Finite Group Databasebeta

← #25106419

Subgroups — #25106419

Order 11008.

1098 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583493C211yesmaximal, characteristic
2#19137211C211yesmaximal, characteristic, complemented
3#19137196C211yesmaximal, characteristic, complemented
4#19135578C212yesmaximal, complemented
5#19135429C212yesmaximal
6#19135054C211yesmaximal, characteristic, complemented
7#19135053C211yesmaximal, characteristic, complemented
8#19135051C211yesmaximal, characteristic, complemented
9#19134582C212yesmaximal, complemented
10#19134581C212yesmaximal, complemented
11C43×#1899C211yesmaximal, characteristic, complemented
12#14583493—22no—
13#14583493—22no—
14#14583493—22no—
15#14583493—22no—
16C2×#13063320C411yescharacteristic, complemented
17C2×#13063318C411yescharacteristic, complemented
18C2×#13063316C411yescharacteristic, complemented
19C2×#13063315C411yescharacteristic, complemented
20C2×#13063309C411yescharacteristic, complemented
21C2×#13063308C2211yescharacteristic
22C2×#13063307C411yescharacteristic, complemented
23C2×#13063305C411yescharacteristic, complemented
24C2×#13063302C411yescharacteristic, complemented
25C2×#13063302C2211yescharacteristic
26C2×#13063297C2211yescharacteristic
27C2×D4×Dic43C2211yescharacteristic
28C2×(C22⋊D43)⋊C4C2211yescharacteristic
29C2×#13063284C2211yescharacteristic
30C22×C4⋊Dic43C2211yescharacteristic
31C2×#13063240C2212yes—
32C2×#13063239C2212yes—
33C2×#13063239C2212yes—
34#14582797—22no—
35#14582795—22no—
36#14582784—22no—
37#14582782—22no—
38#14582762C2211yescharacteristic
39#14582757C2212yes—
40#14582757C2212yes—
41#14582757C2212yes—
42C22⋊C4×Dic43C2212yes—
43#14582666C2212yes—
44#14582665C2212yes—
45#14582665C2212yes—
46C2×#123×C43C2211yescharacteristic
47C2×#117×C43C2211yescharacteristic
48C2×#99×C43C2212yes—
49C43×#381C2211yescharacteristic
50C43×#342C2212yes—
51C22×Dic86C2×C411yescharacteristic
52C22×C22⋊D43C2×C411yescharacteristic
53C22×C22⋊D43C2311yescharacteristic
54C23×Dic43C2×C411yescharacteristic
55C23×Dic43C2311yescharacteristic
56C23×Dic43C2311yescharacteristic
57C22×C4×D43C2×C411yescharacteristic
58#13063320—22no—
59#13063320—22no—
60#13063318—22no—
61#13063318—22no—
62#13063316—22no—
63#13063316—22no—
64#13063315—22no—
65#13063315—22no—
66#13063309—22no—
67#13063309—22no—
68#13063308—21no—
69#13063308—21no—
70#13063308—21no—
71#13063308—21no—
72#13063307—22no—
73#13063307—22no—
74#13063305—22no—
75#13063305—22no—
76#13063302—22no—
77#13063302—22no—
78#13063302—22no—
79#13063302—22no—
80#13063297—22no—
81#13063297—22no—
82D4×Dic43—22no—
83D4×Dic43—22no—
84(C22⋊D43)⋊C4—22no—
85(C22⋊D43)⋊C4—22no—
86#13063284—42no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43C2×C411yescharacteristic
89C2×C4⋊Dic43C2×C411yescharacteristic
90C2×C4⋊Dic43C2×C411yescharacteristic
91C2×C4⋊Dic43C2×C411yescharacteristic
92C2×C4⋊Dic43C2×C411yescharacteristic
93C2×C4⋊Dic43C2×C411yescharacteristic
94C2×C4⋊Dic43D412yes—
95C2×C4⋊Dic43D412yes—
96C2×C4⋊Dic43D412yes—
97C2×C4⋊Dic43D412yes—
98C2×Dic43⋊C4—22no—
99C2×Dic43⋊C4—22no—
100C2×Dic43⋊C4—22no—
101C2×Dic43⋊C4C2×C411yescharacteristic
102C2×Dic43⋊C4C2×C411yescharacteristic
103C2×Dic43⋊C4C2×C411yescharacteristic
104C2×Dic43⋊C4C2×C411yescharacteristic
105C2×Dic43⋊C4C2×C411yescharacteristic
106C2×Dic43⋊C4C2×C411yescharacteristic
107C2×C22⋊Dic43C2×C411yescharacteristic
108C2×C22⋊Dic43C2×C411yescharacteristic
109C2×C22⋊Dic43C2312yes—
110C2×C22⋊Dic43C2312yes—
111C2×C22⋊Dic43C2311yescharacteristic
112C2×(C2×D43)⋊C4C2×C411yescharacteristic
113C2×(C2×D43)⋊C4C2×C411yescharacteristic
114C2×(C2×D43)⋊C4C2×C411yescharacteristic
115C2×(C2×D43)⋊C4C2×C411yescharacteristic
116C2×C4×Dic43—21no—
117C2×C4×Dic43—22no—
118C2×C4×Dic43C2×C411yescharacteristic
119C2×C4×Dic43C2×C411yescharacteristic
120#13063240—42no—
121#13063239—42no—
122#13063239—42no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C22×D4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131#123×C43—21no—
132#123×C43—21no—
133#123×C43—21no—
134#123×C43—21no—
135#117×C43—42no—
136C2×C4⋊C4×C43—21no—
137C2×C4⋊C4×C43C2×C411yescharacteristic
138C2×C4⋊C4×C43C2×C411yescharacteristic
139C2×C22⋊C4×C43C2×C411yescharacteristic
140C2×C22⋊C4×C43C2×C411yescharacteristic
141C2×C22⋊C4×C43C2312yes—
142C2×C22⋊C4×C43C2312yes—
143C2×C22⋊C4×C43C2311yescharacteristic
144C2×C42×C43—21no—
145#99×C43—42no—
146#95×C43—21no—
147#95×C43—21no—
148C24×C43C22×C411yescharacteristic
149C24×C43C2411yescharacteristic
150C23×D43C22×C411yescharacteristic
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—22no—
154C2×D4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43C22×C411yescharacteristic
160C22×C4×C43C22×C411yescharacteristic
161C22×C4×C43C22×C411yescharacteristic
162C22×C4×C43C22×C411yescharacteristic
163C22×C4×C43C22×C411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C2×C22⋊D43—22no—
169C2×C22⋊D43—21no—
170C2×C22⋊D43—21no—
171C2×C22⋊D43—22no—
172C2×C22⋊D43—22no—
173C2×C22⋊D43—81no—
174C22×Dic43—22no—
175C22×Dic43—22no—
176C22×Dic43—22no—
177C22×Dic43—81no—
178C22×Dic43—81no—
179C22×Dic43—81no—
180C22×Dic43C22×C411yescharacteristic
181C22×Dic43C22×C411yescharacteristic
182C22×Dic43C22×C411yescharacteristic
183C22×Dic43C22×C411yescharacteristic
184C22×Dic43C22×C411yescharacteristic
185C22×Dic43C22×C411yescharacteristic
186C22×Dic43C22×C411yescharacteristic
187C22×Dic43C2×D412yes—
188C22×Dic43C2×D412yes—
189C22×Dic43C2×D412yes—
190C22×Dic43C2×D412yes—
191C2×C4×D43—22no—
192C2×C4×D43—81no—
193C2×Dic86—22no—
194C2×Dic86—81no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—42no—
200C22⋊C4×C43—21no—
201C22⋊C4×C43—21no—
202C22⋊C4×C43—21no—
203C22⋊C4×C43—21no—
204C22⋊C4×C43—21no—
205C22⋊C4×C43—21no—
206C22⋊C4×C43—22no—
207C22⋊C4×C43—22no—
208C22⋊C4×C43—22no—
209C22⋊C4×C43—22no—
210C42×C43—42no—
211C22⋊Dic43—22no—
212C22⋊Dic43—22no—
213C22⋊Dic43—21no—
214C22⋊Dic43—21no—
215C22⋊Dic43—22no—
216C22⋊Dic43—22no—
217C22⋊Dic43—22no—
218C22⋊Dic43—22no—
219(C2×D43)⋊C4—21no—
220(C2×D43)⋊C4—21no—
221(C2×D43)⋊C4—21no—
222(C2×D43)⋊C4—21no—
223(C2×D43)⋊C4—22no—
224(C2×D43)⋊C4—22no—
225C4⋊Dic43—22no—
226C4⋊Dic43—22no—
227C4⋊Dic43—42no—
228C4⋊Dic43C22⋊C412yes—
229C4⋊Dic43C22⋊C412yes—
230C4⋊Dic43C22⋊C412yes—
231C4⋊Dic43C22⋊C412yes—
232C4⋊Dic43C22⋊C412yes—
233C4⋊Dic43C22⋊C412yes—
234C4⋊Dic43C22⋊C412yes—
235C4⋊Dic43C22⋊C412yes—
236Dic43⋊C4—21no—
237Dic43⋊C4—21no—
238Dic43⋊C4—21no—
239Dic43⋊C4—21no—
240Dic43⋊C4—22no—
241Dic43⋊C4—22no—
242Dic43⋊C4—22no—
243Dic43⋊C4—22no—
244Dic43⋊C4—82no—
245Dic43⋊C4—82no—
246Dic43⋊C4—82no—
247C4×Dic43—22no—
248C4×Dic43—22no—
249C4×Dic43—42no—
250C4×Dic43—82no—
251C23×C43—21no—
252C23×C43—22no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43C23×C411yescharacteristic
258C23×C43C22×D411yescharacteristic
259C23×C43C22×D411yescharacteristic
260C23×C43H(5,𝔽2)12yes—
261C23×C432−1+412yes—
262C22×D43—21no—
263C22×D43—22no—
264C22×D43—41no—
265C22×D43—41no—
266D4×C43—41no—
267D4×C43—41no—
268D4×C43—42no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—22no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—42no—
284C2×C4×C43—42no—
285C2×C4×C43—42no—
286C2×C4×C43—42no—
287C2×C4×C43—42no—
288C2×C4×C43—42no—
289C2×C4×C43C2×C22⋊C411yescharacteristic
290C2×C4×C43C2×C22⋊C411yescharacteristic
291C2×C4×C43C2×C22⋊C411yescharacteristic
292C2×C4×C43C2×C22⋊C411yescharacteristic
293C22⋊D43—41no—
294C22⋊D43—41no—
295C22⋊D43—42no—
296C22⋊D43—82no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—22no—
301C2×Dic43—42no—
302C2×Dic43—42no—
303C2×Dic43—42no—
304C2×Dic43—42no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43—82no—
318C2×Dic43C2×C22⋊C412yes—
319C2×Dic43C2×C22⋊C412yes—
320C2×Dic43C2×C22⋊C412yes—
321C2×Dic43C2×C22⋊C412yes—
322C4×D43—82no—
323Dic86—82no—
324#21877—431nomaximal, Sylow
325C22×C43—21no—
326C22×C43—21no—
327C22×C43—21no—
328C22×C43—21no—
329C22×C43—21no—
330C22×C43—21no—
331C22×C43—42no—
332C22×C43—42no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43—82no—
337C22×C43C22×C22⋊C411yescharacteristic
338C22×C43#52012yes—
339C22×C43#53511yescharacteristic
340C22×C43#53611yescharacteristic
341C22×C43#53712yes—
342C2×D43—41no—
343C2×D43—41no—
344C2×D43—41no—
345C2×D43—82no—
346C4×C43—21no—
347C4×C43—21no—
348C4×C43—21no—
349C4×C43—21no—
350C4×C43—41no—
351C4×C43—41no—
352C4×C43—41no—
353C4×C43—82no—
354C4×C43—82no—
355Dic43—22no—
356Dic43—22no—
357Dic43—22no—
358Dic43—22no—
359Dic43—41no—
360Dic43—41no—
361Dic43—41no—
362Dic43—82no—
363Dic43—82no—
364C2×#539—431no—
365#2316—431no—
366#2313—431no—
367#1996—432no—
368#1964—432no—
369#1899—431no—
370#1899—431no—
371#1899—431no—
372#1899D4311yescharacteristic, complemented
373#1799—432no—
374#1799—432no—
375C2×C43—21no—
376C2×C43—22no—
377C2×C43—22no—
378C2×C43—21no—
379C2×C43—81no—
380C2×C43#231111yescharacteristic
381C2×C43#288311yescharacteristic
382C2×C43#288411yescharacteristic
383D43—81no—
384#539—862no—
385#539—862no—
386#539—862no—
387#539—862no—
388C2×#126—431no—
389C2×#126—431no—
390C2×#125—431no—
391C2×#125—431no—
392C2×#123—431no—
393C2×#123—431no—
394C2×#123—431no—
395C2×#123C2×D4311yescharacteristic
396C2×C22⋊Q8—431no—
397C2×C22⋊Q8—431no—
398C2×C22⋊Q8—431no—
399C2×#121—431no—
400C2×C4×D4—431no—
401C2×C4×D4—431no—
402C2×#117—431no—
403C2×#117C2×D4311yescharacteristic
404C22×C4⋊C4—431no—
405C2×#99—432no—
406C2×#99—432no—
407C2×#99—432no—
408C2×#99C2×D4312yes—
409#389—862no—
410#389—862no—
411#387—862no—
412#387—862no—
413#381—431no—
414#381C2×D4311yescharacteristic
415#380—432no—
416#380—432no—
417#380—432no—
418C4×C22⋊C4—432no—
419#342—432no—
420#342—432no—
421#342—432no—
422#342C2×D4312yes—
423C43#2187711yescharacteristic, complemented, Sylow
424C22×Q8—431no—
425C22×D4—431no—
426C22×D4—431no—
427C22×D4C22×D4311yescharacteristic
428C23×C4—431no—
429C23×C4—431no—
430C23×C4—431no—
431C23×C4—431no—
432C23×C4C22×D4311yescharacteristic
433#126—862no—
434#126—862no—
435#126—862no—
436#126—862no—
437#125—862no—
438#125—862no—
439#125—862no—
440#125—862no—
441#123—21no—
442#123—21no—
443#123—21no—
444#123—21no—
445#123—862no—
446#123—862no—
447#123—862no—
448#123—862no—
449#123—861no—
450#123—861no—
451#123—861no—
452#123—861no—
453C22⋊Q8—862no—
454C22⋊Q8—862no—
455C22⋊Q8—862no—
456C22⋊Q8—862no—
457C22⋊Q8—862no—
458C22⋊Q8—862no—
459#121—862no—
460#121—862no—
461C4×D4—862no—
462C4×D4—862no—
463C4×D4—862no—
464C4×D4—862no—
465#117—42no—
466#117—1722no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—431no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—432no—
473C2×C4⋊C4—432no—
474C2×C4⋊C4—432no—
475C2×C4⋊C4—432no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—431no—
483C2×C4⋊C4—431no—
484C2×C4⋊C4—862no—
485C2×C4⋊C4—862no—
486C2×C4⋊C4—862no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4C4×D4311yescharacteristic
489C2×C4⋊C4C4×D4311yescharacteristic
490C2×C22⋊C4—431no—
491C2×C22⋊C4—431no—
492C2×C22⋊C4—431no—
493C2×C22⋊C4—431no—
494C2×C22⋊C4—431no—
495C2×C22⋊C4—431no—
496C2×C22⋊C4—431no—
497C2×C22⋊C4—432no—
498C2×C22⋊C4—432no—
499C2×C22⋊C4C4×D4311yescharacteristic
500C2×C22⋊C4C4×D4311yescharacteristic
501C2×C22⋊C4C22×D4312yes—
502C2×C22⋊C4C22×D4312yes—
503C2×C22⋊C4C22×D4311yescharacteristic
504C2×C42—21no—
505C2×C42—431no—
506C2×C42—431no—
507C2×C42—862no—
508C2×C42—861no—
509#99—42no—
510#99—1722no—
511#99—1722no—
512#99—1722no—
513#95—21no—
514#95—21no—
515#95—862no—
516#95—862no—
517#95—862no—
518#95—862no—
519#95—861no—
520#95—861no—
521C24—431no—
522C24C2×C4×D4311yescharacteristic
523C24C23×D4311yescharacteristic
524C2×Q8—862no—
525C2×Q8—3441no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—862no—
531C2×D4—861no—
532C2×D4—861no—
533C2×D4—862no—
534C2×D4—862no—
535C2×D4—3441no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—431no—
541C22×C4—431no—
542C22×C4—431no—
543C22×C4—431no—
544C22×C4—432no—
545C22×C4—432no—
546C22×C4—432no—
547C22×C4—432no—
548C22×C4—431no—
549C22×C4—431no—
550C22×C4—431no—
551C22×C4—862no—
552C22×C4—862no—
553C22×C4—862no—
554C22×C4—862no—
555C22×C4—3441no—
556C22×C4—3441no—
557C22×C4—3441no—
558C22×C4—3441no—
559C22×C4C2×C4×D4311yescharacteristic
560C22×C4C2×C4×D4311yescharacteristic
561C22×C4C2×C4×D4311yescharacteristic
562C22×C4C2×C4×D4311yescharacteristic
563C22×C4C2×C4×D4311yescharacteristic
564C22×C4D4×D4311yescharacteristic
565C22×C4D4×D4311yescharacteristic
566C22×C4D4×D4311yescharacteristic
567C22×C4D4×D4311yescharacteristic
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—42no—
573C4⋊C4—432no—
574C4⋊C4—432no—
575C4⋊C4—432no—
576C4⋊C4—432no—
577C4⋊C4—432no—
578C4⋊C4—432no—
579C4⋊C4—432no—
580C4⋊C4—432no—
581C4⋊C4—862no—
582C4⋊C4—862no—
583C4⋊C4—862no—
584C4⋊C4—862no—
585C4⋊C4—862no—
586C4⋊C4—862no—
587C4⋊C4—861no—
588C4⋊C4—861no—
589C4⋊C4—861no—
590C4⋊C4—861no—
591C4⋊C4—3442no—
592C4⋊C4—3442no—
593C4⋊C4—3442no—
594C4⋊C4—1722no—
595C22⋊C4—21no—
596C22⋊C4—21no—
597C22⋊C4—21no—
598C22⋊C4—21no—
599C22⋊C4—21no—
600C22⋊C4—21no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—862no—
606C22⋊C4—862no—
607C22⋊C4—862no—
608C22⋊C4—862no—
609C22⋊C4—861no—
610C22⋊C4—861no—
611C22⋊C4—861no—
612C22⋊C4—861no—
613C22⋊C4—861no—
614C22⋊C4—861no—
615C22⋊C4—862no—
616C22⋊C4—862no—
617C22⋊C4—862no—
618C22⋊C4—862no—
619C42—42no—
620C42—862no—
621C42—862no—
622C42—3442no—
623C42—1722no—
624C23—21no—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—862no—
631C23—861no—
632C23—1721no—
633C23—1721no—
634C23C22×C4×D4311yescharacteristic
635C23C2×D4×D4311yescharacteristic
636C23C2×D4×D4311yescharacteristic
637C23#1306337012yes—
638C23#1306337212yes—
639Q8—3442no—
640D4—41no—
641D4—41no—
642D4—42no—
643D4—3442no—
644D4—1721no—
645D4—1721no—
646D4—1722no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—432no—
668C2×C4—432no—
669C2×C4—432no—
670C2×C4—432no—
671C2×C4—861no—
672C2×C4—861no—
673C2×C4—861no—
674C2×C4—862no—
675C2×C4—3442no—
676C2×C4—3442no—
677C2×C4—1722no—
678C2×C4—1722no—
679C2×C4—1722no—
680C2×C4—1722no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1722no—
686C2×C4—1722no—
687C2×C4—1722no—
688C2×C4—1722no—
689C2×C4—1722no—
690C2×C4—1722no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4C22⋊C4×D4311yescharacteristic
694C2×C4C22⋊C4×D4311yescharacteristic
695C2×C4C22⋊C4×D4311yescharacteristic
696C2×C4C22⋊C4×D4311yescharacteristic
697C22—21no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—42no—
704C22—42no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—82no—
709C22—3442no—
710C22—1721no—
711C22—1721no—
712C22—1721no—
713C22C2×C22⋊C4×D4311yescharacteristic
714C22#1458337812yes—
715C22#1458346411yescharacteristic
716C22#1458347111yescharacteristic
717C22#1458347612yes—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—82no—
726C4—82no—
727C4—862no—
728C4—862no—
729C4—862no—
730C4—862no—
731C4—3442no—
732C4—3442no—
733C4—1721no—
734C4—1721no—
735C4—1721no—
736C2—21no—
737C2—22no—
738C2—22no—
739C2—21no—
740C2—81no—
741C2—3441no—
742C2#1913718211yescharacteristic
743C2#1914305411yescharacteristic
744C2#1914305711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1899C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063297C22
cosocleC24×C43C24
hypercenter#1899D43
hypocenterC43#21877
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1899

Complements

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

NH ≅ G/Ntype
2. #19137211C2semidirect
3. #19137196C2semidirect
4. #19135578C2semidirect
6. #19135054C2semidirect
7. #19135053C2semidirect
8. #19135051C2semidirect
9. #19134582C2semidirect
10. #19134581C2semidirect
11. C43×#1899C2semidirect
16. C2×#13063320C4semidirect
17. C2×#13063318C4semidirect
18. C2×#13063316C4semidirect
19. C2×#13063315C4semidirect
20. C2×#13063309C4semidirect
22. C2×#13063307C4semidirect
23. C2×#13063305C4semidirect
24. C2×#13063302C4semidirect
372. #1899D43semidirect
423. C43#21877semidirect

Maximal subgroups

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

subgroupindex
C2×#145834932
#191372112
#191371962
#191355782
#191354292
#191350542
#191350532
#191350512
#191345822
#191345812
C43×#18992
#2187743