Finite Group Databasebeta

← #28494151

Subgroups — #28494151

Order 15104.

1298 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×#41×Dic59C211yesmaximal, characteristic
2#21432615C211yesmaximal, characteristic
3C2×#16837173C211yesmaximal, characteristic, complemented
4#21423828C211yesmaximal, characteristic, complemented
5C2×#16837163C211yesmaximal, characteristic, complemented
6C2×#16837161C211yesmaximal, characteristic, complemented
7C2×C59×#421C211yesmaximal, characteristic
8C22×#11745664C2211yescharacteristic
9#41×Dic59—22no—
10#41×Dic59—22no—
11#41×Dic59—22no—
12#41×Dic59C414yescomplemented
13C2×Q8×Dic59—21no—
14C2×D4×Dic59—22no—
15C2×D4×Dic59—21no—
16C2×#14273686—21no—
17C2×#14273686C2211yescharacteristic
18C2×#14273686C2211yescharacteristic
19C22×C4×Dic59—21no—
20C22×C4×Dic59C2211yescharacteristic
21#16837411—21no—
22#16837407—21no—
23#16837403C414yescomplemented
24#16837398—22no—
25#16837173—22no—
26#16837168—22no—
27#16837163—21no—
28#16837163—21no—
29#16837161—22no—
30C22×#41×C59C2211yescharacteristic
31C22×M16×C59C2211yescharacteristic
32C2×#117×C59C2211yescharacteristic
33C59×#421—22no—
34C59×#421C414yescomplemented
35C2×#104×C59—22no—
36C23×Dic59—22no—
37C23×Dic59—21no—
38C2×#11745664—21no—
39C2×#11745664—21no—
40C2×#11745664—21no—
41C2×#11745664—21no—
42C2×#11745664—21no—
43C2×#11745664C2×C412yescomplemented
44C22×C59⋊C8—21no—
45Q8×Dic59—24no—
46Q8×Dic59—24no—
47D4×Dic59—28no—
48D4×Dic59—24no—
49D4×Dic59—24no—
50D4×Dic59—28no—
51#14273686—24no—
52#14273686—21no—
53#14273686—21no—
54#14273686—24no—
55#14273686—21no—
56#14273686—21no—
57#14273686—21no—
58#14273686—21no—
59#14273686C2×C412yes—
60#14273686D412yes—
61C2×C4⋊Dic59—22no—
62C2×C4⋊Dic59—21no—
63C2×C4⋊Dic59C2×C412yescomplemented
64C2×C22⋊Dic59—22no—
65C2×C22⋊Dic59—21no—
66C2×C22⋊Dic59D412yes—
67C2×C4×Dic59—22no—
68C2×C4×Dic59—24no—
69C2×C4×Dic59—21no—
70C2×C4×Dic59—21no—
71C2×C4×Dic59—21no—
72C2×C4×Dic59—21no—
73C2×C4×Dic59—24no—
74C2×C4×Dic59—21no—
75C2×C4×Dic59C2×C412yes—
76C2×C4×Dic59D412yes—
77C2×C4×Dic59D411yescharacteristic
78C2×C4×Dic59D411yescharacteristic
79#14273651—24no—
80#14273648—24no—
81C2×#41×C59—21no—
82C2×#41×C59—21no—
83C2×#41×C59—21no—
84C2×#41×C59—21no—
85C2×#41×C59—21no—
86C2×#41×C59—21no—
87C2×#41×C59C2×C412yes—
88C2×#41×C59C2×C412yes—
89C2×#41×C59C2×C412yes—
90C2×#41×C59D412yes—
91C2×#41×C59D412yes—
92C2×#41×C59Q812yes—
93C22×Q8×C59D411yescharacteristic
94C22×D4×C59—21no—
95C22×D4×C59D411yescharacteristic
96C23×C4×C59—21no—
97C23×C4×C59C2311yescharacteristic
98C2×M16×C59—21no—
99C2×M16×C59—21no—
100C2×M16×C59—21no—
101C2×M16×C59—21no—
102C2×M16×C59—21no—
103C2×M16×C59C2×C412yescomplemented
104C22×C8×C59—21no—
105#117×C59—21no—
106#117×C59—21no—
107#117×C59—21no—
108#117×C59C2×C412yescomplemented
109C2×C4⋊C4×C59—21no—
110C2×C22⋊C4×C59—21no—
111C2×C42×C59—21no—
112#104×C59—28no—
113C24×C59—21no—
114C24×C59C2×D411yescharacteristic
115#41×C59—22no—
116#41×C59—22no—
117#41×C59—22no—
118#41×C59—22no—
119#41×C59—22no—
120#41×C59—22no—
121#41×C59—22no—
122#41×C59—22no—
123#41×C59—22no—
124#41×C59—22no—
125#41×C59—22no—
126#41×C59—22no—
127#41×C59C4214yes—
128#41×C59C22⋊C414yes—
129#41×C59C4⋊C414yes—
130#41×C59C4⋊C414yes—
131C2×Q8×C59—21no—
132C2×Q8×C59—21no—
133C2×Q8×C59—21no—
134C2×Q8×C59C22⋊C412yes—
135C2×Q8×C59C22⋊C412yes—
136C2×Q8×C59C4⋊C412yes—
137C2×D4×C59—22no—
138C2×D4×C59—22no—
139C2×D4×C59—22no—
140C2×D4×C59—22no—
141C2×D4×C59—22no—
142C2×D4×C59—22no—
143C2×D4×C59—21no—
144C2×D4×C59—21no—
145C2×D4×C59—21no—
146C2×D4×C59C22⋊C412yes—
147C2×D4×C59C22⋊C412yes—
148C2×D4×C59C4⋊C412yes—
149C22×C4×C59—21no—
150C22×C4×C59—22no—
151C22×C4×C59—22no—
152C22×C4×C59—22no—
153C22×C4×C59—22no—
154C22×C4×C59—22no—
155C22×C4×C59—22no—
156C22×C4×C59—41no—
157C22×C4×C59C22×C411yescharacteristic
158C22×C4×C59C22×C411yescharacteristic
159C22×C4×C59C22×C411yescharacteristic
160C22×C4×C59C2×D411yescharacteristic
161C22×C4×C59C2×D411yescharacteristic
162C22×C4×C59C2×D411yescharacteristic
163C22×C4×C59C2×D411yescharacteristic
164C22×C4×C59C2×D411yescharacteristic
165C22×C4×C59C2×D411yescharacteristic
166C22×C4×C59C2×Q811yescharacteristic
167C22×C4×C59#4111yescharacteristic
168C22×C4×C59#4111yescharacteristic
169C22×C4×C59#4111yescharacteristic
170C22×C4×C59#4111yescharacteristic
171C22×Dic59—21no—
172C22×Dic59—28no—
173C22×Dic59—22no—
174C22×Dic59—22no—
175C22×Dic59—21no—
176C22×Dic59—22no—
177C22×Dic59—22no—
178C22×Dic59—44no—
179C22×Dic59—48no—
180M16×C59—22no—
181M16×C59—22no—
182M16×C59—41no—
183M16×C59—41no—
184C2×C8×C59—22no—
185C2×C8×C59—41no—
186C2×C8×C59—41no—
187C4⋊C4×C59—22no—
188C4⋊C4×C59—41no—
189C22⋊C4×C59—22no—
190C22⋊C4×C59—41no—
191C42×C59—22no—
192C42×C59—41no—
193C22⋊Dic59—28no—
194C22⋊Dic59—22no—
195C22⋊Dic59—41no—
196C22⋊Dic59—41no—
197C22⋊Dic59C22⋊C414yes—
198C4⋊Dic59—28no—
199C4⋊Dic59—22no—
200C4⋊Dic59—22no—
201C4⋊Dic59—22no—
202C4⋊Dic59—22no—
203C4×Dic59—28no—
204C4×Dic59—22no—
205C4×Dic59—22no—
206C4×Dic59—21no—
207C4×Dic59—22no—
208C4×Dic59—21no—
209C4×Dic59—22no—
210C4×Dic59—41no—
211C4×Dic59—41no—
212C4×Dic59C22⋊C412yes—
213C4×Dic59C22⋊C412yes—
214#11745664—22no—
215#11745664—22no—
216#11745664—41no—
217#11745664—41no—
218C2×C59⋊C8—22no—
219C2×C59⋊C8—41no—
220C2×C59⋊C8—41no—
221C23×C59—22no—
222C23×C59—22no—
223C23×C59—22no—
224C23×C59—42no—
225C23×C59—44no—
226C23×C59C2×C22⋊C411yescharacteristic
227C23×C59C4×D411yescharacteristic
228C23×C59C4×D411yescharacteristic
229C23×C59#12011yescharacteristic
230C23×C59#12011yescharacteristic
231C23×C59#12111yescharacteristic
232C23×C59C22⋊Q811yescharacteristic
233Q8×C59—22no—
234Q8×C59—22no—
235Q8×C59—22no—
236Q8×C59#9514yes—
237D4×C59—24no—
238D4×C59—24no—
239D4×C59—24no—
240D4×C59—24no—
241D4×C59—22no—
242D4×C59—22no—
243D4×C59—22no—
244D4×C59#9514yes—
245C2×C4×C59—22no—
246C2×C4×C59—22no—
247C2×C4×C59—22no—
248C2×C4×C59—24no—
249C2×C4×C59—24no—
250C2×C4×C59—24no—
251C2×C4×C59—24no—
252C2×C4×C59—42no—
253C2×C4×C59—82no—
254C2×C4×C59C2×C4211yescharacteristic
255C2×C4×C59C2×C22⋊C411yescharacteristic
256C2×C4×C59C2×C22⋊C411yescharacteristic
257C2×C4×C59C2×C22⋊C411yescharacteristic
258C2×C4×C59C2×C22⋊C411yescharacteristic
259C2×C4×C59C2×C4⋊C411yescharacteristic
260C2×C4×C59C2×C4⋊C411yescharacteristic
261C2×C4×C59C2×C4⋊C411yescharacteristic
262C2×C4×C59#11711yescharacteristic
263C2×C4×C59#11711yescharacteristic
264C2×C4×C59C4×D411yescharacteristic
265C2×C4×C59C4×D411yescharacteristic
266C2×C4×C59C4×D411yescharacteristic
267C2×C4×C59C4×D411yescharacteristic
268C2×C4×C59C4×D411yescharacteristic
269C2×C4×C59C4×D411yescharacteristic
270C2×C4×C59#12011yescharacteristic
271C2×C4×C59#12011yescharacteristic
272C2×C4×C59#12111yescharacteristic
273C2×C4×C59#12111yescharacteristic
274C2×C4×C59#12111yescharacteristic
275C2×C4×C59C22⋊Q811yescharacteristic
276C2×C4×C59C22⋊Q811yescharacteristic
277C2×C4×C59C22⋊Q811yescharacteristic
278C2×C4×C59#12311yescharacteristic
279C2×C4×C59#12311yescharacteristic
280C2×C4×C59#12311yescharacteristic
281C2×C4×C59#12311yescharacteristic
282C2×Dic59—24no—
283C2×Dic59—22no—
284C2×Dic59—24no—
285C2×Dic59—22no—
286C2×Dic59—44no—
287C2×Dic59—44no—
288C2×Dic59—416no—
289C2×Dic59—44no—
290C2×Dic59—42no—
291C2×Dic59—42no—
292C2×Dic59—82no—
293C8×C59—42no—
294C59⋊C8—42no—
295#10772—591nomaximal, Sylow
296C22×C59—22no—
297C22×C59—22no—
298C22×C59—22no—
299C22×C59—24no—
300C22×C59—41no—
301C22×C59—41no—
302C22×C59—41no—
303C22×C59—41no—
304C22×C59—44no—
305C22×C59—44no—
306C22×C59—44no—
307C22×C59C4×C22⋊C411yescharacteristic
308C22×C59#37911yescharacteristic
309C22×C59#38011yescharacteristic
310C22×C59#38511yescharacteristic
311C22×C59#38511yescharacteristic
312C22×C59#38611yescharacteristic
313C22×C59#38611yescharacteristic
314C4×C59—24no—
315C4×C59—82no—
316C4×C59C2×#9511yescharacteristic
317C4×C59C4×C22⋊C411yescharacteristic
318C4×C59#38011yescharacteristic
319C4×C59#38111yescharacteristic
320C4×C59#38511yescharacteristic
321C4×C59#38511yescharacteristic
322C4×C59#38611yescharacteristic
323C4×C59#38611yescharacteristic
324Dic59—24no—
325Dic59—44no—
326Dic59—42no—
327Dic59—82no—
328C2×C4×#41—591no—
329C2×#421D5911yescharacteristic
330#2896—591no—
331C2×#344—591no—
332#1740—591no—
333C2×#339—591no—
334C2×#339—591no—
335C2×C59—21no—
336C2×C59—21no—
337C2×C59—21no—
338C2×C59—21no—
339C2×C59—21no—
340C2×C59—21no—
341C2×C59—44no—
342C2×C59C22⋊#9511yescharacteristic
343C2×C59#190612yes—
344C22×#41C2×D5911yescharacteristic
345C22×M16—591no—
346C22×M16C2×D5911yescharacteristic
347C4×#41—594no—
348C4×#41—1182no—
349C4×#41—1182no—
350C4×#41—1182no—
351C2×C4×Q8—1181no—
352C2×C4×D4—1182no—
353C2×C4×D4—1181no—
354C2×#117—591no—
355C2×#117—591no—
356C2×#117—1181no—
357C2×#117C2×D5911yescharacteristic
358C22×C42—591no—
359C22×C42—1181no—
360#421—22no—
361#421Dic5914yescomplemented
362C2×#104—22no—
363#419—1181no—
364#418—1181no—
365#417—594no—
366#416—1182no—
367#344—1182no—
368#342—1182no—
369#339—1182no—
370#339—1181no—
371#339—1181no—
372C59#1077211yescharacteristic, complemented, Sylow
373C2×#41—21no—
374C2×#41—21no—
375C2×#41—21no—
376C2×#41—21no—
377C2×#41—21no—
378C2×#41—21no—
379C2×#41Dic11812yes—
380C2×#41C4×D5912yes—
381C2×#41C4×D5912yes—
382C2×#41C2×Dic5912yes—
383C2×#41C22⋊D5912yes—
384C2×#41C22⋊D5912yes—
385C22×Q8D23611yescharacteristic
386C22×D4—21no—
387C22×D4D23611yescharacteristic
388C23×C4—21no—
389C23×C4—1182no—
390C23×C4—1181no—
391C23×C4C22×D5911yescharacteristic
392C2×M16—21no—
393C2×M16—21no—
394C2×M16—21no—
395C2×M16—21no—
396C2×M16—21no—
397C2×M16—592no—
398C2×M16—1181no—
399C2×M16—1181no—
400C2×M16—1181no—
401C2×M16—1181no—
402C2×M16—1181no—
403C2×M16C2×Dic5912yescomplemented
404C22×C8—21no—
405C22×C8—1181no—
406C4×Q8—1184no—
407C4×Q8—1184no—
408C4×D4—1188no—
409C4×D4—1188no—
410C4×D4—1184no—
411C4×D4—1184no—
412#117—21no—
413#117—21no—
414#117—21no—
415#117—592no—
416#117—592no—
417#117—1184no—
418#117—1184no—
419#117—1181no—
420#117—1181no—
421#117—1181no—
422#117—1181no—
423#117—1181no—
424#117—1181no—
425#117C2×Dic5912yescomplemented
426C2×C4⋊C4—21no—
427C2×C4⋊C4—592no—
428C2×C4⋊C4—1182no—
429C2×C4⋊C4—1181no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—592no—
432C2×C22⋊C4—1182no—
433C2×C22⋊C4—1181no—
434C2×C42—21no—
435C2×C42—592no—
436C2×C42—591no—
437C2×C42—592no—
438C2×C42—591no—
439C2×C42—1184no—
440C2×C42—1182no—
441C2×C42—1184no—
442C2×C42—1181no—
443C2×C42—1181no—
444C2×C42—1181no—
445C2×C42—1181no—
446C2×C42—1181no—
447#104—28no—
448#103—1184no—
449#102—1184no—
450C24—21no—
451C24D4×D5911yescharacteristic
452#41—22no—
453#41—22no—
454#41—22no—
455#41—22no—
456#41—22no—
457#41—22no—
458#41—22no—
459#41—22no—
460#41—22no—
461#41—22no—
462#41—22no—
463#41—22no—
464#41C4×Dic5914yes—
465#41Dic59⋊C414yes—
466#41Dic59⋊C414yes—
467#41C22⋊Dic5914yes—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8C4⋊Dic5912yes—
472C2×Q8(C2×D59)⋊C412yes—
473C2×Q8(C2×D59)⋊C412yes—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4C4⋊Dic5912yes—
484C2×D4(C2×D59)⋊C412yes—
485C2×D4(C2×D59)⋊C412yes—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—41no—
494C22×C4—1181no—
495C22×C4—1188no—
496C22×C4—1182no—
497C22×C4—1182no—
498C22×C4—1181no—
499C22×C4—1182no—
500C22×C4—1182no—
501C22×C4—2364no—
502C22×C4—2368no—
503C22×C4C2×Dic11811yescharacteristic
504C22×C4C2×C4×D5911yescharacteristic
505C22×C4C2×C4×D5911yescharacteristic
506C22×C4C2×D23611yescharacteristic
507C22×C4D4×D5911yescharacteristic
508C22×C4D4×D5911yescharacteristic
509C22×C4D4×D5911yescharacteristic
510C22×C4#1174568711yescharacteristic
511C22×C4#1174568711yescharacteristic
512C22×C4#1174568711yescharacteristic
513C22×C4#1174568711yescharacteristic
514C22×C4C22×Dic5911yescharacteristic
515C22×C4C2×C22⋊D5911yescharacteristic
516C22×C4C2×C22⋊D5911yescharacteristic
517M16—22no—
518M16—22no—
519M16—41no—
520M16—41no—
521M16—1182no—
522M16—1182no—
523M16—2361no—
524M16—2361no—
525C2×C8—22no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—1182no—
529C2×C8—2361no—
530C2×C8—2361no—
531C4⋊C4—22no—
532C4⋊C4—41no—
533C4⋊C4—1188no—
534C4⋊C4—1182no—
535C4⋊C4—1182no—
536C4⋊C4—1182no—
537C4⋊C4—1182no—
538C22⋊C4—22no—
539C22⋊C4—41no—
540C22⋊C4—594no—
541C22⋊C4—1188no—
542C22⋊C4—1182no—
543C22⋊C4—2361no—
544C22⋊C4—2361no—
545C42—22no—
546C42—41no—
547C42—592no—
548C42—592no—
549C42—1188no—
550C42—1182no—
551C42—1182no—
552C42—1181no—
553C42—1181no—
554C42—1182no—
555C42—1182no—
556C42—2361no—
557C42—2361no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—42no—
562C23—44no—
563C23C22⋊C4×D5911yescharacteristic
564C23(C22⋊D59)⋊C411yescharacteristic
565C23D4×Dic5911yescharacteristic
566C23#1427369511yescharacteristic
567C23#1427369711yescharacteristic
568C23#1427369911yescharacteristic
569C23#1427370411yescharacteristic
570Q8—22no—
571Q8—22no—
572Q8—22no—
573Q8C59⋊#9514yes—
574D4—24no—
575D4—24no—
576D4—24no—
577D4—24no—
578D4—22no—
579D4—22no—
580D4—22no—
581D4C59⋊#9514yes—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—42no—
590C2×C4—82no—
591C2×C4—1184no—
592C2×C4—1182no—
593C2×C4—1182no—
594C2×C4—1184no—
595C2×C4—4722no—
596C2×C4—2364no—
597C2×C4—2364no—
598C2×C4—23616no—
599C2×C4—2362no—
600C2×C4—2362no—
601C2×C4—2364no—
602C2×C4C2×C4×Dic5911yescharacteristic
603C2×C4C22⋊C4×D5911yescharacteristic
604C2×C4C2×(C2×D59)⋊C411yescharacteristic
605C2×C4C2×(C2×D59)⋊C411yescharacteristic
606C2×C4C2×C22⋊Dic5911yescharacteristic
607C2×C4C2×Dic59⋊C411yescharacteristic
608C2×C4C2×Dic59⋊C411yescharacteristic
609C2×C4C2×C4⋊Dic5911yescharacteristic
610C2×C4#1427368311yescharacteristic
611C2×C4#1427368311yescharacteristic
612C2×C4(C22⋊D59)⋊C411yescharacteristic
613C2×C4(C22⋊D59)⋊C411yescharacteristic
614C2×C4(C22⋊D59)⋊C411yescharacteristic
615C2×C4D4×Dic5911yescharacteristic
616C2×C4D4×Dic5911yescharacteristic
617C2×C4D4×Dic5911yescharacteristic
618C2×C4#1427369511yescharacteristic
619C2×C4#1427369711yescharacteristic
620C2×C4#1427369911yescharacteristic
621C2×C4#1427369911yescharacteristic
622C2×C4#1427369911yescharacteristic
623C2×C4#1427370411yescharacteristic
624C2×C4#1427370411yescharacteristic
625C2×C4#1427370411yescharacteristic
626C2×C4#1427370811yescharacteristic
627C2×C4#1427370811yescharacteristic
628C2×C4#1427371111yescharacteristic
629C2×C4#1427371111yescharacteristic
630C8—42no—
631C8—2362no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—24no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—44no—
641C22—44no—
642C22—44no—
643C22C22⋊C4×Dic5911yescharacteristic
644C22#1683725711yescharacteristic
645C22#1683726011yescharacteristic
646C22#1683727411yescharacteristic
647C22#1683727711yescharacteristic
648C22#1683727911yescharacteristic
649C22#1683728211yescharacteristic
650C4—24no—
651C4—82no—
652C4—1184no—
653C4—4722no—
654C4—2362no—
655C4—2364no—
656C4C2×C59⋊#9511yescharacteristic
657C4C22⋊C4×Dic5911yescharacteristic
658C4#1683726011yescharacteristic
659C4#1683726311yescharacteristic
660C4#1683727411yescharacteristic
661C4#1683727711yescharacteristic
662C4#1683727911yescharacteristic
663C4#1683728211yescharacteristic
664C2—21no—
665C2—21no—
666C2—21no—
667C2—21no—
668C2—21no—
669C2—21no—
670C2—44no—
671C2#2142231811yescharacteristic
672C2#2142459512yes—
subgroupG/H
centerC2×C4#14273699
commutatorC2×C4×C59C2×C42
FrattiniC23×C4C22×D59
FittingC2×C59×#421C2
socleC22×C59#386
prime radicalC22×#41×C59C22
cosocleC23×C4×C59C23
hypercenterC2×#421D59
hypocenterC59#10772
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
3. C2×#16837173C2semidirect
4. #21423828C2semidirect
5. C2×#16837163C2semidirect
6. C2×#16837161C2semidirect
12. #41×Dic59C4semidirect
23. #16837403C4semidirect
34. C59×#421C4semidirect
43. C2×#11745664C2×C4semidirect
63. C2×C4⋊Dic59C2×C4semidirect
103. C2×M16×C59C2×C4semidirect
108. #117×C59C2×C4semidirect
361. #421Dic59semidirect
372. C59#10772semidirect
403. C2×M16C2×Dic59semidirect
425. #117C2×Dic59semidirect

Maximal subgroups

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

subgroupindex
C2×#41×Dic592
#214326152
C2×#168371732
#214238282
C2×#168371632
C2×#168371612
C2×C59×#4212
#1077259