Finite Group Databasebeta

← C22×#5637 #11702164

Subgroups — C22×#5637 #11702164

Order 768.

9526 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×#946C211yesmaximal, characteristic, complemented
3C22×#947C211yesmaximal, characteristic, complemented
4C23×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C22×C4×#67C211yesmaximal, characteristic, complemented
6C2×#5637C2148yesmaximal, direct product factor
7C22×#894C211yesmaximal, characteristic, complemented
8C22×#894C211yesmaximal, characteristic, complemented
9C22×#898C211yesmaximal, characteristic, complemented
10C22×#898C211yesmaximal, characteristic, complemented
11C22×#893C211yesmaximal, characteristic, complemented
12C22×#892C211yesmaximal, characteristic, complemented
13C22×#882C211yesmaximal, characteristic
14C22×D3×C22⋊C4C211yesmaximal, characteristic, complemented
15C22×#886C211yesmaximal, characteristic, complemented
16C22×#877C211yesmaximal, characteristic, complemented
17C22×#551—31nomaximal, Sylow
18C25×D3C2211yescharacteristic
19C23×C3×Q8C2211yescharacteristic, complemented
20C24×C3×C4C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C24×Dic3C2211yescharacteristic
23C23×D12C2211yescharacteristic
24C23×D12C2211yescharacteristic
25C23×C4×D3C2211yescharacteristic
26C23×C4×D3C2211yescharacteristic
27C23×C4×D3C2211yescharacteristic, complemented
28C2×C3×C22⋊Q8C22124yescomplemented
29C22×C3×C4⋊C4C2211yescharacteristic, complemented
30C22×C3×C4⋊C4C2211yescharacteristic, complemented
31C22×C3×C4⋊C4C2211yescharacteristic, complemented
32C22×C3×C22⋊C4C2211yescharacteristic
33C22×C3×C22⋊C4C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C2×#947C22124yescomplemented
36C2×#946C22124yescomplemented
37C2×C4×#67C22124yescomplemented
38C22×(C2×D3)⋊C4C2211yescharacteristic
39C22×(C2×D3)⋊C4C2211yescharacteristic
40C22×(C2×D3)⋊C4C2211yescharacteristic
41C22×(C2×D3)⋊C4C2211yescharacteristic
42C22×(C2×D3)⋊C4C2211yescharacteristic
43C22×(C2×D3)⋊C4C2211yescharacteristic
44C22×(C2×D3)⋊C4C2211yescharacteristic
45C22×(C2×D3)⋊C4C2211yescharacteristic
46C22×(C2×D3)⋊C4C22124yescomplemented
47C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C22×C4⋊Dic3C2211yescharacteristic, complemented
51C22×C4⋊Dic3C2211yescharacteristic, complemented
52C22×Dic3⋊C4C2211yescharacteristic, complemented
53C22×Dic3⋊C4C2211yescharacteristic, complemented
54C22×Dic3⋊C4C2211yescharacteristic, complemented
55C22×C4×Dic3C2211yescharacteristic, complemented
56C22×C4×Dic3C2211yescharacteristic, complemented
57C22×C4×Dic3C2211yescharacteristic, complemented
58#5637C221256yesdirect product factor
59C2×#898C22124yescomplemented
60C2×#898C22124yescomplemented
61C2×#894C22124yescomplemented
62C2×#894C22124yescomplemented
63C2×#893C22124yescomplemented
64C2×#892C22124yescomplemented
65C2×#886C22124yescomplemented
66C2×#882C22124yes—
67C2×D3×C22⋊C4C22124yescomplemented
68C2×#877C22124yescomplemented
69C2×#551—348no—
70C22×#126—31no—
71C22×#126—31no—
72C22×#124—31no—
73C22×#123—31no—
74C22×#123—31no—
75C22×#123—31no—
76C22×C22⋊Q8—31no—
77C22×C22⋊Q8D311yescharacteristic, complemented
78C22×#120—31no—
79C22×C4×D4—31no—
80C22×C4×D4—31no—
81C22×#117—31no—
82C22×#117—31no—
83C23×C22⋊C4—31no—
84C23×C22⋊C4—31no—
85C25×C3C2311yescharacteristic
86C24×D3—28no—
87C24×D3—28no—
88C24×D3—44no—
89C24×D3C2311yescharacteristic
90C24×D3C2311yescharacteristic
91C24×D3C23112yes—
92C24×D3C2311yescharacteristic
93C22×C3×Q8—44no—
94C22×C3×Q8C23112yescomplemented
95C23×C3×C4—44no—
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C23112yes—
103C22×#67—28no—
104C22×#67C23112yes—
105C23×Dic3—28no—
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C23112yes—
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C22×D12—28no—
113C22×D12—44no—
114C22×D12C23112yes—
115C22×D12C23112yes—
116C22×C4×D3—28no—
117C22×C4×D3—44no—
118C22×C4×D3—44no—
119C22×C4×D3C23112yes—
120C22×C4×D3C23112yes—
121C22×C4×D3C23112yescomplemented
122C3×C22⋊Q8C23164yescomplemented
123C2×C3×C4⋊C4C23112yescomplemented
124C2×C3×C4⋊C4C23112yescomplemented
125C2×C3×C4⋊C4C23112yescomplemented
126C2×C3×C22⋊C4C23112yes—
127C2×C3×C22⋊C4C23112yes—
128C2×#217C23112yes—
129#947C23164yescomplemented
130#946C23164yescomplemented
131C4×#67C23164yescomplemented
132C2×(C2×D3)⋊C4C23112yes—
133C2×(C2×D3)⋊C4C23112yes—
134C2×(C2×D3)⋊C4C23112yes—
135C2×(C2×D3)⋊C4C23112yes—
136C2×(C2×D3)⋊C4C23112yes—
137C2×(C2×D3)⋊C4C23112yes—
138C2×(C2×D3)⋊C4C23112yes—
139C2×(C2×D3)⋊C4C23112yes—
140C2×(C2×D3)⋊C4C23164yescomplemented
141C2×(C2×D3)⋊C4C23112yescomplemented
142C2×(C2×D3)⋊C4C23112yescomplemented
143C2×(C2×D3)⋊C4C23112yescomplemented
144C2×C4⋊Dic3C23112yescomplemented
145C2×C4⋊Dic3C23112yescomplemented
146C2×Dic3⋊C4C23112yescomplemented
147C2×Dic3⋊C4C23112yescomplemented
148C2×Dic3⋊C4C23112yescomplemented
149C2×C4×Dic3C23112yescomplemented
150C2×C4×Dic3C23112yescomplemented
151C2×C4×Dic3C23112yescomplemented
152#898C23164yescomplemented
153#898C23164yescomplemented
154#894C23164yescomplemented
155#894C23164yescomplemented
156#893C23164yescomplemented
157#892C23164yescomplemented
158#886C23164yescomplemented
159#882C23164yes—
160D3×C22⋊C4C23164yescomplemented
161#877C23164yescomplemented
162C26—31no—
163C23×Q8C2×D311yescharacteristic, complemented
164C23×D4—31no—
165C23×D4—31no—
166C23×D4—31no—
167C24×C4—31no—
168C24×C4—31no—
169C24×C4—31no—
170C24×C4—31no—
171C24×C4C2×D311yescharacteristic
172#551—3256no—
173C2×#126—324no—
174C2×#126—324no—
175C2×#124—324no—
176C2×#123—324no—
177C2×#123—324no—
178C2×#123—324no—
179C2×C22⋊Q8—324no—
180C2×C22⋊Q8C2×D3124yescomplemented
181C2×#120—324no—
182C2×C4×D4—324no—
183C2×C4×D4—324no—
184C2×#117—324no—
185C2×#117—324no—
186C22×C4⋊C4—31no—
187C22×C4⋊C4—31no—
188C22×C4⋊C4—31no—
189C22×C4⋊C4—31no—
190C22×C4⋊C4—31no—
191C22×C4⋊C4C2×D311yescharacteristic, complemented
192C22×C4⋊C4C2×D311yescharacteristic, complemented
193C22×C4⋊C4C2×D311yescharacteristic, complemented
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4—324no—
202C22×C22⋊C4—31no—
203C22×C22⋊C4—31no—
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—324no—
208C22×C22⋊C4C2×D311yescharacteristic
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C42—31no—
211C22×C42—31no—
212C22×C42—31no—
213C24×C3—24no—
214C24×C3—24no—
215C24×C3#4118yes—
216C24×C3C2416yes—
217C24×C3C2411yescharacteristic
218C23×D3—24no—
219C23×D3—24no—
220C23×D3—24no—
221C23×D3—24no—
222C23×D3—248no—
223C23×D3—24no—
224C23×D3—24no—
225C23×D3—24no—
226C23×D3—24no—
227C23×D3—248no—
228C23×D3—424no—
229C23×D3—464no—
230C23×D3#4118yes—
231C23×D3C2416yes—
232C23×D3C2416yes—
233C23×D3C24116yes—
234C23×D3C2416yes—
235C2×C3×Q8—424no—
236C2×C3×Q8C24116yescomplemented
237C22×C3×C4—24no—
238C22×C3×C4—24no—
239C22×C3×C4—24no—
240C22×C3×C4—24no—
241C22×C3×C4—24no—
242C22×C3×C4—24no—
243C22×C3×C4—424no—
244C22×C3×C4C2416yes—
245C22×C3×C4C2416yes—
246C22×C3×C4C2416yes—
247C22×C3×C4C2416yes—
248C22×C3×C4C2416yes—
249C22×C3×C4C2416yes—
250C22×C3×C4C24116yes—
251C2×#67—248no—
252C2×#67C24116yes—
253C22×Dic3—24no—
254C22×Dic3—248no—
255C22×Dic3—24no—
256C22×Dic3—24no—
257C22×Dic3—24no—
258C22×Dic3—24no—
259C22×Dic3C24116yes—
260C22×Dic3C2416yes—
261C22×Dic3C2416yes—
262C22×Dic3C2416yes—
263C22×Dic3C2416yes—
264C22×Dic3C2416yes—
265C2×D12—248no—
266C2×D12—424no—
267C2×D12C24116yes—
268C2×D12C24116yes—
269C2×C4×D3—248no—
270C2×C4×D3—424no—
271C2×C4×D3—424no—
272C2×C4×D3C24116yes—
273C2×C4×D3C24116yes—
274C2×C4×D3C24116yescomplemented
275C3×C4⋊C4C24116yescomplemented
276C3×C4⋊C4C24116yescomplemented
277C3×C4⋊C4C24116yescomplemented
278C3×C22⋊C4C24116yes—
279C3×C22⋊C4C24116yes—
280#217C24116yes—
281(C2×D3)⋊C4C24116yes—
282(C2×D3)⋊C4C24116yes—
283(C2×D3)⋊C4C24116yes—
284(C2×D3)⋊C4C24116yes—
285(C2×D3)⋊C4C24116yes—
286(C2×D3)⋊C4C24116yes—
287(C2×D3)⋊C4C24116yes—
288(C2×D3)⋊C4C24116yes—
289(C2×D3)⋊C4C24116yescomplemented
290(C2×D3)⋊C4C24116yescomplemented
291(C2×D3)⋊C4C24116yescomplemented
292C4⋊Dic3C24116yescomplemented
293C4⋊Dic3C24116yescomplemented
294Dic3⋊C4C24116yescomplemented
295Dic3⋊C4C24116yescomplemented
296Dic3⋊C4C24116yescomplemented
297C4×Dic3C24116yescomplemented
298C4×Dic3C24116yescomplemented
299C4×Dic3C24116yescomplemented
300C25—31no—
301C25—31no—
302C25—31no—
303C25—312no—
304C25—68no—
305C25—68no—
306C25—124no—
307C25C22×D311yescharacteristic
308C22×Q8—44no—
309C22×Q8C22×D3112yescomplemented
310C22×D4—312no—
311C22×D4—312no—
312C22×D4—312no—
313C22×D4—68no—
314C22×D4—68no—
315C22×D4—124no—
316C23×C4—312no—
317C23×C4—31no—
318C23×C4—31no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4—31no—
322C23×C4—312no—
323C23×C4—312no—
324C23×C4—312no—
325C23×C4—44no—
326C23×C4—68no—
327C23×C4—68no—
328C23×C4—124no—
329C23×C4—124no—
330C23×C4C22×D311yescharacteristic
331C23×C4C22×D311yescharacteristic
332C23×C4C22×D311yescharacteristic
333C23×C4C22×D311yescharacteristic
334C23×C4C22×D311yescharacteristic
335C23×C4C22×D311yescharacteristic
336C23×C4C22×D3112yes—
337#126—364no—
338#126—364no—
339#124—364no—
340#123—364no—
341#123—364no—
342#123—364no—
343C22⋊Q8—364no—
344C22⋊Q8C22×D3164yescomplemented
345#120—364no—
346C4×D4—364no—
347C4×D4—364no—
348#117—364no—
349#117—364no—
350C2×C4⋊C4—312no—
351C2×C4⋊C4—312no—
352C2×C4⋊C4—312no—
353C2×C4⋊C4—312no—
354C2×C4⋊C4—312no—
355C2×C4⋊C4C22×D3112yescomplemented
356C2×C4⋊C4C22×D3112yescomplemented
357C2×C4⋊C4C22×D3112yescomplemented
358C2×C22⋊C4—312no—
359C2×C22⋊C4—312no—
360C2×C22⋊C4—312no—
361C2×C22⋊C4—312no—
362C2×C22⋊C4—312no—
363C2×C22⋊C4—312no—
364C2×C22⋊C4—312no—
365C2×C22⋊C4—364no—
366C2×C22⋊C4—312no—
367C2×C22⋊C4—312no—
368C2×C22⋊C4—312no—
369C2×C22⋊C4—312no—
370C2×C22⋊C4—312no—
371C2×C22⋊C4—364no—
372C2×C22⋊C4C22×D3112yes—
373C2×C22⋊C4C22×D3112yes—
374C2×C42—312no—
375C2×C42—312no—
376C2×C42—312no—
377C23×C3—232no—
378C23×C3—212no—
379C23×C3—212no—
380C23×C3C2×#41124yes—
381C23×C3C2×#4114yes—
382C23×C3C2×#4114yes—
383C23×C3H(5,𝔽2)14yes—
384C23×C3C2514yes—
385C23×C3C2513yes—
386C22×D3—232no—
387C22×D3—212no—
388C22×D3—212no—
389C22×D3—212no—
390C22×D3—212no—
391C22×D3—232no—
392C22×D3—212no—
393C22×D3—212no—
394C22×D3—212no—
395C22×D3—212no—
396C22×D3—232no—
397C22×D3—416no—
398C22×D3—4192no—
399C22×D3—416no—
400C22×D3—416no—
401C22×D3C2×#41124yes—
402C22×D3C2514yes—
403C22×D3C2514yes—
404C22×D3C2514yes—
405C3×Q8—416no—
406C2×C3×C4—212no—
407C2×C3×C4—212no—
408C2×C3×C4—212no—
409C2×C3×C4—212no—
410C2×C3×C4—212no—
411C2×C3×C4—212no—
412C2×C3×C4—416no—
413C2×C3×C4C2514yes—
414C2×C3×C4C2514yes—
415C2×C3×C4C2514yes—
416C2×C3×C4C2514yes—
417C2×C3×C4C2514yes—
418C2×C3×C4C2514yes—
419#67—232no—
420C2×Dic3—212no—
421C2×Dic3—232no—
422C2×Dic3—212no—
423C2×Dic3—212no—
424C2×Dic3—212no—
425C2×Dic3—212no—
426C2×Dic3C2514yes—
427C2×Dic3C2514yes—
428C2×Dic3C2514yes—
429C2×Dic3C2514yes—
430C2×Dic3C2514yes—
431D12—232no—
432D12—416no—
433C4×D3—232no—
434C4×D3—416no—
435C4×D3—416no—
436C24—24no—
437C24—24no—
438C24—38no—
439C24—36no—
440C24—36no—
441C24—36no—
442C24—316no—
443C24—648no—
444C24—64no—
445C24—64no—
446C24—64no—
447C24—64no—
448C24—64no—
449C24—648no—
450C24—64no—
451C24—64no—
452C24—64no—
453C24—1224no—
454C24—1264no—
455C24#23918yes—
456C24C23×D316yes—
457C24C23×D311yescharacteristic
458C2×Q8—424no—
459C2×Q8C23×D3116yescomplemented
460C2×D4—316no—
461C2×D4—316no—
462C2×D4—316no—
463C2×D4—648no—
464C2×D4—648no—
465C2×D4—1224no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—36no—
473C22×C4—36no—
474C22×C4—36no—
475C22×C4—36no—
476C22×C4—36no—
477C22×C4—316no—
478C22×C4—316no—
479C22×C4—316no—
480C22×C4—316no—
481C22×C4—424no—
482C22×C4—648no—
483C22×C4—64no—
484C22×C4—648no—
485C22×C4—64no—
486C22×C4—64no—
487C22×C4—64no—
488C22×C4—64no—
489C22×C4—1224no—
490C22×C4—1224no—
491C22×C4C23×D316yes—
492C22×C4C23×D316yes—
493C22×C4C23×D316yes—
494C22×C4C23×D316yes—
495C22×C4C23×D316yes—
496C22×C4C23×D316yes—
497C22×C4C23×D3116yes—
498C4⋊C4—316no—
499C4⋊C4—316no—
500C4⋊C4—316no—
501C4⋊C4—316no—
502C4⋊C4—316no—
503C4⋊C4C23×D3116yescomplemented
504C4⋊C4C23×D3116yescomplemented
505C4⋊C4C23×D3116yescomplemented
506C22⋊C4—316no—
507C22⋊C4—316no—
508C22⋊C4—316no—
509C22⋊C4—316no—
510C22⋊C4—316no—
511C22⋊C4—316no—
512C22⋊C4—316no—
513C22⋊C4—316no—
514C22⋊C4—316no—
515C22⋊C4—316no—
516C22⋊C4—316no—
517C22⋊C4—316no—
518C22⋊C4C23×D3116yes—
519C22⋊C4C23×D3116yes—
520C42—316no—
521C42—316no—
522C42—316no—
523C22×C3—24no—
524C22×C3—24no—
525C22×C3—248no—
526C22×C3#551116yescomplemented
527C22×C3C22×#4118yes—
528C22×C3C22×#4116yes—
529C22×C3C22×#4116yes—
530C22×C3C2×H(5,𝔽2)16yes—
531C22×C3C2611yescharacteristic
532C2×D3—24no—
533C2×D3—24no—
534C2×D3—248no—
535C2×D3—24no—
536C2×D3—24no—
537C2×D3—24no—
538C2×D3—24no—
539C2×D3—24no—
540C2×D3—24no—
541C2×D3—464no—
542C2×D3—424no—
543C2×D3—424no—
544C2×D3C22×#4118yes—
545C3×C4—24no—
546C3×C4—24no—
547C3×C4—24no—
548C3×C4—24no—
549C3×C4—24no—
550C3×C4—24no—
551Dic3—24no—
552Dic3—24no—
553Dic3—24no—
554Dic3—24no—
555Dic3—24no—
556C23—232no—
557C23—212no—
558C23—212no—
559C23—324no—
560C23—34no—
561C23—34no—
562C23—34no—
563C23—632no—
564C23—632no—
565C23—612no—
566C23—612no—
567C23—612no—
568C23—612no—
569C23—612no—
570C23—632no—
571C23—612no—
572C23—612no—
573C23—612no—
574C23—1216no—
575C23—12192no—
576C23—1216no—
577C23—1216no—
578C23#100414yes—
579C23C2×#239124yes—
580C23C2×#23914yes—
581C23D3×#4114yes—
582C23C24×D314yes—
583C23C24×D313yes—
584Q8—416no—
585D4—632no—
586D4—632no—
587D4—1216no—
588C2×C4—212no—
589C2×C4—212no—
590C2×C4—212no—
591C2×C4—212no—
592C2×C4—212no—
593C2×C4—212no—
594C2×C4—34no—
595C2×C4—34no—
596C2×C4—34no—
597C2×C4—34no—
598C2×C4—34no—
599C2×C4—416no—
600C2×C4—632no—
601C2×C4—612no—
602C2×C4—632no—
603C2×C4—612no—
604C2×C4—612no—
605C2×C4—612no—
606C2×C4—612no—
607C2×C4—1216no—
608C2×C4—1216no—
609C2×C4C24×D314yes—
610C2×C4C24×D314yes—
611C2×C4C24×D314yes—
612C2×C4C24×D314yes—
613C2×C4C24×D314yes—
614C2×C4C24×D314yes—
615C2×C3—28no—
616C2×C3C2×#551112yescomplemented
617C2×C3C23×#4111yescharacteristic
618C2×C3C23×#4111yescharacteristic
619C2×C3C22×H(5,𝔽2)11yescharacteristic
620D3—28no—
621D3—44no—
622D3—44no—
623C22—24no—
624C22—24no—
625C22—248no—
626C22—38no—
627C22—64no—
628C22—64no—
629C22—648no—
630C22—64no—
631C22—64no—
632C22—64no—
633C22—64no—
634C22—64no—
635C22—64no—
636C22—1264no—
637C22—1224no—
638C22—1224no—
639C22#5637116yesdirect product factor
640C22C2×#100416yes—
641C22C22×#23918yes—
642C22C22×#23916yes—
643C22C2×D3×#4116yes—
644C22C25×D311yescharacteristic
645C4—24no—
646C4—24no—
647C4—24no—
648C4—24no—
649C4—24no—
650C4—24no—
651C4—64no—
652C4—64no—
653C4—64no—
654C4—64no—
655C4—64no—
656C3C22×#55111yescharacteristic, complemented, Sylow
657C2—28no—
658C2—68no—
659C2—124no—
660C2—124no—
661C2C2×#5637112yesdirect product factor
662C2C22×#100411yescharacteristic
663C2C23×#23911yescharacteristic
664C2C22×D3×#4111yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC22×C3×C22⋊Q8C2
socleC24×C3C24
prime radicalC22×#882C2
hypercenterC22×C22⋊Q8D3
hypocenterC3C22×#551
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×C22⋊Q8C2semidirect
2. C22×#946C2semidirect
3. C22×#947C2semidirect
4. C23×(C2×D3)⋊C4C2semidirect
5. C22×C4×#67C2semidirect
6. C2×#5637C2direct (N × H)
7. C22×#894C2semidirect
8. C22×#894C2semidirect
9. C22×#898C2semidirect
10. C22×#898C2semidirect
11. C22×#893C2semidirect
12. C22×#892C2semidirect
14. C22×D3×C22⋊C4C2semidirect
15. C22×#886C2semidirect
16. C22×#877C2semidirect
19. C23×C3×Q8C22semidirect
27. C23×C4×D3C22semidirect
28. C2×C3×C22⋊Q8C22semidirect
29. C22×C3×C4⋊C4C22semidirect
30. C22×C3×C4⋊C4C22semidirect
31. C22×C3×C4⋊C4C22semidirect
35. C2×#947C22semidirect
36. C2×#946C22semidirect
37. C2×C4×#67C22semidirect
46. C22×(C2×D3)⋊C4C22semidirect
47. C22×(C2×D3)⋊C4C22semidirect
48. C22×(C2×D3)⋊C4C22semidirect
49. C22×(C2×D3)⋊C4C22semidirect
50. C22×C4⋊Dic3C22semidirect
51. C22×C4⋊Dic3C22semidirect
52. C22×Dic3⋊C4C22semidirect
53. C22×Dic3⋊C4C22semidirect
54. C22×Dic3⋊C4C22semidirect
55. C22×C4×Dic3C22semidirect
56. C22×C4×Dic3C22semidirect
57. C22×C4×Dic3C22semidirect
58. #5637C22direct (N × H)
59. C2×#898C22semidirect
60. C2×#898C22semidirect
61. C2×#894C22semidirect
62. C2×#894C22semidirect
63. C2×#893C22semidirect
64. C2×#892C22semidirect
65. C2×#886C22semidirect
67. C2×D3×C22⋊C4C22semidirect
68. C2×#877C22semidirect
77. C22×C22⋊Q8D3semidirect
94. C22×C3×Q8C23semidirect
121. C22×C4×D3C23semidirect
122. C3×C22⋊Q8C23semidirect
123. C2×C3×C4⋊C4C23semidirect
124. C2×C3×C4⋊C4C23semidirect
125. C2×C3×C4⋊C4C23semidirect
129. #947C23semidirect
130. #946C23semidirect
131. C4×#67C23semidirect
140. C2×(C2×D3)⋊C4C23semidirect
141. C2×(C2×D3)⋊C4C23semidirect
142. C2×(C2×D3)⋊C4C23semidirect
143. C2×(C2×D3)⋊C4C23semidirect
144. C2×C4⋊Dic3C23semidirect
145. C2×C4⋊Dic3C23semidirect
146. C2×Dic3⋊C4C23semidirect
147. C2×Dic3⋊C4C23semidirect
148. C2×Dic3⋊C4C23semidirect
149. C2×C4×Dic3C23semidirect
150. C2×C4×Dic3C23semidirect
151. C2×C4×Dic3C23semidirect
152. #898C23semidirect
153. #898C23semidirect
154. #894C23semidirect
155. #894C23semidirect
156. #893C23semidirect
157. #892C23semidirect
158. #886C23semidirect
160. D3×C22⋊C4C23semidirect
161. #877C23semidirect
163. C23×Q8C2×D3semidirect
180. C2×C22⋊Q8C2×D3semidirect
191. C22×C4⋊C4C2×D3semidirect
192. C22×C4⋊C4C2×D3semidirect
193. C22×C4⋊C4C2×D3semidirect
236. C2×C3×Q8C24semidirect
274. C2×C4×D3C24semidirect
275. C3×C4⋊C4C24semidirect
276. C3×C4⋊C4C24semidirect
277. C3×C4⋊C4C24semidirect
289. (C2×D3)⋊C4C24semidirect
290. (C2×D3)⋊C4C24semidirect
291. (C2×D3)⋊C4C24semidirect
292. C4⋊Dic3C24semidirect
293. C4⋊Dic3C24semidirect
294. Dic3⋊C4C24semidirect
295. Dic3⋊C4C24semidirect
296. Dic3⋊C4C24semidirect
297. C4×Dic3C24semidirect
298. C4×Dic3C24semidirect
299. C4×Dic3C24semidirect
309. C22×Q8C22×D3semidirect
344. C22⋊Q8C22×D3semidirect
355. C2×C4⋊C4C22×D3semidirect
356. C2×C4⋊C4C22×D3semidirect
357. C2×C4⋊C4C22×D3semidirect
459. C2×Q8C23×D3semidirect
503. C4⋊C4C23×D3semidirect
504. C4⋊C4C23×D3semidirect
505. C4⋊C4C23×D3semidirect
526. C22×C3#551semidirect
616. C2×C3C2×#551semidirect
639. C22#5637direct (N × H)
656. C3C22×#551semidirect
661. C2C2×#5637direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
C22×#9462
C22×#9472
C23×(C2×D3)⋊C42
C22×C4×#672
C2×#56372
C22×#8942
C22×#8982
C22×#8932
C22×#8922
C22×#8822
C22×D3×C22⋊C42
C22×#8862
C22×#8772
C22×#5513