Finite Group Databasebeta

← #25101239

Subgroups — #25101239

Order 11008.

1202 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583451C211yesmaximal, characteristic
2#19136997C211yesmaximal, characteristic
3C4×#13063281C211yesmaximal, characteristic
4#19135581C211yesmaximal, characteristic
5#19135580C211yesmaximal, characteristic
6#19135579C211yesmaximal, characteristic
7#19135578C214yesmaximal
8#19134326C214yesmaximal
9C43×#1996C211yesmaximal, characteristic
10#14583451—21no—
11#14583451—21no—
12#14583451—21no—
13#14583451—21no—
14#14583451—21no—
15#14583451—21no—
16#14583451—21no—
17#14583451—21no—
18C2×#13063324C411yescharacteristic, complemented
19C2×#13063323C411yescharacteristic, complemented
20C2×#13063315C412yescomplemented
21C2×#13063304C2211yescharacteristic
22C2×#13063302C2212yes—
23C2×Q8×Dic43C411yescharacteristic, complemented
24C2×#13063290C412yescomplemented
25C2×#13063290C411yescharacteristic, complemented
26C2×#13063281C2212yes—
27C2×#13063281C2212yes—
28C2×#13063281C2212yes—
29C22×C4×Dic43C2211yescharacteristic
30#14582768—21no—
31#14582763—21no—
32#14582759C2211yescharacteristic
33#14582757C2212yes—
34C4⋊C4×Dic43—21no—
35C4×Dic43⋊C4—21no—
36#14582750—21no—
37#14582750—21no—
38C22⋊C4×Dic43C2212yes—
39C4×C22⋊Dic43C2211yescharacteristic
40#14582744—21no—
41C42×Dic43—21no—
42#14582666C2214yes—
43#14582665C2214yes—
44#14582665C2214yes—
45C2×C22⋊Q8×C43C2211yescharacteristic
46C43×#380C2211yescharacteristic
47C4×C22⋊C4×C43C2211yescharacteristic
48C43×#342C2214yes—
49C22×Dic86C2×C412yes—
50C22×Dic86C2×C411yescharacteristic
51C23×Dic43C2311yescharacteristic
52C23×Dic43C2311yescharacteristic
53#13063324—21no—
54#13063324—21no—
55#13063324—21no—
56#13063324—21no—
57#13063323—21no—
58#13063323—21no—
59#13063323—21no—
60#13063323—21no—
61#13063315—22no—
62#13063315—22no—
63#13063315—22no—
64#13063315—22no—
65#13063304—21no—
66#13063304—21no—
67#13063304—21no—
68#13063304—21no—
69#13063302—22no—
70#13063302—22no—
71#13063302—22no—
72#13063302—22no—
73Q8×Dic43—21no—
74Q8×Dic43—21no—
75Q8×Dic43—21no—
76Q8×Dic43—21no—
77#13063290—21no—
78#13063290—21no—
79#13063290—21no—
80#13063290—21no—
81#13063290—22no—
82#13063290—22no—
83#13063290—22no—
84#13063290—22no—
85#13063281—22no—
86#13063281—22no—
87#13063281—22no—
88#13063281—22no—
89#13063281—24no—
90#13063281—28no—
91#13063281Q818yescomplemented
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43C2×C412yes—
94C2×C4⋊Dic43C2×C411yescharacteristic
95C2×Dic43⋊C4—22no—
96C2×Dic43⋊C4—22no—
97C2×Dic43⋊C4—22no—
98C2×Dic43⋊C4C2×C412yes—
99C2×Dic43⋊C4C2×C412yes—
100C2×Dic43⋊C4C2×C412yes—
101C2×Dic43⋊C4C2×C412yes—
102C2×Dic43⋊C4C2×C412yes—
103C2×C22⋊Dic43C2312yes—
104C2×C22⋊Dic43C2312yes—
105C2×C22⋊Dic43C2312yes—
106C2×C4×Dic43—22no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43—22no—
109C2×C4×Dic43—22no—
110C2×C4×Dic43C2×C412yes—
111C2×C4×Dic43C2×C412yes—
112C2×C4×Dic43C2×C411yescharacteristic
113C2×C4×Dic43C2×C411yescharacteristic
114C2×C4×Dic43C2×C411yescharacteristic
115C2×C4×Dic43C2×C411yescharacteristic
116C2×C4×Dic43D411yescharacteristic
117C2×C4×Dic43D411yescharacteristic
118C2×C4×Dic43D411yescharacteristic
119C2×C4×Dic43D411yescharacteristic
120C2×C4×Dic43D411yescharacteristic
121C2×C4×Dic43D411yescharacteristic
122C2×C4×Dic43D411yescharacteristic
123C2×C4×Dic43D411yescharacteristic
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C22×Q8×C43C2×C411yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43—21no—
132C22⋊Q8×C43—21no—
133C22⋊Q8×C43—21no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43C2×C412yes—
136C2×C4⋊C4×C43C2×C411yescharacteristic
137C2×C22⋊C4×C43C2312yes—
138C2×C22⋊C4×C43C2312yes—
139C2×C22⋊C4×C43C2312yes—
140C2×C42×C43—21no—
141#95×C43—21no—
142#95×C43—21no—
143C24×C43C2411yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—42no—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—42no—
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C22×C412yes—
152C22×C4×C43C22×C412yes—
153C22×C4×C43C22×C411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—42no—
161C22×Dic43C22×C411yescharacteristic
162C22×Dic43C22×C412yes—
163C22×Dic43C22×C412yes—
164C22×Dic43C22×C411yescharacteristic
165C22×Dic43C22×C411yescharacteristic
166C22×Dic43C22×C411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175C22×Dic43C2×Q814yes—
176C22×Dic43#4114yes—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—22no—
180C2×Dic86—22no—
181C2×Dic86—44no—
182C2×Dic86—42no—
183C4⋊C4×C43—22no—
184C4⋊C4×C43—22no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—42no—
188C22⋊C4×C43—22no—
189C22⋊C4×C43—22no—
190C22⋊C4×C43—22no—
191C22⋊C4×C43—24no—
192C22⋊C4×C43C2×Q814yes—
193C42×C43—42no—
194C22⋊Dic43—22no—
195C22⋊Dic43—22no—
196C22⋊Dic43—22no—
197C22⋊Dic43—24no—
198C22⋊Dic43C2×Q814yes—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—22no—
202C4⋊Dic43—22no—
203C4⋊Dic43—42no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212Dic43⋊C4—22no—
213Dic43⋊C4—22no—
214Dic43⋊C4—28no—
215Dic43⋊C4—44no—
216Dic43⋊C4—44no—
217C4×Dic43—22no—
218C4×Dic43—22no—
219C4×Dic43—22no—
220C4×Dic43—22no—
221C4×Dic43—28no—
222C4×Dic43—44no—
223C4×Dic43—42no—
224C4×Dic43—44no—
225C4×Dic43C22⋊C411yescharacteristic
226C4×Dic43C22⋊C411yescharacteristic
227C4×Dic43C22⋊C411yescharacteristic
228C4×Dic43C22⋊C411yescharacteristic
229C4×Dic43C22⋊C411yescharacteristic
230C4×Dic43C22⋊C411yescharacteristic
231C4×Dic43C22⋊C411yescharacteristic
232C4×Dic43C22⋊C411yescharacteristic
233C4×Dic43C22⋊C411yescharacteristic
234C4×Dic43C22⋊C411yescharacteristic
235C4×Dic43C22⋊C411yescharacteristic
236C4×Dic43C22⋊C411yescharacteristic
237C4×Dic43C22⋊C411yescharacteristic
238C4×Dic43C22⋊C411yescharacteristic
239C4×Dic43C22⋊C411yescharacteristic
240C4×Dic43C22⋊C411yescharacteristic
241C23×C43—41no—
242C23×C43—41no—
243C23×C43C23×C411yescharacteristic
244C23×C43C22×D411yescharacteristic
245C23×C43C22×D411yescharacteristic
246C23×C43C22×Q812yes—
247C23×C43C2×#4112yes—
248Q8×C43—42no—
249Q8×C43—42no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—22no—
254C2×C4×C43—22no—
255C2×C4×C43—24no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—42no—
260C2×C4×C43—42no—
261C2×C4×C43—42no—
262C2×C4×C43—42no—
263C2×C4×C43—42no—
264C2×C4×C43—42no—
265C2×C4×C43—42no—
266C2×C4×C43C2×C22⋊C411yescharacteristic
267C2×C4×C43C2×C22⋊C411yescharacteristic
268C2×C4×C43C2×C22⋊C411yescharacteristic
269C2×C4×C43C2×C22⋊C411yescharacteristic
270C2×Dic43—22no—
271C2×Dic43—22no—
272C2×Dic43—22no—
273C2×Dic43—22no—
274C2×Dic43—22no—
275C2×Dic43—24no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—42no—
280C2×Dic43—42no—
281C2×Dic43—42no—
282C2×Dic43—42no—
283C2×Dic43—42no—
284C2×Dic43—42no—
285C2×Dic43—42no—
286C2×Dic43C2×C22⋊C411yescharacteristic
287C2×Dic43C2×C22⋊C411yescharacteristic
288C2×Dic43C2×C22⋊C411yescharacteristic
289C2×Dic43C2×C22⋊C411yescharacteristic
290C2×Dic43C2×C22⋊C411yescharacteristic
291C2×Dic43C2×C22⋊C411yescharacteristic
292C2×Dic43C2×C22⋊C411yescharacteristic
293C2×Dic43C2×C22⋊C411yescharacteristic
294C2×Dic43C4×Q814yes—
295C2×Dic43C4×Q814yes—
296C2×Dic43C22⋊Q814yes—
297C2×Dic43C22⋊Q814yes—
298C2×Dic43#12412yes—
299C2×Dic43#12412yes—
300C2×Dic43C4⋊Q812yes—
301C2×Dic43C4⋊Q812yes—
302Dic86—44no—
303Dic86—42no—
304Dic86—42no—
305Dic86—44no—
306#21332—431nomaximal, Sylow
307C22×C43—21no—
308C22×C43—21no—
309C22×C43—21no—
310C22×C43—21no—
311C22×C43—21no—
312C22×C43—21no—
313C22×C43—42no—
314C22×C43—42no—
315C22×C43C22×C22⋊C411yescharacteristic
316C22×C43C2×C4×Q812yes—
317C22×C43C2×C22⋊Q812yes—
318C22×C43C2×#12411yescharacteristic
319C22×C43C2×C4⋊Q811yescharacteristic
320C4×C43—21no—
321C4×C43—21no—
322C4×C43—21no—
323C4×C43—44no—
324C4×C43—42no—
325C4×C43—42no—
326C4×C43—82no—
327C4×C43#41012yes—
328Dic43—21no—
329Dic43—21no—
330Dic43—21no—
331Dic43—44no—
332Dic43—42no—
333Dic43—42no—
334Dic43—82no—
335Dic43#39112yes—
336Dic43#39112yes—
337Dic43#39112yes—
338Dic43#39112yes—
339Dic43#41012yes—
340C2×#533—431no—
341#2285—431no—
342C4×#117—431no—
343#1996—431no—
344#1996—431no—
345#1996—434no—
346#1996—431no—
347#1996D4311yescharacteristic
348#1740—434no—
349C2×C43—22no—
350C2×C43—21no—
351C2×C43—22no—
352C2×C43—21no—
353C2×C43C2×#39111yescharacteristic
354C2×C43C2×#41011yescharacteristic
355C2×C43C2×#41011yescharacteristic
356#533—861no—
357#533—861no—
358#533—861no—
359#533—861no—
360#533—861no—
361#533—861no—
362#533—861no—
363#533—861no—
364C2×C4⋊Q8—431no—
365C2×C4⋊Q8—431no—
366C2×#125—432no—
367C2×C22⋊Q8—431no—
368C2×C22⋊Q8—432no—
369C2×C22⋊Q8C2×D4311yescharacteristic
370C2×C4×Q8—431no—
371C2×C4×Q8—431no—
372C2×C4×Q8—432no—
373C2×#117—432no—
374C2×#117—432no—
375C2×#117—432no—
376C22×C42—431no—
377#384—861no—
378#382—861no—
379#380—431no—
380#380—432no—
381#380C2×D4311yescharacteristic
382C4×C4⋊C4—861no—
383C4×C4⋊C4—861no—
384C4×C4⋊C4—861no—
385C4×C4⋊C4—861no—
386C4×C22⋊C4—431no—
387C4×C22⋊C4—432no—
388C4×C22⋊C4C2×D4311yescharacteristic
389#376—861no—
390C43—861no—
391#342—434no—
392#342—434no—
393#342—434no—
394#342C2×D4314yes—
395C43#2133211yescharacteristic, complemented, Sylow
396C22×Q8—432no—
397C22×Q8—431no—
398C22×Q8C4×D4311yescharacteristic
399C23×C4—431no—
400C23×C4—431no—
401C23×C4C22×D4311yescharacteristic
402C4⋊Q8—861no—
403C4⋊Q8—861no—
404C4⋊Q8—861no—
405C4⋊Q8—861no—
406C4⋊Q8—861no—
407C4⋊Q8—861no—
408C4⋊Q8—861no—
409C4⋊Q8—861no—
410#125—862no—
411#125—862no—
412#125—862no—
413#125—862no—
414C22⋊Q8—21no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8—21no—
418C22⋊Q8—862no—
419C22⋊Q8—862no—
420C22⋊Q8—862no—
421C22⋊Q8—862no—
422C22⋊Q8—861no—
423C22⋊Q8—861no—
424C22⋊Q8—861no—
425C22⋊Q8—861no—
426C4×Q8—862no—
427C4×Q8—862no—
428C4×Q8—862no—
429C4×Q8—862no—
430C4×Q8—861no—
431C4×Q8—861no—
432C4×Q8—861no—
433C4×Q8—861no—
434C4×Q8—861no—
435C4×Q8—861no—
436C4×Q8—861no—
437C4×Q8—861no—
438#117—438no—
439#117—862no—
440#117—862no—
441#117—862no—
442#117—862no—
443#117—864no—
444#117—868no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—432no—
447C2×C4⋊C4—432no—
448C2×C4⋊C4—432no—
449C2×C4⋊C4—432no—
450C2×C4⋊C4—432no—
451C2×C4⋊C4—432no—
452C2×C4⋊C4—431no—
453C2×C4⋊C4—862no—
454C2×C4⋊C4—862no—
455C2×C4⋊C4—862no—
456C2×C4⋊C4—861no—
457C2×C4⋊C4C4×D4312yes—
458C2×C4⋊C4C4×D4311yescharacteristic
459C2×C22⋊C4—432no—
460C2×C22⋊C4—432no—
461C2×C22⋊C4—432no—
462C2×C22⋊C4C22×D4312yes—
463C2×C22⋊C4C22×D4312yes—
464C2×C22⋊C4C22×D4312yes—
465C2×C42—21no—
466C2×C42—431no—
467C2×C42—431no—
468C2×C42—431no—
469C2×C42—431no—
470C2×C42—431no—
471C2×C42—431no—
472C2×C42—431no—
473C2×C42—431no—
474C2×C42—431no—
475C2×C42—431no—
476C2×C42—431no—
477C2×C42—431no—
478C2×C42—432no—
479C2×C42—432no—
480C2×C42—862no—
481C2×C42—862no—
482C2×C42—862no—
483C2×C42—861no—
484#95—21no—
485#95—21no—
486#95—862no—
487#95—862no—
488#95—861no—
489#95—861no—
490C24C23×D4311yescharacteristic
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—42no—
494C2×Q8—862no—
495C2×Q8—862no—
496C2×Q8—861no—
497C2×Q8—861no—
498C2×Q8—1722no—
499C2×Q8—1724no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—42no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—431no—
506C22×C4—431no—
507C22×C4—431no—
508C22×C4—431no—
509C22×C4—434no—
510C22×C4—434no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—432no—
518C22×C4—432no—
519C22×C4—862no—
520C22×C4—862no—
521C22×C4—1722no—
522C22×C4C2×C4×D4311yescharacteristic
523C22×C4C2×C4×D4312yes—
524C22×C4C2×C4×D4312yes—
525C22×C4C2×C4×D4311yescharacteristic
526C22×C4D4×D4311yescharacteristic
527C22×C4D4×D4311yescharacteristic
528C22×C4D4×D4311yescharacteristic
529C22×C4D4×D4311yescharacteristic
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—42no—
535C4⋊C4—862no—
536C4⋊C4—862no—
537C4⋊C4—862no—
538C4⋊C4—862no—
539C4⋊C4—862no—
540C4⋊C4—862no—
541C4⋊C4—862no—
542C4⋊C4—862no—
543C4⋊C4—862no—
544C4⋊C4—862no—
545C4⋊C4—868no—
546C4⋊C4—862no—
547C4⋊C4—862no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—1722no—
551C4⋊C4—1724no—
552C4⋊C4—1724no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—24no—
557C22⋊C4—434no—
558C22⋊C4—862no—
559C22⋊C4—862no—
560C22⋊C4—862no—
561C22⋊C4—864no—
562C22⋊C4Q8×D4314yes—
563C42—42no—
564C42—431no—
565C42—431no—
566C42—431no—
567C42—431no—
568C42—431no—
569C42—431no—
570C42—431no—
571C42—431no—
572C42—431no—
573C42—431no—
574C42—431no—
575C42—431no—
576C42—431no—
577C42—431no—
578C42—431no—
579C42—431no—
580C42—862no—
581C42—862no—
582C42—862no—
583C42—862no—
584C42—868no—
585C42—1722no—
586C42—1724no—
587C42—1724no—
588C23—41no—
589C23—41no—
590C23C22×C4×D4311yescharacteristic
591C23C2×D4×D4311yescharacteristic
592C23C2×D4×D4311yescharacteristic
593C23C2×Q8×D4312yes—
594C23#41×D4312yes—
595Q8—42no—
596Q8—42no—
597Q8—1722no—
598Q8—1724no—
599Q8—1724no—
600Q8—1722no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—24no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—431no—
618C2×C4—431no—
619C2×C4—431no—
620C2×C4—431no—
621C2×C4—431no—
622C2×C4—434no—
623C2×C4—434no—
624C2×C4—434no—
625C2×C4—434no—
626C2×C4—432no—
627C2×C4—432no—
628C2×C4—432no—
629C2×C4—432no—
630C2×C4—431no—
631C2×C4—431no—
632C2×C4—431no—
633C2×C4—862no—
634C2×C4—862no—
635C2×C4—862no—
636C2×C4—862no—
637C2×C4—862no—
638C2×C4—864no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1722no—
643C2×C4—1722no—
644C2×C4—1722no—
645C2×C4—1722no—
646C2×C4—1722no—
647C2×C4—1722no—
648C2×C4—1722no—
649C2×C4C22⋊C4×D4311yescharacteristic
650C2×C4C22⋊C4×D4311yescharacteristic
651C2×C4C22⋊C4×D4311yescharacteristic
652C2×C4C22⋊C4×D4311yescharacteristic
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—42no—
660C22—42no—
661C22C2×C22⋊C4×D4311yescharacteristic
662C22C4×Q8×D4312yes—
663C22C22⋊Q8×D4312yes—
664C22#124×D4311yescharacteristic
665C22C4⋊Q8×D4311yescharacteristic
666C4—21no—
667C4—21no—
668C4—21no—
669C4—44no—
670C4—42no—
671C4—42no—
672C4—82no—
673C4—432no—
674C4—432no—
675C4—432no—
676C4—432no—
677C4—432no—
678C4—861no—
679C4—861no—
680C4—861no—
681C4—3442no—
682C4—1724no—
683C4—1722no—
684C4—1722no—
685C4#1458287112yes—
686C2—22no—
687C2—21no—
688C2—22no—
689C2—21no—
690C2#391×D4311yescharacteristic
691C2#410×D4311yescharacteristic
692C2C2×#1458287111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1996C2
socleC22×C43C22×C22⋊C4
prime radical, cosocleC24×C43C24
hypercenter#1996D43
hypocenterC43#21332
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
18. C2×#13063324C4semidirect
19. C2×#13063323C4semidirect
20. C2×#13063315C4semidirect
23. C2×Q8×Dic43C4semidirect
24. C2×#13063290C4semidirect
25. C2×#13063290C4semidirect
91. #13063281Q8semidirect
395. C43#21332semidirect

Maximal subgroups

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

subgroupindex
C2×#145834512
#191369972
C4×#130632812
#191355812
#191355802
#191355792
#191355782
#191343262
C43×#19962
#2133243