Finite Group Databasebeta

← #33103274

Subgroups — #33103274

Order 18688.

1038 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988586C211yesmaximal, characteristic
2#22612762C211yesmaximal, characteristic
3#22610620C211yesmaximal, characteristic, complemented
4#22610606C211yesmaximal, characteristic, complemented
5#22610572C211yesmaximal, characteristic, complemented
6#22610565C211yesmaximal, characteristic, complemented
7#22610191C211yesmaximal, characteristic, complemented
8#22610177C211yesmaximal, characteristic, complemented
9#22610021C211yesmaximal, characteristic, complemented
10#22609962C211yesmaximal, characteristic, complemented
11#22609869C211yesmaximal, characteristic
12#22609759C211yesmaximal, characteristic, complemented
13C4×#14556511C211yesmaximal, characteristic, complemented
14#22609715C211yesmaximal, characteristic, complemented
15C73×#2344C211yesmaximal, characteristic, complemented
16C22×#11924028C2211yescharacteristic
17C22×#11924012C2211yescharacteristic
18C2×C4×D292C2211yescharacteristic
19C2×C4×D292C2211yescharacteristic
20C2×#14556524C2211yescharacteristic
21C2×#14556522C2211yescharacteristic
22#17988586C418yescomplemented
23C2×#14556514C2211yescharacteristic
24C2×#14556514C2211yescharacteristic
25C2×#14556514C2211yescharacteristic
26C2×#14556514C2211yescharacteristic
27C2×#14556511C2211yescharacteristic
28C2×#14556511C2211yescharacteristic
29C2×#14556511C2211yescharacteristic
30C2×#14556511C2211yescharacteristic
31C2×C22⋊#10596831C2211yescharacteristic
32C2×#14556502C2211yescharacteristic
33C2×C4×#10596831C2211yescharacteristic
34#17988493C2211yescharacteristic
35#17988493C2211yescharacteristic
36#17988463—21no—
37#17988463—21no—
38#17988449—21no—
39#17988447C2211yescharacteristic
40#95×D73—21no—
41#17988349C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988342C2211yescharacteristic
48#17988342C2211yescharacteristic
49C2×#117×C73—21no—
50C22×C4⋊C4×C73C2211yescharacteristic
51#389×C73C2211yescharacteristic
52#389×C73C2211yescharacteristic
53#387×C73—21no—
54#387×C73—21no—
55#381×C73—21no—
56#380×C73C2211yescharacteristic
57C4×C4⋊C4×C73C2211yescharacteristic
58C4×C4⋊C4×C73C2211yescharacteristic
59C4×C22⋊C4×C73C2211yescharacteristic
60C2×#11924028—22no—
61C2×#11924028—22no—
62C2×#11924028—22no—
63C2×#11924028—41no—
64C2×#11924028—41no—
65C2×#11924028C2×C414yes—
66C22×Dic146C2311yescharacteristic
67C22×D292C2311yescharacteristic
68C22×C22⋊D73—21no—
69C22×C4×D73—21no—
70C22×C4×D73—21no—
71C22×C4×D73—21no—
72C2×#11924012—41no—
73C2×#11924012—41no—
74C2×#11924012C2×C414yescomplemented
75C22×#10596831C2311yescharacteristic
76C22×#10596831C2311yescharacteristic
77C22×#10596831C2311yescharacteristic
78C22×#10596831C2311yescharacteristic
79C4×D292—22no—
80C4×D292—22no—
81C4×D292—41no—
82C4×D292—41no—
83C2×C4⋊Dic73C2311yescharacteristic
84C2×C4⋊Dic73C2311yescharacteristic
85C2×C22⋊Dic73—21no—
86C2×#11924005—21no—
87C2×#11924005—21no—
88#14556524—41no—
89#14556522—41no—
90#14556514—41no—
91#14556514—41no—
92#14556514C2×C414yescomplemented
93#14556514C2×C414yescomplemented
94#14556511—22no—
95#14556511—22no—
96#14556511C2×C414yes—
97#14556511C2×C414yes—
98C22⋊#10596831—22no—
99#14556502—41no—
100C4×#10596831—41no—
101#14556498—21no—
102#14556498—21no—
103#14556498—21no—
104#14556498—21no—
105#14556498—21no—
106C23×C4×C73—21no—
107C23×C4×C73C2311yescharacteristic
108#117×C73—44no—
109C2×C4⋊C4×C73—21no—
110C2×C4⋊C4×C73—22no—
111C2×C4⋊C4×C73—21no—
112C2×C4⋊C4×C73—21no—
113C2×C4⋊C4×C73C2×C414yescomplemented
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C4⋊C4×C73C2311yescharacteristic
118C2×C22⋊C4×C73—21no—
119C2×C22⋊C4×C73D411yescharacteristic
120C2×C22⋊C4×C73D411yescharacteristic
121C2×C42×C73—21no—
122C2×C42×C73—21no—
123C2×C42×C73C2311yescharacteristic
124C2×C42×C73C2311yescharacteristic
125#95×C73—21no—
126#95×C73—21no—
127#95×C73—21no—
128#95×C73—21no—
129#95×C73—21no—
130#95×C73D411yescharacteristic
131#95×C73D411yescharacteristic
132C23×D73—21no—
133#11924028—28no—
134#11924028—44no—
135#11924028—44no—
136#11924028—44no—
137C2×Dic146—21no—
138C2×Dic146—21no—
139C2×Dic146—21no—
140C2×Dic146—21no—
141C2×Dic146—21no—
142C2×Dic146C22×C412yes—
143C2×D292—21no—
144C2×D292—21no—
145C2×D292—21no—
146C2×D292C22×C412yes—
147C2×D292#4112yes—
148C2×D292#4112yes—
149C2×C22⋊D73—24no—
150C2×C22⋊D73—42no—
151C2×C22⋊D73—42no—
152C22×Dic73—21no—
153C22×Dic73—21no—
154C22×Dic73—21no—
155C2×C4×D73—24no—
156C2×C4×D73—42no—
157C2×C4×D73—42no—
158C2×C4×D73—42no—
159C2×C4×D73—42no—
160C2×C4×D73—42no—
161C2×C4×D73—42no—
162C2×C4×D73—81no—
163C2×C4×D73—81no—
164#11924012—44no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831—21no—
175C2×#10596831C22×C412yes—
176C2×#10596831C22×C412yes—
177C4⋊Dic73—21no—
178C4⋊Dic73—21no—
179C4⋊Dic73—21no—
180C4⋊Dic73—21no—
181C22⋊Dic73—81no—
182#11924005—42no—
183#11924005—42no—
184C24×C73C2×D411yescharacteristic
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—24no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—42no—
195C22×C4×C73—42no—
196C22×C4×C73C22×C412yes—
197C22×C4×C73C2×D411yescharacteristic
198C22×C4×C73C2×D411yescharacteristic
199C22×C4×C73C2×D411yescharacteristic
200C22×C4×C73C2×D411yescharacteristic
201C22×C4×C73C2×D411yescharacteristic
202C22×C4×C73#4112yes—
203C22×C4×C73C2411yescharacteristic
204C4⋊C4×C73—24no—
205C4⋊C4×C73—21no—
206C4⋊C4×C73—21no—
207C4⋊C4×C73—21no—
208C4⋊C4×C73—21no—
209C4⋊C4×C73—21no—
210C4⋊C4×C73—21no—
211C4⋊C4×C73—42no—
212C4⋊C4×C73—42no—
213C4⋊C4×C73C22×C412yes—
214C4⋊C4×C73C22×C412yes—
215C22⋊C4×C73—22no—
216C22⋊C4×C73—41no—
217C22⋊C4×C73—42no—
218C42×C73—21no—
219C42×C73—21no—
220C42×C73—21no—
221C42×C73—21no—
222C42×C73—42no—
223C42×C73—42no—
224C23×C73—21no—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73C4×D412yes—
231C23×C73C22×D411yescharacteristic
232C22×D73—22no—
233C22×D73—22no—
234C22×D73—22no—
235C22×D73—41no—
236C22×D73—41no—
237C22×D73—41no—
238C22×D73—41no—
239C2×C4×C73—21no—
240C2×C4×C73—21no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—22no—
244C2×C4×C73—22no—
245C2×C4×C73—22no—
246C2×C4×C73—22no—
247C2×C4×C73—22no—
248C2×C4×C73—22no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—21no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—48no—
259C2×C4×C73—41no—
260C2×C4×C73—41no—
261C2×C4×C73—41no—
262C2×C4×C73—41no—
263C2×C4×C73—41no—
264C2×C4×C73—41no—
265C2×C4×C73—41no—
266C2×C4×C73—41no—
267C2×C4×C73—41no—
268C2×C4×C73—41no—
269C2×C4×C73C4×D412yes—
270C2×C4×C73AGL(1,ℤ/8)12yes—
271C2×C4×C73C23×C411yescharacteristic
272C2×C4×C73C2×#4111yescharacteristic
273C2×C4×C73C2×#4111yescharacteristic
274C2×C4×C73C2×#4111yescharacteristic
275C2×C4×C73H(5,𝔽2)11yescharacteristic
276C2×C4×C73H(5,𝔽2)11yescharacteristic
277C22⋊D73—48no—
278C2×Dic73—22no—
279C2×Dic73—41no—
280C2×Dic73—41no—
281C2×Dic73—41no—
282C2×Dic73—41no—
283C2×Dic73—41no—
284C2×Dic73—41no—
285C2×Dic73—41no—
286C2×Dic73—41no—
287D292—22no—
288D292—22no—
289D292—22no—
290D292#11714yescomplemented
291C4×D73—48no—
292C4×D73—84no—
293C4×D73—84no—
294Dic146—22no—
295Dic146—22no—
296Dic146—41no—
297Dic146—41no—
298#10596831—22no—
299#10596831—22no—
300#10596831—41no—
301#10596831—41no—
302C22×C73—22no—
303C22×C73—22no—
304C22×C73—22no—
305C22×C73—41no—
306C22×C73—41no—
307C22×C73—41no—
308C22×C73—41no—
309C22×C73C2×C4×D411yescharacteristic
310C22×C73#54611yescharacteristic
311C22×C73#54611yescharacteristic
312C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
313C22×C73#57511yescharacteristic
314C22×C73#57711yescharacteristic
315C22×C73#57811yescharacteristic
316C2×D73—24no—
317C2×D73—42no—
318C2×D73—42no—
319C2×D73—42no—
320C2×D73—42no—
321C2×D73—42no—
322C2×D73—42no—
323C4×C73—22no—
324C4×C73—22no—
325C4×C73—41no—
326C4×C73—42no—
327C4×C73—42no—
328C4×C73—41no—
329C4×C73—41no—
330C4×C73—81no—
331C4×C73—81no—
332C4×C73C2×#11711yescharacteristic
333C4×C73#51811yescharacteristic
334C4×C73#55111yescharacteristic
335C4×C73#55111yescharacteristic
336Dic73—42no—
337Dic73—81no—
338Dic73—81no—
339#22582—731nomaximal, Sylow
340C2×C73—42no—
341C2×C73#234211yescharacteristic
342C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
343C2×C73#294711yescharacteristic
344C2×C73#330611yescharacteristic
345C2×C73#331511yescharacteristic
346C2×C73#332311yescharacteristic
347C2×C73#333011yescharacteristic
348D73—44no—
349C2×#417—731no—
350#2344D7311yescharacteristic, complemented
351#2339—731no—
352#1935—731no—
353#1933—731no—
354#1928—731no—
355#1927—731no—
356#1864—731no—
357#1862—731no—
358#1824—731no—
359#1809—731no—
360#1788—731no—
361#1762—731no—
362C4×#102—731no—
363#1753—731no—
364C73#2258211yescharacteristic, complemented, Sylow
365C22×#41—731no—
366C22×M16—731no—
367C2×C4×D4—731no—
368C2×C4×D4—731no—
369C2×#117—21no—
370C22×C4⋊C4C2×D7311yescharacteristic
371C2×#107—731no—
372C2×#106—731no—
373#417—738no—
374C2×#103—731no—
375C2×#103—731no—
376C2×#103—731no—
377C2×#103—731no—
378C2×#102—731no—
379C2×#102—731no—
380C2×#102—731no—
381C2×#102—731no—
382C2×C22⋊C8—731no—
383C2×#97—731no—
384C2×C4×C8—731no—
385#391—731no—
386#391—731no—
387#389C2×D7311yescharacteristic
388#389C2×D7311yescharacteristic
389#387—21no—
390#387—21no—
391#386—1461no—
392#386—1461no—
393#381—21no—
394#381—1461no—
395#380—731no—
396#380C2×D7311yescharacteristic
397C4×C4⋊C4C2×D7311yescharacteristic
398C4×C4⋊C4C2×D7311yescharacteristic
399C4×C22⋊C4C2×D7311yescharacteristic
400C2×#95—1461no—
401#340—731no—
402#340—731no—
403#340—731no—
404#340—731no—
405#340—731no—
406#340—731no—
407#336—731no—
408#336—731no—
409C2×#41—2921no—
410C2×#41—2921no—
411C2×#41—734no—
412C2×#41—1462no—
413C2×#41—1462no—
414C2×#41—1462no—
415C22×Q8—731no—
416C22×D4—731no—
417C22×D4—1461no—
418C23×C4—21no—
419C23×C4—1461no—
420C23×C4—1461no—
421C23×C4—1461no—
422C23×C4C22×D7311yescharacteristic
423C2×M16—2921no—
424C2×M16—2921no—
425C2×M16—734no—
426C22×C8—731no—
427C22×C8—731no—
428C22×C8—731no—
429C22×C8—731no—
430C4×D4—2921no—
431C4×D4—2921no—
432C4×D4—1462no—
433C4×D4—1462no—
434#117—44no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—731no—
440C2×C4⋊C4—731no—
441C2×C4⋊C4C4×D7314yescomplemented
442C2×C4⋊C4C22×D7311yescharacteristic
443C2×C4⋊C4C22×D7311yescharacteristic
444C2×C4⋊C4C22×D7311yescharacteristic
445C2×C4⋊C4C22×D7311yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—1461no—
448C2×C22⋊C4—1461no—
449C2×C22⋊C4—1461no—
450C2×C22⋊C4C22⋊D7311yescharacteristic
451C2×C22⋊C4C22⋊D7311yescharacteristic
452C2×C42—21no—
453C2×C42—21no—
454C2×C42C22×D7311yescharacteristic
455C2×C42C22×D7311yescharacteristic
456#107—2921no—
457#106—2921no—
458#103—2921no—
459#103—2921no—
460#103—734no—
461#103—734no—
462#102—734no—
463#102—734no—
464#102—1462no—
465#102—1462no—
466C22⋊C8—1462no—
467#97—2921no—
468C4×C8—2921no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—1461no—
475#95—1461no—
476#95—1461no—
477#95—1461no—
478#95—1461no—
479#95C22⋊D7311yescharacteristic
480#95C22⋊D7311yescharacteristic
481C24—1461no—
482C24C2×C22⋊D7311yescharacteristic
483#41—2924no—
484#41—2924no—
485#41—2924no—
486#41—1468no—
487C2×Q8—732no—
488C2×Q8—1461no—
489C2×Q8—1461no—
490C2×Q8—1461no—
491C2×Q8—1461no—
492C2×Q8—1461no—
493C2×D4—2922no—
494C2×D4—2922no—
495C2×D4—732no—
496C2×D4—732no—
497C2×D4—732no—
498C2×D4—1464no—
499C2×D4—1461no—
500C2×D4—1461no—
501C2×D4—1461no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—24no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—2922no—
514C22×C4—2922no—
515C22×C4—2922no—
516C22×C4—2922no—
517C22×C4—2922no—
518C22×C4—2922no—
519C22×C4—5841no—
520C22×C4—5841no—
521C22×C4—1461no—
522C22×C4—1461no—
523C22×C4—1461no—
524C22×C4—1464no—
525C22×C4C2×C4×D7312yes—
526C22×C4C2×C22⋊D7311yescharacteristic
527C22×C4C2×C22⋊D7311yescharacteristic
528C22×C4C2×C22⋊D7311yescharacteristic
529C22×C4C2×C22⋊D7311yescharacteristic
530C22×C4C2×C22⋊D7311yescharacteristic
531C22×C4#1192402812yes—
532C22×C4C23×D7311yescharacteristic
533M16—2924no—
534C2×C8—732no—
535C2×C8—732no—
536C2×C8—1461no—
537C2×C8—1461no—
538C2×C8—1461no—
539C2×C8—1461no—
540C2×C8—1461no—
541C2×C8—1461no—
542C2×C8—1461no—
543C2×C8—1461no—
544C2×C8—1461no—
545C2×C8—1461no—
546C4⋊C4—24no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—1461no—
556C4⋊C4—1461no—
557C4⋊C4—1461no—
558C4⋊C4—1461no—
559C4⋊C4C2×C4×D7312yes—
560C4⋊C4C2×C4×D7312yes—
561C22⋊C4—22no—
562C22⋊C4—41no—
563C22⋊C4—42no—
564C22⋊C4—2922no—
565C22⋊C4—2922no—
566C22⋊C4—5841no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—42no—
572C42—42no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—2921no—
580C23—2921no—
581C23—2921no—
582C23—2921no—
583C23—1462no—
584C23—1462no—
585C23—1462no—
586C23C4×C22⋊D7312yes—
587C23C22×C22⋊D7311yescharacteristic
588Q8—2921no—
589Q8—2921no—
590Q8—1462no—
591Q8—1462no—
592D4—2928no—
593D4—734no—
594D4—1462no—
595D4—1462no—
596D4—1462no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—48no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—2928no—
628C2×C4—2921no—
629C2×C4—2921no—
630C2×C4—2921no—
631C2×C4—2921no—
632C2×C4—2921no—
633C2×C4—2921no—
634C2×C4—2921no—
635C2×C4—2921no—
636C2×C4—5844no—
637C2×C4—5844no—
638C2×C4—1462no—
639C2×C4C4×C22⋊D7312yes—
640C2×C4#1455661712yes—
641C2×C4C22×C4×D7311yescharacteristic
642C2×C4#41×D7311yescharacteristic
643C2×C4#41×D7311yescharacteristic
644C2×C4C2×#1192402811yescharacteristic
645C2×C4#1455663711yescharacteristic
646C2×C4#1455663711yescharacteristic
647C8—2921no—
648C8—2921no—
649C8—1462no—
650C8—1462no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—41no—
658C22—2922no—
659C22—2922no—
660C22—2922no—
661C22—2922no—
662C22—2922no—
663C22—2922no—
664C22—1464no—
665C22C2×C4×C22⋊D7311yescharacteristic
666C22#1798922511yescharacteristic
667C22#1798922511yescharacteristic
668C22C2×#1455661711yescharacteristic
669C22#1798938511yescharacteristic
670C22#1798939511yescharacteristic
671C22#1798940211yescharacteristic
672C4—22no—
673C4—22no—
674C4—41no—
675C4—41no—
676C4—42no—
677C4—42no—
678C4—41no—
679C4—81no—
680C4—81no—
681C4—2922no—
682C4—5841no—
683C4—5841no—
684C4#117×D7311yescharacteristic
685C4#1798906111yescharacteristic
686C4#1798926111yescharacteristic
687C4#1798926111yescharacteristic
688C2—42no—
689C2—2924no—
690C2#2261278111yescharacteristic
691C2C4×#1455661711yescharacteristic
692C2#2261877411yescharacteristic
693C2#2262188611yescharacteristic
694C2#2262202111yescharacteristic
695C2#2262214111yescharacteristic
696C2#2262223011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2344C2
socleC23×C73C22×D4
prime radicalC22×#11924028C22
cosocleC22×C4×C73C24
hypercenter#2344D73
hypocenterC73#22582
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2344

Complements

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

NH ≅ G/Ntype
3. #22610620C2semidirect
4. #22610606C2semidirect
5. #22610572C2semidirect
6. #22610565C2semidirect
7. #22610191C2semidirect
8. #22610177C2semidirect
9. #22610021C2semidirect
10. #22609962C2semidirect
12. #22609759C2semidirect
13. C4×#14556511C2semidirect
14. #22609715C2semidirect
15. C73×#2344C2semidirect
22. #17988586C4semidirect
74. C2×#11924012C2×C4semidirect
92. #14556514C2×C4semidirect
93. #14556514C2×C4semidirect
113. C2×C4⋊C4×C73C2×C4semidirect
290. D292#117semidirect
350. #2344D73semidirect
364. C73#22582semidirect
441. C2×C4⋊C4C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179885862
#226127622
#226106202
#226106062
#226105722
#226105652
#226101912
#226101772
#226100212
#226099622
#226098692
#226097592
C4×#145565112
#226097152
C73×#23442
#2258273