Finite Group Databasebeta

← #27124516

Subgroups — #27124516

Order 12032.

7094 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257484C214yesmaximal, complemented
2#20257473C214yesmaximal, complemented
3#20257381C218yesmaximal, complemented
4#20257253C216yesmaximal, complemented
5#20257198C211yesmaximal, characteristic, complemented
6#20257159C211yesmaximal, characteristic, complemented
7#20257097C216yesmaximal, complemented
8#20257039C212yesmaximal, complemented
9#20257005C218yesmaximal, complemented
10#20256983C214yesmaximal, complemented
11Q8×#10625350C214yesmaximal, complemented
12#20256821C216yesmaximal, complemented
13#20256684C216yesmaximal, complemented
14C4×#13094072C212yesmaximal, complemented
15C22×C4×Q8×C47C211yesmaximal, characteristic, complemented
16C2×#13094072C2212yes—
17#15689858C22112yescomplemented
18Q8×Dic94C2214yescomplemented
19#15689852C2214yescomplemented
20#15689851C22112yescomplemented
21#15689849C2218yescomplemented
22#15689846C22112yescomplemented
23#15689845C22124yescomplemented
24#15689833C22112yescomplemented
25#15689828C22124yes—
26#15689821C22124yes—
27#15689814C22124yescomplemented
28#15689808C22124yes—
29#15689795C2214yescomplemented
30Q8×D188C2214yescomplemented
31Q8×C22⋊D47C2218yes—
32Q8×C22⋊D47C2218yes—
33#15689785C2218yescomplemented
34#15689784C2218yes—
35#15689784C2218yes—
36#15689774C22124yes—
37#15689754C2216yes—
38#15689745C22124yescomplemented
39#15689731C22124yescomplemented
40#15689720C22124yes—
41#15689704C2216yes—
42#15689697C22112yes—
43#15689680C2216yes—
44#15689680C2216yes—
45#15689680C2216yes—
46#15689677C22124yescomplemented
47#15689673C2216yes—
48#15689673C2216yes—
49#15689673C2216yes—
50#15689660C22124yescomplemented
51#15689657C22112yes—
52#15689657C22112yes—
53#15689657C22112yes—
54#15689657C22112yes—
55#15689657C22112yes—
56#15689657C22112yes—
57#15689634C22112yes—
58#15689634C22112yes—
59#15689634C2214yes—
60#15689605C2218yescomplemented
61#15689604C22112yes—
62#15689601C2212yes—
63#15689599C2218yescomplemented
64C4×#10625354C2218yescomplemented
65C4×#10625350C22112yes—
66C4×#10625350C22112yes—
67C4×#10625350C22112yes—
68C4×Q8×D47C2218yescomplemented
69C23×Q8×C47C2211yescharacteristic
70C2×C4×Q8×C47C2213yes—
71C2×C4×Q8×C47C2211yescharacteristic
72C2×C4×Q8×C47C2214yes—
73C2×C4×Q8×C47C2211yescharacteristic
74C2×C4×Q8×C47C2214yes—
75C2×C4×Q8×C47C2214yes—
76C2×C4×Q8×C47C2213yes—
77C2×C4×Q8×C47C2214yes—
78C22×C4⋊C4×C47C2213yes—
79C22×C42×C47C2213yes—
80#13094072—216no—
81C2×#10625354C2318yes—
82C2×#10625350C2314yes—
83C2×#10625350C23112yes—
84C2×#10625350C23112yes—
85C2×Q8×D47C2318yes—
86#13094024C2316yes—
87#13094024C2316yes—
88#13094024C2316yes—
89#13094023C23124yes—
90#13094022C23124yes—
91#13094021C2316yes—
92#13094019C23148yes—
93#13094018C23124yes—
94#13094018C23124yes—
95#13094016C23112yes—
96#13094016C23112yes—
97#13094016C23112yes—
98#13094015C23124yes—
99#13094014C23148yes—
100#13094013C23124yes—
101#13094012C23112yes—
102#13094012C23112yes—
103#13094012C23112yes—
104#13094009C23148yes—
105#13094007C23124yes—
106#13094007C2318yes—
107#13094007C23124yes—
108#13094004C23124yes—
109#13094003C23112yes—
110#13094003C23112yes—
111#13094003C23112yes—
112#13094003C23112yes—
113#13094003C2314yes—
114#13094003C2314yes—
115#13094002C23148yes—
116#13094000C23124yes—
117#13094000C23124yes—
118#13093999C23124yes—
119#13093998C23112yes—
120#13093998C23112yes—
121#13093998C23112yes—
122#13093998C2314yes—
123#13093998C2314yes—
124#13093998C23112yes—
125#13093993C2318yes—
126Q8×Dic47C2318yes—
127Q8×Dic47C2318yes—
128C4×Dic94C23112yes—
129C4×Dic94C23112yes—
130C4×Dic94C23112yes—
131C4×Dic94C23112yes—
132C4×Dic94C23112yes—
133C4×Dic94C23112yes—
134#13093989C23124yes—
135C4×D188C23112yes—
136C4×D188C23112yes—
137C4×D188C23112yes—
138C4×D188C23112yes—
139C4×D188C23112yes—
140C4×D188C23112yes—
141#13093986C23124yes—
142C4×C22⋊D47C23124yes—
143C4×C22⋊D47C23124yes—
144C4×C22⋊D47C23124yes—
145C4×C22⋊D47C2318yes—
146C4×C22⋊D47C2318yes—
147C4×C22⋊D47C23124yes—
148#13093983C23112yes—
149#13093983C23112yes—
150#13093983C2314yes—
151#13093982C23124yes—
152#13093981C23124yes—
153#13093981C23124yes—
154#13093981C23124yes—
155C4⋊C4×D47C23124yes—
156C42×D47C23124yes—
157C22×Q8×C47—28no—
158C22×Q8×C47C2314yes—
159C22×Q8×C47C2314yes—
160C22×Q8×C47C2313yes—
161C22×Q8×C47C2311yescharacteristic
162C23×C4×C47C2311yescharacteristic
163C23×C4×C47C2313yes—
164C23×C4×C47C2313yes—
165C4×Q8×C47C23112yes—
166C4×Q8×C47C2314yes—
167C4×Q8×C47C2314yes—
168C4×Q8×C47C23112yes—
169C4×Q8×C47C23112yes—
170C4×Q8×C47C2314yes—
171C4×Q8×C47C2314yes—
172C4×Q8×C47C23112yes—
173C2×C4⋊C4×C47C2313yes—
174C2×C4⋊C4×C47C23112yes—
175C2×C4⋊C4×C47C23112yes—
176C2×C4⋊C4×C47C2313yes—
177C2×C4⋊C4×C47C2316yes—
178C2×C42×C47C2313yes—
179C2×C42×C47C2316yes—
180C2×C42×C47C2316yes—
181C2×C42×C47C2313yes—
182C2×C42×C47C2316yes—
183C2×C42×C47C2313yes—
184C2×C42×C47C2316yes—
185C2×C42×C47C2313yes—
186C24×C47C2411yescharacteristic
187C2×Q8×C47—216no—
188C2×Q8×C47—216no—
189C2×Q8×C47—212no—
190C2×Q8×C47#4118yescomplemented
191C2×Q8×C47C24112yes—
192C2×Q8×C47C2414yes—
193C22×C4×C47—212no—
194C22×C4×C47—24no—
195C22×C4×C47—46no—
196C22×C4×C47C2411yescharacteristic
197C22×C4×C47C2411yescharacteristic
198C22×C4×C47C2411yescharacteristic
199C22×C4×C47C2411yescharacteristic
200C22×C4×C47C2411yescharacteristic
201C22×C4×C47C2416yes—
202C22×C4×C47C2416yes—
203C22×C4×C47C2416yes—
204C22×C4×C47C2413yes—
205C22×C4×C47C2413yes—
206C22×C4×C47C2416yes—
207C22×C4×C47C2413yes—
208C22×C4×C47C2413yes—
209C22×C4×C47C2411yescharacteristic
210C2×C22⋊D47C2418yes—
211C2×C22⋊D47C2418yes—
212C2×C22⋊D47C2418yes—
213#10625354—232no—
214Q8×D47—232no—
215#10625350—248no—
216#10625350—216no—
217#10625350—424no—
218C2×D188C24112yes—
219C2×D188C2414yes—
220C2×D188C24112yes—
221C2×C4×D47C2418yes—
222C2×C4×D47C24124yes—
223C2×C4×D47C24124yes—
224C2×Dic94C24112yes—
225C2×Dic94C2414yes—
226C2×Dic94C24112yes—
227C4⋊C4×C47C24112yes—
228C4⋊C4×C47C24112yes—
229C4⋊C4×C47C24124yes—
230C42×C47C2416yes—
231C42×C47C2416yes—
232C42×C47C2416yes—
233C42×C47C2416yes—
234C42×C47C2416yes—
235C42×C47C2416yes—
236C42×C47C2416yes—
237C42×C47C2416yes—
238C22⋊Dic47C2418yes—
239C22⋊Dic47C2418yes—
240C22⋊Dic47C2418yes—
241(C2×D47)⋊C4C2418yes—
242(C2×D47)⋊C4C2418yes—
243(C2×D47)⋊C4C24124yes—
244(C2×D47)⋊C4C24124yes—
245(C2×D47)⋊C4C24124yes—
246(C2×D47)⋊C4C24124yes—
247C4⋊Dic47C24112yes—
248C4⋊Dic47C24112yes—
249C4⋊Dic47C2414yes—
250C4⋊Dic47C2414yes—
251C4⋊Dic47C24112yes—
252C4⋊Dic47C24112yes—
253Dic47⋊C4C24124yes—
254Dic47⋊C4C2418yes—
255Dic47⋊C4C2418yes—
256Dic47⋊C4C24124yes—
257Dic47⋊C4C24124yes—
258Dic47⋊C4C24124yes—
259C4×Dic47C2418yes—
260C4×Dic47C24124yes—
261C4×Dic47C24124yes—
262C23×C47—22no—
263C23×C47—22no—
264C23×C47—22no—
265C23×C47C2511yescharacteristic
266C23×C47C2511yescharacteristic
267C23×C47C2511yescharacteristic
268C22×D47C2518yes—
269Q8×C47—224no—
270Q8×C47C2×#41116yes—
271C2×C4×C47—26no—
272C2×C4×C47—22no—
273C2×C4×C47—212no—
274C2×C4×C47—212no—
275C2×C4×C47—212no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—43no—
281C2×C4×C47—46no—
282C2×C4×C47—43no—
283C2×C4×C47C2×#41112yes—
284C2×C4×C472−1+414yescomplemented
285C2×C4×C47C2516yes—
286C2×C4×C47C2511yescharacteristic
287C2×C4×C47C2511yescharacteristic
288C2×C4×C47C2516yes—
289C2×C4×C47C2516yes—
290C2×C4×C47C2516yes—
291C2×C4×C47C2511yescharacteristic
292C2×C4×C47C2511yescharacteristic
293C22⋊D47—216no—
294C22⋊D47—216no—
295C22⋊D47—216no—
296C2×Dic47C2518yes—
297C2×Dic47C2518yes—
298C2×Dic47C2518yes—
299D188—224no—
300D188—28no—
301D188—412no—
302C4×D47—248no—
303C4×D47—216no—
304C4×D47—424no—
305Dic94—224no—
306Dic94—28no—
307Dic94—412no—
308#62788—471nomaximal, Sylow
309C22×C47—28no—
310C22×C47—21no—
311C22×C47—21no—
312C22×C47—21no—
313C22×C47—21no—
314C22×C47—21no—
315C22×C47—21no—
316C22×C47C22×#4112yes—
317C22×C47C2×2−1+412yes—
318C22×C47#58512yes—
319C22×C47C2611yescharacteristic
320C2×D47—28no—
321C2×D47—28no—
322C2×D47—28no—
323C4×C47—26no—
324C4×C47—21no—
325C4×C47—21no—
326C4×C47—26no—
327C4×C47—26no—
328C4×C47C22×#41112yes—
329C4×C47C2×2−1+412yes—
330C4×C47C2×2−1+412yes—
331Dic47—28no—
332Dic47—28no—
333Dic47—28no—
334#3523—474no—
335#3522—474no—
336#3516—478no—
337#3507—476no—
338#3502—471no—
339#3497—471no—
340#3492—476no—
341#3486—472no—
342#3482—478no—
343#3480—474no—
344Q8×#41—474no—
345#3461—476no—
346#3444—476no—
347C4×2−1+4—472no—
348C22×C4×Q8D4711yescharacteristic, complemented
349C2×C47—22no—
350C2×C47—22no—
351C2×C47—22no—
352C2×C47C23×#4111yescharacteristic
353C2×C47C22×2−1+411yescharacteristic
354C2×C47C2×#58511yescharacteristic
355D47—48no—
356C2×2−1+4—472no—
357C23×Q8C2×D4711yescharacteristic
358#559—4712no—
359Q82—474no—
360#557—478no—
361#557—4712no—
362#557—474no—
363#556—4724no—
364#556—4712no—
365#554—4712no—
366#554—4724no—
367#553—4724no—
368#552—4724no—
369#552—4724no—
370#550—474no—
371D4×Q8—478no—
372D4×Q8—478no—
373D4×Q8—474no—
374#548—478no—
375#548—478no—
376#548—478no—
377#547—4724no—
378#544—476no—
379#542—4724no—
380#541—4724no—
381#539—4724no—
382#537—476no—
383#536—4712no—
384#533—4724no—
385#533—476no—
386#533—476no—
387#533—476no—
388#532—476no—
389#532—476no—
390#532—476no—
391#529—4724no—
392#529—4712no—
393#529—4712no—
394#529—4712no—
395#529—4712no—
396#529—4712no—
397#529—4712no—
398#525—474no—
399#525—4712no—
400#525—4712no—
401#520—478no—
402#520—4712no—
403#519—472no—
404#519—478no—
405C4×#41—478no—
406C4×#41—4712no—
407C4×#41—4712no—
408C4×#41—4712no—
409C2×C4×Q8—478no—
410C2×C4×Q8C2×D4711yescharacteristic
411C2×C4×Q8C2×D4713yes—
412C2×C4×Q8C2×D4714yes—
413C2×C4×Q8C2×D4714yes—
414C2×C4×Q8C2×D4711yescharacteristic
415C2×C4×Q8C2×D4713yes—
416C2×C4×Q8C2×D4714yes—
417C2×C4×Q8C2×D4714yes—
418C22×C4⋊C4C2×D4713yes—
419C22×C42C2×D4713yes—
420C47#6278811yescharacteristic, complemented, Sylow
4212−1+4—9416no—
422C2×#41—478no—
423C2×#41—474no—
424C2×#41—4712no—
425C2×#41—4712no—
426C22×Q8—28no—
427C22×Q8—478no—
428C22×Q8C22×D4713yes—
429C22×Q8C22×D4714yes—
430C22×Q8C22×D4714yes—
431C22×Q8C22×D4711yescharacteristic
432C23×C4C22×D4713yes—
433C23×C4C22×D4711yescharacteristic
434C23×C4C22×D4713yes—
435C4⋊Q8—4724no—
436C4⋊Q8—4724no—
437C4⋊Q8—476no—
438C4⋊Q8—476no—
439C4⋊Q8—476no—
440#127—476no—
441#126—4748no—
442#126—4724no—
443#126—4724no—
444#125—4724no—
445#125—4748no—
446#125—4712no—
447#125—4712no—
448#125—4712no—
449#124—4724no—
450#124—4712no—
451#124—4712no—
452#124—4712no—
453#123—478no—
454#123—4724no—
455#123—4724no—
456#123—4748no—
457C22⋊Q8—4724no—
458C22⋊Q8—4724no—
459C22⋊Q8—474no—
460C22⋊Q8—474no—
461C22⋊Q8—4712no—
462C22⋊Q8—4712no—
463C22⋊Q8—4712no—
464C22⋊Q8—4712no—
465C22⋊Q8—4724no—
466C22⋊Q8—4748no—
467#121—474no—
468#121—474no—
469#121—4712no—
470#121—4712no—
471#121—4712no—
472#121—4712no—
473#121—4724no—
474#120—478no—
475C4×Q8—478no—
476C4×Q8—478no—
477C4×Q8—4724no—
478C4×Q8—4712no—
479C4×Q8—4712no—
480C4×Q8—4712no—
481C4×Q8—4712no—
482C4×Q8—4712no—
483C4×Q8—4712no—
484C4×Q8C22×D4714yes—
485C4×Q8C22×D4714yes—
486C4×Q8C22×D47112yes—
487C4×Q8C22×D47112yes—
488C4×Q8C22×D4714yes—
489C4×Q8C22×D4714yes—
490C4×Q8C22×D47112yes—
491C4×Q8C22×D47112yes—
492C4×D4—478no—
493C4×D4—478no—
494C4×D4—4724no—
495C4×D4—4724no—
496C4×D4—4724no—
497C4×D4—4724no—
498C4×D4—4724no—
499C4×D4—4712no—
500C4×D4—4712no—
501C4×D4—4712no—
502C4×D4—4712no—
503C4×D4—4712no—
504C4×D4—4712no—
505#117—474no—
506#117—4712no—
507#117—4712no—
508#117—4724no—
509#117—4724no—
510#117—4724no—
511#117—4724no—
512C2×C4⋊C4—4724no—
513C2×C4⋊C4C22×D4713yes—
514C2×C4⋊C4C22×D4713yes—
515C2×C4⋊C4C22×D4716yes—
516C2×C4⋊C4C22×D47112yes—
517C2×C4⋊C4C22×D47112yes—
518C2×C42—4724no—
519C2×C42C22×D4713yes—
520C2×C42C22×D4716yes—
521C2×C42C22×D4716yes—
522C2×C42C22×D4716yes—
523C2×C42C22×D4713yes—
524C2×C42C22×D4713yes—
525C2×C42C22×D4716yes—
526C2×C42C22×D4713yes—
527C24C23×D4711yescharacteristic
528#41—9432no—
529#41—9448no—
530#41—9416no—
531#41—18824no—
532C2×Q8—216no—
533C2×Q8—216no—
534C2×Q8—212no—
535C2×Q8—474no—
536C2×Q8—4712no—
537C2×Q8—4712no—
538C2×Q8—9432no—
539C2×Q8#1062535018yescomplemented
540C2×Q8C23×D47112yes—
541C2×Q8C23×D4714yes—
542C2×D4—478no—
543C2×D4—478no—
544C2×D4—478no—
545C2×D4—474no—
546C2×D4—4712no—
547C2×D4—4712no—
548C22×C4—212no—
549C22×C4—24no—
550C22×C4—46no—
551C22×C4—4724no—
552C22×C4—478no—
553C22×C4—4724no—
554C22×C4C23×D4711yescharacteristic
555C22×C4C23×D4711yescharacteristic
556C22×C4C23×D4711yescharacteristic
557C22×C4C23×D4716yes—
558C22×C4C23×D4716yes—
559C22×C4C23×D4716yes—
560C22×C4C23×D4713yes—
561C22×C4C23×D4711yescharacteristic
562C22×C4C23×D4711yescharacteristic
563C22×C4C23×D4713yes—
564C22×C4C23×D4716yes—
565C22×C4C23×D4713yes—
566C22×C4C23×D4713yes—
567C22×C4C23×D4711yescharacteristic
568C4⋊C4—4724no—
569C4⋊C4—478no—
570C4⋊C4—478no—
571C4⋊C4—4724no—
572C4⋊C4—4724no—
573C4⋊C4—4724no—
574C4⋊C4—4712no—
575C4⋊C4—4712no—
576C4⋊C4—474no—
577C4⋊C4—474no—
578C4⋊C4—4712no—
579C4⋊C4—4712no—
580C4⋊C4C23×D47112yes—
581C4⋊C4C23×D47112yes—
582C4⋊C4C23×D47124yes—
583C22⋊C4—478no—
584C22⋊C4—478no—
585C22⋊C4—478no—
586C22⋊C4—4724no—
587C22⋊C4—478no—
588C22⋊C4—478no—
589C22⋊C4—4724no—
590C22⋊C4—4724no—
591C22⋊C4—4724no—
592C42—4724no—
593C42—4724no—
594C42—478no—
595C42C23×D4716yes—
596C42C23×D4716yes—
597C42C23×D4716yes—
598C42C23×D4716yes—
599C42C23×D4716yes—
600C42C23×D4716yes—
601C42C23×D4716yes—
602C42C23×D4716yes—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—478no—
607C23C24×D4711yescharacteristic
608C23C24×D4711yescharacteristic
609C23C24×D4711yescharacteristic
610Q8—224no—
611Q8—9424no—
612Q8—948no—
613Q8—18812no—
614Q8C2×#10625350116yes—
615D4—9416no—
616D4—9416no—
617D4—9416no—
618D4—9424no—
619D4—948no—
620D4—18812no—
621C2×C4—26no—
622C2×C4—22no—
623C2×C4—212no—
624C2×C4—212no—
625C2×C4—212no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—43no—
631C2×C4—46no—
632C2×C4—43no—
633C2×C4—478no—
634C2×C4—478no—
635C2×C4—478no—
636C2×C4—9448no—
637C2×C4—9416no—
638C2×C4—18824no—
639C2×C4C2×#10625350112yes—
640C2×C4#1309407214yescomplemented
641C2×C4C24×D4716yes—
642C2×C4C24×D4711yescharacteristic
643C2×C4C24×D4711yescharacteristic
644C2×C4C24×D4716yes—
645C2×C4C24×D4716yes—
646C2×C4C24×D4716yes—
647C2×C4C24×D4711yescharacteristic
648C2×C4C24×D4711yescharacteristic
649C22—28no—
650C22—21no—
651C22—21no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—948no—
657C22—948no—
658C22—948no—
659C22C22×#1062535012yes—
660C22C2×#1309407212yes—
661C22#1568995912yes—
662C22C25×D4711yescharacteristic
663C4—26no—
664C4—21no—
665C4—21no—
666C4—26no—
667C4—26no—
668C4—948no—
669C4—948no—
670C4—948no—
671C4C22×#10625350112yes—
672C4C2×#1309407212yes—
673C4C2×#1309407212yes—
674C2—22no—
675C2—22no—
676C2—22no—
677C2—1888no—
678C2C23×#1062535011yescharacteristic
679C2C22×#1309407211yescharacteristic
680C2C2×#1568995911yescharacteristic
subgroupG/H
centerC2×C4C24×D47
commutator, socle, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC22×C4×Q8×C47C2
hypercenterC22×C4×Q8D47
hypocenterC47#62788
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #20257484C2semidirect
2. #20257473C2semidirect
3. #20257381C2semidirect
4. #20257253C2semidirect
5. #20257198C2semidirect
6. #20257159C2semidirect
7. #20257097C2semidirect
8. #20257039C2semidirect
9. #20257005C2semidirect
10. #20256983C2semidirect
11. Q8×#10625350C2semidirect
12. #20256821C2semidirect
13. #20256684C2semidirect
14. C4×#13094072C2semidirect
15. C22×C4×Q8×C47C2semidirect
17. #15689858C22semidirect
18. Q8×Dic94C22semidirect
19. #15689852C22semidirect
20. #15689851C22semidirect
21. #15689849C22semidirect
22. #15689846C22semidirect
23. #15689845C22semidirect
24. #15689833C22semidirect
27. #15689814C22semidirect
29. #15689795C22semidirect
30. Q8×D188C22semidirect
33. #15689785C22semidirect
38. #15689745C22semidirect
39. #15689731C22semidirect
46. #15689677C22semidirect
50. #15689660C22semidirect
60. #15689605C22semidirect
63. #15689599C22semidirect
64. C4×#10625354C22semidirect
68. C4×Q8×D47C22semidirect
190. C2×Q8×C47#41semidirect
284. C2×C4×C472−1+4semidirect
348. C22×C4×Q8D47semidirect
420. C47#62788semidirect
539. C2×Q8#10625350semidirect
640. C2×C4#13094072semidirect

Maximal subgroups

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

subgroupindex
#202574842
#202574732
#202573812
#202572532
#202571982
#202571592
#202570972
#202570392
#202570052
#202569832
Q8×#106253502
#202568212
#202566842
C4×#130940722
C22×C4×Q8×C472
#6278847