Finite Group Databasebeta

← C22×#5657 #11701913

Subgroups — C22×#5657 #11701913

Order 768.

9566 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#123C211yesmaximal, characteristic, complemented
2C22×#938C211yesmaximal, characteristic, complemented
3C22×#937C211yesmaximal, characteristic, complemented
4C22×#930C211yesmaximal, characteristic, complemented
5C22×C4×#67C211yesmaximal, characteristic, complemented
6C2×#5657C2148yesmaximal, direct product factor
7C22×#894C211yesmaximal, characteristic, complemented
8C22×#897C211yesmaximal, characteristic, complemented
9C22×#898C211yesmaximal, characteristic, complemented
10C22×#893C211yesmaximal, characteristic, complemented
11C22×#884C211yesmaximal, characteristic, complemented
12C22×#882C211yesmaximal, characteristic, complemented
13C22×D3×C22⋊C4C211yesmaximal, characteristic, complemented
14C22×#879C211yesmaximal, characteristic, complemented
15C22×#885C211yesmaximal, characteristic, complemented
16C22×#885C211yesmaximal, characteristic, complemented
17C22×#538—31nomaximal, Sylow
18C25×D3C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C24×C3×C4C2211yescharacteristic, complemented
21C23×#67C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C23×#67C2211yescharacteristic
24C23×#67C2211yescharacteristic, complemented
25C23×D12C2211yescharacteristic
26C23×D12C2211yescharacteristic
27C23×C4×D3C2211yescharacteristic
28C23×C4×D3C2211yescharacteristic
29C23×C4×D3C2211yescharacteristic, complemented
30C23×Dic6C2211yescharacteristic, complemented
31C2×C3×#123C22124yescomplemented
32C22×C3×C4⋊C4C2211yescharacteristic, complemented
33C22×C3×C4⋊C4C2211yescharacteristic, complemented
34C22×C3×C22⋊C4C2211yescharacteristic
35C22×C3×C22⋊C4C2211yescharacteristic
36C22×C3×C22⋊C4C2211yescharacteristic, complemented
37C22×#217C2211yescharacteristic
38C22×#217C2211yescharacteristic
39C22×#217C2211yescharacteristic, complemented
40C2×#938C22124yescomplemented
41C2×#937C22124yescomplemented
42C2×#930C22124yescomplemented
43C2×C4×#67C22124yescomplemented
44C22×(C2×D3)⋊C4C2211yescharacteristic
45C22×(C2×D3)⋊C4C2211yescharacteristic
46C22×(C2×D3)⋊C4C2211yescharacteristic
47C22×(C2×D3)⋊C4C2211yescharacteristic
48C22×(C2×D3)⋊C4C2211yescharacteristic
49C22×(C2×D3)⋊C4C2211yescharacteristic
50C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
52C22×C4⋊Dic3C2211yescharacteristic, complemented
53C22×C4⋊Dic3C2211yescharacteristic, complemented
54C22×Dic3⋊C4C2211yescharacteristic, complemented
55C22×Dic3⋊C4C2211yescharacteristic, complemented
56C22×C4×Dic3C2211yescharacteristic, complemented
57C22×C4×Dic3C2211yescharacteristic, complemented
58#5657C221256yesdirect product factor
59C2×#898C22124yescomplemented
60C2×#897C22124yescomplemented
61C2×#894C22124yescomplemented
62C2×#893C22124yescomplemented
63C2×#885C22124yescomplemented
64C2×#885C22124yescomplemented
65C2×#884C22124yescomplemented
66C2×#882C22124yescomplemented
67C2×D3×C22⋊C4C22124yescomplemented
68C2×#879C22124yescomplemented
69C2×#538—348no—
70C22×#126—31no—
71C22×#126—31no—
72C22×#124—31no—
73C22×#124—31no—
74C22×#123—31no—
75C22×#123D311yescharacteristic, complemented
76C22×C22⋊Q8—31no—
77C22×#121—31no—
78C22×#121—31no—
79C22×#121—31no—
80C22×#120—31no—
81C22×#120—31no—
82C22×C4×D4—31no—
83C22×C4×D4—31no—
84C23×C22⋊C4—31no—
85C25×C3C2311yescharacteristic
86C25×C3C2311yescharacteristic
87C24×D3—28no—
88C24×D3—44no—
89C24×D3—44no—
90C24×D3C2311yescharacteristic
91C24×D3C2311yescharacteristic
92C24×D3C2311yescharacteristic
93C24×D3C23112yes—
94C22×C3×D4—44no—
95C22×C3×D4C23112yes—
96C23×C3×C4—44no—
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C23112yescomplemented
103C22×#67—28no—
104C22×#67—44no—
105C22×#67—44no—
106C22×#67—44no—
107C22×#67C23112yes—
108C22×#67C23112yes—
109C22×#67C23112yes—
110C22×#67C23112yescomplemented
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C22×D12—28no—
117C22×D12—44no—
118C22×D12C23112yes—
119C22×D12C23112yes—
120C22×C4×D3—44no—
121C22×C4×D3—44no—
122C22×C4×D3—44no—
123C22×C4×D3C23112yes—
124C22×C4×D3C23112yes—
125C22×C4×D3C23112yescomplemented
126C22×Dic6—44no—
127C22×Dic6C23112yescomplemented
128C3×#123C23164yescomplemented
129C2×C3×C4⋊C4C23112yescomplemented
130C2×C3×C4⋊C4C23112yescomplemented
131C2×C3×C22⋊C4C23112yes—
132C2×C3×C22⋊C4C23112yes—
133C2×C3×C22⋊C4C23112yescomplemented
134C2×#217C23112yes—
135C2×#217C23112yes—
136C2×#217C23112yescomplemented
137#938C23164yescomplemented
138#937C23164yescomplemented
139#930C23164yescomplemented
140C4×#67C23164yescomplemented
141C2×(C2×D3)⋊C4C23112yes—
142C2×(C2×D3)⋊C4C23112yes—
143C2×(C2×D3)⋊C4C23112yes—
144C2×(C2×D3)⋊C4C23112yes—
145C2×(C2×D3)⋊C4C23112yes—
146C2×(C2×D3)⋊C4C23112yes—
147C2×(C2×D3)⋊C4C23112yescomplemented
148C2×(C2×D3)⋊C4C23112yescomplemented
149C2×C4⋊Dic3C23112yescomplemented
150C2×C4⋊Dic3C23112yescomplemented
151C2×Dic3⋊C4C23112yescomplemented
152C2×Dic3⋊C4C23112yescomplemented
153C2×C4×Dic3C23112yescomplemented
154C2×C4×Dic3C23112yescomplemented
155#898C23164yescomplemented
156#897C23164yescomplemented
157#894C23164yescomplemented
158#893C23164yescomplemented
159#885C23164yescomplemented
160#885C23164yescomplemented
161#884C23164yescomplemented
162#882C23164yescomplemented
163D3×C22⋊C4C23164yescomplemented
164#879C23164yescomplemented
165C26—31no—
166C23×Q8—31no—
167C23×D4—31no—
168C23×D4—31no—
169C23×D4—31no—
170C23×D4—31no—
171C23×D4—31no—
172C23×D4—31no—
173C23×D4C2×D311yescharacteristic
174C24×C4—31no—
175C24×C4—31no—
176C24×C4—31no—
177C24×C4C2×D311yescharacteristic, complemented
178#538—3256no—
179C2×#126—324no—
180C2×#126—324no—
181C2×#124—324no—
182C2×#124—324no—
183C2×#123—324no—
184C2×#123C2×D3124yescomplemented
185C2×C22⋊Q8—324no—
186C2×#121—324no—
187C2×#121—324no—
188C2×#121—324no—
189C2×#120—324no—
190C2×#120—324no—
191C2×C4×D4—324no—
192C2×C4×D4—324no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—31no—
196C22×C4⋊C4—31no—
197C22×C4⋊C4C2×D311yescharacteristic, complemented
198C22×C4⋊C4C2×D311yescharacteristic, complemented
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
202C22×C22⋊C4—31no—
203C22×C22⋊C4—31no—
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4—31no—
210C22×C22⋊C4—324no—
211C22×C22⋊C4C2×D311yescharacteristic
212C22×C22⋊C4C2×D311yescharacteristic
213C22×C22⋊C4C2×D311yescharacteristic, complemented
214C22×C42—31no—
215C22×C42—31no—
216C24×C3—24no—
217C24×C3—24no—
218C24×C3—24no—
219C24×C3—24no—
220C24×C3—24no—
221C24×C3—24no—
222C24×C3C2416yes—
223C24×C3C2416yes—
224C24×C3C2411yescharacteristic
225C23×D3—24no—
226C23×D3—24no—
227C23×D3—24no—
228C23×D3—24no—
229C23×D3—24no—
230C23×D3—24no—
231C23×D3—24no—
232C23×D3—24no—
233C23×D3—248no—
234C23×D3—424no—
235C23×D3—424no—
236C23×D3—464no—
237C23×D3#4118yes—
238C23×D3C2416yes—
239C23×D3C2416yes—
240C23×D3C2416yes—
241C23×D3C24116yes—
242C2×C3×D4—424no—
243C2×C3×D4C24116yes—
244C22×C3×C4—24no—
245C22×C3×C4—24no—
246C22×C3×C4—24no—
247C22×C3×C4—24no—
248C22×C3×C4—24no—
249C22×C3×C4—424no—
250C22×C3×C4C2416yes—
251C22×C3×C4C2416yes—
252C22×C3×C4C2416yes—
253C22×C3×C4C2416yes—
254C22×C3×C4C2416yes—
255C22×C3×C4C24116yescomplemented
256C2×#67—248no—
257C2×#67—424no—
258C2×#67—424no—
259C2×#67—424no—
260C2×#67C24116yes—
261C2×#67C24116yes—
262C2×#67C24116yes—
263C2×#67C24116yescomplemented
264C22×Dic3—24no—
265C22×Dic3—24no—
266C22×Dic3—24no—
267C22×Dic3—24no—
268C22×Dic3—24no—
269C22×Dic3C2416yes—
270C22×Dic3C2416yes—
271C22×Dic3C2416yes—
272C22×Dic3C2416yes—
273C22×Dic3C2416yes—
274C2×D12—248no—
275C2×D12—424no—
276C2×D12C24116yes—
277C2×D12C24116yes—
278C2×C4×D3—424no—
279C2×C4×D3—424no—
280C2×C4×D3—424no—
281C2×C4×D3C24116yes—
282C2×C4×D3C24116yes—
283C2×C4×D3C24116yescomplemented
284C2×Dic6—424no—
285C2×Dic6C24116yescomplemented
286C3×C4⋊C4C24116yescomplemented
287C3×C4⋊C4C24116yescomplemented
288C3×C22⋊C4C24116yes—
289C3×C22⋊C4C24116yes—
290C3×C22⋊C4C24116yescomplemented
291#217C24116yes—
292#217C24116yes—
293#217C24116yescomplemented
294(C2×D3)⋊C4C24116yes—
295(C2×D3)⋊C4C24116yes—
296(C2×D3)⋊C4C24116yes—
297(C2×D3)⋊C4C24116yes—
298(C2×D3)⋊C4C24116yes—
299(C2×D3)⋊C4C24116yes—
300(C2×D3)⋊C4C24116yescomplemented
301(C2×D3)⋊C4C24116yescomplemented
302C4⋊Dic3C24116yescomplemented
303C4⋊Dic3C24116yescomplemented
304Dic3⋊C4C24116yescomplemented
305Dic3⋊C4C24116yescomplemented
306C4×Dic3C24116yescomplemented
307C4×Dic3C24116yescomplemented
308C25—31no—
309C25—31no—
310C25—31no—
311C25—312no—
312C25—68no—
313C25—124no—
314C25—124no—
315C25C22×D311yescharacteristic
316C25C22×D311yescharacteristic
317C22×Q8—312no—
318C22×Q8—124no—
319C22×D4—312no—
320C22×D4—312no—
321C22×D4—312no—
322C22×D4—312no—
323C22×D4—312no—
324C22×D4—312no—
325C22×D4—44no—
326C22×D4—68no—
327C22×D4—68no—
328C22×D4—124no—
329C22×D4—124no—
330C22×D4—124no—
331C22×D4—124no—
332C22×D4C22×D3112yes—
333C23×C4—31no—
334C23×C4—31no—
335C23×C4—31no—
336C23×C4—31no—
337C23×C4—31no—
338C23×C4—312no—
339C23×C4—312no—
340C23×C4—312no—
341C23×C4—44no—
342C23×C4—124no—
343C23×C4—124no—
344C23×C4—124no—
345C23×C4C22×D311yescharacteristic
346C23×C4C22×D311yescharacteristic
347C23×C4C22×D311yescharacteristic
348C23×C4C22×D311yescharacteristic
349C23×C4C22×D311yescharacteristic
350C23×C4C22×D3112yescomplemented
351#126—364no—
352#126—364no—
353#124—364no—
354#124—364no—
355#123—364no—
356#123C22×D3164yescomplemented
357C22⋊Q8—364no—
358#121—364no—
359#121—364no—
360#121—364no—
361#120—364no—
362#120—364no—
363C4×D4—364no—
364C4×D4—364no—
365C2×C4⋊C4—312no—
366C2×C4⋊C4—312no—
367C2×C4⋊C4—312no—
368C2×C4⋊C4—312no—
369C2×C4⋊C4C22×D3112yescomplemented
370C2×C4⋊C4C22×D3112yescomplemented
371C2×C22⋊C4—312no—
372C2×C22⋊C4—312no—
373C2×C22⋊C4—312no—
374C2×C22⋊C4—312no—
375C2×C22⋊C4—312no—
376C2×C22⋊C4—312no—
377C2×C22⋊C4—312no—
378C2×C22⋊C4—312no—
379C2×C22⋊C4—312no—
380C2×C22⋊C4—312no—
381C2×C22⋊C4—312no—
382C2×C22⋊C4—364no—
383C2×C22⋊C4C22×D3112yes—
384C2×C22⋊C4C22×D3112yes—
385C2×C22⋊C4C22×D3112yescomplemented
386C2×C42—312no—
387C2×C42—312no—
388C23×C3—212no—
389C23×C3—212no—
390C23×C3—212no—
391C23×C3—212no—
392C23×C3—212no—
393C23×C3—212no—
394C23×C3—416no—
395C23×C3—416no—
396C23×C3C2×#4114yes—
397C23×C3H(5,𝔽2)14yes—
398C23×C3H(5,𝔽2)14yes—
399C23×C3C2514yes—
400C23×C3C2514yes—
401C23×C3C2513yes—
402C22×D3—232no—
403C22×D3—212no—
404C22×D3—212no—
405C22×D3—212no—
406C22×D3—212no—
407C22×D3—212no—
408C22×D3—212no—
409C22×D3—212no—
410C22×D3—212no—
411C22×D3—232no—
412C22×D3—416no—
413C22×D3—416no—
414C22×D3—4192no—
415C22×D3—416no—
416C22×D3—416no—
417C22×D3C2×#41124yes—
418C22×D3C2514yes—
419C22×D3C2514yes—
420C22×D3C2514yes—
421C3×D4—416no—
422C2×C3×C4—212no—
423C2×C3×C4—212no—
424C2×C3×C4—212no—
425C2×C3×C4—212no—
426C2×C3×C4—212no—
427C2×C3×C4—416no—
428C2×C3×C4C2514yes—
429C2×C3×C4C2514yes—
430C2×C3×C4C2514yes—
431C2×C3×C4C2514yes—
432C2×C3×C4C2514yes—
433#67—232no—
434#67—416no—
435#67—416no—
436#67—416no—
437C2×Dic3—212no—
438C2×Dic3—212no—
439C2×Dic3—212no—
440C2×Dic3—212no—
441C2×Dic3—212no—
442C2×Dic3C2514yes—
443C2×Dic3C2514yes—
444C2×Dic3C2514yes—
445C2×Dic3C2514yes—
446C2×Dic3C2514yes—
447D12—232no—
448D12—416no—
449C4×D3—416no—
450C4×D3—416no—
451C4×D3—416no—
452Dic6—416no—
453C24—24no—
454C24—24no—
455C24—24no—
456C24—24no—
457C24—24no—
458C24—24no—
459C24—38no—
460C24—36no—
461C24—36no—
462C24—36no—
463C24—316no—
464C24—648no—
465C24—64no—
466C24—64no—
467C24—64no—
468C24—64no—
469C24—64no—
470C24—64no—
471C24—64no—
472C24—64no—
473C24—1224no—
474C24—1224no—
475C24—1264no—
476C24C23×D316yes—
477C24C23×D316yes—
478C24C23×D311yescharacteristic
479C2×Q8—316no—
480C2×Q8—1224no—
481C2×D4—316no—
482C2×D4—316no—
483C2×D4—316no—
484C2×D4—316no—
485C2×D4—316no—
486C2×D4—316no—
487C2×D4—424no—
488C2×D4—648no—
489C2×D4—648no—
490C2×D4—1224no—
491C2×D4—1224no—
492C2×D4—1224no—
493C2×D4—1224no—
494C2×D4C23×D3116yes—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—36no—
501C22×C4—36no—
502C22×C4—36no—
503C22×C4—36no—
504C22×C4—36no—
505C22×C4—316no—
506C22×C4—316no—
507C22×C4—316no—
508C22×C4—424no—
509C22×C4—64no—
510C22×C4—64no—
511C22×C4—64no—
512C22×C4—64no—
513C22×C4—64no—
514C22×C4—1224no—
515C22×C4—1224no—
516C22×C4—1224no—
517C22×C4C23×D316yes—
518C22×C4C23×D316yes—
519C22×C4C23×D316yes—
520C22×C4C23×D316yes—
521C22×C4C23×D316yes—
522C22×C4C23×D3116yescomplemented
523C4⋊C4—316no—
524C4⋊C4—316no—
525C4⋊C4—316no—
526C4⋊C4—316no—
527C4⋊C4C23×D3116yescomplemented
528C4⋊C4C23×D3116yescomplemented
529C22⋊C4—316no—
530C22⋊C4—316no—
531C22⋊C4—316no—
532C22⋊C4—316no—
533C22⋊C4—316no—
534C22⋊C4—316no—
535C22⋊C4—316no—
536C22⋊C4—316no—
537C22⋊C4—316no—
538C22⋊C4—316no—
539C22⋊C4—316no—
540C22⋊C4C23×D3116yes—
541C22⋊C4C23×D3116yes—
542C22⋊C4C23×D3116yescomplemented
543C42—316no—
544C42—316no—
545C22×C3—24no—
546C22×C3—24no—
547C22×C3—24no—
548C22×C3—24no—
549C22×C3—24no—
550C22×C3—24no—
551C22×C3—424no—
552C22×C3—424no—
553C22×C3#538116yescomplemented
554C22×C3C22×#4116yes—
555C22×C3C2×H(5,𝔽2)16yes—
556C22×C3C2×H(5,𝔽2)16yes—
557C22×C3C2611yescharacteristic
558C2×D3—24no—
559C2×D3—24no—
560C2×D3—248no—
561C2×D3—24no—
562C2×D3—24no—
563C2×D3—24no—
564C2×D3—24no—
565C2×D3—24no—
566C2×D3—24no—
567C2×D3—464no—
568C2×D3—424no—
569C2×D3—424no—
570C2×D3C22×#4118yes—
571C3×C4—24no—
572C3×C4—24no—
573C3×C4—24no—
574C3×C4—24no—
575C3×C4—24no—
576Dic3—24no—
577Dic3—24no—
578Dic3—24no—
579Dic3—24no—
580Dic3—24no—
581C23—212no—
582C23—212no—
583C23—212no—
584C23—212no—
585C23—212no—
586C23—212no—
587C23—324no—
588C23—34no—
589C23—34no—
590C23—34no—
591C23—416no—
592C23—416no—
593C23—632no—
594C23—632no—
595C23—612no—
596C23—612no—
597C23—612no—
598C23—612no—
599C23—612no—
600C23—612no—
601C23—612no—
602C23—612no—
603C23—1216no—
604C23—1216no—
605C23—12192no—
606C23—1216no—
607C23—1216no—
608C23#100414yes—
609C23D3×#4114yes—
610C23#100914yes—
611C23C24×D314yes—
612C23C24×D314yes—
613C23C24×D313yes—
614Q8—1216no—
615D4—416no—
616D4—632no—
617D4—632no—
618D4—1216no—
619D4—1216no—
620D4—1216no—
621D4—1216no—
622C2×C4—212no—
623C2×C4—212no—
624C2×C4—212no—
625C2×C4—212no—
626C2×C4—212no—
627C2×C4—34no—
628C2×C4—34no—
629C2×C4—34no—
630C2×C4—34no—
631C2×C4—34no—
632C2×C4—416no—
633C2×C4—612no—
634C2×C4—612no—
635C2×C4—612no—
636C2×C4—612no—
637C2×C4—612no—
638C2×C4—1216no—
639C2×C4—1216no—
640C2×C4—1216no—
641C2×C4C24×D314yes—
642C2×C4C24×D314yes—
643C2×C4C24×D314yes—
644C2×C4C24×D314yes—
645C2×C4C24×D314yes—
646C2×C3—44no—
647C2×C3—44no—
648C2×C3C2×#538112yescomplemented
649C2×C3C23×#4111yescharacteristic
650C2×C3C22×H(5,𝔽2)11yescharacteristic
651C2×C3C22×H(5,𝔽2)11yescharacteristic
652D3—28no—
653D3—44no—
654D3—44no—
655C22—24no—
656C22—24no—
657C22—24no—
658C22—24no—
659C22—24no—
660C22—24no—
661C22—38no—
662C22—424no—
663C22—424no—
664C22—64no—
665C22—64no—
666C22—648no—
667C22—64no—
668C22—64no—
669C22—64no—
670C22—64no—
671C22—64no—
672C22—64no—
673C22—1264no—
674C22—1224no—
675C22—1224no—
676C22#5657116yesdirect product factor
677C22C2×#100416yes—
678C22C2×D3×#4116yes—
679C22C2×#100916yes—
680C22C25×D311yescharacteristic
681C4—24no—
682C4—24no—
683C4—24no—
684C4—24no—
685C4—24no—
686C4—64no—
687C4—64no—
688C4—64no—
689C4—64no—
690C4—64no—
691C3C22×#53811yescharacteristic, complemented, Sylow
692C2—44no—
693C2—44no—
694C2—68no—
695C2—124no—
696C2—124no—
697C2C2×#5657112yesdirect product factor
698C2C22×#100411yescharacteristic
699C2C22×D3×#4111yescharacteristic
700C2C22×#100911yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC22×C3×#123C2
socleC24×C3C24
hypercenterC22×#123D3
hypocenterC3C22×#538
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×C3×#123C2semidirect
2. C22×#938C2semidirect
3. C22×#937C2semidirect
4. C22×#930C2semidirect
5. C22×C4×#67C2semidirect
6. C2×#5657C2direct (N × H)
7. C22×#894C2semidirect
8. C22×#897C2semidirect
9. C22×#898C2semidirect
10. C22×#893C2semidirect
11. C22×#884C2semidirect
12. C22×#882C2semidirect
13. C22×D3×C22⋊C4C2semidirect
14. C22×#879C2semidirect
15. C22×#885C2semidirect
16. C22×#885C2semidirect
20. C24×C3×C4C22semidirect
24. C23×#67C22semidirect
29. C23×C4×D3C22semidirect
30. C23×Dic6C22semidirect
31. C2×C3×#123C22semidirect
32. C22×C3×C4⋊C4C22semidirect
33. C22×C3×C4⋊C4C22semidirect
36. C22×C3×C22⋊C4C22semidirect
39. C22×#217C22semidirect
40. C2×#938C22semidirect
41. C2×#937C22semidirect
42. C2×#930C22semidirect
43. C2×C4×#67C22semidirect
50. C22×(C2×D3)⋊C4C22semidirect
51. C22×(C2×D3)⋊C4C22semidirect
52. C22×C4⋊Dic3C22semidirect
53. C22×C4⋊Dic3C22semidirect
54. C22×Dic3⋊C4C22semidirect
55. C22×Dic3⋊C4C22semidirect
56. C22×C4×Dic3C22semidirect
57. C22×C4×Dic3C22semidirect
58. #5657C22direct (N × H)
59. C2×#898C22semidirect
60. C2×#897C22semidirect
61. C2×#894C22semidirect
62. C2×#893C22semidirect
63. C2×#885C22semidirect
64. C2×#885C22semidirect
65. C2×#884C22semidirect
66. C2×#882C22semidirect
67. C2×D3×C22⋊C4C22semidirect
68. C2×#879C22semidirect
75. C22×#123D3semidirect
102. C23×C3×C4C23semidirect
110. C22×#67C23semidirect
125. C22×C4×D3C23semidirect
127. C22×Dic6C23semidirect
128. C3×#123C23semidirect
129. C2×C3×C4⋊C4C23semidirect
130. C2×C3×C4⋊C4C23semidirect
133. C2×C3×C22⋊C4C23semidirect
136. C2×#217C23semidirect
137. #938C23semidirect
138. #937C23semidirect
139. #930C23semidirect
140. C4×#67C23semidirect
147. C2×(C2×D3)⋊C4C23semidirect
148. C2×(C2×D3)⋊C4C23semidirect
149. C2×C4⋊Dic3C23semidirect
150. C2×C4⋊Dic3C23semidirect
151. C2×Dic3⋊C4C23semidirect
152. C2×Dic3⋊C4C23semidirect
153. C2×C4×Dic3C23semidirect
154. C2×C4×Dic3C23semidirect
155. #898C23semidirect
156. #897C23semidirect
157. #894C23semidirect
158. #893C23semidirect
159. #885C23semidirect
160. #885C23semidirect
161. #884C23semidirect
162. #882C23semidirect
163. D3×C22⋊C4C23semidirect
164. #879C23semidirect
177. C24×C4C2×D3semidirect
184. C2×#123C2×D3semidirect
197. C22×C4⋊C4C2×D3semidirect
198. C22×C4⋊C4C2×D3semidirect
213. C22×C22⋊C4C2×D3semidirect
255. C22×C3×C4C24semidirect
263. C2×#67C24semidirect
283. C2×C4×D3C24semidirect
285. C2×Dic6C24semidirect
286. C3×C4⋊C4C24semidirect
287. C3×C4⋊C4C24semidirect
290. C3×C22⋊C4C24semidirect
293. #217C24semidirect
300. (C2×D3)⋊C4C24semidirect
301. (C2×D3)⋊C4C24semidirect
302. C4⋊Dic3C24semidirect
303. C4⋊Dic3C24semidirect
304. Dic3⋊C4C24semidirect
305. Dic3⋊C4C24semidirect
306. C4×Dic3C24semidirect
307. C4×Dic3C24semidirect
350. C23×C4C22×D3semidirect
356. #123C22×D3semidirect
369. C2×C4⋊C4C22×D3semidirect
370. C2×C4⋊C4C22×D3semidirect
385. C2×C22⋊C4C22×D3semidirect
522. C22×C4C23×D3semidirect
527. C4⋊C4C23×D3semidirect
528. C4⋊C4C23×D3semidirect
542. C22⋊C4C23×D3semidirect
553. C22×C3#538semidirect
648. C2×C3C2×#538semidirect
676. C22#5657direct (N × H)
691. C3C22×#538semidirect
697. C2C2×#5657direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1232
C22×#9382
C22×#9372
C22×#9302
C22×C4×#672
C2×#56572
C22×#8942
C22×#8972
C22×#8982
C22×#8932
C22×#8842
C22×#8822
C22×D3×C22⋊C42
C22×#8792
C22×#8852
C22×#5383