Finite Group Databasebeta

← #29842918

Subgroups — #29842918

Order 15616.

2098 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840316C211yesmaximal, characteristic
2#21449003C214yesmaximal, complemented
3#21448878C212yesmaximal, complemented
4#21448876C212yesmaximal, complemented
5#21448778C211yesmaximal, characteristic, complemented
6#21448771C212yesmaximal, complemented
7Q8×C4⋊Dic61C211yesmaximal, characteristic, complemented
8C4⋊C4×Dic122C212yesmaximal, complemented
9C4⋊C4×Dic122C211yesmaximal, characteristic, complemented
10#21448504C212yesmaximal
11#21448502C212yesmaximal
12#21448500C214yesmaximal
13#21448429C212yesmaximal
14#21448424C212yesmaximal
15#21448224C211yesmaximal, characteristic
16#21448223C211yesmaximal, characteristic
17C61×#2355C211yesmaximal, characteristic, complemented
18#16840316C4116yescomplemented
19C2×#14519776C2211yescharacteristic
20C2×#14519775C2211yescharacteristic
21C2×#14519767C2212yes—
22C2×#14519757C2211yescharacteristic
23C2×#14519755C2212yes—
24C2×#14519753C2211yescharacteristic
25C2×Q8×Dic61C2212yes—
26C2×C4×Dic122C2214yes—
27C2×C4×Dic122C2212yes—
28C2×C4×Dic122C2212yes—
29C2×C4×Dic122C2211yescharacteristic
30C2×#14519735C2212yes—
31C2×#14519734C2212yes—
32C2×#14519734C2212yes—
33C2×C42×D61C2211yescharacteristic
34#16839667C2212yes—
35#16839666C2214yes—
36#16839661C2214yes—
37#16839661C2212yes—
38#16839660C2214yes—
39#16839660C2212yes—
40#16839659C2214yes—
41#16839659C2214yes—
42#16839659C2214yes—
43#16839654C2214yes—
44#16839654C2214yes—
45#16839653C2214yes—
46#16839651C2214yes—
47#16839649C2214yes—
48#16839649C2214yes—
49#16839647C2214yes—
50#16839646C2214yes—
51#16839644C2214yes—
52#16839644C2214yes—
53#16839643C2214yes—
54#16839632C2211yescharacteristic
55#16839632C2212yes—
56#16839631C2211yescharacteristic
57#16839631C2212yes—
58#16839631C2211yescharacteristic
59#16839627C2212yes—
60#16839627C2212yes—
61#16839626C2212yes—
62#16839621C2212yes—
63#16839619C2211yescharacteristic
64#16839619C2211yescharacteristic
65#16839619C2212yes—
66#16839619C2212yes—
67C4⋊C4×Dic61C2212yes—
68C4⋊C4×Dic61C2212yes—
69C4⋊C4×Dic61C2212yes—
70C4⋊C4×Dic61C2212yes—
71C4⋊C4×Dic61C2212yes—
72C4×#11758196C2212yes—
73C4×C4⋊Dic61C2211yescharacteristic
74C4×C4⋊Dic61C2212yes—
75#16839613C2214yes—
76C2×C4×Q8×C61C2211yescharacteristic
77C61×#391C2212yes—
78C61×#387C2214yes—
79C61×#384C2211yescharacteristic
80C61×#382C2212yes—
81C4×C4⋊C4×C61C2211yescharacteristic
82C4×C4⋊C4×C61C2212yes—
83C4×C4⋊C4×C61C2212yes—
84C22×Dic122C2312yes—
85C22×Dic122C2311yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C22×C4×D61C2311yescharacteristic
88C22×C4×D61C2311yescharacteristic
89#14519776C2×C418yes—
90#14519775C2×C418yes—
91#14519767C2×C4116yes—
92#14519757C2×C418yes—
93#14519755C2×C4116yes—
94#14519753C2×C418yes—
95Q8×Dic61—44no—
96C4×Dic122—48no—
97C4×Dic122—44no—
98C4×Dic122C2×C4116yes—
99C4×Dic122C2×C418yes—
100#14519735—44no—
101#14519734—44no—
102#14519734C2×C4116yes—
103C2×C4⋊Dic61C2312yes—
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2312yes—
107C2×C4⋊Dic61C2312yes—
108C2×C4⋊Dic61C2314yes—
109C2×C4⋊Dic61C2314yes—
110C2×C4⋊Dic61C2311yescharacteristic
111C2×C4⋊Dic61C2312yes—
112C2×#11758196C2312yes—
113C2×#11758196C2312yes—
114C2×#11758196C2312yes—
115C2×#11758196C2312yes—
116C2×#11758196C2314yes—
117C2×#11758196C2314yes—
118C2×#11758196C2312yes—
119C2×#11758196C2312yes—
120C2×#11758196C2312yes—
121C2×#11758196C2312yes—
122C2×#11758196C2312yes—
123C2×#11758198C2312yes—
124C2×#11758198C2312yes—
125C2×#11758198C2314yes—
126C2×#11758198C2312yes—
127C2×#11758198C2312yes—
128C2×C4×Dic61C2312yes—
129C2×C4×Dic61C2314yes—
130C2×C4×Dic61C2314yes—
131C2×C4×Dic61C2314yes—
132C2×C4×Dic61C2314yes—
133C2×C4×Dic61C2311yescharacteristic
134C2×C4×Dic61C2311yescharacteristic
135C2×C4×Dic61C2311yescharacteristic
136C2×C4×Dic61C2312yes—
137C42×D61C2×C418yes—
138#14519684C2314yes—
139#14519684C2312yes—
140#14519684C2314yes—
141#14519684C2312yes—
142#14519684C2312yes—
143#14519684C2314yes—
144#14519684C2314yes—
145#14519684C2314yes—
146#14519684C2314yes—
147#14519684C2314yes—
148C22×Q8×C61C2311yescharacteristic
149C4×Q8×C61C2×C418yes—
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2312yes—
153C2×C4⋊C4×C61C2312yes—
154C2×C4⋊C4×C61C2312yes—
155C2×C4⋊C4×C61C2312yes—
156C2×C4⋊C4×C61C2311yescharacteristic
157C2×C42×C61C2312yes—
158C2×C42×C61C2314yes—
159C2×C42×C61C2311yescharacteristic
160C2×C42×C61C2312yes—
161#95×C61C2314yes—
162#95×C61C2312yes—
163#95×C61C2314yes—
164#95×C61C2314yes—
165C23×D61C2411yescharacteristic
166C2×Q8×C61—22no—
167C2×Q8×C61—22no—
168C2×Q8×C61C22×C414yes—
169C22×C4×C61C2412yes—
170C22×C4×C61C2412yes—
171C22×C4×C61C2414yes—
172C22×C4×C61C2411yescharacteristic
173C22×C4×C61C2412yes—
174C22×C4×C61C2412yes—
175C22×C4×C61C2411yescharacteristic
176C22×C4×C61C2411yescharacteristic
177C22×Dic61C2412yes—
178C22×Dic61C2412yes—
179C22×Dic61C2414yes—
180C22×Dic61C2411yescharacteristic
181C22×Dic61C2411yescharacteristic
182C22×Dic61C2412yes—
183C22×Dic61C2412yes—
184C22×Dic61C2411yescharacteristic
185C2×C4×D61—22no—
186C2×C4×D61—22no—
187C2×C4×D61—22no—
188C2×C4×D61—22no—
189C2×C4×D61—22no—
190C2×C4×D61—22no—
191C2×C4×D61C22×C414yes—
192C2×C4×D61C22×C414yes—
193C2×C4×D61C22×C414yes—
194C2×Dic122—22no—
195C2×Dic122—22no—
196C2×Dic122—24no—
197C2×Dic122—24no—
198C2×Dic122C22×C418yes—
199C2×Dic122C22×C414yes—
200C4⋊C4×C61—22no—
201C4⋊C4×C61—24no—
202C4⋊C4×C61—22no—
203C4⋊C4×C61—24no—
204C4⋊C4×C61—42no—
205C4⋊C4×C61C22×C418yes—
206C4⋊C4×C61C22×C414yes—
207C42×C61—24no—
208C42×C61—44no—
209C42×C61C22×C414yes—
210C42×C61C22×C418yes—
211#11758198—42no—
212#11758198—42no—
213#11758198—44no—
214#11758198C22×C418yes—
215#11758198C22×C418yes—
216C4⋊Dic61—24no—
217C4⋊Dic61—22no—
218C4⋊Dic61—22no—
219C4⋊Dic61—24no—
220C4⋊Dic61—42no—
221C4⋊Dic61—44no—
222C4⋊Dic61—44no—
223C4⋊Dic61C22×C414yes—
224C4⋊Dic61C22×C418yes—
225#11758196—24no—
226#11758196—24no—
227#11758196—42no—
228#11758196—42no—
229#11758196—44no—
230#11758196—44no—
231#11758196C22×C418yes—
232#11758196C22×C418yes—
233#11758196C22×C418yes—
234#11758196C22×C418yes—
235#11758196C22×C418yes—
236C4×Dic61—24no—
237C4×Dic61—28no—
238C4×Dic61—44no—
239C4×Dic61—44no—
240C4×Dic61—44no—
241C4×Dic61C22×C414yes—
242C4×Dic61C22×C414yes—
243C4×Dic61C22×C414yes—
244C4×Dic61C22×C418yes—
245C23×C61C2511yescharacteristic
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61C23×C412yes—
253Q8×C61—28no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—21no—
257C2×C4×C61—22no—
258C2×C4×C61—21no—
259C2×C4×C61—22no—
260C2×C4×C61—24no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—24no—
268C2×C4×C61—24no—
269C2×C4×C61C23×C412yes—
270C2×C4×C61C23×C414yes—
271C2×C4×C61C23×C414yes—
272C2×C4×C61C23×C412yes—
273C2×C4×C61C23×C412yes—
274C2×C4×C61H(5,𝔽2)12yes—
275C2×C4×C612−1+412yes—
276C2×C4×C612−1+412yes—
277C2×C4×C612−1+412yes—
278C2×Dic61—22no—
279C2×Dic61—22no—
280C2×Dic61—21no—
281C2×Dic61—22no—
282C2×Dic61—22no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—22no—
287C2×Dic61—24no—
288C2×Dic61—22no—
289C2×Dic61—22no—
290C2×Dic61—24no—
291C2×Dic61—22no—
292C2×Dic61—22no—
293C2×Dic61—24no—
294C2×Dic61—22no—
295C2×Dic61C23×C412yes—
296C2×Dic61C23×C412yes—
297C2×Dic61C23×C414yes—
298C2×Dic61C23×C414yes—
299C2×Dic61C23×C412yes—
300C2×Dic61H(5,𝔽2)12yes—
301C2×Dic612−1+412yes—
302C4×D61—28no—
303C4×D61—28no—
304C4×D61—28no—
305Dic122—28no—
306Dic122—216no—
307#34374—611nomaximal, Sylow
308C22×C61C24×C411yescharacteristic
309C22×C61C2×H(5,𝔽2)11yescharacteristic
310C22×C61C2×H(5,𝔽2)11yescharacteristic
311C22×C61C2×2−1+411yescharacteristic
312C22×C61C2×2−1+411yescharacteristic
313C22×C61C2×2−1+411yescharacteristic
314C22×C61C2×2−1+411yescharacteristic
315C2×D61—22no—
316C2×D61—22no—
317C2×D61—22no—
318C2×D61—41no—
319C2×D61—41no—
320C2×D61—41no—
321C2×D61—41no—
322C4×C61—24no—
323C4×C61—22no—
324C4×C61—24no—
325C4×C61—42no—
326C4×C61—44no—
327C4×C61—42no—
328C4×C61#51914yes—
329C4×C61#52014yes—
330Dic61—22no—
331Dic61—24no—
332Dic61—24no—
333Dic61—22no—
334Dic61—42no—
335Dic61—44no—
336Dic61—42no—
337Dic61#52014yes—
338C2×#533—611no—
339#2382—614no—
340#2365—612no—
341#2365—612no—
342#2355—611no—
343#2355—612no—
344#2355D6111yescharacteristic, complemented
345Q8×C4⋊C4—611no—
346Q8×C4⋊C4—612no—
347Q8×C4⋊C4—611no—
348#2323—612no—
349#2323—614no—
350#2323—612no—
351#2314—612no—
352#2314—612no—
353#2285—611no—
354#2285—611no—
355C2×C61C2×#51911yescharacteristic
356C2×C61C2×#52011yescharacteristic
357C2×C61C2×#52011yescharacteristic
358C2×C61#354811yescharacteristic
359C2×C61#355011yescharacteristic
360C2×C61#355011yescharacteristic
361C2×C61#355611yescharacteristic
362D61—42no—
363#533—6116no—
364C2×C4⋊Q8—611no—
365C2×C4⋊Q8—611no—
366C2×#125—612no—
367C2×C22⋊Q8—611no—
368C2×C22⋊Q8—612no—
369C2×C22⋊Q8—611no—
370C2×C4×Q8—612no—
371C2×C4×Q8—611no—
372C2×C4×Q8—612no—
373C2×C4×Q8—614no—
374C2×C4×Q8—612no—
375C2×C4×Q8C2×D6111yescharacteristic
376C2×#117—612no—
377C2×#117—612no—
378C2×#117—612no—
379C22×C42—611no—
380#391—612no—
381#391—614no—
382#391C2×D6112yes—
383#389—612no—
384#389—614no—
385#389—612no—
386#389—614no—
387#389—614no—
388#389—614no—
389#389—614no—
390#388—614no—
391#388—614no—
392#388—614no—
393#388—614no—
394#387—614no—
395#387—614no—
396#387—614no—
397#387—614no—
398#387—614no—
399#387—614no—
400#387—614no—
401#387C2×D6114yes—
402#384—612no—
403#384—611no—
404#384—611no—
405#384—612no—
406#384—611no—
407#384C2×D6111yescharacteristic
408#382—612no—
409#382—612no—
410#382—612no—
411#382C2×D6112yes—
412#380—611no—
413#380—612no—
414#380—611no—
415#380—612no—
416#380—612no—
417C4×C4⋊C4—612no—
418C4×C4⋊C4—612no—
419C4×C4⋊C4—612no—
420C4×C4⋊C4—612no—
421C4×C4⋊C4—612no—
422C4×C4⋊C4—612no—
423C4×C4⋊C4—611no—
424C4×C4⋊C4—612no—
425C4×C4⋊C4—614no—
426C4×C4⋊C4C2×D6112yes—
427C4×C4⋊C4C2×D6112yes—
428C4×C4⋊C4C2×D6111yescharacteristic
429C61#3437411yescharacteristic, complemented, Sylow
430C22×Q8—612no—
431C22×Q8—611no—
432C22×Q8C22×D6111yescharacteristic
433C23×C4—611no—
434C23×C4—611no—
435C23×C4—611no—
436C4⋊Q8—618no—
437C4⋊Q8—618no—
438#125—6116no—
439C22⋊Q8—618no—
440C22⋊Q8—6116no—
441C22⋊Q8—618no—
442C4×Q8—6116no—
443C4×Q8—618no—
444C4×Q8—2444no—
445C4×Q8—2448no—
446C4×Q8—2444no—
447C4×Q8C4×D6118yes—
448#117—6116no—
449#117—2444no—
450#117—2444no—
451C2×C4⋊C4—612no—
452C2×C4⋊C4—612no—
453C2×C4⋊C4—612no—
454C2×C4⋊C4—612no—
455C2×C4⋊C4—612no—
456C2×C4⋊C4—612no—
457C2×C4⋊C4—611no—
458C2×C4⋊C4—612no—
459C2×C4⋊C4—612no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—612no—
463C2×C4⋊C4—612no—
464C2×C4⋊C4—612no—
465C2×C4⋊C4—612no—
466C2×C4⋊C4—612no—
467C2×C4⋊C4—614no—
468C2×C4⋊C4—614no—
469C2×C4⋊C4—614no—
470C2×C4⋊C4—614no—
471C2×C4⋊C4C22×D6112yes—
472C2×C4⋊C4C22×D6111yescharacteristic
473C2×C4⋊C4C22×D6112yes—
474C2×C4⋊C4C22×D6111yescharacteristic
475C2×C4⋊C4C22×D6112yes—
476C2×C4⋊C4C22×D6112yes—
477C2×C4⋊C4C22×D6111yescharacteristic
478C2×C22⋊C4—612no—
479C2×C22⋊C4—612no—
480C2×C22⋊C4—612no—
481C2×C22⋊C4—614no—
482C2×C22⋊C4—612no—
483C2×C42—612no—
484C2×C42—611no—
485C2×C42—611no—
486C2×C42—611no—
487C2×C42—618no—
488C2×C42—614no—
489C2×C42—612no—
490C2×C42—614no—
491C2×C42—614no—
492C2×C42—614no—
493C2×C42C22×D6112yes—
494C2×C42C22×D6114yes—
495C2×C42C22×D6112yes—
496C2×C42C22×D6111yescharacteristic
497#95—612no—
498#95—614no—
499#95—612no—
500#95—614no—
501#95—612no—
502#95—614no—
503#95—614no—
504#95—614no—
505#95—614no—
506#95—614no—
507#95C22×D6114yes—
508#95C22×D6112yes—
509#95C22×D6114yes—
510#95C22×D6114yes—
511C24—611no—
512C2×Q8—22no—
513C2×Q8—22no—
514C2×Q8—618no—
515C2×Q8—614no—
516C2×Q8—1224no—
517C2×Q8—1224no—
518C2×Q8—1222no—
519C2×Q8—1222no—
520C2×Q8C2×C4×D6114yes—
521C22×C4—611no—
522C22×C4—611no—
523C22×C4—612no—
524C22×C4—612no—
525C22×C4—611no—
526C22×C4—614no—
527C22×C4—614no—
528C22×C4—614no—
529C22×C4—612no—
530C22×C4—614no—
531C22×C4—612no—
532C22×C4—1222no—
533C22×C4—1222no—
534C22×C4—1222no—
535C22×C4—1222no—
536C22×C4—1222no—
537C22×C4—1222no—
538C22×C4C23×D6114yes—
539C22×C4C23×D6112yes—
540C22×C4C23×D6112yes—
541C22×C4C23×D6111yescharacteristic
542C22×C4C23×D6112yes—
543C22×C4C23×D6112yes—
544C22×C4C23×D6111yescharacteristic
545C22×C4C23×D6111yescharacteristic
546C4⋊C4—24no—
547C4⋊C4—22no—
548C4⋊C4—24no—
549C4⋊C4—22no—
550C4⋊C4—42no—
551C4⋊C4—618no—
552C4⋊C4—618no—
553C4⋊C4—618no—
554C4⋊C4—618no—
555C4⋊C4—618no—
556C4⋊C4—618no—
557C4⋊C4—614no—
558C4⋊C4—1224no—
559C4⋊C4—1224no—
560C4⋊C4—1224no—
561C4⋊C4—1222no—
562C4⋊C4—1222no—
563C4⋊C4—1224no—
564C4⋊C4—2442no—
565C4⋊C4—2442no—
566C4⋊C4—2444no—
567C4⋊C4—2444no—
568C4⋊C4—2442no—
569C4⋊C4—2444no—
570C4⋊C4—2444no—
571C4⋊C4C2×C4×D6118yes—
572C4⋊C4C2×C4×D6114yes—
573C22⋊C4—618no—
574C22⋊C4—618no—
575C22⋊C4—2444no—
576C22⋊C4—2442no—
577C22⋊C4—2442no—
578C42—24no—
579C42—44no—
580C42—614no—
581C42—614no—
582C42—614no—
583C42—618no—
584C42—1228no—
585C42—1224no—
586C42—2444no—
587C42—2444no—
588C42—2444no—
589C42C2×C4×D6114yes—
590C42C2×C4×D6118yes—
591C23—612no—
592C23—1221no—
593C23—1221no—
594C23—1221no—
595C23—1221no—
596C23—1221no—
597C23—1221no—
598C23C24×D6111yescharacteristic
599Q8—28no—
600Q8—12216no—
601Q8—1228no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—24no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—612no—
618C2×C4—612no—
619C2×C4—612no—
620C2×C4—612no—
621C2×C4—612no—
622C2×C4—614no—
623C2×C4—614no—
624C2×C4—1228no—
625C2×C4—1222no—
626C2×C4—1222no—
627C2×C4—1221no—
628C2×C4—1222no—
629C2×C4—1221no—
630C2×C4—1221no—
631C2×C4—1222no—
632C2×C4—1221no—
633C2×C4—1228no—
634C2×C4—1228no—
635C2×C4—1224no—
636C2×C4—1222no—
637C2×C4—1222no—
638C2×C4—1222no—
639C2×C4—1224no—
640C2×C4—1222no—
641C2×C4—1222no—
642C2×C4—1224no—
643C2×C4—1222no—
644C2×C4C22×C4×D6112yes—
645C2×C4C22×C4×D6114yes—
646C2×C4C22×C4×D6114yes—
647C2×C4C22×C4×D6112yes—
648C2×C4C22×C4×D6112yes—
649C2×C4#1451982312yes—
650C2×C4#1451982412yes—
651C2×C4#1451982412yes—
652C2×C4#1451982512yes—
653C22—1222no—
654C22—1222no—
655C22—1222no—
656C22—2441no—
657C22—2441no—
658C22—2441no—
659C22—2441no—
660C22C23×C4×D6111yescharacteristic
661C22H(5,𝔽2)×D6111yescharacteristic
662C22C2×#1451982311yescharacteristic
663C222−1+4×D6111yescharacteristic
664C22C2×#1451982411yescharacteristic
665C22C2×#1451982411yescharacteristic
666C22C2×#1451982511yescharacteristic
667C4—22no—
668C4—24no—
669C4—24no—
670C4—44no—
671C4—42no—
672C4—42no—
673C4—614no—
674C4—1222no—
675C4—1224no—
676C4—1222no—
677C4—1224no—
678C4—2442no—
679C4—2444no—
680C4—2442no—
681C4#1684023814yes—
682C4#1684024214yes—
683C2—2442no—
684C2C2×#1684023811yescharacteristic
685C2#520×D6111yescharacteristic
686C2C2×#1684024211yescharacteristic
687C2#2146021811yescharacteristic
688C2#2146023111yescharacteristic
689C2#2146023211yescharacteristic
690C2#2146031111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC61×#2355C2
socle, cosocleC23×C61C25
prime radicalC23×D61C24
hypercenter#2355D61
hypocenterC61#34374
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2355

Complements

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

NH ≅ G/Ntype
2. #21449003C2semidirect
3. #21448878C2semidirect
4. #21448876C2semidirect
5. #21448778C2semidirect
6. #21448771C2semidirect
7. Q8×C4⋊Dic61C2semidirect
8. C4⋊C4×Dic122C2semidirect
9. C4⋊C4×Dic122C2semidirect
17. C61×#2355C2semidirect
18. #16840316C4semidirect
344. #2355D61semidirect
429. C61#34374semidirect

Maximal subgroups

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

subgroupindex
C2×#168403162
#214490032
#214488782
#214488762
#214487782
#214487712
Q8×C4⋊Dic612
C4⋊C4×Dic1222
#214485042
#214485022
#214485002
#214484292
#214484242
#214482242
#214482232
C61×#23552
#3437461