Finite Group Databasebeta

← #33093009

Subgroups — #33093009

Order 18688.

924 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988662C211yesmaximal, characteristic
2C2×C4×#11924011C211yesmaximal, characteristic, complemented
3C4×#14556573C211yesmaximal, characteristic
4#22610541C211yesmaximal, characteristic, complemented
5#22610496C211yesmaximal, characteristic, complemented
6#22610488C211yesmaximal, characteristic, complemented
7#22610225C211yesmaximal, characteristic
8#22610112C211yesmaximal, characteristic, complemented
9#22609998C211yesmaximal, characteristic, complemented
10#22609808C211yesmaximal, characteristic, complemented
11#22609792C211yesmaximal, characteristic, complemented
12#22609717C211yesmaximal, characteristic, complemented
13#22609715C211yesmaximal, characteristic, complemented
14#22609713C211yesmaximal, characteristic, complemented
15C73×#1923C211yesmaximal, characteristic, complemented
16C22×#11924012C2211yescharacteristic
17C22×#11924011C2211yescharacteristic
18C22×#11924011C2211yescharacteristic
19C2×#14556573C411yescharacteristic
20C2×C4×C22⋊D73C2211yescharacteristic
21C2×C42×D73C2211yescharacteristic
22#17988662—24no—
23C2×#14556520C2211yescharacteristic
24C2×#14556520C2211yescharacteristic
25C2×C22⋊#10596831C2211yescharacteristic
26C2×#14556503C2211yescharacteristic
27C2×#14556503C2211yescharacteristic
28C4×#11924011—24no—
29C2×#14556502C2211yescharacteristic
30C2×#14556501C2211yescharacteristic
31C2×#14556501C2211yescharacteristic
32C2×C4×#10596831C2211yescharacteristic
33C2×C8×Dic73C2211yescharacteristic
34C2×C8×Dic73C2211yescharacteristic
35#17988481C411yescharacteristic
36#17988480C411yescharacteristic
37#17988470C411yescharacteristic
38#17988469C411yescharacteristic
39#17988463C411yescharacteristic
40#17988461C411yescharacteristic
41#17988449C411yescharacteristic
42C4×#11924007C2211yescharacteristic
43C4×C4⋊Dic73C2211yescharacteristic
44C4×#11924005C2211yescharacteristic
45C4×C22⋊Dic73C2211yescharacteristic
46#17988342C2211yescharacteristic
47#17988342C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54C2×C4⋊C8×C73C2211yescharacteristic
55C2×C22⋊C8×C73C2211yescharacteristic
56C2×C22⋊C8×C73C2211yescharacteristic
57C2×C4×C8×C73C2211yescharacteristic
58C4×C22⋊C4×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×C22⋊D73C2×C411yescharacteristic
62C22×C4×D73C2×C411yescharacteristic
63C22×C4×D73C2×C411yescharacteristic
64C22×C4×D73C2311yescharacteristic
65C2×#11924012—22no—
66C2×#11924012—22no—
67C2×#11924012—22no—
68C2×#11924011—22no—
69C2×#11924011—22no—
70C2×#11924011—22no—
71C2×#11924011—22no—
72C2×#11924011—22no—
73C2×#11924011D414yes—
74C22×#10596831C2311yescharacteristic
75C22×#10596831C2311yescharacteristic
76C22×#10596831C2311yescharacteristic
77C22×#10596831C2311yescharacteristic
78#14556573—24no—
79C4×C22⋊D73—22no—
80C4×C22⋊D73—22no—
81C2×C4⋊Dic73C2×C411yescharacteristic
82C2×C4⋊Dic73C2×C411yescharacteristic
83C2×#11924007C2×C411yescharacteristic
84C2×#11924007C2×C411yescharacteristic
85C2×#11924007C2×C411yescharacteristic
86C2×C22⋊Dic73C2×C411yescharacteristic
87C2×C22⋊Dic73C2×C411yescharacteristic
88C2×C22⋊Dic73C2×C411yescharacteristic
89C2×#11924005C2×C411yescharacteristic
90C2×#11924005C2×C411yescharacteristic
91C2×#11924005C2×C411yescharacteristic
92C2×C4×Dic73C2×C411yescharacteristic
93C2×C4×Dic73C2×C411yescharacteristic
94C2×C4×Dic73C2311yescharacteristic
95C2×C4×Dic73C2311yescharacteristic
96C2×C4×Dic73C2311yescharacteristic
97C42×D73—22no—
98C42×D73—22no—
99#14556520—22no—
100#14556520—22no—
101C22⋊#10596831—22no—
102#14556503—22no—
103#14556503—22no—
104#14556502—22no—
105#14556501—22no—
106#14556501—22no—
107C4×#10596831—22no—
108C8×Dic73—22no—
109C8×Dic73—22no—
110#14556498C2×C411yescharacteristic
111#14556498C2×C411yescharacteristic
112#14556498C2×C411yescharacteristic
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118C23×C4×C73C2311yescharacteristic
119C22×C8×C73C2311yescharacteristic
120C22×C8×C73C2311yescharacteristic
121C22×C8×C73C2311yescharacteristic
122C22×C8×C73C2311yescharacteristic
123C2×C22⋊C4×C73C2×C411yescharacteristic
124C2×C22⋊C4×C73C2×C411yescharacteristic
125C2×C42×C73C2311yescharacteristic
126C2×C42×C73C2311yescharacteristic
127C4⋊C8×C73—22no—
128C22⋊C8×C73—22no—
129C22⋊C8×C73—22no—
130C4×C8×C73—22no—
131#95×C73C2×C411yescharacteristic
132#95×C73C2×C411yescharacteristic
133C23×D73C22×C411yescharacteristic
134C2×C22⋊D73—22no—
135C2×C22⋊D73—22no—
136C2×C22⋊D73—41no—
137C22×Dic73C22×C411yescharacteristic
138C22×Dic73C22×C411yescharacteristic
139C22×Dic73C22×C411yescharacteristic
140C22×Dic73C22×C411yescharacteristic
141C22×Dic73C22×C411yescharacteristic
142C22×Dic73C22×C411yescharacteristic
143C22×Dic73C22×C411yescharacteristic
144C2×C4×D73—21no—
145C2×C4×D73—21no—
146C2×C4×D73—21no—
147C2×C4×D73—21no—
148C2×C4×D73—22no—
149C2×C4×D73—22no—
150C2×C4×D73—22no—
151C2×C4×D73—22no—
152C2×C4×D73—41no—
153C2×C4×D73—41no—
154C2×C4×D73C2×D412yes—
155C2×C4×D73#4112yes—
156#11924012—44no—
157#11924011—28no—
158#11924011—28no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831C2×D412yes—
168C2×#10596831#4112yes—
169C2×#10596831#4112yes—
170C2×#10596831#4112yes—
171C4⋊Dic73—22no—
172C4⋊Dic73—41no—
173#11924007—22no—
174#11924007—22no—
175#11924007M1614yescomplemented
176C22⋊Dic73—22no—
177C22⋊Dic73—22no—
178C22⋊Dic73—41no—
179#11924005—22no—
180#11924005—22no—
181#11924005—41no—
182C4×Dic73—21no—
183C4×Dic73—21no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—22no—
189C4×Dic73—22no—
190C24×C73C22×C411yescharacteristic
191C22×C4×C73—21no—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73C22×C411yescharacteristic
198C22×C4×C73C22×C411yescharacteristic
199C22×C4×C73C22×C411yescharacteristic
200C22×C4×C73C22×C411yescharacteristic
201C22×C4×C73C22×C411yescharacteristic
202C22×C4×C73C2411yescharacteristic
203C2×C8×C73—21no—
204C2×C8×C73—21no—
205C2×C8×C73—21no—
206C2×C8×C73—21no—
207C2×C8×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73—21no—
211C2×C8×C73—21no—
212C2×C8×C73—21no—
213C2×C8×C73C2×D412yes—
214C2×C8×C73#4112yes—
215C22⋊C4×C73—22no—
216C22⋊C4×C73—22no—
217C42×C73—21no—
218C42×C73—21no—
219C42×C73—21no—
220C42×C73—21no—
221C23×C73—21no—
222C23×C73—21no—
223C23×C73—21no—
224C23×C73—21no—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73C23×C411yescharacteristic
229C22×D73—21no—
230C22×D73—21no—
231C22×D73—21no—
232C22×D73—21no—
233C22×D73—21no—
234C22×D73—21no—
235C22×D73C4×D412yes—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—21no—
240C2×C4×C73—21no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
249C2×C4×C73—41no—
250C2×C4×C73—41no—
251C2×C4×C73—41no—
252C2×C4×C73—41no—
253C2×C4×C73C2×M1612yes—
254C2×C4×C73#13112yes—
255C2×C4×C73C22×D411yescharacteristic
256C2×C4×C73C2×#4111yescharacteristic
257C2×C4×C73C2×#4111yescharacteristic
258C2×C4×C73C2×#4111yescharacteristic
259C2×C4×C73C2×#4111yescharacteristic
260C2×C4×C73C2×#4111yescharacteristic
261C22⋊D73—44no—
262C2×Dic73—21no—
263C2×Dic73—21no—
264C2×Dic73—21no—
265C2×Dic73—21no—
266C2×Dic73—21no—
267C2×Dic73—21no—
268C2×Dic73—21no—
269C2×Dic73—21no—
270C2×Dic73—21no—
271C2×Dic73—21no—
272C2×Dic73—21no—
273C2×Dic73—21no—
274C2×Dic73—21no—
275C2×Dic73—21no—
276C2×Dic73—21no—
277C2×Dic73—21no—
278C2×Dic73—21no—
279C2×Dic73—21no—
280C2×Dic73C4×D412yes—
281C2×Dic73C2×M1612yes—
282C2×Dic73C2×M1612yes—
283C4×D73—22no—
284C4×D73—22no—
285C4×D73—22no—
286C4×D73—22no—
287C4×D73—44no—
288C4×D73—44no—
289C8×C73—22no—
290C8×C73—22no—
291C8×C73—41no—
292C8×C73—41no—
293#10596831—22no—
294#10596831—41no—
295#10596831—41no—
296#10596831#12314yescomplemented
297C22×C73—41no—
298C22×C73—41no—
299C22×C73—41no—
300C22×C73—41no—
301C22×C73—41no—
302C22×C73—41no—
303C22×C73—41no—
304C22×C73C2×C4×D411yescharacteristic
305C22×C73C4×#4111yescharacteristic
306C22×C73C4×#4111yescharacteristic
307C22×C73C22×M1611yescharacteristic
308C22×C73C2×#13111yescharacteristic
309C22×C73#56811yescharacteristic
310C22×C73#56811yescharacteristic
311C2×D73—22no—
312C2×D73—22no—
313C2×D73—22no—
314C2×D73—41no—
315C2×D73—41no—
316C2×D73—41no—
317C2×D73—41no—
318C4×C73—22no—
319C4×C73—22no—
320C4×C73—41no—
321C4×C73—41no—
322C4×C73—41no—
323C4×C73C2×#12311yescharacteristic
324C4×C73#52511yescharacteristic
325C4×C73#52911yescharacteristic
326C4×C73#52911yescharacteristic
327Dic73—22no—
328Dic73—22no—
329Dic73—22no—
330Dic73—41no—
331Dic73—41no—
332Dic73—41no—
333Dic73—41no—
334#21565—731nomaximal, Sylow
335C2×C73—81no—
336C2×C73C4×#12311yescharacteristic
337C2×C73#293311yescharacteristic
338C2×C73D4×M1611yescharacteristic
339C2×C73#296511yescharacteristic
340C2×C73#296711yescharacteristic
341C2×C73#296911yescharacteristic
342C2×C73#297111yescharacteristic
343D73—42no—
344C2×#436—731no—
345C2×C4×M16—731no—
346C4×#123—731no—
347#1924—731no—
348#1923D7311yescharacteristic, complemented
349#1917—731no—
350#1916—731no—
351#1870—731no—
352#1851—731no—
353#1817—731no—
354#1771—731no—
355C8×C4⋊C4—731no—
356#1753—731no—
357#1753—731no—
358#1753—731no—
359C73#2156511yescharacteristic, complemented, Sylow
360C22×M16—731no—
361C22×M16—731no—
362C22×M16—731no—
363C2×#123—731no—
364C2×C4×D4—731no—
365C22×C42—731no—
366#436—1464no—
367C2×C4⋊C8—731no—
368C2×C4⋊C8—731no—
369C2×C4⋊C8C2×D7311yescharacteristic
370C2×C22⋊C8—731no—
371C2×C22⋊C8—731no—
372C2×C22⋊C8—731no—
373C2×C22⋊C8C2×D7311yescharacteristic
374C2×C22⋊C8C2×D7311yescharacteristic
375C4×M16—1464no—
376C2×#97—731no—
377C2×#97—731no—
378C2×#97—731no—
379C2×C4×C8—731no—
380C2×C4×C8—731no—
381C2×C4×C8—731no—
382C2×C4×C8C2×D7311yescharacteristic
383#388—731no—
384#388—731no—
385#387—731no—
386#387—731no—
387#386—731no—
388#385—731no—
389#381—731no—
390C4×C4⋊C4—731no—
391C4×C4⋊C4—731no—
392C4×C22⋊C4—731no—
393C4×C22⋊C4—731no—
394C4×C22⋊C4C2×D7311yescharacteristic
395#336—731no—
396#336—731no—
397#336—731no—
398#336—731no—
399#336—731no—
400#336—731no—
401#336—731no—
402#336—731no—
403#336C2×D7311yescharacteristic
404#336C2×D7311yescharacteristic
405C22×D4—731no—
406C23×C4—731no—
407C23×C4—731no—
408C23×C4—731no—
409C23×C4C22×D7311yescharacteristic
410C2×M16—734no—
411C2×M16—1462no—
412C2×M16—1462no—
413C2×M16—1462no—
414C2×M16—1462no—
415C2×M16—1462no—
416C2×M16—1462no—
417C2×M16—1462no—
418C2×M16—1462no—
419C22×C8—731no—
420C22×C8—731no—
421C22×C8—731no—
422C22×C8—731no—
423C22×C8C22×D7311yescharacteristic
424C22×C8C22×D7311yescharacteristic
425C22×C8C22×D7311yescharacteristic
426C22×C8C22×D7311yescharacteristic
427#123—1464no—
428C4×D4—1462no—
429C4×D4—1462no—
430C2×C4⋊C4—731no—
431C2×C4⋊C4—731no—
432C2×C4⋊C4—731no—
433C2×C4⋊C4—731no—
434C2×C4⋊C4—731no—
435C2×C22⋊C4—731no—
436C2×C22⋊C4—731no—
437C2×C22⋊C4—731no—
438C2×C22⋊C4—731no—
439C2×C22⋊C4—731no—
440C2×C22⋊C4—731no—
441C2×C22⋊C4C4×D7311yescharacteristic
442C2×C22⋊C4C4×D7311yescharacteristic
443C2×C42—731no—
444C2×C42—731no—
445C2×C42—731no—
446C2×C42—731no—
447C2×C42—731no—
448C2×C42—1462no—
449C2×C42—1462no—
450C2×C42C22×D7311yescharacteristic
451C2×C42C22×D7311yescharacteristic
452C4⋊C8—22no—
453C4⋊C8—1462no—
454C4⋊C8—1462no—
455C22⋊C8—22no—
456C22⋊C8—22no—
457C22⋊C8—1462no—
458C22⋊C8—1462no—
459C22⋊C8—1462no—
460#97—1462no—
461#97—1462no—
462#97—1462no—
463C4×C8—22no—
464C4×C8—1462no—
465C4×C8—1462no—
466C4×C8—1462no—
467#95—731no—
468#95—731no—
469#95—731no—
470#95—731no—
471#95—731no—
472#95—731no—
473#95—731no—
474#95—731no—
475#95C4×D7311yescharacteristic
476#95C4×D7311yescharacteristic
477C24—731no—
478C24C2×C4×D7311yescharacteristic
479C2×D4—2921no—
480C2×D4—1462no—
481C2×D4—1462no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—2921no—
489C22×C4—2921no—
490C22×C4—731no—
491C22×C4—731no—
492C22×C4—731no—
493C22×C4—732no—
494C22×C4—732no—
495C22×C4—731no—
496C22×C4—731no—
497C22×C4—731no—
498C22×C4—731no—
499C22×C4—1462no—
500C22×C4—1462no—
501C22×C4—1462no—
502C22×C4—1462no—
503C22×C4—1461no—
504C22×C4—1461no—
505C22×C4—1461no—
506C22×C4—1461no—
507C22×C4C2×C4×D7311yescharacteristic
508C22×C4C2×C4×D7311yescharacteristic
509C22×C4C2×C4×D7311yescharacteristic
510C22×C4C2×C4×D7311yescharacteristic
511C22×C4C2×C4×D7311yescharacteristic
512C22×C4C23×D7311yescharacteristic
513M16—2924no—
514M16—1468no—
515M16—1468no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—732no—
527C2×C8—732no—
528C2×C8—732no—
529C2×C8—732no—
530C2×C8—1461no—
531C2×C8—1461no—
532C2×C8—1461no—
533C2×C8—1461no—
534C2×C8—1461no—
535C2×C8—1461no—
536C2×C8—1461no—
537C2×C8—1461no—
538C2×C8D4×D7312yes—
539C2×C8#1192402712yes—
540C4⋊C4—2921no—
541C4⋊C4—734no—
542C4⋊C4—1462no—
543C4⋊C4—1462no—
544C4⋊C4—1462no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—2921no—
548C22⋊C4—2921no—
549C22⋊C4—1462no—
550C22⋊C4—1462no—
551C22⋊C4—1462no—
552C22⋊C4—1462no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—1462no—
558C42—1462no—
559C42—1461no—
560C42—1461no—
561C42—1461no—
562C42—1461no—
563C42—1461no—
564C42—1461no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—732no—
573C23—1461no—
574C23—1461no—
575C23—1461no—
576C23—1461no—
577C23—1461no—
578C23—1461no—
579C23C22×C4×D7311yescharacteristic
580D4—2924no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—2924no—
599C2×C4—2924no—
600C2×C4—732no—
601C2×C4—732no—
602C2×C4—732no—
603C2×C4—1461no—
604C2×C4—1461no—
605C2×C4—1461no—
606C2×C4—1461no—
607C2×C4—1461no—
608C2×C4—1461no—
609C2×C4—1461no—
610C2×C4—1461no—
611C2×C4—1461no—
612C2×C4—1461no—
613C2×C4—1461no—
614C2×C4—1461no—
615C2×C4—1461no—
616C2×C4—1461no—
617C2×C4—1461no—
618C2×C4—1461no—
619C2×C4—1461no—
620C2×C4—1461no—
621C2×C4—1462no—
622C2×C4—1462no—
623C2×C4—1462no—
624C2×C4—1462no—
625C2×C4M16×D7312yes—
626C2×C4#1455659712yes—
627C2×C4C2×D4×D7311yescharacteristic
628C2×C4#41×D7311yescharacteristic
629C2×C4#41×D7311yescharacteristic
630C2×C4#41×D7311yescharacteristic
631C2×C4#41×D7311yescharacteristic
632C2×C4C2×#1192402711yescharacteristic
633C8—22no—
634C8—22no—
635C8—41no—
636C8—41no—
637C8—2921no—
638C8—2921no—
639C8—734no—
640C8—1462no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—2921no—
649C22—2921no—
650C22—2921no—
651C22—2921no—
652C22—1462no—
653C22—1462no—
654C22—1462no—
655C22C4×D4×D7311yescharacteristic
656C22C4×#1192402711yescharacteristic
657C22#1798905511yescharacteristic
658C22C2×M16×D7311yescharacteristic
659C22C2×#1455659711yescharacteristic
660C22#1798935211yescharacteristic
661C22#1798935211yescharacteristic
662C4—22no—
663C4—22no—
664C4—41no—
665C4—41no—
666C4—41no—
667C4—2921no—
668C4—2921no—
669C4—2921no—
670C4—2921no—
671C4—1462no—
672C4—1462no—
673C4—1462no—
674C4#123×D7311yescharacteristic
675C4#1798909711yescharacteristic
676C4#1798911611yescharacteristic
677C4#1798912011yescharacteristic
678C2—81no—
679C2—2922no—
680C2#2261245811yescharacteristic
681C2#2261865111yescharacteristic
682C2#2261866411yescharacteristic
683C2#2261889511yescharacteristic
684C2#2261891411yescharacteristic
685C2#2261893211yescharacteristic
686C2#2261894711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1923C2
prime radicalC22×C22⋊D73C2×C4
cosocleC22×C4×C73C24
hypercenter#1923D73
hypocenterC73#21565
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11924011C2semidirect
4. #22610541C2semidirect
5. #22610496C2semidirect
6. #22610488C2semidirect
8. #22610112C2semidirect
9. #22609998C2semidirect
10. #22609808C2semidirect
11. #22609792C2semidirect
12. #22609717C2semidirect
13. #22609715C2semidirect
14. #22609713C2semidirect
15. C73×#1923C2semidirect
175. #11924007M16semidirect
296. #10596831#123semidirect
348. #1923D73semidirect
359. C73#21565semidirect

Maximal subgroups

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

subgroupindex
C2×#179886622
C2×C4×#119240112
C4×#145565732
#226105412
#226104962
#226104882
#226102252
#226101122
#226099982
#226098082
#226097922
#226097172
#226097152
#226097132
C73×#19232
#2156573