Finite Group Databasebeta

← C2×#26145 #6438519

Subgroups — C2×#26145 #6438519

Order 512.

2554 conjugacy classes of subgroups.

The subgroup lattice has 741 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#484C211yesmaximal, characteristic, complemented
2C22×#428C211yesmaximal, characteristic, complemented
3C2×#2417C211yesmaximal, characteristic
4C2×#2352C211yesmaximal, characteristic
5#26145C2116yesmaximal, direct product factor
6C2×#2097C211yesmaximal, characteristic, complemented
7C2×#2085C211yesmaximal, characteristic, complemented
8C2×#2077C211yesmaximal, characteristic, complemented
9C2×#2035C211yesmaximal, characteristic, complemented
10C2×#1928C211yesmaximal, characteristic, complemented
11C2×#1918C211yesmaximal, characteristic, complemented
12C2×#1894C211yesmaximal, characteristic, complemented
13C2×#1873C211yesmaximal, characteristic, complemented
14C2×#1870C211yesmaximal, characteristic
15C2×#1852C211yesmaximal, characteristic, complemented
16C2×#1852C211yesmaximal, characteristic, complemented
17C23×M16C2211yescharacteristic
18C22×C22⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C4×D4C2211yescharacteristic
21C22×#117C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C2×#484—28no—
25C2×#484C2218yescomplemented
26C2×#428—28no—
27C2×#428C2218yescomplemented
28C22×#107C2211yescharacteristic
29C22×#107C2211yescharacteristic
30C22×#107C2211yescharacteristic
31C22×#107C2211yescharacteristic
32C22×#106C2211yescharacteristic
33C22×#106C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×C22⋊C8C2211yescharacteristic
39C22×C22⋊C8C2211yescharacteristic
40C22×C22⋊C8C2211yescharacteristic
41#2417—24no—
42#2417C2218yes—
43C2×#398—21no—
44C2×#396—21no—
45#2352—24no—
46#2352C2218yes—
47C2×#391C2211yescharacteristic
48C2×#389C2211yescharacteristic
49C2×#388—21no—
50C2×#387—21no—
51C2×#386—21no—
52C2×#386—21no—
53C2×#382C2211yescharacteristic
54C2×#380—21no—
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4—21no—
60#2097C2218yescomplemented
61#2085C2218yescomplemented
62#2077C2218yescomplemented
63#2035C2218yescomplemented
64#1928C2218yescomplemented
65#1918C2218yescomplemented
66#1894C2218yescomplemented
67#1873C2218yescomplemented
68#1870C2218yes—
69#1852C2218yescomplemented
70#1852C2218yescomplemented
71C2×#340C2211yescharacteristic
72C2×#340C2211yescharacteristic
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C23×Q8C2311yescharacteristic
80C23×D4D411yescharacteristic
81C24×C4—21no—
82C24×C4—21no—
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C22×M16—24no—
86C22×M16—24no—
87C22×M16—24no—
88C22×M16C2314yes—
89C23×C8C2311yescharacteristic
90C23×C8C2311yescharacteristic
91C23×C8C2311yescharacteristic
92C23×C8C2311yescharacteristic
93C2×C22⋊Q8—22no—
94C2×C22⋊Q8—22no—
95C2×C22⋊Q8—24no—
96C2×C22⋊Q8—24no—
97C2×C22⋊Q8—24no—
98C2×C22⋊Q8—42no—
99C2×C22⋊Q8C2314yes—
100C2×C22⋊Q8C2314yes—
101C2×C4×D4—24no—
102C2×C4×D4—24no—
103C2×C4×D4D414yes—
104C2×C4×D4C2314yes—
105C2×#117—22no—
106C2×#117—24no—
107C2×#117—42no—
108C2×#117C2314yes—
109C22×C4⋊C4—24no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—22no—
112C22×C4⋊C4—21no—
113C22×C4⋊C4—21no—
114C22×C4⋊C4—21no—
115C22×C4⋊C4—22no—
116C22×C4⋊C4—21no—
117C22×C4⋊C4—21no—
118C22×C4⋊C4—42no—
119C22×C4⋊C4—42no—
120C22×C4⋊C4D411yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4—21no—
136C22×C22⋊C4D411yescharacteristic
137C22×C22⋊C4D411yescharacteristic
138C22×C42—21no—
139C22×C42—21no—
140C22×C42C2311yescharacteristic
141#484—232no—
142#428—232no—
143C2×#107—24no—
144C2×#107—24no—
145C2×#107—42no—
146C2×#107D418yescomplemented
147C2×#107C2314yes—
148C2×#107C2314yes—
149C2×#107C2314yes—
150C2×#107C2314yes—
151C2×#106—24no—
152C2×#106—24no—
153C2×#106C2314yes—
154C2×#106C2314yes—
155C2×#103—24no—
156C2×#103—24no—
157C2×#103—24no—
158C2×#103—42no—
159C2×#103C2314yes—
160C2×#103C2314yes—
161C2×#103C2314yes—
162C2×#103C2314yes—
163C2×C22⋊C8—24no—
164C2×C22⋊C8—24no—
165C2×C22⋊C8—24no—
166C2×C22⋊C8C2314yes—
167C2×C22⋊C8C2314yes—
168C2×C22⋊C8C2314yes—
169#398—28no—
170#396—28no—
171#391—22no—
172#391C2314yes—
173#389—22no—
174#389C2314yes—
175#388—28no—
176#387—28no—
177#386—28no—
178#386—28no—
179#382—22no—
180#382C2314yes—
181#380—22no—
182#380—22no—
183#380—22no—
184#380—28no—
185#380C2314yes—
186#380C2314yes—
187#380C2314yes—
188C4×C4⋊C4—22no—
189C4×C4⋊C4C2314yes—
190C4×C22⋊C4—28no—
191C2×#95—21no—
192C2×#95—21no—
193C2×#95—21no—
194C2×#95—21no—
195C2×#95—21no—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95—21no—
199C2×#95—21no—
200#340C2314yes—
201#340C2314yes—
202#340C2314yes—
203#340C2314yes—
204#340C2314yes—
205#340C2314yes—
206#336C2314yes—
207#336C2314yes—
208C25C2×D411yescharacteristic
209C25C2×D411yescharacteristic
210C22×Q8—21no—
211C22×Q8—22no—
212C22×Q8—22no—
213C22×Q8—22no—
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8C2412yes—
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—42no—
221C22×D4C2×D414yes—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—44no—
243C23×C4—44no—
244C23×C4—44no—
245C23×C4—44no—
246C23×C4—82no—
247C23×C4—82no—
248C23×C4C2×D412yes—
249C23×C4C2×D411yescharacteristic
250C23×C4C2×D411yescharacteristic
251C23×C4C2×D411yescharacteristic
252C23×C4C2×D412yes—
253C23×C4C2×D411yescharacteristic
254C23×C4#4114yes—
255C23×C4#4114yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2411yescharacteristic
259C2×M16—232no—
260C2×M16—28no—
261C2×M16—28no—
262C2×M16—28no—
263C22×C8—22no—
264C22×C8—22no—
265C22×C8—22no—
266C22×C8—22no—
267C22×C8—22no—
268C22×C8—22no—
269C22×C8—22no—
270C22×C8—22no—
271C22×C8—22no—
272C22×C8—22no—
273C22×C8C2×D414yes—
274C22×C8#4114yes—
275C22×C8C2412yes—
276C22×C8C2412yes—
277C22×C8C2412yes—
278C22×C8C2412yes—
279C22⋊Q8—28no—
280C22⋊Q8—28no—
281C22⋊Q8—28no—
282C22⋊Q8—44no—
283C22⋊Q8—48no—
284C22⋊Q8—48no—
285C4×D4—216no—
286C4×D4—28no—
287C4×D4—28no—
288#117—28no—
289#117—44no—
290#117—48no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—48no—
321C2×C4⋊C4—48no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—82no—
327C2×C4⋊C4C2×D414yes—
328C2×C4⋊C4C2×D414yes—
329C2×C4⋊C4C2×D414yes—
330C2×C4⋊C4C2412yes—
331C2×C4⋊C4C2412yes—
332C2×C4⋊C4C2412yes—
333C2×C4⋊C4C2412yes—
334C2×C4⋊C4C2412yes—
335C2×C4⋊C4C2412yes—
336C2×C4⋊C4C2412yes—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—82no—
350C2×C22⋊C4—82no—
351C2×C22⋊C4C2×D414yes—
352C2×C22⋊C4C2×D414yes—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—24no—
356C2×C42—24no—
357C2×C42—44no—
358C2×C42—82no—
359C2×C42C2×D412yes—
360C2×C42C2412yes—
361#107—28no—
362#107—28no—
363#107—44no—
364#107C2×D4116yescomplemented
365#106—28no—
366#106—28no—
367#103—28no—
368#103—28no—
369#103—28no—
370#103—44no—
371C22⋊C8—28no—
372C22⋊C8—28no—
373C22⋊C8—28no—
374#95—24no—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—24no—
382#95—24no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24#12314yes—
396C24#13714yes—
397C24C22×D412yes—
398C24C22×D412yes—
399C24C22×D411yescharacteristic
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—42no—
407C2×Q8—42no—
408C2×Q8—42no—
409C2×Q8—44no—
410C2×Q8—44no—
411C2×Q8—44no—
412C2×Q8—44no—
413C2×D4—28no—
414C2×D4—28no—
415C2×D4—44no—
416C2×D4—416no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—28no—
420C22×C4—28no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—28no—
424C22×C4—28no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—48no—
458C22×C4—48no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—44no—
464C22×C4—44no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—48no—
468C22×C4—48no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—84no—
488C22×C4—84no—
489C22×C4—816no—
490C22×C4—816no—
491C22×C4#12314yes—
492C22×C4#12318yes—
493C22×C4C22×D412yes—
494C22×C4C22×D412yes—
495C22×C4C22×D412yes—
496C22×C4C22×D412yes—
497C22×C4C22×D411yescharacteristic
498C22×C4C22×D412yes—
499C22×C4C2×#4114yes—
500C22×C4C2×#4114yes—
501C22×C4C2×#4112yes—
502C22×C4C2×#4112yes—
503C22×C4C2×#4112yes—
504C22×C4H(5,𝔽2)12yes—
505C22×C42−1+412yes—
506C22×C4C2511yescharacteristic
507M16—232no—
508C2×C8—28no—
509C2×C8—28no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—44no—
521C2×C8—44no—
522C2×C8C22×D414yes—
523C2×C8C2×#4114yes—
524C4⋊C4—28no—
525C4⋊C4—24no—
526C4⋊C4—24no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—48no—
540C4⋊C4—48no—
541C4⋊C4—48no—
542C4⋊C4—42no—
543C4⋊C4—48no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—84no—
549C4⋊C4C22×D414yes—
550C4⋊C4C22×D414yes—
551C22⋊C4—28no—
552C22⋊C4—28no—
553C22⋊C4—48no—
554C22⋊C4—48no—
555C22⋊C4—48no—
556C22⋊C4—48no—
557C22⋊C4—84no—
558C22⋊C4—84no—
559C42—24no—
560C42—22no—
561C42—22no—
562C42—48no—
563C42—84no—
564C23—28no—
565C23—28no—
566C23—28no—
567C23—28no—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—28no—
574C23—28no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—44no—
583C23—44no—
584C23—44no—
585C23—44no—
586C23—44no—
587C23—44no—
588C23—44no—
589C23—44no—
590C23C2×#12314yes—
591C23C2×#12312yes—
592C23D4212yes—
593C23#54712yes—
594C23C2×#13714yes—
595C23C2×#13712yes—
596C23#57512yes—
597C23#57612yes—
598C23#57812yes—
599C23C23×D411yescharacteristic
600Q8—42no—
601Q8—42no—
602Q8—42no—
603Q8—42no—
604Q8—84no—
605D4—416no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—28no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—216no—
613C2×C4—24no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—44no—
626C2×C4—44no—
627C2×C4—44no—
628C2×C4—48no—
629C2×C4—48no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—48no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—816no—
658C2×C4—816no—
659C2×C4—84no—
660C2×C4—84no—
661C2×C4—84no—
662C2×C4—84no—
663C2×C4—84no—
664C2×C4—84no—
665C2×C4C2×#12314yes—
666C2×C4C2×#12312yes—
667C2×C4#52514yes—
668C2×C4#53914yes—
669C2×C4D4212yes—
670C2×C4#54712yes—
671C2×C4#54814yes—
672C2×C4#55314yes—
673C2×C4C23×D411yescharacteristic
674C2×C4C22×#4111yescharacteristic
675C2×C4C22×#4111yescharacteristic
676C2×C4C22×#4111yescharacteristic
677C2×C4C2×H(5,𝔽2)11yescharacteristic
678C2×C4C2×2−1+411yescharacteristic
679C8—24no—
680C8—24no—
681C8—42no—
682C8—42no—
683C22—24no—
684C22—24no—
685C22—24no—
686C22—24no—
687C22—24no—
688C22—24no—
689C22—416no—
690C22—416no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22#244314yes—
700C22#309514yes—
701C22#309814yes—
702C22#327014yes—
703C22#327314yes—
704C22#334614yes—
705C22#335214yes—
706C22C22×#12311yescharacteristic
707C22C2×D4211yescharacteristic
708C22C2×#54711yescharacteristic
709C22C22×#13711yescharacteristic
710C22C2×#57511yescharacteristic
711C22C2×#57611yescharacteristic
712C22C2×#57811yescharacteristic
713C4—24no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—44no—
718C4—44no—
719C4—82no—
720C4—82no—
721C4—82no—
722C4—82no—
723C4—82no—
724C4—82no—
725C4#244314yes—
726C4C2×#52511yescharacteristic
727C4C2×#53911yescharacteristic
728C4C2×#54811yescharacteristic
729C4C2×#55311yescharacteristic
730C2—44no—
731C2—44no—
732C2#2614518yesdirect product factor
733C2C2×#244311yescharacteristic
734C2C2×#309511yescharacteristic
735C2C2×#309811yescharacteristic
736C2C2×#327011yescharacteristic
737C2C2×#327311yescharacteristic
738C2C2×#334611yescharacteristic
739C2C2×#335211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#484C2semidirect
2. C22×#428C2semidirect
5. #26145C2direct (N × H)
6. C2×#2097C2semidirect
7. C2×#2085C2semidirect
8. C2×#2077C2semidirect
9. C2×#2035C2semidirect
10. C2×#1928C2semidirect
11. C2×#1918C2semidirect
12. C2×#1894C2semidirect
13. C2×#1873C2semidirect
15. C2×#1852C2semidirect
16. C2×#1852C2semidirect
25. C2×#484C22semidirect
27. C2×#428C22semidirect
60. #2097C22semidirect
61. #2085C22semidirect
62. #2077C22semidirect
63. #2035C22semidirect
64. #1928C22semidirect
65. #1918C22semidirect
66. #1894C22semidirect
67. #1873C22semidirect
69. #1852C22semidirect
70. #1852C22semidirect
146. C2×#107D4semidirect
364. #107C2×D4semidirect
732. C2#26145direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4842
C22×#4282
C2×#24172
C2×#23522
#261452
C2×#20972
C2×#20852
C2×#20772
C2×#20352
C2×#19282
C2×#19182
C2×#18942
C2×#18732
C2×#18702
C2×#18522