Finite Group Databasebeta

← #11903461

Subgroups — #11903461

Order 1152.

1698 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#556C211yesmaximal, characteristic, complemented
2#10589830C211yesmaximal, characteristic, complemented
3#10589828C211yesmaximal, characteristic, complemented
4#10589808C214yesmaximal, complemented
5#10589807C214yesmaximal, complemented
6#10589782C212yesmaximal, complemented
7#10589778C212yesmaximal, complemented
8#10589741C212yesmaximal, complemented
9#10589729C212yesmaximal, complemented
10#10589683C212yesmaximal, complemented
11#10589681C211yesmaximal, characteristic, complemented
12C4×#3701C211yesmaximal, characteristic, complemented
13C4×#3701C212yesmaximal, complemented
14#10589665C211yesmaximal, characteristic, complemented
15C4×D4×D9C211yesmaximal, characteristic, complemented
16#10589632C212yesmaximal, complemented
17D9×#117C212yesmaximal, complemented
18#86979—31nomaximal
19C2×#3701C2211yescharacteristic
20C2×#3701C2212yes—
21C2×D4×D9C2211yescharacteristic
22C22×C4×D9C2212yes—
23C9×C4⋊Q8C2211yescharacteristic, complemented
24C9×#126C2214yescomplemented
25C9×#124C2212yes—
26C9×C22⋊Q8C2212yescomplemented
27C4×Q8×C9C2211yescharacteristic, complemented
28C4×Q8×C9C2212yescomplemented
29C4×D4×C9C2211yescharacteristic
30C9×#117C2212yescomplemented
31#63508C2212yes—
32#63508C2212yescomplemented
33#63508C2212yescomplemented
34Q8×Dic9C2211yescharacteristic, complemented
35Q8×Dic9C2212yescomplemented
36#63500C2212yes—
37D4×Dic9C2211yescharacteristic
38#63492C2212yescomplemented
39C4×#611C2212yes—
40#63488C2212yescomplemented
41#63459C2212yes—
42#63458C2214yescomplemented
43#63457C2212yescomplemented
44#63456C2214yes—
45#63456C2214yescomplemented
46#63455C2212yes—
47#63455C2211yescharacteristic
48#63455C2214yescomplemented
49#63455C2211yescharacteristic, complemented
50#63454C2212yes—
51#63454C2211yescharacteristic
52#63454C2214yescomplemented
53#63454C2212yescomplemented
54#63454C2212yescomplemented
55C4⋊C4×D9C2211yescharacteristic
56C4⋊C4×D9C2212yescomplemented
57C4⋊C4×D9C2212yescomplemented
58#63452C2212yescomplemented
59#63451C2214yescomplemented
60#63449C2212yescomplemented
61#63447C2214yescomplemented
62#63446C2214yes—
63#63445C2214yes—
64#63445C2214yescomplemented
65#63444C2214yes—
66#611⋊C4C2212yes—
67#611⋊C4C2214yescomplemented
68C22⋊C4×D9C2214yes—
69C22⋊C4×D9C2212yes—
70#63441C2214yescomplemented
71#63439C2214yescomplemented
72#63438C2214yescomplemented
73C4×D36C2212yes—
74C4×D36C2212yes—
75C4×D36C2211yescharacteristic
76C4×D36C2214yescomplemented
77C4×D36C2211yescharacteristic, complemented
78#63434C2214yes—
79C42×D9C2211yescharacteristic
80C42×D9C2212yescomplemented
81C42×D9C2214yescomplemented
82#63432C2212yescomplemented
83#63431C2211yescharacteristic, complemented
84C3×#556D311yescharacteristic
85#5728—31no—
86#5726—31no—
87#5706—34no—
88#5705—34no—
89#5680—32no—
90#5676—32no—
91#5639—32no—
92#5627—32no—
93#5581—32no—
94#5579—31no—
95C4×#239—31no—
96C4×#239—32no—
97#5563—31no—
98C4×D3×D4—31no—
99#5530—32no—
100D3×#117—32no—
101C23×D9C2312yes—
102C2×Q8×C9C2312yes—
103C2×Q8×C9C2311yescharacteristic
104C2×D4×C9C2311yescharacteristic
105C22×C4×C9C2312yes—
106C2×#611C2312yes—
107C2×#611C2314yes—
108C22×Dic9C2312yes—
109#3701—28no—
110#3701—24no—
111D4×D9—24no—
112C2×D36C2311yescharacteristic
113C2×D36C2312yes—
114C2×D36C2314yes—
115C2×D36C2311yescharacteristic
116C2×C4×D9—28no—
117C2×C4×D9C2312yes—
118C2×C4×D9C2312yes—
119C2×C4×D9C2311yescharacteristic
120C2×C4×D9C2312yes—
121C2×C4×D9C2314yes—
122C2×C4×D9C2312yes—
123C2×C4×D9C2312yes—
124C2×C4×D9C2311yescharacteristic
125C2×C4×D9C2314yes—
126C2×C4×D9C2312yes—
127C2×C4×D9C2311yescharacteristic
128C2×Dic18C2312yes—
129C9×C4⋊C4C2311yescharacteristic
130C9×C4⋊C4C2312yes—
131C9×C4⋊C4C2311yescharacteristic
132C9×C4⋊C4C2314yes—
133C9×C4⋊C4C2312yes—
134C9×C4⋊C4C2312yes—
135C9×C22⋊C4C2314yes—
136C9×C22⋊C4C2312yes—
137C9×C22⋊C4C2314yes—
138C42×C9C2314yes—
139C42×C9C2311yescharacteristic
140C42×C9C2312yes—
141#3676C2314yes—
142#3676C2312yes—
143(C2×D9)⋊C4C2312yes—
144(C2×D9)⋊C4C2314yes—
145(C2×D9)⋊C4C2314yes—
146(C2×D9)⋊C4C2314yes—
147(C2×D9)⋊C4C2314yes—
148(C2×D9)⋊C4C2312yes—
149(C2×D9)⋊C4C2312yes—
150(C2×D9)⋊C4C2312yes—
151(C2×D9)⋊C4C2312yes—
152C4⋊Dic9C2311yescharacteristic
153C4⋊Dic9C2312yes—
154C4⋊Dic9C2311yescharacteristic
155C4⋊Dic9C2312yes—
156C4⋊Dic9C2312yes—
157C4⋊Dic9C2314yes—
158Dic9⋊C4C2312yes—
159Dic9⋊C4C2314yes—
160Dic9⋊C4C2314yes—
161Dic9⋊C4C2314yes—
162Dic9⋊C4C2314yes—
163C4×Dic9C2314yes—
164C4×Dic9C2311yescharacteristic
165C4×Dic9C2311yescharacteristic
166C4×Dic9C2314yes—
167C4×Dic9C2312yes—
168C4×Dic9C2311yescharacteristic
169C4×Dic9C2312yes—
170#3475—91noSylow
171C2×#239—32no—
172C2×#239—31no—
173C2×D3×D4—31no—
174C22×C4×D3—32no—
175C3×C4⋊Q8C2×D311yescharacteristic
176C3×#126C2×D314yes—
177C3×#124C2×D312yes—
178C3×C22⋊Q8C2×D312yes—
179C3×C4×Q8C2×D311yescharacteristic
180C3×C4×Q8C2×D312yes—
181C3×C4×D4C2×D311yescharacteristic
182C3×#117C2×D312yes—
183#946—32no—
184#946—32no—
185#946—32no—
186Q8×Dic3—31no—
187Q8×Dic3—32no—
188#938—32no—
189D4×Dic3—31no—
190#930—32no—
191C4×#67—32no—
192#926—32no—
193#897—32no—
194#896—34no—
195#895—32no—
196#894—34no—
197#894—34no—
198#893—32no—
199#893—34no—
200#893—31no—
201#893—31no—
202#892—34no—
203#892—32no—
204#892—32no—
205#892—31no—
206#892—32no—
207D3×C4⋊C4—32no—
208D3×C4⋊C4—32no—
209D3×C4⋊C4—31no—
210#890—32no—
211#889—34no—
212#887—32no—
213#885—34no—
214#884—34no—
215#883—34no—
216#883—34no—
217#882—34no—
218#67⋊C4—34no—
219#67⋊C4—32no—
220D3×C22⋊C4—34no—
221D3×C22⋊C4—32no—
222#879—34no—
223#877—34no—
224#876—34no—
225C4×D12—32no—
226C4×D12—32no—
227C4×D12—34no—
228C4×D12—31no—
229C4×D12—31no—
230#872—34no—
231C42×D3—32no—
232C42×D3—34no—
233C42×D3—31no—
234#870—32no—
235#869—31no—
236C23×C9C2412yes—
237C22×D9—24no—
238C22×D9—24no—
239C22×D9—42no—
240C22×D9C2412yes—
241C22×D9C2411yescharacteristic
242C22×D9C2412yes—
243Q8×C9—24no—
244Q8×C9—22no—
245D4×C9—22no—
246C2×C4×C9—24no—
247C2×C4×C9C2412yes—
248C2×C4×C9C2414yes—
249C2×C4×C9C2412yes—
250C2×C4×C9C2412yes—
251C2×C4×C9C2411yescharacteristic
252C2×C4×C9C2411yescharacteristic
253C2×C4×C9C2411yescharacteristic
254#611—24no—
255#611—44no—
256C2×Dic9—24no—
257C2×Dic9C2412yes—
258C2×Dic9C2411yescharacteristic
259C2×Dic9C2411yescharacteristic
260C2×Dic9C2414yes—
261C2×Dic9C2412yes—
262C2×Dic9C2411yescharacteristic
263D36—24no—
264D36—28no—
265D36—22no—
266D36#4114yescomplemented
267C4×D9—24no—
268C4×D9—28no—
269C4×D9—24no—
270C4×D9—22no—
271C4×D9—24no—
272C4×D9—24no—
273C4×D9—24no—
274C4×D9—44no—
275C4×D9—41no—
276C4×D9—42no—
277C4×D9#4114yescomplemented
278Dic18—42no—
279#556D911yescharacteristic, complemented
280#555—91no—
281#554—91no—
282#553—92no—
283#552—92no—
284#552—92no—
285#551—94no—
286#547—91no—
287#546—92no—
288#533—91no—
289#529—94no—
290#529—92no—
291#525—92no—
292C4×#41—92no—
293C4×#41—91no—
294C2×C4×D4—91no—
295C2×#117—92no—
296C23×D3—32no—
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C22×D312yes—
299C2×C3×D4C22×D311yescharacteristic
300C22×C3×C4C22×D312yes—
301C2×#67—32no—
302C2×#67—34no—
303C22×Dic3—32no—
304#239—64no—
305#239—68no—
306D3×D4—64no—
307C2×D12—31no—
308C2×D12—32no—
309C2×D12—34no—
310C2×D12—31no—
311C2×C4×D3—31no—
312C2×C4×D3—32no—
313C2×C4×D3—31no—
314C2×C4×D3—32no—
315C2×C4×D3—34no—
316C2×C4×D3—32no—
317C2×C4×D3—32no—
318C2×C4×D3—32no—
319C2×C4×D3—34no—
320C2×C4×D3—32no—
321C2×C4×D3—31no—
322C2×C4×D3—68no—
323C2×Dic6—32no—
324C3×C4⋊C4C22×D312yes—
325C3×C4⋊C4C22×D314yes—
326C3×C4⋊C4C22×D312yes—
327C3×C4⋊C4C22×D311yescharacteristic
328C3×C4⋊C4C22×D311yescharacteristic
329C3×C4⋊C4C22×D312yes—
330C3×C22⋊C4C22×D314yes—
331C3×C22⋊C4C22×D314yes—
332C3×C22⋊C4C22×D312yes—
333C3×C42C22×D311yescharacteristic
334C3×C42C22×D312yes—
335C3×C42C22×D314yes—
336#217—34no—
337#217—32no—
338(C2×D3)⋊C4—32no—
339(C2×D3)⋊C4—34no—
340(C2×D3)⋊C4—32no—
341(C2×D3)⋊C4—32no—
342(C2×D3)⋊C4—34no—
343(C2×D3)⋊C4—32no—
344(C2×D3)⋊C4—34no—
345(C2×D3)⋊C4—32no—
346(C2×D3)⋊C4—34no—
347C4⋊Dic3—32no—
348C4⋊Dic3—32no—
349C4⋊Dic3—31no—
350C4⋊Dic3—34no—
351C4⋊Dic3—32no—
352C4⋊Dic3—31no—
353Dic3⋊C4—34no—
354Dic3⋊C4—34no—
355Dic3⋊C4—34no—
356Dic3⋊C4—32no—
357Dic3⋊C4—34no—
358C4×Dic3—32no—
359C4×Dic3—31no—
360C4×Dic3—34no—
361C4×Dic3—34no—
362C4×Dic3—32no—
363C4×Dic3—31no—
364C4×Dic3—31no—
365C22×C9—22no—
366C22×C9—22no—
367C22×C9—22no—
368C22×C9C2511yescharacteristic
369C2×D9—22no—
370C2×D9—21no—
371C2×D9—22no—
372C2×D9—21no—
373C2×D9—22no—
374C2×D9—22no—
375C2×D9—22no—
376C2×D9—48no—
377C2×D9C2×#4112yes—
378C2×D9C2×#4114yes—
379C4×C9—22no—
380C4×C9—24no—
381C4×C9—22no—
382C4×C9—21no—
383C4×C9—22no—
384C4×C9C2×#4112yes—
385C4×C9C2×#4112yes—
386Dic9—22no—
387Dic9—22no—
388Dic9—21no—
389Dic9—24no—
390Dic9—21no—
391Dic9C2×#4112yes—
392C2×#41—91no—
393C2×#41—92no—
394C22×D4—91no—
395C23×C4—92no—
396C4⋊Q8—91no—
397C4⋊Q8C2×D911yescharacteristic, complemented
398#126—94no—
399#126—94no—
400#126C2×D914yescomplemented
401#125—94no—
402#125—92no—
403#125—92no—
404#124—94no—
405#124C2×D912yes—
406#123—94no—
407#123—94no—
408#123—94no—
409#123—94no—
410C22⋊Q8—92no—
411C22⋊Q8—92no—
412C22⋊Q8—92no—
413C22⋊Q8—94no—
414C22⋊Q8—92no—
415C22⋊Q8C2×D912yescomplemented
416#121—92no—
417#121—92no—
418#121—92no—
419#121—94no—
420#120—94no—
421C4×Q8—92no—
422C4×Q8—91no—
423C4×Q8—92no—
424C4×Q8C2×D912yescomplemented
425C4×Q8C2×D911yescharacteristic, complemented
426C4×D4—91no—
427C4×D4—92no—
428C4×D4—91no—
429C4×D4—94no—
430C4×D4—92no—
431C4×D4—91no—
432C4×D4—92no—
433C4×D4—94no—
434C4×D4—91no—
435C4×D4—92no—
436C4×D4—92no—
437C4×D4—91no—
438C4×D4—94no—
439C4×D4C2×D911yescharacteristic
440#117—92no—
441#117—91no—
442#117—92no—
443#117—92no—
444#117—94no—
445#117—92no—
446#117—94no—
447#117—94no—
448#117C2×D912yescomplemented
449C2×C4⋊C4—92no—
450C2×C4⋊C4—92no—
451C2×C4⋊C4—91no—
452C2×C22⋊C4—94no—
453C2×C22⋊C4—92no—
454C2×C42—94no—
455C2×C42—91no—
456C2×C42—92no—
457C23×C3C23×D312yes—
458C22×D3—31no—
459C22×D3—32no—
460C22×D3—32no—
461C22×D3—64no—
462C22×D3—64no—
463C22×D3—122no—
464C3×Q8—22no—
465C3×Q8—24no—
466C3×D4—22no—
467C2×C3×C4—24no—
468C2×C3×C4C23×D312yes—
469C2×C3×C4C23×D314yes—
470C2×C3×C4C23×D312yes—
471C2×C3×C4C23×D312yes—
472C2×C3×C4C23×D311yescharacteristic
473C2×C3×C4C23×D311yescharacteristic
474C2×C3×C4C23×D311yescharacteristic
475#67—64no—
476#67—124no—
477C2×Dic3—31no—
478C2×Dic3—32no—
479C2×Dic3—31no—
480C2×Dic3—31no—
481C2×Dic3—34no—
482C2×Dic3—32no—
483C2×Dic3—64no—
484D12—34no—
485D12—64no—
486D12—68no—
487D12—62no—
488C4×D3—34no—
489C4×D3—64no—
490C4×D3—64no—
491C4×D3—64no—
492C4×D3—68no—
493C4×D3—64no—
494C4×D3—62no—
495C4×D3—64no—
496C4×D3—124no—
497C4×D3—121no—
498C4×D3—122no—
499Dic6—122no—
500C2×C9—42no—
501C2×C9C22×#4111yescharacteristic
502C2×C9C22×#4111yescharacteristic
503C2×C9#58511yescharacteristic
504D9—22no—
505D9—24no—
506D9—42no—
507C24—92no—
508#41—184no—
509#41—188no—
510C2×Q8—92no—
511C2×Q8C22×D911yescharacteristic
512C2×Q8C22×D912yes—
513C2×D4—92no—
514C2×D4—94no—
515C2×D4—91no—
516C2×D4—92no—
517C2×D4—94no—
518C2×D4—91no—
519C2×D4—184no—
520C2×D4C22×D911yescharacteristic
521C22×C4—91no—
522C22×C4—92no—
523C22×C4—92no—
524C22×C4—94no—
525C22×C4—91no—
526C22×C4—92no—
527C22×C4—92no—
528C22×C4—92no—
529C22×C4—92no—
530C22×C4—91no—
531C22×C4—94no—
532C22×C4—92no—
533C22×C4—188no—
534C22×C4C22×D912yes—
535C4⋊C4—91no—
536C4⋊C4—92no—
537C4⋊C4—94no—
538C4⋊C4—94no—
539C4⋊C4—91no—
540C4⋊C4—92no—
541C4⋊C4—92no—
542C4⋊C4—94no—
543C4⋊C4—92no—
544C4⋊C4—94no—
545C4⋊C4—94no—
546C4⋊C4C22×D911yescharacteristic
547C4⋊C4C22×D911yescharacteristic
548C4⋊C4C22×D912yes—
549C4⋊C4C22×D912yes—
550C4⋊C4C22×D914yes—
551C4⋊C4C22×D912yes—
552C22⋊C4—94no—
553C22⋊C4—92no—
554C22⋊C4—92no—
555C22⋊C4—92no—
556C22⋊C4—94no—
557C22⋊C4—92no—
558C22⋊C4—94no—
559C22⋊C4—92no—
560C22⋊C4—94no—
561C22⋊C4—92no—
562C22⋊C4—94no—
563C22⋊C4C22×D914yes—
564C22⋊C4C22×D912yes—
565C22⋊C4C22×D914yes—
566C42—92no—
567C42—91no—
568C42—94no—
569C42—94no—
570C42—91no—
571C42—92no—
572C42—91no—
573C42C22×D914yes—
574C42C22×D911yescharacteristic
575C42C22×D912yes—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3—22no—
579C22×C3C24×D311yescharacteristic
580C2×D3—32no—
581C2×D3—34no—
582C2×D3—62no—
583C2×D3—61no—
584C2×D3—62no—
585C2×D3—61no—
586C2×D3—62no—
587C2×D3—62no—
588C2×D3—62no—
589C2×D3—128no—
590C3×C4—22no—
591C3×C4—22no—
592C3×C4—24no—
593C3×C4—21no—
594C3×C4—22no—
595C3×C4D3×#4112yes—
596C3×C4D3×#4112yes—
597Dic3—32no—
598Dic3—62no—
599Dic3—62no—
600Dic3—61no—
601Dic3—64no—
602Dic3—61no—
603C9#347511yescharacteristic, complemented, Sylow
604C23—91no—
605C23—92no—
606C23—92no—
607C23—184no—
608C23—184no—
609C23—362no—
610C23C23×D912yes—
611Q8—22no—
612Q8—24no—
613Q8—362no—
614D4—22no—
615D4—94no—
616D4—184no—
617D4—188no—
618D4—184no—
619D4—182no—
620D4—364no—
621C2×C4—24no—
622C2×C4—91no—
623C2×C4—94no—
624C2×C4—92no—
625C2×C4—91no—
626C2×C4—94no—
627C2×C4—91no—
628C2×C4—92no—
629C2×C4—184no—
630C2×C4—184no—
631C2×C4—184no—
632C2×C4—188no—
633C2×C4—184no—
634C2×C4—184no—
635C2×C4—182no—
636C2×C4—184no—
637C2×C4—362no—
638C2×C4—364no—
639C2×C4—361no—
640C2×C4C23×D912yes—
641C2×C4C23×D912yes—
642C2×C4C23×D911yescharacteristic
643C2×C4C23×D914yes—
644C2×C4C23×D912yes—
645C2×C4C23×D911yescharacteristic
646C2×C4C23×D911yescharacteristic
647C2×C3—42no—
648C2×C3C2×D3×#4111yescharacteristic
649C2×C3C2×D3×#4111yescharacteristic
650C2×C3#596811yescharacteristic
651D3—62no—
652D3—64no—
653D3—122no—
654C22—22no—
655C22—22no—
656C22—22no—
657C22—92no—
658C22—94no—
659C22—182no—
660C22—181no—
661C22—182no—
662C22—181no—
663C22—182no—
664C22—182no—
665C22—182no—
666C22—368no—
667C22C24×D911yescharacteristic
668C4—22no—
669C4—22no—
670C4—24no—
671C4—22no—
672C4—21no—
673C4—92no—
674C4—182no—
675C4—182no—
676C4—181no—
677C4—181no—
678C4—184no—
679C4#41×D912yes—
680C4#41×D912yes—
681C3#8697911yescharacteristic
682C2—42no—
683C2—182no—
684C2—184no—
685C2—362no—
686C2C2×#41×D911yescharacteristic
687C2C2×#41×D911yescharacteristic
688C2#1059314311yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#556C2
hypercenter#556D9
hypocenterC9#3475
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #556

Complements

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

NH ≅ G/Ntype
1. C9×#556C2semidirect
2. #10589830C2semidirect
3. #10589828C2semidirect
4. #10589808C2semidirect
5. #10589807C2semidirect
6. #10589782C2semidirect
7. #10589778C2semidirect
8. #10589741C2semidirect
9. #10589729C2semidirect
10. #10589683C2semidirect
11. #10589681C2semidirect
12. C4×#3701C2semidirect
13. C4×#3701C2semidirect
14. #10589665C2semidirect
15. C4×D4×D9C2semidirect
16. #10589632C2semidirect
17. D9×#117C2semidirect
23. C9×C4⋊Q8C22semidirect
24. C9×#126C22semidirect
26. C9×C22⋊Q8C22semidirect
27. C4×Q8×C9C22semidirect
28. C4×Q8×C9C22semidirect
30. C9×#117C22semidirect
32. #63508C22semidirect
33. #63508C22semidirect
34. Q8×Dic9C22semidirect
35. Q8×Dic9C22semidirect
38. #63492C22semidirect
40. #63488C22semidirect
42. #63458C22semidirect
43. #63457C22semidirect
45. #63456C22semidirect
48. #63455C22semidirect
49. #63455C22semidirect
52. #63454C22semidirect
53. #63454C22semidirect
54. #63454C22semidirect
56. C4⋊C4×D9C22semidirect
57. C4⋊C4×D9C22semidirect
58. #63452C22semidirect
59. #63451C22semidirect
60. #63449C22semidirect
61. #63447C22semidirect
64. #63445C22semidirect
67. #611⋊C4C22semidirect
70. #63441C22semidirect
71. #63439C22semidirect
72. #63438C22semidirect
76. C4×D36C22semidirect
77. C4×D36C22semidirect
80. C42×D9C22semidirect
81. C42×D9C22semidirect
82. #63432C22semidirect
83. #63431C22semidirect
266. D36#41semidirect
277. C4×D9#41semidirect
279. #556D9semidirect
397. C4⋊Q8C2×D9semidirect
400. #126C2×D9semidirect
415. C22⋊Q8C2×D9semidirect
424. C4×Q8C2×D9semidirect
425. C4×Q8C2×D9semidirect
448. #117C2×D9semidirect
603. C9#3475semidirect

Maximal subgroups

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

subgroupindex
C9×#5562
#105898302
#105898282
#105898082
#105898072
#105897822
#105897782
#105897412
#105897292
#105896832
#105896812
C4×#37012
#105896652
C4×D4×D92
#105896322
D9×#1172
#869793