Finite Group Databasebeta

← #25113353

Subgroups — #25113353

Order 11008.

1172 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583598C211yesmaximal, characteristic
2#19137473C212yesmaximal, complemented
3#19135431C212yesmaximal, complemented
4#19135429C212yesmaximal, complemented
5#19135429C212yesmaximal, complemented
6#19134583C211yesmaximal, characteristic, complemented
7#19134582C211yesmaximal, characteristic, complemented
8#19134582C211yesmaximal, characteristic, complemented
9#19134382C211yesmaximal, characteristic, complemented
10#19134382C211yesmaximal, characteristic, complemented
11C4×#99×C43C211yesmaximal, characteristic, complemented
12#14583598—22no—
13#14583598—22no—
14#14583598—22no—
15#14583598—22no—
16C2×#13063319C411yescharacteristic, complemented
17C2×#13063318C411yescharacteristic, complemented
18C2×#13063315C411yescharacteristic, complemented
19C2×#13063310C411yescharacteristic, complemented
20C2×#13063308C411yescharacteristic, complemented
21C2×#13063299C2211yescharacteristic
22C2×#13063298C411yescharacteristic, complemented
23C2×#13063297C2211yescharacteristic
24C2×#13063297C2211yescharacteristic
25C2×C4×C22⋊D43C411yescharacteristic, complemented
26C2×(C22⋊D43)⋊C4C2211yescharacteristic
27C2×(C22⋊D43)⋊C4C2211yescharacteristic
28C2×#13063282C411yescharacteristic, complemented
29C22×Dic43⋊C4C2211yescharacteristic
30C2×#13063240C2212yes—
31C2×#13063239C2212yes—
32C2×#13063239C2212yes—
33C2×#13063239C2212yes—
34C2×#13063239C2212yes—
35#14582796—22no—
36#14582786—22no—
37#14582783—22no—
38#14582759C2212yes—
39#14582757C2212yes—
40#14582757C2212yes—
41C4×Dic43⋊C4—22no—
42C22⋊C4×Dic43C2212yes—
43C22⋊C4×Dic43C2212yes—
44#14582666C2211yescharacteristic
45#14582666C2211yescharacteristic
46C2×C4×D4×C43C2211yescharacteristic
47C2×#99×C43C2212yes—
48C4×C22⋊C4×C43C2212yes—
49C43×#342C2211yescharacteristic
50C43×#342C2211yescharacteristic
51C22×D172C2×C411yescharacteristic
52C22×C22⋊D43C2×C411yescharacteristic
53C22×C22⋊D43C2×C411yescharacteristic
54C22×C22⋊D43C2311yescharacteristic
55C22×C22⋊D43C2311yescharacteristic
56C23×Dic43C2311yescharacteristic
57C23×Dic43C2311yescharacteristic
58C22×C4×D43C2×C411yescharacteristic
59C22×C4×D43C2×C411yescharacteristic
60#13063319—22no—
61#13063319—22no—
62#13063318—22no—
63#13063318—22no—
64#13063315—22no—
65#13063315—22no—
66#13063310—22no—
67#13063310—22no—
68#13063308—22no—
69#13063308—22no—
70#13063299—22no—
71#13063299—22no—
72#13063298—22no—
73#13063298—22no—
74#13063297—22no—
75#13063297—22no—
76#13063297—22no—
77#13063297—22no—
78C4×C22⋊D43—21no—
79C4×C22⋊D43—21no—
80C4×C22⋊D43—21no—
81C4×C22⋊D43—21no—
82(C22⋊D43)⋊C4—22no—
83(C22⋊D43)⋊C4—22no—
84(C22⋊D43)⋊C4—22no—
85(C22⋊D43)⋊C4—22no—
86#13063282—21no—
87#13063282—21no—
88#13063282—21no—
89#13063282—21no—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43C2×C411yescharacteristic
92C2×Dic43⋊C4—22no—
93C2×Dic43⋊C4—22no—
94C2×Dic43⋊C4C2×C411yescharacteristic
95C2×Dic43⋊C4C2×C411yescharacteristic
96C2×Dic43⋊C4C2×C411yescharacteristic
97C2×Dic43⋊C4C2×C411yescharacteristic
98C2×Dic43⋊C4C2×C411yescharacteristic
99C2×Dic43⋊C4C2×C411yescharacteristic
100C2×Dic43⋊C4C2×C411yescharacteristic
101C2×Dic43⋊C4C2×C411yescharacteristic
102C2×Dic43⋊C4D412yes—
103C2×Dic43⋊C4D412yes—
104C2×Dic43⋊C4D412yes—
105C2×Dic43⋊C4D412yes—
106C2×C22⋊Dic43C2×C411yescharacteristic
107C2×C22⋊Dic43C2×C411yescharacteristic
108C2×C22⋊Dic43C2312yes—
109C2×C22⋊Dic43C2312yes—
110C2×(C2×D43)⋊C4C2×C411yescharacteristic
111C2×(C2×D43)⋊C4C2×C411yescharacteristic
112C2×(C2×D43)⋊C4C2×C411yescharacteristic
113C2×(C2×D43)⋊C4C2×C411yescharacteristic
114C2×(C2×D43)⋊C4C2×C411yescharacteristic
115C2×(C2×D43)⋊C4C2×C411yescharacteristic
116C2×C4×Dic43—22no—
117C2×C4×Dic43—22no—
118C2×C4×Dic43C2×C411yescharacteristic
119C2×C4×Dic43C2×C411yescharacteristic
120#13063240—42no—
121#13063239—24no—
122#13063239—24no—
123#13063239—42no—
124#13063239—42no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C22×D4×C43C2311yescharacteristic
131C23×C4×C43C2×C411yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C4×D4×C43—22no—
134C4×D4×C43—22no—
135C2×C4⋊C4×C43C2×C411yescharacteristic
136C2×C22⋊C4×C43C2×C411yescharacteristic
137C2×C22⋊C4×C43C2312yes—
138C2×C22⋊C4×C43C2311yescharacteristic
139C2×C22⋊C4×C43C2312yes—
140C2×C42×C43—22no—
141C2×C42×C43C2×C411yescharacteristic
142#99×C43—24no—
143#95×C43—22no—
144C24×C43C22×C411yescharacteristic
145C24×C43C2411yescharacteristic
146C23×D43C22×C411yescharacteristic
147C23×D43C22×C411yescharacteristic
148C2×D4×C43—22no—
149C2×D4×C43—22no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—81no—
157C22×C4×C43—81no—
158C22×C4×C43C22×C411yescharacteristic
159C22×C4×C43C22×C411yescharacteristic
160C22×C4×C43C22×C411yescharacteristic
161C22×C4×C43C22×C411yescharacteristic
162C22×C4×C43C22×C411yescharacteristic
163C22×C4×C43C2×D412yes—
164C22×C4×C43C2×D412yes—
165C2×C22⋊D43—21no—
166C2×C22⋊D43—21no—
167C2×C22⋊D43—22no—
168C2×C22⋊D43—22no—
169C2×C22⋊D43—22no—
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—42no—
177C2×C22⋊D43—81no—
178C22×Dic43—22no—
179C22×Dic43—22no—
180C22×Dic43—42no—
181C22×Dic43—81no—
182C22×Dic43C22×C411yescharacteristic
183C22×Dic43C22×C411yescharacteristic
184C22×Dic43C22×C411yescharacteristic
185C22×Dic43C22×C411yescharacteristic
186C22×Dic43C22×C411yescharacteristic
187C22×Dic43C22×C411yescharacteristic
188C22×Dic43C2×D412yes—
189C22×Dic43C2×D412yes—
190C22×Dic43C2×D412yes—
191C22×Dic43C2×D412yes—
192C2×D172—22no—
193C2×D172—81no—
194C2×C4×D43—21no—
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—21no—
198C2×C4×D43—42no—
199C2×C4×D43—81no—
200C4⋊C4×C43—22no—
201C22⋊C4×C43—22no—
202C22⋊C4×C43—22no—
203C22⋊C4×C43—22no—
204C22⋊C4×C43—22no—
205C22⋊C4×C43—22no—
206C22⋊C4×C43#4114yes—
207C42×C43—21no—
208C42×C43—21no—
209C42×C43—82no—
210C22⋊Dic43—21no—
211C22⋊Dic43—21no—
212C22⋊Dic43—22no—
213C22⋊Dic43—22no—
214C22⋊Dic43—22no—
215C22⋊Dic43—22no—
216C22⋊Dic43—22no—
217(C2×D43)⋊C4—21no—
218(C2×D43)⋊C4—21no—
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—
225(C2×D43)⋊C4—22no—
226C4⋊Dic43—22no—
227C4⋊Dic43—82no—
228Dic43⋊C4—21no—
229Dic43⋊C4—21no—
230Dic43⋊C4—22no—
231Dic43⋊C4—22no—
232Dic43⋊C4—22no—
233Dic43⋊C4—44no—
234Dic43⋊C4—82no—
235Dic43⋊C4C22⋊C411yescharacteristic
236Dic43⋊C4C22⋊C411yescharacteristic
237Dic43⋊C4C22⋊C411yescharacteristic
238Dic43⋊C4C22⋊C411yescharacteristic
239Dic43⋊C4C22⋊C412yes—
240Dic43⋊C4C22⋊C412yes—
241Dic43⋊C4C22⋊C412yes—
242Dic43⋊C4C22⋊C412yes—
243Dic43⋊C4C22⋊C412yes—
244Dic43⋊C4C22⋊C412yes—
245C4×Dic43—21no—
246C4×Dic43—21no—
247C4×Dic43—21no—
248C4×Dic43—21no—
249C4×Dic43—44no—
250C4×Dic43—82no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43C23×C411yescharacteristic
259C23×C43C22×D412yes—
260C23×C43C2×#4112yes—
261C23×C43H(5,𝔽2)11yescharacteristic
262C23×C432−1+411yescharacteristic
263C22×D43—21no—
264C22×D43—21no—
265C22×D43—21no—
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273D4×C43—42no—
274D4×C43—42no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—24no—
281C2×C4×C43—42no—
282C2×C4×C43—42no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—42no—
286C2×C4×C43—42no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—42no—
290C2×C4×C43—42no—
291C2×C4×C43—42no—
292C2×C4×C43—81no—
293C2×C4×C43—81no—
294C2×C4×C43C2×C22⋊C412yes—
295C2×C4×C43C2×C22⋊C411yescharacteristic
296C2×C4×C43C2×C22⋊C411yescharacteristic
297C22⋊D43—42no—
298C22⋊D43—42no—
299C22⋊D43—42no—
300C22⋊D43—42no—
301C22⋊D43—42no—
302C22⋊D43—42no—
303C22⋊D43—82no—
304C2×Dic43—24no—
305C2×Dic43—22no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—42no—
317C2×Dic43—41no—
318C2×Dic43—42no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43C2×C22⋊C411yescharacteristic
325C2×Dic43C2×C22⋊C411yescharacteristic
326C2×Dic43C2×C22⋊C411yescharacteristic
327C2×Dic43C2×C22⋊C412yes—
328C2×Dic43C2×C22⋊C412yes—
329C2×Dic43C2×C22⋊C411yescharacteristic
330D172—82no—
331C4×D43—42no—
332C4×D43—42no—
333C4×D43—81no—
334C4×D43—81no—
335#22535—431nomaximal, Sylow
336C22×C43—21no—
337C22×C43—22no—
338C22×C43—21no—
339C22×C43—22no—
340C22×C43—42no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—81no—
347C22×C43—81no—
348C22×C43C22×C22⋊C411yescharacteristic
349C22×C43C4×#4111yescharacteristic
350C22×C43#52011yescharacteristic
351C22×C43#54812yes—
352C22×C43#55012yes—
353C2×D43—41no—
354C2×D43—41no—
355C2×D43—41no—
356C2×D43—41no—
357C2×D43—41no—
358C2×D43—41no—
359C2×D43—81no—
360C2×D43—81no—
361C2×D43—81no—
362C2×D43—81no—
363C4×C43—22no—
364C4×C43—21no—
365C4×C43—21no—
366C4×C43—44no—
367C4×C43—41no—
368C4×C43—41no—
369C4×C43—41no—
370C4×C43—82no—
371Dic43—21no—
372Dic43—22no—
373Dic43—21no—
374Dic43—21no—
375Dic43—22no—
376Dic43—41no—
377Dic43—41no—
378Dic43—82no—
379Dic43—82no—
380Dic43#41012yes—
381C2×#553—431no—
382#2345—432no—
383#1964—432no—
384#1964—432no—
385#1964—432no—
386#1799—431no—
387#1799—431no—
388#1799—431no—
389C4×#99—431no—
390C4×#99—431no—
391C4×#99D4311yescharacteristic, complemented
392C2×C43—22no—
393C2×C43—22no—
394C2×C43—21no—
395C2×C43—21no—
396C2×C43—81no—
397C2×C43#234111yescharacteristic
398C2×C43C2×#41011yescharacteristic
399C2×C43#288311yescharacteristic
400D43—81no—
401D43—81no—
402#553—862no—
403#553—862no—
404#553—862no—
405#553—862no—
406C2×#126—431no—
407C2×#126—431no—
408C2×#125—431no—
409C2×#123—431no—
410C2×#123—431no—
411C2×#121—431no—
412C2×#121—431no—
413C2×#121—431no—
414C2×#121—431no—
415C2×C4×D4—431no—
416C2×C4×D4—431no—
417C2×C4×D4—431no—
418C2×C4×D4C2×D4311yescharacteristic
419C2×#117—431no—
420C22×C4⋊C4—431no—
421C2×#99—432no—
422C2×#99—432no—
423C2×#99—432no—
424C2×#99—432no—
425C2×#99—432no—
426C2×#99C2×D4312yes—
427#389—862no—
428#387—862no—
429#387—862no—
430#380—432no—
431#380—432no—
432#380—432no—
433C4×C4⋊C4—862no—
434C4×C22⋊C4—432no—
435C4×C22⋊C4—432no—
436C4×C22⋊C4C2×D4312yes—
437#342—431no—
438#342—431no—
439#342C2×D4311yescharacteristic
440#342C2×D4311yescharacteristic
441C43#2253511yescharacteristic, complemented, Sylow
442C22×D4—431no—
443C22×D4—431no—
444C22×D4—431no—
445C22×D4—431no—
446C22×D4—431no—
447C22×D4C22×D4311yescharacteristic
448C23×C4—431no—
449C23×C4—431no—
450C23×C4—431no—
451C23×C4—431no—
452C23×C4C4×D4311yescharacteristic
453C23×C4C22×D4311yescharacteristic
454#126—862no—
455#126—862no—
456#126—862no—
457#126—862no—
458#125—862no—
459#125—862no—
460#123—862no—
461#123—862no—
462#123—862no—
463#123—862no—
464#121—862no—
465#121—862no—
466#121—862no—
467#121—862no—
468#121—862no—
469#121—862no—
470#121—862no—
471#121—862no—
472C4×D4—22no—
473C4×D4—22no—
474C4×D4—862no—
475C4×D4—862no—
476C4×D4—862no—
477C4×D4—862no—
478C4×D4—861no—
479C4×D4—861no—
480C4×D4—861no—
481C4×D4—861no—
482#117—861no—
483#117—861no—
484#117—861no—
485#117—861no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—431no—
488C2×C4⋊C4—431no—
489C2×C4⋊C4—431no—
490C2×C4⋊C4—432no—
491C2×C4⋊C4—432no—
492C2×C4⋊C4—432no—
493C2×C4⋊C4—432no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—862no—
500C2×C4⋊C4—862no—
501C2×C4⋊C4—862no—
502C2×C4⋊C4C4×D4311yescharacteristic
503C2×C22⋊C4—431no—
504C2×C22⋊C4—431no—
505C2×C22⋊C4—431no—
506C2×C22⋊C4—431no—
507C2×C22⋊C4—431no—
508C2×C22⋊C4—431no—
509C2×C22⋊C4—431no—
510C2×C22⋊C4—431no—
511C2×C22⋊C4—432no—
512C2×C22⋊C4—432no—
513C2×C22⋊C4C4×D4311yescharacteristic
514C2×C22⋊C4C22×D4312yes—
515C2×C22⋊C4C22×D4311yescharacteristic
516C2×C22⋊C4C22×D4312yes—
517C2×C42—22no—
518C2×C42—431no—
519C2×C42—431no—
520C2×C42—862no—
521C2×C42—862no—
522C2×C42C4×D4311yescharacteristic
523#99—24no—
524#99—864no—
525#99—864no—
526#99—1722no—
527#99—1722no—
528#99—1722no—
529#95—22no—
530#95—862no—
531#95—862no—
532#95—862no—
533#95—862no—
534#95—862no—
535C24—431no—
536C24—431no—
537C24C2×C4×D4311yescharacteristic
538C24C23×D4311yescharacteristic
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—862no—
544C2×D4—861no—
545C2×D4—861no—
546C2×D4—862no—
547C2×D4—862no—
548C2×D4—862no—
549C2×D4—862no—
550C2×D4—861no—
551C2×D4—861no—
552C2×D4—861no—
553C2×D4—861no—
554C2×D4—862no—
555C2×D4—3441no—
556C2×D4—3441no—
557C2×D4—1722no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—81no—
563C22×C4—81no—
564C22×C4—431no—
565C22×C4—432no—
566C22×C4—431no—
567C22×C4—431no—
568C22×C4—431no—
569C22×C4—432no—
570C22×C4—432no—
571C22×C4—432no—
572C22×C4—431no—
573C22×C4—431no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—862no—
579C22×C4—862no—
580C22×C4—3441no—
581C22×C4—3441no—
582C22×C4—1722no—
583C22×C4—1722no—
584C22×C4C2×C4×D4311yescharacteristic
585C22×C4C2×C4×D4311yescharacteristic
586C22×C4C2×C4×D4311yescharacteristic
587C22×C4C2×C4×D4311yescharacteristic
588C22×C4C2×C4×D4311yescharacteristic
589C22×C4D4×D4312yes—
590C22×C4D4×D4312yes—
591C4⋊C4—22no—
592C4⋊C4—431no—
593C4⋊C4—431no—
594C4⋊C4—431no—
595C4⋊C4—431no—
596C4⋊C4—432no—
597C4⋊C4—432no—
598C4⋊C4—432no—
599C4⋊C4—432no—
600C4⋊C4—432no—
601C4⋊C4—432no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4—862no—
605C4⋊C4—862no—
606C4⋊C4—862no—
607C4⋊C4—862no—
608C4⋊C4—3442no—
609C4⋊C4—3442no—
610C4⋊C4—1724no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—861no—
617C22⋊C4—861no—
618C22⋊C4—862no—
619C22⋊C4—862no—
620C22⋊C4—862no—
621C22⋊C4—861no—
622C22⋊C4—861no—
623C22⋊C4—862no—
624C22⋊C4—861no—
625C22⋊C4—861no—
626C22⋊C4—861no—
627C22⋊C4—861no—
628C22⋊C4—862no—
629C22⋊C4—862no—
630C22⋊C4—862no—
631C22⋊C4—862no—
632C22⋊C4#1062189814yes—
633C42—21no—
634C42—21no—
635C42—82no—
636C42—861no—
637C42—861no—
638C42—861no—
639C42—861no—
640C42—3442no—
641C42—1724no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—861no—
650C23—861no—
651C23—861no—
652C23—861no—
653C23—861no—
654C23—861no—
655C23—1721no—
656C23—1721no—
657C23—1721no—
658C23—1721no—
659C23C22×C4×D4311yescharacteristic
660C23C2×D4×D4312yes—
661C23C2×#1062189812yes—
662C23#1306337111yescharacteristic
663C23#1306337211yescharacteristic
664D4—42no—
665D4—42no—
666D4—3442no—
667D4—3442no—
668D4—1722no—
669D4—1722no—
670D4—1722no—
671D4—1722no—
672D4—1722no—
673D4—1722no—
674C2×C4—24no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4—431no—
694C2×C4—431no—
695C2×C4—431no—
696C2×C4—431no—
697C2×C4—432no—
698C2×C4—432no—
699C2×C4—864no—
700C2×C4—862no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—861no—
704C2×C4—861no—
705C2×C4—861no—
706C2×C4—861no—
707C2×C4—3441no—
708C2×C4—3441no—
709C2×C4—1722no—
710C2×C4—1722no—
711C2×C4—1722no—
712C2×C4—1722no—
713C2×C4—1721no—
714C2×C4—1721no—
715C2×C4—1722no—
716C2×C4—1721no—
717C2×C4—1722no—
718C2×C4—1722no—
719C2×C4—1722no—
720C2×C4—1722no—
721C2×C4—1722no—
722C2×C4—1722no—
723C2×C4C22⋊C4×D4311yescharacteristic
724C2×C4C22⋊C4×D4311yescharacteristic
725C2×C4C22⋊C4×D4312yes—
726C22—22no—
727C22—21no—
728C22—22no—
729C22—21no—
730C22—42no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—81no—
737C22—81no—
738C22—3441no—
739C22—3441no—
740C22—3441no—
741C22—3441no—
742C22—1721no—
743C22—1721no—
744C22—1721no—
745C22—1721no—
746C22—1721no—
747C22—1721no—
748C22C2×C22⋊C4×D4311yescharacteristic
749C22C4×#1062189811yescharacteristic
750C22#1458337911yescharacteristic
751C22#1458355812yes—
752C22#1458357012yes—
753C4—21no—
754C4—21no—
755C4—22no—
756C4—44no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—82no—
761C4—432no—
762C4—861no—
763C4—862no—
764C4—861no—
765C4—861no—
766C4—862no—
767C4—3442no—
768C4—3442no—
769C4—1721no—
770C4—1721no—
771C2—22no—
772C2—22no—
773C2—21no—
774C2—21no—
775C2—81no—
776C2—3441no—
777C2—3441no—
778C2#1913743511yescharacteristic
779C2#410×D4311yescharacteristic
780C2#1914305311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC4×#99×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583598C2
cosocleC24×C43C24
hypercenterC4×#99D43
hypocenterC43#22535
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #19137473C2semidirect
3. #19135431C2semidirect
4. #19135429C2semidirect
5. #19135429C2semidirect
6. #19134583C2semidirect
7. #19134582C2semidirect
8. #19134582C2semidirect
9. #19134382C2semidirect
10. #19134382C2semidirect
11. C4×#99×C43C2semidirect
16. C2×#13063319C4semidirect
17. C2×#13063318C4semidirect
18. C2×#13063315C4semidirect
19. C2×#13063310C4semidirect
20. C2×#13063308C4semidirect
22. C2×#13063298C4semidirect
25. C2×C4×C22⋊D43C4semidirect
28. C2×#13063282C4semidirect
391. C4×#99D43semidirect
441. C43#22535semidirect

Maximal subgroups

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

subgroupindex
C2×#145835982
#191374732
#191354312
#191354292
#191345832
#191345822
#191343822
C4×#99×C432
#2253543