Finite Group Databasebeta

← #25113351

Subgroups — #25113351

Order 11008.

1172 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583601C211yesmaximal, characteristic
2#19137474C211yesmaximal, characteristic, complemented
3#19137470C211yesmaximal, characteristic, complemented
4#19135432C211yesmaximal, characteristic, complemented
5#19135429C212yesmaximal, complemented
6#19135429C212yesmaximal, complemented
7#19134581C212yesmaximal, complemented
8#19134580C211yesmaximal, characteristic, complemented
9#99×Dic43C212yesmaximal, complemented
10C4×#13063239C211yesmaximal, characteristic, complemented
11C43×#1964C211yesmaximal, characteristic, complemented
12#14583601—22no—
13#14583601—21no—
14#14583601—21no—
15#14583601—21no—
16#14583601—21no—
17#14583601—22no—
18C2×#13063318C412yescomplemented
19C2×#13063316C411yescharacteristic, complemented
20C2×#13063309C412yescomplemented
21C2×#13063297C2212yes—
22C2×#13063296C411yescharacteristic, complemented
23C2×D4×Dic43C411yescharacteristic, complemented
24C2×D4×Dic43C2212yes—
25C2×C4×C22⋊D43C2211yescharacteristic
26C2×#13063283C411yescharacteristic, complemented
27C22×C4⋊Dic43C2211yescharacteristic
28C2×#13063240C2212yes—
29C2×#13063240C2212yes—
30C2×#13063239C2211yescharacteristic
31C2×#13063239C2211yescharacteristic
32C2×#13063239C2212yes—
33#14582797—21no—
34#14582795—21no—
35#14582784—22no—
36#14582782—22no—
37#14582759C2211yescharacteristic
38#14582757C2212yes—
39#14582757C2212yes—
40C4⋊C4×Dic43—21no—
41C4×C4⋊Dic43—21no—
42C22⋊C4×Dic43C2212yes—
43C22⋊C4×Dic43C2212yes—
44C4×C22⋊Dic43C2211yescharacteristic
45#14582665C2212yes—
46#14582665C2211yescharacteristic
47#14582665C2211yescharacteristic
48C2×#121×C43C2211yescharacteristic
49C2×#99×C43C2212yes—
50C2×#99×C43C2212yes—
51C43×#380C2211yescharacteristic
52C4×C22⋊C4×C43C2211yescharacteristic
53C22×C22⋊D43C2×C412yes—
54C22×C22⋊D43C2311yescharacteristic
55C23×Dic43C2×C412yes—
56C23×Dic43C2312yes—
57C22×C4×D43C2×C411yescharacteristic
58#13063318—22no—
59#13063318—22no—
60#13063318—22no—
61#13063318—22no—
62#13063316—22no—
63#13063316—21no—
64#13063316—21no—
65#13063309—22no—
66#13063309—22no—
67#13063309—22no—
68#13063309—22no—
69#13063297—22no—
70#13063297—22no—
71#13063297—22no—
72#13063297—22no—
73#13063296—22no—
74#13063296—21no—
75#13063296—21no—
76D4×Dic43—22no—
77D4×Dic43—22no—
78D4×Dic43—22no—
79D4×Dic43—22no—
80D4×Dic43—22no—
81D4×Dic43—21no—
82D4×Dic43—21no—
83C4×C22⋊D43—21no—
84C4×C22⋊D43—21no—
85C4×C22⋊D43—21no—
86C4×C22⋊D43—21no—
87#13063283—22no—
88#13063283—21no—
89#13063283—21no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43C2×C412yes—
92C2×C4⋊Dic43C2×C411yescharacteristic
93C2×C4⋊Dic43C2×C411yescharacteristic
94C2×C4⋊Dic43C2×C412yes—
95C2×C4⋊Dic43D412yes—
96C2×C4⋊Dic43D411yescharacteristic
97C2×C4⋊Dic43D411yescharacteristic
98C2×C4⋊Dic43D411yescharacteristic
99C2×C4⋊Dic43D411yescharacteristic
100C2×C4⋊Dic43D412yes—
101C2×Dic43⋊C4—22no—
102C2×Dic43⋊C4—22no—
103C2×Dic43⋊C4C2×C411yescharacteristic
104C2×Dic43⋊C4C2×C412yes—
105C2×C22⋊Dic43C2×C412yes—
106C2×C22⋊Dic43C2×C412yes—
107C2×C22⋊Dic43C2311yescharacteristic
108C2×C22⋊Dic43C2312yes—
109C2×C22⋊Dic43C2311yescharacteristic
110C2×C22⋊Dic43C2311yescharacteristic
111C2×(C2×D43)⋊C4C2×C412yes—
112C2×(C2×D43)⋊C4C2×C411yescharacteristic
113C2×C4×Dic43—21no—
114C2×C4×Dic43—22no—
115C2×C4×Dic43—22no—
116C2×C4×Dic43C2×C412yes—
117C2×C4×Dic43C2×C411yescharacteristic
118#13063240—24no—
119#13063240—42no—
120#13063239—22no—
121#13063239—22no—
122#13063239—42no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C22×D4×C43C2×C411yescharacteristic
130C22×D4×C43C2312yes—
131C23×C4×C43C2311yescharacteristic
132#121×C43—21no—
133#121×C43—21no—
134#121×C43—21no—
135#121×C43—21no—
136C2×C4⋊C4×C43—21no—
137C2×C4⋊C4×C43C2×C411yescharacteristic
138C2×C22⋊C4×C43C2×C412yes—
139C2×C22⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43C2312yes—
141C2×C22⋊C4×C43C2311yescharacteristic
142C2×C42×C43—21no—
143#99×C43—24no—
144#99×C43—42no—
145#95×C43—21no—
146#95×C43—21no—
147C24×C43C22×C412yes—
148C24×C43C2411yescharacteristic
149C23×D43C22×C411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—22no—
153C2×D4×C43—22no—
154C2×D4×C43—22no—
155C2×D4×C43—22no—
156C2×D4×C43—22no—
157C2×D4×C43—22no—
158C2×D4×C43—42no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—22no—
162C22×C4×C43—42no—
163C22×C4×C43C22×C412yes—
164C22×C4×C43C22×C411yescharacteristic
165C22×C4×C43C22×C411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2×D411yescharacteristic
170C2×C22⋊D43—22no—
171C2×C22⋊D43—22no—
172C2×C22⋊D43—21no—
173C2×C22⋊D43—21no—
174C2×C22⋊D43—21no—
175C2×C22⋊D43—21no—
176C2×C22⋊D43—21no—
177C2×C22⋊D43—21no—
178C2×C22⋊D43—82no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—22no—
184C22×Dic43—82no—
185C22×Dic43—82no—
186C22×Dic43C22×C411yescharacteristic
187C22×Dic43C22×C411yescharacteristic
188C22×Dic43C22×C411yescharacteristic
189C22×Dic43C22×C412yes—
190C22×Dic43C22×C412yes—
191C22×Dic43C2×D412yes—
192C22×Dic43C2×D412yes—
193C22×Dic43C2×D412yes—
194C22×Dic43C2×D412yes—
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—42no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—42no—
201C22⋊C4×C43—22no—
202C22⋊C4×C43—22no—
203C22⋊C4×C43—22no—
204C22⋊C4×C43—21no—
205C22⋊C4×C43—21no—
206C22⋊C4×C43—22no—
207C22⋊C4×C43—21no—
208C22⋊C4×C43#4112yes—
209C42×C43—42no—
210C22⋊Dic43—22no—
211C22⋊Dic43—22no—
212C22⋊Dic43—22no—
213C22⋊Dic43—22no—
214C22⋊Dic43—21no—
215C22⋊Dic43—21no—
216C22⋊Dic43—21no—
217C22⋊Dic43—22no—
218C22⋊Dic43—22no—
219C22⋊Dic43—21no—
220C22⋊Dic43—21no—
221C22⋊Dic43#4112yes—
222(C2×D43)⋊C4—21no—
223(C2×D43)⋊C4—21no—
224(C2×D43)⋊C4—22no—
225(C2×D43)⋊C4—22no—
226C4⋊Dic43—22no—
227C4⋊Dic43—22no—
228C4⋊Dic43—42no—
229C4⋊Dic43C22⋊C412yes—
230C4⋊Dic43C22⋊C411yescharacteristic
231C4⋊Dic43C22⋊C411yescharacteristic
232C4⋊Dic43C22⋊C412yes—
233C4⋊Dic43C22⋊C411yescharacteristic
234C4⋊Dic43C22⋊C411yescharacteristic
235C4⋊Dic43C22⋊C412yes—
236C4⋊Dic43C22⋊C412yes—
237C4⋊Dic43C22⋊C412yes—
238C4⋊Dic43C22⋊C412yes—
239Dic43⋊C4—21no—
240Dic43⋊C4—21no—
241Dic43⋊C4—22no—
242Dic43⋊C4—22no—
243Dic43⋊C4—82no—
244Dic43⋊C4—82no—
245C4×Dic43—21no—
246C4×Dic43—21no—
247C4×Dic43—22no—
248C4×Dic43—22no—
249C4×Dic43—42no—
250C4×Dic43—82no—
251C4×Dic43—82no—
252C23×C43—22no—
253C23×C43—22no—
254C23×C43—22no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—42no—
258C23×C43—42no—
259C23×C43C23×C411yescharacteristic
260C23×C43C22×D411yescharacteristic
261C23×C43C22×D411yescharacteristic
262C23×C43C2×#4111yescharacteristic
263C23×C43C2×#4111yescharacteristic
264C23×C43H(5,𝔽2)11yescharacteristic
265C23×C432−1+411yescharacteristic
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—41no—
270C22×D43—41no—
271D4×C43—42no—
272D4×C43—42no—
273D4×C43—42no—
274D4×C43—42no—
275D4×C43—42no—
276D4×C43—42no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—42no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—42no—
293C2×C4×C43—41no—
294C2×C4×C43—42no—
295C2×C4×C43C2×C22⋊C411yescharacteristic
296C2×C4×C43C2×C22⋊C411yescharacteristic
297C2×C4×C43C2×C22⋊C411yescharacteristic
298C2×C4×C43C2×C22⋊C411yescharacteristic
299C22⋊D43—41no—
300C22⋊D43—41no—
301C22⋊D43—41no—
302C22⋊D43—41no—
303C22⋊D43—82no—
304C22⋊D43—82no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—22no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—42no—
323C2×Dic43—41no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—41no—
327C2×Dic43—82no—
328C2×Dic43—82no—
329C2×Dic43C2×C22⋊C412yes—
330C2×Dic43C2×C22⋊C412yes—
331C2×Dic43C2×C22⋊C412yes—
332C2×Dic43C2×C22⋊C412yes—
333C4×D43—42no—
334C4×D43—42no—
335#22535—431nomaximal, Sylow
336C22×C43—21no—
337C22×C43—21no—
338C22×C43—21no—
339C22×C43—21no—
340C22×C43—21no—
341C22×C43—21no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—82no—
350C22×C43—82no—
351C22×C43C22×C22⋊C411yescharacteristic
352C22×C43C4×#4111yescharacteristic
353C22×C43#52011yescharacteristic
354C22×C43#54811yescharacteristic
355C22×C43#54811yescharacteristic
356C22×C43#55011yescharacteristic
357C22×C43#55011yescharacteristic
358C2×D43—41no—
359C2×D43—41no—
360C2×D43—41no—
361C2×D43—81no—
362C2×D43—81no—
363C4×C43—21no—
364C4×C43—21no—
365C4×C43—21no—
366C4×C43—42no—
367C4×C43—42no—
368C4×C43—81no—
369C4×C43—82no—
370C4×C43#41012yes—
371Dic43—22no—
372Dic43—22no—
373Dic43—22no—
374Dic43—22no—
375Dic43—42no—
376Dic43—41no—
377Dic43—41no—
378Dic43—41no—
379Dic43—82no—
380Dic43—81no—
381C2×#553—431no—
382#2345—431no—
383#2345—431no—
384#1964—432no—
385#1964—432no—
386#1964—431no—
387#1964D4311yescharacteristic, complemented
388#1799—432no—
389#1799—431no—
390C4×#99—432no—
391C4×#99—431no—
392C2×C43—21no—
393C2×C43—21no—
394C2×C43—21no—
395C2×C43—21no—
396C2×C43—21no—
397C2×C43—21no—
398C2×C43—82no—
399C2×C43#234111yescharacteristic
400C2×C43C2×#41011yescharacteristic
401C2×C43#288311yescharacteristic
402D43—81no—
403#553—861no—
404#553—861no—
405#553—862no—
406#553—862no—
407#553—861no—
408#553—861no—
409C2×#126—432no—
410C2×#125—431no—
411C2×#123—432no—
412C2×#121—432no—
413C2×#121—431no—
414C2×#121C2×D4311yescharacteristic
415C2×C4×D4—432no—
416C2×C4×D4—431no—
417C2×C4×D4—431no—
418C2×#117—431no—
419C22×C4⋊C4—431no—
420C2×#99—432no—
421C2×#99—431no—
422C2×#99—431no—
423C2×#99—432no—
424C2×#99—432no—
425C2×#99C2×D4312yes—
426C2×#99C2×D4312yes—
427#389—861no—
428#389—861no—
429#387—862no—
430#387—862no—
431#380—431no—
432#380—432no—
433#380—432no—
434#380C2×D4311yescharacteristic
435C4×C4⋊C4—861no—
436C4×C4⋊C4—861no—
437C4×C22⋊C4—431no—
438C4×C22⋊C4—432no—
439C4×C22⋊C4—432no—
440C4×C22⋊C4C2×D4311yescharacteristic
441#342—432no—
442#342—431no—
443#342—431no—
444C43#2253511yescharacteristic, complemented, Sylow
445C22×D4—431no—
446C22×D4—432no—
447C22×D4C4×D4311yescharacteristic
448C22×D4C22×D4312yes—
449C23×C4—432no—
450C23×C4—432no—
451C23×C4—431no—
452C23×C4C22×D4311yescharacteristic
453#126—862no—
454#126—862no—
455#126—862no—
456#126—862no—
457#125—862no—
458#125—861no—
459#125—861no—
460#123—862no—
461#123—862no—
462#123—862no—
463#123—862no—
464#121—21no—
465#121—21no—
466#121—21no—
467#121—21no—
468#121—862no—
469#121—861no—
470#121—861no—
471#121—862no—
472#121—862no—
473#121—862no—
474#121—862no—
475C4×D4—862no—
476C4×D4—861no—
477C4×D4—861no—
478C4×D4—862no—
479C4×D4—862no—
480C4×D4—862no—
481C4×D4—862no—
482C4×D4—861no—
483C4×D4—861no—
484C4×D4—861no—
485C4×D4—861no—
486#117—862no—
487#117—861no—
488#117—861no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—431no—
491C2×C4⋊C4—431no—
492C2×C4⋊C4—432no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—432no—
496C2×C4⋊C4—432no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—432no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—432no—
502C2×C4⋊C4—862no—
503C2×C4⋊C4—862no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4C4×D4311yescharacteristic
506C2×C22⋊C4—431no—
507C2×C22⋊C4—432no—
508C2×C22⋊C4—432no—
509C2×C22⋊C4—431no—
510C2×C22⋊C4—432no—
511C2×C22⋊C4—431no—
512C2×C22⋊C4—432no—
513C2×C22⋊C4—431no—
514C2×C22⋊C4C4×D4312yes—
515C2×C22⋊C4C22×D4312yes—
516C2×C22⋊C4C22×D4311yescharacteristic
517C2×C22⋊C4C22×D4311yescharacteristic
518C2×C42—21no—
519C2×C42—432no—
520C2×C42—431no—
521C2×C42—862no—
522C2×C42—862no—
523C2×C42—861no—
524#99—24no—
525#99—42no—
526#99—862no—
527#99—864no—
528#99—862no—
529#99—1722no—
530#99—1722no—
531#95—21no—
532#95—21no—
533#95—862no—
534#95—862no—
535#95—862no—
536#95—862no—
537#95—861no—
538#95—861no—
539C24—431no—
540C24C2×C4×D4312yes—
541C24C23×D4311yescharacteristic
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—42no—
551C2×D4—862no—
552C2×D4—862no—
553C2×D4—861no—
554C2×D4—861no—
555C2×D4—861no—
556C2×D4—861no—
557C2×D4—861no—
558C2×D4—861no—
559C2×D4—3442no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—42no—
564C22×C4—432no—
565C22×C4—432no—
566C22×C4—432no—
567C22×C4—432no—
568C22×C4—432no—
569C22×C4—432no—
570C22×C4—431no—
571C22×C4—431no—
572C22×C4—431no—
573C22×C4—862no—
574C22×C4—862no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—862no—
579C22×C4—861no—
580C22×C4—3442no—
581C22×C4—3442no—
582C22×C4—1722no—
583C22×C4C2×C4×D4312yes—
584C22×C4C2×C4×D4311yescharacteristic
585C22×C4C2×C4×D4311yescharacteristic
586C22×C4D4×D4311yescharacteristic
587C22×C4D4×D4311yescharacteristic
588C22×C4D4×D4311yescharacteristic
589C22×C4D4×D4311yescharacteristic
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—42no—
593C4⋊C4—432no—
594C4⋊C4—431no—
595C4⋊C4—431no—
596C4⋊C4—432no—
597C4⋊C4—431no—
598C4⋊C4—431no—
599C4⋊C4—432no—
600C4⋊C4—432no—
601C4⋊C4—432no—
602C4⋊C4—432no—
603C4⋊C4—862no—
604C4⋊C4—862no—
605C4⋊C4—862no—
606C4⋊C4—862no—
607C4⋊C4—861no—
608C4⋊C4—861no—
609C4⋊C4—3442no—
610C4⋊C4—3442no—
611C4⋊C4—1722no—
612C22⋊C4—21no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—21no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—22no—
619C22⋊C4—432no—
620C22⋊C4—862no—
621C22⋊C4—862no—
622C22⋊C4—862no—
623C22⋊C4—862no—
624C22⋊C4—862no—
625C22⋊C4—862no—
626C22⋊C4—861no—
627C22⋊C4—861no—
628C22⋊C4—861no—
629C22⋊C4—861no—
630C22⋊C4—861no—
631C22⋊C4—862no—
632C22⋊C4—861no—
633C22⋊C4—862no—
634C22⋊C4—861no—
635C22⋊C4#1062190012yes—
636C42—42no—
637C42—862no—
638C42—862no—
639C42—861no—
640C42—861no—
641C42—3442no—
642C42—3442no—
643C42—1722no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—41no—
648C23—41no—
649C23—42no—
650C23—42no—
651C23—861no—
652C23—861no—
653C23—861no—
654C23—1721no—
655C23—1721no—
656C23C22×C4×D4311yescharacteristic
657C23C2×D4×D4311yescharacteristic
658C23C2×D4×D4311yescharacteristic
659C23#41×D4311yescharacteristic
660C23C2×#1062190011yescharacteristic
661C23#1306337011yescharacteristic
662C23#1306337211yescharacteristic
663D4—42no—
664D4—42no—
665D4—42no—
666D4—42no—
667D4—42no—
668D4—42no—
669D4—3442no—
670D4—3442no—
671D4—1721no—
672D4—1721no—
673D4—1721no—
674D4—1721no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—432no—
694C2×C4—432no—
695C2×C4—432no—
696C2×C4—432no—
697C2×C4—862no—
698C2×C4—861no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—3442no—
704C2×C4—3442no—
705C2×C4—1722no—
706C2×C4—1722no—
707C2×C4—1722no—
708C2×C4—1722no—
709C2×C4—1722no—
710C2×C4—1722no—
711C2×C4—1722no—
712C2×C4—1722no—
713C2×C4—1721no—
714C2×C4—1721no—
715C2×C4—1722no—
716C2×C4—1722no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1722no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4C22⋊C4×D4311yescharacteristic
724C2×C4C22⋊C4×D4311yescharacteristic
725C2×C4C22⋊C4×D4311yescharacteristic
726C2×C4C22⋊C4×D4311yescharacteristic
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—82no—
741C22—82no—
742C22—3441no—
743C22—3441no—
744C22—1721no—
745C22—1721no—
746C22—1721no—
747C22C2×C22⋊C4×D4311yescharacteristic
748C22C4×#1062190011yescharacteristic
749C22#1458337811yescharacteristic
750C22#1458355511yescharacteristic
751C22#1458355711yescharacteristic
752C22#1458356711yescharacteristic
753C22#1458356911yescharacteristic
754C4—21no—
755C4—21no—
756C4—21no—
757C4—42no—
758C4—42no—
759C4—82no—
760C4—81no—
761C4—862no—
762C4—862no—
763C4—862no—
764C4—862no—
765C4—3441no—
766C4—3442no—
767C4—1722no—
768C4—1721no—
769C4—1721no—
770C4—1721no—
771C4#1458287112yes—
772C2—21no—
773C2—21no—
774C2—21no—
775C2—21no—
776C2—21no—
777C2—21no—
778C2—82no—
779C2—3441no—
780C2#1913743411yescharacteristic
781C2C2×#1458287111yescharacteristic
782C2#1914305411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1964C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583601C2
cosocleC24×C43C24
hypercenter#1964D43
hypocenterC43#22535
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. #19137474C2semidirect
3. #19137470C2semidirect
4. #19135432C2semidirect
5. #19135429C2semidirect
6. #19135429C2semidirect
7. #19134581C2semidirect
8. #19134580C2semidirect
9. #99×Dic43C2semidirect
10. C4×#13063239C2semidirect
11. C43×#1964C2semidirect
18. C2×#13063318C4semidirect
19. C2×#13063316C4semidirect
20. C2×#13063309C4semidirect
22. C2×#13063296C4semidirect
23. C2×D4×Dic43C4semidirect
26. C2×#13063283C4semidirect
387. #1964D43semidirect
444. C43#22535semidirect

Maximal subgroups

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

subgroupindex
C2×#145836012
#191374742
#191374702
#191354322
#191354292
#191345812
#191345802
#99×Dic432
C4×#130632392
C43×#19642
#2253543