidirect
47. C32×#95C22semidirect
48. C32×#95C22semidirect
49. C32×#95C22semidirect
50. C32×#95C22semidirect
51. C32×#95C22semidirect
52. C32×#95C22semidirect
53. C32×#95C22semidirect
54. C2×C3×#126C2×C3semidirect
56. C3×#397C2×C3semidirect
57. C3×#397C2×C3semidirect
58. C3×#397C2×C3semidirect
59. C3×#396C2×C3semidirect
60. C3×#388C2×C3semidirect
61. C3×#388C2×C3semidirect
62. C3×#388C2×C3semidirect
63. C3×#385C2×C3semidirect
64. C3×#385C2×C3semidirect
65. C3×#380C2×C3semidirect
68. C3×C4×C22⋊C4C2×C3semidirect
121. #2480C32direct (N × H)
126. C2×C3×C4⋊C4C22×C3semidirect
127. C2×C3×C4⋊C4C22×C3semidirect
128. C2×C3×C4⋊C4C22×C3semidirect
129. C2×C3×C4⋊C4C22×C3semidirect
130. C2×C3×C4⋊C4C22×C3semidirect
131. C2×C3×C4⋊C4C22×C3semidirect
149. C2×C3×C42C22×C3semidirect
150. C2×C3×C42C22×C3semidirect
151. C3×#95C22×C3semidirect
152. C3×#95C22×C3semidirect
153. C3×#95C22×C3semidirect
154. C3×#95C22×C3semidirect
155. C3×#95C22×C3semidirect
156. C3×#95C22×C3semidirect
157. C3×#95C22×C3semidirect
158. C3×#95C22×C3semidirect
226. C2×#126C2×C32semidirect
228. #397C2×C32semidirect
229. #397C2×C32semidirect
230. #397C2×C32semidirect
231. #396C2×C32semidirect
232. #388C2×C32semidirect
233. #388C2×C32semidirect
234. #388C2×C32semidirect
235. #385C2×C32semidirect
236. #385C2×C32semidirect
237. #380C2×C32semidirect
240. C4×C22⋊C4C2×C32semidirect
314. C22×C32#126semidirect
338. C2×C4⋊C4C22×C32semidirect
339. C2×C4⋊C4C22×C32semidirect
340. C2×C4⋊C4C22×C32semidirect
341. C2×C4⋊C4C22×C32semidirect
342. C2×C4⋊C4C22×C32semidirect
343. C2×C4⋊C4C22×C32semidirect
361. C2×C42C22×C32semidirect
362. C2×C42C22×C32semidirect
363. #95C22×C32semidirect
364. #95C22×C32semidirect
365. #95C22×C32semidirect
366. #95C22×C32semidirect
367. #95C22×C32semidirect
368. #95C22×C32semidirect
369. #95C22×C32semidirect
370. #95C22×C32semidirect
521. C22×C3C3×#126semidirect
541. C32#2480direct (N × H)
640. C22C32×#126semidirect
660. C3C3×#2480direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1262
C22×C32×C22⋊C42
C32×#3972
C32×#3962
C32×#3882
C32×#3852
C32×#3802
C32×#3792
C32×C4×C22⋊C42
C3×#24803