Finite Group Databasebeta

← C32×#2464 #11769513

Subgroups — C32×#2464 #11769513

Order 1152.

2130 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#123C211yesmaximal, characteristic, complemented
2C2×C32×#121C211yesmaximal, characteristic, complemented
3C2×C32×#121C211yesmaximal, characteristic, complemented
4C2×C32×C4×D4C211yesmaximal, characteristic, complemented
5C32×#398C211yesmaximal, characteristic, complemented
6C32×#394C211yesmaximal, characteristic, complemented
7C32×#392C211yesmaximal, characteristic, complemented
8C32×#392C211yesmaximal, characteristic, complemented
9C32×#390C211yesmaximal, characteristic, complemented
10C32×#388C211yesmaximal, characteristic, complemented
11C32×#388C211yesmaximal, characteristic, complemented
12C32×#386C211yesmaximal, characteristic, complemented
13C32×#386C211yesmaximal, characteristic, complemented
14C32×#385C211yesmaximal, characteristic, complemented
15C32×C4×C22⋊C4C211yesmaximal, characteristic, complemented
16C3×#2464C314yesmaximal, direct product factor
17C22×C32×D4C2211yescharacteristic
18C22×C32×D4C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C22×C32×D4C2211yescharacteristic
22C22×C32×D4C2211yescharacteristic
23C23×C32×C4C2211yescharacteristic
24C23×C32×C4C2211yescharacteristic
25C23×C32×C4C2211yescharacteristic
26C32×#123—24no—
27C32×#121—24no—
28C32×#121—24no—
29C32×C4×D4—24no—
30C2×C32×C4⋊C4C2211yescharacteristic
31C2×C32×C4⋊C4C2211yescharacteristic
32C2×C32×C4⋊C4C2211yescharacteristic
33C2×C32×C4⋊C4C2211yescharacteristic
34C2×C32×C4⋊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×C22⋊C4C2211yescharacteristic
45C2×C32×C22⋊C4C2211yescharacteristic
46C2×C32×C22⋊C4C2211yescharacteristic
47C2×C32×C22⋊C4C2211yescharacteristic
48C2×C32×C42C2211yescharacteristic
49C2×C32×C42C2211yescharacteristic
50C32×#95C2211yescharacteristic
51C32×#95C2211yescharacteristic
52C32×#95C2211yescharacteristic
53C32×#95C2211yescharacteristic
54C32×#95C2211yescharacteristic
55C32×#95C2211yescharacteristic
56C2×C3×#123C2×C314yescomplemented
57C2×C3×#121C2×C314yescomplemented
58C2×C3×#121C2×C314yescomplemented
59C2×C3×C4×D4C2×C314yescomplemented
60C3×#398C2×C314yescomplemented
61C3×#394C2×C314yescomplemented
62C3×#392C2×C314yescomplemented
63C3×#392C2×C314yescomplemented
64C3×#390C2×C314yescomplemented
65C3×#388C2×C314yescomplemented
66C3×#388C2×C314yescomplemented
67C3×#386C2×C314yescomplemented
68C3×#386C2×C314yescomplemented
69C3×#385C2×C314yescomplemented
70C3×C4×C22⋊C4C2×C314yescomplemented
71C24×C32C2311yescharacteristic
72C24×C32C2311yescharacteristic
73C24×C32C2311yescharacteristic
74C24×C32C2311yescharacteristic
75C2×C32×D4—22no—
76C2×C32×D4—22no—
77C2×C32×D4—22no—
78C2×C32×D4—22no—
79C2×C32×D4—22no—
80C2×C32×D4—22no—
81C2×C32×D4—22no—
82C2×C32×D4—22no—
83C2×C32×D4—22no—
84C2×C32×D4—22no—
85C2×C32×D4—22no—
86C2×C32×D4—22no—
87C2×C32×D4—22no—
88C2×C32×D4—41no—
89C2×C32×D4—41no—
90C2×C32×D4—41no—
91C2×C32×D4—41no—
92C2×C32×D4—41no—
93C22×C32×C4—22no—
94C22×C32×C4—22no—
95C22×C32×C4—22no—
96C22×C32×C4—22no—
97C22×C32×C4—22no—
98C22×C32×C4—22no—
99C22×C32×C4—41no—
100C22×C32×C4—41no—
101C22×C32×C4—41no—
102C22×C32×C4C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C32×C4⋊C4—22no—
114C32×C4⋊C4—22no—
115C32×C4⋊C4—22no—
116C32×C4⋊C4—22no—
117C32×C4⋊C4—22no—
118C32×C22⋊C4—22no—
119C32×C22⋊C4—22no—
120C32×C22⋊C4—22no—
121C32×C22⋊C4—22no—
122C32×C22⋊C4—22no—
123C32×C22⋊C4—22no—
124C32×C22⋊C4—22no—
125C32×C22⋊C4—22no—
126C32×C22⋊C4—41no—
127C32×C22⋊C4—41no—
128C32×C22⋊C4—41no—
129C32×C22⋊C4D414yescomplemented
130C32×C22⋊C4D414yescomplemented
131C32×C42—22no—
132C32×C42—41no—
133#2464C3211yescharacteristic, direct product factor, Sylow
134C22×C3×D4C22×C314yes—
135C22×C3×D4C22×C314yes—
136C22×C3×D4C22×C314yes—
137C22×C3×D4C22×C314yes—
138C22×C3×D4C22×C314yes—
139C22×C3×D4C22×C314yes—
140C23×C3×C4C22×C314yes—
141C23×C3×C4C22×C314yes—
142C23×C3×C4C22×C314yes—
143C3×#123—216no—
144C3×#121—216no—
145C3×#121—216no—
146C3×C4×D4—216no—
147C2×C3×C4⋊C4C22×C314yes—
148C2×C3×C4⋊C4C22×C314yes—
149C2×C3×C4⋊C4C22×C314yes—
150C2×C3×C4⋊C4C22×C314yes—
151C2×C3×C4⋊C4C22×C314yes—
152C2×C3×C22⋊C4C22×C314yes—
153C2×C3×C22⋊C4C22×C314yes—
154C2×C3×C22⋊C4C22×C314yes—
155C2×C3×C22⋊C4C22×C314yes—
156C2×C3×C22⋊C4C22×C314yes—
157C2×C3×C22⋊C4C22×C314yes—
158C2×C3×C22⋊C4C22×C314yes—
159C2×C3×C22⋊C4C22×C314yes—
160C2×C3×C22⋊C4C22×C314yes—
161C2×C3×C22⋊C4C22×C314yes—
162C2×C3×C22⋊C4C22×C314yes—
163C2×C3×C22⋊C4C22×C314yes—
164C2×C3×C22⋊C4C22×C314yes—
165C2×C3×C42C22×C314yes—
166C2×C3×C42C22×C314yes—
167C3×#95C22×C314yes—
168C3×#95C22×C314yes—
169C3×#95C22×C314yes—
170C3×#95C22×C314yes—
171C3×#95C22×C314yes—
172C3×#95C22×C314yes—
173C23×C32—21no—
174C23×C32—21no—
175C23×C32—21no—
176C23×C32—21no—
177C23×C32—21no—
178C23×C32—21no—
179C23×C32—21no—
180C23×C32—21no—
181C23×C32—21no—
182C23×C32—21no—
183C23×C32—21no—
184C23×C32—21no—
185C23×C32—21no—
186C23×C32—21no—
187C23×C32—21no—
188C23×C32—21no—
189C23×C32—21no—
190C23×C32—21no—
191C23×C32—21no—
192C23×C32—21no—
193C23×C32—21no—
194C23×C32—21no—
195C23×C32—21no—
196C23×C32—21no—
197C23×C32—21no—
198C23×C32C2×D412yes—
199C23×C32C2×D412yes—
200C23×C32#4112yes—
201C23×C32C2411yescharacteristic
202C32×D4—28no—
203C32×D4—44no—
204C32×D4—44no—
205C32×D4—44no—
206C32×D4—44no—
207C32×D4—44no—
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—21no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—44no—
236C2×C32×C4—44no—
237C2×C32×C4—44no—
238C2×C32×C4C2×D412yes—
239C2×C32×C4C2×D412yes—
240C2×C32×C4C2×D412yes—
241C2×C32×C4C2×D412yes—
242C2×C32×C4#4112yes—
243C2×C32×C4#4112yes—
244C2×#123C2×C3211yescharacteristic, complemented
245C2×#121C2×C3211yescharacteristic, complemented
246C2×#121C2×C3211yescharacteristic, complemented
247C2×C4×D4C2×C3211yescharacteristic, complemented
248#398C2×C3211yescharacteristic, complemented
249#394C2×C3211yescharacteristic, complemented
250#392C2×C3211yescharacteristic, complemented
251#392C2×C3211yescharacteristic, complemented
252#390C2×C3211yescharacteristic, complemented
253#388C2×C3211yescharacteristic, complemented
254#388C2×C3211yescharacteristic, complemented
255#386C2×C3211yescharacteristic, complemented
256#386C2×C3211yescharacteristic, complemented
257#385C2×C3211yescharacteristic, complemented
258C4×C22⋊C4C2×C3211yescharacteristic, complemented
259C24×C3C23×C314yes—
260C24×C3C23×C314yes—
261C24×C3C23×C314yes—
262C24×C3C23×C314yes—
263C2×C3×D4—28no—
264C2×C3×D4—28no—
265C2×C3×D4—28no—
266C2×C3×D4—28no—
267C2×C3×D4—28no—
268C2×C3×D4—28no—
269C2×C3×D4—28no—
270C2×C3×D4—28no—
271C2×C3×D4—28no—
272C2×C3×D4—28no—
273C2×C3×D4—28no—
274C2×C3×D4—28no—
275C2×C3×D4—28no—
276C2×C3×D4—44no—
277C2×C3×D4—44no—
278C2×C3×D4—44no—
279C2×C3×D4—44no—
280C2×C3×D4—44no—
281C22×C3×C4—28no—
282C22×C3×C4—28no—
283C22×C3×C4—28no—
284C22×C3×C4—28no—
285C22×C3×C4—28no—
286C22×C3×C4—28no—
287C22×C3×C4—44no—
288C22×C3×C4—44no—
289C22×C3×C4—44no—
290C22×C3×C4C23×C314yes—
291C22×C3×C4C23×C314yes—
292C22×C3×C4C23×C314yes—
293C22×C3×C4C23×C314yes—
294C22×C3×C4C23×C314yes—
295C22×C3×C4C23×C314yes—
296C22×C3×C4C23×C314yes—
297C22×C3×C4C23×C314yes—
298C22×C3×C4C23×C314yes—
299C22×C3×C4C23×C314yes—
300C22×C3×C4C23×C314yes—
301C3×C4⋊C4—28no—
302C3×C4⋊C4—28no—
303C3×C4⋊C4—28no—
304C3×C4⋊C4—28no—
305C3×C4⋊C4—28no—
306C3×C22⋊C4—28no—
307C3×C22⋊C4—28no—
308C3×C22⋊C4—28no—
309C3×C22⋊C4—28no—
310C3×C22⋊C4—28no—
311C3×C22⋊C4—28no—
312C3×C22⋊C4—28no—
313C3×C22⋊C4—28no—
314C3×C22⋊C4—44no—
315C3×C22⋊C4—44no—
316C3×C22⋊C4—44no—
317C3×C22⋊C4C3×D4116yescomplemented
318C3×C22⋊C4C3×D4116yescomplemented
319C3×C42—28no—
320C3×C42—44no—
321C22×C32—22no—
322C22×C32—22no—
323C22×C32—22no—
324C22×C32—22no—
325C22×C32—22no—
326C22×C32—22no—
327C22×C32—22no—
328C22×C32—22no—
329C22×C32—22no—
330C22×C32—41no—
331C22×C32—41no—
332C22×C32—41no—
333C22×C32—41no—
334C22×C32—41no—
335C22×C32—41no—
336C22×C32—41no—
337C22×C32—41no—
338C22×C32—41no—
339C22×C32—41no—
340C22×C32—41no—
341C22×C32—41no—
342C22×C32—41no—
343C22×C32—41no—
344C22×C32—41no—
345C22×C32—41no—
346C22×C32—41no—
347C22×C32—41no—
348C22×C32—41no—
349C22×C32C22×D411yescharacteristic
350C22×C32C22×D411yescharacteristic
351C22×C32C2×#4111yescharacteristic
352C22×C32C2×#4111yescharacteristic
353C22×C32C2×#4111yescharacteristic
354C22×C32H(5,𝔽2)11yescharacteristic
355C22×C32H(5,𝔽2)11yescharacteristic
356C32×C4—22no—
357C32×C4—22no—
358C32×C4—22no—
359C32×C4—22no—
360C32×C4—22no—
361C32×C4—22no—
362C32×C4—41no—
363C32×C4—41no—
364C32×C4—41no—
365C32×C4—41no—
366C32×C4—41no—
367C22×D4C22×C3211yescharacteristic
368C22×D4C22×C3211yescharacteristic
369C22×D4C22×C3211yescharacteristic
370C22×D4C22×C3211yescharacteristic
371C22×D4C22×C3211yescharacteristic
372C22×D4C22×C3211yescharacteristic
373C23×C4C22×C3211yescharacteristic
374C23×C4C22×C3211yescharacteristic
375C23×C4C22×C3211yescharacteristic
376#123—24no—
377#121—24no—
378#121—24no—
379C4×D4—24no—
380C2×C4⋊C4C22×C3211yescharacteristic
381C2×C4⋊C4C22×C3211yescharacteristic
382C2×C4⋊C4C22×C3211yescharacteristic
383C2×C4⋊C4C22×C3211yescharacteristic
384C2×C4⋊C4C22×C3211yescharacteristic
385C2×C22⋊C4C22×C3211yescharacteristic
386C2×C22⋊C4C22×C3211yescharacteristic
387C2×C22⋊C4C22×C3211yescharacteristic
388C2×C22⋊C4C22×C3211yescharacteristic
389C2×C22⋊C4C22×C3211yescharacteristic
390C2×C22⋊C4C22×C3211yescharacteristic
391C2×C22⋊C4C22×C3211yescharacteristic
392C2×C22⋊C4C22×C3211yescharacteristic
393C2×C22⋊C4C22×C3211yescharacteristic
394C2×C22⋊C4C22×C3211yescharacteristic
395C2×C22⋊C4C22×C3211yescharacteristic
396C2×C22⋊C4C22×C3211yescharacteristic
397C2×C22⋊C4C22×C3211yescharacteristic
398C2×C42C22×C3211yescharacteristic
399C2×C42C22×C3211yescharacteristic
400#95C22×C3211yescharacteristic
401#95C22×C3211yescharacteristic
402#95C22×C3211yescharacteristic
403#95C22×C3211yescharacteristic
404#95C22×C3211yescharacteristic
405#95C22×C3211yescharacteristic
406C23×C3—24no—
407C23×C3—24no—
408C23×C3—24no—
409C23×C3—24no—
410C23×C3—24no—
411C23×C3—24no—
412C23×C3—24no—
413C23×C3—24no—
414C23×C3—24no—
415C23×C3—24no—
416C23×C3—24no—
417C23×C3—24no—
418C23×C3—24no—
419C23×C3—24no—
420C23×C3—24no—
421C23×C3—24no—
422C23×C3—24no—
423C23×C3—24no—
424C23×C3—24no—
425C23×C3—24no—
426C23×C3—24no—
427C23×C3—24no—
428C23×C3—24no—
429C23×C3—24no—
430C23×C3—24no—
431C23×C3C2×C3×D418yes—
432C23×C3C2×C3×D418yes—
433C23×C3C3×#4118yes—
434C23×C3C24×C314yes—
435C3×D4—232no—
436C3×D4—416no—
437C3×D4—416no—
438C3×D4—416no—
439C3×D4—416no—
440C3×D4—416no—
441C2×C3×C4—24no—
442C2×C3×C4—24no—
443C2×C3×C4—24no—
444C2×C3×C4—24no—
445C2×C3×C4—24no—
446C2×C3×C4—24no—
447C2×C3×C4—24no—
448C2×C3×C4—24no—
449C2×C3×C4—24no—
450C2×C3×C4—24no—
451C2×C3×C4—24no—
452C2×C3×C4—24no—
453C2×C3×C4—24no—
454C2×C3×C4—24no—
455C2×C3×C4—24no—
456C2×C3×C4—24no—
457C2×C3×C4—24no—
458C2×C3×C4—24no—
459C2×C3×C4—24no—
460C2×C3×C4—24no—
461C2×C3×C4—24no—
462C2×C3×C4—24no—
463C2×C3×C4—24no—
464C2×C3×C4—24no—
465C2×C3×C4—24no—
466C2×C3×C4—24no—
467C2×C3×C4—24no—
468C2×C3×C4—416no—
469C2×C3×C4—416no—
470C2×C3×C4—416no—
471C2×C3×C4C2×C3×D418yes—
472C2×C3×C4C2×C3×D418yes—
473C2×C3×C4C2×C3×D418yes—
474C2×C3×C4C2×C3×D418yes—
475C2×C3×C4C3×#4118yes—
476C2×C3×C4C3×#4118yes—
477C2×C32—42no—
478C2×C32—42no—
479C2×C32—42no—
480C2×C32—81no—
481C2×C32#52511yescharacteristic
482C2×C32#53211yescharacteristic
483C2×C32#54011yescharacteristic
484C2×C32D4211yescharacteristic
485C2×C32#54611yescharacteristic
486C2×C32#54611yescharacteristic
487C2×C32#55311yescharacteristic
488C24C23×C3211yescharacteristic
489C24C23×C3211yescharacteristic
490C24C23×C3211yescharacteristic
491C24C23×C3211yescharacteristic
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—41no—
509C2×D4—41no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4C23×C3211yescharacteristic
520C22×C4C23×C3211yescharacteristic
521C22×C4C23×C3211yescharacteristic
522C22×C4C23×C3211yescharacteristic
523C22×C4C23×C3211yescharacteristic
524C22×C4C23×C3211yescharacteristic
525C22×C4C23×C3211yescharacteristic
526C22×C4C23×C3211yescharacteristic
527C22×C4C23×C3211yescharacteristic
528C22×C4C23×C3211yescharacteristic
529C22×C4C23×C3211yescharacteristic
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—41no—
544C22⋊C4—41no—
545C22⋊C4—41no—
546C22⋊C4C32×D414yescomplemented
547C22⋊C4C32×D414yescomplemented
548C42—22no—
549C42—41no—
550C22×C3—28no—
551C22×C3—28no—
552C22×C3—28no—
553C22×C3—28no—
554C22×C3—28no—
555C22×C3—28no—
556C22×C3—28no—
557C22×C3—28no—
558C22×C3—28no—
559C22×C3—44no—
560C22×C3—44no—
561C22×C3—44no—
562C22×C3—44no—
563C22×C3—44no—
564C22×C3—44no—
565C22×C3—44no—
566C22×C3—44no—
567C22×C3—44no—
568C22×C3—44no—
569C22×C3—44no—
570C22×C3—44no—
571C22×C3—44no—
572C22×C3—44no—
573C22×C3—44no—
574C22×C3—44no—
575C22×C3—44no—
576C22×C3—44no—
577C22×C3—44no—
578C22×C3C22×C3×D414yes—
579C22×C3C22×C3×D414yes—
580C22×C3C2×C3×#4114yes—
581C22×C3C2×C3×#4114yes—
582C22×C3C2×C3×#4114yes—
583C22×C3C3×H(5,𝔽2)14yes—
584C22×C3C3×H(5,𝔽2)14yes—
585C3×C4—28no—
586C3×C4—28no—
587C3×C4—28no—
588C3×C4—28no—
589C3×C4—28no—
590C3×C4—28no—
591C3×C4—44no—
592C3×C4—44no—
593C3×C4—44no—
594C3×C4—44no—
595C3×C4—44no—
596C32#246411yescharacteristic, direct product factor, Sylow
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23C2×C32×D412yes—
623C23C2×C32×D412yes—
624C23C32×#4112yes—
625C23C24×C3211yescharacteristic
626D4—28no—
627D4—44no—
628D4—44no—
629D4—44no—
630D4—44no—
631D4—44no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4C2×C32×D412yes—
663C2×C4C2×C32×D412yes—
664C2×C4C2×C32×D412yes—
665C2×C4C2×C32×D412yes—
666C2×C4C32×#4112yes—
667C2×C4C32×#4112yes—
668C2×C3—48no—
669C2×C3—48no—
670C2×C3—48no—
671C2×C3—84no—
672C2×C3C3×#52514yes—
673C2×C3C3×#53214yes—
674C2×C3C3×#54014yes—
675C2×C3C3×D4214yes—
676C2×C3C3×#54614yes—
677C2×C3C3×#54614yes—
678C2×C3C3×#55314yes—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22C22×C32×D411yescharacteristic
708C22C22×C32×D411yescharacteristic
709C22C2×C32×#4111yescharacteristic
710C22C2×C32×#4111yescharacteristic
711C22C2×C32×#4111yescharacteristic
712C22C32×H(5,𝔽2)11yescharacteristic
713C22C32×H(5,𝔽2)11yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—22no—
719C4—22no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—41no—
725C3C3×#246414yesdirect product factor
726C2—42no—
727C2—42no—
728C2—42no—
729C2—81no—
730C2C32×#52511yescharacteristic
731C2C32×#53211yescharacteristic
732C2C32×#54011yescharacteristic
733C2C32×D4211yescharacteristic
734C2C32×#54611yescharacteristic
735C2C32×#54611yescharacteristic
736C2C32×#55311yescharacteristic
subgroupG/H
center, socleC23×C32C24
commutator, Frattini, cosocleC23C24×C32
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C32 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C32×#123C2semidirect
2. C2×C32×#121C2semidirect
3. C2×C32×#121C2semidirect
4. C2×C32×C4×D4C2semidirect
5. C32×#398C2semidirect
6. C32×#394C2semidirect
7. C32×#392C2semidirect
8. C32×#392C2semidirect
9. C32×#390C2semidirect
10. C32×#388C2semidirect
11. C32×#388C2semidirect
12. C32×#386C2semidirect
13. C32×#386C2semidirect
14. C32×#385C2semidirect
15. C32×C4×C22⋊C4C2semidirect
16. C3×#2464C3direct (N × H)
56. C2×C3×#123C2×C3semidirect
57. C2×C3×#121C2×C3semidirect
58. C2×C3×#121C2×C3semidirect
59. C2×C3×C4×D4C2×C3semidirect
60. C3×#398C2×C3semidirect
61. C3×#394C2×C3semidirect
62. C3×#392C2×C3semidirect
63. C3×#392C2×C3semidirect
64. C3×#390C2×C3semidirect
65. C3×#388C2×C3semidirect
66. C3×#388C2×C3semidirect
67. C3×#386C2×C3semidirect
68. C3×#386C2×C3semidirect
69. C3×#385C2×C3semidirect
70. C3×C4×C22⋊C4C2×C3semidirect
129. C32×C22⋊C4D4semidirect
130. C32×C22⋊C4D4semidirect
133. #2464C32direct (N × H)
244. C2×#123C2×C32semidirect
245. C2×#121C2×C32semidirect
246. C2×#121C2×C32semidirect
247. C2×C4×D4C2×C32semidirect
248. #398C2×C32semidirect
249. #394C2×C32semidirect
250. #392C2×C32semidirect
251. #392C2×C32semidirect
252. #390C2×C32semidirect
253. #388C2×C32semidirect
254. #388C2×C32semidirect
255. #386C2×C32semidirect
256. #386C2×C32semidirect
257. #385C2×C32semidirect
258. C4×C22⋊C4C2×C32semidirect
317. C3×C22⋊C4C3×D4semidirect
318. C3×C22⋊C4C3×D4semidirect
546. C22⋊C4C32×D4semidirect
547. C22⋊C4C32×D4semidirect
596. C32#2464direct (N × H)
725. C3C3×#2464direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1232
C2×C32×#1212
C2×C32×C4×D42
C32×#3982
C32×#3942
C32×#3922
C32×#3902
C32×#3882
C32×#3862
C32×#3852
C32×C4×C22⋊C42
C3×#24643