Finite Group Databasebeta

← #29698345

Subgroups — #29698345

Order 15616.

1086 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839875C211yesmaximal, characteristic
2C2×#16839873C211yesmaximal, characteristic
3C2×#16839844C211yesmaximal, characteristic
4#21448727C211yesmaximal, characteristic, complemented
5#21448719C211yesmaximal, characteristic, complemented
6#21446560C211yesmaximal, characteristic, complemented
7#21446545C211yesmaximal, characteristic, complemented
8#21446077C211yesmaximal, characteristic, complemented
9#21446077C211yesmaximal, characteristic, complemented
10#21446063C211yesmaximal, characteristic, complemented
11#21446063C211yesmaximal, characteristic, complemented
12#21445826C211yesmaximal, characteristic, complemented
13#21445816C211yesmaximal, characteristic, complemented
14#21445691C211yesmaximal, characteristic, complemented
15C61×#1847C211yesmaximal, characteristic, complemented
16C22×D488C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×#14519739C2211yescharacteristic
20C2×#14519739C2211yescharacteristic
21C2×#14519739C2211yescharacteristic
22C2×#14519739C2211yescharacteristic
23C2×C4⋊C4×D61—21no—
24#16839875C418yescomplemented
25#16839873—24no—
26#16839844—24no—
27C2×#14519709C2211yescharacteristic
28C2×C4⋊#92418C2211yescharacteristic
29C2×#14519699C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519687C2211yescharacteristic
36C2×C8×Dic61C2211yescharacteristic
37#16839658C2211yescharacteristic
38#16839658C2211yescharacteristic
39#16839658C2211yescharacteristic
40#16839658C2211yescharacteristic
41#16839636—21no—
42#16839636—21no—
43#16839633—21no—
44#16839633—21no—
45#16839621—21no—
46#16839619—21no—
47C4×C4⋊Dic61C2211yescharacteristic
48#95×D61—21no—
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C2×#107×C61C2211yescharacteristic
56C2×#107×C61C2211yescharacteristic
57C2×#106×C61C2211yescharacteristic
58C2×#106×C61C2211yescharacteristic
59C2×#97×C61C2211yescharacteristic
60C61×#384C2211yescharacteristic
61C61×#382C2211yescharacteristic
62C22×D244C2311yescharacteristic
63C22×D244C2311yescharacteristic
64C22×C4×D61—21no—
65C22×C4×D61—21no—
66C22×C4×D61—21no—
67C22×C4×D61—21no—
68C22×C4×D61—21no—
69C22×C4×D61—21no—
70C2×D488C2×C414yes—
71C2×D488D414yes—
72C2×D488Q814yes—
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C4×D244—22no—
76C4×D244—22no—
77C4×D244C2×C414yescomplemented
78C4×D244C2×C414yescomplemented
79#14519739—22no—
80#14519739—22no—
81#14519739—22no—
82#14519739—22no—
83#14519739—41no—
84#14519739—41no—
85#14519739—41no—
86#14519739—41no—
87C2×C4⋊Dic61D411yescharacteristic
88C2×C4⋊Dic61D411yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×#11758196—21no—
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×#11758196—21no—
95C4⋊C4×D61—44no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×C4×Dic61C2311yescharacteristic
103C2×C4×Dic61C2311yescharacteristic
104#14519709C2×C414yescomplemented
105C4⋊#92418—22no—
106#14519699C2×C414yescomplemented
107#14519699C2×C414yescomplemented
108#14519697—22no—
109#14519697—22no—
110#14519697—22no—
111#14519697—22no—
112#14519687—22no—
113C8×Dic61—22no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684D411yescharacteristic
119#14519684D411yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122C2×C4⋊C4×C61—21no—
123C2×C4⋊C4×C61—21no—
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C42×C61C2311yescharacteristic
129#107×C61—22no—
130#107×C61—41no—
131#106×C61—22no—
132#106×C61—41no—
133#97×C61C2×C414yescomplemented
134#95×C61—21no—
135#95×C61—21no—
136C23×D61—21no—
137C23×D61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2411yescharacteristic
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61C2×D411yescharacteristic
148C22×Dic61C2×D411yescharacteristic
149C22×Dic61C2×D411yescharacteristic
150C22×Dic61C2×D411yescharacteristic
151C2×D244—21no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244—21no—
156C2×D244—21no—
157C2×D244C22×C412yes—
158C2×D244C22×C412yes—
159C2×D244C2×D412yes—
160C2×D244C2×D412yes—
161C2×D244C2×Q812yes—
162C2×D244C2×Q812yes—
163C2×C4×D61—24no—
164C2×C4×D61—24no—
165C2×C4×D61—42no—
166C2×C4×D61—42no—
167C2×C4×D61—42no—
168C2×C4×D61—42no—
169C2×C4×D61—42no—
170C2×C4×D61—42no—
171C2×C4×D61—42no—
172C2×C4×D61—42no—
173C2×C4×D61—42no—
174C2×C4×D61—42no—
175C2×C4×D61—81no—
176C2×C4×D61—81no—
177C2×C4×D61—81no—
178C2×C4×D61—81no—
179C2×C4×D61—81no—
180C2×C4×D61—81no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61C22×C412yes—
184C2×C8×C61C22×C412yes—
185C2×C8×C61C2×D412yes—
186C2×C8×C61C2×Q812yes—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—42no—
196C4⋊C4×C61—81no—
197C42×C61C22×C412yes—
198C42×C61#4112yes—
199#11758198—24no—
200#11758198—24no—
201#11758198—42no—
202#11758198—42no—
203#11758198—42no—
204#11758198—42no—
205C4⋊Dic61—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61—22no—
208C4⋊Dic61—41no—
209C4⋊Dic61C22×C412yes—
210C4⋊Dic61C22×C412yes—
211#11758196—42no—
212#11758196—42no—
213#11758196—81no—
214#11758196—81no—
215C4×Dic61—21no—
216C4×Dic61—21no—
217C4×Dic61—21no—
218C4×Dic61—21no—
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—21no—
224C2×#92418—21no—
225D488C4⋊C4116yescomplemented
226C23×C61C22×D411yescharacteristic
227C22×D61—22no—
228C22×D61—22no—
229C22×D61—22no—
230C22×D61—22no—
231C22×D61—22no—
232C22×D61—22no—
233C22×D61—41no—
234C22×D61—41no—
235C22×D61—41no—
236C22×D61—41no—
237C22×D61—41no—
238C22×D61—41no—
239C22×D61—41no—
240C22×D61—41no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61C4×D412yes—
258C2×C4×C61C4×D412yes—
259C2×C4×C61C23×C411yescharacteristic
260C2×C4×C61C22×D411yescharacteristic
261C2×C4×C61C22×Q811yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C2×C4×C61H(5,𝔽2)11yescharacteristic
264C2×C4×C612−1+411yescharacteristic
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—22no—
268C2×Dic61—22no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61AGL(1,ℤ/8)12yes—
283D244—22no—
284D244—22no—
285D244—22no—
286D244—22no—
287D244—22no—
288D244—22no—
289D244C2×C4⋊C414yes—
290D244C2×C4⋊C414yescomplemented
291C4×D61—48no—
292C4×D61—84no—
293C4×D61—84no—
294C4×D61—84no—
295C4×D61—84no—
296C4×D61—84no—
297C8×C61—22no—
298C8×C61C2×C4⋊C414yescomplemented
299#92418—41no—
300#92418—41no—
301#22676—611nomaximal, Sylow
302C22×C61C2×C4×D411yescharacteristic
303C22×C61D4211yescharacteristic
304C22×C61D4×Q811yescharacteristic
305C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
306C22×C61#57511yescharacteristic
307C22×C61#57611yescharacteristic
308C22×C61#57711yescharacteristic
309C2×D61—24no—
310C2×D61—24no—
311C2×D61—42no—
312C2×D61—42no—
313C2×D61—42no—
314C2×D61—42no—
315C2×D61—42no—
316C2×D61—42no—
317C2×D61—42no—
318C2×D61—42no—
319C2×D61—42no—
320C2×D61—42no—
321C2×D61—42no—
322C2×D61—42no—
323C4×C61—22no—
324C4×C61—22no—
325C4×C61—81no—
326C4×C61—81no—
327C4×C61—81no—
328C4×C61—81no—
329C4×C61C22×C4⋊C411yescharacteristic
330C4×C61#52011yescharacteristic
331C4×C61#54711yescharacteristic
332C4×C61#55411yescharacteristic
333Dic61—22no—
334Dic61—42no—
335Dic61—42no—
336Dic61—41no—
337Dic61—41no—
338Dic61—41no—
339C2×#442—611no—
340C2×#442—611no—
341C2×C4×D8—611no—
342#2349—611no—
343D4×C4⋊C4—611no—
344#1944—611no—
345#1941—611no—
346#1864—611no—
347#1864—611no—
348#1862—611no—
349#1862—611no—
350#1847D6111yescharacteristic, complemented
351#1804—611no—
352#1802—611no—
353#1771—611no—
354C2×C61D4×C4⋊C411yescharacteristic
355C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
356C2×C61#294611yescharacteristic
357C2×C61#326411yescharacteristic
358C2×C61#326711yescharacteristic
359C2×C61#338411yescharacteristic
360C2×C61#338911yescharacteristic
361D61—44no—
362D61—44no—
363C22×D8—611no—
364C2×C4×D4—611no—
365C2×C4×D4—611no—
366C2×C4×D4—611no—
367C2×C4×D4—611no—
368C2×C4×D4—611no—
369C2×C4×D4—611no—
370C22×C4⋊C4—1221no—
371#442—618no—
372#442—1224no—
373C4×D8—1224no—
374C2×#107C2×D6111yescharacteristic
375C2×#107C2×D6111yescharacteristic
376C2×#106—611no—
377C2×#106C2×D6111yescharacteristic
378C2×#106C2×D6111yescharacteristic
379C2×C4⋊C8—611no—
380C2×#102—611no—
381C2×#102—611no—
382C2×#102—611no—
383C2×#102—611no—
384C2×#102—611no—
385C2×#102—611no—
386C2×#97—611no—
387C2×#97C2×D6111yescharacteristic
388C2×C4×C8—611no—
389#389—611no—
390#389—611no—
391#389—611no—
392#389—611no—
393#385—1221no—
394#385—1221no—
395#385—1221no—
396#385—1221no—
397#384C2×D6111yescharacteristic
398#382C2×D6111yescharacteristic
399#380—1221no—
400#380—1221no—
401C4×C4⋊C4—611no—
402C2×#95—1221no—
403#340—611no—
404#340—611no—
405#340—611no—
406#340—611no—
407#336—611no—
408#336—611no—
409C61#2267611yescharacteristic, complemented, Sylow
410C22×D4—611no—
411C22×D4—611no—
412C23×C4—1221no—
413C23×C4—1221no—
414C23×C4—1221no—
415C23×C4—1221no—
416C23×C4—1221no—
417C23×C4—1221no—
418C2×D8—614no—
419C2×D8—614no—
420C2×D8—614no—
421C22×C8—611no—
422C22×C8—611no—
423C22×C8C22×D6111yescharacteristic
424C22×C8C22×D6111yescharacteristic
425C4×D4—614no—
426C4×D4—614no—
427C4×D4—1222no—
428C4×D4—1222no—
429C4×D4—1222no—
430C4×D4—1222no—
431C4×D4—1222no—
432C4×D4—1222no—
433C4×D4—2441no—
434C4×D4—2441no—
435C4×D4—2441no—
436C4×D4—2441no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—611no—
440C2×C4⋊C4—611no—
441C2×C4⋊C4—611no—
442C2×C4⋊C4—611no—
443C2×C4⋊C4—1221no—
444C2×C4⋊C4—1221no—
445C2×C4⋊C4—1221no—
446C2×C4⋊C4—1221no—
447C2×C4⋊C4—2444no—
448C2×C4⋊C4C22×D6111yescharacteristic
449C2×C4⋊C4C22×D6111yescharacteristic
450C2×C4⋊C4C22×D6111yescharacteristic
451C2×C4⋊C4C22×D6111yescharacteristic
452C2×C22⋊C4—1221no—
453C2×C22⋊C4—1221no—
454C2×C22⋊C4—1221no—
455C2×C22⋊C4—1221no—
456C2×C22⋊C4—1221no—
457C2×C22⋊C4—1221no—
458C2×C42—611no—
459C2×C42—611no—
460C2×C42C22×D6111yescharacteristic
461#107—22no—
462#107—41no—
463#106—22no—
464#106—41no—
465#106—614no—
466C4⋊C8—1222no—
467#102—614no—
468#102—614no—
469#102—1222no—
470#102—1222no—
471#102—1222no—
472#102—1222no—
473#97—1222no—
474#97C4×D6114yescomplemented
475C4×C8—1222no—
476#95—21no—
477#95—21no—
478#95—611no—
479#95—611no—
480#95—1221no—
481#95—1221no—
482#95—1221no—
483#95—1221no—
484C24—1221no—
485C24—1221no—
486C2×D4—612no—
487C2×D4—612no—
488C2×D4—612no—
489C2×D4—612no—
490C2×D4—612no—
491C2×D4—612no—
492C2×D4—1221no—
493C2×D4—1221no—
494C2×D4—1221no—
495C2×D4—1221no—
496C2×D4—1221no—
497C2×D4—1221no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—611no—
505C22×C4—611no—
506C22×C4—1221no—
507C22×C4—1221no—
508C22×C4—1224no—
509C22×C4—1224no—
510C22×C4—4881no—
511C22×C4—4881no—
512C22×C4—4881no—
513C22×C4—4881no—
514C22×C4—4881no—
515C22×C4—4881no—
516C22×C4—2442no—
517C22×C4—2442no—
518C22×C4—2442no—
519C22×C4—2442no—
520C22×C4—2442no—
521C22×C4—2442no—
522C22×C4—2442no—
523C22×C4—2442no—
524C22×C4—2442no—
525C22×C4—2442no—
526C22×C4D4×D6111yescharacteristic
527C22×C4D4×D6111yescharacteristic
528C22×C4C23×D6111yescharacteristic
529D8—6116no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—1221no—
533C2×C8—1221no—
534C2×C8—1221no—
535C2×C8—1221no—
536C2×C8—1221no—
537C2×C8—1221no—
538C2×C8C2×C4×D6112yes—
539C2×C8C2×C4×D6112yes—
540C2×C8D4×D6112yes—
541C2×C8Q8×D6112yes—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—42no—
551C4⋊C4—81no—
552C4⋊C4—612no—
553C4⋊C4—612no—
554C4⋊C4—1222no—
555C4⋊C4—1221no—
556C4⋊C4—1221no—
557C4⋊C4—4881no—
558C4⋊C4—4881no—
559C4⋊C4—2441no—
560C4⋊C4—2442no—
561C4⋊C4—2442no—
562C22⋊C4—1224no—
563C22⋊C4—1224no—
564C22⋊C4—2442no—
565C22⋊C4—2442no—
566C22⋊C4—2442no—
567C22⋊C4—2442no—
568C42—1221no—
569C42—1221no—
570C42—1221no—
571C42—1221no—
572C42C2×C4×D6112yes—
573C42#1175822612yes—
574C23—1222no—
575C23—1222no—
576C23—1222no—
577C23—1222no—
578C23—1222no—
579C23—1222no—
580C23—2441no—
581C23—2441no—
582C23—2441no—
583C23—2441no—
584C23—2441no—
585C23—2441no—
586C23—2441no—
587C23—2441no—
588C23C2×D4×D6111yescharacteristic
589D4—614no—
590D4—614no—
591D4—1222no—
592D4—1222no—
593D4—1222no—
594D4—1222no—
595D4—1222no—
596D4—1222no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—612no—
614C2×C4—1221no—
615C2×C4—1221no—
616C2×C4—1222no—
617C2×C4—1222no—
618C2×C4—1221no—
619C2×C4—1221no—
620C2×C4—1221no—
621C2×C4—1221no—
622C2×C4—1221no—
623C2×C4—1221no—
624C2×C4—1221no—
625C2×C4—1221no—
626C2×C4—1221no—
627C2×C4—4884no—
628C2×C4—4884no—
629C2×C4—4884no—
630C2×C4—4884no—
631C2×C4—4884no—
632C2×C4—2448no—
633C2×C4—2441no—
634C2×C4—2441no—
635C2×C4—2441no—
636C2×C4—2441no—
637C2×C4#1451973912yes—
638C2×C4#1451973912yes—
639C2×C4C22×C4×D6111yescharacteristic
640C2×C4C2×D4×D6111yescharacteristic
641C2×C4C2×Q8×D6111yescharacteristic
642C2×C4C2×#1175822611yescharacteristic
643C2×C4#1451982211yescharacteristic
644C2×C4#1451982511yescharacteristic
645C8—22no—
646C8—2441no—
647C8—2441no—
648C8C4⋊C4×D6114yescomplemented
649C22—1224no—
650C22—1224no—
651C22—2442no—
652C22—2442no—
653C22—2442no—
654C22—2442no—
655C22—2442no—
656C22—2442no—
657C22—2442no—
658C22—2442no—
659C22—2442no—
660C22—2442no—
661C22—2442no—
662C22—2442no—
663C22C2×#1451973911yescharacteristic
664C22#1684039711yescharacteristic
665C22#1684042711yescharacteristic
666C22AGL(1,ℤ/8)×D6111yescharacteristic
667C22#1684056111yescharacteristic
668C22#1684056611yescharacteristic
669C22#1684057111yescharacteristic
670C4—22no—
671C4—22no—
672C4—81no—
673C4—81no—
674C4—81no—
675C4—81no—
676C4—1222no—
677C4—2442no—
678C4—2442no—
679C4—2441no—
680C4—2441no—
681C4—2441no—
682C4C2×C4⋊C4×D6111yescharacteristic
683C4#1684024311yescharacteristic
684C4#1684041511yescharacteristic
685C4#1684047311yescharacteristic
686C2—2444no—
687C2—2444no—
688C2#2144871911yescharacteristic
689C2#2145462611yescharacteristic
690C2#2145464911yescharacteristic
691C2#2145729811yescharacteristic
692C2#2145734311yescharacteristic
693C2#2145871511yescharacteristic
694C2#2145877411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1847C2
socleC23×C61C22×D4
prime radicalC22×D488C22
cosocleC22×C4×C61C24
hypercenter#1847D61
hypocenterC61#22676
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
4. #21448727C2semidirect
5. #21448719C2semidirect
6. #21446560C2semidirect
7. #21446545C2semidirect
8. #21446077C2semidirect
9. #21446077C2semidirect
10. #21446063C2semidirect
11. #21446063C2semidirect
12. #21445826C2semidirect
13. #21445816C2semidirect
14. #21445691C2semidirect
15. C61×#1847C2semidirect
24. #16839875C4semidirect
77. C4×D244C2×C4semidirect
78. C4×D244C2×C4semidirect
104. #14519709C2×C4semidirect
106. #14519699C2×C4semidirect
107. #14519699C2×C4semidirect
133. #97×C61C2×C4semidirect
225. D488C4⋊C4semidirect
290. D244C2×C4⋊C4semidirect
298. C8×C61C2×C4⋊C4semidirect
350. #1847D61semidirect
409. C61#22676semidirect
474. #97C4×D61semidirect
648. C8C4⋊C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398752
C2×#168398732
C2×#168398442
#214487272
#214487192
#214465602
#214465452
#214460772
#214460632
#214458262
#214458162
#214456912
C61×#18472
#2267661