Finite Group Databasebeta

← #29843024

Subgroups — #29843024

Order 15616.

2218 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840296C211yesmaximal, characteristic
2#21449004C212yesmaximal, complemented
3#21448990C212yesmaximal, complemented
4#21448807C214yesmaximal, complemented
5#21448771C212yesmaximal, complemented
6#21448745C212yesmaximal, complemented
7#21448744C212yesmaximal, complemented
8C4⋊C4×C22⋊D61C212yesmaximal, complemented
9#21448590C214yesmaximal, complemented
10#21448552C212yesmaximal, complemented
11#21448522C212yesmaximal
12#21448444C212yesmaximal, complemented
13#21448429C212yesmaximal, complemented
14#21448226C211yesmaximal, characteristic, complemented
15C2×C61×#382C211yesmaximal, characteristic, complemented
16#16840296C4116yescomplemented
17C2×#14519771C2212yes—
18C2×#14519769C2211yescharacteristic
19C2×#14519765C2211yescharacteristic
20C2×#14519760C2212yes—
21C2×#14519756C2211yescharacteristic
22C2×#14519751C2211yescharacteristic
23C2×C4×Dic122C2211yescharacteristic
24C2×C4×D244C2211yescharacteristic
25C2×C4×C22⋊D61C2214yes—
26C2×C4×C22⋊D61C2212yes—
27C2×#14519736C2212yes—
28C2×#14519735C2212yes—
29C2×#14519734C2212yes—
30C2×C4⋊C4×D61C2212yes—
31#16839666C2214yes—
32#16839659C2214yes—
33#16839659C2214yes—
34#16839657C2214yes—
35#16839654C2214yes—
36#16839654C2214yes—
37#16839652C2214yes—
38#16839651C2214yes—
39#16839649C2214yes—
40#16839649C2214yes—
41#16839647C2214yes—
42#16839645C2214yes—
43#16839644C2214yes—
44#16839643C2214yes—
45#16839641C2214yes—
46#16839640C2214yes—
47#16839636C2214yes—
48#16839636C2214yes—
49#16839635C2214yes—
50#16839633C2214yes—
51#16839632C2211yescharacteristic
52#16839632C2211yescharacteristic
53#16839631C2212yes—
54#16839628C2212yes—
55#16839627C2212yes—
56#16839622C2212yes—
57#16839622C2212yes—
58#16839619C2212yes—
59#16839619C2212yes—
60C4⋊C4×Dic61C2212yes—
61C4⋊C4×Dic61C2212yes—
62C4×C4⋊Dic61C2212yes—
63C4×C4⋊Dic61C2212yes—
64#16839613C2214yes—
65C4×C22⋊Dic61C2214yes—
66#16839609C2214yes—
67C22×C4⋊C4×C61C2211yescharacteristic
68C22×C4⋊C4×C61C2211yescharacteristic
69C22×C42×C61C2211yescharacteristic
70C61×#382C2212yes—
71C61×#382C2212yes—
72C61×#382C2212yes—
73C61×#382C2212yes—
74C2×#95×C61C2212yes—
75C2×#95×C61C2212yes—
76C22×Dic122C2311yescharacteristic
77C22×D244C2311yescharacteristic
78C22×C22⋊D61C2312yes—
79C22×C4×D61C2312yes—
80C22×C4×D61C2314yes—
81#14519771C2×C4116yescomplemented
82#14519769C2×C418yescomplemented
83#14519765C2×C418yescomplemented
84#14519760C2×C4116yescomplemented
85#14519756C2×C418yescomplemented
86#14519751C2×C418yes—
87C4×Dic122C2×C418yescomplemented
88C4×D244C2×C418yescomplemented
89C4×C22⋊D61—48no—
90C4×C22⋊D61C2×C4116yescomplemented
91#14519736—44no—
92#14519735—44no—
93#14519734C2×C4116yescomplemented
94C2×C4⋊Dic61C2312yes—
95C2×C4⋊Dic61C2312yes—
96C2×C4⋊Dic61C2312yes—
97C2×C4⋊Dic61C2312yes—
98C2×C4⋊Dic61C2312yes—
99C2×C4⋊Dic61C2312yes—
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×#11758196C2314yes—
103C2×#11758196C2314yes—
104C2×#11758196C2314yes—
105C2×#11758196C2312yes—
106C2×#11758196C2312yes—
107C2×#11758196C2312yes—
108C2×#11758196C2312yes—
109C4⋊C4×D61—44no—
110C2×C22⋊Dic61C2314yes—
111C2×C22⋊Dic61C2312yes—
112C2×#11758198C2314yes—
113C2×#11758198C2314yes—
114C2×#11758198C2314yes—
115C2×#11758198C2312yes—
116C2×#11758198C2312yes—
117C2×#11758198C2312yes—
118C2×#11758198C2312yes—
119C2×C4×Dic61C2314yes—
120C2×C4×Dic61C2314yes—
121C2×C4×Dic61C2314yes—
122C2×C4×Dic61C2314yes—
123C2×C4×Dic61C2312yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129#14519684C2314yes—
130#14519684C2314yes—
131#14519684C2314yes—
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2312yes—
135C23×C4×C61C2312yes—
136C23×C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61—42no—
138C2×C4⋊C4×C61—42no—
139C2×C4⋊C4×C61C2312yes—
140C2×C4⋊C4×C61C2312yes—
141C2×C4⋊C4×C61C2312yes—
142C2×C4⋊C4×C61C2312yes—
143C2×C42×C61C2×C418yescomplemented
144C2×C42×C61C2311yescharacteristic
145C2×C42×C61C2311yescharacteristic
146C2×C42×C61C2311yescharacteristic
147C2×C42×C61C2311yescharacteristic
148#95×C61C2314yes—
149#95×C61C2314yes—
150#95×C61C2314yes—
151#95×C61C2314yes—
152C24×C61C2411yescharacteristic
153C23×D61C2412yes—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—24no—
159C22×C4×C61—24no—
160C22×C4×C61—41no—
161C22×C4×C61—41no—
162C22×C4×C61—42no—
163C22×C4×C61—42no—
164C22×C4×C61—42no—
165C22×C4×C61—42no—
166C22×C4×C61C22×C414yes—
167C22×C4×C61C22×C414yes—
168C22×C4×C61C22×C414yes—
169C22×C4×C61C2414yes—
170C22×C4×C61C2414yes—
171C22×C4×C61C2411yescharacteristic
172C22×C4×C61C2411yescharacteristic
173C22×C4×C61C2411yescharacteristic
174C22×C4×C61C2411yescharacteristic
175C22×C4×C61C2411yescharacteristic
176C22×C4×C61C2411yescharacteristic
177C2×C22⋊D61—24no—
178C2×C22⋊D61—24no—
179C2×C22⋊D61C22×C418yes—
180C22×Dic61C2414yes—
181C22×Dic61C2414yes—
182C22×Dic61C2412yes—
183C22×Dic61C2412yes—
184C22×Dic61C2412yes—
185C2×D244—41no—
186C2×D244—41no—
187C2×D244C22×C414yes—
188C2×C4×D61—24no—
189C2×C4×D61—24no—
190C2×C4×D61—44no—
191C2×C4×D61—44no—
192C2×C4×D61—44no—
193C2×C4×D61C22×C418yes—
194C2×Dic122—41no—
195C2×Dic122—41no—
196C2×Dic122C22×C414yes—
197C4⋊C4×C61—24no—
198C4⋊C4×C61—24no—
199C4⋊C4×C61—42no—
200C4⋊C4×C61—42no—
201C42×C61C22×C414yes—
202C42×C61C22×C414yes—
203C42×C61C22×C414yes—
204C42×C61C22×C414yes—
205C22⋊Dic61—28no—
206C22⋊Dic61C22×C418yes—
207#11758198—44no—
208#11758198—44no—
209#11758198—44no—
210#11758198C22×C418yes—
211#11758198C22×C418yes—
212#11758198C22×C418yes—
213#11758198C22×C418yes—
214C4⋊Dic61—24no—
215C4⋊Dic61—24no—
216C4⋊Dic61—42no—
217C4⋊Dic61—42no—
218C4⋊Dic61—42no—
219C4⋊Dic61—42no—
220C4⋊Dic61C22×C414yes—
221C4⋊Dic61C22×C414yes—
222#11758196—44no—
223#11758196—44no—
224#11758196—44no—
225#11758196C22×C418yes—
226#11758196C22×C418yes—
227#11758196C22×C418yes—
228#11758196C22×C418yes—
229C4×Dic61—44no—
230C4×Dic61—44no—
231C4×Dic61—44no—
232C4×Dic61—44no—
233C4×Dic61C22×C418yes—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61C23×C412yes—
239C23×C61H(5,𝔽2)12yes—
240C23×C612−1+412yes—
241C23×C61C2511yescharacteristic
242C22×D61—22no—
243C22×D61—22no—
244C22×D61—22no—
245C22×D61—22no—
246C22×D61—22no—
247C22×D61—22no—
248C22×D61C23×C414yes—
249C2×C4×C61—28no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—28no—
261C2×C4×C61—24no—
262C2×C4×C61—24no—
263C2×C4×C61—24no—
264C2×C4×C61—24no—
265C2×C4×C61—24no—
266C2×C4×C61—24no—
267C2×C4×C61—44no—
268C2×C4×C61—84no—
269C2×C4×C61—84no—
270C2×C4×C61C23×C412yes—
271C2×C4×C61C23×C412yes—
272C2×C4×C61C23×C412yes—
273C2×C4×C61C23×C412yes—
274C2×C4×C61C23×C412yes—
275C2×C4×C61C23×C412yes—
276C2×C4×C61H(5,𝔽2)12yes—
277C2×C4×C612−1+412yes—
278C22⋊D61—216no—
279C2×Dic61—22no—
280C2×Dic61—22no—
281C2×Dic61—22no—
282C2×Dic61—22no—
283C2×Dic61—22no—
284C2×Dic61—22no—
285C2×Dic61—24no—
286C2×Dic61—24no—
287C2×Dic61—24no—
288C2×Dic61—24no—
289C2×Dic61—24no—
290C2×Dic61—24no—
291C2×Dic61C23×C414yes—
292C2×Dic61C23×C414yes—
293C2×Dic61C23×C414yes—
294D244—44no—
295C4×D61—216no—
296C4×D61—88no—
297Dic122—44no—
298#34382—611nomaximal, Sylow
299C22×C61—22no—
300C22×C61—22no—
301C22×C61—22no—
302C22×C61—22no—
303C22×C61—22no—
304C22×C61—22no—
305C22×C61#52014yes—
306C22×C61C24×C411yescharacteristic
307C22×C61C2×H(5,𝔽2)11yescharacteristic
308C22×C61C2×H(5,𝔽2)11yescharacteristic
309C22×C61C2×2−1+411yescharacteristic
310C22×C61C2×2−1+411yescharacteristic
311C22×C61#58511yescharacteristic
312C22×C61#58511yescharacteristic
313C2×D61—24no—
314C2×D61—24no—
315C2×D61—24no—
316C2×D61—42no—
317C2×D61—42no—
318C2×D61—42no—
319C2×D61—42no—
320C4×C61—22no—
321C4×C61—22no—
322C4×C61—22no—
323C4×C61—22no—
324C4×C61—22no—
325C4×C61—44no—
326C4×C61—44no—
327C4×C61#52014yes—
328Dic61—24no—
329Dic61—24no—
330Dic61—24no—
331Dic61—44no—
332Dic61—44no—
333C2×#529—611no—
334#2382—612no—
335#2379—612no—
336#2359—614no—
337#2355—612no—
338#2352—612no—
339#2352—612no—
340D4×C4⋊C4—612no—
341#2334—614no—
342#2329—612no—
343#2325—612no—
344#2317—612no—
345#2314—612no—
346#2285—611no—
347C2×#382D6111yescharacteristic, complemented
348C2×C61—24no—
349C2×C61C2×#52011yescharacteristic
350C2×C61C2×#52011yescharacteristic
351C2×C61#342811yescharacteristic
352C2×C61#355811yescharacteristic
353C2×C61#355911yescharacteristic
354C2×C61#356111yescharacteristic
355C2×C61#356311yescharacteristic
356D61—44no—
357#529—6116no—
358C2×#126—612no—
359C2×#125—611no—
360C2×#124—611no—
361C2×#123—612no—
362C2×C22⋊Q8—611no—
363C2×#121—611no—
364C2×C4×Q8—611no—
365C2×C4×D4—612no—
366C2×C4×D4—614no—
367C2×C4×D4—611no—
368C2×#117—612no—
369C2×#117—612no—
370C2×#117—612no—
371C22×C4⋊C4—612no—
372C22×C4⋊C4C2×D6111yescharacteristic
373C22×C4⋊C4C2×D6111yescharacteristic
374C22×C42C2×D6111yescharacteristic
375#391—614no—
376#389—614no—
377#389—614no—
378#389—614no—
379#388—614no—
380#388—614no—
381#388—614no—
382#388—614no—
383#387—614no—
384#387—614no—
385#387—614no—
386#387—614no—
387#387—614no—
388#387—614no—
389#386—614no—
390#386—614no—
391#385—614no—
392#385—614no—
393#385—614no—
394#385—614no—
395#384—612no—
396#384—611no—
397#384—611no—
398#382—612no—
399#382—612no—
400#382C2×D6112yes—
401#382C2×D6112yes—
402#382C2×D6112yes—
403#382C2×D6112yes—
404#380—612no—
405#380—612no—
406#380—612no—
407#380—612no—
408C4×C4⋊C4—612no—
409C4×C4⋊C4—612no—
410C4×C4⋊C4—612no—
411C4×C4⋊C4—612no—
412C4×C4⋊C4—614no—
413C4×C22⋊C4—614no—
414C4×C22⋊C4—614no—
415C2×#95C2×D6112yes—
416C2×#95C2×D6112yes—
417C61#3438211yescharacteristic, complemented, Sylow
418C22×Q8—611no—
419C22×D4—612no—
420C22×D4—611no—
421C23×C4—612no—
422C23×C4—614no—
423C23×C4C22×D6111yescharacteristic
424C23×C4C22×D6111yescharacteristic
425C23×C4C22×D6112yes—
426C23×C4C22×D6112yes—
427C23×C4C22×D6111yescharacteristic
428#126—6116no—
429#125—618no—
430#124—618no—
431#123—6116no—
432C22⋊Q8—618no—
433#121—618no—
434C4×Q8—618no—
435C4×D4—6116no—
436C4×D4—618no—
437C4×D4—2448no—
438#117—6116no—
439#117—2444no—
440#117—2444no—
441C2×C4⋊C4—42no—
442C2×C4⋊C4—42no—
443C2×C4⋊C4—612no—
444C2×C4⋊C4—612no—
445C2×C4⋊C4—611no—
446C2×C4⋊C4—612no—
447C2×C4⋊C4—611no—
448C2×C4⋊C4—612no—
449C2×C4⋊C4—612no—
450C2×C4⋊C4—612no—
451C2×C4⋊C4—614no—
452C2×C4⋊C4—612no—
453C2×C4⋊C4—612no—
454C2×C4⋊C4—614no—
455C2×C4⋊C4—612no—
456C2×C4⋊C4—612no—
457C2×C4⋊C4—614no—
458C2×C4⋊C4—2444no—
459C2×C4⋊C4C22×D6112yes—
460C2×C4⋊C4C22×D6112yes—
461C2×C4⋊C4C22×D6112yes—
462C2×C4⋊C4C22×D6112yes—
463C2×C22⋊C4—612no—
464C2×C22⋊C4—612no—
465C2×C22⋊C4—612no—
466C2×C22⋊C4—612no—
467C2×C22⋊C4—612no—
468C2×C22⋊C4—614no—
469C2×C22⋊C4—614no—
470C2×C22⋊C4—614no—
471C2×C22⋊C4—614no—
472C2×C42—612no—
473C2×C42—614no—
474C2×C42—614no—
475C2×C42—614no—
476C2×C42—614no—
477C2×C42C4×D6118yescomplemented
478C2×C42C22×D6111yescharacteristic
479C2×C42C22×D6111yescharacteristic
480C2×C42C22×D6111yescharacteristic
481C2×C42C22×D6111yescharacteristic
482#95—614no—
483#95—614no—
484#95—614no—
485#95—614no—
486#95—614no—
487#95—614no—
488#95—614no—
489#95—614no—
490#95C22×D6114yes—
491#95C22×D6114yes—
492#95C22×D6114yes—
493#95C22×D6114yes—
494C24—612no—
495C24C23×D6111yescharacteristic
496C2×Q8—614no—
497C2×Q8—2441no—
498C2×Q8—2441no—
499C2×D4—618no—
500C2×D4—614no—
501C2×D4—1224no—
502C2×D4—1224no—
503C2×D4—2441no—
504C2×D4—2441no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—612no—
518C22×C4—612no—
519C22×C4—612no—
520C22×C4—618no—
521C22×C4—614no—
522C22×C4—614no—
523C22×C4—1224no—
524C22×C4—1224no—
525C22×C4—2444no—
526C22×C4—2444no—
527C22×C4—2444no—
528C22×C4C2×C4×D6114yes—
529C22×C4C2×C4×D6114yes—
530C22×C4C2×C4×D6114yes—
531C22×C4C23×D6114yes—
532C22×C4C23×D6114yes—
533C22×C4C23×D6111yescharacteristic
534C22×C4C23×D6111yescharacteristic
535C22×C4C23×D6111yescharacteristic
536C22×C4C23×D6111yescharacteristic
537C22×C4C23×D6111yescharacteristic
538C22×C4C23×D6111yescharacteristic
539C4⋊C4—24no—
540C4⋊C4—24no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—618no—
544C4⋊C4—618no—
545C4⋊C4—618no—
546C4⋊C4—618no—
547C4⋊C4—614no—
548C4⋊C4—614no—
549C4⋊C4—1224no—
550C4⋊C4—1224no—
551C4⋊C4—2444no—
552C4⋊C4—2444no—
553C4⋊C4—2444no—
554C4⋊C4—2442no—
555C4⋊C4—2442no—
556C4⋊C4—2442no—
557C4⋊C4—2442no—
558C22⋊C4—618no—
559C22⋊C4—618no—
560C22⋊C4—618no—
561C22⋊C4—618no—
562C22⋊C4—618no—
563C22⋊C4—1228no—
564C22⋊C4—2444no—
565C22⋊C4—2444no—
566C22⋊C4—2444no—
567C42—618no—
568C42—2444no—
569C42—2444no—
570C42—2444no—
571C42—2444no—
572C42C2×C4×D6114yes—
573C42C2×C4×D6114yes—
574C42C2×C4×D6114yes—
575C42C2×C4×D6114yes—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—614no—
581C23—1222no—
582C23—1222no—
583C23—1222no—
584C23—1222no—
585C23—1222no—
586C23—1222no—
587C23C22×C4×D6112yes—
588C23#1451982312yes—
589C23#1451982412yes—
590C23C24×D6111yescharacteristic
591Q8—2444no—
592D4—12216no—
593D4—2444no—
594C2×C4—28no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—28no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—44no—
613C2×C4—84no—
614C2×C4—84no—
615C2×C4—614no—
616C2×C4—614no—
617C2×C4—614no—
618C2×C4—1222no—
619C2×C4—1222no—
620C2×C4—1222no—
621C2×C4—1222no—
622C2×C4—1222no—
623C2×C4—1222no—
624C2×C4—12216no—
625C2×C4—1224no—
626C2×C4—1224no—
627C2×C4—1224no—
628C2×C4—1224no—
629C2×C4—1224no—
630C2×C4—1224no—
631C2×C4—4888no—
632C2×C4C22×C4×D6112yes—
633C2×C4C22×C4×D6112yes—
634C2×C4C22×C4×D6112yes—
635C2×C4C22×C4×D6112yes—
636C2×C4C22×C4×D6112yes—
637C2×C4C22×C4×D6112yes—
638C2×C4#1451982212yes—
639C2×C4#1451982512yes—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—1224no—
647C22—1224no—
648C22—1224no—
649C22—2442no—
650C22—2442no—
651C22—2442no—
652C22—2442no—
653C22#1684024214yes—
654C22C23×C4×D6111yescharacteristic
655C22C2×#1451982211yescharacteristic
656C22C2×#1451982311yescharacteristic
657C22C2×#1451982411yescharacteristic
658C22C2×#1451982511yescharacteristic
659C22#1684059811yescharacteristic
660C22#1684059811yescharacteristic
661C4—22no—
662C4—22no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—44no—
667C4—44no—
668C4—1224no—
669C4—1224no—
670C4—1224no—
671C4—2444no—
672C4—2444no—
673C4#1684024314yes—
674C2—24no—
675C2—2444no—
676C2C2×#1684024211yescharacteristic
677C2C2×#1684024311yescharacteristic
678C2#2145902011yescharacteristic
679C2#2146033811yescharacteristic
680C2#2146035311yescharacteristic
681C2#2146039111yescharacteristic
682C2#2146042511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC2×C61×#382C2
socle, cosocleC23×C61C25
prime radicalC2×#14519751C22
hypercenterC2×#382D61
hypocenterC61#34382
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
2. #21449004C2semidirect
3. #21448990C2semidirect
4. #21448807C2semidirect
5. #21448771C2semidirect
6. #21448745C2semidirect
7. #21448744C2semidirect
8. C4⋊C4×C22⋊D61C2semidirect
9. #21448590C2semidirect
10. #21448552C2semidirect
12. #21448444C2semidirect
13. #21448429C2semidirect
14. #21448226C2semidirect
15. C2×C61×#382C2semidirect
16. #16840296C4semidirect
81. #14519771C2×C4semidirect
82. #14519769C2×C4semidirect
83. #14519765C2×C4semidirect
84. #14519760C2×C4semidirect
85. #14519756C2×C4semidirect
87. C4×Dic122C2×C4semidirect
88. C4×D244C2×C4semidirect
90. C4×C22⋊D61C2×C4semidirect
93. #14519734C2×C4semidirect
143. C2×C42×C61C2×C4semidirect
347. C2×#382D61semidirect
417. C61#34382semidirect
477. C2×C42C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402962
#214490042
#214489902
#214488072
#214487712
#214487452
#214487442
C4⋊C4×C22⋊D612
#214485902
#214485522
#214485222
#214484442
#214484292
#214482262
C2×C61×#3822
#3438261