Finite Group Databasebeta

← #25018359

Subgroups — #25018359

Order 11008.

2118 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063281C211yesmaximal, characteristic
2C2×C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
3C2×#14582750C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic43C212yesmaximal
5#19132849C211yesmaximal, characteristic, complemented
6#19132846C212yesmaximal, complemented
7#19132845C211yesmaximal, characteristic, complemented
8#19132840C211yesmaximal, characteristic
9#19132838C212yesmaximal
10#95×Dic43C212yesmaximal, complemented
11C43×#1439C211yesmaximal, characteristic
12C24×Dic43C2211yescharacteristic
13C2×#13063281—24no—
14C2×#13063281—24no—
15C2×#13063281C418yescomplemented
16C22×C4⋊Dic43C2211yescharacteristic
17C22×Dic43⋊C4C2212yes—
18C22×Dic43⋊C4C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×C22⋊Dic43C2212yes—
21C22×C22⋊Dic43C2211yescharacteristic
22C22×C4×Dic43C2212yes—
23C22×C4×Dic43C2212yes—
24C22×C4×Dic43C2211yescharacteristic
25C22×C4×Dic43C2211yescharacteristic
26C4⋊C4×Dic43—24no—
27#14582750—24no—
28C22⋊C4×Dic43—28no—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2211yescharacteristic
35C2×C43⋊#95C2212yes—
36C22×C4⋊C4×C43C2211yescharacteristic
37C22×C22⋊C4×C43C2212yes—
38C22×C22⋊C4×C43C2211yescharacteristic
39C2×#95×C43C2212yes—
40C2×#95×C43C2211yescharacteristic
41C23×Dic43—22no—
42C23×Dic43—22no—
43C23×Dic43—22no—
44C23×Dic43—22no—
45C23×Dic43C2×C414yes—
46C23×Dic43D414yes—
47C23×Dic43Q814yes—
48C23×Dic43C2311yescharacteristic
49C23×Dic43C2312yes—
50C23×Dic43C2312yes—
51C23×Dic43C2311yescharacteristic
52C23×Dic43C2311yescharacteristic
53C23×Dic43C2311yescharacteristic
54#13063281—232no—
55C2×C4⋊Dic43—22no—
56C2×C4⋊Dic43—24no—
57C2×Dic43⋊C4—22no—
58C2×Dic43⋊C4—22no—
59C2×Dic43⋊C4—24no—
60C2×Dic43⋊C4—22no—
61C2×Dic43⋊C4—22no—
62C2×Dic43⋊C4—24no—
63C2×Dic43⋊C4—24no—
64C2×Dic43⋊C4C2×C414yes—
65C2×Dic43⋊C4C2×C414yes—
66C2×C22⋊Dic43—24no—
67C2×C22⋊Dic43—22no—
68C2×C22⋊Dic43—22no—
69C2×C22⋊Dic43—24no—
70C2×C22⋊Dic43—24no—
71C2×C22⋊Dic43C2×C414yes—
72C2×C4×Dic43—22no—
73C2×C4×Dic43—22no—
74C2×C4×Dic43—24no—
75C2×C4×Dic43—24no—
76C2×C4×Dic43—24no—
77C2×C4×Dic43—24no—
78C2×C4×Dic43—24no—
79C2×C4×Dic43—24no—
80C2×C4×Dic43C2×C414yes—
81C2×C4×Dic43C2×C414yes—
82C2×C4×Dic43D414yes—
83C2×C4×Dic43D414yes—
84C43⋊#95—22no—
85C43⋊#95—24no—
86C43⋊#95—24no—
87C43⋊#95—24no—
88C43⋊#95—24no—
89C43⋊#95—24no—
90C43⋊#95—24no—
91C25×C43C2311yescharacteristic
92C23×C4×C43C2311yescharacteristic
93C23×C4×C43C2312yes—
94C23×C4×C43C2312yes—
95C23×C4×C43C2311yescharacteristic
96C2×C4⋊C4×C43—22no—
97C2×C4⋊C4×C43—24no—
98C2×C22⋊C4×C43—24no—
99C2×C22⋊C4×C43—22no—
100C2×C22⋊C4×C43—22no—
101C2×C22⋊C4×C43—24no—
102C2×C22⋊C4×C43—24no—
103C2×C22⋊C4×C43C2×C414yes—
104#95×C43—22no—
105#95×C43—24no—
106C24×C43—21no—
107C24×C43—21no—
108C24×C43—22no—
109C24×C43—22no—
110C24×C43—22no—
111C24×C43—22no—
112C24×C43—21no—
113C24×C43—21no—
114C24×C43C22×C412yes—
115C24×C43C2×D412yes—
116C24×C43C2×Q812yes—
117C24×C43C2411yescharacteristic
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
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×C43C22×C412yes—
137C22×C4×C43C22×C412yes—
138C22×C4×C43C2×D412yes—
139C22×C4×C43C2×D412yes—
140C22×C4×C43#4114yes—
141C22×C4×C43#4114yes—
142C22×Dic43—28no—
143C22×Dic43—28no—
144C22×Dic43—28no—
145C22×Dic43—28no—
146C22×Dic43—28no—
147C22×Dic43—28no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—21no—
159C22×Dic43—21no—
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×Dic43C4⋊C4116yescomplemented
171C22×Dic43C22×C412yes—
172C22×Dic43C22×C412yes—
173C22×Dic43C22×C412yes—
174C22×Dic43C22×C412yes—
175C22×Dic43C2×D412yes—
176C22×Dic43C2×D412yes—
177C22×Dic43C2×D412yes—
178C22×Dic43C2×D412yes—
179C22×Dic43C2×D412yes—
180C22×Dic43C2×D412yes—
181C22×Dic43C2×Q812yes—
182C22×Dic43C2×Q812yes—
183C22×Dic43#4114yes—
184C22×Dic43#4114yes—
185C22×Dic43#4112yes—
186C22×Dic43#4112yes—
187C4⋊C4×C43—28no—
188C22⋊C4×C43—216no—
189C22⋊C4×C43—28no—
190C22⋊Dic43—216no—
191C22⋊Dic43—28no—
192C4⋊Dic43—28no—
193Dic43⋊C4—216no—
194Dic43⋊C4—28no—
195Dic43⋊C4—28no—
196C4×Dic43—28no—
197C4×Dic43—48no—
198C4×Dic43—48no—
199C4×Dic43C22⋊C4116yescomplemented
200C23×C43—22no—
201C23×C43—22no—
202C23×C43—24no—
203C23×C43—24no—
204C23×C43—22no—
205C23×C43—22no—
206C23×C43—22no—
207C23×C43—22no—
208C23×C43—24no—
209C23×C43—24no—
210C23×C43—24no—
211C23×C43—24no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—42no—
215C23×C43—42no—
216C23×C43—42no—
217C23×C43—42no—
218C23×C43—42no—
219C23×C43—42no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43C2×C4⋊C414yes—
223C23×C43C23×C411yescharacteristic
224C23×C43C22×D411yescharacteristic
225C23×C43C22×D411yescharacteristic
226C23×C43C22×D411yescharacteristic
227C23×C43C22×Q811yescharacteristic
228C23×C43C2×#4111yescharacteristic
229C23×C43C2×#4111yescharacteristic
230C23×C43C2×#4112yes—
231C23×C43C2×#4112yes—
232C23×C43C2×#4112yes—
233C23×C43C2×#4112yes—
234C2×C4×C43—24no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—24no—
238C2×C4×C43—22no—
239C2×C4×C43—24no—
240C2×C4×C43—24no—
241C2×C4×C43—24no—
242C2×C4×C43—24no—
243C2×C4×C43—24no—
244C2×C4×C43—24no—
245C2×C4×C43—24no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43—42no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43C2×C22⋊C414yes—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—24no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—24no—
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—232no—
269C2×Dic43—22no—
270C2×Dic43—24no—
271C2×Dic43—24no—
272C2×Dic43—24no—
273C2×Dic43—24no—
274C2×Dic43—24no—
275C2×Dic43—24no—
276C2×Dic43—24no—
277C2×Dic43—42no—
278C2×Dic43—42no—
279C2×Dic43—42no—
280C2×Dic43—41no—
281C2×Dic43—42no—
282C2×Dic43—41no—
283C2×Dic43—42no—
284C2×Dic43—42no—
285C2×Dic43—42no—
286C2×Dic43—42no—
287C2×Dic43—42no—
288C2×Dic43C2×C22⋊C414yes—
289C2×Dic43C2×C22⋊C414yes—
290C2×Dic43C2×C4⋊C414yes—
291C2×Dic43C2×C4⋊C414yes—
292C2×Dic43#11714yes—
293C2×Dic43#12114yes—
294C2×Dic43#12114yes—
295C2×Dic43C22⋊Q814yes—
296C2×Dic43C22⋊Q814yes—
297#13852—431nomaximal, Sylow
298C22×C43—24no—
299C22×C43—28no—
300C22×C43—42no—
301C22×C43—42no—
302C22×C43—44no—
303C22×C43—42no—
304C22×C43—42no—
305C22×C43—44no—
306C22×C43—42no—
307C22×C43—42no—
308C22×C43—44no—
309C22×C43C22×C22⋊C411yescharacteristic
310C22×C43C22×C4⋊C411yescharacteristic
311C22×C43C2×#11711yescharacteristic
312C22×C43C4×#4112yes—
313C22×C43C4×#4112yes—
314C22×C43C2×#12111yescharacteristic
315C22×C43C2×#12111yescharacteristic
316C22×C43C2×C22⋊Q811yescharacteristic
317C22×C43C2×C22⋊Q811yescharacteristic
318C22×C43#52512yes—
319C22×C43#52511yescharacteristic
320C22×C43#52512yes—
321C22×C43#52511yescharacteristic
322C22×C43#52512yes—
323C22×C43#52912yes—
324C22×C43#52912yes—
325C22×C43#52912yes—
326C22×C43#52912yes—
327C22×C43#53212yes—
328C22×C43#53211yescharacteristic
329C22×C43#53211yescharacteristic
330C22×C43#53312yes—
331C22×C43#53312yes—
332C4×C43—24no—
333C4×C43—44no—
334C4×C43—44no—
335C4×C43—42no—
336Dic43—24no—
337Dic43—24no—
338Dic43—44no—
339Dic43—44no—
340Dic43—42no—
341Dic43#38018yes—
342C22×#117—431no—
343C2×C4×C4⋊C4—431no—
344C2×C4×C4⋊C4—431no—
345C2×C4×C22⋊C4—432no—
346#1441—432no—
347#1441—431no—
348#1441—431no—
349#1439—432no—
350#1439—431no—
351#1439D4311yescharacteristic
352C4×#95—432no—
353C2×C43—44no—
354C2×C43C2×#38011yescharacteristic
355C2×C43#229612yes—
356C2×C43#229711yescharacteristic
357C2×C43#229711yescharacteristic
358C2×C43#229812yes—
359C2×C43#239211yescharacteristic
360C2×C43#239211yescharacteristic
361C2×C43#239212yes—
362C2×C43#239611yescharacteristic
363C2×C43#239611yescharacteristic
364C2×C43#239612yes—
365C24×C4—431no—
366C2×#117—438no—
367C2×#117—864no—
368C2×#117—864no—
369C22×C4⋊C4—431no—
370C22×C4⋊C4—431no—
371C22×C4⋊C4—432no—
372C22×C4⋊C4—431no—
373C22×C4⋊C4C2×D4311yescharacteristic
374C22×C22⋊C4—431no—
375C22×C22⋊C4—432no—
376C22×C22⋊C4C2×D4312yes—
377C22×C22⋊C4C2×D4311yescharacteristic
378C22×C42—431no—
379C22×C42—431no—
380C22×C42—432no—
381C22×C42—432no—
382C4×C4⋊C4—864no—
383C4×C4⋊C4—864no—
384C4×C22⋊C4—868no—
385C2×#95—432no—
386C2×#95—432no—
387C2×#95—432no—
388C2×#95—432no—
389C2×#95—431no—
390C2×#95—432no—
391C2×#95—432no—
392C2×#95C2×D4312yes—
393C2×#95C2×D4311yescharacteristic
394C43#1385211yescharacteristic, complemented, Sylow
395C25C22×D4311yescharacteristic
396C23×C4—431no—
397C23×C4—434no—
398C23×C4—434no—
399C23×C4—434no—
400C23×C4—431no—
401C23×C4—431no—
402C23×C4—431no—
403C23×C4—432no—
404C23×C4—432no—
405C23×C4—862no—
406C23×C4—862no—
407C23×C4—862no—
408C23×C4—862no—
409C23×C4C22×D4311yescharacteristic
410C23×C4C22×D4312yes—
411C23×C4C22×D4312yes—
412C23×C4C22×D4311yescharacteristic
413#117—8632no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—434no—
417C2×C4⋊C4—434no—
418C2×C4⋊C4—862no—
419C2×C4⋊C4—862no—
420C2×C4⋊C4—864no—
421C2×C4⋊C4—864no—
422C2×C4⋊C4—864no—
423C2×C4⋊C4—862no—
424C2×C4⋊C4—862no—
425C2×C4⋊C4—862no—
426C2×C4⋊C4—864no—
427C2×C22⋊C4—24no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4—434no—
433C2×C22⋊C4—862no—
434C2×C22⋊C4—862no—
435C2×C22⋊C4—864no—
436C2×C22⋊C4—864no—
437C2×C22⋊C4—864no—
438C2×C22⋊C4C4×D4314yes—
439C2×C42—434no—
440C2×C42—434no—
441C2×C42—434no—
442C2×C42—434no—
443C2×C42—862no—
444C2×C42—862no—
445C2×C42—864no—
446C2×C42—864no—
447C2×C42—864no—
448C2×C42—864no—
449C2×C42—864no—
450C2×C42—864no—
451#95—22no—
452#95—24no—
453#95—864no—
454#95—864no—
455#95—864no—
456#95—864no—
457#95—864no—
458#95—862no—
459#95—864no—
460C24—21no—
461C24—21no—
462C24—22no—
463C24—22no—
464C24—21no—
465C24—21no—
466C24—22no—
467C24—22no—
468C24C2×C4×D4312yes—
469C24D4×D4312yes—
470C24Q8×D4312yes—
471C24C23×D4311yescharacteristic
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—432no—
491C22×C4—432no—
492C22×C4—432no—
493C22×C4—432no—
494C22×C4—432no—
495C22×C4—432no—
496C22×C4—432no—
497C22×C4—4316no—
498C22×C4—432no—
499C22×C4—432no—
500C22×C4—432no—
501C22×C4—432no—
502C22×C4—432no—
503C22×C4—432no—
504C22×C4—432no—
505C22×C4—434no—
506C22×C4—434no—
507C22×C4—868no—
508C22×C4—868no—
509C22×C4—868no—
510C22×C4—868no—
511C22×C4—868no—
512C22×C4—868no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—862no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—862no—
519C22×C4—862no—
520C22×C4—862no—
521C22×C4—862no—
522C22×C4—862no—
523C22×C4—861no—
524C22×C4—861no—
525C22×C4—862no—
526C22×C4—862no—
527C22×C4—862no—
528C22×C4—862no—
529C22×C4—862no—
530C22×C4—862no—
531C22×C4—862no—
532C22×C4—862no—
533C22×C4—862no—
534C22×C4—862no—
535C22×C4C2×C4×D4312yes—
536C22×C4C2×C4×D4312yes—
537C22×C4D4×D4312yes—
538C22×C4D4×D4312yes—
539C22×C4#1062190014yes—
540C22×C4#1062190014yes—
541C4⋊C4—28no—
542C4⋊C4—868no—
543C4⋊C4—8616no—
544C4⋊C4—868no—
545C4⋊C4—868no—
546C22⋊C4—216no—
547C22⋊C4—28no—
548C22⋊C4—868no—
549C22⋊C4—8616no—
550C42—4316no—
551C42—868no—
552C42—1728no—
553C42—1728no—
554C23—22no—
555C23—22no—
556C23—24no—
557C23—24no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—41no—
567C23—41no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—41no—
575C23—41no—
576C23C4⋊C4×D4314yes—
577C23C22×C4×D4311yescharacteristic
578C23C2×D4×D4311yescharacteristic
579C23C2×D4×D4311yescharacteristic
580C23C2×D4×D4311yescharacteristic
581C23C2×Q8×D4311yescharacteristic
582C23#41×D4311yescharacteristic
583C23#41×D4311yescharacteristic
584C23#41×D4312yes—
585C23#41×D4312yes—
586C23C2×#1062190012yes—
587C23C2×#1062190012yes—
588C2×C4—24no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—24no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—434no—
612C2×C4—434no—
613C2×C4—434no—
614C2×C4—434no—
615C2×C4—434no—
616C2×C4—434no—
617C2×C4—434no—
618C2×C4—434no—
619C2×C4—434no—
620C2×C4—8632no—
621C2×C4—862no—
622C2×C4—862no—
623C2×C4—864no—
624C2×C4—862no—
625C2×C4—862no—
626C2×C4—862no—
627C2×C4—862no—
628C2×C4—864no—
629C2×C4—862no—
630C2×C4—862no—
631C2×C4—862no—
632C2×C4—864no—
633C2×C4—864no—
634C2×C4—864no—
635C2×C4—864no—
636C2×C4—864no—
637C2×C4—864no—
638C2×C4—864no—
639C2×C4—1722no—
640C2×C4—1722no—
641C2×C4—1722no—
642C2×C4—1721no—
643C2×C4—1722no—
644C2×C4—1721no—
645C2×C4—1722no—
646C2×C4—1722no—
647C2×C4—1722no—
648C2×C4—1722no—
649C2×C4—1722no—
650C2×C4C22⋊C4×D4314yes—
651C22—28no—
652C22—24no—
653C22—42no—
654C22—42no—
655C22—44no—
656C22—42no—
657C22—42no—
658C22—44no—
659C22—42no—
660C22—42no—
661C22—44no—
662C22C2×C22⋊C4×D4311yescharacteristic
663C22C2×C4⋊C4×D4311yescharacteristic
664C22#117×D4311yescharacteristic
665C22C4×#1062190012yes—
666C22C4×#1062190012yes—
667C22#121×D4311yescharacteristic
668C22#121×D4311yescharacteristic
669C22C22⋊Q8×D4311yescharacteristic
670C22C22⋊Q8×D4311yescharacteristic
671C22#1458340512yes—
672C22#1458340511yescharacteristic
673C22#1458340712yes—
674C22#1458340711yescharacteristic
675C22#1458340912yes—
676C22#1458342612yes—
677C22#1458342812yes—
678C22#1458343012yes—
679C22#1458343212yes—
680C22#1458344412yes—
681C22#1458344711yescharacteristic
682C22#1458344811yescharacteristic
683C22#1458345112yes—
684C22#1458345112yes—
685C4—24no—
686C4—44no—
687C4—44no—
688C4—42no—
689C4—438no—
690C4—864no—
691C4—864no—
692C4—1724no—
693C4—1724no—
694C4—1722no—
695C2—44no—
696C2#380×D4311yescharacteristic
697C2#1913707412yes—
698C2#1913708011yescharacteristic
699C2#1913708211yescharacteristic
700C2#1913708912yes—
701C2#1913783011yescharacteristic
702C2#1913783211yescharacteristic
703C2#1913783812yes—
704C2#1913786211yescharacteristic
705C2#1913786411yescharacteristic
706C2#1913787012yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1439C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenter#1439D43
hypocenterC43#13852
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic43C2semidirect
3. C2×#14582750C2semidirect
5. #19132849C2semidirect
6. #19132846C2semidirect
7. #19132845C2semidirect
10. #95×Dic43C2semidirect
15. C2×#13063281C4semidirect
170. C22×Dic43C4⋊C4semidirect
199. C4×Dic43C22⋊C4semidirect
394. C43#13852semidirect

Maximal subgroups

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

subgroupindex
C22×#130632812
C2×C4⋊C4×Dic432
C2×#145827502
C2×C22⋊C4×Dic432
#191328492
#191328462
#191328452
#191328402
#191328382
#95×Dic432
C43×#14392
#1385243