Finite Group Databasebeta

← C2×#20246084 #26375035

Subgroups — C2×#20246084 #26375035

Order 12032.

3934 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093995C211yesmaximal, characteristic
2C22×D4×Dic47C211yesmaximal, characteristic, complemented
3C22×#13093981C211yesmaximal, characteristic, complemented
4#20246084C2116yesmaximal, direct product factor
5C2×#15689023C212yesmaximal, complemented
6C2×#15689021C211yesmaximal, characteristic, complemented
7C2×#15689011C212yesmaximal, complemented
8C2×#15689000C212yesmaximal, complemented
9C2×#15688995C212yesmaximal, complemented
10C2×#15688980C211yesmaximal, characteristic, complemented
11C2×C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
12C2×C47×#390C211yesmaximal, characteristic, complemented
13C23×C22⋊D47C2212yes—
14C24×Dic47C2212yes—
15C23×C4×D47C2211yescharacteristic
16C2×#13093995C4116yescomplemented
17C2×#13093995C2218yes—
18C2×D4×Dic47—28no—
19C2×D4×Dic47C2218yescomplemented
20C2×#13093981—28no—
21C2×#13093981C2218yescomplemented
22C22×C4⋊Dic47C2211yescharacteristic
23C22×C4⋊Dic47C2211yescharacteristic
24C22×Dic47⋊C4C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2212yes—
27C22×C22⋊Dic47C2212yes—
28C22×C22⋊Dic47C2212yes—
29C22×(C2×D47)⋊C4C2211yescharacteristic
30C22×(C2×D47)⋊C4C2211yescharacteristic
31C22×(C2×D47)⋊C4C2212yes—
32C22×C4×Dic47C2212yes—
33C22×C4×Dic47C2211yescharacteristic
34#15689023C22116yescomplemented
35#15689021C2218yescomplemented
36#15689011C22116yescomplemented
37#15689000C22116yescomplemented
38#15688995C22116yescomplemented
39#15688980C2218yescomplemented
40C4⋊C4×Dic47C2218yescomplemented
41C2×C47⋊#95C2212yes—
42C2×C47⋊#95C2212yes—
43C2×C47⋊#95C2212yes—
44C23×D4×C47C2211yescharacteristic
45C22×C4⋊C4×C47C2211yescharacteristic
46C22×C22⋊C4×C47C2212yes—
47C22×C22⋊C4×C47C2212yes—
48C22×C42×C47C2211yescharacteristic
49C47×#390C2218yescomplemented
50C24×D47C2311yescharacteristic
51C22×C22⋊D47—44no—
52C22×C22⋊D47—44no—
53C22×C22⋊D47C2×C4116yescomplemented
54C22×C22⋊D47C2318yes—
55C23×Dic47—28no—
56C23×Dic47—44no—
57C23×Dic47—44no—
58C23×Dic47C2312yes—
59C23×Dic47C2312yes—
60C23×Dic47C2311yescharacteristic
61C23×Dic47C2311yescharacteristic
62C23×Dic47C2311yescharacteristic
63C23×Dic47C2318yes—
64C22×C4×D47—24no—
65C22×C4×D47—24no—
66C22×C4×D47C2×C418yescomplemented
67C22×C4×D47C2314yes—
68#13093995C2×C4164yescomplemented
69D4×Dic47—232no—
70#13093981—232no—
71C2×C4⋊Dic47—24no—
72C2×C4⋊Dic47C2×C418yescomplemented
73C2×C4⋊Dic47C2314yes—
74C2×C4⋊Dic47C2314yes—
75C2×Dic47⋊C4—24no—
76C2×Dic47⋊C4—24no—
77C2×Dic47⋊C4—44no—
78C2×Dic47⋊C4C2314yes—
79C2×Dic47⋊C4C2314yes—
80C2×Dic47⋊C4C2318yes—
81C2×C22⋊Dic47—28no—
82C2×C22⋊Dic47C2×C4116yescomplemented
83C2×C22⋊Dic47C2318yes—
84C2×C22⋊Dic47C2318yes—
85C2×(C2×D47)⋊C4—24no—
86C2×(C2×D47)⋊C4—24no—
87C2×(C2×D47)⋊C4—44no—
88C2×(C2×D47)⋊C4C2314yes—
89C2×(C2×D47)⋊C4C2314yes—
90C2×(C2×D47)⋊C4C2318yes—
91C2×C4×Dic47—44no—
92C2×C4×Dic47D418yescomplemented
93C2×C4×Dic47C2318yes—
94C2×C4×Dic47C2314yes—
95C47⋊#95C2318yes—
96C47⋊#95C2318yes—
97C47⋊#95C2318yes—
98C25×C47C2312yes—
99C22×D4×C47—24no—
100C22×D4×C47—24no—
101C22×D4×C47C2×C418yes—
102C22×D4×C47C2314yes—
103C23×C4×C47C2311yescharacteristic
104C23×C4×C47C2312yes—
105C23×C4×C47C2311yescharacteristic
106C23×C4×C47C2311yescharacteristic
107C2×C4⋊C4×C47—24no—
108C2×C4⋊C4×C47C2314yes—
109C2×C22⋊C4×C47—44no—
110C2×C22⋊C4×C47—44no—
111C2×C22⋊C4×C47C2318yes—
112C2×C22⋊C4×C47C2318yes—
113C2×C42×C47—24no—
114C2×C42×C47C2314yes—
115C24×C47—24no—
116C24×C47—24no—
117C24×C47—24no—
118C24×C47—24no—
119C24×C47—24no—
120C24×C47—24no—
121C24×C47C22×C418yes—
122C24×C47C2414yes—
123C24×C47C2411yescharacteristic
124C23×D47—22no—
125C23×D47—22no—
126C23×D47—22no—
127C23×D47—22no—
128C23×D47—22no—
129C23×D47—22no—
130C23×D47C22×C414yes—
131C23×D47C2412yes—
132C2×D4×C47—232no—
133C2×D4×C47—28no—
134C2×D4×C47—28no—
135C2×D4×C47C22×C4116yes—
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—24no—
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—24no—
142C22×C4×C47—24no—
143C22×C4×C47—22no—
144C22×C4×C47—22no—
145C22×C4×C47C22×C414yes—
146C22×C4×C47C2×D414yes—
147C22×C4×C47#4114yes—
148C22×C4×C47C2412yes—
149C22×C4×C47C2412yes—
150C22×C4×C47C2414yes—
151C22×C4×C47C2412yes—
152C2×C22⋊D47—432no—
153C2×C22⋊D47—48no—
154C2×C22⋊D47—48no—
155C2×C22⋊D47C22×C4132yescomplemented
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—24no—
160C22×Dic47—24no—
161C22×Dic47—22no—
162C22×Dic47—22no—
163C22×Dic47—22no—
164C22×Dic47—24no—
165C22×Dic47—24no—
166C22×Dic47—24no—
167C22×Dic47—216no—
168C22×Dic47—48no—
169C22×Dic47—48no—
170C22×Dic47—432no—
171C22×Dic47C22×C414yes—
172C22×Dic47C22×C418yes—
173C22×Dic47C2×D414yes—
174C22×Dic47C2×D414yes—
175C22×Dic47C2414yes—
176C22×Dic47C2414yes—
177C22×Dic47C2412yes—
178C22×Dic47C2412yes—
179C22×Dic47C2412yes—
180C2×C4×D47—232no—
181C2×C4×D47—28no—
182C2×C4×D47—28no—
183C2×C4×D47C22×C4116yescomplemented
184C4⋊C4×C47—28no—
185C22⋊C4×C47—48no—
186C22⋊C4×C47—48no—
187C42×C47—28no—
188C22⋊Dic47—216no—
189C22⋊Dic47C22×C4132yescomplemented
190(C2×D47)⋊C4—28no—
191(C2×D47)⋊C4—28no—
192(C2×D47)⋊C4—48no—
193C4⋊Dic47—28no—
194C4⋊Dic47C22×C4116yescomplemented
195Dic47⋊C4—28no—
196Dic47⋊C4—28no—
197Dic47⋊C4—48no—
198C4×Dic47—48no—
199C4×Dic47C2×D4116yescomplemented
200C23×C47—216no—
201C23×C47—216no—
202C23×C47—216no—
203C23×C47—24no—
204C23×C47—24no—
205C23×C47—24no—
206C23×C47—24no—
207C23×C47—24no—
208C23×C47—24no—
209C23×C47—48no—
210C23×C47—48no—
211C23×C47—48no—
212C23×C47—48no—
213C23×C47C23×C418yes—
214C23×C47C23×C412yes—
215C23×C47C22×D412yes—
216C23×C47C2×#4112yes—
217C23×C47H(5,𝔽2)12yes—
218C23×C47H(5,𝔽2)12yes—
219C23×C47H(5,𝔽2)12yes—
220C23×C472−1+412yes—
221C23×C47C2511yescharacteristic
222C22×D47—28no—
223C22×D47—28no—
224C22×D47—28no—
225C22×D47—22no—
226C22×D47—22no—
227C22×D47—22no—
228C22×D47—22no—
229C22×D47—22no—
230C22×D47—22no—
231C22×D47—44no—
232C22×D47—44no—
233C22×D47—44no—
234C22×D47—44no—
235C22×D47C23×C414yes—
236D4×C47—232no—
237C2×C4×C47—22no—
238C2×C4×C47—22no—
239C2×C4×C47—24no—
240C2×C4×C47—24no—
241C2×C4×C47—22no—
242C2×C4×C47—24no—
243C2×C4×C47—22no—
244C2×C4×C47—22no—
245C2×C4×C47—22no—
246C2×C4×C47—44no—
247C2×C4×C47—44no—
248C2×C4×C47—48no—
249C2×C4×C47C4×D4116yes—
250C2×C4×C47C23×C414yes—
251C2×C4×C47C22×D414yes—
252C2×C4×C47C2×#4114yes—
253C22⋊D47—432no—
254C2×Dic47—28no—
255C2×Dic47—216no—
256C2×Dic47—28no—
257C2×Dic47—28no—
258C2×Dic47—22no—
259C2×Dic47—22no—
260C2×Dic47—22no—
261C2×Dic47—24no—
262C2×Dic47—24no—
263C2×Dic47—22no—
264C2×Dic47—22no—
265C2×Dic47—22no—
266C2×Dic47—24no—
267C2×Dic47—24no—
268C2×Dic47—24no—
269C2×Dic47—432no—
270C2×Dic47—48no—
271C2×Dic47C23×C418yes—
272C2×Dic47C23×C414yes—
273C2×Dic47C22×D414yes—
274C2×Dic47C22×D414yes—
275C4×D47—232no—
276C2×#2324—471nomaximal, Sylow
277C22×C47—28no—
278C22×C47—28no—
279C22×C47—28no—
280C22×C47—432no—
281C22×C47—44no—
282C22×C47—44no—
283C22×C47—44no—
284C22×C47—44no—
285C22×C47C2×C4×D414yes—
286C22×C47#51814yes—
287C22×C47#52014yes—
288C22×C47#53514yes—
289C22×C47#53714yes—
290C22×C47#54014yes—
291C22×C47#54214yes—
292C22×C47C24×C411yescharacteristic
293C22×C47C23×D411yescharacteristic
294C22×C47C22×#4111yescharacteristic
295C22×C47C2×H(5,𝔽2)11yescharacteristic
296C22×C47C2×H(5,𝔽2)11yescharacteristic
297C22×C47C2×H(5,𝔽2)11yescharacteristic
298C22×C47C2×2−1+411yescharacteristic
299C2×D47—24no—
300C2×D47—24no—
301C2×D47—24no—
302C2×D47—416no—
303C2×D47—42no—
304C2×D47—42no—
305C2×D47—42no—
306C2×D47—42no—
307C4×C47—42no—
308C4×C47—42no—
309C4×C47—44no—
310C4×C47C2×C4×D418yes—
311Dic47—24no—
312Dic47—28no—
313Dic47—24no—
314Dic47—24no—
315Dic47—44no—
316C22×#121—471no—
317C22×C4×D4—471no—
318C22×#117—471no—
319#2324—4716no—
320C2×#390—472no—
321C2×#390D4711yescharacteristic, complemented
322C2×#389—471no—
323C2×#388—472no—
324C2×#386—472no—
325C2×#385—472no—
326C2×#380—471no—
327C2×C4×C4⋊C4—471no—
328C2×C47—48no—
329C2×C47#232418yescomplemented
330C2×C47C22×C4×D411yescharacteristic
331C2×C47C2×#51811yescharacteristic
332C2×C47C2×#52011yescharacteristic
333C2×C47C2×#53511yescharacteristic
334C2×C47C2×#53711yescharacteristic
335C2×C47C2×#54011yescharacteristic
336C2×C47C2×#54211yescharacteristic
337D47—44no—
338C23×D4—472no—
339C23×D4C2×D4711yescharacteristic
340C24×C4—471no—
341C24×C4—472no—
342C2×#121—4716no—
343C2×#121—478no—
344C2×C4×D4—478no—
345C2×C4×D4—948no—
346C2×#117—478no—
347C2×#117—948no—
348C22×C4⋊C4—471no—
349C22×C4⋊C4—471no—
350C22×C4⋊C4—471no—
351C22×C4⋊C4—471no—
352C22×C4⋊C4—472no—
353C22×C4⋊C4C2×D4711yescharacteristic
354C22×C22⋊C4—472no—
355C22×C22⋊C4—472no—
356C22×C22⋊C4—471no—
357C22×C22⋊C4—471no—
358C22×C22⋊C4—472no—
359C22×C22⋊C4C2×D4712yes—
360C22×C22⋊C4C2×D4712yes—
361C22×C42—471no—
362C22×C42—472no—
363C22×C42C2×D4711yescharacteristic
364#390—4716no—
365#390C2×D4718yescomplemented
366#389—478no—
367#388—4716no—
368#386—4716no—
369#385—4716no—
370#380—478no—
371C4×C4⋊C4—478no—
372C2×#95—472no—
373C2×#95—472no—
374C2×#95—472no—
375C47C2×#232411yescharacteristic, complemented, Sylow
376C25—471no—
377C25C22×D4712yes—
378C22×D4—24no—
379C22×D4—24no—
380C22×D4—4716no—
381C22×D4—478no—
382C22×D4—1884no—
383C22×D4—1884no—
384C22×D4C4×D4718yes—
385C22×D4C22×D4714yes—
386C23×C4—471no—
387C23×C4—471no—
388C23×C4—472no—
389C23×C4—471no—
390C23×C4—478no—
391C23×C4—474no—
392C23×C4—472no—
393C23×C4—478no—
394C23×C4—948no—
395C23×C4—944no—
396C23×C4—944no—
397C23×C4—1884no—
398C23×C4—1884no—
399C23×C4C22×D4711yescharacteristic
400C23×C4C22×D4711yescharacteristic
401C23×C4C22×D4712yes—
402C23×C4C22×D4711yescharacteristic
403#121—4764no—
404C4×D4—9432no—
405#117—9432no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—478no—
408C2×C4⋊C4—474no—
409C2×C4⋊C4—474no—
410C2×C4⋊C4—474no—
411C2×C4⋊C4—474no—
412C2×C4⋊C4—478no—
413C2×C4⋊C4—944no—
414C2×C4⋊C4—944no—
415C2×C4⋊C4—944no—
416C2×C4⋊C4—1884no—
417C2×C4⋊C4C22×D4714yes—
418C2×C22⋊C4—44no—
419C2×C22⋊C4—44no—
420C2×C22⋊C4—4716no—
421C2×C22⋊C4—478no—
422C2×C22⋊C4—478no—
423C2×C22⋊C4—474no—
424C2×C22⋊C4—474no—
425C2×C22⋊C4—478no—
426C2×C22⋊C4—944no—
427C2×C22⋊C4—944no—
428C2×C22⋊C4—948no—
429C2×C22⋊C4—1884no—
430C2×C22⋊C4C22×D4718yes—
431C2×C22⋊C4C22×D4718yes—
432C2×C42—24no—
433C2×C42—478no—
434C2×C42—474no—
435C2×C42—478no—
436C2×C42—1884no—
437C2×C42C22×D4714yes—
438#95—478no—
439#95—478no—
440#95—478no—
441C24—24no—
442C24—24no—
443C24—24no—
444C24—24no—
445C24—24no—
446C24—24no—
447C24—474no—
448C24—472no—
449C24—942no—
450C24—942no—
451C24—942no—
452C24—942no—
453C24—942no—
454C24—942no—
455C24C2×C4×D4718yes—
456C24C23×D4714yes—
457C24C23×D4711yescharacteristic
458C2×D4—232no—
459C2×D4—28no—
460C2×D4—28no—
461C2×D4—4732no—
462C2×D4—18832no—
463C2×D4—1888no—
464C2×D4—1888no—
465C2×D4C2×C4×D47116yes—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—474no—
476C22×C4—478no—
477C22×C4—474no—
478C22×C4—474no—
479C22×C4—474no—
480C22×C4—472no—
481C22×C4—472no—
482C22×C4—472no—
483C22×C4—4716no—
484C22×C4—474no—
485C22×C4—9416no—
486C22×C4—942no—
487C22×C4—942no—
488C22×C4—942no—
489C22×C4—944no—
490C22×C4—942no—
491C22×C4—944no—
492C22×C4—942no—
493C22×C4—942no—
494C22×C4—9432no—
495C22×C4—948no—
496C22×C4—948no—
497C22×C4—944no—
498C22×C4—944no—
499C22×C4—944no—
500C22×C4—1888no—
501C22×C4—1888no—
502C22×C4—18832no—
503C22×C4C2×C4×D4714yes—
504C22×C4D4×D4714yes—
505C22×C4#1062535214yes—
506C22×C4C23×D4714yes—
507C22×C4C23×D4712yes—
508C22×C4C23×D4712yes—
509C22×C4C23×D4712yes—
510C4⋊C4—28no—
511C4⋊C4—4716no—
512C4⋊C4—948no—
513C4⋊C4—948no—
514C4⋊C4—948no—
515C4⋊C4—1888no—
516C22⋊C4—48no—
517C22⋊C4—48no—
518C22⋊C4—4732no—
519C22⋊C4—948no—
520C22⋊C4—948no—
521C22⋊C4—9416no—
522C22⋊C4—1888no—
523C42—28no—
524C42—4716no—
525C42—1888no—
526C23—216no—
527C23—216no—
528C23—216no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—24no—
535C23—48no—
536C23—48no—
537C23—48no—
538C23—48no—
539C23—474no—
540C23—948no—
541C23—948no—
542C23—948no—
543C23—942no—
544C23—942no—
545C23—942no—
546C23—942no—
547C23—942no—
548C23—942no—
549C23—1884no—
550C23—1884no—
551C23—1884no—
552C23—1884no—
553C23C22×C4×D4718yes—
554C23C22×C4×D4712yes—
555C23C2×D4×D4712yes—
556C23C2×#1062535212yes—
557C23#1309406912yes—
558C23#1309406912yes—
559C23#1309407012yes—
560C23#1309407112yes—
561C23C24×D4711yescharacteristic
562D4—232no—
563D4—18832no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—44no—
574C2×C4—44no—
575C2×C4—48no—
576C2×C4—474no—
577C2×C4—478no—
578C2×C4—474no—
579C2×C4—474no—
580C2×C4—948no—
581C2×C4—9416no—
582C2×C4—942no—
583C2×C4—948no—
584C2×C4—942no—
585C2×C4—942no—
586C2×C4—944no—
587C2×C4—942no—
588C2×C4—944no—
589C2×C4—942no—
590C2×C4—942no—
591C2×C4—948no—
592C2×C4—9432no—
593C2×C4—944no—
594C2×C4—944no—
595C2×C4—944no—
596C2×C4—18832no—
597C2×C4—1888no—
598C2×C4(C22⋊D47)⋊C4116yes—
599C2×C4C22×C4×D4714yes—
600C2×C4C2×D4×D4714yes—
601C2×C4C2×#1062535214yes—
602C22—28no—
603C22—28no—
604C22—28no—
605C22—432no—
606C22—44no—
607C22—44no—
608C22—44no—
609C22—44no—
610C22—944no—
611C22—944no—
612C22—944no—
613C22—18816no—
614C22—1882no—
615C22—1882no—
616C22—1882no—
617C22—1882no—
618C22C2×(C22⋊D47)⋊C414yes—
619C22#1568959514yes—
620C22#1568960214yes—
621C22#1568968914yes—
622C22#1568970214yes—
623C22#1568972714yes—
624C22#1568974214yes—
625C22C23×C4×D4711yescharacteristic
626C22C22×D4×D4711yescharacteristic
627C22C22×#1062535211yescharacteristic
628C22C2×#1309406911yescharacteristic
629C22C2×#1309406911yescharacteristic
630C22C2×#1309407011yescharacteristic
631C22C2×#1309407111yescharacteristic
632C4—42no—
633C4—42no—
634C4—44no—
635C4—944no—
636C4—948no—
637C4—944no—
638C4—944no—
639C4—1884no—
640C4C2×(C22⋊D47)⋊C418yes—
641C2—48no—
642C2—1884no—
643C2#2024608418yesdirect product factor
644C2C22×(C22⋊D47)⋊C411yescharacteristic
645C2C2×#1568959511yescharacteristic
646C2C2×#1568960211yescharacteristic
647C2C2×#1568968911yescharacteristic
648C2C2×#1568970211yescharacteristic
649C2C2×#1568972711yescharacteristic
650C2C2×#1568974211yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#390C2
socleC24×C47C24
prime radicalC22×#13093995C2
cosocleC23×C47C25
hypercenterC2×#390D47
hypocenterC47C2×#2324
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C22×D4×Dic47C2semidirect
3. C22×#13093981C2semidirect
4. #20246084C2direct (N × H)
5. C2×#15689023C2semidirect
6. C2×#15689021C2semidirect
7. C2×#15689011C2semidirect
8. C2×#15689000C2semidirect
9. C2×#15688995C2semidirect
10. C2×#15688980C2semidirect
11. C2×C4⋊C4×Dic47C2semidirect
12. C2×C47×#390C2semidirect
16. C2×#13093995C4semidirect
19. C2×D4×Dic47C22semidirect
21. C2×#13093981C22semidirect
34. #15689023C22semidirect
35. #15689021C22semidirect
36. #15689011C22semidirect
37. #15689000C22semidirect
38. #15688995C22semidirect
39. #15688980C22semidirect
40. C4⋊C4×Dic47C22semidirect
49. C47×#390C22semidirect
53. C22×C22⋊D47C2×C4semidirect
66. C22×C4×D47C2×C4semidirect
68. #13093995C2×C4semidirect
72. C2×C4⋊Dic47C2×C4semidirect
82. C2×C22⋊Dic47C2×C4semidirect
92. C2×C4×Dic47D4semidirect
155. C2×C22⋊D47C22×C4semidirect
183. C2×C4×D47C22×C4semidirect
189. C22⋊Dic47C22×C4semidirect
194. C4⋊Dic47C22×C4semidirect
199. C4×Dic47C2×D4semidirect
321. C2×#390D47semidirect
329. C2×C47#2324semidirect
365. #390C2×D47semidirect
375. C47C2×#2324semidirect
643. C2#20246084direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939952
C22×D4×Dic472
C22×#130939812
#202460842
C2×#156890232
C2×#156890212
C2×#156890112
C2×#156890002
C2×#156889952
C2×#156889802
C2×C4⋊C4×Dic472
C2×C47×#3902
C2×#232447