Finite Group Databasebeta

← #10701673

Subgroups — #10701673

Order 768.

1902 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×#67C211yesmaximal, characteristic
2C22×C3×C22⋊C8C211yesmaximal, characteristic, complemented
3C22×#830C211yesmaximal, characteristic, complemented
4C22×(C2×D3)⋊C8C212yesmaximal, complemented
5C2×#4550C212yesmaximal, complemented
6#10964—31nomaximal, Sylow
7C24×C3×C4C2211yescharacteristic
8C23×#67C411yescharacteristic
9C23×C4×D3C2211yescharacteristic
10C23×C3×C8C2212yes—
11C22×#217C411yescharacteristic
12C2×C4×#67—22no—
13C2×C4×#67—22no—
14C2×C4×#67—24no—
15C2×C4×#67—24no—
16C22×(C2×D3)⋊C4C411yescharacteristic
17C22×Dic3⋊C4C411yescharacteristic
18C22×C4×Dic3C2211yescharacteristic
19C23×C3⋊C8C2212yes—
20C2×C3×C22⋊C8—22no—
21C2×C3×C22⋊C8—24no—
22C2×#830—22no—
23C2×#830—24no—
24C2×(C2×D3)⋊C8—24no—
25C2×(C2×D3)⋊C8—24no—
26C2×(C2×D3)⋊C8—24no—
27#4550—24no—
28C22×C4×D4—31no—
29C22×C22⋊C8—31no—
30C22×C22⋊C8—32no—
31C22×C22⋊C8D311yescharacteristic, complemented
32C2×#336—32no—
33C25×C3C2×C411yescharacteristic
34C24×D3C2×C411yescharacteristic
35C23×C3×C4—22no—
36C23×C3×C4—22no—
37C23×C3×C4—22no—
38C23×C3×C4—22no—
39C23×C3×C4—22no—
40C23×C3×C4—22no—
41C23×C3×C4C2×C411yescharacteristic
42C23×C3×C4D412yes—
43C23×C3×C4D412yes—
44C23×C3×C4C2311yescharacteristic
45C22×#67—22no—
46C22×#67—22no—
47C22×#67—22no—
48C22×#67—22no—
49C22×#67—22no—
50C22×#67—22no—
51C22×#67C814yescomplemented
52C23×Dic3C2×C411yescharacteristic
53C23×Dic3C2×C411yescharacteristic
54C23×Dic3C2×C411yescharacteristic
55C22×C4×D3—21no—
56C22×C4×D3—22no—
57C22×C4×D3—21no—
58C22×C4×D3—22no—
59C22×C4×D3—22no—
60C22×C4×D3—22no—
61C22×C4×D3—22no—
62C22×C4×D3D414yes—
63C22×C3×C8—22no—
64C22×C3×C8—22no—
65C22×C3×C8—22no—
66C22×C3×C8—22no—
67C22×C3×C8—22no—
68C22×C3×C8—22no—
69C22×C3×C8D414yescomplemented
70C2×#217—22no—
71C2×#217—22no—
72C2×#217—22no—
73C4×#67—216no—
74C4×#67—216no—
75C2×(C2×D3)⋊C4—22no—
76C2×(C2×D3)⋊C4—22no—
77C2×(C2×D3)⋊C4—22no—
78C2×Dic3⋊C4—22no—
79C2×Dic3⋊C4—22no—
80C2×Dic3⋊C4—22no—
81C2×C4×Dic3—21no—
82C2×C4×Dic3—22no—
83C2×C4×Dic3—21no—
84C2×C4×Dic3D414yes—
85C22×C3⋊C8—22no—
86C22×C3⋊C8—22no—
87C22×C3⋊C8—22no—
88C22×C3⋊C8—22no—
89C22×C3⋊C8—22no—
90C22×C3⋊C8—22no—
91C22×C3⋊C8D414yescomplemented
92C3×C22⋊C8—28no—
93#830—28no—
94(C2×D3)⋊C8—216no—
95C23×D4—31no—
96C24×C4—31no—
97C24×C4C2×D311yescharacteristic
98C23×C8—32no—
99C23×C8C2×D312yes—
100C2×C4×D4—64no—
101C2×C4×D4—64no—
102C2×C4×D4—62no—
103C2×C4×D4—62no—
104C22×C4⋊C4—31no—
105C22×C22⋊C4—31no—
106C22×C22⋊C4—31no—
107C22×C42—31no—
108C2×C22⋊C8—22no—
109C2×C22⋊C8—24no—
110C2×C22⋊C8—64no—
111C2×C22⋊C8—64no—
112C2×C22⋊C8—64no—
113C2×C22⋊C8—62no—
114C2×C22⋊C8—64no—
115#336—64no—
116C24×C3—21no—
117C24×C3—21no—
118C24×C3—22no—
119C24×C3—22no—
120C24×C3—21no—
121C24×C3—21no—
122C24×C3—22no—
123C24×C3—22no—
124C24×C3C22⋊C412yes—
125C24×C3C2×C812yes—
126C24×C3M1612yes—
127C24×C3C22×C411yescharacteristic
128C23×D3—21no—
129C23×D3—21no—
130C23×D3—22no—
131C23×D3—22no—
132C23×D3—21no—
133C23×D3—21no—
134C23×D3—22no—
135C23×D3—22no—
136C23×D3C22⋊C412yes—
137C23×D3C2×C812yes—
138C23×D3M1612yes—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
143C22×C3×C4—22no—
144C22×C3×C4—22no—
145C22×C3×C4—24no—
146C22×C3×C4—24no—
147C22×C3×C4—24no—
148C22×C3×C4—24no—
149C22×C3×C4—22no—
150C22×C3×C4—22no—
151C22×C3×C4—42no—
152C22×C3×C4—42no—
153C22×C3×C4—42no—
154C22×C3×C4—42no—
155C22×C3×C4—42no—
156C22×C3×C4—42no—
157C22×C3×C4—42no—
158C22×C3×C4—42no—
159C22×C3×C4C22⋊C412yes—
160C22×C3×C4C2×D411yescharacteristic
161C22×C3×C4C2×D412yes—
162C22×C3×C4C2×D412yes—
163C22×C3×C4C2×D412yes—
164C22×C3×C4C2×D411yescharacteristic
165C22×C3×C4C2×D412yes—
166C22×C3×C4#4112yes—
167C22×C3×C4#4112yes—
168C2×#67—28no—
169C2×#67—28no—
170C2×#67—28no—
171C2×#67—28no—
172C2×#67—28no—
173C2×#67—28no—
174C2×#67—28no—
175C22×Dic3—21no—
176C22×Dic3—21no—
177C22×Dic3—21no—
178C22×Dic3—21no—
179C22×Dic3—21no—
180C22×Dic3—21no—
181C22×Dic3—21no—
182C22×Dic3—21no—
183C22×Dic3—22no—
184C22×Dic3—22no—
185C22×Dic3—22no—
186C22×Dic3—22no—
187C22×Dic3C22⋊C412yes—
188C22×Dic3C22⋊C412yes—
189C22×Dic3C22⋊C412yes—
190C22×Dic3C2×C812yes—
191C22×Dic3M1612yes—
192C2×C4×D3—24no—
193C2×C4×D3—24no—
194C2×C4×D3—24no—
195C2×C4×D3—24no—
196C2×C4×D3—24no—
197C2×C4×D3—24no—
198C2×C4×D3—41no—
199C2×C4×D3—41no—
200C2×C4×D3—42no—
201C2×C4×D3—42no—
202C2×C4×D3—42no—
203C2×C4×D3—42no—
204C2×C4×D3—41no—
205C2×C4×D3—41no—
206C2×C4×D3—42no—
207C2×C4×D3—42no—
208C2×C3×C8—24no—
209C2×C3×C8—24no—
210C2×C3×C8—24no—
211C2×C3×C8—42no—
212C2×C3×C8—42no—
213C2×C3×C8—42no—
214C2×C3×C8—42no—
215#217—28no—
216(C2×D3)⋊C4—28no—
217Dic3⋊C4—28no—
218C4×Dic3—24no—
219C4×Dic3—24no—
220C2×C3⋊C8—24no—
221C2×C3⋊C8—24no—
222C2×C3⋊C8—24no—
223C2×C3⋊C8—42no—
224C2×C3⋊C8—42no—
225C2×C3⋊C8—42no—
226C2×C3⋊C8—42no—
227C25—31no—
228C25C4×D311yescharacteristic
229C22×D4—34no—
230C22×D4—62no—
231C22×D4—62no—
232C22×D4—62no—
233C22×D4—62no—
234C22×D4—62no—
235C22×D4—62no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—31no—
243C23×C4—31no—
244C23×C4—31no—
245C23×C4—34no—
246C23×C4—61no—
247C23×C4—62no—
248C23×C4—62no—
249C23×C4—62no—
250C23×C4—62no—
251C23×C4—61no—
252C23×C4—62no—
253C23×C4C4×D311yescharacteristic
254C23×C4D1212yes—
255C23×C4#6712yes—
256C23×C4C22×D311yescharacteristic
257C22×C8—22no—
258C22×C8—22no—
259C22×C8—22no—
260C22×C8—22no—
261C22×C8—22no—
262C22×C8—22no—
263C22×C8—34no—
264C22×C8—62no—
265C22×C8—62no—
266C22×C8—62no—
267C22×C8—62no—
268C22×C8—62no—
269C22×C8—62no—
270C22×C8#6714yescomplemented
271C4×D4—616no—
272C4×D4—616no—
273C2×C4⋊C4—62no—
274C2×C4⋊C4—62no—
275C2×C4⋊C4—62no—
276C2×C22⋊C4—62no—
277C2×C22⋊C4—62no—
278C2×C22⋊C4—62no—
279C2×C22⋊C4—62no—
280C2×C22⋊C4—62no—
281C2×C22⋊C4—62no—
282C2×C42—34no—
283C2×C42—61no—
284C2×C42—62no—
285C2×C42—61no—
286C22⋊C8—28no—
287C22⋊C8—616no—
288C22⋊C8—68no—
289C23×C3—22no—
290C23×C3—22no—
291C23×C3—22no—
292C23×C3—22no—
293C23×C3—22no—
294C23×C3—22no—
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—22no—
298C23×C3—22no—
299C23×C3—24no—
300C23×C3—24no—
301C23×C3—24no—
302C23×C3—24no—
303C23×C3—42no—
304C23×C3—42no—
305C23×C3—42no—
306C23×C3—42no—
307C23×C3—42no—
308C23×C3—42no—
309C23×C3—42no—
310C23×C3—42no—
311C23×C3C22⋊C814yescomplemented
312C23×C3C2×C22⋊C411yescharacteristic
313C23×C3C2×C22⋊C411yescharacteristic
314C23×C3C2×C22⋊C411yescharacteristic
315C23×C3C4×D412yes—
316C23×C3C4×D412yes—
317C23×C3C22×C811yescharacteristic
318C23×C3C2×M1611yescharacteristic
319C23×C3C2×M1611yescharacteristic
320C23×C3C2×M1611yescharacteristic
321C23×C3#13112yes—
322C23×C3#13112yes—
323C22×D3—22no—
324C22×D3—24no—
325C22×D3—22no—
326C22×D3—22no—
327C22×D3—22no—
328C22×D3—22no—
329C22×D3—22no—
330C22×D3—24no—
331C22×D3—24no—
332C22×D3—24no—
333C22×D3—24no—
334C22×D3—24no—
335C22×D3—41no—
336C22×D3—41no—
337C22×D3—42no—
338C22×D3—41no—
339C22×D3—42no—
340C22×D3—41no—
341C22×D3—42no—
342C22×D3—42no—
343C22×D3—42no—
344C22×D3—42no—
345C22×D3C22⋊C814yescomplemented
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—42no—
350C2×C3×C4—42no—
351C2×C3×C4—44no—
352C2×C3×C4—44no—
353C2×C3×C4—44no—
354C2×C3×C4—44no—
355C2×C3×C4#12011yescharacteristic
356C2×C3×C4#12012yes—
357C2×C3×C4#12012yes—
358C2×C3×C4#12012yes—
359C2×C3×C4#12011yescharacteristic
360C2×C3×C4#12112yes—
361C2×C3×C4#12112yes—
362C2×C3×C4#12112yes—
363C2×C3×C4#12112yes—
364C2×C3×C4#12112yes—
365C2×C3×C4#12112yes—
366C2×C3×C4#12312yes—
367C2×C3×C4#12311yescharacteristic
368C2×C3×C4#12311yescharacteristic
369C2×C3×C4#12412yes—
370C2×C3×C4#12712yes—
371#67—232no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—24no—
381C2×Dic3—24no—
382C2×Dic3—41no—
383C2×Dic3—41no—
384C2×Dic3—42no—
385C2×Dic3—41no—
386C2×Dic3—42no—
387C2×Dic3—41no—
388C2×Dic3C22⋊C814yescomplemented
389C4×D3—44no—
390C4×D3—44no—
391C4×D3—44no—
392C4×D3—44no—
393C3×C8—44no—
394C3⋊C8—44no—
395C24—21no—
396C24—21no—
397C24—22no—
398C24—22no—
399C24—21no—
400C24—21no—
401C24—22no—
402C24—22no—
403C24—32no—
404C24—32no—
405C24—32no—
406C24—61no—
407C24—62no—
408C24—61no—
409C24—62no—
410C24—61no—
411C24—62no—
412C24—61no—
413C24—62no—
414C24D3×C812yes—
415C24ΓL(1,𝔽25)12yes—
416C24(C2×D3)⋊C412yes—
417C24C2×C4×D311yescharacteristic
418C2×D4—68no—
419C2×D4—68no—
420C2×D4—68no—
421C2×D4—68no—
422C2×D4—68no—
423C2×D4—68no—
424C2×D4—68no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—32no—
438C22×C4—32no—
439C22×C4—32no—
440C22×C4—32no—
441C22×C4—32no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—61no—
451C22×C4—61no—
452C22×C4—61no—
453C22×C4—61no—
454C22×C4—61no—
455C22×C4—61no—
456C22×C4—62no—
457C22×C4—62no—
458C22×C4—62no—
459C22×C4—61no—
460C22×C4—61no—
461C22×C4—62no—
462C22×C4—64no—
463C22×C4—64no—
464C22×C4—64no—
465C22×C4—64no—
466C22×C4—64no—
467C22×C4—64no—
468C22×C4—121no—
469C22×C4—122no—
470C22×C4—122no—
471C22×C4—121no—
472C22×C4—121no—
473C22×C4—122no—
474C22×C4—122no—
475C22×C4—122no—
476C22×C4—122no—
477C22×C4—121no—
478C22×C4(C2×D3)⋊C412yes—
479C22×C4C2×D1211yescharacteristic
480C22×C4#23512yes—
481C22×C4D3×D412yes—
482C22×C4D3×D412yes—
483C22×C4D3×D412yes—
484C22×C4#23712yes—
485C22×C4C2×#6711yescharacteristic
486C22×C4C2×#6712yes—
487C2×C8—24no—
488C2×C8—24no—
489C2×C8—24no—
490C2×C8—42no—
491C2×C8—42no—
492C2×C8—42no—
493C2×C8—42no—
494C2×C8—64no—
495C2×C8—64no—
496C2×C8—64no—
497C2×C8—122no—
498C2×C8—122no—
499C2×C8—122no—
500C2×C8—122no—
501C4⋊C4—68no—
502C22⋊C4—68no—
503C22⋊C4—68no—
504C42—64no—
505C42—64no—
506C22×C3—24no—
507C22×C3—24no—
508C22×C3—24no—
509C22×C3—44no—
510C22×C3—42no—
511C22×C3—42no—
512C22×C3—44no—
513C22×C3—42no—
514C22×C3—44no—
515C22×C3—44no—
516C22×C3—42no—
517C22×C3#37911yescharacteristic
518C22×C3#38612yes—
519C22×C3#38611yescharacteristic
520C22×C3#38611yescharacteristic
521C22×C3#39012yes—
522C22×C3C2×C22⋊C811yescharacteristic
523C22×C3C2×C22⋊C811yescharacteristic
524C22×C3C2×C22⋊C811yescharacteristic
525C22×C3#40711yescharacteristic
526C22×C3#40711yescharacteristic
527C22×C3#40711yescharacteristic
528C22×C3#40811yescharacteristic
529C22×C3#40812yes—
530C22×C3#40812yes—
531C22×C3#40811yescharacteristic
532C22×C3C8×D412yes—
533C22×C3C8×D412yes—
534C22×C3#43512yes—
535C22×C3#43512yes—
536C22×C3#43512yes—
537C22×C3#43512yes—
538C22×C3#43612yes—
539C22×C3#43612yes—
540C2×D3—28no—
541C2×D3—24no—
542C2×D3—42no—
543C2×D3—42no—
544C2×D3—42no—
545C2×D3—42no—
546C2×D3—44no—
547C2×D3—42no—
548C2×D3—44no—
549C2×D3—44no—
550C2×D3—42no—
551C3×C4—42no—
552C3×C4#39212yes—
553C3×C4#39212yes—
554C3×C4#39412yes—
555C3×C4#39412yes—
556Dic3—24no—
557Dic3—42no—
558Dic3—42no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—22no—
564C23—22no—
565C23—22no—
566C23—24no—
567C23—22no—
568C23—22no—
569C23—24no—
570C23—24no—
571C23—22no—
572C23—24no—
573C23—34no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—62no—
583C23—64no—
584C23—62no—
585C23—64no—
586C23—62no—
587C23—64no—
588C23—62no—
589C23—62no—
590C23—64no—
591C23—64no—
592C23—62no—
593C23—64no—
594C23—122no—
595C23—121no—
596C23—122no—
597C23—121no—
598C23—121no—
599C23—122no—
600C23—122no—
601C23—122no—
602C23—121no—
603C23—122no—
604C23(C2×D3)⋊C814yescomplemented
605C23D3×C22⋊C411yescharacteristic
606C23D3×C22⋊C411yescharacteristic
607C23#67⋊C412yes—
608C23C2×D3×C811yescharacteristic
609C23C2×ΓL(1,𝔽25)11yescharacteristic
610C23#90112yes—
611C23D3×M1611yescharacteristic
612C23D3×M1611yescharacteristic
613C23#90712yes—
614C23C2×(C2×D3)⋊C411yescharacteristic
615C23C4×#6712yes—
616D4—632no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—34no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—44no—
624C2×C4—44no—
625C2×C4—44no—
626C2×C4—44no—
627C2×C4—62no—
628C2×C4—62no—
629C2×C4—62no—
630C2×C4—62no—
631C2×C4—62no—
632C2×C4—62no—
633C2×C4—62no—
634C2×C4—62no—
635C2×C4—64no—
636C2×C4—64no—
637C2×C4—121no—
638C2×C4—122no—
639C2×C4—121no—
640C2×C4—121no—
641C2×C4—122no—
642C2×C4—121no—
643C2×C4—124no—
644C2×C4—124no—
645C2×C4—124no—
646C2×C4—124no—
647C2×C4#88211yescharacteristic
648C2×C4#88212yes—
649C2×C4#88312yes—
650C2×C4#88412yes—
651C2×C4#88412yes—
652C2×C4#88512yes—
653C2×C4#88611yescharacteristic
654C2×C4#92911yescharacteristic
655C2×C4#93012yes—
656C2×C4#93712yes—
657C2×C4#93712yes—
658C2×C4#93812yes—
659C2×C4#93912yes—
660C2×C4#93912yes—
661C2×C4#94012yes—
662C2×C4#95311yescharacteristic
663C8—44no—
664C8—124no—
665C2×C3—44no—
666C2×C3#143811yescharacteristic
667C2×C3#177911yescharacteristic
668C2×C3#178011yescharacteristic
669C2×C3#186911yescharacteristic
670C2×C3#186911yescharacteristic
671C2×C3#186912yes—
672C2×C3#187011yescharacteristic
673C2×C3#187011yescharacteristic
674C2×C3#187012yes—
675C2×C3#195412yes—
676C2×C3#195512yes—
677D3—44no—
678C22—24no—
679C22—24no—
680C22—24no—
681C22—44no—
682C22—44no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—44no—
687C22—44no—
688C22—42no—
689C22—64no—
690C22—68no—
691C22—124no—
692C22—124no—
693C22—122no—
694C22—122no—
695C22—122no—
696C22—122no—
697C22—122no—
698C22—124no—
699C22—122no—
700C22D3×C22⋊C811yescharacteristic
701C22D3×C22⋊C811yescharacteristic
702C22#67⋊C812yes—
703C22#472611yescharacteristic
704C22#472611yescharacteristic
705C22#472712yes—
706C22#472712yes—
707C22#472812yes—
708C22#472912yes—
709C22#473012yes—
710C22#495511yescharacteristic
711C22#495612yes—
712C22#495712yes—
713C22#495811yescharacteristic
714C22C2×(C2×D3)⋊C811yescharacteristic
715C22C8×#6712yes—
716C22#511011yescharacteristic
717C22#511112yes—
718C22#512611yescharacteristic
719C22#512712yes—
720C22#512812yes—
721C22#512911yescharacteristic
722C22#521311yescharacteristic
723C4—42no—
724C4—64no—
725C4—122no—
726C4—122no—
727C4#495912yes—
728C4#496012yes—
729C4#496112yes—
730C4#522312yes—
731C3#1096411yescharacteristic, complemented, Sylow
732C2—44no—
733C2—124no—
734C2#6991612yes—
735C2#6991712yes—
736C2#6995211yescharacteristic
737C2#6995311yescharacteristic
738C2#6995511yescharacteristic
739C2#6995611yescharacteristic
740C2#6995712yes—
741C2#6995812yes—
742C2#7155011yescharacteristic
743C2#7197511yescharacteristic
744C2#7199611yescharacteristic
subgroupG/H
center, FrattiniC23×C4C22×D3
commutatorC23×C3C22×C8
FittingC22×C3×C22⋊C8C2
socleC24×C3C22×C4
prime radicalC23×#67C4
cosocleC23×C3×C4C23
hypercenterC22×C22⋊C8D3
hypocenterC3#10964
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×C3×C22⋊C8C2semidirect
3. C22×#830C2semidirect
4. C22×(C2×D3)⋊C8C2semidirect
5. C2×#4550C2semidirect
31. C22×C22⋊C8D3semidirect
51. C22×#67C8semidirect
69. C22×C3×C8D4semidirect
91. C22×C3⋊C8D4semidirect
270. C22×C8#67semidirect
311. C23×C3C22⋊C8semidirect
345. C22×D3C22⋊C8semidirect
388. C2×Dic3C22⋊C8semidirect
604. C23(C2×D3)⋊C8semidirect
731. C3#10964semidirect

Maximal subgroups

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

subgroupindex
C22×C4×#672
C22×C3×C22⋊C82
C22×#8302
C22×(C2×D3)⋊C82
C2×#45502
#109643