Finite Group Databasebeta

← C22×#5655 #11702126

Subgroups — C22×#5655 #11702126

Order 768.

12230 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#237C211yesmaximal, characteristic, complemented
2C23×#235C211yesmaximal, characteristic, complemented
3C22×C3×#123C211yesmaximal, characteristic, complemented
4C22×#939C211yesmaximal, characteristic, complemented
5C23×Dic3⋊C4C211yesmaximal, characteristic, complemented
6C2×#5655C2148yesmaximal, direct product factor
7C22×#894C211yesmaximal, characteristic, complemented
8C22×#896C211yesmaximal, characteristic, complemented
9C22×D3×C4⋊C4C211yesmaximal, characteristic, complemented
10C22×#888C211yesmaximal, characteristic, complemented
11C22×#883C211yesmaximal, characteristic, complemented
12C22×#884C211yesmaximal, characteristic, complemented
13C22×#886C211yesmaximal, characteristic, complemented
14C22×#878C211yesmaximal, characteristic, complemented
15C22×#67⋊C4C211yesmaximal, characteristic, complemented
16C22×#67⋊C4C211yesmaximal, characteristic, complemented
17C22×#547—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C23×#67C2211yescharacteristic
24C24×Dic3C2211yescharacteristic
25C24×Dic3C2211yescharacteristic
26C24×Dic3C2211yescharacteristic
27C22×#237—216no—
28C22×#237C22124yescomplemented
29C22×#235—216no—
30C22×#235C22124yescomplemented
31C23×D12C2211yescharacteristic
32C23×C4×D3C2211yescharacteristic
33C23×C4×D3C2211yescharacteristic
34C23×C4×D3C2211yescharacteristic
35C23×C4×D3C2211yescharacteristic
36C23×Dic6C2211yescharacteristic
37C23×Dic6C2211yescharacteristic
38C2×C3×#123C22124yescomplemented
39C22×C3×C4⋊C4C2211yescharacteristic
40C22×C3×C4⋊C4C2211yescharacteristic
41C22×C3×C22⋊C4C2211yescharacteristic
42C22×C3×C22⋊C4C2211yescharacteristic
43C22×C3×C22⋊C4C2211yescharacteristic
44C22×#217C2211yescharacteristic
45C2×#939C22124yescomplemented
46C22×(C2×D3)⋊C4C2211yescharacteristic
47C22×(C2×D3)⋊C4C2211yescharacteristic
48C22×(C2×D3)⋊C4C2211yescharacteristic
49C22×(C2×D3)⋊C4C2211yescharacteristic
50C22×C4⋊Dic3C2211yescharacteristic
51C22×C4⋊Dic3C2211yescharacteristic
52C22×Dic3⋊C4C2211yescharacteristic
53C22×Dic3⋊C4C2211yescharacteristic
54C22×Dic3⋊C4C2211yescharacteristic
55C22×Dic3⋊C4C2211yescharacteristic
56C22×Dic3⋊C4C2211yescharacteristic
57C22×Dic3⋊C4C2211yescharacteristic
58C22×Dic3⋊C4C22124yescomplemented
59C22×C4×Dic3C2211yescharacteristic
60#5655C221256yesdirect product factor
61C2×#896C22124yescomplemented
62C2×#894C22124yescomplemented
63C2×D3×C4⋊C4C22124yescomplemented
64C2×#888C22124yescomplemented
65C2×#886C22124yescomplemented
66C2×#884C22124yescomplemented
67C2×#883C22124yescomplemented
68C2×#67⋊C4C22124yescomplemented
69C2×#67⋊C4C22124yescomplemented
70C2×#878C22124yescomplemented
71C23×#41—31no—
72C23×#41—31no—
73C2×#547—348no—
74C22×C4⋊Q8—31no—
75C22×#123—31no—
76C22×#123—31no—
77C22×#123—31no—
78C22×#123D311yescharacteristic, complemented
79C22×C22⋊Q8—31no—
80C22×C22⋊Q8—31no—
81C22×#121—31no—
82C22×#121—31no—
83C22×C4×D4—31no—
84C22×C4×D4—31no—
85C23×C4⋊C4—31no—
86C23×C4⋊C4—31no—
87C25×C3C2311yescharacteristic
88C25×C3C2311yescharacteristic
89C24×D3C2311yescharacteristic
90C24×D3C2311yescharacteristic
91C22×C3×D4—28no—
92C22×C3×D4C23112yes—
93C23×C3×C4—28no—
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C23112yes—
99C23×C3×C4C2311yescharacteristic
100C22×#67—28no—
101C22×#67—28no—
102C22×#67—28no—
103C22×#67D4116yescomplemented
104C22×#67C23112yes—
105C22×#67C23112yes—
106C22×#67C23112yes—
107C22×#67C23112yes—
108C23×Dic3—28no—
109C23×Dic3—28no—
110C23×Dic3—28no—
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C23×Dic3C23112yes—
115C23×Dic3C23112yes—
116C23×Dic3C23112yes—
117C23×Dic3C2311yescharacteristic
118C23×Dic3C2311yescharacteristic
119C23×Dic3C2311yescharacteristic
120C2×#237—2192no—
121C2×#237C23164yescomplemented
122C2×#235—2192no—
123C2×#235C23164yescomplemented
124C22×D12—28no—
125C22×D12C23112yes—
126C22×C4×D3—28no—
127C22×C4×D3—28no—
128C22×C4×D3—28no—
129C22×C4×D3—28no—
130C22×C4×D3C23112yes—
131C22×C4×D3C23112yes—
132C22×C4×D3C23112yes—
133C22×C4×D3C23112yes—
134C22×Dic6—28no—
135C22×Dic6—28no—
136C22×Dic6C23112yes—
137C22×Dic6C23112yes—
138C3×#123C23164yescomplemented
139C2×C3×C4⋊C4C23112yes—
140C2×C3×C4⋊C4C23112yes—
141C2×C3×C22⋊C4C23112yes—
142C2×C3×C22⋊C4C23112yes—
143C2×C3×C22⋊C4C23112yes—
144C2×#217C23112yes—
145#939C23164yescomplemented
146C2×(C2×D3)⋊C4C23112yes—
147C2×(C2×D3)⋊C4C23112yes—
148C2×(C2×D3)⋊C4C23112yes—
149C2×(C2×D3)⋊C4C23112yes—
150C2×C4⋊Dic3C23112yes—
151C2×C4⋊Dic3C23112yes—
152C2×Dic3⋊C4C23112yes—
153C2×Dic3⋊C4C23112yes—
154C2×Dic3⋊C4C23112yes—
155C2×Dic3⋊C4C23112yes—
156C2×Dic3⋊C4C23112yes—
157C2×Dic3⋊C4C23112yes—
158C2×Dic3⋊C4C23164yescomplemented
159C2×C4×Dic3C23112yes—
160#896C23164yescomplemented
161#894C23164yescomplemented
162D3×C4⋊C4C23164yescomplemented
163#888C23164yescomplemented
164#886C23164yescomplemented
165#884C23164yescomplemented
166#883C23164yescomplemented
167#67⋊C4C23164yescomplemented
168#67⋊C4C23164yescomplemented
169#878C23164yescomplemented
170C22×#41—324no—
171C22×#41—324no—
172C22×#41—616no—
173C22×#41—616no—
174C23×Q8—31no—
175C23×Q8—31no—
176C23×D4—31no—
177C23×D4—31no—
178C23×D4—31no—
179C23×D4—31no—
180C23×D4—31no—
181C23×D4C2×D311yescharacteristic
182C24×C4—31no—
183C24×C4—31no—
184C24×C4—31no—
185C24×C4—31no—
186C24×C4—31no—
187C24×C4—31no—
188C24×C4—31no—
189C24×C4C2×D311yescharacteristic
190#547—3256no—
191C2×C4⋊Q8—324no—
192C2×#123—324no—
193C2×#123—324no—
194C2×#123—324no—
195C2×#123C2×D3124yescomplemented
196C2×C22⋊Q8—324no—
197C2×C22⋊Q8—324no—
198C2×#121—324no—
199C2×#121—324no—
200C2×C4×D4—324no—
201C2×C4×D4—324no—
202C22×C4⋊C4—31no—
203C22×C4⋊C4—31no—
204C22×C4⋊C4—31no—
205C22×C4⋊C4—31no—
206C22×C4⋊C4—31no—
207C22×C4⋊C4—31no—
208C22×C4⋊C4—324no—
209C22×C4⋊C4—31no—
210C22×C4⋊C4—31no—
211C22×C4⋊C4—324no—
212C22×C4⋊C4C2×D311yescharacteristic
213C22×C4⋊C4C2×D311yescharacteristic
214C22×C22⋊C4—31no—
215C22×C22⋊C4—31no—
216C22×C22⋊C4—31no—
217C22×C22⋊C4—31no—
218C22×C22⋊C4—31no—
219C22×C22⋊C4C2×D311yescharacteristic
220C22×C22⋊C4C2×D311yescharacteristic
221C22×C22⋊C4C2×D311yescharacteristic
222C22×C42—31no—
223C24×C3—24no—
224C24×C3—24no—
225C24×C3—24no—
226C24×C3—24no—
227C24×C3—24no—
228C24×C3C2×D418yes—
229C24×C3C2416yes—
230C24×C3C2416yes—
231C24×C3C2411yescharacteristic
232C23×D3—24no—
233C23×D3—24no—
234C23×D3—24no—
235C23×D3—24no—
236C23×D3—24no—
237C23×D3C2×D418yes—
238C23×D3C2416yes—
239C23×D3C2416yes—
240C2×C3×D4—248no—
241C2×C3×D4C24116yes—
242C22×C3×C4—24no—
243C22×C3×C4—24no—
244C22×C3×C4—24no—
245C22×C3×C4—248no—
246C22×C3×C4—24no—
247C22×C3×C4—24no—
248C22×C3×C4C2416yes—
249C22×C3×C4C2416yes—
250C22×C3×C4C2416yes—
251C22×C3×C4C2416yes—
252C22×C3×C4C2416yes—
253C22×C3×C4C24116yes—
254C2×#67—248no—
255C2×#67—248no—
256C2×#67—248no—
257C2×#67C2×D4196yescomplemented
258C2×#67C24116yes—
259C2×#67C24116yes—
260C2×#67C24116yes—
261C2×#67C24116yes—
262C22×Dic3—24no—
263C22×Dic3—24no—
264C22×Dic3—24no—
265C22×Dic3—248no—
266C22×Dic3—24no—
267C22×Dic3—248no—
268C22×Dic3—248no—
269C22×Dic3C2×D418yes—
270C22×Dic3#4118yescomplemented
271C22×Dic3C24116yes—
272C22×Dic3C24116yes—
273C22×Dic3C24116yes—
274C22×Dic3C2416yes—
275C22×Dic3C2416yes—
276C22×Dic3C2416yes—
277C22×Dic3C2416yes—
278C22×Dic3C2416yes—
279C22×Dic3C2416yes—
280#237—2256no—
281#235—2256no—
282C2×D12—248no—
283C2×D12C24116yes—
284C2×C4×D3—248no—
285C2×C4×D3—248no—
286C2×C4×D3—248no—
287C2×C4×D3—248no—
288C2×C4×D3C24116yes—
289C2×C4×D3C24116yes—
290C2×C4×D3C24116yes—
291C2×C4×D3C24116yes—
292C2×Dic6—248no—
293C2×Dic6—248no—
294C2×Dic6C24116yes—
295C2×Dic6C24116yes—
296C3×C4⋊C4C24116yes—
297C3×C4⋊C4C24116yes—
298C3×C22⋊C4C24116yes—
299C3×C22⋊C4C24116yes—
300C3×C22⋊C4C24116yes—
301#217C24116yes—
302(C2×D3)⋊C4C24116yes—
303(C2×D3)⋊C4C24116yes—
304(C2×D3)⋊C4C24116yes—
305(C2×D3)⋊C4C24116yes—
306C4⋊Dic3C24116yes—
307C4⋊Dic3C24116yes—
308Dic3⋊C4C24116yes—
309Dic3⋊C4C24116yes—
310Dic3⋊C4C24116yes—
311Dic3⋊C4C24116yes—
312Dic3⋊C4C24116yes—
313Dic3⋊C4C24116yes—
314C4×Dic3C24116yes—
315C25—31no—
316C25—31no—
317C25C22×D311yescharacteristic
318C25C22×D311yescharacteristic
319C2×#41—364no—
320C2×#41—364no—
321C2×#41—6192no—
322C2×#41—6192no—
323C22×Q8—312no—
324C22×Q8—312no—
325C22×Q8—68no—
326C22×Q8—68no—
327C22×D4—28no—
328C22×D4—316no—
329C22×D4—312no—
330C22×D4—312no—
331C22×D4—312no—
332C22×D4—312no—
333C22×D4—312no—
334C22×D4—68no—
335C22×D4—68no—
336C22×D4—68no—
337C22×D4—68no—
338C22×D4C22×D3112yes—
339C23×C4—28no—
340C23×C4—31no—
341C23×C4—31no—
342C23×C4—312no—
343C23×C4—312no—
344C23×C4—312no—
345C23×C4—31no—
346C23×C4—31no—
347C23×C4—31no—
348C23×C4—31no—
349C23×C4—312no—
350C23×C4—312no—
351C23×C4—312no—
352C23×C4—312no—
353C23×C4—68no—
354C23×C4—68no—
355C23×C4—68no—
356C23×C4—68no—
357C23×C4—68no—
358C23×C4—68no—
359C23×C4—68no—
360C23×C4C22×D3112yes—
361C23×C4C22×D311yescharacteristic
362C23×C4C22×D311yescharacteristic
363C23×C4C22×D311yescharacteristic
364C23×C4C22×D311yescharacteristic
365C23×C4C22×D311yescharacteristic
366C4⋊Q8—364no—
367#123—364no—
368#123—364no—
369#123—364no—
370#123C22×D3164yescomplemented
371C22⋊Q8—364no—
372C22⋊Q8—364no—
373#121—364no—
374#121—364no—
375C4×D4—364no—
376C4×D4—364no—
377C2×C4⋊C4—312no—
378C2×C4⋊C4—312no—
379C2×C4⋊C4—312no—
380C2×C4⋊C4—312no—
381C2×C4⋊C4—312no—
382C2×C4⋊C4—312no—
383C2×C4⋊C4—364no—
384C2×C4⋊C4—312no—
385C2×C4⋊C4—312no—
386C2×C4⋊C4—364no—
387C2×C4⋊C4C22×D3112yes—
388C2×C4⋊C4C22×D3112yes—
389C2×C22⋊C4—312no—
390C2×C22⋊C4—312no—
391C2×C22⋊C4—312no—
392C2×C22⋊C4—312no—
393C2×C22⋊C4—312no—
394C2×C22⋊C4C22×D3112yes—
395C2×C22⋊C4C22×D3112yes—
396C2×C22⋊C4C22×D3112yes—
397C2×C42—312no—
398C23×C3—232no—
399C23×C3—212no—
400C23×C3—212no—
401C23×C3—212no—
402C23×C3—212no—
403C23×C3—212no—
404C23×C3—416no—
405C23×C3C22×D4124yes—
406C23×C3C22×D414yes—
407C23×C3C2×#4114yes—
408C23×C32−1+414yes—
409C23×C3C2514yes—
410C23×C3C2514yes—
411C23×C3C2513yes—
412C22×D3—232no—
413C22×D3—212no—
414C22×D3—212no—
415C22×D3—212no—
416C22×D3—212no—
417C22×D3—212no—
418C22×D3—416no—
419C22×D3C22×D4124yes—
420C22×D3C2514yes—
421C22×D3C2514yes—
422C3×D4—232no—
423C2×C3×C4—212no—
424C2×C3×C4—212no—
425C2×C3×C4—212no—
426C2×C3×C4—232no—
427C2×C3×C4—212no—
428C2×C3×C4—212no—
429C2×C3×C4C2514yes—
430C2×C3×C4C2514yes—
431C2×C3×C4C2514yes—
432C2×C3×C4C2514yes—
433C2×C3×C4C2514yes—
434#67—232no—
435#67—232no—
436#67—232no—
437#67C22×D4164yescomplemented
438C2×Dic3—212no—
439C2×Dic3—212no—
440C2×Dic3—212no—
441C2×Dic3—232no—
442C2×Dic3—212no—
443C2×Dic3—232no—
444C2×Dic3—232no—
445C2×Dic3C22×D4124yes—
446C2×Dic3C2×#41124yescomplemented
447C2×Dic3C2514yes—
448C2×Dic3C2514yes—
449C2×Dic3C2514yes—
450C2×Dic3C2514yes—
451C2×Dic3C2514yes—
452C2×Dic3C2514yes—
453D12—232no—
454C4×D3—232no—
455C4×D3—232no—
456C4×D3—232no—
457C4×D3—232no—
458Dic6—232no—
459Dic6—232no—
460C24—24no—
461C24—24no—
462C24—24no—
463C24—24no—
464C24—24no—
465C24—38no—
466C24—36no—
467C24—36no—
468C24—64no—
469C24—64no—
470C24—64no—
471C24—64no—
472C24—64no—
473C24D3×D418yes—
474C24C23×D316yes—
475C24C23×D316yes—
476C24C23×D311yescharacteristic
477#41—6256no—
478#41—6256no—
479C2×Q8—316no—
480C2×Q8—316no—
481C2×Q8—648no—
482C2×Q8—648no—
483C2×D4—248no—
484C2×D4—396no—
485C2×D4—316no—
486C2×D4—316no—
487C2×D4—316no—
488C2×D4—316no—
489C2×D4—316no—
490C2×D4—648no—
491C2×D4—648no—
492C2×D4—648no—
493C2×D4—648no—
494C2×D4C23×D3116yes—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—248no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—38no—
502C22×C4—38no—
503C22×C4—36no—
504C22×C4—36no—
505C22×C4—36no—
506C22×C4—36no—
507C22×C4—36no—
508C22×C4—36no—
509C22×C4—316no—
510C22×C4—316no—
511C22×C4—316no—
512C22×C4—316no—
513C22×C4—316no—
514C22×C4—316no—
515C22×C4—316no—
516C22×C4—648no—
517C22×C4—648no—
518C22×C4—648no—
519C22×C4—648no—
520C22×C4—648no—
521C22×C4—648no—
522C22×C4—64no—
523C22×C4—64no—
524C22×C4—64no—
525C22×C4—648no—
526C22×C4—64no—
527C22×C4C23×D316yes—
528C22×C4C23×D316yes—
529C22×C4C23×D316yes—
530C22×C4C23×D316yes—
531C22×C4C23×D316yes—
532C22×C4C23×D3116yes—
533C4⋊C4—316no—
534C4⋊C4—316no—
535C4⋊C4—316no—
536C4⋊C4—316no—
537C4⋊C4—316no—
538C4⋊C4—316no—
539C4⋊C4—316no—
540C4⋊C4—316no—
541C4⋊C4C23×D3116yes—
542C4⋊C4C23×D3116yes—
543C22⋊C4—316no—
544C22⋊C4—316no—
545C22⋊C4—316no—
546C22⋊C4—316no—
547C22⋊C4—316no—
548C22⋊C4C23×D3116yes—
549C22⋊C4C23×D3116yes—
550C22⋊C4C23×D3116yes—
551C42—316no—
552C22×C3—24no—
553C22×C3—24no—
554C22×C3—248no—
555C22×C3—24no—
556C22×C3—24no—
557C22×C3—24no—
558C22×C3—424no—
559C22×C3#547116yescomplemented
560C22×C3C23×D418yes—
561C22×C3C23×D416yes—
562C22×C3C22×#4116yes—
563C22×C3C2×2−1+416yes—
564C22×C3C2611yescharacteristic
565C2×D3—24no—
566C2×D3—24no—
567C2×D3—248no—
568C2×D3—24no—
569C2×D3—24no—
570C2×D3—24no—
571C2×D3—424no—
572C2×D3C23×D418yes—
573C3×C4—24no—
574C3×C4—24no—
575C3×C4—24no—
576C3×C4—24no—
577C3×C4—24no—
578Dic3—24no—
579Dic3—24no—
580Dic3—24no—
581Dic3—24no—
582Dic3C23×D418yes—
583Dic3C22×#4118yescomplemented
584C23—232no—
585C23—212no—
586C23—212no—
587C23—212no—
588C23—212no—
589C23—212no—
590C23—324no—
591C23—34no—
592C23—34no—
593C23—416no—
594C23—632no—
595C23—612no—
596C23—612no—
597C23—612no—
598C23—612no—
599C23—612no—
600C23—1216no—
601C23C2×D3×D4124yes—
602C23C2×D3×D414yes—
603C23D3×#4114yes—
604C23#101014yes—
605C23C24×D314yes—
606C23C24×D314yes—
607C23C24×D313yes—
608Q8—632no—
609Q8—632no—
610D4—232no—
611D4—364no—
612D4—632no—
613D4—632no—
614D4—632no—
615D4—632no—
616C2×C4—212no—
617C2×C4—212no—
618C2×C4—232no—
619C2×C4—212no—
620C2×C4—212no—
621C2×C4—212no—
622C2×C4—324no—
623C2×C4—324no—
624C2×C4—34no—
625C2×C4—34no—
626C2×C4—34no—
627C2×C4—34no—
628C2×C4—34no—
629C2×C4—34no—
630C2×C4—632no—
631C2×C4—632no—
632C2×C4—632no—
633C2×C4—632no—
634C2×C4—632no—
635C2×C4—632no—
636C2×C4—612no—
637C2×C4—612no—
638C2×C4—612no—
639C2×C4—632no—
640C2×C4—612no—
641C2×C4C24×D314yes—
642C2×C4C24×D314yes—
643C2×C4C24×D314yes—
644C2×C4C24×D314yes—
645C2×C4C24×D314yes—
646C2×C3—28no—
647C2×C3—44no—
648C2×C3C2×#547112yescomplemented
649C2×C3C24×D411yescharacteristic
650C2×C3C23×#4111yescharacteristic
651C2×C3C22×2−1+411yescharacteristic
652D3—28no—
653D3—44no—
654C22—24no—
655C22—24no—
656C22—248no—
657C22—24no—
658C22—24no—
659C22—24no—
660C22—38no—
661C22—424no—
662C22—64no—
663C22—64no—
664C22—648no—
665C22—64no—
666C22—64no—
667C22—64no—
668C22—1224no—
669C22#5655116yesdirect product factor
670C22C22×D3×D418yes—
671C22C22×D3×D416yes—
672C22C2×D3×#4116yes—
673C22C2×#101016yes—
674C22C25×D311yescharacteristic
675C4—24no—
676C4—24no—
677C4—24no—
678C4—24no—
679C4—24no—
680C4—38no—
681C4—38no—
682C4—64no—
683C4—64no—
684C4—64no—
685C4—64no—
686C3C22×#54711yescharacteristic, complemented, Sylow
687C2—28no—
688C2—44no—
689C2—68no—
690C2—124no—
691C2C2×#5655112yesdirect product factor
692C2C23×D3×D411yescharacteristic
693C2C22×#101011yescharacteristic
694C2C22×D3×#4111yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC22×C3×#123C2
socleC24×C3C24
hypercenterC22×#123D3
hypocenterC3C22×#547
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C23×#237C2semidirect
2. C23×#235C2semidirect
3. C22×C3×#123C2semidirect
4. C22×#939C2semidirect
5. C23×Dic3⋊C4C2semidirect
6. C2×#5655C2direct (N × H)
7. C22×#894C2semidirect
8. C22×#896C2semidirect
9. C22×D3×C4⋊C4C2semidirect
10. C22×#888C2semidirect
11. C22×#883C2semidirect
12. C22×#884C2semidirect
13. C22×#886C2semidirect
14. C22×#878C2semidirect
15. C22×#67⋊C4C2semidirect
16. C22×#67⋊C4C2semidirect
28. C22×#237C22semidirect
30. C22×#235C22semidirect
38. C2×C3×#123C22semidirect
45. C2×#939C22semidirect
58. C22×Dic3⋊C4C22semidirect
60. #5655C22direct (N × H)
61. C2×#896C22semidirect
62. C2×#894C22semidirect
63. C2×D3×C4⋊C4C22semidirect
64. C2×#888C22semidirect
65. C2×#886C22semidirect
66. C2×#884C22semidirect
67. C2×#883C22semidirect
68. C2×#67⋊C4C22semidirect
69. C2×#67⋊C4C22semidirect
70. C2×#878C22semidirect
78. C22×#123D3semidirect
103. C22×#67D4semidirect
121. C2×#237C23semidirect
123. C2×#235C23semidirect
138. C3×#123C23semidirect
145. #939C23semidirect
158. C2×Dic3⋊C4C23semidirect
160. #896C23semidirect
161. #894C23semidirect
162. D3×C4⋊C4C23semidirect
163. #888C23semidirect
164. #886C23semidirect
165. #884C23semidirect
166. #883C23semidirect
167. #67⋊C4C23semidirect
168. #67⋊C4C23semidirect
169. #878C23semidirect
195. C2×#123C2×D3semidirect
257. C2×#67C2×D4semidirect
270. C22×Dic3#41semidirect
370. #123C22×D3semidirect
437. #67C22×D4semidirect
446. C2×Dic3C2×#41semidirect
559. C22×C3#547semidirect
583. Dic3C22×#41semidirect
648. C2×C3C2×#547semidirect
669. C22#5655direct (N × H)
686. C3C22×#547semidirect
691. C2C2×#5655direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#2372
C23×#2352
C22×C3×#1232
C22×#9392
C23×Dic3⋊C42
C2×#56552
C22×#8942
C22×#8962
C22×D3×C4⋊C42
C22×#8882
C22×#8832
C22×#8842
C22×#8862
C22×#8782
C22×#67⋊C42
C22×#5473