Finite Group Databasebeta

← #33136143

Subgroups — #33136143

Order 18688.

914 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988887C211yesmaximal, characteristic, complemented
2C2×D4×#10596831C211yesmaximal, characteristic, complemented
3#22615097C211yesmaximal, characteristic, complemented
4#22611368C211yesmaximal, characteristic, complemented
5#22611362C211yesmaximal, characteristic, complemented
6#22611117C211yesmaximal, characteristic, complemented
7#22611110C211yesmaximal, characteristic, complemented
8#22610895C211yesmaximal, characteristic, complemented
9#22610697C211yesmaximal, characteristic, complemented
10#22610360C211yesmaximal, characteristic, complemented
11#22610360C211yesmaximal, characteristic, complemented
12#22609958C211yesmaximal, characteristic, complemented
13#22609954C211yesmaximal, characteristic, complemented
14C4×#14556512C211yesmaximal, characteristic, complemented
15C73×#2535C211yesmaximal, characteristic
16C23×#10596831C2211yescharacteristic
17C23×#10596831C2211yescharacteristic
18C2×#14556583C2211yescharacteristic
19#17988887—24no—
20D4×#10596831—24no—
21C2×#14556524C2211yescharacteristic
22C2×#14556524C2211yescharacteristic
23C2×#14556522C2211yescharacteristic
24C2×#14556522C2211yescharacteristic
25C2×C4⋊#10596831C2211yescharacteristic
26C2×#14556512C2211yescharacteristic
27C2×#14556512C2211yescharacteristic
28C2×#14556512C2211yescharacteristic
29C2×#14556512C2211yescharacteristic
30C2×C22⋊#10596831C2211yescharacteristic
31C2×C22⋊#10596831C2211yescharacteristic
32C2×C4×#10596831C2211yescharacteristic
33#17988525—21no—
34#17988501—21no—
35#17988481—21no—
36#17988481—21no—
37#17988447C2211yescharacteristic
38#17988447C2211yescharacteristic
39#17988447C2211yescharacteristic
40#17988447C2211yescharacteristic
41C4×C4⋊Dic73C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50C2×#121×C73C2211yescharacteristic
51C2×#121×C73C2211yescharacteristic
52C2×C4×D4×C73C2211yescharacteristic
53C2×C4×D4×C73C2211yescharacteristic
54#397×C73—21no—
55#392×C73—21no—
56#386×C73—21no—
57#386×C73—21no—
58#382×C73C2211yescharacteristic
59#380×C73C2211yescharacteristic
60#380×C73C2211yescharacteristic
61C22×#10596831—22no—
62C22×#10596831—22no—
63C22×#10596831—22no—
64C22×#10596831—22no—
65C22×#10596831—41no—
66C22×#10596831—41no—
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71#14556583—22no—
72#14556583—22no—
73C2×C4⋊Dic73C2311yescharacteristic
74C2×C4⋊Dic73C2311yescharacteristic
75C2×C4⋊Dic73C2311yescharacteristic
76C2×C4⋊Dic73C2311yescharacteristic
77C2×#11924007—21no—
78C2×#11924007—21no—
79C2×C22⋊Dic73—21no—
80C2×C22⋊Dic73—21no—
81C2×C22⋊Dic73—21no—
82C2×C22⋊Dic73—21no—
83C2×C4×Dic73—21no—
84#14556524—22no—
85#14556524—41no—
86#14556522—22no—
87#14556522—41no—
88C4⋊#10596831D414yescomplemented
89#14556512—22no—
90#14556512—22no—
91#14556512—22no—
92#14556512—22no—
93C22⋊#10596831—22no—
94C22⋊#10596831—22no—
95C4×#10596831—22no—
96#14556498—21no—
97#14556498—21no—
98#14556498—21no—
99#14556498—21no—
100#14556498—21no—
101C22×D4×C73—21no—
102C22×D4×C73—21no—
103C22×D4×C73D411yescharacteristic
104C22×D4×C73C2311yescharacteristic
105C23×C4×C73—21no—
106C23×C4×C73C2311yescharacteristic
107C23×C4×C73C2311yescharacteristic
108#121×C73—22no—
109#121×C73—22no—
110#121×C73—41no—
111#121×C73—41no—
112C4×D4×C73—22no—
113C4×D4×C73—22no—
114C4×D4×C73—22no—
115C4×D4×C73—22no—
116C2×C4⋊C4×C73D411yescharacteristic
117C2×C4⋊C4×C73C2311yescharacteristic
118C2×C4⋊C4×C73C2311yescharacteristic
119C2×C4⋊C4×C73C2311yescharacteristic
120C2×C22⋊C4×C73—21no—
121C2×C22⋊C4×C73—21no—
122C2×C22⋊C4×C73—21no—
123C2×C22⋊C4×C73—21no—
124C2×C22⋊C4×C73—21no—
125C2×C22⋊C4×C73D411yescharacteristic
126C2×C22⋊C4×C73D411yescharacteristic
127C2×C42×C73C2311yescharacteristic
128#95×C73—21no—
129#95×C73—21no—
130#95×C73—21no—
131#95×C73—21no—
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73—21no—
135C22×Dic73—21no—
136C2×#10596831—21no—
137C2×#10596831—21no—
138C2×#10596831—21no—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831—21no—
143C2×#10596831—21no—
144C2×#10596831—21no—
145C2×#10596831—44no—
146C2×#10596831—44no—
147C2×#10596831C2×D412yes—
148C2×#10596831C2×D412yes—
149C2×#10596831#4112yes—
150C4⋊Dic73—21no—
151C4⋊Dic73—21no—
152C4⋊Dic73—21no—
153C4⋊Dic73—21no—
154C4⋊Dic73—21no—
155C4⋊Dic73—21no—
156C4⋊Dic73—21no—
157C4⋊Dic73—21no—
158#11924007—42no—
159#11924007—42no—
160C22⋊Dic73—42no—
161C22⋊Dic73—42no—
162C22⋊Dic73—81no—
163C22⋊Dic73—81no—
164C4×Dic73—81no—
165C24×C73—21no—
166C24×C73C2×D411yescharacteristic
167C24×C73C2×D411yescharacteristic
168C2×D4×C73—22no—
169C2×D4×C73—22no—
170C2×D4×C73—22no—
171C2×D4×C73—21no—
172C2×D4×C73—21no—
173C2×D4×C73—21no—
174C2×D4×C73—21no—
175C2×D4×C73—21no—
176C2×D4×C73—42no—
177C2×D4×C73—42no—
178C2×D4×C73—42no—
179C2×D4×C73—42no—
180C2×D4×C73—81no—
181C2×D4×C73—81no—
182C2×D4×C73#4112yes—
183C22×C4×C73—21no—
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
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×C73—21no—
198C22×C4×C73—42no—
199C22×C4×C73—81no—
200C22×C4×C73—81no—
201C22×C4×C73C2×D411yescharacteristic
202C22×C4×C73C2×D411yescharacteristic
203C22×C4×C73C2×D411yescharacteristic
204C22×C4×C73C2×D411yescharacteristic
205C22×C4×C73C2411yescharacteristic
206C4⋊C4×C73—22no—
207C4⋊C4×C73—21no—
208C4⋊C4×C73—21no—
209C4⋊C4×C73—21no—
210C4⋊C4×C73—21no—
211C4⋊C4×C73—21no—
212C4⋊C4×C73—21no—
213C22⋊C4×C73—22no—
214C22⋊C4×C73—22no—
215C22⋊C4×C73—42no—
216C22⋊C4×C73—42no—
217C22⋊C4×C73—42no—
218C22⋊C4×C73—81no—
219C22⋊C4×C73—81no—
220C42×C73C2×D412yes—
221C42×C73#4112yes—
222C23×C73—21no—
223C23×C73—21no—
224C23×C73—21no—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—22no—
235C23×C73—41no—
236C23×C73—41no—
237C23×C73—41no—
238C23×C73—41no—
239C23×C73—41no—
240C23×C73—41no—
241C23×C73#13512yes—
242C23×C73#13512yes—
243C23×C73C22×D411yescharacteristic
244D4×C73—28no—
245D4×C73—22no—
246D4×C73—22no—
247D4×C73—41no—
248D4×C73—41no—
249D4×C73—84no—
250D4×C73—84no—
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—21no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
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×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—41no—
276C2×C4×C73—41no—
277C2×C4×C73—41no—
278C2×C4×C73—84no—
279C2×C4×C73#12112yes—
280C2×C4×C73#12112yes—
281C2×C4×C73C22×D411yescharacteristic
282C2×C4×C73C2×#4111yescharacteristic
283C2×C4×C73C2×#4111yescharacteristic
284C2×C4×C73C2×#4111yescharacteristic
285C2×C4×C73H(5,𝔽2)11yescharacteristic
286C2×C4×C732−1+411yescharacteristic
287C2×Dic73—41no—
288C2×Dic73—41no—
289C2×Dic73—41no—
290C2×Dic73—41no—
291C2×Dic73—41no—
292C2×Dic73—41no—
293C2×Dic73—41no—
294C2×Dic73—41no—
295C2×Dic73—41no—
296C2×Dic73—41no—
297C2×Dic73—41no—
298C2×Dic73—41no—
299#10596831—22no—
300#10596831—22no—
301#10596831—22no—
302#10596831—41no—
303C22×C73—22no—
304C22×C73—22no—
305C22×C73—22no—
306C22×C73—22no—
307C22×C73—22no—
308C22×C73—22no—
309C22×C73—41no—
310C22×C73—41no—
311C22×C73—41no—
312C22×C73—41no—
313C22×C73—41no—
314C22×C73—41no—
315C22×C73—41no—
316C22×C73—41no—
317C22×C73—42no—
318C22×C73—42no—
319C22×C73—42no—
320C22×C73—81no—
321C22×C73—81no—
322C22×C73—81no—
323C22×C73—81no—
324C22×C73C2×#12111yescharacteristic
325C22×C73#54611yescharacteristic
326C22×C73#54711yescharacteristic
327C22×C73C2×#13511yescharacteristic
328C22×C73C2×#13511yescharacteristic
329C22×C73#57611yescharacteristic
330C22×C73#57711yescharacteristic
331C4×C73—22no—
332C4×C73—22no—
333C4×C73—41no—
334C4×C73—41no—
335C4×C73—81no—
336C4×C73—81no—
337C4×C73—81no—
338C4×C73#52911yescharacteristic
339C4×C73#54211yescharacteristic
340C4×C73#54611yescharacteristic
341C4×C73#54811yescharacteristic
342Dic73—81no—
343Dic73—81no—
344Dic73—81no—
345Dic73—81no—
346#25342—731nomaximal, Sylow
347C2×C73—42no—
348C2×C73—42no—
349C2×C73—82no—
350C2×C73#242711yescharacteristic
351C2×C73#305011yescharacteristic
352C2×C73#306211yescharacteristic
353C2×C73#329611yescharacteristic
354C2×C73#329711yescharacteristic
355C2×C73#333711yescharacteristic
356C2×C73#333911yescharacteristic
357C2×#478—731no—
358C2×C8×D4—731no—
359#2562—731no—
360#2535D7311yescharacteristic
361#2077—731no—
362#2076—731no—
363#2034—731no—
364#2033—731no—
365#1991—731no—
366#1949—731no—
367#1893—731no—
368#1893—731no—
369#1808—731no—
370#1807—731no—
371C4×#102—731no—
372C73#2534211yescharacteristic, complemented, Sylow
373C23×C8—731no—
374C23×C8—731no—
375C2×#125—731no—
376C2×#121C2×D7311yescharacteristic
377C2×#121C2×D7311yescharacteristic
378C2×C4×D4C2×D7311yescharacteristic
379C2×C4×D4C2×D7311yescharacteristic
380#478—1464no—
381C8×D4—1464no—
382C2×#107—731no—
383C2×#107—731no—
384C2×#106—731no—
385C2×#106—731no—
386C2×C4⋊C8—731no—
387C2×#102—731no—
388C2×#102—731no—
389C2×#102—731no—
390C2×#102—731no—
391C2×C22⋊C8—731no—
392C2×C22⋊C8—731no—
393C2×C4×C8—731no—
394#400—1461no—
395#397—21no—
396#394—1461no—
397#392—21no—
398#388—1461no—
399#388—1461no—
400#386—21no—
401#386—21no—
402#382C2×D7311yescharacteristic
403#380—731no—
404#380—731no—
405#380—731no—
406#380—731no—
407#380C2×D7311yescharacteristic
408#380C2×D7311yescharacteristic
409C4×C4⋊C4—731no—
410#340—731no—
411#340—731no—
412#340—731no—
413#340—731no—
414#340—731no—
415#340—731no—
416#340—731no—
417#340—731no—
418C22×D4—21no—
419C22×D4—21no—
420C22×D4C22⋊D7311yescharacteristic
421C22×D4C22×D7311yescharacteristic
422C23×C4—21no—
423C23×C4C22×D7311yescharacteristic
424C23×C4C22×D7311yescharacteristic
425C22×C8—2921no—
426C22×C8—2921no—
427C22×C8—731no—
428C22×C8—731no—
429C22×C8—731no—
430C22×C8—731no—
431C22×C8—1462no—
432C22×C8—1462no—
433C22×C8—1462no—
434C22×C8—1462no—
435#125—1462no—
436#125—1462no—
437#121—22no—
438#121—22no—
439#121—41no—
440#121—41no—
441C4×D4—22no—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—22no—
445C2×C4⋊C4—731no—
446C2×C4⋊C4—731no—
447C2×C4⋊C4—731no—
448C2×C4⋊C4—731no—
449C2×C4⋊C4—1461no—
450C2×C4⋊C4—1461no—
451C2×C4⋊C4C22⋊D7311yescharacteristic
452C2×C4⋊C4C22×D7311yescharacteristic
453C2×C4⋊C4C22×D7311yescharacteristic
454C2×C4⋊C4C22×D7311yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—1461no—
461C2×C22⋊C4—1461no—
462C2×C22⋊C4—1461no—
463C2×C22⋊C4—1461no—
464C2×C22⋊C4C22⋊D7311yescharacteristic
465C2×C22⋊C4C22⋊D7311yescharacteristic
466C2×C42—1461no—
467C2×C42C22×D7311yescharacteristic
468#107—2921no—
469#107—1462no—
470#106—2921no—
471#106—1462no—
472C4⋊C8—734no—
473#102—1462no—
474#102—1462no—
475#102—1462no—
476#102—1462no—
477C22⋊C8—1462no—
478C22⋊C8—1462no—
479C4×C8—1462no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—1461no—
485#95—1461no—
486#95—1461no—
487#95—1461no—
488#95—1461no—
489C24—21no—
490C24C2×C22⋊D7311yescharacteristic
491C24C2×C22⋊D7311yescharacteristic
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—81no—
505C2×D4—81no—
506C2×D4#1192402712yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—42no—
523C22×C4—81no—
524C22×C4—81no—
525C22×C4—1461no—
526C22×C4—1461no—
527C22×C4—1461no—
528C22×C4—1461no—
529C22×C4C2×C22⋊D7311yescharacteristic
530C22×C4C2×C22⋊D7311yescharacteristic
531C22×C4C2×C22⋊D7311yescharacteristic
532C22×C4C2×C22⋊D7311yescharacteristic
533C22×C4C23×D7311yescharacteristic
534C2×C8—2924no—
535C2×C8—2924no—
536C2×C8—732no—
537C2×C8—732no—
538C2×C8—732no—
539C2×C8—1461no—
540C2×C8—1461no—
541C2×C8—1461no—
542C2×C8—1461no—
543C2×C8—1461no—
544C2×C8—1461no—
545C2×C8—1461no—
546C2×C8—1461no—
547C2×C8—1461no—
548C4⋊C4—22no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—2922no—
556C4⋊C4—2922no—
557C4⋊C4—1461no—
558C4⋊C4—1461no—
559C4⋊C4—1461no—
560C4⋊C4—1461no—
561C4⋊C4—1461no—
562C4⋊C4—1461no—
563C4⋊C4—1461no—
564C4⋊C4—1461no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—81no—
571C22⋊C4—81no—
572C22⋊C4—2922no—
573C22⋊C4—2922no—
574C22⋊C4—5841no—
575C22⋊C4—5841no—
576C42—5841no—
577C42D4×D7312yes—
578C42#1192402712yes—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—22no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23#1455661112yes—
599C23#1455661112yes—
600C23C22×C22⋊D7311yescharacteristic
601D4—28no—
602D4—22no—
603D4—22no—
604D4—41no—
605D4—41no—
606D4—84no—
607D4—84no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
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—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—84no—
636C2×C4—2921no—
637C2×C4—2921no—
638C2×C4—2921no—
639C2×C4—2921no—
640C2×C4—2921no—
641C2×C4—2921no—
642C2×C4—2921no—
643C2×C4—2921no—
644C2×C4—2921no—
645C2×C4—2921no—
646C2×C4—2921no—
647C2×C4—2921no—
648C2×C4#1455656312yes—
649C2×C4#1455656312yes—
650C2×C4C2×D4×D7311yescharacteristic
651C2×C4#41×D7311yescharacteristic
652C2×C4C2×#1192402711yescharacteristic
653C2×C4C2×#1192402711yescharacteristic
654C2×C4#1455663611yescharacteristic
655C2×C4#1455663811yescharacteristic
656C8—2921no—
657C8—1462no—
658C8—1462no—
659C8—1462no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22C2×#1455656311yescharacteristic
682C22#1798923111yescharacteristic
683C22#1798923611yescharacteristic
684C22C2×#1455661111yescharacteristic
685C22C2×#1455661111yescharacteristic
686C22#1798939011yescharacteristic
687C22#1798939811yescharacteristic
688C4—22no—
689C4—22no—
690C4—41no—
691C4—41no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4—5841no—
696C4—5841no—
697C4—5841no—
698C4—5841no—
699C4#1798911811yescharacteristic
700C4#1798920411yescharacteristic
701C4#1798923411yescharacteristic
702C4#1798924311yescharacteristic
703C2—42no—
704C2—42no—
705C2—82no—
706C2#2261351011yescharacteristic
707C2#2261950911yescharacteristic
708C2#2261960711yescharacteristic
709C2#2262176611yescharacteristic
710C2#2262178111yescharacteristic
711C2#2262230411yescharacteristic
712C2#2262232711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
Fitting, prime radicalC73×#2535C2
socleC23×C73C22×D4
hypercenter#2535D73
hypocenterC73#25342
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. C2×#17988887C2semidirect
2. C2×D4×#10596831C2semidirect
3. #22615097C2semidirect
4. #22611368C2semidirect
5. #22611362C2semidirect
6. #22611117C2semidirect
7. #22611110C2semidirect
8. #22610895C2semidirect
9. #22610697C2semidirect
10. #22610360C2semidirect
11. #22610360C2semidirect
12. #22609958C2semidirect
13. #22609954C2semidirect
14. C4×#14556512C2semidirect
88. C4⋊#10596831D4semidirect
372. C73#25342semidirect

Maximal subgroups

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

subgroupindex
C2×#179888872
C2×D4×#105968312
#226150972
#226113682
#226113622
#226111172
#226111102
#226108952
#226106972
#226103602
#226099582
#226099542
C4×#145565122
C73×#25352
#2534273