Finite Group Databasebeta

← C32×#3282 #11770331

Subgroups — C32×#3282 #11770331

Order 1152.

1512 conjugacy classes of subgroups.

The subgroup lattice has 627 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#135C211yesmaximal, characteristic, complemented
2C22×C32×SD16C211yesmaximal, characteristic, complemented
3C32×#548C211yesmaximal, characteristic, complemented
4C32×#546C211yesmaximal, characteristic, complemented
5C32×#495C211yesmaximal, characteristic, complemented
6C32×#465C211yesmaximal, characteristic, complemented
7C32×#465C211yesmaximal, characteristic, complemented
8C32×#464C211yesmaximal, characteristic, complemented
9C32×#463C211yesmaximal, characteristic, complemented
10C32×#452C211yesmaximal, characteristic, complemented
11C32×#451C211yesmaximal, characteristic, complemented
12C32×#449C211yesmaximal, characteristic, complemented
13C32×#447C211yesmaximal, characteristic, complemented
14C32×C4×SD16C211yesmaximal, characteristic, complemented
15C32×C8×D4C211yesmaximal, characteristic, complemented
16C3×#3282C314yesmaximal, direct product factor
17C2×C32×#41C2211yescharacteristic
18C2×C32×#41C2211yescharacteristic, complemented
19C22×C32×Q8C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C32×#135—24no—
22C2×C32×Q16C2211yescharacteristic, complemented
23C2×C32×Q16C2211yescharacteristic, complemented
24C2×C32×SD16—24no—
25C2×C32×SD16C2211yescharacteristic
26C2×C32×SD16C2211yescharacteristic
27C2×C32×SD16C2211yescharacteristic
28C2×C32×SD16C2211yescharacteristic
29C2×C32×SD16C2211yescharacteristic, complemented
30C2×C32×D8C2211yescharacteristic
31C2×C32×D8C2211yescharacteristic
32C22×C32×C8C2211yescharacteristic
33C22×C32×C8C2211yescharacteristic, complemented
34C32×#124—21no—
35C32×#124C2211yescharacteristic
36C32×#124C2211yescharacteristic, complemented
37C32×#123—21no—
38C32×C22⋊Q8—21no—
39C32×C22⋊Q8C2211yescharacteristic
40C32×C22⋊Q8C2211yescharacteristic, complemented
41C32×#121—21no—
42C32×#121—21no—
43C32×#121C2211yescharacteristic
44C32×#121C2211yescharacteristic
45C32×#120—21no—
46C32×C4×Q8C2211yescharacteristic, complemented
47C32×C4×D4—21no—
48C32×C4×D4C2211yescharacteristic
49C32×C4×D4C2211yescharacteristic
50C2×C32×C22⋊C4—21no—
51C32×#106C2211yescharacteristic, complemented
52C32×C4⋊C8C2211yescharacteristic, complemented
53C32×#103C2211yescharacteristic, complemented
54C32×#103C2211yescharacteristic, complemented
55C32×#103C2211yescharacteristic, complemented
56C32×#102C2211yescharacteristic
57C32×#102C2211yescharacteristic
58C32×#102C2211yescharacteristic, complemented
59C32×C22⋊C8C2211yescharacteristic
60C32×C22⋊C8C2211yescharacteristic, complemented
61C32×C4×C8C2211yescharacteristic, complemented
62C2×C3×#135C2×C314yescomplemented
63C22×C3×SD16C2×C314yescomplemented
64C3×#548C2×C314yescomplemented
65C3×#546C2×C314yescomplemented
66C3×#495C2×C314yescomplemented
67C3×#465C2×C314yescomplemented
68C3×#465C2×C314yescomplemented
69C3×#464C2×C314yescomplemented
70C3×#463C2×C314yescomplemented
71C3×#452C2×C314yescomplemented
72C3×#451C2×C314yescomplemented
73C3×#449C2×C314yescomplemented
74C3×#447C2×C314yescomplemented
75C3×C4×SD16C2×C314yescomplemented
76C3×C8×D4C2×C314yescomplemented
77C24×C32—21no—
78C32×#41—22no—
79C32×#41—22no—
80C32×#41—41no—
81C32×#41—41no—
82C2×C32×Q8—21no—
83C2×C32×Q8—22no—
84C2×C32×Q8—41no—
85C2×C32×Q8C2311yescharacteristic
86C2×C32×Q8C2311yescharacteristic
87C2×C32×Q8C2311yescharacteristic
88C2×C32×D4—22no—
89C2×C32×D4—21no—
90C2×C32×D4—21no—
91C2×C32×D4—21no—
92C2×C32×D4—21no—
93C2×C32×D4—21no—
94C2×C32×D4—41no—
95C2×C32×D4D411yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4—21no—
100C22×C32×C4—21no—
101C22×C32×C4—21no—
102C22×C32×C4—21no—
103C22×C32×C4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C32×Q16—22no—
106C32×Q16—41no—
107C32×SD16—22no—
108C32×SD16—22no—
109C32×SD16—22no—
110C32×SD16—22no—
111C32×SD16D414yescomplemented
112C32×D8—22no—
113C32×D8—41no—
114C2×C32×C8—22no—
115C2×C32×C8—22no—
116C2×C32×C8C2311yescharacteristic
117C2×C32×C8C2311yescharacteristic
118C2×C32×C8C2311yescharacteristic
119C2×C32×C8C2311yescharacteristic
120C32×C4⋊C4—21no—
121C32×C4⋊C4—21no—
122C32×C4⋊C4—21no—
123C32×C4⋊C4D411yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125C32×C4⋊C4C2311yescharacteristic
126C32×C22⋊C4—21no—
127C32×C22⋊C4—21no—
128C32×C22⋊C4—21no—
129C32×C22⋊C4—21no—
130C32×C22⋊C4—21no—
131C32×C22⋊C4—21no—
132C32×C22⋊C4—21no—
133C32×C22⋊C4—21no—
134C32×C22⋊C4—21no—
135C32×C22⋊C4D411yescharacteristic
136C32×C22⋊C4D411yescharacteristic
137C32×C42—21no—
138C32×C42C2311yescharacteristic
139#3282C3211yescharacteristic, direct product factor, Sylow
140C2×C3×#41C22×C314yes—
141C2×C3×#41C22×C314yescomplemented
142C22×C3×Q8C22×C314yes—
143C22×C3×D4C22×C314yes—
144C3×#135—216no—
145C2×C3×Q16C22×C314yescomplemented
146C2×C3×Q16C22×C314yescomplemented
147C2×C3×SD16—216no—
148C2×C3×SD16C22×C314yes—
149C2×C3×SD16C22×C314yes—
150C2×C3×SD16C22×C314yes—
151C2×C3×SD16C22×C314yes—
152C2×C3×SD16C22×C314yescomplemented
153C2×C3×D8C22×C314yes—
154C2×C3×D8C22×C314yes—
155C22×C3×C8C22×C314yes—
156C22×C3×C8C22×C314yescomplemented
157C3×#124—24no—
158C3×#124C22×C314yes—
159C3×#124C22×C314yescomplemented
160C3×#123—24no—
161C3×C22⋊Q8—24no—
162C3×C22⋊Q8C22×C314yes—
163C3×C22⋊Q8C22×C314yescomplemented
164C3×#121—24no—
165C3×#121—24no—
166C3×#121C22×C314yes—
167C3×#121C22×C314yes—
168C3×#120—24no—
169C3×C4×Q8C22×C314yescomplemented
170C3×C4×D4—24no—
171C3×C4×D4C22×C314yes—
172C3×C4×D4C22×C314yes—
173C2×C3×C22⋊C4—24no—
174C3×#106C22×C314yescomplemented
175C3×C4⋊C8C22×C314yescomplemented
176C3×#103C22×C314yescomplemented
177C3×#103C22×C314yescomplemented
178C3×#103C22×C314yescomplemented
179C3×#102C22×C314yes—
180C3×#102C22×C314yes—
181C3×#102C22×C314yescomplemented
182C3×C22⋊C8C22×C314yes—
183C3×C22⋊C8C22×C314yescomplemented
184C3×C4×C8C22×C314yescomplemented
185C23×C32—21no—
186C23×C32—21no—
187C23×C32—21no—
188C23×C32—42no—
189C23×C32—42no—
190C23×C32—81no—
191C23×C32C2×D411yescharacteristic
192C23×C32C2×D411yescharacteristic
193C32×Q8—21no—
194C32×Q8—21no—
195C32×Q8—21no—
196C32×Q8—21no—
197C32×Q8—21no—
198C32×Q8—42no—
199C32×Q8C2×D412yes—
200C32×D4—22no—
201C32×D4—21no—
202C32×D4—21no—
203C32×D4—21no—
204C32×D4—21no—
205C32×D4—21no—
206C32×D4—42no—
207C32×D4—42no—
208C32×D4—42no—
209C32×D4—42no—
210C32×D4—81no—
211C32×D4C2×D412yes—
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—42no—
222C2×C32×C4—42no—
223C2×C32×C4—42no—
224C2×C32×C4—81no—
225C2×C32×C4C2×D411yescharacteristic
226C2×C32×C4C2×D411yescharacteristic
227C2×C32×C4C2×D411yescharacteristic
228C2×C32×C4C2×D411yescharacteristic
229C2×C32×C4C2411yescharacteristic
230C32×C8—21no—
231C32×C8—21no—
232C32×C8—21no—
233C32×C8C2×D412yes—
234C2×#135C2×C3211yescharacteristic, complemented
235C22×SD16C2×C3211yescharacteristic, complemented
236#548C2×C3211yescharacteristic, complemented
237#546C2×C3211yescharacteristic, complemented
238#495C2×C3211yescharacteristic, complemented
239#465C2×C3211yescharacteristic, complemented
240#465C2×C3211yescharacteristic, complemented
241#464C2×C3211yescharacteristic, complemented
242#463C2×C3211yescharacteristic, complemented
243#452C2×C3211yescharacteristic, complemented
244#451C2×C3211yescharacteristic, complemented
245#449C2×C3211yescharacteristic, complemented
246#447C2×C3211yescharacteristic, complemented
247C4×SD16C2×C3211yescharacteristic, complemented
248C8×D4C2×C3211yescharacteristic, complemented
249C24×C3—24no—
250C3×#41—28no—
251C3×#41—28no—
252C3×#41—44no—
253C3×#41—44no—
254C2×C3×Q8—24no—
255C2×C3×Q8—28no—
256C2×C3×Q8—44no—
257C2×C3×Q8C23×C314yes—
258C2×C3×Q8C23×C314yes—
259C2×C3×Q8C23×C314yes—
260C2×C3×D4—28no—
261C2×C3×D4—24no—
262C2×C3×D4—24no—
263C2×C3×D4—24no—
264C2×C3×D4—24no—
265C2×C3×D4—24no—
266C2×C3×D4—44no—
267C2×C3×D4C3×D414yes—
268C2×C3×D4C23×C314yes—
269C2×C3×D4C23×C314yes—
270C2×C3×D4C23×C314yes—
271C22×C3×C4—24no—
272C22×C3×C4—24no—
273C22×C3×C4—24no—
274C22×C3×C4—24no—
275C22×C3×C4C23×C314yes—
276C22×C3×C4C23×C314yes—
277C3×Q16—28no—
278C3×Q16—44no—
279C3×SD16—28no—
280C3×SD16—28no—
281C3×SD16—28no—
282C3×SD16—28no—
283C3×SD16C3×D4116yescomplemented
284C3×D8—28no—
285C3×D8—44no—
286C2×C3×C8—28no—
287C2×C3×C8—28no—
288C2×C3×C8C23×C314yes—
289C2×C3×C8C23×C314yes—
290C2×C3×C8C23×C314yes—
291C2×C3×C8C23×C314yes—
292C3×C4⋊C4—24no—
293C3×C4⋊C4—24no—
294C3×C4⋊C4—24no—
295C3×C4⋊C4C3×D414yes—
296C3×C4⋊C4C23×C314yes—
297C3×C4⋊C4C23×C314yes—
298C3×C22⋊C4—24no—
299C3×C22⋊C4—24no—
300C3×C22⋊C4—24no—
301C3×C22⋊C4—24no—
302C3×C22⋊C4—24no—
303C3×C22⋊C4—24no—
304C3×C22⋊C4—24no—
305C3×C22⋊C4—24no—
306C3×C22⋊C4—24no—
307C3×C22⋊C4C3×D414yes—
308C3×C22⋊C4C3×D414yes—
309C3×C42—24no—
310C3×C42C23×C314yes—
311C22×C32—21no—
312C22×C32—21no—
313C22×C32—21no—
314C22×C32—22no—
315C22×C32—21no—
316C22×C32—21no—
317C22×C32—41no—
318C22×C32—41no—
319C22×C32—41no—
320C22×C32—41no—
321C22×C32—41no—
322C22×C32—41no—
323C22×C32—41no—
324C22×C32—41no—
325C22×C32—84no—
326C22×C32#13512yescomplemented
327C22×C32C22×D411yescharacteristic
328C32×C4—21no—
329C32×C4—21no—
330C32×C4—22no—
331C32×C4—21no—
332C32×C4—21no—
333C32×C4—41no—
334C32×C4—41no—
335C32×C4—41no—
336C32×C4—41no—
337C32×C4C22×D411yescharacteristic
338C32×C4H(5,𝔽2)11yescharacteristic
339C2×#41C22×C3211yescharacteristic
340C2×#41C22×C3211yescharacteristic, complemented
341C22×Q8C22×C3211yescharacteristic
342C22×D4C22×C3211yescharacteristic
343#135—24no—
344C2×Q16C22×C3211yescharacteristic, complemented
345C2×Q16C22×C3211yescharacteristic, complemented
346C2×SD16—24no—
347C2×SD16C22×C3211yescharacteristic
348C2×SD16C22×C3211yescharacteristic
349C2×SD16C22×C3211yescharacteristic
350C2×SD16C22×C3211yescharacteristic
351C2×SD16C22×C3211yescharacteristic, complemented
352C2×D8C22×C3211yescharacteristic
353C2×D8C22×C3211yescharacteristic
354C22×C8C22×C3211yescharacteristic
355C22×C8C22×C3211yescharacteristic, complemented
356#124—21no—
357#124C22×C3211yescharacteristic
358#124C22×C3211yescharacteristic, complemented
359#123—21no—
360C22⋊Q8—21no—
361C22⋊Q8C22×C3211yescharacteristic
362C22⋊Q8C22×C3211yescharacteristic, complemented
363#121—21no—
364#121—21no—
365#121C22×C3211yescharacteristic
366#121C22×C3211yescharacteristic
367#120—21no—
368C4×Q8C22×C3211yescharacteristic, complemented
369C4×D4—21no—
370C4×D4C22×C3211yescharacteristic
371C4×D4C22×C3211yescharacteristic
372C2×C22⋊C4—21no—
373#106C22×C3211yescharacteristic, complemented
374C4⋊C8C22×C3211yescharacteristic, complemented
375#103C22×C3211yescharacteristic, complemented
376#103C22×C3211yescharacteristic, complemented
377#103C22×C3211yescharacteristic, complemented
378#102C22×C3211yescharacteristic
379#102C22×C3211yescharacteristic
380#102C22×C3211yescharacteristic, complemented
381C22⋊C8C22×C3211yescharacteristic
382C22⋊C8C22×C3211yescharacteristic, complemented
383C4×C8C22×C3211yescharacteristic, complemented
384C23×C3—24no—
385C23×C3—24no—
386C23×C3—24no—
387C23×C3—48no—
388C23×C3—48no—
389C23×C3—84no—
390C23×C3C2×C3×D414yes—
391C23×C3C2×C3×D414yes—
392C3×Q8—24no—
393C3×Q8—24no—
394C3×Q8—24no—
395C3×Q8—24no—
396C3×Q8—24no—
397C3×Q8—48no—
398C3×Q8C2×C3×D418yes—
399C3×D4—28no—
400C3×D4—24no—
401C3×D4—24no—
402C3×D4—24no—
403C3×D4—24no—
404C3×D4—24no—
405C3×D4—48no—
406C3×D4—48no—
407C3×D4—48no—
408C3×D4—48no—
409C3×D4—84no—
410C3×D4C2×C3×D418yes—
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—48no—
421C2×C3×C4—48no—
422C2×C3×C4—48no—
423C2×C3×C4—84no—
424C2×C3×C4C2×C3×D414yes—
425C2×C3×C4C2×C3×D414yes—
426C2×C3×C4C2×C3×D414yes—
427C2×C3×C4C2×C3×D414yes—
428C2×C3×C4C24×C314yes—
429C3×C8—24no—
430C3×C8—24no—
431C3×C8—24no—
432C3×C8C2×C3×D418yes—
433C2×C32—22no—
434C2×C32—41no—
435C2×C32—42no—
436C2×C32—81no—
437C2×C32—81no—
438C2×C32D4211yescharacteristic
439C2×C32C2×#13511yescharacteristic
440C2×C32#57711yescharacteristic
441C24—21no—
442#41—22no—
443#41—22no—
444#41—41no—
445#41—41no—
446C2×Q8—21no—
447C2×Q8—22no—
448C2×Q8—41no—
449C2×Q8C23×C3211yescharacteristic
450C2×Q8C23×C3211yescharacteristic
451C2×Q8C23×C3211yescharacteristic
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—41no—
459C2×D4C32×D411yescharacteristic
460C2×D4C23×C3211yescharacteristic
461C2×D4C23×C3211yescharacteristic
462C2×D4C23×C3211yescharacteristic
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4C23×C3211yescharacteristic
468C22×C4C23×C3211yescharacteristic
469Q16—22no—
470Q16—41no—
471SD16—22no—
472SD16—22no—
473SD16—22no—
474SD16—22no—
475SD16C32×D414yescomplemented
476D8—22no—
477D8—41no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8C23×C3211yescharacteristic
481C2×C8C23×C3211yescharacteristic
482C2×C8C23×C3211yescharacteristic
483C2×C8C23×C3211yescharacteristic
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4C32×D411yescharacteristic
488C4⋊C4C23×C3211yescharacteristic
489C4⋊C4C23×C3211yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4C32×D411yescharacteristic
500C22⋊C4C32×D411yescharacteristic
501C42—21no—
502C42C23×C3211yescharacteristic
503C22×C3—24no—
504C22×C3—24no—
505C22×C3—24no—
506C22×C3—24no—
507C22×C3—24no—
508C22×C3—28no—
509C22×C3—44no—
510C22×C3—44no—
511C22×C3—44no—
512C22×C3—44no—
513C22×C3—44no—
514C22×C3—44no—
515C22×C3—44no—
516C22×C3—44no—
517C22×C3—816no—
518C22×C3C3×#13518yescomplemented
519C22×C3C22×C3×D414yes—
520C3×C4—24no—
521C3×C4—24no—
522C3×C4—24no—
523C3×C4—24no—
524C3×C4—28no—
525C3×C4—44no—
526C3×C4—44no—
527C3×C4—44no—
528C3×C4—44no—
529C3×C4C22×C3×D414yes—
530C3×C4C3×H(5,𝔽2)14yes—
531C32#328211yescharacteristic, direct product factor, Sylow
532C23—21no—
533C23—21no—
534C23—21no—
535C23—42no—
536C23—42no—
537C23—81no—
538C23C2×C32×D411yescharacteristic
539C23C2×C32×D411yescharacteristic
540Q8—21no—
541Q8—21no—
542Q8—21no—
543Q8—21no—
544Q8—21no—
545Q8—42no—
546Q8C2×C32×D412yes—
547D4—22no—
548D4—21no—
549D4—21no—
550D4—21no—
551D4—21no—
552D4—21no—
553D4—42no—
554D4—42no—
555D4—42no—
556D4—42no—
557D4—81no—
558D4C2×C32×D412yes—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—81no—
572C2×C4C2×C32×D411yescharacteristic
573C2×C4C2×C32×D411yescharacteristic
574C2×C4C2×C32×D411yescharacteristic
575C2×C4C2×C32×D411yescharacteristic
576C2×C4C24×C3211yescharacteristic
577C8—21no—
578C8—21no—
579C8—21no—
580C8C2×C32×D412yes—
581C2×C3—28no—
582C2×C3—44no—
583C2×C3—48no—
584C2×C3—84no—
585C2×C3—84no—
586C2×C3C3×D4214yes—
587C2×C3C2×C3×#13514yes—
588C2×C3C3×#57714yes—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—84no—
604C22C32×#13512yescomplemented
605C22C22×C32×D411yescharacteristic
606C4—21no—
607C4—21no—
608C4—21no—
609C4—21no—
610C4—22no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4C22×C32×D411yescharacteristic
616C4C32×H(5,𝔽2)11yescharacteristic
617C3C3×#328214yesdirect product factor
618C2—22no—
619C2—41no—
620C2—42no—
621C2—81no—
622C2—81no—
623C2C32×D4211yescharacteristic
624C2C2×C32×#13511yescharacteristic
625C2C32×#57711yescharacteristic
subgroupG/H
center, socleC22×C32C22×D4
commutator, Frattini, cosocleC2×C4C24×C32
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C32 ◁ C32×C4×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C32×#135C2semidirect
2. C22×C32×SD16C2semidirect
3. C32×#548C2semidirect
4. C32×#546C2semidirect
5. C32×#495C2semidirect
6. C32×#465C2semidirect
7. C32×#465C2semidirect
8. C32×#464C2semidirect
9. C32×#463C2semidirect
10. C32×#452C2semidirect
11. C32×#451C2semidirect
12. C32×#449C2semidirect
13. C32×#447C2semidirect
14. C32×C4×SD16C2semidirect
15. C32×C8×D4C2semidirect
16. C3×#3282C3direct (N × H)
18. C2×C32×#41C22semidirect
22. C2×C32×Q16C22semidirect
23. C2×C32×Q16C22semidirect
29. C2×C32×SD16C22semidirect
33. C22×C32×C8C22semidirect
36. C32×#124C22semidirect
40. C32×C22⋊Q8C22semidirect
46. C32×C4×Q8C22semidirect
51. C32×#106C22semidirect
52. C32×C4⋊C8C22semidirect
53. C32×#103C22semidirect
54. C32×#103C22semidirect
55. C32×#103C22semidirect
58. C32×#102C22semidirect
60. C32×C22⋊C8C22semidirect
61. C32×C4×C8C22semidirect
62. C2×C3×#135C2×C3semidirect
63. C22×C3×SD16C2×C3semidirect
64. C3×#548C2×C3semidirect
65. C3×#546C2×C3semidirect
66. C3×#495C2×C3semidirect
67. C3×#465C2×C3semidirect
68. C3×#465C2×C3semidirect
69. C3×#464C2×C3semidirect
70. C3×#463C2×C3semidirect
71. C3×#452C2×C3semidirect
72. C3×#451C2×C3semidirect
73. C3×#449C2×C3semidirect
74. C3×#447C2×C3semidirect
75. C3×C4×SD16C2×C3semidirect
76. C3×C8×D4C2×C3semidirect
111. C32×SD16D4semidirect
139. #3282C32direct (N × H)
141. C2×C3×#41C22×C3semidirect
145. C2×C3×Q16C22×C3semidirect
146. C2×C3×Q16C22×C3semidirect
152. C2×C3×SD16C22×C3semidirect
156. C22×C3×C8C22×C3semidirect
159. C3×#124C22×C3semidirect
163. C3×C22⋊Q8C22×C3semidirect
169. C3×C4×Q8C22×C3semidirect
174. C3×#106C22×C3semidirect
175. C3×C4⋊C8C22×C3semidirect
176. C3×#103C22×C3semidirect
177. C3×#103C22×C3semidirect
178. C3×#103C22×C3semidirect
181. C3×#102C22×C3semidirect
183. C3×C22⋊C8C22×C3semidirect
184. C3×C4×C8C22×C3semidirect
234. C2×#135C2×C32semidirect
235. C22×SD16C2×C32semidirect
236. #548C2×C32semidirect
237. #546C2×C32semidirect
238. #495C2×C32semidirect
239. #465C2×C32semidirect
240. #465C2×C32semidirect
241. #464C2×C32semidirect
242. #463C2×C32semidirect
243. #452C2×C32semidirect
244. #451C2×C32semidirect
245. #449C2×C32semidirect
246. #447C2×C32semidirect
247. C4×SD16C2×C32semidirect
248. C8×D4C2×C32semidirect
283. C3×SD16C3×D4semidirect
326. C22×C32#135semidirect
340. C2×#41C22×C32semidirect
344. C2×Q16C22×C32semidirect
345. C2×Q16C22×C32semidirect
351. C2×SD16C22×C32semidirect
355. C22×C8C22×C32semidirect
358. #124C22×C32semidirect
362. C22⋊Q8C22×C32semidirect
368. C4×Q8C22×C32semidirect
373. #106C22×C32semidirect
374. C4⋊C8C22×C32semidirect
375. #103C22×C32semidirect
376. #103C22×C32semidirect
377. #103C22×C32semidirect
380. #102C22×C32semidirect
382. C22⋊C8C22×C32semidirect
383. C4×C8C22×C32semidirect
475. SD16C32×D4semidirect
518. C22×C3C3×#135semidirect
531. C32#3282direct (N × H)
604. C22C32×#135semidirect
617. C3C3×#3282direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1352
C22×C32×SD162
C32×#5482
C32×#5462
C32×#4952
C32×#4652
C32×#4642
C32×#4632
C32×#4522
C32×#4512
C32×#4492
C32×#4472
C32×C4×SD162
C32×C8×D42
C3×#32823