Finite Group Databasebeta

← C2×#22598274 #32865242

Subgroups — C2×#22598274 #32865242

Order 18176.

2346 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986511C211yesmaximal, characteristic
2C22×#14556086C211yesmaximal, characteristic, complemented
3#22598274C2116yesmaximal, direct product factor
4C2×#17986343C212yesmaximal, complemented
5C2×#17986342C212yesmaximal, complemented
6C2×#17986326C212yesmaximal, complemented
7C2×#17986325C212yesmaximal, complemented
8C2×#17986042C211yesmaximal, characteristic, complemented
9C2×#17986001C211yesmaximal, characteristic, complemented
10C2×#17985998C211yesmaximal, characteristic, complemented
11C2×#17985962C211yesmaximal, characteristic, complemented
12C2×#428×C71C211yesmaximal, characteristic, complemented
13C22×#11765865C2211yescharacteristic
14C23×C4×D71C2211yescharacteristic
15C22×#11765849C2211yescharacteristic
16#17986511—24no—
17#17986511C2218yes—
18C2×#14556112—21no—
19C2×#14556108C2211yescharacteristic
20C2×#14556108C2211yescharacteristic
21C2×#14556103C2211yescharacteristic
22C2×#14556103C2211yescharacteristic
23C2×#14556098—21no—
24C2×C4×D284—21no—
25C2×C4×D284—21no—
26C2×#14556086—21no—
27C2×#14556086—21no—
28C2×#14556086—24no—
29C2×#14556086C2212yes—
30C2×#14556086C2212yes—
31C2×#14556086C2218yescomplemented
32C22×C4⋊Dic71C2211yescharacteristic
33C22×(C2×D71)⋊C4—21no—
34C22×C4×Dic71—21no—
35#17986343C22116yescomplemented
36#17986342C22116yescomplemented
37#17986326C22116yescomplemented
38#17986325C22116yescomplemented
39#17986042C2218yescomplemented
40C2×#14556061C2212yescomplemented
41C2×#14556059C2212yescomplemented
42#17986001C2218yescomplemented
43#17985998C2218yescomplemented
44C2×#14556053C2212yescomplemented
45C2×#14556051C2212yescomplemented
46C2×#14556050C2212yescomplemented
47C2×#14556048C2212yescomplemented
48#17985962C2218yescomplemented
49C2×(C2×D71)⋊C8C2212yes—
50C2×(C2×D71)⋊C8C2212yes—
51C22×M16×C71C2211yescharacteristic
52C2×#117×C71C2211yescharacteristic
53C22×C4⋊C4×C71C2211yescharacteristic
54#428×C71C2218yescomplemented
55C2×#107×C71C2212yescomplemented
56C2×#106×C71C2212yescomplemented
57C24×D71D411yescharacteristic
58C2×#11765865—22no—
59C2×#11765865—24no—
60C2×#11765865—24no—
61C2×#11765865C2314yes—
62C22×Dic142C2311yescharacteristic
63C22×D284—21no—
64C22×D284—21no—
65C22×D284C2311yescharacteristic
66C22×C22⋊D71—21no—
67C23×Dic71—21no—
68C23×Dic71D411yescharacteristic
69C22×C4×D71—21no—
70C22×C4×D71—24no—
71C22×C4×D71—24no—
72C22×C4×D71D411yescharacteristic
73C22×C4×D71D411yescharacteristic
74C22×C4×D71D414yes—
75C22×C4×D71C2311yescharacteristic
76C22×C4×D71C2311yescharacteristic
77C22×C4×D71C2314yes—
78C2×#11765849—24no—
79C2×#11765849C2314yes—
80C22×C71⋊C8C2312yes—
81#14556112—28no—
82#14556108—22no—
83#14556108—22no—
84#14556108C2314yes—
85#14556108C2314yes—
86#14556103—22no—
87#14556103—22no—
88#14556103C2314yes—
89#14556103C2314yes—
90#14556098—28no—
91C4×D284—28no—
92C4×D284—28no—
93#14556086—24no—
94#14556086—24no—
95#14556086—28no—
96#14556086—28no—
97#14556086C2318yes—
98#14556086C2318yes—
99C2×C4⋊Dic71—21no—
100C2×C4⋊Dic71—21no—
101C2×C4⋊Dic71—21no—
102C2×C4⋊Dic71—22no—
103C2×C4⋊Dic71C2312yes—
104C2×C4⋊Dic71C2314yes—
105C2×(C2×D71)⋊C4—22no—
106C2×(C2×D71)⋊C4—22no—
107C2×(C2×D71)⋊C4—28no—
108C2×(C2×D71)⋊C4—21no—
109C2×(C2×D71)⋊C4—21no—
110C2×(C2×D71)⋊C4—21no—
111C2×(C2×D71)⋊C4—21no—
112C2×C4×Dic71—22no—
113C2×C4×Dic71—22no—
114C2×C4×Dic71—28no—
115#14556061C2318yescomplemented
116#14556059C2318yescomplemented
117#14556053C2318yescomplemented
118#14556051C2318yescomplemented
119#14556050C2318yescomplemented
120#14556048C2318yescomplemented
121(C2×D71)⋊C8C2318yes—
122(C2×D71)⋊C8C2318yes—
123C23×C4×C71—21no—
124C23×C4×C71C2311yescharacteristic
125C2×M16×C71—24no—
126C2×M16×C71C2314yes—
127C22×C8×C71C2312yes—
128#117×C71—22no—
129#117×C71C2314yes—
130C2×C4⋊C4×C71—21no—
131C2×C4⋊C4×C71—22no—
132C2×C4⋊C4×C71C2311yescharacteristic
133C2×C4⋊C4×C71C2312yes—
134C2×C4⋊C4×C71C2311yescharacteristic
135C2×C4⋊C4×C71C2314yes—
136C2×C22⋊C4×C71—21no—
137C2×C42×C71—21no—
138#107×C71C2318yescomplemented
139#106×C71C2318yescomplemented
140C23×D71—24no—
141C23×D71—21no—
142C23×D71—42no—
143C23×D71—42no—
144C23×D71C2×D411yescharacteristic
145C23×D71C2×D411yescharacteristic
146C23×D71C2×D414yes—
147#11765865—28no—
148#11765865—28no—
149#11765865—48no—
150C2×Dic142—22no—
151C2×Dic142—22no—
152C2×Dic142—21no—
153C2×Dic142C2412yes—
154C2×D284—22no—
155C2×D284—22no—
156C2×D284—24no—
157C2×D284—24no—
158C2×D284—21no—
159C2×D284—44no—
160C2×D284—44no—
161C2×D284C2412yes—
162C2×C22⋊D71—24no—
163C2×C22⋊D71—44no—
164C22×Dic71—24no—
165C22×Dic71—21no—
166C22×Dic71—24no—
167C22×Dic71—22no—
168C22×Dic71—44no—
169C22×Dic71C2×D411yescharacteristic
170C22×Dic71C2×D411yescharacteristic
171C22×Dic71C2×D414yes—
172C2×C4×D71—24no—
173C2×C4×D71—24no—
174C2×C4×D71—216no—
175C2×C4×D71—22no—
176C2×C4×D71—22no—
177C2×C4×D71—28no—
178C2×C4×D71—22no—
179C2×C4×D71—22no—
180C2×C4×D71—28no—
181C2×C4×D71—24no—
182C2×C4×D71—44no—
183C2×C4×D71C2×D414yes—
184C2×C4×D71C2×D414yes—
185C2×C4×D71C2×D412yes—
186C2×C4×D71C2×D412yes—
187C2×C4×D71C2412yes—
188C2×C4×D71C2412yes—
189#11765849—28no—
190C2×C71⋊C8—24no—
191C2×C71⋊C8C2414yes—
192C4⋊Dic71—24no—
193C4⋊Dic71—22no—
194C4⋊Dic71—24no—
195C4⋊Dic71—24no—
196C4⋊Dic71C2414yes—
197(C2×D71)⋊C4—28no—
198(C2×D71)⋊C4—28no—
199(C2×D71)⋊C4—24no—
200(C2×D71)⋊C4—24no—
201(C2×D71)⋊C4—24no—
202(C2×D71)⋊C4—24no—
203C4×Dic71—28no—
204C4×Dic71—28no—
205C24×C71C2×D411yescharacteristic
206C22×C4×C71—21no—
207C22×C4×C71—21no—
208C22×C4×C71—24no—
209C22×C4×C71—22no—
210C22×C4×C71—44no—
211C22×C4×C71C2×D411yescharacteristic
212C22×C4×C71C2×D412yes—
213C22×C4×C71#4114yes—
214C22×C4×C71#4114yes—
215C22×C4×C71C2411yescharacteristic
216C22×C4×C71C2412yes—
217M16×C71—28no—
218C2×C8×C71—24no—
219C2×C8×C71C2414yes—
220C4⋊C4×C71—24no—
221C4⋊C4×C71—22no—
222C4⋊C4×C71—21no—
223C4⋊C4×C71—21no—
224C4⋊C4×C71C2412yes—
225C4⋊C4×C71C2414yes—
226C4⋊C4×C71C2412yes—
227C22⋊C4×C71—24no—
228C42×C71—24no—
229C23×C71—22no—
230C23×C71—22no—
231C23×C71#12314yes—
232C23×C71C22×D412yes—
233C23×C71C22×D411yescharacteristic
234C22×D71—28no—
235C22×D71—22no—
236C22×D71—22no—
237C22×D71—22no—
238C22×D71—22no—
239C22×D71—22no—
240C22×D71—22no—
241C22×D71—22no—
242C22×D71—44no—
243C22×D71—44no—
244C22×D71—416no—
245C22×D71—42no—
246C22×D71—42no—
247C22×D71—42no—
248C22×D71C22×D412yes—
249C22×D71C22×D412yes—
250C2×C4×C71—22no—
251C2×C4×C71—22no—
252C2×C4×C71—24no—
253C2×C4×C71—48no—
254C2×C4×C71—44no—
255C2×C4×C71—42no—
256C2×C4×C71—42no—
257C2×C4×C71#12314yes—
258C2×C4×C71#12318yes—
259C2×C4×C71C22×D412yes—
260C2×C4×C71C22×D411yescharacteristic
261C2×C4×C71C2×#4112yes—
262C2×C4×C71C2×#4114yes—
263C2×C4×C71C2×#4112yes—
264C2×C4×C71C2×#4114yes—
265C2×C4×C71C2511yescharacteristic
266C22⋊D71—48no—
267C2×Dic71—28no—
268C2×Dic71—22no—
269C2×Dic71—22no—
270C2×Dic71—24no—
271C2×Dic71—22no—
272C2×Dic71—48no—
273C2×Dic71—42no—
274C2×Dic71—44no—
275C2×Dic71C22×D412yes—
276C2×Dic71C22×D412yes—
277D284—22no—
278D284—22no—
279D284—48no—
280D284—48no—
281D284—42no—
282C4×D71—24no—
283C4×D71—24no—
284C4×D71—28no—
285C4×D71—28no—
286C4×D71—22no—
287C4×D71—22no—
288C4×D71—22no—
289C4×D71—22no—
290C4×D71—48no—
291Dic142—22no—
292Dic142—22no—
293Dic142—42no—
294C8×C71—24no—
295C71⋊C8—24no—
296C22×C71—28no—
297C22×C71—22no—
298C22×C71—22no—
299C22×C71C2×#12314yes—
300C22×C71C2×#12312yes—
301C22×C71#57512yes—
302C22×C71#57512yes—
303C22×C71C23×D411yescharacteristic
304C2×D71—22no—
305C2×D71—22no—
306C2×D71—22no—
307C2×D71—22no—
308C2×D71—22no—
309C2×D71—22no—
310C2×D71—416no—
311C2×D71—44no—
312C2×D71—44no—
313C2×D71—42no—
314C2×D71—42no—
315C2×D71—42no—
316C2×D71—84no—
317C4×C71—42no—
318C4×C71—42no—
319C4×C71—44no—
320C4×C71C2×#12312yes—
321C4×C71C2×#12314yes—
322C4×C71C22×#4111yescharacteristic
323C4×C71C22×#4111yescharacteristic
324Dic71—22no—
325Dic71—22no—
326Dic71—42no—
327Dic71—44no—
328C2×#3093—711nomaximal, Sylow
329C2×C71—24no—
330C2×C71#309314yescomplemented
331C2×C71C22×#12311yescharacteristic
332C2×C71C2×#57511yescharacteristic
333C2×C71C2×#57511yescharacteristic
334D71—42no—
335D71—42no—
336D71—82no—
337C2×#525—711no—
338C22×#117—711no—
339#3093—7116no—
340C2×#485—712no—
341C2×#485—712no—
342C2×#482—712no—
343C2×#482—712no—
344C2×#428—711no—
345C2×#428D7111yescharacteristic, complemented
346C2×#417—711no—
347C2×#417—711no—
348C2×#407—711no—
349C71C2×#309311yescharacteristic, complemented, Sylow
350C22×#41—711no—
351C24×C4—711no—
352C22×M16—711no—
353C22×M16C2×D7111yescharacteristic
354#525—718no—
355#525—1424no—
356C2×#123—1421no—
357C2×C22⋊Q8—711no—
358C2×C22⋊Q8—711no—
359C2×#121—711no—
360C2×#121—711no—
361C2×#120—1421no—
362C2×C4×D4—1421no—
363C2×C4×D4—1421no—
364C2×#117—712no—
365C2×#117—712no—
366C2×#117—718no—
367C2×#117—1421no—
368C2×#117—1421no—
369C2×#117—1424no—
370C2×#117C2×D7111yescharacteristic
371C22×C4⋊C4—711no—
372C22×C4⋊C4C2×D7111yescharacteristic
373C22×C22⋊C4—1421no—
374C22×C42—1421no—
375#485—7116no—
376#485—7116no—
377#482—7116no—
378#482—7116no—
379#428—718no—
380#428C2×D7118yescomplemented
381C2×#107—712no—
382C2×#107C2×D7112yescomplemented
383C2×#106—712no—
384C2×#106C2×D7112yescomplemented
385#417—718no—
386#417—718no—
387C2×#103—712no—
388C2×#103—712no—
389C2×#102—712no—
390C2×#102—712no—
391#407—718no—
392C2×C22⋊C8—712no—
393C2×C22⋊C8—712no—
394C25—711no—
395C2×#41—714no—
396C2×#41—1424no—
397C2×#41—1424no—
398C2×#41—1422no—
399C22×Q8—711no—
400C22×D4—711no—
401C22×D4—1421no—
402C22×D4—1421no—
403C22×D4—1421no—
404C23×C4—21no—
405C23×C4—711no—
406C23×C4—711no—
407C23×C4—711no—
408C23×C4—714no—
409C23×C4—711no—
410C23×C4—711no—
411C23×C4—714no—
412C23×C4—1421no—
413C23×C4—1421no—
414C23×C4—1424no—
415C23×C4—1424no—
416C23×C4C22×D7111yescharacteristic
417C2×M16—24no—
418C2×M16—714no—
419C2×M16—1424no—
420C2×M16C22×D7114yes—
421C22×C8—712no—
422C22×C8C22×D7112yes—
423#123—1428no—
424C22⋊Q8—714no—
425C22⋊Q8—714no—
426C22⋊Q8—1422no—
427C22⋊Q8—1422no—
428#121—714no—
429#121—714no—
430#121—1422no—
431#121—1422no—
432#120—1428no—
433C4×D4—1428no—
434C4×D4—1428no—
435#117—22no—
436#117—718no—
437#117—718no—
438#117—1428no—
439#117—1428no—
440#117—1424no—
441#117—1424no—
442#117C22×D7114yes—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—712no—
446C2×C4⋊C4—714no—
447C2×C4⋊C4—1421no—
448C2×C4⋊C4—1421no—
449C2×C4⋊C4—1422no—
450C2×C4⋊C4—1421no—
451C2×C4⋊C4C22×D7112yes—
452C2×C4⋊C4C22×D7114yes—
453C2×C4⋊C4C22×D7111yescharacteristic
454C2×C4⋊C4C22×D7111yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—1421no—
457C2×C22⋊C4—1421no—
458C2×C22⋊C4—1428no—
459C2×C22⋊C4—1422no—
460C2×C22⋊C4—1422no—
461C2×C22⋊C4—1421no—
462C2×C22⋊C4—1421no—
463C2×C42—21no—
464C2×C42—1428no—
465C2×C42—1422no—
466C2×C42—1422no—
467#107—718no—
468#107C22×D7118yescomplemented
469#106—718no—
470#106C22×D7118yescomplemented
471#103—718no—
472#103—718no—
473#102—718no—
474#102—718no—
475C22⋊C8—718no—
476C22⋊C8—718no—
477C24—2842no—
478C24—2842no—
479C24—714no—
480C24—711no—
481C24—711no—
482C24—1421no—
483C24—1424no—
484C24D4×D7111yescharacteristic
485#41—2848no—
486#41—1428no—
487#41—1428no—
488C2×Q8—712no—
489C2×Q8—1422no—
490C2×Q8—1422no—
491C2×Q8—1421no—
492C2×D4—2844no—
493C2×D4—2844no—
494C2×D4—2844no—
495C2×D4—712no—
496C2×D4—1424no—
497C2×D4—1424no—
498C2×D4—1424no—
499C2×D4—1421no—
500C2×D4—1422no—
501C2×D4—1422no—
502C22×C4—24no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—44no—
507C22×C4—2844no—
508C22×C4—2844no—
509C22×C4—714no—
510C22×C4—711no—
511C22×C4—711no—
512C22×C4—714no—
513C22×C4—714no—
514C22×C4—712no—
515C22×C4—712no—
516C22×C4—712no—
517C22×C4—712no—
518C22×C4—1424no—
519C22×C4—1422no—
520C22×C4—1421no—
521C22×C4—1424no—
522C22×C4—1424no—
523C22×C4—1422no—
524C22×C4—1422no—
525C22×C4—1428no—
526C22×C4—1422no—
527C22×C4—1422no—
528C22×C4—1428no—
529C22×C4—1424no—
530C22×C4—1424no—
531C22×C4—14216no—
532C22×C4D4×D7112yes—
533C22×C4D4×D7111yescharacteristic
534C22×C4#1176586514yes—
535C22×C4#1176586614yes—
536C22×C4C23×D7112yes—
537C22×C4C23×D7111yescharacteristic
538M16—28no—
539M16—1428no—
540C2×C8—24no—
541C2×C8—714no—
542C2×C8—1424no—
543C2×C8C23×D7114yes—
544C4⋊C4—24no—
545C4⋊C4—22no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—714no—
549C4⋊C4—1424no—
550C4⋊C4—1424no—
551C4⋊C4—1424no—
552C4⋊C4—1422no—
553C4⋊C4C23×D7114yes—
554C4⋊C4C23×D7112yes—
555C4⋊C4C23×D7112yes—
556C22⋊C4—24no—
557C22⋊C4—1424no—
558C22⋊C4—1424no—
559C22⋊C4—1428no—
560C22⋊C4—1428no—
561C22⋊C4—1424no—
562C22⋊C4—1424no—
563C42—24no—
564C42—1428no—
565C42—1428no—
566C23—22no—
567C23—22no—
568C23—28416no—
569C23—2844no—
570C23—2844no—
571C23—2842no—
572C23—2842no—
573C23—2842no—
574C23—712no—
575C23—712no—
576C23—1422no—
577C23—1428no—
578C23—1422no—
579C23—1422no—
580C23—1422no—
581C23—1422no—
582C23—1422no—
583C23—1422no—
584C23#1455611314yes—
585C23C2×D4×D7112yes—
586C23C2×D4×D7111yescharacteristic
587Q8—2842no—
588Q8—1422no—
589Q8—1422no—
590D4—2848no—
591D4—2848no—
592D4—2848no—
593D4—2842no—
594D4—1422no—
595D4—1422no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—24no—
599C2×C4—48no—
600C2×C4—44no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—2848no—
604C2×C4—2842no—
605C2×C4—2844no—
606C2×C4—2848no—
607C2×C4—712no—
608C2×C4—712no—
609C2×C4—1424no—
610C2×C4—1422no—
611C2×C4—1428no—
612C2×C4—1422no—
613C2×C4—1422no—
614C2×C4—1422no—
615C2×C4—1422no—
616C2×C4—1422no—
617C2×C4—1422no—
618C2×C4—1428no—
619C2×C4—1428no—
620C2×C4—1424no—
621C2×C4—1424no—
622C2×C4#1455611314yes—
623C2×C4#1455611318yes—
624C2×C4C2×D4×D7112yes—
625C2×C4C2×D4×D7111yescharacteristic
626C2×C4C2×#1176586512yes—
627C2×C4C2×#1176586514yes—
628C2×C4C2×#1176586612yes—
629C2×C4C2×#1176586614yes—
630C2×C4C24×D7111yescharacteristic
631C8—24no—
632C8—1424no—
633C22—22no—
634C22—22no—
635C22—28no—
636C22—28416no—
637C22—2844no—
638C22—2844no—
639C22—2842no—
640C22—2842no—
641C22—2842no—
642C22—5684no—
643C22—1422no—
644C22—1422no—
645C22—1422no—
646C22—1422no—
647C22—1422no—
648C22—1422no—
649C22C2×#1455611314yes—
650C22C2×#1455611312yes—
651C22#1798679512yes—
652C22#1798679812yes—
653C22C22×D4×D7111yescharacteristic
654C4—44no—
655C4—42no—
656C4—42no—
657C4—2844no—
658C4—2842no—
659C4—1422no—
660C4—1422no—
661C4C2×#1455611314yes—
662C4C2×#1455611312yes—
663C4C22×#1176586511yescharacteristic
664C4C22×#1176586611yescharacteristic
665C2—24no—
666C2—2842no—
667C2—2842no—
668C2—5682no—
669C2#2259827414yesdirect product factor
670C2C22×#1455611311yescharacteristic
671C2C2×#1798679511yescharacteristic
672C2C2×#1798679811yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#428×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986511C2
hypercenterC2×#428D71
hypocenterC71C2×#3093
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
2. C22×#14556086C2semidirect
3. #22598274C2direct (N × H)
4. C2×#17986343C2semidirect
5. C2×#17986342C2semidirect
6. C2×#17986326C2semidirect
7. C2×#17986325C2semidirect
8. C2×#17986042C2semidirect
9. C2×#17986001C2semidirect
10. C2×#17985998C2semidirect
11. C2×#17985962C2semidirect
12. C2×#428×C71C2semidirect
31. C2×#14556086C22semidirect
35. #17986343C22semidirect
36. #17986342C22semidirect
37. #17986326C22semidirect
38. #17986325C22semidirect
39. #17986042C22semidirect
40. C2×#14556061C22semidirect
41. C2×#14556059C22semidirect
42. #17986001C22semidirect
43. #17985998C22semidirect
44. C2×#14556053C22semidirect
45. C2×#14556051C22semidirect
46. C2×#14556050C22semidirect
47. C2×#14556048C22semidirect
48. #17985962C22semidirect
54. #428×C71C22semidirect
55. C2×#107×C71C22semidirect
56. C2×#106×C71C22semidirect
115. #14556061C23semidirect
116. #14556059C23semidirect
117. #14556053C23semidirect
118. #14556051C23semidirect
119. #14556050C23semidirect
120. #14556048C23semidirect
138. #107×C71C23semidirect
139. #106×C71C23semidirect
330. C2×C71#3093semidirect
345. C2×#428D71semidirect
349. C71C2×#3093semidirect
380. #428C2×D71semidirect
382. C2×#107C2×D71semidirect
384. C2×#106C2×D71semidirect
468. #107C22×D71semidirect
470. #106C22×D71semidirect
669. C2#22598274direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865112
C22×#145560862
#225982742
C2×#179863432
C2×#179863422
C2×#179863262
C2×#179863252
C2×#179860422
C2×#179860012
C2×#179859982
C2×#179859622
C2×#428×C712
C2×#309371