Finite Group Databasebeta

← #650956

Subgroups — #650956

Order 512.

2688 conjugacy classes of subgroups.

The subgroup lattice has 1506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2477C211yesmaximal, characteristic
2C2×C4×#123C211yesmaximal, characteristic
3#16086C211yesmaximal, characteristic, complemented
4#15930C211yesmaximal, characteristic, complemented
5#15752C211yesmaximal, characteristic, complemented
6#15672C211yesmaximal, characteristic, complemented
7#15560C211yesmaximal, characteristic, complemented
8#15472C211yesmaximal, characteristic, complemented
9#15463C211yesmaximal, characteristic
10#15269C211yesmaximal, characteristic
11#14992C211yesmaximal, characteristic, complemented
12#14962C211yesmaximal, characteristic, complemented
13#14907C211yesmaximal, characteristic, complemented
14#14906C211yesmaximal, characteristic, complemented
15#14846C211yesmaximal, characteristic, complemented
16#14830C211yesmaximal, characteristic, complemented
17#14823C211yesmaximal, characteristic
18#14768C211yesmaximal, characteristic, complemented
19#14705C211yesmaximal, characteristic, complemented
20#14229C211yesmaximal, characteristic, complemented
21#14216C211yesmaximal, characteristic, complemented
22#14197C211yesmaximal, characteristic, complemented
23#14197C211yesmaximal, characteristic, complemented
24#14103C211yesmaximal, characteristic, complemented
25#14064C211yesmaximal, characteristic
26#14059C211yesmaximal, characteristic, complemented
27#14052C211yesmaximal, characteristic, complemented
28#14033C211yesmaximal, characteristic, complemented
29#13894C211yesmaximal, characteristic
30#13802C211yesmaximal, characteristic, complemented
31#13756C211yesmaximal, characteristic, complemented
32C22×#123C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C22×#117C2211yescharacteristic
37C23×C42C2211yescharacteristic
38#2477—28no—
39C2×#400C2211yescharacteristic
40C2×#400C2211yescharacteristic
41C2×#398C2211yescharacteristic
42C2×#398C2211yescharacteristic
43C2×#397C2211yescharacteristic
44C2×#397C2211yescharacteristic
45C2×#397C2211yescharacteristic
46C2×#397C2211yescharacteristic
47C2×#397C2211yescharacteristic
48C2×#394C2211yescharacteristic
49C2×#393C2211yescharacteristic
50C4×#123—28no—
51C2×#391C2211yescharacteristic
52C2×#391C2211yescharacteristic
53C2×#389C2211yescharacteristic
54C2×#388C2211yescharacteristic
55C2×#388C2211yescharacteristic
56C2×#388C2211yescharacteristic
57C2×#388C2211yescharacteristic
58C2×#387C2211yescharacteristic
59C2×#387C2211yescharacteristic
60C2×#387C2211yescharacteristic
61C2×#387C2211yescharacteristic
62C2×#386C2211yescharacteristic
63C2×#386C2211yescharacteristic
64C2×#386C2211yescharacteristic
65C2×#385C2211yescharacteristic
66C2×#385C2211yescharacteristic
67C2×#385C2211yescharacteristic
68C2×#385C2211yescharacteristic
69C2×#381C2211yescharacteristic
70C2×#381C2211yescharacteristic
71C2×#381C2211yescharacteristic
72C2×#380C2211yescharacteristic
73C2×C4×C4⋊C4C2211yescharacteristic
74C2×C4×C4⋊C4C2211yescharacteristic
75C2×C4×C22⋊C4C2211yescharacteristic
76C2×C4×C22⋊C4C2211yescharacteristic
77C2×C4×C22⋊C4C2211yescharacteristic
78C2×C4×C22⋊C4C2211yescharacteristic
79C2×C4×C22⋊C4C2211yescharacteristic
80C22×#95C2211yescharacteristic
81#1446C2211yescharacteristic
82#1446C2211yescharacteristic
83#1446C2211yescharacteristic
84#1445C2211yescharacteristic
85#1445C2211yescharacteristic
86#1445C2211yescharacteristic
87#1445C2211yescharacteristic
88#1445C2211yescharacteristic
89#1444C2211yescharacteristic
90#1444C2211yescharacteristic
91#1443C2211yescharacteristic
92#1443C2211yescharacteristic
93#1443C2211yescharacteristic
94#1443C2211yescharacteristic
95#1443C2211yescharacteristic
96#1443C2211yescharacteristic
97#1442C2211yescharacteristic
98#1442C2211yescharacteristic
99#1442C2211yescharacteristic
100#1442C2211yescharacteristic
101#1442C2211yescharacteristic
102#1442C2211yescharacteristic
103#1442C2211yescharacteristic
104#1442C2211yescharacteristic
105#1442C2211yescharacteristic
106#1441C2211yescharacteristic
107#1441C2211yescharacteristic
108#1441C2211yescharacteristic
109#1441C2211yescharacteristic
110#1441C2211yescharacteristic
111#1441C2211yescharacteristic
112#1441C2211yescharacteristic
113#1441C2211yescharacteristic
114#1441C2211yescharacteristic
115#1441C2211yescharacteristic
116#1441C2211yescharacteristic
117#1440C2211yescharacteristic
118#1440C2211yescharacteristic
119#1440C2211yescharacteristic
120#1440C2211yescharacteristic
121#1440C2211yescharacteristic
122#1440C2211yescharacteristic
123#1439C2211yescharacteristic
124#1439C2211yescharacteristic
125#1439C2211yescharacteristic
126#1439C2211yescharacteristic
127#1439C2211yescharacteristic
128#1439C2211yescharacteristic
129#1438C2211yescharacteristic
130#1437C2211yescharacteristic
131#1437C2211yescharacteristic
132#1436C2211yescharacteristic
133#1436C2211yescharacteristic
134#1436C2211yescharacteristic
135#1436C2211yescharacteristic
136#1436C2211yescharacteristic
137#1436C2211yescharacteristic
138#1436C2211yescharacteristic
139#1436C2211yescharacteristic
140#1436C2211yescharacteristic
141#1436C2211yescharacteristic
142#1436C2211yescharacteristic
143#1436C2211yescharacteristic
144#1436C2211yescharacteristic
145#1436C2211yescharacteristic
146#1436C2211yescharacteristic
147#1436C2211yescharacteristic
148#1436C2211yescharacteristic
149#1436C2211yescharacteristic
150#1436C2211yescharacteristic
151#1436C2211yescharacteristic
152#1436C2211yescharacteristic
153#1436C2211yescharacteristic
154#1436C2211yescharacteristic
155#1436C2211yescharacteristic
156C4⋊#95C2211yescharacteristic
157C4⋊#95C2211yescharacteristic
158C4⋊#95C2211yescharacteristic
159C4⋊#95C2211yescharacteristic
160#1434C2211yescharacteristic
161#1434C2211yescharacteristic
162#1434C2211yescharacteristic
163#1434C2211yescharacteristic
164#1434C2211yescharacteristic
165#1434C2211yescharacteristic
166#1434C2211yescharacteristic
167#1434C2211yescharacteristic
168#1434C2211yescharacteristic
169#1434C2211yescharacteristic
170C22⋊#95C2211yescharacteristic
171C22⋊#95C2211yescharacteristic
172C22⋊#95C2211yescharacteristic
173C22⋊#95C2211yescharacteristic
174C22⋊#95C2211yescharacteristic
175C22⋊#95C2211yescharacteristic
176C22⋊#95C2211yescharacteristic
177C22⋊#95C2211yescharacteristic
178C22⋊#95C2211yescharacteristic
179C22⋊#95C2211yescharacteristic
180C22⋊#95C2211yescharacteristic
181C22⋊#95C2211yescharacteristic
182C22⋊#95C2211yescharacteristic
183C22⋊#95C2211yescharacteristic
184C4×#95C2211yescharacteristic
185C4×#95C2211yescharacteristic
186C4×#95C2211yescharacteristic
187C4×#95C2211yescharacteristic
188C4×#95C2211yescharacteristic
189C23×Q8C2311yescharacteristic
190C23×D4C2311yescharacteristic
191C24×C4C2311yescharacteristic
192C24×C4C2311yescharacteristic
193C24×C4C2311yescharacteristic
194C24×C4C2311yescharacteristic
195C24×C4C2311yescharacteristic
196C24×C4C2311yescharacteristic
197C2×#123—24no—
198C2×#123—24no—
199C2×#123—24no—
200C2×C22⋊Q8—24no—
201C2×C22⋊Q8—24no—
202C2×C22⋊Q8—42no—
203C2×C4×D4—24no—
204C2×C4×D4—24no—
205C2×C4×D4—42no—
206C2×#117—24no—
207C2×#117—24no—
208C2×#117—24no—
209C2×#117—42no—
210C2×#117—42no—
211C2×#117—42no—
212C22×C4⋊C4C2311yescharacteristic
213C22×C4⋊C4C2311yescharacteristic
214C22×C4⋊C4C2311yescharacteristic
215C22×C4⋊C4C2311yescharacteristic
216C22×C4⋊C4C2311yescharacteristic
217C22×C4⋊C4C2311yescharacteristic
218C22×C4⋊C4C2311yescharacteristic
219C22×C4⋊C4C2311yescharacteristic
220C22×C4⋊C4C2311yescharacteristic
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C22⋊C4C2311yescharacteristic
233C22×C22⋊C4C2311yescharacteristic
234C22×C22⋊C4C2311yescharacteristic
235C22×C22⋊C4C2311yescharacteristic
236C22×C22⋊C4C2311yescharacteristic
237C22×C22⋊C4C2311yescharacteristic
238C22×C22⋊C4C2311yescharacteristic
239C22×C22⋊C4C2311yescharacteristic
240C22×C22⋊C4C2311yescharacteristic
241C22×C22⋊C4C2311yescharacteristic
242C22×C22⋊C4C2311yescharacteristic
243C22×C22⋊C4C2311yescharacteristic
244C22×C22⋊C4C2311yescharacteristic
245C22×C22⋊C4C2311yescharacteristic
246C22×C22⋊C4C2311yescharacteristic
247C22×C22⋊C4C2311yescharacteristic
248C22×C22⋊C4C2311yescharacteristic
249C22×C22⋊C4C2311yescharacteristic
250C22×C22⋊C4C2311yescharacteristic
251C22×C22⋊C4C2311yescharacteristic
252C22×C22⋊C4C2311yescharacteristic
253C22×C22⋊C4C2311yescharacteristic
254C22×C42—24no—
255C22×C42—24no—
256C22×C42—42no—
257C22×C42C2311yescharacteristic
258C22×C42C2311yescharacteristic
259C22×C42C2311yescharacteristic
260C22×C42C2311yescharacteristic
261C22×C42C2311yescharacteristic
262C22×C42C2311yescharacteristic
263C22×C42C2311yescharacteristic
264C22×C42C2311yescharacteristic
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268C22×C42C2311yescharacteristic
269C22×C42C2311yescharacteristic
270#400—24no—
271#400—24no—
272#398—42no—
273#398—42no—
274#397—24no—
275#397—24no—
276#397—24no—
277#397—24no—
278#397—42no—
279#394—24no—
280#393—24no—
281#391—24no—
282#391—24no—
283#389—24no—
284#388—24no—
285#388—24no—
286#388—24no—
287#388—24no—
288#387—24no—
289#387—24no—
290#387—24no—
291#387—24no—
292#386—24no—
293#386—42no—
294#386D418yes—
295#385—24no—
296#385—24no—
297#385—42no—
298#385—42no—
299#381—24no—
300#381—24no—
301#381—24no—
302#380—24no—
303C4×C4⋊C4—24no—
304C4×C4⋊C4—24no—
305C4×C22⋊C4—24no—
306C4×C22⋊C4—24no—
307C4×C22⋊C4—24no—
308C4×C22⋊C4—24no—
309C4×C22⋊C4—24no—
310C2×#95—24no—
311C2×#95C2311yescharacteristic
312C2×#95C2311yescharacteristic
313C2×#95C2311yescharacteristic
314C2×#95C2311yescharacteristic
315C2×#95C2311yescharacteristic
316C2×#95C2311yescharacteristic
317C2×#95C2311yescharacteristic
318C2×#95C2311yescharacteristic
319C2×#95C2311yescharacteristic
320C2×#95C2311yescharacteristic
321C2×#95C2311yescharacteristic
322C2×#95C2311yescharacteristic
323C2×#95C2311yescharacteristic
324C2×#95C2311yescharacteristic
325C2×#95C2311yescharacteristic
326C2×#95C2311yescharacteristic
327C2×#95C2311yescharacteristic
328C2×#95C2311yescharacteristic
329C2×#95C2311yescharacteristic
330C2×#95C2311yescharacteristic
331C2×#95C2311yescharacteristic
332C2×#95C2311yescharacteristic
333C2×#95C2311yescharacteristic
334C2×#95C2311yescharacteristic
335C2×#95C2311yescharacteristic
336C2×#95C2311yescharacteristic
337C2×#95C2311yescharacteristic
338C2×#95C2311yescharacteristic
339C2×#95C2311yescharacteristic
340C2×#95C2311yescharacteristic
341C2×#95C2311yescharacteristic
342C2×#95C2311yescharacteristic
343C2×#95C2311yescharacteristic
344C2×#95C2311yescharacteristic
345C2×#95C2311yescharacteristic
346C2×#95C2311yescharacteristic
347C2×#95C2311yescharacteristic
348C2×#95C2311yescharacteristic
349C2×#95C2311yescharacteristic
350C2×#95C2311yescharacteristic
351C2×#95C2311yescharacteristic
352C2×#95C2311yescharacteristic
353C2×#95C2311yescharacteristic
354C2×#95C2311yescharacteristic
355C2×#95C2311yescharacteristic
356C2×#95C2311yescharacteristic
357C2×#95C2311yescharacteristic
358C2×#95C2311yescharacteristic
359C2×#95C2311yescharacteristic
360C2×#95C2311yescharacteristic
361C2×#95C2311yescharacteristic
362C2×#95C2311yescharacteristic
363C2×#95C2311yescharacteristic
364C2×#95C2311yescharacteristic
365C2×#95C2311yescharacteristic
366C2×#95C2311yescharacteristic
367C2×#95C2311yescharacteristic
368C2×#95C2311yescharacteristic
369C2×#95C2311yescharacteristic
370C2×#95C2311yescharacteristic
371C2×#95C2311yescharacteristic
372C2×#95C2311yescharacteristic
373C2×#95C2311yescharacteristic
374C2×#95C2311yescharacteristic
375C2×#95C2311yescharacteristic
376C2×#95C2311yescharacteristic
377C2×#95C2311yescharacteristic
378C2×#95C2311yescharacteristic
379C2×#95C2311yescharacteristic
380C2×#95C2311yescharacteristic
381C2×#95C2311yescharacteristic
382C2×#95C2311yescharacteristic
383C2×#95C2311yescharacteristic
384C2×#95C2311yescharacteristic
385C2×#95C2311yescharacteristic
386C2×#95C2311yescharacteristic
387C2×#95C2311yescharacteristic
388C2×#95C2311yescharacteristic
389C2×#95C2311yescharacteristic
390C2×#95C2311yescharacteristic
391C2×#95C2311yescharacteristic
392C2×#95C2311yescharacteristic
393C2×#95C2311yescharacteristic
394C2×#95C2311yescharacteristic
395C2×#95C2311yescharacteristic
396C2×#95C2311yescharacteristic
397C2×#95C2311yescharacteristic
398C2×#95C2311yescharacteristic
399C2×#95C2311yescharacteristic
400C2×#95C2311yescharacteristic
401C2×#95C2311yescharacteristic
402C2×#95C2311yescharacteristic
403C25C2411yescharacteristic
404C25C2411yescharacteristic
405C22×Q8—22no—
406C22×Q8—22no—
407C22×Q8—22no—
408C22×Q8—41no—
409C22×Q8—41no—
410C22×Q8—41no—
411C22×Q8—41no—
412C22×D4—22no—
413C22×D4—22no—
414C22×D4—22no—
415C22×D4—22no—
416C22×D4—41no—
417C22×D4—41no—
418C22×D4C2×D414yes—
419C23×C4—22no—
420C23×C4—22no—
421C23×C4—22no—
422C23×C4—22no—
423C23×C4—22no—
424C23×C4—22no—
425C23×C4—22no—
426C23×C4—22no—
427C23×C4—22no—
428C23×C4—22no—
429C23×C4—22no—
430C23×C4—22no—
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—22no—
439C23×C4—22no—
440C23×C4—22no—
441C23×C4—22no—
442C23×C4—22no—
443C23×C4—22no—
444C23×C4—41no—
445C23×C4—41no—
446C23×C4—41no—
447C23×C4—41no—
448C23×C4—41no—
449C23×C4—41no—
450C23×C4—41no—
451C23×C4—41no—
452C23×C4—41no—
453C23×C4—41no—
454C23×C4—41no—
455C23×C4—41no—
456C23×C4—41no—
457C23×C4—41no—
458C23×C4—41no—
459C23×C4C2×D414yes—
460C23×C4#4114yes—
461C23×C4C2411yescharacteristic
462C23×C4C2411yescharacteristic
463C23×C4C2411yescharacteristic
464C23×C4C2411yescharacteristic
465C23×C4C2411yescharacteristic
466C23×C4C2411yescharacteristic
467C23×C4C2411yescharacteristic
468C23×C4C2411yescharacteristic
469C23×C4C2411yescharacteristic
470C23×C4C2411yescharacteristic
471C23×C4C2411yescharacteristic
472C23×C4C2411yescharacteristic
473C23×C4C2411yescharacteristic
474C23×C4C2411yescharacteristic
475C23×C4C2411yescharacteristic
476C23×C4C2411yescharacteristic
477C23×C4C2411yescharacteristic
478C23×C4C2411yescharacteristic
479C23×C4C2411yescharacteristic
480C23×C4C2411yescharacteristic
481C23×C4C2411yescharacteristic
482C23×C4C2411yescharacteristic
483C23×C4C2411yescharacteristic
484C23×C4C2411yescharacteristic
485C23×C4C2411yescharacteristic
486C23×C4C2411yescharacteristic
487C23×C4C2411yescharacteristic
488C23×C4C2411yescharacteristic
489C23×C4C2411yescharacteristic
490#123—232no—
491C22⋊Q8—416no—
492C4×D4—416no—
493#117—416no—
494#117—416no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—22no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—41no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4—41no—
538C2×C4⋊C4—41no—
539C2×C4⋊C4—41no—
540C2×C4⋊C4—41no—
541C2×C4⋊C4—41no—
542C2×C4⋊C4—41no—
543C2×C4⋊C4—41no—
544C2×C4⋊C4—41no—
545C2×C4⋊C4—41no—
546C2×C4⋊C4—41no—
547C2×C4⋊C4—41no—
548C2×C4⋊C4—41no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4—41no—
553C2×C4⋊C4—41no—
554C2×C4⋊C4#4114yes—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—41no—
600C2×C22⋊C4—41no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4—41no—
605C2×C22⋊C4—41no—
606C2×C22⋊C4—41no—
607C2×C22⋊C4—41no—
608C2×C22⋊C4—41no—
609C2×C22⋊C4—41no—
610C2×C22⋊C4—41no—
611C2×C22⋊C4—41no—
612C2×C22⋊C4—41no—
613C2×C22⋊C4—41no—
614C2×C22⋊C4—41no—
615C2×C22⋊C4—41no—
616C2×C22⋊C4C2×D414yes—
617C2×C22⋊C4C2×D414yes—
618C2×C22⋊C4C2×D414yes—
619C2×C22⋊C4#4114yes—
620C2×C22⋊C4#4114yes—
621C2×C42—22no—
622C2×C42—22no—
623C2×C42—22no—
624C2×C42—22no—
625C2×C42—22no—
626C2×C42—22no—
627C2×C42—22no—
628C2×C42—22no—
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—22no—
634C2×C42—22no—
635C2×C42—22no—
636C2×C42—22no—
637C2×C42—22no—
638C2×C42—22no—
639C2×C42—22no—
640C2×C42—22no—
641C2×C42—22no—
642C2×C42—41no—
643C2×C42—41no—
644C2×C42—41no—
645C2×C42—41no—
646C2×C42—41no—
647C2×C42—41no—
648C2×C42—41no—
649C2×C42—41no—
650C2×C42—41no—
651C2×C42—41no—
652C2×C42—41no—
653C2×C42—41no—
654C2×C42—41no—
655C2×C42—416no—
656C2×C42—41no—
657C2×C42—41no—
658C2×C42—41no—
659C2×C42—41no—
660C2×C42#4114yes—
661#95—22no—
662#95—22no—
663#95—22no—
664#95—22no—
665#95—22no—
666#95—22no—
667#95—22no—
668#95—22no—
669#95—22no—
670#95—22no—
671#95—22no—
672#95—22no—
673#95—22no—
674#95—22no—
675#95—22no—
676#95—22no—
677#95—22no—
678#95—22no—
679#95—22no—
680#95—22no—
681#95—22no—
682#95—22no—
683#95—22no—
684#95—22no—
685#95—22no—
686#95—22no—
687#95—22no—
688#95—22no—
689#95—22no—
690#95—22no—
691#95—22no—
692#95—22no—
693#95—22no—
694#95—22no—
695#95—22no—
696#95—22no—
697#95—22no—
698#95—22no—
699#95—22no—
700#95—22no—
701#95—22no—
702#95—22no—
703#95—22no—
704#95—22no—
705#95—22no—
706#95—22no—
707#95—22no—
708#95—22no—
709#95—22no—
710#95—22no—
711#95—22no—
712#95—22no—
713#95—22no—
714#95—22no—
715#95—22no—
716#95—41no—
717#95—41no—
718#95—41no—
719#95—41no—
720#95—41no—
721#95—41no—
722#95—41no—
723#95—41no—
724#95—41no—
725#95—41no—
726#95—41no—
727#95—41no—
728#95—41no—
729#95—41no—
730#95—41no—
731#95—41no—
732#95—41no—
733#95—41no—
734#95—41no—
735#95—41no—
736#95—41no—
737#95—41no—
738#95—41no—
739#95—41no—
740#95—41no—
741#95—41no—
742#95—41no—
743#95—41no—
744#95—41no—
745#95—41no—
746#95—41no—
747#95—41no—
748#95—41no—
749#95—41no—
750#95C2×D414yes—
751#95C2×D414yes—
752#95#4114yes—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24C22×D412yes—
778C24C22×D412yes—
779C24C2×#4112yes—
780C24C2×#4112yes—
781C24C2×#4112yes—
782C24H(5,𝔽2)12yes—
783C24C2511yescharacteristic
784C2×Q8—44no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×Q8—82no—
788C2×Q8—82no—
789C2×Q8—82no—
790C2×Q8—82no—
791C2×D4—28no—
792C2×D4—28no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
797C2×D4—44no—
798C22×C4—28no—
799C22×C4—28no—
800C22×C4—28no—
801C22×C4—28no—
802C22×C4—28no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—28no—
816C22×C4—28no—
817C22×C4—28no—
818C22×C4—28no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—28no—
904C22×C4—28no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—82no—
1008C22×C4—82no—
1009C22×C4—82no—
1010C22×C4—82no—
1011C22×C4—82no—
1012C22×C4—82no—
1013C22×C4—82no—
1014C22×C4—82no—
1015C22×C4—82no—
1016C22×C4—82no—
1017C22×C4—82no—
1018C22×C4—82no—
1019C22×C4—82no—
1020C22×C4C22×D412yes—
1021C22×C4C22×D412yes—
1022C22×C4C22×D412yes—
1023C22×C4C22×D412yes—
1024C22×C4C22×D412yes—
1025C22×C4C2×#4112yes—
1026C22×C4C2×#4112yes—
1027C22×C4C2×#4112yes—
1028C22×C4C2×#4112yes—
1029C22×C4C2×#4112yes—
1030C22×C4C2×#4112yes—
1031C22×C4C2×#4112yes—
1032C22×C4C2×#4112yes—
1033C22×C4C2×#4112yes—
1034C22×C4C2×#4112yes—
1035C22×C4C2×#4112yes—
1036C22×C4C2×#4112yes—
1037C22×C4C2×#4112yes—
1038C22×C4C2×#4112yes—
1039C22×C4C2×#4112yes—
1040C22×C4H(5,𝔽2)12yes—
1041C22×C42−1+412yes—
1042C22×C42−1+412yes—
1043C4⋊C4—28no—
1044C4⋊C4—28no—
1045C4⋊C4—28no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—82no—
1057C4⋊C4—82no—
1058C4⋊C4—82no—
1059C4⋊C4—82no—
1060C4⋊C4—82no—
1061C4⋊C4—82no—
1062C4⋊C4—82no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—82no—
1083C22⋊C4—82no—
1084C22⋊C4—82no—
1085C42—44no—
1086C42—44no—
1087C42—44no—
1088C42—44no—
1089C42—44no—
1090C42—44no—
1091C42—44no—
1092C42—44no—
1093C42—44no—
1094C42—44no—
1095C42—44no—
1096C42—82no—
1097C42—82no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—22no—
1111C23—22no—
1112C23—22no—
1113C23—22no—
1114C23—22no—
1115C23—22no—
1116C23—22no—
1117C23—22no—
1118C23—22no—
1119C23—22no—
1120C23—22no—
1121C23—22no—
1122C23—22no—
1123C23—22no—
1124C23—22no—
1125C23—22no—
1126C23—22no—
1127C23—22no—
1128C23—22no—
1129C23—22no—
1130C23—22no—
1131C23—22no—
1132C23—22no—
1133C23—22no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23#52514yes—
1167C23#54614yes—
1168C23C23×D411yescharacteristic
1169C23C22×#4111yescharacteristic
1170C23C22×#4111yescharacteristic
1171C23C22×#4111yescharacteristic
1172C23C22×#4111yescharacteristic
1173C23C22×#4111yescharacteristic
1174C23C22×#4111yescharacteristic
1175C23C2×H(5,𝔽2)11yescharacteristic
1176C23C2×H(5,𝔽2)11yescharacteristic
1177C23C2×2−1+411yescharacteristic
1178C23C2×2−1+411yescharacteristic
1179C23#58511yescharacteristic
1180C23#58511yescharacteristic
1181C23#58511yescharacteristic
1182C23#58511yescharacteristic
1183Q8—88no—
1184D4—416no—
1185C2×C4—232no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—416no—
1247C2×C4—416no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—41no—
1322C2×C4—41no—
1323C2×C4—41no—
1324C2×C4—41no—
1325C2×C4—41no—
1326C2×C4—41no—
1327C2×C4—41no—
1328C2×C4—41no—
1329C2×C4—41no—
1330C2×C4—41no—
1331C2×C4—41no—
1332C2×C4—41no—
1333C2×C4—41no—
1334C2×C4—41no—
1335C2×C4—41no—
1336C2×C4—41no—
1337C2×C4—41no—
1338C2×C4—41no—
1339C2×C4—41no—
1340C2×C4—41no—
1341C2×C4—41no—
1342C2×C4—41no—
1343C2×C4—41no—
1344C2×C4—41no—
1345C2×C4—41no—
1346C2×C4—41no—
1347C2×C4—41no—
1348C2×C4—41no—
1349C2×C4—41no—
1350C2×C4—41no—
1351C2×C4—41no—
1352C2×C4—41no—
1353C2×C4—41no—
1354C2×C4—41no—
1355C2×C4—41no—
1356C2×C4—41no—
1357C2×C4—41no—
1358C2×C4—41no—
1359C2×C4—41no—
1360C2×C4—41no—
1361C2×C4—41no—
1362C2×C4—41no—
1363C2×C4—41no—
1364C2×C4—41no—
1365C2×C4—41no—
1366C2×C4—41no—
1367C2×C4—41no—
1368C2×C4—41no—
1369C2×C4—41no—
1370C2×C4—41no—
1371C2×C4—41no—
1372C2×C4—41no—
1373C2×C4—41no—
1374C2×C4—41no—
1375C2×C4—41no—
1376C2×C4—41no—
1377C2×C4—41no—
1378C2×C4—41no—
1379C2×C4—41no—
1380C2×C4—41no—
1381C2×C4—41no—
1382C2×C4—41no—
1383C2×C4—41no—
1384C2×C4—41no—
1385C2×C4—41no—
1386C2×C4—41no—
1387C2×C4—41no—
1388C2×C4—88no—
1389C2×C4—88no—
1390C2×C4—88no—
1391C2×C4#54614yes—
1392C2×C4#54714yes—
1393C2×C4#55214yes—
1394C22—24no—
1395C22—24no—
1396C22—24no—
1397C22—24no—
1398C22—24no—
1399C22—24no—
1400C22—42no—
1401C22—42no—
1402C22—42no—
1403C22—42no—
1404C22—42no—
1405C22—42no—
1406C22—42no—
1407C22—42no—
1408C22—42no—
1409C22—42no—
1410C22—42no—
1411C22—42no—
1412C22—42no—
1413C22—42no—
1414C22—42no—
1415C22—42no—
1416C22—42no—
1417C22—42no—
1418C22—42no—
1419C22—42no—
1420C22—42no—
1421C22—42no—
1422C22—42no—
1423C22—42no—
1424C22C2×#52511yescharacteristic
1425C22#344411yescharacteristic
1426C22#344411yescharacteristic
1427C22#346111yescharacteristic
1428C22#346111yescharacteristic
1429C22C2×#54611yescharacteristic
1430C22C2×#54611yescharacteristic
1431C22C2×#54711yescharacteristic
1432C22D4×#4111yescharacteristic
1433C22C2×#55211yescharacteristic
1434C22#347511yescharacteristic
1435C22#347511yescharacteristic
1436C22#347511yescharacteristic
1437C22#347511yescharacteristic
1438C22#348011yescharacteristic
1439C22#348211yescharacteristic
1440C22#348211yescharacteristic
1441C22#348511yescharacteristic
1442C22#348911yescharacteristic
1443C22#349011yescharacteristic
1444C22#349111yescharacteristic
1445C22#349211yescharacteristic
1446C22#349211yescharacteristic
1447C22#351011yescharacteristic
1448C22#351111yescharacteristic
1449C22#351311yescharacteristic
1450C22#351311yescharacteristic
1451C22#351311yescharacteristic
1452C22#351411yescharacteristic
1453C22#351411yescharacteristic
1454C22#352111yescharacteristic
1455C22#353511yescharacteristic
1456C22#355511yescharacteristic
1457C22#355711yescharacteristic
1458C22#356211yescharacteristic
1459C4—24no—
1460C4—24no—
1461C4—24no—
1462C4—42no—
1463C4—42no—
1464C4—42no—
1465C4—42no—
1466C4—42no—
1467C4—42no—
1468C4—42no—
1469C4—42no—
1470C4—42no—
1471C4—42no—
1472C4—42no—
1473C4—42no—
1474C4—42no—
1475C4—42no—
1476C4—81no—
1477C4—81no—
1478C4—81no—
1479C4—81no—
1480C4—81no—
1481C4—81no—
1482C4—81no—
1483C4—81no—
1484C4—81no—
1485C4—81no—
1486C4—81no—
1487C4—81no—
1488C2—44no—
1489C2—44no—
1490C2#3473511yescharacteristic
1491C2#3487311yescharacteristic
1492C2#3540811yescharacteristic
1493C2#3614611yescharacteristic
1494C2#3615911yescharacteristic
1495C2#3637411yescharacteristic
1496C2#3652411yescharacteristic
1497C2#3779611yescharacteristic
1498C2#3800811yescharacteristic
1499C2#3877711yescharacteristic
1500C2#4022811yescharacteristic
1501C2#5901211yescharacteristic
1502C2#5910311yescharacteristic
1503C2#5929511yescharacteristic
1504C2#5962211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #16086C2semidirect
4. #15930C2semidirect
5. #15752C2semidirect
6. #15672C2semidirect
7. #15560C2semidirect
8. #15472C2semidirect
11. #14992C2semidirect
12. #14962C2semidirect
13. #14907C2semidirect
14. #14906C2semidirect
15. #14846C2semidirect
16. #14830C2semidirect
18. #14768C2semidirect
19. #14705C2semidirect
20. #14229C2semidirect
21. #14216C2semidirect
22. #14197C2semidirect
23. #14197C2semidirect
24. #14103C2semidirect
26. #14059C2semidirect
27. #14052C2semidirect
28. #14033C2semidirect
30. #13802C2semidirect
31. #13756C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24772
C2×C4×#1232
#160862
#159302
#157522
#156722
#155602
#154722
#154632
#152692
#149922
#149622
#149072
#149062
#148462
#148302
#148232
#147682
#147052
#142292
#142162
#141972
#141032
#140642
#140592
#140522
#140332
#138942
#138022
#137562