Finite Group Databasebeta

← C22×#5620 #11702054

Subgroups — C22×#5620 #11702054

Order 768.

9606 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
1C22×C3×#121C211yesmaximal, characteristic, complemented
2C22×#938C211yesmaximal, characteristic, complemented
3C22×#937C211yesmaximal, characteristic, complemented
4C22×#937C211yesmaximal, characteristic, complemented
5C22×#940C211yesmaximal, characteristic, complemented
6C22×#939C211yesmaximal, characteristic, complemented
7C22×#939C211yesmaximal, characteristic, complemented
8C22×#929C211yesmaximal, characteristic, complemented
9C22×#930C211yesmaximal, characteristic, complemented
10C2×#5620C2148yesmaximal, direct product factor
11C22×#894C211yesmaximal, characteristic, complemented
12C22×#898C211yesmaximal, characteristic, complemented
13C22×#884C211yesmaximal, characteristic, complemented
14C22×#882C211yesmaximal, characteristic, complemented
15C22×#879C211yesmaximal, characteristic, complemented
16C22×#886C211yesmaximal, characteristic, complemented
17C22×#560—31nomaximal, Sylow
18C25×D3C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C23×C3×D4C2211yescharacteristic
21C23×C3×D4C2211yescharacteristic, complemented
22C24×C3×C4C2211yescharacteristic, complemented
23C23×#67C2211yescharacteristic
24C23×#67C2211yescharacteristic
25C23×#67C2211yescharacteristic
26C23×#67C2211yescharacteristic
27C23×#67C2211yescharacteristic
28C23×#67C2211yescharacteristic, complemented
29C23×#67C2211yescharacteristic, complemented
30C24×Dic3C2211yescharacteristic, complemented
31C23×D12C2211yescharacteristic
32C23×D12C2211yescharacteristic
33C23×C4×D3C2211yescharacteristic, complemented
34C2×C3×#121C22124yescomplemented
35C22×C3×C4⋊C4C2211yescharacteristic, complemented
36C22×C3×C22⋊C4C2211yescharacteristic
37C22×C3×C22⋊C4C2211yescharacteristic, complemented
38C22×#217C2211yescharacteristic
39C22×#217C2211yescharacteristic
40C22×#217C2211yescharacteristic, complemented
41C2×#940C22124yescomplemented
42C2×#939C22124yescomplemented
43C2×#939C22124yescomplemented
44C2×#938C22124yescomplemented
45C2×#937C22124yescomplemented
46C2×#937C22124yescomplemented
47C2×#930C22124yescomplemented
48C2×#929C22124yescomplemented
49C22×(C2×D3)⋊C4C2211yescharacteristic
50C22×(C2×D3)⋊C4C2211yescharacteristic
51C22×(C2×D3)⋊C4C2211yescharacteristic
52C22×(C2×D3)⋊C4C2211yescharacteristic
53C22×(C2×D3)⋊C4C2211yescharacteristic
54C22×(C2×D3)⋊C4C2211yescharacteristic
55C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
56C22×C4⋊Dic3C2211yescharacteristic, complemented
57C22×C4⋊Dic3C2211yescharacteristic, complemented
58C22×Dic3⋊C4C2211yescharacteristic, complemented
59C22×Dic3⋊C4C2211yescharacteristic, complemented
60C22×Dic3⋊C4C2211yescharacteristic, complemented
61C22×C4×Dic3C2211yescharacteristic, complemented
62#5620C221256yesdirect product factor
63C2×#898C22124yescomplemented
64C2×#894C22124yescomplemented
65C2×#886C22124yescomplemented
66C2×#884C22124yescomplemented
67C2×#882C22124yescomplemented
68C2×#879C22124yescomplemented
69C2×#560—348no—
70C22×#127—31no—
71C22×#126—31no—
72C22×#126—31no—
73C22×#123—31no—
74C22×#123—31no—
75C22×#123—31no—
76C22×#121—31no—
77C22×#121—31no—
78C22×#121—31no—
79C22×#121—31no—
80C22×#121—31no—
81C22×#121D311yescharacteristic, complemented
82C22×#120—31no—
83C22×#120—31no—
84C22×#120—31no—
85C25×C3C2311yescharacteristic
86C25×C3C2311yescharacteristic
87C25×C3C2311yescharacteristic
88C24×D3—44no—
89C24×D3—44no—
90C24×D3—44no—
91C24×D3C2311yescharacteristic
92C24×D3C2311yescharacteristic
93C24×D3C2311yescharacteristic
94C24×D3C23112yes—
95C22×C3×D4—44no—
96C22×C3×D4—44no—
97C22×C3×D4—44no—
98C22×C3×D4C23112yes—
99C22×C3×D4C23112yes—
100C22×C3×D4C23112yescomplemented
101C23×C3×C4—44no—
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C23112yescomplemented
107C22×#67—44no—
108C22×#67—44no—
109C22×#67—44no—
110C22×#67—44no—
111C22×#67—44no—
112C22×#67—44no—
113C22×#67—44no—
114C22×#67C23112yes—
115C22×#67C23112yes—
116C22×#67C23112yes—
117C22×#67C23112yes—
118C22×#67C23112yes—
119C22×#67C23112yescomplemented
120C22×#67C23112yescomplemented
121C23×Dic3—44no—
122C23×Dic3C2311yescharacteristic
123C23×Dic3C2311yescharacteristic
124C23×Dic3C2311yescharacteristic
125C23×Dic3C2311yescharacteristic
126C23×Dic3C2311yescharacteristic
127C23×Dic3C23112yescomplemented
128C22×D12—44no—
129C22×D12—44no—
130C22×D12C23112yes—
131C22×D12C23112yes—
132C22×C4×D3—44no—
133C22×C4×D3C23112yescomplemented
134C3×#121C23164yescomplemented
135C2×C3×C4⋊C4C23112yescomplemented
136C2×C3×C22⋊C4C23112yes—
137C2×C3×C22⋊C4C23112yescomplemented
138C2×#217C23112yes—
139C2×#217C23112yes—
140C2×#217C23112yescomplemented
141#940C23164yescomplemented
142#939C23164yescomplemented
143#939C23164yescomplemented
144#938C23164yescomplemented
145#937C23164yescomplemented
146#937C23164yescomplemented
147#930C23164yescomplemented
148#929C23164yescomplemented
149C2×(C2×D3)⋊C4C23112yes—
150C2×(C2×D3)⋊C4C23112yes—
151C2×(C2×D3)⋊C4C23112yes—
152C2×(C2×D3)⋊C4C23112yes—
153C2×(C2×D3)⋊C4C23112yes—
154C2×(C2×D3)⋊C4C23112yes—
155C2×(C2×D3)⋊C4C23112yescomplemented
156C2×C4⋊Dic3C23112yescomplemented
157C2×C4⋊Dic3C23112yescomplemented
158C2×Dic3⋊C4C23112yescomplemented
159C2×Dic3⋊C4C23112yescomplemented
160C2×Dic3⋊C4C23112yescomplemented
161C2×C4×Dic3C23112yescomplemented
162#898C23164yescomplemented
163#894C23164yescomplemented
164#886C23164yescomplemented
165#884C23164yescomplemented
166#882C23164yescomplemented
167#879C23164yescomplemented
168C26—31no—
169C23×D4—31no—
170C23×D4—31no—
171C23×D4—31no—
172C23×D4—31no—
173C23×D4—31no—
174C23×D4—31no—
175C23×D4—31no—
176C23×D4—31no—
177C23×D4—31no—
178C23×D4C2×D311yescharacteristic
179C23×D4C2×D311yescharacteristic
180C23×D4C2×D311yescharacteristic, complemented
181C24×C4—31no—
182C24×C4—31no—
183C24×C4C2×D311yescharacteristic, complemented
184#560—3256no—
185C2×#127—324no—
186C2×#126—324no—
187C2×#126—324no—
188C2×#123—324no—
189C2×#123—324no—
190C2×#123—324no—
191C2×#121—324no—
192C2×#121—324no—
193C2×#121—324no—
194C2×#121—324no—
195C2×#121—324no—
196C2×#121C2×D3124yescomplemented
197C2×#120—324no—
198C2×#120—324no—
199C2×#120—324no—
200C22×C4⋊C4—31no—
201C22×C4⋊C4—31no—
202C22×C4⋊C4—31no—
203C22×C4⋊C4—31no—
204C22×C4⋊C4—31no—
205C22×C4⋊C4C2×D311yescharacteristic, complemented
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C22⋊C4—31no—
212C22×C22⋊C4—31no—
213C22×C22⋊C4—31no—
214C22×C22⋊C4—31no—
215C22×C22⋊C4—31no—
216C22×C22⋊C4C2×D311yescharacteristic
217C22×C22⋊C4C2×D311yescharacteristic, complemented
218C22×C42—31no—
219C24×C3—24no—
220C24×C3—24no—
221C24×C3—24no—
222C24×C3—24no—
223C24×C3—24no—
224C24×C3—24no—
225C24×C3—24no—
226C24×C3—24no—
227C24×C3—24no—
228C24×C3C2416yes—
229C24×C3C2416yes—
230C24×C3C2416yes—
231C24×C3C2411yescharacteristic
232C23×D3—24no—
233C23×D3—24no—
234C23×D3—24no—
235C23×D3—24no—
236C23×D3—24no—
237C23×D3—24no—
238C23×D3—24no—
239C23×D3—24no—
240C23×D3—24no—
241C23×D3—424no—
242C23×D3—424no—
243C23×D3—424no—
244C23×D3—464no—
245C23×D3C2416yes—
246C23×D3C2416yes—
247C23×D3C2416yes—
248C23×D3C24116yes—
249C2×C3×D4—424no—
250C2×C3×D4—424no—
251C2×C3×D4—424no—
252C2×C3×D4C24116yes—
253C2×C3×D4C24116yes—
254C2×C3×D4C24116yescomplemented
255C22×C3×C4—24no—
256C22×C3×C4—24no—
257C22×C3×C4—24no—
258C22×C3×C4—24no—
259C22×C3×C4—424no—
260C22×C3×C4C2416yes—
261C22×C3×C4C2416yes—
262C22×C3×C4C2416yes—
263C22×C3×C4C2416yes—
264C22×C3×C4C24116yescomplemented
265C2×#67—424no—
266C2×#67—424no—
267C2×#67—424no—
268C2×#67—424no—
269C2×#67—424no—
270C2×#67—424no—
271C2×#67—424no—
272C2×#67C24116yes—
273C2×#67C24116yes—
274C2×#67C24116yes—
275C2×#67C24116yes—
276C2×#67C24116yes—
277C2×#67C24116yescomplemented
278C2×#67C24116yescomplemented
279C22×Dic3—24no—
280C22×Dic3—24no—
281C22×Dic3—24no—
282C22×Dic3—24no—
283C22×Dic3—24no—
284C22×Dic3—424no—
285C22×Dic3C2416yes—
286C22×Dic3C2416yes—
287C22×Dic3C2416yes—
288C22×Dic3C2416yes—
289C22×Dic3C2416yes—
290C22×Dic3C24116yescomplemented
291C2×D12—424no—
292C2×D12—424no—
293C2×D12C24116yes—
294C2×D12C24116yes—
295C2×C4×D3—424no—
296C2×C4×D3C24116yescomplemented
297C3×C4⋊C4C24116yescomplemented
298C3×C22⋊C4C24116yes—
299C3×C22⋊C4C24116yescomplemented
300#217C24116yes—
301#217C24116yes—
302#217C24116yescomplemented
303(C2×D3)⋊C4C24116yes—
304(C2×D3)⋊C4C24116yes—
305(C2×D3)⋊C4C24116yes—
306(C2×D3)⋊C4C24116yes—
307(C2×D3)⋊C4C24116yes—
308(C2×D3)⋊C4C24116yes—
309(C2×D3)⋊C4C24116yescomplemented
310C4⋊Dic3C24116yescomplemented
311C4⋊Dic3C24116yescomplemented
312Dic3⋊C4C24116yescomplemented
313Dic3⋊C4C24116yescomplemented
314Dic3⋊C4C24116yescomplemented
315C4×Dic3C24116yescomplemented
316C25—31no—
317C25—31no—
318C25—31no—
319C25—312no—
320C25—124no—
321C25—124no—
322C25—124no—
323C25C22×D311yescharacteristic
324C25C22×D311yescharacteristic
325C25C22×D311yescharacteristic
326C22×D4—312no—
327C22×D4—312no—
328C22×D4—312no—
329C22×D4—312no—
330C22×D4—312no—
331C22×D4—312no—
332C22×D4—312no—
333C22×D4—312no—
334C22×D4—312no—
335C22×D4—44no—
336C22×D4—44no—
337C22×D4—44no—
338C22×D4—124no—
339C22×D4—124no—
340C22×D4—124no—
341C22×D4—124no—
342C22×D4—124no—
343C22×D4—124no—
344C22×D4—124no—
345C22×D4—124no—
346C22×D4—124no—
347C22×D4C22×D3112yes—
348C22×D4C22×D3112yes—
349C22×D4C22×D3112yescomplemented
350C23×C4—31no—
351C23×C4—31no—
352C23×C4—31no—
353C23×C4—31no—
354C23×C4—31no—
355C23×C4—312no—
356C23×C4—312no—
357C23×C4—44no—
358C23×C4—124no—
359C23×C4—124no—
360C23×C4C22×D311yescharacteristic
361C23×C4C22×D311yescharacteristic
362C23×C4C22×D311yescharacteristic
363C23×C4C22×D311yescharacteristic
364C23×C4C22×D3112yescomplemented
365#127—364no—
366#126—364no—
367#126—364no—
368#123—364no—
369#123—364no—
370#123—364no—
371#121—364no—
372#121—364no—
373#121—364no—
374#121—364no—
375#121—364no—
376#121C22×D3164yescomplemented
377#120—364no—
378#120—364no—
379#120—364no—
380C2×C4⋊C4—312no—
381C2×C4⋊C4—312no—
382C2×C4⋊C4—312no—
383C2×C4⋊C4—312no—
384C2×C4⋊C4—312no—
385C2×C4⋊C4C22×D3112yescomplemented
386C2×C22⋊C4—312no—
387C2×C22⋊C4—312no—
388C2×C22⋊C4—312no—
389C2×C22⋊C4—312no—
390C2×C22⋊C4—312no—
391C2×C22⋊C4—312no—
392C2×C22⋊C4—312no—
393C2×C22⋊C4—312no—
394C2×C22⋊C4—312no—
395C2×C22⋊C4—312no—
396C2×C22⋊C4C22×D3112yes—
397C2×C22⋊C4C22×D3112yescomplemented
398C2×C42—312no—
399C23×C3—212no—
400C23×C3—212no—
401C23×C3—212no—
402C23×C3—212no—
403C23×C3—212no—
404C23×C3—212no—
405C23×C3—212no—
406C23×C3—212no—
407C23×C3—212no—
408C23×C3—416no—
409C23×C3—416no—
410C23×C3—416no—
411C23×C3H(5,𝔽2)14yes—
412C23×C3H(5,𝔽2)14yes—
413C23×C3H(5,𝔽2)14yes—
414C23×C3C2514yes—
415C23×C3C2514yes—
416C23×C3C2514yes—
417C23×C3C2513yes—
418C22×D3—212no—
419C22×D3—212no—
420C22×D3—212no—
421C22×D3—212no—
422C22×D3—212no—
423C22×D3—212no—
424C22×D3—212no—
425C22×D3—212no—
426C22×D3—212no—
427C22×D3—416no—
428C22×D3—416no—
429C22×D3—416no—
430C22×D3—4192no—
431C22×D3—416no—
432C22×D3—416no—
433C22×D3—416no—
434C22×D3C2514yes—
435C22×D3C2514yes—
436C22×D3C2514yes—
437C3×D4—416no—
438C3×D4—416no—
439C3×D4—416no—
440C2×C3×C4—212no—
441C2×C3×C4—212no—
442C2×C3×C4—212no—
443C2×C3×C4—212no—
444C2×C3×C4—416no—
445C2×C3×C4C2514yes—
446C2×C3×C4C2514yes—
447C2×C3×C4C2514yes—
448C2×C3×C4C2514yes—
449#67—416no—
450#67—416no—
451#67—416no—
452#67—416no—
453#67—416no—
454#67—416no—
455#67—416no—
456C2×Dic3—212no—
457C2×Dic3—212no—
458C2×Dic3—212no—
459C2×Dic3—212no—
460C2×Dic3—212no—
461C2×Dic3—416no—
462C2×Dic3C2514yes—
463C2×Dic3C2514yes—
464C2×Dic3C2514yes—
465C2×Dic3C2514yes—
466C2×Dic3C2514yes—
467D12—416no—
468D12—416no—
469C4×D3—416no—
470C24—24no—
471C24—24no—
472C24—24no—
473C24—24no—
474C24—24no—
475C24—24no—
476C24—24no—
477C24—24no—
478C24—24no—
479C24—36no—
480C24—36no—
481C24—36no—
482C24—316no—
483C24—64no—
484C24—64no—
485C24—64no—
486C24—64no—
487C24—64no—
488C24—64no—
489C24—64no—
490C24—64no—
491C24—64no—
492C24—1224no—
493C24—1224no—
494C24—1224no—
495C24—1264no—
496C24C23×D316yes—
497C24C23×D316yes—
498C24C23×D316yes—
499C24C23×D311yescharacteristic
500C2×D4—316no—
501C2×D4—316no—
502C2×D4—316no—
503C2×D4—316no—
504C2×D4—316no—
505C2×D4—316no—
506C2×D4—316no—
507C2×D4—316no—
508C2×D4—316no—
509C2×D4—424no—
510C2×D4—424no—
511C2×D4—424no—
512C2×D4—1224no—
513C2×D4—1224no—
514C2×D4—1224no—
515C2×D4—1224no—
516C2×D4—1224no—
517C2×D4—1224no—
518C2×D4—1224no—
519C2×D4—1224no—
520C2×D4—1224no—
521C2×D4C23×D3116yes—
522C2×D4C23×D3116yes—
523C2×D4C23×D3116yescomplemented
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—36no—
529C22×C4—36no—
530C22×C4—36no—
531C22×C4—36no—
532C22×C4—36no—
533C22×C4—316no—
534C22×C4—316no—
535C22×C4—424no—
536C22×C4—64no—
537C22×C4—64no—
538C22×C4—64no—
539C22×C4—64no—
540C22×C4—64no—
541C22×C4—1224no—
542C22×C4—1224no—
543C22×C4C23×D316yes—
544C22×C4C23×D316yes—
545C22×C4C23×D316yes—
546C22×C4C23×D316yes—
547C22×C4C23×D3116yescomplemented
548C4⋊C4—316no—
549C4⋊C4—316no—
550C4⋊C4—316no—
551C4⋊C4—316no—
552C4⋊C4—316no—
553C4⋊C4C23×D3116yescomplemented
554C22⋊C4—316no—
555C22⋊C4—316no—
556C22⋊C4—316no—
557C22⋊C4—316no—
558C22⋊C4—316no—
559C22⋊C4—316no—
560C22⋊C4—316no—
561C22⋊C4—316no—
562C22⋊C4—316no—
563C22⋊C4—316no—
564C22⋊C4C23×D3116yes—
565C22⋊C4C23×D3116yescomplemented
566C42—316no—
567C22×C3—24no—
568C22×C3—24no—
569C22×C3—24no—
570C22×C3—24no—
571C22×C3—24no—
572C22×C3—24no—
573C22×C3—24no—
574C22×C3—24no—
575C22×C3—24no—
576C22×C3—424no—
577C22×C3—424no—
578C22×C3—424no—
579C22×C3#560116yescomplemented
580C22×C3C2×H(5,𝔽2)16yes—
581C22×C3C2×H(5,𝔽2)16yes—
582C22×C3C2×H(5,𝔽2)16yes—
583C22×C3C2611yescharacteristic
584C2×D3—24no—
585C2×D3—24no—
586C2×D3—24no—
587C2×D3—24no—
588C2×D3—24no—
589C2×D3—24no—
590C2×D3—24no—
591C2×D3—24no—
592C2×D3—24no—
593C2×D3—464no—
594C2×D3—424no—
595C2×D3—424no—
596C2×D3—424no—
597C3×C4—24no—
598C3×C4—24no—
599C3×C4—24no—
600C3×C4—24no—
601Dic3—24no—
602Dic3—24no—
603Dic3—24no—
604Dic3—24no—
605Dic3—24no—
606C23—212no—
607C23—212no—
608C23—212no—
609C23—212no—
610C23—212no—
611C23—212no—
612C23—212no—
613C23—212no—
614C23—212no—
615C23—34no—
616C23—34no—
617C23—34no—
618C23—416no—
619C23—416no—
620C23—416no—
621C23—612no—
622C23—612no—
623C23—612no—
624C23—612no—
625C23—612no—
626C23—612no—
627C23—612no—
628C23—612no—
629C23—612no—
630C23—1216no—
631C23—1216no—
632C23—1216no—
633C23—12192no—
634C23—1216no—
635C23—1216no—
636C23—1216no—
637C23#100414yes—
638C23#100414yes—
639C23#100914yes—
640C23C24×D314yes—
641C23C24×D314yes—
642C23C24×D314yes—
643C23C24×D313yes—
644D4—416no—
645D4—416no—
646D4—416no—
647D4—1216no—
648D4—1216no—
649D4—1216no—
650D4—1216no—
651D4—1216no—
652D4—1216no—
653D4—1216no—
654D4—1216no—
655D4—1216no—
656C2×C4—212no—
657C2×C4—212no—
658C2×C4—212no—
659C2×C4—212no—
660C2×C4—34no—
661C2×C4—34no—
662C2×C4—34no—
663C2×C4—34no—
664C2×C4—34no—
665C2×C4—416no—
666C2×C4—612no—
667C2×C4—612no—
668C2×C4—612no—
669C2×C4—612no—
670C2×C4—612no—
671C2×C4—1216no—
672C2×C4—1216no—
673C2×C4C24×D314yes—
674C2×C4C24×D314yes—
675C2×C4C24×D314yes—
676C2×C4C24×D314yes—
677C2×C3—44no—
678C2×C3—44no—
679C2×C3—44no—
680C2×C3C2×#560112yescomplemented
681C2×C3C22×H(5,𝔽2)11yescharacteristic
682C2×C3C22×H(5,𝔽2)11yescharacteristic
683C2×C3C22×H(5,𝔽2)11yescharacteristic
684D3—44no—
685D3—44no—
686D3—44no—
687C22—24no—
688C22—24no—
689C22—24no—
690C22—24no—
691C22—24no—
692C22—24no—
693C22—24no—
694C22—24no—
695C22—24no—
696C22—424no—
697C22—424no—
698C22—424no—
699C22—64no—
700C22—64no—
701C22—64no—
702C22—64no—
703C22—64no—
704C22—64no—
705C22—64no—
706C22—64no—
707C22—64no—
708C22—1264no—
709C22—1224no—
710C22—1224no—
711C22—1224no—
712C22#5620116yesdirect product factor
713C22C2×#100416yes—
714C22C2×#100416yes—
715C22C2×#100916yes—
716C22C25×D311yescharacteristic
717C4—24no—
718C4—24no—
719C4—24no—
720C4—24no—
721C4—64no—
722C4—64no—
723C4—64no—
724C4—64no—
725C4—64no—
726C3C22×#56011yescharacteristic, complemented, Sylow
727C2—44no—
728C2—44no—
729C2—44no—
730C2—124no—
731C2—124no—
732C2—124no—
733C2C2×#5620112yesdirect product factor
734C2C22×#100411yescharacteristic
735C2C22×#100411yescharacteristic
736C2C22×#100911yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC22×C3×#121C2
socleC24×C3C24
hypercenterC22×#121D3
hypocenterC3C22×#560
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×C3×#121C2semidirect
2. C22×#938C2semidirect
3. C22×#937C2semidirect
4. C22×#937C2semidirect
5. C22×#940C2semidirect
6. C22×#939C2semidirect
7. C22×#939C2semidirect
8. C22×#929C2semidirect
9. C22×#930C2semidirect
10. C2×#5620C2direct (N × H)
11. C22×#894C2semidirect
12. C22×#898C2semidirect
13. C22×#884C2semidirect
14. C22×#882C2semidirect
15. C22×#879C2semidirect
16. C22×#886C2semidirect
21. C23×C3×D4C22semidirect
22. C24×C3×C4C22semidirect
28. C23×#67C22semidirect
29. C23×#67C22semidirect
30. C24×Dic3C22semidirect
33. C23×C4×D3C22semidirect
34. C2×C3×#121C22semidirect
35. C22×C3×C4⋊C4C22semidirect
37. C22×C3×C22⋊C4C22semidirect
40. C22×#217C22semidirect
41. C2×#940C22semidirect
42. C2×#939C22semidirect
43. C2×#939C22semidirect
44. C2×#938C22semidirect
45. C2×#937C22semidirect
46. C2×#937C22semidirect
47. C2×#930C22semidirect
48. C2×#929C22semidirect
55. C22×(C2×D3)⋊C4C22semidirect
56. C22×C4⋊Dic3C22semidirect
57. C22×C4⋊Dic3C22semidirect
58. C22×Dic3⋊C4C22semidirect
59. C22×Dic3⋊C4C22semidirect
60. C22×Dic3⋊C4C22semidirect
61. C22×C4×Dic3C22semidirect
62. #5620C22direct (N × H)
63. C2×#898C22semidirect
64. C2×#894C22semidirect
65. C2×#886C22semidirect
66. C2×#884C22semidirect
67. C2×#882C22semidirect
68. C2×#879C22semidirect
81. C22×#121D3semidirect
100. C22×C3×D4C23semidirect
106. C23×C3×C4C23semidirect
119. C22×#67C23semidirect
120. C22×#67C23semidirect
127. C23×Dic3C23semidirect
133. C22×C4×D3C23semidirect
134. C3×#121C23semidirect
135. C2×C3×C4⋊C4C23semidirect
137. C2×C3×C22⋊C4C23semidirect
140. C2×#217C23semidirect
141. #940C23semidirect
142. #939C23semidirect
143. #939C23semidirect
144. #938C23semidirect
145. #937C23semidirect
146. #937C23semidirect
147. #930C23semidirect
148. #929C23semidirect
155. C2×(C2×D3)⋊C4C23semidirect
156. C2×C4⋊Dic3C23semidirect
157. C2×C4⋊Dic3C23semidirect
158. C2×Dic3⋊C4C23semidirect
159. C2×Dic3⋊C4C23semidirect
160. C2×Dic3⋊C4C23semidirect
161. C2×C4×Dic3C23semidirect
162. #898C23semidirect
163. #894C23semidirect
164. #886C23semidirect
165. #884C23semidirect
166. #882C23semidirect
167. #879C23semidirect
180. C23×D4C2×D3semidirect
183. C24×C4C2×D3semidirect
196. C2×#121C2×D3semidirect
205. C22×C4⋊C4C2×D3semidirect
217. C22×C22⋊C4C2×D3semidirect
254. C2×C3×D4C24semidirect
264. C22×C3×C4C24semidirect
277. C2×#67C24semidirect
278. C2×#67C24semidirect
290. C22×Dic3C24semidirect
296. C2×C4×D3C24semidirect
297. C3×C4⋊C4C24semidirect
299. C3×C22⋊C4C24semidirect
302. #217C24semidirect
309. (C2×D3)⋊C4C24semidirect
310. C4⋊Dic3C24semidirect
311. C4⋊Dic3C24semidirect
312. Dic3⋊C4C24semidirect
313. Dic3⋊C4C24semidirect
314. Dic3⋊C4C24semidirect
315. C4×Dic3C24semidirect
349. C22×D4C22×D3semidirect
364. C23×C4C22×D3semidirect
376. #121C22×D3semidirect
385. C2×C4⋊C4C22×D3semidirect
397. C2×C22⋊C4C22×D3semidirect
523. C2×D4C23×D3semidirect
547. C22×C4C23×D3semidirect
553. C4⋊C4C23×D3semidirect
565. C22⋊C4C23×D3semidirect
579. C22×C3#560semidirect
680. C2×C3C2×#560semidirect
712. C22#5620direct (N × H)
726. C3C22×#560semidirect
733. C2C2×#5620direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1212
C22×#9382
C22×#9372
C22×#9402
C22×#9392
C22×#9292
C22×#9302
C2×#56202
C22×#8942
C22×#8982
C22×#8842
C22×#8822
C22×#8792
C22×#8862
C22×#5603