Finite Group Databasebeta

← #29586545

Subgroups — #29586545

Order 15616.

1258 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840338C211yesmaximal, characteristic
2C2×#16839744C211yesmaximal, characteristic
3C22×#14519695C211yesmaximal, characteristic, complemented
4C22×#14519695C211yesmaximal, characteristic, complemented
5#21454263C211yesmaximal, characteristic
6C2×#16839532C211yesmaximal, characteristic, complemented
7C2×C61×#344C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C23×Dic122C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C22×#11758194C2211yescharacteristic
12#16840338—22no—
13#16840338—22no—
14#16840338—22no—
15#16840338—22no—
16C2×#14519777—21no—
17C2×#14519765—21no—
18C2×#14519761C414yes—
19C2×#14519757—22no—
20#16839744—22no—
21#16839744—22no—
22C2×#14519695—22no—
23C2×#14519695—22no—
24C2×#14519695—22no—
25C2×#14519695—22no—
26C2×#14519695—22no—
27C2×#14519695—22no—
28C2×#14519695—21no—
29C2×#14519693—21no—
30#16839730—22no—
31#16839728—22no—
32#16839725—22no—
33#16839532—22no—
34C22×M16×C61C2211yescharacteristic
35C22×M16×C61C2211yescharacteristic
36C2×#117×C61C2211yescharacteristic
37C61×#344—22no—
38C2×#11758222—21no—
39C2×#11758222—21no—
40C2×#11758222—21no—
41C2×#11758222—21no—
42C2×#11758222—21no—
43C2×#11758222—21no—
44C2×#11758222—21no—
45C2×#11758222—21no—
46C2×#11758222—21no—
47C2×#11758222—21no—
48C2×#11758222—21no—
49C2×#11758222—21no—
50C22×Dic122—21no—
51C22×Dic122—21no—
52C22×Dic122—21no—
53C22×Dic122—21no—
54C22×Dic122—21no—
55C22×Dic122—21no—
56C22×Dic122—21no—
57C22×Dic122—21no—
58C22×Dic122—21no—
59C22×Dic122—21no—
60C22×Dic122—21no—
61C22×Dic122—21no—
62C22×Dic122D411yescharacteristic
63C22×Dic122D412yes—
64C22×Dic122D412yes—
65C22×D244D411yescharacteristic
66C22×C22⋊D61C2×C412yes—
67C23×Dic61C2×C412yes—
68C22×C4×D61D412yes—
69C2×#11758194—21no—
70C2×#11758194—21no—
71C2×#11758194—21no—
72C2×#11758194—21no—
73C2×#11758194—21no—
74C2×#11758194—21no—
75C2×#11758194—21no—
76C2×#11758194—21no—
77C2×#11758194—21no—
78C2×#11758194—21no—
79C2×#11758194D412yes—
80C2×#11758194D412yes—
81C22×#92418—21no—
82C22×#92418—21no—
83#14519777—24no—
84#14519777—24no—
85#14519765—24no—
86#14519765—24no—
87#14519761—28no—
88#14519761—28no—
89#14519757—28no—
90#14519757—28no—
91C2×C4⋊Dic61—24no—
92C2×#11758198—24no—
93#14519695—28no—
94#14519695—28no—
95#14519695—24no—
96#14519693—24no—
97#14519689—28no—
98C23×C4×C61C2311yescharacteristic
99C2×M16×C61—21no—
100C2×M16×C61—21no—
101C2×M16×C61—21no—
102C2×M16×C61—21no—
103C2×M16×C61—21no—
104C2×M16×C61—21no—
105C2×M16×C61—21no—
106C2×M16×C61—21no—
107C2×M16×C61—21no—
108C2×M16×C61—21no—
109C2×M16×C61D412yes—
110C2×M16×C61D412yes—
111C22×C8×C61—21no—
112C22×C8×C61—21no—
113#117×C61—21no—
114#117×C61—21no—
115#117×C61D412yes—
116#117×C61D412yes—
117C2×C4⋊C4×C61—21no—
118C2×C22⋊C4×C61C2×C412yes—
119C2×C42×C61—21no—
120C24×C61C22×C411yescharacteristic
121C23×D61C22⋊C412yes—
122C22×C4×C61—22no—
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61#4111yescharacteristic
134C22×C4×C61#4111yescharacteristic
135C22×C4×C61#4111yescharacteristic
136C22×C4×C61#4111yescharacteristic
137C2×C22⋊D61—22no—
138C2×C22⋊D61—22no—
139C2×C22⋊D61—22no—
140C2×C22⋊D61—22no—
141C2×C22⋊D61—22no—
142C2×C22⋊D61—22no—
143C22×Dic61—22no—
144C22×Dic61—22no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61C22⋊C412yes—
150C22×Dic61C22⋊C414yes—
151#11758222—41no—
152#11758222—41no—
153#11758222—41no—
154#11758222—41no—
155#11758222—41no—
156#11758222—41no—
157#11758222—41no—
158#11758222—41no—
159#11758222—41no—
160#11758222—41no—
161#11758222—41no—
162#11758222—41no—
163#11758222—41no—
164#11758222—41no—
165#11758222—41no—
166#11758222—41no—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—21no—
173C2×C4×D61—22no—
174C2×C4×D61—22no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—22no—
178C2×C4×D61—22no—
179C2×Dic122—22no—
180C2×Dic122—22no—
181C2×Dic122—22no—
182C2×Dic122—22no—
183C2×Dic122—22no—
184C2×Dic122—22no—
185C2×Dic122—21no—
186C2×Dic122—21no—
187C2×Dic122—21no—
188C2×Dic122—22no—
189C2×Dic122—22no—
190C2×Dic122—22no—
191C2×Dic122—22no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—22no—
195C2×Dic122—22no—
196C2×Dic122—21no—
197C2×Dic122—41no—
198C2×Dic122—41no—
199C2×Dic122—41no—
200C2×Dic122—41no—
201C2×Dic122—41no—
202C2×Dic122—41no—
203C2×Dic122—41no—
204C2×Dic122—41no—
205C2×Dic122—41no—
206C2×Dic122—41no—
207C2×Dic122—41no—
208C2×Dic122—41no—
209C2×Dic122—41no—
210C2×Dic122—41no—
211C2×Dic122—41no—
212C2×Dic122—41no—
213M16×C61—22no—
214M16×C61—22no—
215M16×C61—22no—
216M16×C61—22no—
217M16×C61—41no—
218M16×C61—41no—
219M16×C61—41no—
220M16×C61—41no—
221C2×C8×C61—22no—
222C2×C8×C61—22no—
223C2×C8×C61—41no—
224C2×C8×C61—41no—
225C2×C8×C61—41no—
226C2×C8×C61—41no—
227C4⋊C4×C61—22no—
228C4⋊C4×C61—22no—
229C22⋊C4×C61—22no—
230C22⋊C4×C61C22⋊C414yes—
231C42×C61—22no—
232C42×C61—22no—
233#11758198—216no—
234C4⋊Dic61—216no—
235#11758194—22no—
236#11758194—22no—
237#11758194—22no—
238#11758194—22no—
239#11758194—41no—
240#11758194—41no—
241#11758194—41no—
242#11758194—41no—
243C2×#92418—22no—
244C2×#92418—22no—
245C2×#92418—41no—
246C2×#92418—41no—
247C2×#92418—41no—
248C2×#92418—41no—
249C23×C61—42no—
250C23×C61C2×C22⋊C411yescharacteristic
251C23×C61C2×C22⋊C411yescharacteristic
252C23×C61C2×C22⋊C411yescharacteristic
253C23×C61C4×D411yescharacteristic
254C23×C61C4×D411yescharacteristic
255C23×C61C4×D411yescharacteristic
256C23×C61C4×D411yescharacteristic
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—44no—
261C2×C4×C61—24no—
262C2×C4×C61—44no—
263C2×C4×C61#12011yescharacteristic
264C2×C4×C61#12011yescharacteristic
265C2×C4×C61#12011yescharacteristic
266C2×C4×C61#12011yescharacteristic
267C2×C4×C61#12011yescharacteristic
268C2×C4×C61#12011yescharacteristic
269C2×C4×C61#12011yescharacteristic
270C2×C4×C61#12011yescharacteristic
271C2×C4×C61#12111yescharacteristic
272C2×C4×C61#12111yescharacteristic
273C2×C4×C61#12111yescharacteristic
274C2×C4×C61#12111yescharacteristic
275C2×C4×C61#12111yescharacteristic
276C2×C4×C61#12111yescharacteristic
277C2×C4×C61#12111yescharacteristic
278C2×C4×C61#12111yescharacteristic
279C2×C4×C61#12111yescharacteristic
280C2×C4×C61#12111yescharacteristic
281C2×C4×C61#12111yescharacteristic
282C2×C4×C61#12111yescharacteristic
283C2×C4×C61#12311yescharacteristic
284C2×C4×C61#12311yescharacteristic
285C2×C4×C61#12311yescharacteristic
286C2×C4×C61#12311yescharacteristic
287C2×C4×C61#12411yescharacteristic
288C2×C4×C61#12411yescharacteristic
289C2×C4×C61#12711yescharacteristic
290C2×C4×C61#12711yescharacteristic
291C22⋊D61—42no—
292C22⋊D61—42no—
293C22⋊D61—42no—
294C22⋊D61—42no—
295C2×Dic61—22no—
296C2×Dic61—24no—
297C2×Dic61—24no—
298C2×Dic61—24no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—42no—
302C2×Dic61—42no—
303C2×Dic61—42no—
304C2×Dic61—42no—
305D244—41no—
306D244—41no—
307D244—41no—
308D244—41no—
309C4×D61—42no—
310C4×D61—42no—
311C4×D61—42no—
312C4×D61—42no—
313Dic122—42no—
314Dic122—42no—
315Dic122—42no—
316Dic122—42no—
317Dic122—41no—
318Dic122—41no—
319Dic122—42no—
320Dic122—42no—
321Dic122—42no—
322Dic122—42no—
323Dic122—41no—
324Dic122—41no—
325C8×C61—42no—
326C8×C61—42no—
327#92418—42no—
328#92418—42no—
329#10974—611nomaximal, Sylow
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61#37911yescharacteristic
338C22×C61#38611yescharacteristic
339C22×C61#38611yescharacteristic
340C22×C61#38611yescharacteristic
341C22×C61#38611yescharacteristic
342C22×C61#39011yescharacteristic
343C22×C61#39011yescharacteristic
344C2×D61—44no—
345C2×D61—44no—
346C2×D61—42no—
347C2×D61—82no—
348C4×C61—44no—
349C4×C61#39211yescharacteristic
350C4×C61#39211yescharacteristic
351C4×C61#39211yescharacteristic
352C4×C61#39211yescharacteristic
353C4×C61#39411yescharacteristic
354C4×C61#39411yescharacteristic
355C4×C61#39411yescharacteristic
356C4×C61#39411yescharacteristic
357Dic61—44no—
358Dic61—42no—
359C2×#536—611no—
360C2×#413—611no—
361C22×#101—611no—
362C22×#101—611no—
363#2879—611no—
364C2×#344—611no—
365C2×#344D6111yescharacteristic, complemented
366C2×C61—21no—
367C2×C61—21no—
368C2×C61—21no—
369C2×C61—21no—
370C2×C61—21no—
371C2×C61—21no—
372C2×C61#143811yescharacteristic
373C2×C61#191512yes—
374D61—82no—
375C22×#41—611no—
376C23×Q8—611no—
377C22×M16—611no—
378C22×M16—611no—
379C22×M16C2×D6111yescharacteristic
380C22×M16C2×D6111yescharacteristic
381#536—1222no—
382#536—1222no—
383#536—1222no—
384#536—1222no—
385C2×C4⋊Q8—1221no—
386C2×#124—1221no—
387C2×#123—614no—
388C2×C22⋊Q8—1222no—
389C2×#117C2×D6111yescharacteristic
390#413—1222no—
391#413—1222no—
392C2×#101—1222no—
393C2×#101—1222no—
394C2×#101—1222no—
395C2×#101—1222no—
396C2×#101—1221no—
397C2×#101—1222no—
398C2×#101—1222no—
399C2×#100—1221no—
400#408—1222no—
401#408—1222no—
402#407—1222no—
403#344—22no—
404#344—1222no—
405C61#1097411yescharacteristic, complemented, Sylow
406C2×#41—1221no—
407C2×#41—1221no—
408C2×#41—1221no—
409C2×#41—1221no—
410C2×#41—1221no—
411C2×#41—1221no—
412C2×#41—1221no—
413C2×#41—1221no—
414C2×#41—1221no—
415C2×#41—1221no—
416C2×#41—1221no—
417C2×#41—1221no—
418C22×Q8—611no—
419C22×Q8—612no—
420C22×Q8—612no—
421C22×Q8—1221no—
422C22×Q8—1221no—
423C22×Q8—1221no—
424C22×Q8—1221no—
425C22×Q8—1221no—
426C22×Q8—1221no—
427C22×Q8—1221no—
428C22×Q8—1221no—
429C22×Q8—1221no—
430C22×Q8—1221no—
431C22×Q8—1221no—
432C22×Q8—1221no—
433C22×D4—612no—
434C22×D4—611no—
435C23×C4—612no—
436C23×C4—612no—
437C23×C4C22×D6111yescharacteristic
438C2×M16—21no—
439C2×M16—21no—
440C2×M16—21no—
441C2×M16—21no—
442C2×M16—21no—
443C2×M16—21no—
444C2×M16—21no—
445C2×M16—21no—
446C2×M16—21no—
447C2×M16—21no—
448C2×M16—612no—
449C2×M16—612no—
450C2×M16—1221no—
451C2×M16—1221no—
452C2×M16—1221no—
453C2×M16—1221no—
454C2×M16—1221no—
455C2×M16—1221no—
456C2×M16—1221no—
457C2×M16—1221no—
458C2×M16—1221no—
459C2×M16—1221no—
460C2×M16D24412yes—
461C2×M16D24412yes—
462C22×C8—21no—
463C22×C8—21no—
464C22×C8—1221no—
465C22×C8—1221no—
466C4⋊Q8—1224no—
467C4⋊Q8—1224no—
468#124—1224no—
469#124—1224no—
470#123—1228no—
471#123—1228no—
472C22⋊Q8—1228no—
473C22⋊Q8—1228no—
474#117—21no—
475#117—21no—
476#117D24412yes—
477#117C22⋊D6112yes—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—1224no—
480C2×C22⋊C4—1224no—
481C2×C22⋊C4C4×D6112yes—
482C2×C42—21no—
483#101—1228no—
484#101—1228no—
485#101—1224no—
486#100—1224no—
487C22⋊C8—1228no—
488C24—612no—
489C24C2×C4×D6111yescharacteristic
490#41—2441no—
491#41—2441no—
492#41—2441no—
493#41—2441no—
494#41—2441no—
495#41—2441no—
496#41—2441no—
497#41—2441no—
498#41—2441no—
499#41—2441no—
500#41—2441no—
501#41—2441no—
502#41—2441no—
503#41—2441no—
504#41—2441no—
505#41—2441no—
506C2×Q8—1222no—
507C2×Q8—1222no—
508C2×Q8—1221no—
509C2×Q8—1222no—
510C2×Q8—1222no—
511C2×Q8—1221no—
512C2×Q8—1222no—
513C2×Q8—1222no—
514C2×Q8—1221no—
515C2×Q8—1222no—
516C2×Q8—1222no—
517C2×Q8—1221no—
518C2×Q8—1222no—
519C2×Q8—1222no—
520C2×Q8—1221no—
521C2×Q8—1222no—
522C2×Q8—1222no—
523C2×Q8—1221no—
524C2×Q8—2441no—
525C2×Q8—2441no—
526C2×Q8—2441no—
527C2×Q8—2441no—
528C2×Q8—2441no—
529C2×Q8—2441no—
530C2×Q8—2441no—
531C2×Q8—2441no—
532C2×Q8—2441no—
533C2×Q8—2441no—
534C2×Q8—2441no—
535C2×Q8—2441no—
536C2×Q8—2441no—
537C2×Q8—2441no—
538C2×Q8—2441no—
539C2×Q8—2441no—
540C2×D4—1222no—
541C2×D4—1222no—
542C2×D4—1222no—
543C2×D4—1222no—
544C2×D4—1222no—
545C2×D4—1222no—
546C2×D4—1221no—
547C2×D4—1221no—
548C2×D4—1221no—
549C2×D4—1221no—
550C2×D4—1221no—
551C2×D4—1221no—
552C22×C4—22no—
553C22×C4—612no—
554C22×C4—614no—
555C22×C4—1222no—
556C22×C4—1222no—
557C22×C4—1222no—
558C22×C4—1222no—
559C22×C4—1222no—
560C22×C4—1222no—
561C22×C4—1222no—
562C22×C4—1222no—
563C22×C4—1222no—
564C22×C4—1222no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4C2×D24411yescharacteristic
568C22×C4C2×D24411yescharacteristic
569C22×C4C2×D24411yescharacteristic
570C22×C4#1175822211yescharacteristic
571C22×C4#1175822211yescharacteristic
572C22×C4D4×D6111yescharacteristic
573C22×C4D4×D6111yescharacteristic
574C22×C4D4×D6111yescharacteristic
575C22×C4D4×D6111yescharacteristic
576C22×C4D4×D6111yescharacteristic
577C22×C4D4×D6111yescharacteristic
578C22×C4#1175822611yescharacteristic
579C22×C4#1175822611yescharacteristic
580C22×C4C2×C22⋊D6111yescharacteristic
581M16—22no—
582M16—22no—
583M16—22no—
584M16—22no—
585M16—41no—
586M16—41no—
587M16—41no—
588M16—41no—
589M16—1222no—
590M16—1222no—
591M16—1222no—
592M16—1222no—
593M16—2441no—
594M16—2441no—
595M16—2441no—
596M16—2441no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—41no—
600C2×C8—41no—
601C2×C8—41no—
602C2×C8—41no—
603C2×C8—1222no—
604C2×C8—1222no—
605C2×C8—2441no—
606C2×C8—2441no—
607C2×C8—2441no—
608C2×C8—2441no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—12216no—
612C22⋊C4—22no—
613C22⋊C4—12216no—
614C22⋊C4#1175819814yes—
615C42—22no—
616C42—22no—
617C23—42no—
618C23—1222no—
619C23—1222no—
620C23—1222no—
621C23—2444no—
622C23C22⋊C4×D6111yescharacteristic
623C23C22⋊C4×D6111yescharacteristic
624C23C2×#1175819811yescharacteristic
625C23#1451973911yescharacteristic
626C23#1451973911yescharacteristic
627C23C4×D24411yescharacteristic
628C23C4×D24411yescharacteristic
629Q8—2442no—
630Q8—2442no—
631Q8—2441no—
632Q8—2442no—
633Q8—2442no—
634Q8—2441no—
635Q8—2442no—
636Q8—2442no—
637Q8—2441no—
638Q8—2442no—
639Q8—2442no—
640Q8—2441no—
641D4—2442no—
642D4—2442no—
643D4—2442no—
644D4—2442no—
645D4—2441no—
646D4—2441no—
647D4—2441no—
648D4—2441no—
649C2×C4—24no—
650C2×C4—44no—
651C2×C4—1224no—
652C2×C4—1222no—
653C2×C4—1222no—
654C2×C4—1224no—
655C2×C4—1224no—
656C2×C4—1222no—
657C2×C4—2442no—
658C2×C4—2442no—
659C2×C4—2442no—
660C2×C4—2442no—
661C2×C4—2442no—
662C2×C4—2442no—
663C2×C4—2442no—
664C2×C4—2442no—
665C2×C4#1451974511yescharacteristic
666C2×C4#1451974511yescharacteristic
667C2×C4#1451974711yescharacteristic
668C2×C4#1451974711yescharacteristic
669C2×C4#1451974711yescharacteristic
670C2×C4#1451974711yescharacteristic
671C2×C4#1451974711yescharacteristic
672C2×C4#1451974711yescharacteristic
673C2×C4#1451975011yescharacteristic
674C2×C4#1451975011yescharacteristic
675C2×C4#1451975011yescharacteristic
676C2×C4#1451975011yescharacteristic
677C2×C4#1451975111yescharacteristic
678C2×C4#1451975111yescharacteristic
679C2×C4#1451975211yescharacteristic
680C2×C4#1451975211yescharacteristic
681C2×C4#1451975211yescharacteristic
682C2×C4#1451975211yescharacteristic
683C2×C4#1451975211yescharacteristic
684C2×C4#1451975211yescharacteristic
685C2×C4#1451976211yescharacteristic
686C2×C4#1451976211yescharacteristic
687C2×C4#1451976211yescharacteristic
688C2×C4#1451976211yescharacteristic
689C2×C4#1451976511yescharacteristic
690C2×C4#1451976611yescharacteristic
691C2×C4#1451977311yescharacteristic
692C2×C4#1451977411yescharacteristic
693C8—42no—
694C8—42no—
695C8—2442no—
696C8—2442no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—4882no—
705C22—2444no—
706C22—2442no—
707C22—2444no—
708C22#1683961711yescharacteristic
709C22#1683964011yescharacteristic
710C22#1683964011yescharacteristic
711C22#1683964011yescharacteristic
712C22#1683964011yescharacteristic
713C22#1683966311yescharacteristic
714C22#1683966411yescharacteristic
715C4—44no—
716C4—2442no—
717C4—2444no—
718C4#1683967111yescharacteristic
719C4#1683967111yescharacteristic
720C4#1683967211yescharacteristic
721C4#1683967211yescharacteristic
722C4#1683967911yescharacteristic
723C4#1683967911yescharacteristic
724C4#1683968011yescharacteristic
725C4#1683968011yescharacteristic
726C2—21no—
727C2—21no—
728C2—21no—
729C2—21no—
730C2—21no—
731C2—21no—
732C2—4882no—
733C2#2144405911yescharacteristic
734C2#2144637012yes—
subgroupG/H
centerC22#16839640
commutatorC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#344C2
socleC22×C61#386
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenterC2×#344D61
hypocenterC61#10974
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
3. C22×#14519695C2semidirect
4. C22×#14519695C2semidirect
6. C2×#16839532C2semidirect
7. C2×C61×#344C2semidirect
365. C2×#344D61semidirect
405. C61#10974semidirect

Maximal subgroups

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

subgroupindex
C2×#168403382
C2×#168397442
C22×#145196952
#214542632
C2×#168395322
C2×C61×#3442
#1097461