Finite Group Databasebeta

← C2×C4×#937 #10953599

Subgroups — C2×C4×#937 #10953599

Order 768.

8582 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C4×D3C211yesmaximal, characteristic, complemented
2C22×C3×C4×D4C211yesmaximal, characteristic, complemented
3C22×#937C211yesmaximal, characteristic
4C22×C4×#67C212yesmaximal, complemented
5C2×#5220C211yesmaximal, characteristic, complemented
6C2×C4×#217C211yesmaximal, characteristic, complemented
7C4×#937C2116yesmaximal, direct product factor
8C2×#4989C212yesmaximal, complemented
9C2×#4956C212yesmaximal, complemented
10C2×#4955C211yesmaximal, characteristic, complemented
11C2×#4946C211yesmaximal, characteristic, complemented
12C2×C4×(C2×D3)⋊C4C212yesmaximal, complemented
13C2×C4×#120—31nomaximal, Sylow
14C25×D3C2211yescharacteristic
15C23×C3×D4C2211yescharacteristic
16C24×C3×C4C2211yescharacteristic
17C24×C3×C4C2211yescharacteristic, complemented
18C23×#67C2212yes—
19C24×Dic3C2211yescharacteristic
20C23×C4×D3—28no—
21C23×C4×D3—216no—
22C23×C4×D3C2212yes—
23C23×C4×D3C2212yes—
24C23×C4×D3C2218yescomplemented
25C2×C3×C4×D4—28no—
26C2×C3×C4×D4C2218yescomplemented
27C22×C3×C4⋊C4C2211yescharacteristic, complemented
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic, complemented
30C22×C3×C42C2211yescharacteristic, complemented
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2212yescomplemented
34C2×#937C4116yesdirect product factor
35C2×#937C2218yes—
36C2×C4×#67—216no—
37C2×C4×#67C22116yescomplemented
38C22×(C2×D3)⋊C4C2212yes—
39C22×(C2×D3)⋊C4C2212yes—
40C22×(C2×D3)⋊C4C2212yes—
41C22×Dic3⋊C4C2212yescomplemented
42C22×C4×Dic3C2212yescomplemented
43#5220C2218yescomplemented
44C4×#217C2218yescomplemented
45C2×C3⋊#95C2212yescomplemented
46C2×C3⋊#95C2212yescomplemented
47C2×C3⋊#95C2212yescomplemented
48#4989C22116yescomplemented
49#4956C22116yescomplemented
50#4955C2218yescomplemented
51#4946C2218yescomplemented
52C4×(C2×D3)⋊C4C22116yescomplemented
53C25×C4—31no—
54C22×#120—31no—
55C22×C4×D4—32no—
56C22×C4×D4D311yescharacteristic, complemented
57C4×#120—316no—
58C2×#386—31no—
59C2×#386—32no—
60C2×#385—32no—
61C2×#385—31no—
62C2×#379—31no—
63C2×C4×C22⋊C4—32no—
64C2×C4×C22⋊C4—31no—
65C25×C3C2311yescharacteristic
66C25×C3C2311yescharacteristic
67C24×D3—24no—
68C24×D3—24no—
69C24×D3—28no—
70C24×D3—28no—
71C24×D3C2×C418yescomplemented
72C24×D3C2314yes—
73C24×D3C2312yes—
74C22×C3×D4—24no—
75C22×C3×D4—24no—
76C22×C3×D4C2×C418yescomplemented
77C22×C3×D4C2314yes—
78C23×C3×C4—28no—
79C23×C3×C4—28no—
80C23×C3×C4—24no—
81C23×C3×C4D418yescomplemented
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2314yes—
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2314yescomplemented
89C22×#67—28no—
90C22×#67—28no—
91C22×#67C2×C4116yescomplemented
92C22×#67C2318yes—
93C23×Dic3—24no—
94C23×Dic3—28no—
95C23×Dic3C2314yes—
96C23×Dic3C2312yes—
97C23×Dic3C2312yes—
98C23×Dic3C2312yes—
99C22×C4×D3—2128no—
100C22×C4×D3—28no—
101C22×C4×D3—28no—
102C22×C4×D3—28no—
103C22×C4×D3—28no—
104C22×C4×D3—232no—
105C22×C4×D3—28no—
106C22×C4×D3—264no—
107C22×C4×D3D4116yescomplemented
108C22×C4×D3C2318yes—
109C22×C4×D3C2318yes—
110C3×C4×D4—232no—
111C2×C3×C4⋊C4—24no—
112C2×C3×C4⋊C4C2314yescomplemented
113C2×C3×C22⋊C4—24no—
114C2×C3×C22⋊C4—24no—
115C2×C3×C22⋊C4C2314yes—
116C2×C3×C22⋊C4C2314yescomplemented
117C2×C3×C42—24no—
118C2×C3×C42C2314yescomplemented
119C2×#217—24no—
120C2×#217—28no—
121C2×#217C2×C418yescomplemented
122C2×#217C2314yes—
123C2×#217C2314yes—
124C2×#217C2318yescomplemented
125#937C2×C4164yesdirect product factor
126C4×#67—264no—
127C2×(C2×D3)⋊C4—28no—
128C2×(C2×D3)⋊C4—28no—
129C2×(C2×D3)⋊C4C2×C4116yescomplemented
130C2×(C2×D3)⋊C4C2318yes—
131C2×(C2×D3)⋊C4C2318yes—
132C2×(C2×D3)⋊C4C2318yes—
133C2×Dic3⋊C4—28no—
134C2×Dic3⋊C4C2318yescomplemented
135C2×C4×Dic3—28no—
136C2×C4×Dic3C2318yescomplemented
137C3⋊#95C2318yescomplemented
138C3⋊#95C2318yescomplemented
139C3⋊#95C2318yescomplemented
140C26—31no—
141C23×D4—32no—
142C23×D4C2×D311yescharacteristic
143C24×C4—32no—
144C24×C4—31no—
145C24×C4—32no—
146C24×C4—38no—
147C24×C4—616no—
148C24×C4—68no—
149C24×C4C2×D311yescharacteristic
150C24×C4C2×D311yescharacteristic, complemented
151C2×#120—316no—
152C2×#120—38no—
153C2×C4×D4—28no—
154C2×C4×D4—316no—
155C2×C4×D4—616no—
156C2×C4×D4C2×D318yescomplemented
157C22×C4⋊C4—32no—
158C22×C4⋊C4C2×D311yescharacteristic, complemented
159C22×C22⋊C4—31no—
160C22×C22⋊C4—32no—
161C22×C22⋊C4—32no—
162C22×C22⋊C4—31no—
163C22×C22⋊C4—32no—
164C22×C22⋊C4—32no—
165C22×C22⋊C4C2×D311yescharacteristic
166C22×C22⋊C4C2×D311yescharacteristic, complemented
167C22×C42—32no—
168C22×C42C2×D311yescharacteristic, complemented
169#386—38no—
170#386—316no—
171#385—316no—
172#385—38no—
173#379—38no—
174C4×C22⋊C4—38no—
175C4×C22⋊C4—316no—
176C2×#95—32no—
177C2×#95—32no—
178C2×#95—32no—
179C24×C3—24no—
180C24×C3—24no—
181C24×C3—24no—
182C24×C3—22no—
183C24×C3—24no—
184C24×C3—22no—
185C24×C3C22×C414yes—
186C24×C3C22×C414yescomplemented
187C24×C3C2×D414yes—
188C24×C3#4114yes—
189C24×C3C2412yes—
190C24×C3C2412yes—
191C24×C3C2411yescharacteristic
192C23×D3—232no—
193C23×D3—264no—
194C23×D3—232no—
195C23×D3—232no—
196C23×D3—24no—
197C23×D3—28no—
198C23×D3—24no—
199C23×D3—28no—
200C23×D3—24no—
201C23×D3—24no—
202C23×D3—264no—
203C23×D3—216no—
204C23×D3—216no—
205C23×D3C22×C418yes—
206C23×D3C22×C4116yescomplemented
207C23×D3C2×D418yes—
208C23×D3#4118yes—
209C23×D3C2414yes—
210C2×C3×D4—232no—
211C2×C3×D4—28no—
212C2×C3×D4—28no—
213C2×C3×D4C22×C4116yescomplemented
214C22×C3×C4—22no—
215C22×C3×C4—24no—
216C22×C3×C4—22no—
217C22×C3×C4—232no—
218C22×C3×C4—216no—
219C22×C3×C4—24no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—24no—
223C22×C3×C4—216no—
224C22×C3×C4—28no—
225C22×C3×C4—416no—
226C22×C3×C4C22×C414yescomplemented
227C22×C3×C4C2×D418yes—
228C22×C3×C4C2×D414yes—
229C22×C3×C4C2×D414yes—
230C22×C3×C4C2×D4116yescomplemented
231C22×C3×C4C2412yes—
232C22×C3×C4C2412yes—
233C22×C3×C4C2412yes—
234C22×C3×C4C2412yes—
235C22×C3×C4C2412yes—
236C2×#67—264no—
237C2×#67—216no—
238C2×#67—216no—
239C2×#67C22×C4132yescomplemented
240C22×Dic3—232no—
241C22×Dic3—24no—
242C22×Dic3—24no—
243C22×Dic3—28no—
244C22×Dic3—24no—
245C22×Dic3—24no—
246C22×Dic3—216no—
247C22×Dic3—24no—
248C22×Dic3—24no—
249C22×Dic3—24no—
250C22×Dic3C22×C418yescomplemented
251C22×Dic3C2×D418yes—
252C22×Dic3C2414yes—
253C22×Dic3C2414yes—
254C22×Dic3C2414yes—
255C2×C4×D3—264no—
256C2×C4×D3—2256no—
257C2×C4×D3—216no—
258C2×C4×D3—264no—
259C2×C4×D3—216no—
260C2×C4×D3—216no—
261C2×C4×D3—216no—
262C2×C4×D3—216no—
263C2×C4×D3C2×D4132yescomplemented
264C3×C4⋊C4—28no—
265C3×C22⋊C4—28no—
266C3×C22⋊C4—28no—
267C3×C42—28no—
268#217—28no—
269#217—216no—
270#217C22×C4116yescomplemented
271(C2×D3)⋊C4—216no—
272(C2×D3)⋊C4—216no—
273(C2×D3)⋊C4C22×C4132yescomplemented
274Dic3⋊C4—216no—
275C4×Dic3—216no—
276C25—32no—
277C25—38no—
278C25—34no—
279C25—68no—
280C25—68no—
281C25—64no—
282C25—64no—
283C25C22×D311yescharacteristic
284C25C22×D311yescharacteristic
285C22×D4—24no—
286C22×D4—24no—
287C22×D4—316no—
288C22×D4—38no—
289C22×D4—68no—
290C22×D4—68no—
291C22×D4C4×D318yescomplemented
292C22×D4C22×D314yes—
293C23×C4—28no—
294C23×C4—28no—
295C23×C4—24no—
296C23×C4—32no—
297C23×C4—32no—
298C23×C4—316no—
299C23×C4—38no—
300C23×C4—32no—
301C23×C4—34no—
302C23×C4—38no—
303C23×C4—68no—
304C23×C4—664no—
305C23×C4—68no—
306C23×C4—6128no—
307C23×C4—68no—
308C23×C4—64no—
309C23×C4—68no—
310C23×C4—68no—
311C23×C4—68no—
312C23×C4—632no—
313C23×C4#6718yescomplemented
314C23×C4C22×D311yescharacteristic
315C23×C4C22×D311yescharacteristic
316C23×C4C22×D311yescharacteristic
317C23×C4C22×D311yescharacteristic
318C23×C4C22×D314yes—
319C23×C4C22×D311yescharacteristic
320C23×C4C22×D314yescomplemented
321#120—364no—
322C4×D4—232no—
323C4×D4—664no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—38no—
326C2×C4⋊C4—68no—
327C2×C4⋊C4C22×D314yescomplemented
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—38no—
331C2×C22⋊C4—34no—
332C2×C22⋊C4—316no—
333C2×C22⋊C4—38no—
334C2×C22⋊C4—38no—
335C2×C22⋊C4—34no—
336C2×C22⋊C4—38no—
337C2×C22⋊C4—38no—
338C2×C22⋊C4—68no—
339C2×C22⋊C4—68no—
340C2×C22⋊C4—68no—
341C2×C22⋊C4—64no—
342C2×C22⋊C4C22×D314yes—
343C2×C22⋊C4C22×D314yescomplemented
344C2×C42—24no—
345C2×C42—38no—
346C2×C42—68no—
347C2×C42C22×D314yescomplemented
348#95—38no—
349#95—38no—
350#95—38no—
351C23×C3—216no—
352C23×C3—28no—
353C23×C3—28no—
354C23×C3—216no—
355C23×C3—24no—
356C23×C3—24no—
357C23×C3—216no—
358C23×C3—28no—
359C23×C3—24no—
360C23×C3—22no—
361C23×C3—24no—
362C23×C3—22no—
363C23×C3—44no—
364C23×C3—48no—
365C23×C3—44no—
366C23×C3C4×D4116yescomplemented
367C23×C3C23×C414yes—
368C23×C3C23×C412yes—
369C23×C3C23×C414yescomplemented
370C23×C3C22×D414yes—
371C23×C3C22×D414yes—
372C23×C3C22×D412yes—
373C23×C3C2×#4114yes—
374C23×C3C2×#4112yes—
375C23×C3C2×#4114yes—
376C23×C3C2511yescharacteristic
377C22×D3—232no—
378C22×D3—264no—
379C22×D3—232no—
380C22×D3—2256no—
381C22×D3—216no—
382C22×D3—216no—
383C22×D3—232no—
384C22×D3—216no—
385C22×D3—216no—
386C22×D3—216no—
387C22×D3—216no—
388C22×D3—24no—
389C22×D3—24no—
390C22×D3—24no—
391C22×D3—24no—
392C22×D3—264no—
393C22×D3C4×D4132yescomplemented
394C22×D3C23×C418yes—
395C22×D3C22×D418yes—
396C22×D3C2×#4118yes—
397C3×D4—232no—
398C2×C3×C4—28no—
399C2×C3×C4—28no—
400C2×C3×C4—22no—
401C2×C3×C4—24no—
402C2×C3×C4—22no—
403C2×C3×C4—232no—
404C2×C3×C4—24no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—24no—
408C2×C3×C4—44no—
409C2×C3×C4—44no—
410C2×C3×C4—416no—
411C2×C3×C4#120116yescomplemented
412C2×C3×C4C23×C414yescomplemented
413C2×C3×C4C22×D418yes—
414C2×C3×C4C22×D414yes—
415C2×C3×C4C22×D414yes—
416#67—264no—
417C2×Dic3—232no—
418C2×Dic3—216no—
419C2×Dic3—216no—
420C2×Dic3—24no—
421C2×Dic3—24no—
422C2×Dic3—24no—
423C2×Dic3—24no—
424C2×Dic3—24no—
425C2×Dic3—24no—
426C2×Dic3—24no—
427C2×Dic3—48no—
428C2×Dic3C23×C418yescomplemented
429C2×Dic3C22×D418yes—
430C4×D3—264no—
431C4×D3—264no—
432C24—24no—
433C24—24no—
434C24—22no—
435C24—24no—
436C24—24no—
437C24—22no—
438C24—38no—
439C24—38no—
440C24—38no—
441C24—34no—
442C24—316no—
443C24—616no—
444C24—616no—
445C24—664no—
446C24—632no—
447C24—664no—
448C24—632no—
449C24—632no—
450C24—68no—
451C24—64no—
452C24—64no—
453C24—64no—
454C24—68no—
455C24—64no—
456C24C2×C4×D314yes—
457C24C2×C4×D314yescomplemented
458C24#23514yes—
459C24C2×#6714yes—
460C24C23×D312yes—
461C24C23×D312yes—
462C24C23×D311yescharacteristic
463C2×D4—232no—
464C2×D4—28no—
465C2×D4—28no—
466C2×D4—332no—
467C2×D4—616no—
468C2×D4—616no—
469C2×D4—664no—
470C2×D4C2×C4×D3116yescomplemented
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—232no—
475C22×C4—216no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—216no—
481C22×C4—28no—
482C22×C4—38no—
483C22×C4—38no—
484C22×C4—34no—
485C22×C4—34no—
486C22×C4—332no—
487C22×C4—34no—
488C22×C4—416no—
489C22×C4—616no—
490C22×C4—616no—
491C22×C4—664no—
492C22×C4—6256no—
493C22×C4—616no—
494C22×C4—632no—
495C22×C4—64no—
496C22×C4—64no—
497C22×C4—64no—
498C22×C4—68no—
499C22×C4—64no—
500C22×C4—664no—
501C22×C4—616no—
502C22×C4—616no—
503C22×C4—616no—
504C22×C4—64no—
505C22×C4—64no—
506C22×C4—64no—
507C22×C4C2×C4×D314yescomplemented
508C22×C4D3×D418yes—
509C22×C4C2×#6714yes—
510C22×C4C2×#6714yes—
511C22×C4C2×#67116yescomplemented
512C22×C4C23×D312yes—
513C22×C4C23×D312yes—
514C22×C4C23×D312yes—
515C22×C4C23×D312yes—
516C22×C4C23×D312yes—
517C4⋊C4—28no—
518C4⋊C4—616no—
519C22⋊C4—28no—
520C22⋊C4—28no—
521C22⋊C4—316no—
522C22⋊C4—332no—
523C22⋊C4—616no—
524C22⋊C4—616no—
525C22⋊C4—616no—
526C22⋊C4—68no—
527C42—28no—
528C42—616no—
529C22×C3—28no—
530C22×C3—24no—
531C22×C3—24no—
532C22×C3—28no—
533C22×C3—232no—
534C22×C3—28no—
535C22×C3—24no—
536C22×C3—42no—
537C22×C3—44no—
538C22×C3—42no—
539C22×C3—416no—
540C22×C3C2×C4×D414yes—
541C22×C3C2×C4×D418yes—
542C22×C3C2×C4×D418yescomplemented
543C22×C3C2×#12014yes—
544C22×C3#52518yes—
545C22×C3#52514yes—
546C22×C3C24×C411yescharacteristic
547C22×C3C23×D412yes—
548C22×C3C23×D411yescharacteristic
549C22×C3C22×#4111yescharacteristic
550C22×C3C22×#4112yes—
551C2×D3—2128no—
552C2×D3—28no—
553C2×D3—28no—
554C2×D3—28no—
555C2×D3—28no—
556C2×D3—28no—
557C2×D3—28no—
558C2×D3—264no—
559C2×D3C2×C4×D4116yescomplemented
560C3×C4—24no—
561C3×C4—24no—
562C3×C4—42no—
563C3×C4—42no—
564C3×C4C2×#12018yescomplemented
565Dic3—28no—
566Dic3—28no—
567Dic3—44no—
568C23—24no—
569C23—24no—
570C23—28no—
571C23—216no—
572C23—216no—
573C23—28no—
574C23—22no—
575C23—24no—
576C23—24no—
577C23—22no—
578C23—28no—
579C23—216no—
580C23—38no—
581C23—38no—
582C23—38no—
583C23—332no—
584C23—44no—
585C23—48no—
586C23—44no—
587C23—664no—
588C23—632no—
589C23—664no—
590C23—6256no—
591C23—632no—
592C23—64no—
593C23—64no—
594C23—64no—
595C23—64no—
596C23—616no—
597C23—632no—
598C23—616no—
599C23—616no—
600C23—616no—
601C23—616no—
602C23—616no—
603C23C4×#67116yescomplemented
604C23C22×C4×D314yes—
605C23C22×C4×D312yes—
606C23C22×C4×D314yescomplemented
607C23C2×#23514yes—
608C23C2×#23512yes—
609C23C2×D3×D414yes—
610C23D3×#4114yes—
611C23C22×#6714yes—
612C23C22×#6712yes—
613C23C24×D311yescharacteristic
614D4—232no—
615D4—664no—
616C2×C4—22no—
617C2×C4—24no—
618C2×C4—22no—
619C2×C4—28no—
620C2×C4—28no—
621C2×C4—232no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—38no—
627C2×C4—38no—
628C2×C4—44no—
629C2×C4—44no—
630C2×C4—416no—
631C2×C4—664no—
632C2×C4—632no—
633C2×C4—64no—
634C2×C4—64no—
635C2×C4—64no—
636C2×C4—64no—
637C2×C4—616no—
638C2×C4—616no—
639C2×C4—664no—
640C2×C4—64no—
641C2×C4—64no—
642C2×C4—64no—
643C2×C4—128no—
644C2×C4#937116yesdirect product factor
645C2×C4C22×C4×D314yescomplemented
646C2×C4C2×D3×D418yes—
647C2×C4C22×#6714yes—
648C2×C4C22×#6714yes—
649C2×C3—28no—
650C2×C3—44no—
651C2×C3C4×#12018yescomplemented
652C2×C3C22×C4×D412yes—
653C2×C3C22×C4×D411yescharacteristic
654C2×C3C22×#12011yescharacteristic
655C2×C3C2×#52512yes—
656C2×C3C2×#52511yescharacteristic
657D3—216no—
658C22—28no—
659C22—28no—
660C22—24no—
661C22—232no—
662C22—24no—
663C22—28no—
664C22—24no—
665C22—316no—
666C22—44no—
667C22—42no—
668C22—416no—
669C22—42no—
670C22—6128no—
671C22—68no—
672C22—68no—
673C22—68no—
674C22—68no—
675C22—68no—
676C22—664no—
677C22—68no—
678C22C4×D3×D418yes—
679C22#554718yes—
680C22C2×C4×#6714yes—
681C22C2×C4×#6718yescomplemented
682C22C2×#93714yes—
683C22#582814yes—
684C22C23×C4×D311yescharacteristic
685C22C22×#23511yescharacteristic
686C22C22×D3×D412yes—
687C22C2×D3×#4112yes—
688C22C23×#6711yescharacteristic
689C4—24no—
690C4—24no—
691C4—42no—
692C4—42no—
693C4—68no—
694C4—68no—
695C4—124no—
696C4C2×#93718yesdirect product factor
697C3C2×C4×#12011yescharacteristic, complemented, Sylow
698C2—28no—
699C2—44no—
700C2—616no—
701C2C4×#93718yesdirect product factor
702C2C2×C4×D3×D412yes—
703C2C2×#554712yes—
704C2C22×C4×#6711yescharacteristic
705C2C22×#93711yescharacteristic
706C2C2×#582811yescharacteristic
subgroupG/H
centerC23×C4C22×D3
commutatorC22×C3C24×C4
FrattiniC23C24×D3
FittingC22×C3×C4×D4C2
socleC24×C3C24
prime radicalC22×#937C2
cosocleC23×C3C25
hypercenterC22×C4×D4D3
hypocenterC3C2×C4×#120
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C24×C4×D3C2semidirect
2. C22×C3×C4×D4C2semidirect
4. C22×C4×#67C2semidirect
5. C2×#5220C2semidirect
6. C2×C4×#217C2semidirect
7. C4×#937C2direct (N × H)
8. C2×#4989C2semidirect
9. C2×#4956C2semidirect
10. C2×#4955C2semidirect
11. C2×#4946C2semidirect
12. C2×C4×(C2×D3)⋊C4C2semidirect
17. C24×C3×C4C22semidirect
24. C23×C4×D3C22semidirect
26. C2×C3×C4×D4C22semidirect
27. C22×C3×C4⋊C4C22semidirect
29. C22×C3×C22⋊C4C22semidirect
30. C22×C3×C42C22semidirect
33. C22×#217C22semidirect
34. C2×#937C4direct (N × H)
37. C2×C4×#67C22semidirect
41. C22×Dic3⋊C4C22semidirect
42. C22×C4×Dic3C22semidirect
43. #5220C22semidirect
44. C4×#217C22semidirect
45. C2×C3⋊#95C22semidirect
46. C2×C3⋊#95C22semidirect
47. C2×C3⋊#95C22semidirect
48. #4989C22semidirect
49. #4956C22semidirect
50. #4955C22semidirect
51. #4946C22semidirect
52. C4×(C2×D3)⋊C4C22semidirect
56. C22×C4×D4D3semidirect
71. C24×D3C2×C4semidirect
76. C22×C3×D4C2×C4semidirect
81. C23×C3×C4D4semidirect
88. C23×C3×C4C23semidirect
91. C22×#67C2×C4semidirect
107. C22×C4×D3D4semidirect
112. C2×C3×C4⋊C4C23semidirect
116. C2×C3×C22⋊C4C23semidirect
118. C2×C3×C42C23semidirect
121. C2×#217C2×C4semidirect
124. C2×#217C23semidirect
125. #937C2×C4direct (N × H)
129. C2×(C2×D3)⋊C4C2×C4semidirect
134. C2×Dic3⋊C4C23semidirect
136. C2×C4×Dic3C23semidirect
137. C3⋊#95C23semidirect
138. C3⋊#95C23semidirect
139. C3⋊#95C23semidirect
150. C24×C4C2×D3semidirect
156. C2×C4×D4C2×D3semidirect
158. C22×C4⋊C4C2×D3semidirect
166. C22×C22⋊C4C2×D3semidirect
168. C22×C42C2×D3semidirect
186. C24×C3C22×C4semidirect
206. C23×D3C22×C4semidirect
213. C2×C3×D4C22×C4semidirect
226. C22×C3×C4C22×C4semidirect
230. C22×C3×C4C2×D4semidirect
239. C2×#67C22×C4semidirect
250. C22×Dic3C22×C4semidirect
263. C2×C4×D3C2×D4semidirect
270. #217C22×C4semidirect
273. (C2×D3)⋊C4C22×C4semidirect
291. C22×D4C4×D3semidirect
313. C23×C4#67semidirect
320. C23×C4C22×D3semidirect
327. C2×C4⋊C4C22×D3semidirect
343. C2×C22⋊C4C22×D3semidirect
347. C2×C42C22×D3semidirect
366. C23×C3C4×D4semidirect
369. C23×C3C23×C4semidirect
393. C22×D3C4×D4semidirect
411. C2×C3×C4#120semidirect
412. C2×C3×C4C23×C4semidirect
428. C2×Dic3C23×C4semidirect
457. C24C2×C4×D3semidirect
470. C2×D4C2×C4×D3semidirect
507. C22×C4C2×C4×D3semidirect
511. C22×C4C2×#67semidirect
542. C22×C3C2×C4×D4semidirect
559. C2×D3C2×C4×D4semidirect
564. C3×C4C2×#120semidirect
603. C23C4×#67semidirect
606. C23C22×C4×D3semidirect
644. C2×C4#937direct (N × H)
645. C2×C4C22×C4×D3semidirect
651. C2×C3C4×#120semidirect
681. C22C2×C4×#67semidirect
696. C4C2×#937direct (N × H)
697. C3C2×C4×#120semidirect
701. C2C4×#937direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C4×D32
C22×C3×C4×D42
C22×#9372
C22×C4×#672
C2×#52202
C2×C4×#2172
C4×#9372
C2×#49892
C2×#49562
C2×#49552
C2×#49462
C2×C4×(C2×D3)⋊C42
C2×C4×#1203