Finite Group Databasebeta

← #25019141

Subgroups — #25019141

Order 11008.

2230 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063287C211yesmaximal, characteristic
2C2×#14582761C211yesmaximal, characteristic, complemented
3C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
4#19132843C212yesmaximal, complemented
5#19132835C212yesmaximal
6#19132833C211yesmaximal, characteristic, complemented
7#19132831C211yesmaximal, characteristic, complemented
8#19132827C211yesmaximal, characteristic, complemented
9#19132821C212yesmaximal, complemented
10(C2×D43)⋊#95C212yesmaximal, complemented
11C43×#1436C211yesmaximal, characteristic, complemented
12C23×D172C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C23×C4×D43C2211yescharacteristic
15C2×#13063287—24no—
16C2×#13063287—24no—
17C2×#13063287C418yescomplemented
18C22×(C2×D43)⋊C4C2212yes—
19C22×(C2×D43)⋊C4C2212yes—
20C22×(C2×D43)⋊C4C2212yes—
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C22×(C2×D43)⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C2212yes—
24C22×C4×Dic43C2211yescharacteristic
25C22×C4×Dic43C2211yescharacteristic
26#14582761—24no—
27C4×(C2×D43)⋊C4—24no—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2211yescharacteristic
34C2×C43⋊#95C2212yes—
35C22×C4⋊C4×C43C2211yescharacteristic
36C22×C42×C43C2211yescharacteristic
37C2×#95×C43C2212yes—
38C2×#95×C43C2211yescharacteristic
39C2×#95×C43C2212yes—
40C24×D43C2311yescharacteristic
41C24×D43C2311yescharacteristic
42C22×D172—22no—
43C22×D172—22no—
44C22×D172—24no—
45C22×D172—24no—
46C22×D172C2×C414yes—
47C23×Dic43C2312yes—
48C23×Dic43C2311yescharacteristic
49C23×Dic43C2312yes—
50C23×Dic43C2311yescharacteristic
51C22×C4×D43—22no—
52C22×C4×D43—22no—
53C22×C4×D43—42no—
54C22×C4×D43—42no—
55C22×C4×D43—42no—
56C22×C4×D43—42no—
57C22×C4×D43C2×C414yes—
58C22×C4×D43C2×C414yes—
59C22×C4×D43D414yes—
60C22×C4×D43D414yes—
61#13063287—232no—
62C2×(C2×D43)⋊C4—22no—
63C2×(C2×D43)⋊C4—22no—
64C2×(C2×D43)⋊C4—24no—
65C2×(C2×D43)⋊C4—22no—
66C2×(C2×D43)⋊C4—22no—
67C2×(C2×D43)⋊C4—24no—
68C2×(C2×D43)⋊C4—24no—
69C2×(C2×D43)⋊C4—24no—
70C2×(C2×D43)⋊C4—24no—
71C2×(C2×D43)⋊C4—24no—
72C2×(C2×D43)⋊C4—24no—
73C2×(C2×D43)⋊C4—24no—
74C2×(C2×D43)⋊C4—42no—
75C2×(C2×D43)⋊C4—42no—
76C2×(C2×D43)⋊C4—42no—
77C2×(C2×D43)⋊C4—42no—
78C2×(C2×D43)⋊C4C2×C414yes—
79C2×(C2×D43)⋊C4C2×C414yes—
80C2×C4×Dic43—22no—
81C2×C4×Dic43—22no—
82C2×C4×Dic43—22no—
83C2×C4×Dic43—42no—
84C2×C4×Dic43C2×C414yes—
85C43⋊#95—22no—
86C43⋊#95—24no—
87C43⋊#95—24no—
88C43⋊#95—24no—
89C43⋊#95—24no—
90C43⋊#95—24no—
91C43⋊#95—42no—
92C23×C4×C43C2312yes—
93C23×C4×C43C2311yescharacteristic
94C23×C4×C43C2312yes—
95C23×C4×C43C2311yescharacteristic
96C23×C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43—22no—
98C2×C4⋊C4×C43—22no—
99C2×C4⋊C4×C43C2×C414yes—
100C2×C42×C43—22no—
101C2×C42×C43—42no—
102#95×C43—22no—
103#95×C43—24no—
104#95×C43—42no—
105C24×C43C2411yescharacteristic
106C23×D43—21no—
107C23×D43—21no—
108C23×D43—22no—
109C23×D43—22no—
110C23×D43—22no—
111C23×D43—22no—
112C23×D43—22no—
113C23×D43—22no—
114C23×D43—22no—
115C23×D43—22no—
116C23×D43—22no—
117C23×D43—22no—
118C23×D43—22no—
119C23×D43C22×C412yes—
120C23×D43C22×C412yes—
121C23×D43C2×D412yes—
122C23×D43C2×D412yes—
123C23×D43#4114yes—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—22no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43C22×C412yes—
147C22×C4×C43C22×C412yes—
148C22×C4×C43C22×C412yes—
149C22×C4×C43C2×D412yes—
150C22×C4×C43C2×D412yes—
151C22×C4×C43#4114yes—
152C22×C4×C43#4114yes—
153C22×Dic43—22no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—22no—
164C22×Dic43—22no—
165C22×Dic43—22no—
166C22×Dic43—22no—
167C22×Dic43—22no—
168C22×Dic43—22no—
169C22×Dic43—22no—
170C22×Dic43—22no—
171C22×Dic43—22no—
172C22×Dic43C22×C412yes—
173C22×Dic43C22×C412yes—
174C22×Dic43C2×D412yes—
175C22×Dic43C2×D412yes—
176C22×Dic43#4114yes—
177C2×D172—216no—
178C2×D172—216no—
179C2×D172—28no—
180C2×D172—28no—
181C2×D172—28no—
182C2×C4×D43—28no—
183C2×C4×D43—48no—
184C2×C4×D43—48no—
185C2×C4×D43—48no—
186C2×C4×D43—44no—
187C2×C4×D43—44no—
188C2×C4×D43—48no—
189C2×C4×D43—44no—
190C2×C4×D43—44no—
191C2×C4×D43C22⋊C4116yescomplemented
192C4⋊C4×C43—28no—
193C42×C43—44no—
194(C2×D43)⋊C4—216no—
195(C2×D43)⋊C4—28no—
196(C2×D43)⋊C4—28no—
197(C2×D43)⋊C4—48no—
198(C2×D43)⋊C4—48no—
199(C2×D43)⋊C4—48no—
200C4×Dic43—28no—
201C4×Dic43—44no—
202C23×C43C23×C411yescharacteristic
203C23×C43C22×D411yescharacteristic
204C23×C43C22×D411yescharacteristic
205C23×C43C2×#4112yes—
206C23×C43C2×#4112yes—
207C23×C43C2×#4112yes—
208C23×C43C2×#4112yes—
209C23×C43H(5,𝔽2)12yes—
210C23×C43H(5,𝔽2)12yes—
211C22×D43—22no—
212C22×D43—22no—
213C22×D43—22no—
214C22×D43—22no—
215C22×D43—24no—
216C22×D43—24no—
217C22×D43—24no—
218C22×D43—24no—
219C22×D43—24no—
220C22×D43—24no—
221C22×D43—24no—
222C22×D43—24no—
223C22×D43—24no—
224C22×D43—22no—
225C22×D43—22no—
226C22×D43—24no—
227C22×D43—22no—
228C22×D43—22no—
229C22×D43—24no—
230C22×D43—24no—
231C22×D43—24no—
232C22×D43—24no—
233C22×D43—42no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—42no—
237C22×D43—41no—
238C22×D43—41no—
239C22×D43—42no—
240C22×D43—42no—
241C22×D43—42no—
242C22×D43—42no—
243C22×D43—42no—
244C22×D43—42no—
245C22×D43—42no—
246C22×D43—42no—
247C22×D43—42no—
248C22×D43—42no—
249C22×D43—42no—
250C22×D43—42no—
251C22×D43C2×C22⋊C414yes—
252C22×D43#11714yes—
253C2×C4×C43—22no—
254C2×C4×C43—22no—
255C2×C4×C43—24no—
256C2×C4×C43—24no—
257C2×C4×C43—24no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—24no—
261C2×C4×C43—22no—
262C2×C4×C43—24no—
263C2×C4×C43—24no—
264C2×C4×C43—24no—
265C2×C4×C43—24no—
266C2×C4×C43—42no—
267C2×C4×C43—42no—
268C2×C4×C43—42no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—42no—
272C2×C4×C43—42no—
273C2×C4×C43—42no—
274C2×C4×C43—42no—
275C2×C4×C43—42no—
276C2×C4×C43—42no—
277C2×C4×C43—42no—
278C2×C4×C43—42no—
279C2×C4×C43—42no—
280C2×C4×C43C2×C22⋊C414yes—
281C2×C4×C43#11714yes—
282C2×Dic43—24no—
283C2×Dic43—24no—
284C2×Dic43—22no—
285C2×Dic43—22no—
286C2×Dic43—22no—
287C2×Dic43—24no—
288C2×Dic43—24no—
289C2×Dic43—24no—
290C2×Dic43—24no—
291C2×Dic43—42no—
292C2×Dic43—42no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—42no—
296C2×Dic43—42no—
297C2×Dic43—42no—
298C2×Dic43—42no—
299C2×Dic43—42no—
300C2×Dic43—42no—
301C2×Dic43—42no—
302C2×Dic43—42no—
303C2×Dic43—42no—
304C2×Dic43—42no—
305C2×Dic43C2×C22⋊C414yes—
306D172—232no—
307C4×D43—416no—
308C4×D43—416no—
309#13940—431nomaximal, Sylow
310C22×C43C22×C22⋊C411yescharacteristic
311C22×C43C2×#11711yescharacteristic
312C22×C43C2×#11711yescharacteristic
313C22×C43C4×#4112yes—
314C22×C43#51812yes—
315C22×C43#52512yes—
316C22×C43#52512yes—
317C22×C43#52512yes—
318C22×C43#53211yescharacteristic
319C22×C43#53211yescharacteristic
320C22×C43#53412yes—
321C22×C43#53411yescharacteristic
322C22×C43#53411yescharacteristic
323C22×C43#55112yes—
324C22×C43#55112yes—
325C22×C43#55312yes—
326C22×C43#55312yes—
327C22×C43#55312yes—
328C22×C43#55312yes—
329C22×C43#55912yes—
330C22×C43#55912yes—
331C2×D43—24no—
332C2×D43—28no—
333C2×D43—24no—
334C2×D43—24no—
335C2×D43—24no—
336C2×D43—42no—
337C2×D43—44no—
338C2×D43—44no—
339C2×D43—44no—
340C2×D43—44no—
341C2×D43—44no—
342C2×D43—44no—
343C2×D43—44no—
344C2×D43—44no—
345C2×D43—44no—
346C2×D43—44no—
347C2×D43—44no—
348C2×D43—42no—
349C4×C43—24no—
350C4×C43—24no—
351C4×C43—42no—
352C4×C43—44no—
353C4×C43—82no—
354Dic43—24no—
355Dic43—44no—
356Dic43—42no—
357Dic43—82no—
358C22×C4×D4—431no—
359C2×#381—431no—
360C2×C4×C22⋊C4—431no—
361#1440—432no—
362#1438—432no—
363#1437—431no—
364#1437—431no—
365#1436—431no—
366#1436D4311yescharacteristic, complemented
367#1434—432no—
368C22⋊#95—432no—
369C2×C43#228011yescharacteristic
370C2×C43#229711yescharacteristic
371C2×C43#230811yescharacteristic
372C2×C43#235312yes—
373C2×C43#235712yes—
374C2×C43#260012yes—
375C2×C43#260012yes—
376C2×C43#260212yes—
377C2×C43#260212yes—
378D43—44no—
379D43—44no—
380C23×D4—431no—
381C24×C4—431no—
382C24×C4—431no—
383C2×C4×D4—438no—
384C2×C4×D4—864no—
385C2×C4×D4—864no—
386C22×C4⋊C4C2×D4311yescharacteristic
387C22×C22⋊C4—431no—
388C22×C22⋊C4—431no—
389C22×C22⋊C4—432no—
390C22×C22⋊C4—432no—
391C22×C22⋊C4—432no—
392C22×C22⋊C4—432no—
393C22×C42—431no—
394C22×C42—431no—
395C22×C42C2×D4311yescharacteristic
396#381—864no—
397C4×C22⋊C4—864no—
398C2×#95—432no—
399C2×#95—432no—
400C2×#95—432no—
401C2×#95—432no—
402C2×#95—432no—
403C2×#95—431no—
404C2×#95—432no—
405C2×#95C2×D4312yes—
406C2×#95C2×D4311yescharacteristic
407C2×#95C2×D4312yes—
408C43#1394011yescharacteristic, complemented, Sylow
409C25—431no—
410C25—431no—
411C22×D4—434no—
412C22×D4—862no—
413C22×D4—862no—
414C22×D4—864no—
415C22×D4—864no—
416C23×C4—431no—
417C23×C4—434no—
418C23×C4—434no—
419C23×C4—434no—
420C23×C4—431no—
421C23×C4—432no—
422C23×C4—434no—
423C23×C4—432no—
424C23×C4—862no—
425C23×C4—862no—
426C23×C4—1722no—
427C23×C4—1722no—
428C23×C4—1722no—
429C23×C4—1722no—
430C23×C4C22×D4312yes—
431C23×C4C22×D4311yescharacteristic
432C23×C4C22×D4312yes—
433C23×C4C22×D4311yescharacteristic
434C23×C4C22×D4311yescharacteristic
435C4×D4—8632no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4C4×D4314yes—
439C2×C22⋊C4—434no—
440C2×C22⋊C4—434no—
441C2×C22⋊C4—864no—
442C2×C22⋊C4—862no—
443C2×C22⋊C4—862no—
444C2×C22⋊C4—864no—
445C2×C22⋊C4—862no—
446C2×C22⋊C4—862no—
447C2×C22⋊C4—864no—
448C2×C22⋊C4—864no—
449C2×C22⋊C4—864no—
450C2×C22⋊C4—864no—
451C2×C22⋊C4—864no—
452C2×C22⋊C4—864no—
453C2×C22⋊C4—1722no—
454C2×C22⋊C4—1722no—
455C2×C22⋊C4—1722no—
456C2×C22⋊C4—1722no—
457C2×C42—22no—
458C2×C42—42no—
459C2×C42—434no—
460C2×C42—862no—
461C2×C42—862no—
462C2×C42—862no—
463C2×C42—1722no—
464#95—24no—
465#95—22no—
466#95—42no—
467#95—864no—
468#95—864no—
469#95—864no—
470#95—864no—
471#95—862no—
472#95—864no—
473#95—1722no—
474C24—432no—
475C24—432no—
476C24—432no—
477C24—432no—
478C24—434no—
479C24—861no—
480C24—861no—
481C24—862no—
482C24—862no—
483C24—862no—
484C24—862no—
485C24—862no—
486C24—862no—
487C24—862no—
488C24—862no—
489C24—862no—
490C24—862no—
491C24—862no—
492C24C23×D4311yescharacteristic
493C2×D4—868no—
494C2×D4—868no—
495C2×D4—8616no—
496C2×D4—8616no—
497C2×D4—868no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—432no—
521C22×C4—432no—
522C22×C4—432no—
523C22×C4—4316no—
524C22×C4—432no—
525C22×C4—434no—
526C22×C4—868no—
527C22×C4—862no—
528C22×C4—862no—
529C22×C4—862no—
530C22×C4—861no—
531C22×C4—861no—
532C22×C4—862no—
533C22×C4—862no—
534C22×C4—862no—
535C22×C4—862no—
536C22×C4—862no—
537C22×C4—862no—
538C22×C4—862no—
539C22×C4—862no—
540C22×C4—862no—
541C22×C4—862no—
542C22×C4—862no—
543C22×C4—862no—
544C22×C4—862no—
545C22×C4—862no—
546C22×C4—1728no—
547C22×C4—1728no—
548C22×C4—1724no—
549C22×C4—1724no—
550C22×C4—1728no—
551C22×C4—1728no—
552C22×C4—1724no—
553C22×C4—1724no—
554C22×C4C2×C4×D4312yes—
555C22×C4C2×C4×D4312yes—
556C22×C4C2×C4×D4312yes—
557C22×C4#1062189814yes—
558C22×C4D4×D4312yes—
559C22×C4D4×D4312yes—
560C22×C4#1062190214yes—
561C4⋊C4—28no—
562C22⋊C4—868no—
563C22⋊C4—8616no—
564C22⋊C4—868no—
565C22⋊C4—1728no—
566C22⋊C4—1728no—
567C22⋊C4—1728no—
568C42—44no—
569C42—868no—
570C42—1724no—
571C23—434no—
572C23—434no—
573C23—864no—
574C23—864no—
575C23—864no—
576C23—862no—
577C23—864no—
578C23—862no—
579C23—862no—
580C23—862no—
581C23—864no—
582C23—864no—
583C23—864no—
584C23—864no—
585C23—864no—
586C23—864no—
587C23—864no—
588C23—864no—
589C23—864no—
590C23—862no—
591C23—862no—
592C23—864no—
593C23—862no—
594C23—862no—
595C23—1722no—
596C23—1722no—
597C23—1722no—
598C23—1722no—
599C23—1722no—
600C23—1722no—
601C23—1722no—
602C23—1722no—
603C23—1722no—
604C23—1722no—
605C23—1722no—
606C23—1722no—
607C23—1722no—
608C23—1721no—
609C23—1721no—
610C23—1722no—
611C23—1721no—
612C23—1721no—
613C23C22×C4×D4311yescharacteristic
614C23C2×D4×D4311yescharacteristic
615C23C2×D4×D4311yescharacteristic
616C23#41×D4312yes—
617C23#41×D4312yes—
618C23C2×#1062189812yes—
619C23C2×#1062190212yes—
620C23#1306337012yes—
621C23#1306337112yes—
622D4—8632no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—22no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—434no—
651C2×C4—864no—
652C2×C4—864no—
653C2×C4—862no—
654C2×C4—862no—
655C2×C4—864no—
656C2×C4—864no—
657C2×C4—862no—
658C2×C4—864no—
659C2×C4—864no—
660C2×C4—17216no—
661C2×C4—17216no—
662C2×C4—1722no—
663C2×C4—1722no—
664C2×C4—1722no—
665C2×C4—1722no—
666C2×C4—1722no—
667C2×C4—1722no—
668C2×C4—1722no—
669C2×C4—1722no—
670C2×C4—1722no—
671C2×C4—1722no—
672C2×C4—1722no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1722no—
676C2×C4C22⋊C4×D4314yes—
677C2×C4#1306328214yes—
678C22—864no—
679C22—864no—
680C22—864no—
681C22—864no—
682C22—868no—
683C22—1724no—
684C22—1724no—
685C22—1722no—
686C22—1724no—
687C22—1724no—
688C22—1724no—
689C22—1724no—
690C22—1724no—
691C22—1724no—
692C22—1724no—
693C22—1724no—
694C22—1722no—
695C22—1724no—
696C22C2×C22⋊C4×D4311yescharacteristic
697C22#117×D4311yescharacteristic
698C22C2×#1306328211yescharacteristic
699C22C4×#1062190212yes—
700C22#1458337112yes—
701C22#1458340812yes—
702C22#1458340812yes—
703C22#1458341212yes—
704C22#1458344811yescharacteristic
705C22#1458345011yescharacteristic
706C22#1458345712yes—
707C22#1458345911yescharacteristic
708C22#1458346011yescharacteristic
709C22#1458357412yes—
710C22#1458357612yes—
711C22#1458359312yes—
712C22#1458359412yes—
713C22#1458359712yes—
714C22#1458360212yes—
715C22#1458363212yes—
716C22#1458363412yes—
717C4—24no—
718C4—24no—
719C4—44no—
720C4—42no—
721C4—82no—
722C4—864no—
723C4—3442no—
724C4—1722no—
725C4—1724no—
726C2—1724no—
727C2—1724no—
728C2#1913697611yescharacteristic
729C2#1913708411yescharacteristic
730C2#1913716911yescharacteristic
731C2#1913753412yes—
732C2#1913756412yes—
733C2#1914018112yes—
734C2#1914018412yes—
735C2#1914020612yes—
736C2#1914021412yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1436C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1436D43
hypocenterC43#13940
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#14582761C2semidirect
3. C2×C4×(C2×D43)⋊C4C2semidirect
4. #19132843C2semidirect
6. #19132833C2semidirect
7. #19132831C2semidirect
8. #19132827C2semidirect
9. #19132821C2semidirect
10. (C2×D43)⋊#95C2semidirect
11. C43×#1436C2semidirect
17. C2×#13063287C4semidirect
191. C2×C4×D43C22⋊C4semidirect
366. #1436D43semidirect
408. C43#13940semidirect

Maximal subgroups

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

subgroupindex
C22×#130632872
C2×#145827612
C2×C4×(C2×D43)⋊C42
#191328432
#191328352
#191328332
#191328312
#191328272
#191328212
(C2×D43)⋊#952
C43×#14362
#1394043