Finite Group Databasebeta

← #36717439

Subgroups — #36717439

Order 22784.

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×#19152132C211yesmaximal, characteristic
2#26023437C212yesmaximal, complemented
3#26023423C212yesmaximal, complemented
4#26023240C214yesmaximal, complemented
5#26023204C212yesmaximal, complemented
6#26023178C212yesmaximal, complemented
7#26023177C212yesmaximal, complemented
8C4⋊C4×C22⋊D89C212yesmaximal, complemented
9#26023023C214yesmaximal, complemented
10#26022985C212yesmaximal, complemented
11#26022955C212yesmaximal
12#26022877C212yesmaximal, complemented
13#26022862C212yesmaximal, complemented
14#26022659C211yesmaximal, characteristic, complemented
15C2×#382×C89C211yesmaximal, characteristic, complemented
16#19152132C4116yescomplemented
17C2×#15668006C2212yes—
18C2×#15668004C2211yescharacteristic
19C2×#15668000C2211yescharacteristic
20C2×#15667995C2212yes—
21C2×#15667991C2211yescharacteristic
22C2×#15667986C2211yescharacteristic
23C2×C4×Dic178C2211yescharacteristic
24C2×C4×D356C2211yescharacteristic
25C2×C4×C22⋊D89C2214yes—
26C2×C4×C22⋊D89C2212yes—
27C2×#15667971C2212yes—
28C2×#15667970C2212yes—
29C2×#15667969C2212yes—
30C2×C4⋊C4×D89C2212yes—
31#19151502C2214yes—
32#19151495C2214yes—
33#19151495C2214yes—
34#19151493C2214yes—
35#19151490C2214yes—
36#19151490C2214yes—
37#19151488C2214yes—
38#19151487C2214yes—
39#19151485C2214yes—
40#19151485C2214yes—
41#19151483C2214yes—
42#19151481C2214yes—
43#19151480C2214yes—
44#19151479C2214yes—
45#19151477C2214yes—
46#19151476C2214yes—
47#19151472C2214yes—
48#19151472C2214yes—
49#19151471C2214yes—
50#19151469C2214yes—
51#19151468C2211yescharacteristic
52#19151468C2211yescharacteristic
53#19151467C2212yes—
54#19151464C2212yes—
55#19151463C2212yes—
56#19151458C2212yes—
57#19151458C2212yes—
58#19151455C2212yes—
59#19151455C2212yes—
60C4⋊C4×Dic89C2212yes—
61C4⋊C4×Dic89C2212yes—
62C4×C4⋊Dic89C2212yes—
63C4×C4⋊Dic89C2212yes—
64#19151449C2214yes—
65C4×C22⋊Dic89C2214yes—
66#19151445C2214yes—
67C22×C4⋊C4×C89C2211yescharacteristic
68C22×C4⋊C4×C89C2211yescharacteristic
69C22×C42×C89C2211yescharacteristic
70#382×C89C2212yes—
71#382×C89C2212yes—
72#382×C89C2212yes—
73#382×C89C2212yes—
74C2×#95×C89C2212yes—
75C2×#95×C89C2212yes—
76C22×Dic178C2311yescharacteristic
77C22×D356C2311yescharacteristic
78C22×C22⋊D89C2312yes—
79C22×C4×D89C2312yes—
80C22×C4×D89C2314yes—
81#15668006C2×C4116yescomplemented
82#15668004C2×C418yescomplemented
83#15668000C2×C418yescomplemented
84#15667995C2×C4116yescomplemented
85#15667991C2×C418yescomplemented
86#15667986C2×C418yes—
87C4×Dic178C2×C418yescomplemented
88C4×D356C2×C418yescomplemented
89C4×C22⋊D89—48no—
90C4×C22⋊D89C2×C4116yescomplemented
91#15667971—44no—
92#15667970—44no—
93#15667969C2×C4116yescomplemented
94C2×C4⋊Dic89C2312yes—
95C2×C4⋊Dic89C2312yes—
96C2×C4⋊Dic89C2312yes—
97C2×C4⋊Dic89C2312yes—
98C2×C4⋊Dic89C2312yes—
99C2×C4⋊Dic89C2312yes—
100C2×C4⋊Dic89C2311yescharacteristic
101C2×C4⋊Dic89C2311yescharacteristic
102C2×#13083553C2314yes—
103C2×#13083553C2314yes—
104C2×#13083553C2314yes—
105C2×#13083553C2312yes—
106C2×#13083553C2312yes—
107C2×#13083553C2312yes—
108C2×#13083553C2312yes—
109C4⋊C4×D89—44no—
110C2×C22⋊Dic89C2314yes—
111C2×C22⋊Dic89C2312yes—
112C2×#13083551C2314yes—
113C2×#13083551C2314yes—
114C2×#13083551C2314yes—
115C2×#13083551C2312yes—
116C2×#13083551C2312yes—
117C2×#13083551C2312yes—
118C2×#13083551C2312yes—
119C2×C4×Dic89C2314yes—
120C2×C4×Dic89C2314yes—
121C2×C4×Dic89C2314yes—
122C2×C4×Dic89C2314yes—
123C2×C4×Dic89C2312yes—
124#15667919C2314yes—
125#15667919C2314yes—
126#15667919C2314yes—
127#15667919C2314yes—
128#15667919C2314yes—
129#15667919C2314yes—
130#15667919C2314yes—
131#15667919C2314yes—
132C23×C4×C89C2311yescharacteristic
133C23×C4×C89C2311yescharacteristic
134C23×C4×C89C2312yes—
135C23×C4×C89C2312yes—
136C23×C4×C89C2311yescharacteristic
137C2×C4⋊C4×C89—42no—
138C2×C4⋊C4×C89—42no—
139C2×C4⋊C4×C89C2312yes—
140C2×C4⋊C4×C89C2312yes—
141C2×C4⋊C4×C89C2312yes—
142C2×C4⋊C4×C89C2312yes—
143C2×C42×C89C2×C418yescomplemented
144C2×C42×C89C2311yescharacteristic
145C2×C42×C89C2311yescharacteristic
146C2×C42×C89C2311yescharacteristic
147C2×C42×C89C2311yescharacteristic
148#95×C89C2314yes—
149#95×C89C2314yes—
150#95×C89C2314yes—
151#95×C89C2314yes—
152C23×D89C2412yes—
153C2×Dic178—41no—
154C2×Dic178—41no—
155C2×Dic178C22×C414yes—
156C2×D356—41no—
157C2×D356—41no—
158C2×D356C22×C414yes—
159C2×C22⋊D89—24no—
160C2×C22⋊D89—24no—
161C2×C22⋊D89C22×C418yes—
162C22×Dic89C2414yes—
163C22×Dic89C2414yes—
164C22×Dic89C2412yes—
165C22×Dic89C2412yes—
166C22×Dic89C2412yes—
167C2×C4×D89—24no—
168C2×C4×D89—24no—
169C2×C4×D89—44no—
170C2×C4×D89—44no—
171C2×C4×D89—44no—
172C2×C4×D89C22×C418yes—
173C4⋊Dic89—24no—
174C4⋊Dic89—24no—
175C4⋊Dic89—42no—
176C4⋊Dic89—42no—
177C4⋊Dic89—42no—
178C4⋊Dic89—42no—
179C4⋊Dic89C22×C414yes—
180C4⋊Dic89C22×C414yes—
181#13083553—44no—
182#13083553—44no—
183#13083553—44no—
184#13083553C22×C418yes—
185#13083553C22×C418yes—
186#13083553C22×C418yes—
187#13083553C22×C418yes—
188C22⋊Dic89—28no—
189C22⋊Dic89C22×C418yes—
190#13083551—44no—
191#13083551—44no—
192#13083551—44no—
193#13083551C22×C418yes—
194#13083551C22×C418yes—
195#13083551C22×C418yes—
196#13083551C22×C418yes—
197C4×Dic89—44no—
198C4×Dic89—44no—
199C4×Dic89—44no—
200C4×Dic89—44no—
201C4×Dic89C22×C418yes—
202C24×C89C2411yescharacteristic
203C22×C4×C89—22no—
204C22×C4×C89—22no—
205C22×C4×C89—22no—
206C22×C4×C89—22no—
207C22×C4×C89—24no—
208C22×C4×C89—24no—
209C22×C4×C89—41no—
210C22×C4×C89—41no—
211C22×C4×C89—42no—
212C22×C4×C89—42no—
213C22×C4×C89—42no—
214C22×C4×C89—42no—
215C22×C4×C89C22×C414yes—
216C22×C4×C89C22×C414yes—
217C22×C4×C89C22×C414yes—
218C22×C4×C89C2414yes—
219C22×C4×C89C2414yes—
220C22×C4×C89C2411yescharacteristic
221C22×C4×C89C2411yescharacteristic
222C22×C4×C89C2411yescharacteristic
223C22×C4×C89C2411yescharacteristic
224C22×C4×C89C2411yescharacteristic
225C22×C4×C89C2411yescharacteristic
226C4⋊C4×C89—24no—
227C4⋊C4×C89—24no—
228C4⋊C4×C89—42no—
229C4⋊C4×C89—42no—
230C42×C89C22×C414yes—
231C42×C89C22×C414yes—
232C42×C89C22×C414yes—
233C42×C89C22×C414yes—
234C23×C89—21no—
235C23×C89—21no—
236C23×C89—21no—
237C23×C89—21no—
238C23×C89C23×C412yes—
239C23×C89H(5,𝔽2)12yes—
240C23×C892−1+412yes—
241C23×C89C2511yescharacteristic
242C22×D89—22no—
243C22×D89—22no—
244C22×D89—22no—
245C22×D89—22no—
246C22×D89—22no—
247C22×D89—22no—
248C22×D89C23×C414yes—
249C2×C4×C89—28no—
250C2×C4×C89—21no—
251C2×C4×C89—21no—
252C2×C4×C89—21no—
253C2×C4×C89—21no—
254C2×C4×C89—21no—
255C2×C4×C89—21no—
256C2×C4×C89—21no—
257C2×C4×C89—21no—
258C2×C4×C89—21no—
259C2×C4×C89—21no—
260C2×C4×C89—28no—
261C2×C4×C89—24no—
262C2×C4×C89—24no—
263C2×C4×C89—24no—
264C2×C4×C89—24no—
265C2×C4×C89—24no—
266C2×C4×C89—24no—
267C2×C4×C89—44no—
268C2×C4×C89—84no—
269C2×C4×C89—84no—
270C2×C4×C89C23×C412yes—
271C2×C4×C89C23×C412yes—
272C2×C4×C89C23×C412yes—
273C2×C4×C89C23×C412yes—
274C2×C4×C89C23×C412yes—
275C2×C4×C89C23×C412yes—
276C2×C4×C89H(5,𝔽2)12yes—
277C2×C4×C892−1+412yes—
278C22⋊D89—216no—
279C2×Dic89—22no—
280C2×Dic89—22no—
281C2×Dic89—22no—
282C2×Dic89—22no—
283C2×Dic89—22no—
284C2×Dic89—22no—
285C2×Dic89—24no—
286C2×Dic89—24no—
287C2×Dic89—24no—
288C2×Dic89—24no—
289C2×Dic89—24no—
290C2×Dic89—24no—
291C2×Dic89C23×C414yes—
292C2×Dic89C23×C414yes—
293C2×Dic89C23×C414yes—
294D356—44no—
295C4×D89—216no—
296C4×D89—88no—
297Dic178—44no—
298C22×C89—22no—
299C22×C89—22no—
300C22×C89—22no—
301C22×C89—22no—
302C22×C89—22no—
303C22×C89—22no—
304C22×C89#52014yes—
305C22×C89C24×C411yescharacteristic
306C22×C89C2×H(5,𝔽2)11yescharacteristic
307C22×C89C2×H(5,𝔽2)11yescharacteristic
308C22×C89C2×2−1+411yescharacteristic
309C22×C89C2×2−1+411yescharacteristic
310C22×C89#58511yescharacteristic
311C22×C89#58511yescharacteristic
312C2×D89—24no—
313C2×D89—24no—
314C2×D89—24no—
315C2×D89—42no—
316C2×D89—42no—
317C2×D89—42no—
318C2×D89—42no—
319C4×C89—22no—
320C4×C89—22no—
321C4×C89—22no—
322C4×C89—22no—
323C4×C89—22no—
324C4×C89—44no—
325C4×C89—44no—
326C4×C89#52014yes—
327Dic89—24no—
328Dic89—24no—
329Dic89—24no—
330Dic89—44no—
331Dic89—44no—
332#34382—891nomaximal, Sylow
333C2×C89—24no—
334C2×C89C2×#52011yescharacteristic
335C2×C89C2×#52011yescharacteristic
336C2×C89#342811yescharacteristic
337C2×C89#355811yescharacteristic
338C2×C89#355911yescharacteristic
339C2×C89#356111yescharacteristic
340C2×C89#356311yescharacteristic
341D89—44no—
342C2×#529—891no—
343#2382—892no—
344#2379—892no—
345#2359—894no—
346#2355—892no—
347#2352—892no—
348#2352—892no—
349D4×C4⋊C4—892no—
350#2334—894no—
351#2329—892no—
352#2325—892no—
353#2317—892no—
354#2314—892no—
355#2285—891no—
356C2×#382D8911yescharacteristic, complemented
357C89#3438211yescharacteristic, complemented, Sylow
358#529—8916no—
359C2×#126—892no—
360C2×#125—891no—
361C2×#124—891no—
362C2×#123—892no—
363C2×C22⋊Q8—891no—
364C2×#121—891no—
365C2×C4×Q8—891no—
366C2×C4×D4—892no—
367C2×C4×D4—894no—
368C2×C4×D4—891no—
369C2×#117—892no—
370C2×#117—892no—
371C2×#117—892no—
372C22×C4⋊C4—892no—
373C22×C4⋊C4C2×D8911yescharacteristic
374C22×C4⋊C4C2×D8911yescharacteristic
375C22×C42C2×D8911yescharacteristic
376#391—894no—
377#389—894no—
378#389—894no—
379#389—894no—
380#388—894no—
381#388—894no—
382#388—894no—
383#388—894no—
384#387—894no—
385#387—894no—
386#387—894no—
387#387—894no—
388#387—894no—
389#387—894no—
390#386—894no—
391#386—894no—
392#385—894no—
393#385—894no—
394#385—894no—
395#385—894no—
396#384—892no—
397#384—891no—
398#384—891no—
399#382—892no—
400#382—892no—
401#382C2×D8912yes—
402#382C2×D8912yes—
403#382C2×D8912yes—
404#382C2×D8912yes—
405#380—892no—
406#380—892no—
407#380—892no—
408#380—892no—
409C4×C4⋊C4—892no—
410C4×C4⋊C4—892no—
411C4×C4⋊C4—892no—
412C4×C4⋊C4—892no—
413C4×C4⋊C4—894no—
414C4×C22⋊C4—894no—
415C4×C22⋊C4—894no—
416C2×#95C2×D8912yes—
417C2×#95C2×D8912yes—
418C22×Q8—891no—
419C22×D4—892no—
420C22×D4—891no—
421C23×C4—892no—
422C23×C4—894no—
423C23×C4C22×D8911yescharacteristic
424C23×C4C22×D8911yescharacteristic
425C23×C4C22×D8912yes—
426C23×C4C22×D8912yes—
427C23×C4C22×D8911yescharacteristic
428#126—8916no—
429#125—898no—
430#124—898no—
431#123—8916no—
432C22⋊Q8—898no—
433#121—898no—
434C4×Q8—898no—
435C4×D4—8916no—
436C4×D4—898no—
437C4×D4—3568no—
438#117—8916no—
439#117—3564no—
440#117—3564no—
441C2×C4⋊C4—42no—
442C2×C4⋊C4—42no—
443C2×C4⋊C4—892no—
444C2×C4⋊C4—892no—
445C2×C4⋊C4—891no—
446C2×C4⋊C4—892no—
447C2×C4⋊C4—891no—
448C2×C4⋊C4—892no—
449C2×C4⋊C4—894no—
450C2×C4⋊C4—892no—
451C2×C4⋊C4—892no—
452C2×C4⋊C4—894no—
453C2×C4⋊C4—892no—
454C2×C4⋊C4—892no—
455C2×C4⋊C4—894no—
456C2×C4⋊C4—892no—
457C2×C4⋊C4—892no—
458C2×C4⋊C4—3564no—
459C2×C4⋊C4C22×D8912yes—
460C2×C4⋊C4C22×D8912yes—
461C2×C4⋊C4C22×D8912yes—
462C2×C4⋊C4C22×D8912yes—
463C2×C22⋊C4—892no—
464C2×C22⋊C4—892no—
465C2×C22⋊C4—892no—
466C2×C22⋊C4—892no—
467C2×C22⋊C4—892no—
468C2×C22⋊C4—894no—
469C2×C22⋊C4—894no—
470C2×C22⋊C4—894no—
471C2×C22⋊C4—894no—
472C2×C42—892no—
473C2×C42—894no—
474C2×C42—894no—
475C2×C42—894no—
476C2×C42—894no—
477C2×C42C4×D8918yescomplemented
478C2×C42C22×D8911yescharacteristic
479C2×C42C22×D8911yescharacteristic
480C2×C42C22×D8911yescharacteristic
481C2×C42C22×D8911yescharacteristic
482#95—894no—
483#95—894no—
484#95—894no—
485#95—894no—
486#95—894no—
487#95—894no—
488#95—894no—
489#95—894no—
490#95C22×D8914yes—
491#95C22×D8914yes—
492#95C22×D8914yes—
493#95C22×D8914yes—
494C24—892no—
495C24C23×D8911yescharacteristic
496C2×Q8—894no—
497C2×Q8—3561no—
498C2×Q8—3561no—
499C2×D4—898no—
500C2×D4—894no—
501C2×D4—3561no—
502C2×D4—3561no—
503C2×D4—1784no—
504C2×D4—1784no—
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—892no—
518C22×C4—892no—
519C22×C4—892no—
520C22×C4—898no—
521C22×C4—894no—
522C22×C4—894no—
523C22×C4—3564no—
524C22×C4—3564no—
525C22×C4—3564no—
526C22×C4—1784no—
527C22×C4—1784no—
528C22×C4C2×C4×D8914yes—
529C22×C4C2×C4×D8914yes—
530C22×C4C2×C4×D8914yes—
531C22×C4C23×D8914yes—
532C22×C4C23×D8914yes—
533C22×C4C23×D8911yescharacteristic
534C22×C4C23×D8911yescharacteristic
535C22×C4C23×D8911yescharacteristic
536C22×C4C23×D8911yescharacteristic
537C22×C4C23×D8911yescharacteristic
538C22×C4C23×D8911yescharacteristic
539C4⋊C4—24no—
540C4⋊C4—24no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—898no—
544C4⋊C4—898no—
545C4⋊C4—894no—
546C4⋊C4—898no—
547C4⋊C4—894no—
548C4⋊C4—898no—
549C4⋊C4—3564no—
550C4⋊C4—3562no—
551C4⋊C4—3562no—
552C4⋊C4—3564no—
553C4⋊C4—3564no—
554C4⋊C4—3562no—
555C4⋊C4—3562no—
556C4⋊C4—1784no—
557C4⋊C4—1784no—
558C22⋊C4—898no—
559C22⋊C4—898no—
560C22⋊C4—898no—
561C22⋊C4—898no—
562C22⋊C4—898no—
563C22⋊C4—3564no—
564C22⋊C4—3564no—
565C22⋊C4—3564no—
566C22⋊C4—1788no—
567C42—898no—
568C42—3564no—
569C42—3564no—
570C42—3564no—
571C42—3564no—
572C42C2×C4×D8914yes—
573C42C2×C4×D8914yes—
574C42C2×C4×D8914yes—
575C42C2×C4×D8914yes—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—894no—
581C23—1782no—
582C23—1782no—
583C23—1782no—
584C23—1782no—
585C23—1782no—
586C23—1782no—
587C23C22×C4×D8912yes—
588C23#1566805812yes—
589C23#1566805912yes—
590C23C24×D8911yescharacteristic
591Q8—3564no—
592D4—3564no—
593D4—17816no—
594C2×C4—21no—
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—28no—
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—894no—
616C2×C4—894no—
617C2×C4—894no—
618C2×C4—1784no—
619C2×C4—1784no—
620C2×C4—1784no—
621C2×C4—1784no—
622C2×C4—1784no—
623C2×C4—1784no—
624C2×C4—1782no—
625C2×C4—1782no—
626C2×C4—1782no—
627C2×C4—1782no—
628C2×C4—1782no—
629C2×C4—1782no—
630C2×C4—17816no—
631C2×C4—7128no—
632C2×C4C22×C4×D8912yes—
633C2×C4C22×C4×D8912yes—
634C2×C4C22×C4×D8912yes—
635C2×C4C22×C4×D8912yes—
636C2×C4C22×C4×D8912yes—
637C2×C4C22×C4×D8912yes—
638C2×C4#1566805712yes—
639C2×C4#1566806012yes—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—3562no—
647C22—3562no—
648C22—3562no—
649C22—3562no—
650C22—1784no—
651C22—1784no—
652C22—1784no—
653C22#1915207814yes—
654C22C23×C4×D8911yescharacteristic
655C22C2×#1566805711yescharacteristic
656C22C2×#1566805811yescharacteristic
657C22C2×#1566805911yescharacteristic
658C22C2×#1566806011yescharacteristic
659C22#1915243411yescharacteristic
660C22#1915243411yescharacteristic
661C4—22no—
662C4—22no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—44no—
667C4—44no—
668C4—3564no—
669C4—3564no—
670C4—1784no—
671C4—1784no—
672C4—1784no—
673C4#1915207914yes—
674C2—24no—
675C2—3564no—
676C2C2×#1915207811yescharacteristic
677C2C2×#1915207911yescharacteristic
678C2#2603345311yescharacteristic
679C2#2603477111yescharacteristic
680C2#2603478611yescharacteristic
681C2#2603482411yescharacteristic
682C2#2603485811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D89
commutatorC22×C89C24×C4
FittingC2×#382×C89C2
socle, cosocleC23×C89C25
prime radicalC2×#15667986C22
hypercenterC2×#382D89
hypocenterC89#34382
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
2. #26023437C2semidirect
3. #26023423C2semidirect
4. #26023240C2semidirect
5. #26023204C2semidirect
6. #26023178C2semidirect
7. #26023177C2semidirect
8. C4⋊C4×C22⋊D89C2semidirect
9. #26023023C2semidirect
10. #26022985C2semidirect
12. #26022877C2semidirect
13. #26022862C2semidirect
14. #26022659C2semidirect
15. C2×#382×C89C2semidirect
16. #19152132C4semidirect
81. #15668006C2×C4semidirect
82. #15668004C2×C4semidirect
83. #15668000C2×C4semidirect
84. #15667995C2×C4semidirect
85. #15667991C2×C4semidirect
87. C4×Dic178C2×C4semidirect
88. C4×D356C2×C4semidirect
90. C4×C22⋊D89C2×C4semidirect
93. #15667969C2×C4semidirect
143. C2×C42×C89C2×C4semidirect
356. C2×#382D89semidirect
357. C89#34382semidirect
477. C2×C42C4×D89semidirect

Maximal subgroups

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

subgroupindex
C2×#191521322
#260234372
#260234232
#260232402
#260232042
#260231782
#260231772
C4⋊C4×C22⋊D892
#260230232
#260229852
#260229552
#260228772
#260228622
#260226592
C2×#382×C892
#3438289