Finite Group Databasebeta

← C3×#83943 #11868078

Subgroups — C3×#83943 #11868078

Order 1152.

1081 conjugacy classes of subgroups.

The subgroup lattice has 669 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C3×#5822C211yesmaximal, characteristic, complemented
3C3×#5819C211yesmaximal, characteristic, complemented
4C2×C3×#932C211yesmaximal, characteristic, complemented
5C2×C3×#833C211yesmaximal, characteristic, complemented
6C3×#5200C214yesmaximal, complemented
7C3×#5199C214yesmaximal, complemented
8C3×#5132C211yesmaximal, characteristic, complemented
9C3×#5124C211yesmaximal, characteristic, complemented
10C3×#3068—31nomaximal
11#83943C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C22×C32×D4C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15C32×AGL(1,ℤ/8)—22no—
16C32×AGL(1,ℤ/8)C2214yes—
17C2×C32×SD16—21no—
18C2×C32×D8—21no—
19C2×C32×M16C2211yescharacteristic
20C3×#951C2212yescomplemented
21C3×#950—22no—
22C3×#949C2212yescomplemented
23C3×#948—22no—
24C3×#948C2214yescomplemented
25C3×#942—21no—
26C2×C3×#214C2212yescomplemented
27C3×#932—21no—
28C3×#932—22no—
29C3×#932—22no—
30C2×C3×#213C2212yescomplemented
31C2×C3×#208—22no—
32C2×C3×#208C2211yescharacteristic
33C2×C3×#208C2211yescharacteristic
34C2×C3×#208C2211yescharacteristic
35C3×#833C2214yescomplemented
36C3×#824C2212yescomplemented
37C3×#823C2212yescomplemented
38C3×#822C2214yescomplemented
39C3×#575—31no—
40C2×C3×AGL(1,ℤ/8)—21no—
41C2×C3×AGL(1,ℤ/8)—31no—
42C2×C3×AGL(1,ℤ/8)D311yescharacteristic, complemented
43C2×C3×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
44C3×#568—31no—
45#5822C2×C311yescharacteristic, complemented
46#5819C2×C311yescharacteristic, complemented
47C2×#932C2×C311yescharacteristic, complemented
48C3×#472—34no—
49C3×#471—34no—
50C3×#430—31no—
51C3×#413—31no—
52C2×C3×#100—31no—
53C2×#833C2×C311yescharacteristic, complemented
54#5200C2×C314yescomplemented
55#5199C2×C314yescomplemented
56#5132C2×C311yescharacteristic, complemented
57#5124C2×C311yescharacteristic, complemented
58C24×C32—21no—
59C32×#41—21no—
60C32×#41—21no—
61C32×#41D412yes—
62C32×#41C2312yes—
63C2×C32×Q8D411yescharacteristic
64C2×C32×D4—21no—
65C2×C32×D4—21no—
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4—21no—
69C2×C32×D4—21no—
70C2×C32×D4D411yescharacteristic
71C2×C32×D4C2312yes—
72C22×C32×C4—21no—
73C22×C32×C4C2311yescharacteristic
74C2×C3×#67—21no—
75C3×#235—21no—
76C3×#235—21no—
77C3×#235—21no—
78C3×#235—21no—
79C2×C3×D12C2311yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×Dic6C2311yescharacteristic
82C32×SD16—24no—
83C32×D8—24no—
84C32×M16—21no—
85C32×M16C2312yes—
86C2×C32×C8—21no—
87C3×#216—22no—
88C3×#215—22no—
89C3×#214—22no—
90C3×#214—24no—
91C3×#213—22no—
92C3×#213—24no—
93C3×#208—21no—
94C3×#208—21no—
95C3×#208—24no—
96C3×#208D412yes—
97C3×#208D412yes—
98C3×#208C2312yes—
99C3×#208C2312yes—
100C2×C3×C3⋊C8—21no—
101C2×C3×C3⋊C8—21no—
102C2×C3×C3⋊C8—24no—
103C2×C3×C3⋊C8C2312yes—
104#3068—31noSylow
105C2×C3×#41—21no—
106C2×C3×#41—31no—
107C2×C3×#41C2×D311yescharacteristic
108C2×C3×#41C22×C311yescharacteristic
109C22×C3×D4—21no—
110C22×C3×D4C2×D311yescharacteristic
111C22×C3×D4C22×C311yescharacteristic
112C2×#235C22×C311yescharacteristic
113C3×#137—32no—
114C3×#137—61no—
115C3×AGL(1,ℤ/8)—24no—
116C3×AGL(1,ℤ/8)—22no—
117C3×AGL(1,ℤ/8)—22no—
118C3×AGL(1,ℤ/8)—24no—
119C3×AGL(1,ℤ/8)—32no—
120C3×AGL(1,ℤ/8)—62no—
121C3×AGL(1,ℤ/8)—62no—
122C3×AGL(1,ℤ/8)—61no—
123C3×AGL(1,ℤ/8)C2×D314yes—
124C3×AGL(1,ℤ/8)C22×C314yes—
125C3×#135—62no—
126C2×C3×SD16—22no—
127C2×C3×SD16—21no—
128C2×C3×SD16—21no—
129C2×C3×SD16—32no—
130C2×C3×D8—22no—
131C2×C3×D8—21no—
132C2×C3×D8—21no—
133C2×C3×D8—32no—
134C3×#131—34no—
135C3×#131—62no—
136C2×C3×M16—21no—
137C2×C3×M16—31no—
138C2×C3×M16—31no—
139C2×C3×M16—31no—
140C2×C3×M16—62no—
141C2×C3×M16C2×D311yescharacteristic
142C2×C3×M16C22×C311yescharacteristic
143#951C22×C312yescomplemented
144#950—22no—
145#949C22×C312yescomplemented
146#948—22no—
147#948C22×C314yescomplemented
148#942—21no—
149C2×#214C22×C312yescomplemented
150#932—21no—
151#932—22no—
152#932—22no—
153C2×#213C22×C312yescomplemented
154C2×#208—22no—
155C2×#208C22×C311yescharacteristic
156C2×#208C22×C311yescharacteristic
157C2×#208C22×C311yescharacteristic
158C3×#108—34no—
159C3×#101—32no—
160C3×#100—34no—
161C3×#100—32no—
162#833C22×C314yescomplemented
163#824C22×C312yescomplemented
164#823C22×C312yescomplemented
165#822C22×C314yescomplemented
166C23×C32—21no—
167C23×C32—22no—
168C23×C32—41no—
169C23×C32—41no—
170C23×C32—82no—
171C23×C32#4111yescharacteristic
172C22×C3×D3—21no—
173C32×Q8—21no—
174C32×Q8C2×D412yes—
175C32×D4—22no—
176C32×D4—22no—
177C32×D4—22no—
178C32×D4—21no—
179C32×D4—22no—
180C32×D4—41no—
181C32×D4—41no—
182C32×D4C2×D412yes—
183C2×C32×C4—21no—
184C2×C32×C4—22no—
185C2×C32×C4—22no—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4#4111yescharacteristic
191C2×C32×C4C2411yescharacteristic
192C3×#67—41no—
193C3×#67—41no—
194C2×C3×Dic3—21no—
195C3×D12—21no—
196C3×D12—21no—
197C3×C4×D3—41no—
198C3×C4×D3—41no—
199C3×Dic6—21no—
200C3×Dic6—21no—
201C32×C8—22no—
202C3×C3⋊C8—22no—
203C3×C3⋊C8—22no—
204C3×C3⋊C8C2×D414yes—
205#575—31no—
206C2×AGL(1,ℤ/8)—31no—
207C2×AGL(1,ℤ/8)C3×D311yescharacteristic, complemented
208#568—31no—
209#472—34no—
210#471—34no—
211#430—31no—
212#413—31no—
213C2×#100—31no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3—41no—
217C3×#41—21no—
218C3×#41—21no—
219C3×#41—21no—
220C3×#41—21no—
221C3×#41—22no—
222C3×#41—22no—
223C3×#41—41no—
224C3×#41—41no—
225C3×#41—61no—
226C3×#41—61no—
227C3×#41—61no—
228C3×#41—61no—
229C3×#41#6712yes—
230C3×#41C3×D412yes—
231C3×#41C22×D312yes—
232C3×#41C23×C312yes—
233C2×C3×Q8—21no—
234C2×C3×Q8—31no—
235C2×C3×Q8#6711yescharacteristic
236C2×C3×Q8C3×D411yescharacteristic
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—22no—
240C2×C3×D4—22no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4—22no—
253C2×C3×D4—31no—
254C2×C3×D4—41no—
255C2×C3×D4—41no—
256C2×C3×D4—41no—
257C2×C3×D4—41no—
258C2×C3×D4—61no—
259C2×C3×D4#6711yescharacteristic
260C2×C3×D4C3×D411yescharacteristic
261C2×C3×D4C22×D312yes—
262C2×C3×D4C23×C312yes—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—41no—
267C22×C3×C4—61no—
268C22×C3×C4C22×D311yescharacteristic
269C22×C3×C4C23×C311yescharacteristic
270C2×#67—21no—
271#235—21no—
272#235—21no—
273#235—21no—
274#235—21no—
275C2×D12C23×C311yescharacteristic
276C2×C4×D3—21no—
277C2×Dic6C23×C311yescharacteristic
278C3×Q16—62no—
279C3×SD16—28no—
280C3×SD16—24no—
281C3×SD16—24no—
282C3×SD16—64no—
283C3×SD16—62no—
284C3×SD16—62no—
285C3×D8—28no—
286C3×D8—24no—
287C3×D8—24no—
288C3×D8—64no—
289C3×D8—62no—
290C3×M16—22no—
291C3×M16—21no—
292C3×M16—21no—
293C3×M16—22no—
294C3×M16—32no—
295C3×M16—32no—
296C3×M16—32no—
297C3×M16—32no—
298C3×M16—64no—
299C3×M16—61no—
300C3×M16—61no—
301C3×M16C22×D312yes—
302C3×M16C23×C312yes—
303C2×C3×C8—22no—
304C2×C3×C8—21no—
305C2×C3×C8—21no—
306C2×C3×C8—32no—
307C2×C3×C8—64no—
308C2×C3×C8—61no—
309C2×C3×C8—61no—
310#216—22no—
311#215—22no—
312#214—22no—
313#214—24no—
314#213—22no—
315#213—24no—
316#208—21no—
317#208—21no—
318#208—24no—
319#208C3×D412yes—
320#208C3×D412yes—
321#208C23×C312yes—
322#208C23×C312yes—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—24no—
326C2×C3⋊C8C23×C312yes—
327C22×C32—22no—
328C22×C32—41no—
329C22×C32—42no—
330C22×C32—81no—
331C22×C32—82no—
332C22×C32—82no—
333C22×C32—82no—
334C22×C32#12111yescharacteristic
335C22×C32#12111yescharacteristic
336C22×C32C2×#4111yescharacteristic
337C2×C3×D3—41no—
338C2×C3×D3—81no—
339C32×C4—22no—
340C32×C4#12111yescharacteristic
341C32×C4#12111yescharacteristic
342C32×C4C22×D411yescharacteristic
343C32×C4C22×D411yescharacteristic
344C3×Dic3—41no—
345C2×#41—31no—
346C2×#41C2×C3×D311yescharacteristic
347C22×D4C2×C3×D311yescharacteristic
348#137—32no—
349#137—61no—
350AGL(1,ℤ/8)—22no—
351AGL(1,ℤ/8)—32no—
352AGL(1,ℤ/8)—62no—
353AGL(1,ℤ/8)—62no—
354AGL(1,ℤ/8)—61no—
355AGL(1,ℤ/8)C2×C3×D314yes—
356#135—62no—
357C2×SD16—21no—
358C2×SD16—32no—
359C2×D8—21no—
360C2×D8—32no—
361#131—34no—
362#131—62no—
363C2×M16—31no—
364C2×M16—31no—
365C2×M16—31no—
366C2×M16—62no—
367C2×M16C2×C3×D311yescharacteristic
368#108—34no—
369#101—32no—
370#100—34no—
371#100—32no—
372C23×C3—21no—
373C23×C3—21no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—21no—
377C23×C3—41no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—41no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—61no—
386C23×C3—82no—
387C23×C3—82no—
388C23×C3—84no—
389C23×C3#23711yescharacteristic
390C23×C3C3×#4111yescharacteristic
391C22×D3—21no—
392C3×Q8—21no—
393C3×Q8—21no—
394C3×Q8—22no—
395C3×Q8—41no—
396C3×Q8—61no—
397C3×Q8—61no—
398C3×Q8C2×#6712yes—
399C3×Q8C2×C3×D412yes—
400C3×D4—22no—
401C3×D4—22no—
402C3×D4—22no—
403C3×D4—22no—
404C3×D4—24no—
405C3×D4—21no—
406C3×D4—21no—
407C3×D4—22no—
408C3×D4—22no—
409C3×D4—22no—
410C3×D4—22no—
411C3×D4—22no—
412C3×D4—42no—
413C3×D4—41no—
414C3×D4—42no—
415C3×D4—42no—
416C3×D4—42no—
417C3×D4—42no—
418C3×D4—41no—
419C3×D4—41no—
420C3×D4—41no—
421C3×D4—41no—
422C3×D4—61no—
423C3×D4—61no—
424C3×D4—121no—
425C3×D4—121no—
426C3×D4C2×#6712yes—
427C3×D4C2×C3×D412yes—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—42no—
441C2×C3×C4—42no—
442C2×C3×C4—41no—
443C2×C3×C4—61no—
444C2×C3×C4—121no—
445C2×C3×C4—121no—
446C2×C3×C4D3×D411yescharacteristic
447C2×C3×C4D3×D411yescharacteristic
448C2×C3×C4#23711yescharacteristic
449C2×C3×C4C2×#6711yescharacteristic
450C2×C3×C4C2×#6711yescharacteristic
451C2×C3×C4C2×C3×D411yescharacteristic
452C2×C3×C4C2×C3×D411yescharacteristic
453C2×C3×C4C2×C3×D411yescharacteristic
454C2×C3×C4C2×C3×D411yescharacteristic
455C2×C3×C4C3×#4111yescharacteristic
456C2×C3×C4C23×D311yescharacteristic
457C2×C3×C4C24×C311yescharacteristic
458#67—41no—
459#67—41no—
460C2×Dic3—21no—
461D12—21no—
462D12—21no—
463C4×D3—41no—
464C4×D3—41no—
465Dic6—21no—
466Dic6—21no—
467C3×C8—24no—
468C3×C8—22no—
469C3×C8—22no—
470C3×C8—34no—
471C3×C8—62no—
472C3×C8—62no—
473C3⋊C8—22no—
474C3⋊C8—22no—
475C3⋊C8C2×C3×D414yes—
476C2×C32—21no—
477C2×C32—21no—
478C2×C32—21no—
479C2×C32—42no—
480C2×C32—82no—
481C2×C32C2×#12111yescharacteristic
482C3×D3—81no—
483C24—21no—
484#41—21no—
485#41—21no—
486#41—61no—
487#41—61no—
488#41—61no—
489#41—61no—
490#41C3×#6712yes—
491#41C22×C3×D312yes—
492C2×Q8—31no—
493C2×Q8C3×#6711yescharacteristic
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—31no—
501C2×D4—61no—
502C2×D4C3×#6711yescharacteristic
503C2×D4C22×C3×D312yes—
504C22×C4—21no—
505C22×C4—61no—
506C22×C4C22×C3×D311yescharacteristic
507Q16—62no—
508SD16—24no—
509SD16—64no—
510SD16—62no—
511SD16—62no—
512D8—24no—
513D8—64no—
514D8—62no—
515M16—21no—
516M16—32no—
517M16—32no—
518M16—32no—
519M16—32no—
520M16—64no—
521M16—61no—
522M16—61no—
523M16C22×C3×D312yes—
524C2×C8—21no—
525C2×C8—32no—
526C2×C8—64no—
527C2×C8—61no—
528C2×C8—61no—
529C22×C3—22no—
530C22×C3—22no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—42no—
535C22×C3—41no—
536C22×C3—41no—
537C22×C3—42no—
538C22×C3—44no—
539C22×C3—42no—
540C22×C3—42no—
541C22×C3—81no—
542C22×C3—81no—
543C22×C3—82no—
544C22×C3—82no—
545C22×C3—84no—
546C22×C3—82no—
547C22×C3—82no—
548C22×C3—82no—
549C22×C3—82no—
550C22×C3—82no—
551C22×C3—84no—
552C22×C3—84no—
553C22×C3—121no—
554C22×C3—241no—
555C22×C3#93911yescharacteristic
556C22×C3#93911yescharacteristic
557C22×C3C3×#12111yescharacteristic
558C22×C3C3×#12111yescharacteristic
559C22×C3C2×#23711yescharacteristic
560C22×C3C2×C3×#4111yescharacteristic
561C2×D3—41no—
562C2×D3—81no—
563C3×C4—22no—
564C3×C4—22no—
565C3×C4—21no—
566C3×C4—21no—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—42no—
570C3×C4—121no—
571C3×C4#93911yescharacteristic
572C3×C4#93911yescharacteristic
573C3×C4C3×#12111yescharacteristic
574C3×C4C3×#12111yescharacteristic
575C3×C4C2×D3×D411yescharacteristic
576C3×C4C22×#6711yescharacteristic
577C3×C4C22×C3×D411yescharacteristic
578C3×C4C22×C3×D411yescharacteristic
579Dic3—41no—
580C32#306811yescharacteristic, complemented, Sylow
581C23—21no—
582C23—22no—
583C23—41no—
584C23—41no—
585C23—61no—
586C23—82no—
587C23C3×#23711yescharacteristic
588Q8—21no—
589Q8—61no—
590Q8—61no—
591Q8C2×C3×#6712yes—
592D4—22no—
593D4—22no—
594D4—21no—
595D4—22no—
596D4—22no—
597D4—41no—
598D4—41no—
599D4—61no—
600D4—61no—
601D4—121no—
602D4—121no—
603D4C2×C3×#6712yes—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—61no—
608C2×C4—121no—
609C2×C4—121no—
610C2×C4C3×D3×D411yescharacteristic
611C2×C4C3×D3×D411yescharacteristic
612C2×C4C3×#23711yescharacteristic
613C2×C4C2×C3×#6711yescharacteristic
614C2×C4C2×C3×#6711yescharacteristic
615C2×C4C23×C3×D311yescharacteristic
616C8—22no—
617C8—34no—
618C8—62no—
619C8—62no—
620C2×C3—22no—
621C2×C3—21no—
622C2×C3—21no—
623C2×C3—21no—
624C2×C3—21no—
625C2×C3—21no—
626C2×C3—21no—
627C2×C3—21no—
628C2×C3—41no—
629C2×C3—41no—
630C2×C3—42no—
631C2×C3—42no—
632C2×C3—82no—
633C2×C3—84no—
634C2×C3—82no—
635C2×C3—82no—
636C2×C3—241no—
637C2×C3C2×#93911yescharacteristic
638C2×C3C2×C3×#12111yescharacteristic
639D3—81no—
640C22—22no—
641C22—41no—
642C22—42no—
643C22—81no—
644C22—82no—
645C22—82no—
646C22—82no—
647C22—121no—
648C22—241no—
649C22C3×#93911yescharacteristic
650C22C3×#93911yescharacteristic
651C22C2×C3×#23711yescharacteristic
652C4—22no—
653C4—121no—
654C4C3×#93911yescharacteristic
655C4C3×#93911yescharacteristic
656C4C2×C3×D3×D411yescharacteristic
657C4C22×C3×#6711yescharacteristic
658C3—21no—
659C3#8394311yescharacteristic, direct product factor
660C3C3×#306811yescharacteristic, complemented
661C2—21no—
662C2—21no—
663C2—21no—
664C2—42no—
665C2—82no—
666C2—241no—
667C2C2×C3×#93911yescharacteristic
subgroupG/H
centerC2×C3C2×#939
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×AGL(1,ℤ/8)C2
socleC2×C32C2×#121
hypercenterC2×C3×AGL(1,ℤ/8)D3
hypocenterC3C3×#3068
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C2×C3×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×C32×AGL(1,ℤ/8)C2semidirect
2. C3×#5822C2semidirect
3. C3×#5819C2semidirect
4. C2×C3×#932C2semidirect
5. C2×C3×#833C2semidirect
6. C3×#5200C2semidirect
7. C3×#5199C2semidirect
8. C3×#5132C2semidirect
9. C3×#5124C2semidirect
11. #83943C3direct (N × H)
20. C3×#951C22semidirect
22. C3×#949C22semidirect
24. C3×#948C22semidirect
26. C2×C3×#214C22semidirect
30. C2×C3×#213C22semidirect
35. C3×#833C22semidirect
36. C3×#824C22semidirect
37. C3×#823C22semidirect
38. C3×#822C22semidirect
42. C2×C3×AGL(1,ℤ/8)D3semidirect
43. C2×C3×AGL(1,ℤ/8)C2×C3semidirect
45. #5822C2×C3semidirect
46. #5819C2×C3semidirect
47. C2×#932C2×C3semidirect
53. C2×#833C2×C3semidirect
54. #5200C2×C3semidirect
55. #5199C2×C3semidirect
56. #5132C2×C3semidirect
57. #5124C2×C3semidirect
143. #951C22×C3semidirect
145. #949C22×C3semidirect
147. #948C22×C3semidirect
149. C2×#214C22×C3semidirect
153. C2×#213C22×C3semidirect
162. #833C22×C3semidirect
163. #824C22×C3semidirect
164. #823C22×C3semidirect
165. #822C22×C3semidirect
207. C2×AGL(1,ℤ/8)C3×D3semidirect
580. C32#3068semidirect
659. C3#83943direct (N × H)
660. C3C3×#3068semidirect

Maximal subgroups

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

subgroupindex
C2×C32×AGL(1,ℤ/8)2
C3×#58222
C3×#58192
C2×C3×#9322
C2×C3×#8332
C3×#52002
C3×#51992
C3×#51322
C3×#51242
C3×#30683
#839433