Finite Group Databasebeta

← #29601442

Subgroups — #29601442

Order 15616.

2182 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×#16839620C211yesmaximal, characteristic
2C2×C22⋊C4×Dic61C211yesmaximal, characteristic
3C2×C22⋊C4×Dic61C211yesmaximal, characteristic
4C22×#14519684C211yesmaximal, characteristic
5#21444052C212yesmaximal, complemented
6#21444050C212yesmaximal, complemented
7#21444045C212yesmaximal, complemented
8#21444042C211yesmaximal, characteristic
9#21444041C211yesmaximal, characteristic
10C4×#14519684C212yesmaximal, complemented
11C2×C4×C22⋊C4×C61C211yesmaximal, characteristic
12C24×Dic61C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C22×#11758196C2212yes—
15C22×C22⋊Dic61C2211yescharacteristic
16C22×C22⋊Dic61C2211yescharacteristic
17C22×C4×Dic61C2212yes—
18C22×C4×Dic61C2212yes—
19#16839620C418yescomplemented
20C22⋊C4×Dic61—24no—
21C22⋊C4×Dic61C418yescomplemented
22C2×#14519684C418yescomplemented
23C2×#14519684C2212yes—
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2211yescharacteristic
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2211yescharacteristic
31C2×#14519684C2211yescharacteristic
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C24×C4×C61C2211yescharacteristic
35C22×C22⋊C4×C61C2211yescharacteristic
36C22×C22⋊C4×C61C2211yescharacteristic
37C22×C42×C61C2212yes—
38C4×C22⋊C4×C61—24no—
39C2×#95×C61C2212yes—
40C23×Dic61—22no—
41C23×Dic61—22no—
42C23×Dic61—24no—
43C23×Dic61—42no—
44C23×Dic61—42no—
45C23×Dic61—42no—
46C23×Dic61C2×C414yes—
47C23×Dic61C2×C414yes—
48C23×Dic61C2×C414yes—
49C23×Dic61C2×C414yes—
50C23×Dic61C2312yes—
51C23×Dic61C2312yes—
52C23×Dic61C2311yescharacteristic
53C23×Dic61C2311yescharacteristic
54C23×Dic61C2311yescharacteristic
55C23×Dic61C2311yescharacteristic
56C2×#11758196—42no—
57C2×#11758196—42no—
58C2×#11758196C2×C418yescomplemented
59C2×C22⋊Dic61—22no—
60C2×C22⋊Dic61—22no—
61C2×C22⋊Dic61—22no—
62C2×C22⋊Dic61—22no—
63C2×C22⋊Dic61C2×C414yes—
64C2×C22⋊Dic61C2×C414yes—
65C2×C4×Dic61—24no—
66C2×C4×Dic61—24no—
67C2×C4×Dic61—42no—
68C2×C4×Dic61—42no—
69C2×C4×Dic61—42no—
70C2×C4×Dic61C2×C418yescomplemented
71#14519684—24no—
72#14519684—24no—
73#14519684—24no—
74#14519684—42no—
75#14519684—42no—
76#14519684C2×C414yes—
77#14519684C2×C414yes—
78#14519684C2×C414yes—
79#14519684C2×C414yes—
80#14519684C2×C418yescomplemented
81#14519684C2×C418yescomplemented
82C25×C61C2311yescharacteristic
83C23×C4×C61—22no—
84C23×C4×C61—22no—
85C23×C4×C61—24no—
86C23×C4×C61—42no—
87C23×C4×C61C2×C414yes—
88C23×C4×C61C2312yes—
89C23×C4×C61C2311yescharacteristic
90C23×C4×C61C2312yes—
91C23×C4×C61C2311yescharacteristic
92C2×C22⋊C4×C61—22no—
93C2×C22⋊C4×C61—22no—
94C2×C22⋊C4×C61C2×C414yes—
95C2×C22⋊C4×C61C2×C414yes—
96C2×C22⋊C4×C61D414yes—
97C2×C22⋊C4×C61Q814yes—
98C2×C42×C61—24no—
99C2×C42×C61—24no—
100C2×C42×C61—42no—
101#95×C61—24no—
102C24×C61—22no—
103C24×C61—22no—
104C24×C61—22no—
105C24×C61—22no—
106C24×C61C22×C412yes—
107C24×C61C22×C412yes—
108C24×C61C22×C412yes—
109C24×C61C2×D412yes—
110C24×C61C2×Q812yes—
111C24×C61#4112yes—
112C24×C61#4112yes—
113C24×C61C2411yescharacteristic
114C22×C4×C61—21no—
115C22×C4×C61—22no—
116C22×C4×C61—21no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—28no—
122C22×C4×C61—21no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—21no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61—28no—
133C22×C4×C61—44no—
134C22×C4×C61—48no—
135C22×C4×C61—48no—
136C22×C4×C61C22×C414yes—
137C22×C4×C61C22×C412yes—
138C22×C4×C61C22×C414yes—
139C22×C4×C61C22×C412yes—
140C22×C4×C61C2×D414yes—
141C22×C4×C61C2×Q814yes—
142C22×C4×C61#4114yes—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—28no—
151C22×Dic61—21no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—21no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61—22no—
163C22×Dic61—22no—
164C22×Dic61—22no—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—28no—
168C22×Dic61—48no—
169C22×Dic61—48no—
170C22×Dic61—44no—
171C22×Dic61—44no—
172C22×Dic61—44no—
173C22×Dic61—48no—
174C22×Dic61—48no—
175C22×Dic61C42116yescomplemented
176C22×Dic61C22×C412yes—
177C22×Dic61C22×C414yes—
178C22×Dic61C22×C414yes—
179C22×Dic61C22×C412yes—
180C22×Dic61C22×C412yes—
181C22×Dic61C22×C412yes—
182C22×Dic61C22×C412yes—
183C22×Dic61C22×C412yes—
184C22×Dic61C22×C412yes—
185C22×Dic61C22×C412yes—
186C22×Dic61#4114yes—
187C22⋊C4×C61—28no—
188C22⋊C4×C61C4⋊C4116yescomplemented
189C42×C61—48no—
190C22⋊Dic61—28no—
191C22⋊Dic61—28no—
192#11758196—48no—
193C4×Dic61—48no—
194C4×Dic61—48no—
195C23×C61—22no—
196C23×C61—22no—
197C23×C61—24no—
198C23×C61—24no—
199C23×C61—22no—
200C23×C61—22no—
201C23×C61—24no—
202C23×C61—24no—
203C23×C61—24no—
204C23×C61—24no—
205C23×C61—24no—
206C23×C61—24no—
207C23×C61—24no—
208C23×C61—24no—
209C23×C61—24no—
210C23×C61—24no—
211C23×C61C2×C4214yes—
212C23×C61C2×C4⋊C414yes—
213C23×C61#11714yes—
214C23×C61C4×D414yes—
215C23×C61C4×D414yes—
216C23×C61C4×Q814yes—
217C23×C61C4×Q814yes—
218C23×C61C23×C411yescharacteristic
219C23×C61C23×C411yescharacteristic
220C23×C61C23×C411yescharacteristic
221C23×C61C22×D411yescharacteristic
222C23×C61C22×Q811yescharacteristic
223C23×C61C2×#4111yescharacteristic
224C23×C61C2×#4111yescharacteristic
225C23×C61C2×#4112yes—
226C23×C61C2×#4112yes—
227C23×C61H(5,𝔽2)12yes—
228C23×C61H(5,𝔽2)12yes—
229C2×C4×C61—22no—
230C2×C4×C61—24no—
231C2×C4×C61—24no—
232C2×C4×C61—22no—
233C2×C4×C61—24no—
234C2×C4×C61—24no—
235C2×C4×C61—24no—
236C2×C4×C61—24no—
237C2×C4×C61—24no—
238C2×C4×C61—24no—
239C2×C4×C61—22no—
240C2×C4×C61—24no—
241C2×C4×C61—22no—
242C2×C4×C61—24no—
243C2×C4×C61—24no—
244C2×C4×C61—22no—
245C2×C4×C61—416no—
246C2×C4×C61—42no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61—42no—
250C2×C4×C61—42no—
251C2×C4×C61—42no—
252C2×C4×C61C2×C4⋊C418yes—
253C2×C4×C61#11714yes—
254C2×Dic61—22no—
255C2×Dic61—24no—
256C2×Dic61—24no—
257C2×Dic61—22no—
258C2×Dic61—24no—
259C2×Dic61—24no—
260C2×Dic61—22no—
261C2×Dic61—22no—
262C2×Dic61—22no—
263C2×Dic61—22no—
264C2×Dic61—24no—
265C2×Dic61—24no—
266C2×Dic61—24no—
267C2×Dic61—22no—
268C2×Dic61—24no—
269C2×Dic61—22no—
270C2×Dic61—24no—
271C2×Dic61—24no—
272C2×Dic61—24no—
273C2×Dic61—24no—
274C2×Dic61—22no—
275C2×Dic61—416no—
276C2×Dic61—416no—
277C2×Dic61—42no—
278C2×Dic61—42no—
279C2×Dic61—42no—
280C2×Dic61—42no—
281C2×Dic61—42no—
282C2×Dic61—42no—
283C2×Dic61—42no—
284C2×Dic61—42no—
285C2×Dic61—42no—
286C2×Dic61—42no—
287C2×Dic61C2×C4214yes—
288C2×Dic61C2×C4214yes—
289C2×Dic61#11714yes—
290#13802—611nomaximal, Sylow
291C22×C61—24no—
292C22×C61—24no—
293C22×C61—24no—
294C22×C61—24no—
295C22×C61—28no—
296C22×C61—28no—
297C22×C61—28no—
298C22×C61—28no—
299C22×C61—24no—
300C22×C61—24no—
301C22×C61C4×C4⋊C418yes—
302C22×C61C22×C4211yescharacteristic
303C22×C61C22×C4⋊C411yescharacteristic
304C22×C61C2×#11711yescharacteristic
305C22×C61C2×#11711yescharacteristic
306C22×C61C2×#11711yescharacteristic
307C22×C61C2×C4×D411yescharacteristic
308C22×C61C2×C4×D411yescharacteristic
309C22×C61C2×C4×Q811yescharacteristic
310C22×C61C2×C4×Q811yescharacteristic
311C22×C61C4×#4112yes—
312C22×C61C4×#4112yes—
313C22×C61#51812yes—
314C22×C61#51812yes—
315C22×C61#51811yescharacteristic
316C22×C61#51811yescharacteristic
317C22×C61#54612yes—
318C22×C61#54612yes—
319C22×C61#55112yes—
320C22×C61#55112yes—
321C22×C61#55312yes—
322C22×C61#55312yes—
323C22×C61#55412yes—
324C22×C61#55412yes—
325C4×C61—24no—
326C4×C61—28no—
327C4×C61—42no—
328C4×C61—44no—
329Dic61—24no—
330Dic61—24no—
331Dic61—24no—
332Dic61—42no—
333Dic61—44no—
334Dic61—44no—
335C2×#380—611no—
336C2×C4×C22⋊C4—611no—
337C2×C4×C22⋊C4—611no—
338C2×C4×C22⋊C4D6111yescharacteristic
339C22×#95—611no—
340#1436—612no—
341#1436—612no—
342#1434—612no—
343C22⋊#95—611no—
344C22⋊#95—611no—
345C4×#95—612no—
346C2×C61—28no—
347C2×C61C2×C4×C4⋊C411yescharacteristic
348C2×C61C4×#11711yescharacteristic
349C2×C61#227311yescharacteristic
350C2×C61#234211yescharacteristic
351C2×C61#234211yescharacteristic
352C2×C61#234511yescharacteristic
353C2×C61#234511yescharacteristic
354C2×C61#234912yes—
355C2×C61#235312yes—
356C2×C61#236412yes—
357C2×C61#236812yes—
358C24×C4—611no—
359C24×C4—611no—
360C24×C4C2×D6111yescharacteristic
361C22×C4⋊C4—612no—
362C22×C22⋊C4—611no—
363C22×C22⋊C4—611no—
364C22×C22⋊C4C2×D6111yescharacteristic
365C22×C22⋊C4C2×D6111yescharacteristic
366C22×C42—612no—
367C22×C42—612no—
368C22×C42C2×D6112yes—
369#380—618no—
370C4×C22⋊C4—24no—
371C4×C22⋊C4—618no—
372C4×C22⋊C4—1224no—
373C2×#95—618no—
374C2×#95—611no—
375C2×#95—612no—
376C2×#95—611no—
377C2×#95—611no—
378C2×#95—611no—
379C2×#95—612no—
380C2×#95—612no—
381C2×#95—612no—
382C2×#95—612no—
383C2×#95—612no—
384C2×#95—612no—
385C2×#95C2×D6112yes—
386C61#1380211yescharacteristic, complemented, Sylow
387C25C22×D6111yescharacteristic
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—24no—
391C23×C4—42no—
392C23×C4—611no—
393C23×C4—611no—
394C23×C4—611no—
395C23×C4—614no—
396C23×C4—614no—
397C23×C4—614no—
398C23×C4—612no—
399C23×C4—612no—
400C23×C4—611no—
401C23×C4—614no—
402C23×C4—1224no—
403C23×C4—1222no—
404C23×C4—1222no—
405C23×C4—2442no—
406C23×C4—2442no—
407C23×C4—2442no—
408C23×C4C4×D6114yes—
409C23×C4C22×D6112yes—
410C23×C4C22×D6111yescharacteristic
411C23×C4C22×D6112yes—
412C23×C4C22×D6111yescharacteristic
413C2×C4⋊C4—618no—
414C2×C4⋊C4—2442no—
415C2×C4⋊C4—2442no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—614no—
419C2×C22⋊C4—614no—
420C2×C22⋊C4—1222no—
421C2×C22⋊C4—1222no—
422C2×C22⋊C4—1222no—
423C2×C22⋊C4—1222no—
424C2×C22⋊C4Dic12214yes—
425C2×C22⋊C4C4×D6114yes—
426C2×C22⋊C4C4×D6114yes—
427C2×C22⋊C4C22⋊D6114yes—
428C2×C42—24no—
429C2×C42—24no—
430C2×C42—42no—
431C2×C42—618no—
432C2×C42—1224no—
433C2×C42—1224no—
434C2×C42—2442no—
435C2×C42—2442no—
436C2×C42—2442no—
437#95—24no—
438#95—614no—
439#95—614no—
440#95—614no—
441#95—614no—
442#95—618no—
443#95—618no—
444#95—1224no—
445#95—1224no—
446#95—1224no—
447#95—2442no—
448#95—2442no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24C2×Dic12212yes—
454C24C2×C4×D6112yes—
455C24C2×C4×D6112yes—
456C24C2×C4×D6112yes—
457C24#1175822212yes—
458C24#1175822212yes—
459C24C2×C22⋊D6112yes—
460C24C23×D6111yescharacteristic
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—44no—
481C22×C4—48no—
482C22×C4—48no—
483C22×C4—612no—
484C22×C4—612no—
485C22×C4—612no—
486C22×C4—612no—
487C22×C4—612no—
488C22×C4—612no—
489C22×C4—612no—
490C22×C4—614no—
491C22×C4—6116no—
492C22×C4—612no—
493C22×C4—614no—
494C22×C4—614no—
495C22×C4—1228no—
496C22×C4—1221no—
497C22×C4—1221no—
498C22×C4—1222no—
499C22×C4—1222no—
500C22×C4—1222no—
501C22×C4—1222no—
502C22×C4—1222no—
503C22×C4—1221no—
504C22×C4—1222no—
505C22×C4—1222no—
506C22×C4—1222no—
507C22×C4—1222no—
508C22×C4—1222no—
509C22×C4—1222no—
510C22×C4—1222no—
511C22×C4—1222no—
512C22×C4—1222no—
513C22×C4—1221no—
514C22×C4—1222no—
515C22×C4—1222no—
516C22×C4—1222no—
517C22×C4—1222no—
518C22×C4—1222no—
519C22×C4—1228no—
520C22×C4—2448no—
521C22×C4—2448no—
522C22×C4—2444no—
523C22×C4—2444no—
524C22×C4—2444no—
525C22×C4—2448no—
526C22×C4—2448no—
527C22×C4C2×Dic12214yes—
528C22×C4C2×C4×D6112yes—
529C22×C4C2×C4×D6114yes—
530C22×C4C2×C4×D6114yes—
531C22×C4C2×C4×D6112yes—
532C22×C4#1175822414yes—
533C22×C4C2×C22⋊D6114yes—
534C4⋊C4—2448no—
535C22⋊C4—28no—
536C22⋊C4—1228no—
537C22⋊C4—1228no—
538C22⋊C4#11758196116yescomplemented
539C42—48no—
540C42—2448no—
541C42—2448no—
542C23—24no—
543C23—24no—
544C23—24no—
545C23—22no—
546C23—22no—
547C23—24no—
548C23—24no—
549C23—24no—
550C23—24no—
551C23—24no—
552C23—22no—
553C23—22no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—24no—
558C23C42×D6114yes—
559C23C2×#1175819614yes—
560C23#1451973414yes—
561C23C4×C22⋊D6114yes—
562C23C4×C22⋊D6114yes—
563C23C4×Dic12214yes—
564C23C4×Dic12214yes—
565C23C22×C4×D6111yescharacteristic
566C23C22×C4×D6111yescharacteristic
567C23C22×C4×D6111yescharacteristic
568C23C22×C22⋊D6111yescharacteristic
569C23C22×Dic12211yescharacteristic
570C23#41×D6112yes—
571C23C2×#1175822412yes—
572C23C2×#1175822211yescharacteristic
573C23C2×#1175822211yescharacteristic
574C23#1451982212yes—
575C23#1451982312yes—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—24no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—22no—
592C2×C4—416no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—614no—
600C2×C4—614no—
601C2×C4—614no—
602C2×C4—1222no—
603C2×C4—1224no—
604C2×C4—1224no—
605C2×C4—1224no—
606C2×C4—1224no—
607C2×C4—1222no—
608C2×C4—1222no—
609C2×C4—1222no—
610C2×C4—1222no—
611C2×C4—1222no—
612C2×C4—1224no—
613C2×C4—1224no—
614C2×C4—1222no—
615C2×C4—1224no—
616C2×C4—1224no—
617C2×C4—1222no—
618C2×C4—1224no—
619C2×C4—1224no—
620C2×C4—1224no—
621C2×C4—1224no—
622C2×C4—1222no—
623C2×C4—24416no—
624C2×C4—24416no—
625C2×C4—2442no—
626C2×C4—2442no—
627C2×C4—2442no—
628C2×C4—2442no—
629C2×C4—2442no—
630C2×C4—2442no—
631C2×C4—2442no—
632C2×C4—2442no—
633C2×C4—2442no—
634C2×C4—2442no—
635C2×C4C2×#1175819618yes—
636C2×C4#1451973314yes—
637C22—28no—
638C22—28no—
639C22—28no—
640C22—28no—
641C22—24no—
642C22—24no—
643C22—24no—
644C22—24no—
645C22—24no—
646C22—24no—
647C22C4×#1175819618yes—
648C22C2×C42×D6111yescharacteristic
649C22C22×#1175819611yescharacteristic
650C22#117×D6111yescharacteristic
651C22C2×#1451973311yescharacteristic
652C22C2×#1451973411yescharacteristic
653C22C2×C4×C22⋊D6111yescharacteristic
654C22C2×C4×C22⋊D6111yescharacteristic
655C22C2×C4×Dic12211yescharacteristic
656C22C2×C4×Dic12211yescharacteristic
657C22C4×#1175822412yes—
658C22C4×#1175822412yes—
659C22#1684023412yes—
660C22#1684023412yes—
661C22#1684023511yescharacteristic
662C22#1684023611yescharacteristic
663C22#1684040012yes—
664C22#1684040612yes—
665C22#1684043612yes—
666C22#1684043812yes—
667C22#1684045812yes—
668C22#1684046112yes—
669C22#1684046912yes—
670C22#1684047112yes—
671C4—28no—
672C4—24no—
673C4—44no—
674C4—42no—
675C4—1224no—
676C4—1224no—
677C4—1224no—
678C4—2444no—
679C4—2444no—
680C4—2442no—
681C2—28no—
682C2C2×C4×#1175819611yescharacteristic
683C2C4×#1451973311yescharacteristic
684C2#2144817111yescharacteristic
685C2#2144866411yescharacteristic
686C2#2144866911yescharacteristic
687C2#2144869411yescharacteristic
688C2#2144869711yescharacteristic
689C2#2144872412yes—
690C2#2144875312yes—
691C2#2144886412yes—
692C2#2144889712yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC2×C4×C22⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×C4×C22⋊C4D61
hypocenterC61#13802
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
5. #21444052C2semidirect
6. #21444050C2semidirect
7. #21444045C2semidirect
10. C4×#14519684C2semidirect
19. #16839620C4semidirect
21. C22⋊C4×Dic61C4semidirect
22. C2×#14519684C4semidirect
58. C2×#11758196C2×C4semidirect
70. C2×C4×Dic61C2×C4semidirect
80. #14519684C2×C4semidirect
81. #14519684C2×C4semidirect
175. C22×Dic61C42semidirect
188. C22⋊C4×C61C4⋊C4semidirect
386. C61#13802semidirect
538. C22⋊C4#11758196semidirect

Maximal subgroups

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

subgroupindex
C2×#168396202
C2×C22⋊C4×Dic612
C22×#145196842
#214440522
#214440502
#214440452
#214440422
#214440412
C4×#145196842
C2×C4×C22⋊C4×C612
#1380261