Finite Group Databasebeta

← #25112745

Subgroups — #25112745

Order 11008.

1132 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583582C211yesmaximal, characteristic
2#19137465C212yesmaximal, complemented
3#19135578C212yesmaximal, complemented
4#19135053C212yesmaximal
5#19135052C212yesmaximal
6#19134672C211yesmaximal, characteristic, complemented
7#19134671C211yesmaximal, characteristic, complemented
8#19134582C211yesmaximal, characteristic
9#19134382C211yesmaximal, characteristic
10#19134326C211yesmaximal, characteristic, complemented
11C43×#1740C211yesmaximal, characteristic, complemented
12#14583582—22no—
13#14583582—22no—
14#14583582—22no—
15#14583582—22no—
16C2×#13063320C411yescharacteristic, complemented
17C2×#13063319C411yescharacteristic, complemented
18C2×#13063317C411yescharacteristic, complemented
19C2×#13063315C411yescharacteristic, complemented
20C2×#13063315C411yescharacteristic, complemented
21C2×#13063309C2211yescharacteristic
22C2×#13063308C2211yescharacteristic
23C2×#13063303C411yescharacteristic, complemented
24C2×#13063302C2211yescharacteristic
25C2×C4×Dic86C411yescharacteristic, complemented
26C2×(C22⋊D43)⋊C4C2211yescharacteristic
27C2×#13063282C411yescharacteristic, complemented
28C2×#13063281C2212yes—
29C2×#13063281C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C2×#13063239C2212yes—
32C2×#13063239C2212yes—
33#14582794—22no—
34#14582783—22no—
35#14582780—22no—
36#14582762C2212yes—
37#14582760C2212yes—
38#14582757C2212yes—
39C4×Dic43⋊C4—22no—
40C22⋊C4×Dic43C2212yes—
41#14582666C2212yes—
42#14582666C2211yescharacteristic
43#14582666C2211yescharacteristic
44#14582665C2212yes—
45#14582665C2212yes—
46C2×#117×C43C2212yes—
47C2×#117×C43C2211yescharacteristic
48C43×#342C2212yes—
49C43×#342C2211yescharacteristic
50C43×#342C2211yescharacteristic
51C22×Dic86C2×C411yescharacteristic
52C22×C22⋊D43C2311yescharacteristic
53C23×Dic43C2311yescharacteristic
54C23×Dic43C2311yescharacteristic
55C22×C4×D43C2×C411yescharacteristic
56#13063320—22no—
57#13063320—22no—
58#13063319—22no—
59#13063319—22no—
60#13063317—22no—
61#13063317—22no—
62#13063315—22no—
63#13063315—22no—
64#13063315—22no—
65#13063315—22no—
66#13063309—22no—
67#13063309—22no—
68#13063308—22no—
69#13063308—22no—
70#13063303—22no—
71#13063303—22no—
72#13063302—22no—
73#13063302—22no—
74C4×Dic86—21no—
75C4×Dic86—21no—
76C4×Dic86—21no—
77C4×Dic86—21no—
78(C22⋊D43)⋊C4—22no—
79(C22⋊D43)⋊C4—22no—
80#13063282—21no—
81#13063282—21no—
82#13063282—21no—
83#13063282—21no—
84#13063281—22no—
85#13063281—22no—
86#13063281—24no—
87#13063281—42no—
88C2×C4⋊Dic43C2×C411yescharacteristic
89C2×C4⋊Dic43C2×C411yescharacteristic
90C2×C4⋊Dic43C2×C411yescharacteristic
91C2×Dic43⋊C4—22no—
92C2×Dic43⋊C4—22no—
93C2×Dic43⋊C4C2×C411yescharacteristic
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⋊C4C2×C411yescharacteristic
103C2×Dic43⋊C4C2×C411yescharacteristic
104C2×Dic43⋊C4D412yes—
105C2×Dic43⋊C4D412yes—
106C2×Dic43⋊C4D412yes—
107C2×Dic43⋊C4D412yes—
108C2×C22⋊Dic43C2312yes—
109C2×C22⋊Dic43C2312yes—
110C2×C22⋊Dic43C2311yescharacteristic
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
120C2×C4×Dic43C2×C411yescharacteristic
121#13063239—24no—
122#13063239—42no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C23×C4×C43C2311yescharacteristic
130#117×C43—22no—
131#117×C43—22no—
132#117×C43—24no—
133#117×C43—42no—
134C2×C4⋊C4×C43—22no—
135C2×C4⋊C4×C43C2×C411yescharacteristic
136C2×C4⋊C4×C43C2×C411yescharacteristic
137C2×C22⋊C4×C43C2312yes—
138C2×C22⋊C4×C43C2311yescharacteristic
139C2×C22⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43C2312yes—
141C2×C42×C43—22no—
142C2×C42×C43C2×C411yescharacteristic
143C2×C42×C43C2×C411yescharacteristic
144C24×C43C2411yescharacteristic
145C23×D43C22×C411yescharacteristic
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C22×C411yescharacteristic
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C22×C411yescharacteristic
154C22×C4×C43C22×C411yescharacteristic
155C22×C4×C43C22×C411yescharacteristic
156C22×C4×C43C22×C411yescharacteristic
157C22×C4×C43C2×D412yes—
158C22×C4×C43C2×D412yes—
159C2×C22⋊D43—22no—
160C2×C22⋊D43—22no—
161C2×C22⋊D43—21no—
162C2×C22⋊D43—21no—
163C22×Dic43—22no—
164C22×Dic43—22no—
165C22×Dic43—22no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—42no—
169C22×Dic43C22×C411yescharacteristic
170C22×Dic43C22×C411yescharacteristic
171C22×Dic43C22×C411yescharacteristic
172C22×Dic43C22×C411yescharacteristic
173C22×Dic43C22×C411yescharacteristic
174C22×Dic43C22×C411yescharacteristic
175C22×Dic43C22×C411yescharacteristic
176C22×Dic43C2×D412yes—
177C22×Dic43C2×D412yes—
178C22×Dic43C2×D412yes—
179C22×Dic43C2×D412yes—
180C2×C4×D43—21no—
181C2×C4×D43—21no—
182C2×C4×D43—42no—
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—42no—
186C4⋊C4×C43—22no—
187C4⋊C4×C43—22no—
188C4⋊C4×C43—44no—
189C22⋊C4×C43—22no—
190C22⋊C4×C43—22no—
191C22⋊C4×C43—22no—
192C22⋊C4×C43—22no—
193C22⋊C4×C43—22no—
194C22⋊C4×C43#4114yes—
195C42×C43—21no—
196C42×C43—21no—
197C42×C43—21no—
198C42×C43—21no—
199C42×C43—44no—
200C22⋊Dic43—22no—
201C22⋊Dic43—22no—
202C22⋊Dic43—22no—
203C22⋊Dic43—22no—
204C22⋊Dic43—22no—
205(C2×D43)⋊C4—21no—
206(C2×D43)⋊C4—21no—
207(C2×D43)⋊C4—22no—
208(C2×D43)⋊C4—21no—
209(C2×D43)⋊C4—21no—
210(C2×D43)⋊C4—22no—
211(C2×D43)⋊C4—22no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—22no—
215C4⋊Dic43—22no—
216Dic43⋊C4—21no—
217Dic43⋊C4—21no—
218Dic43⋊C4—22no—
219Dic43⋊C4—22no—
220Dic43⋊C4—22no—
221Dic43⋊C4—21no—
222Dic43⋊C4—21no—
223Dic43⋊C4—22no—
224Dic43⋊C4—22no—
225Dic43⋊C4—44no—
226Dic43⋊C4—44no—
227Dic43⋊C4C22⋊C411yescharacteristic
228Dic43⋊C4C22⋊C411yescharacteristic
229Dic43⋊C4C22⋊C411yescharacteristic
230Dic43⋊C4C22⋊C411yescharacteristic
231Dic43⋊C4C22⋊C412yes—
232Dic43⋊C4C22⋊C412yes—
233Dic43⋊C4C22⋊C412yes—
234Dic43⋊C4C22⋊C412yes—
235Dic43⋊C4C22⋊C412yes—
236Dic43⋊C4C22⋊C412yes—
237C4×Dic43—21no—
238C4×Dic43—21no—
239C4×Dic43—21no—
240C4×Dic43—21no—
241C4×Dic43—21no—
242C4×Dic43—21no—
243C4×Dic43—44no—
244C4×Dic43—44no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43C23×C411yescharacteristic
248C23×C43C22×D412yes—
249C23×C43C2×#4112yes—
250C23×C43H(5,𝔽2)11yescharacteristic
251C23×C432−1+411yescharacteristic
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—41no—
256C22×D43—41no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—24no—
270C2×C4×C43—42no—
271C2×C4×C43—42no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—42no—
277C2×C4×C43—42no—
278C2×C4×C43—42no—
279C2×C4×C43C2×C22⋊C411yescharacteristic
280C2×C4×C43C2×C22⋊C411yescharacteristic
281C2×C4×C43C2×C22⋊C412yes—
282C22⋊D43—42no—
283C22⋊D43—42no—
284C2×Dic43—21no—
285C2×Dic43—21no—
286C2×Dic43—21no—
287C2×Dic43—21no—
288C2×Dic43—22no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—22no—
292C2×Dic43—24no—
293C2×Dic43—22no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—41no—
300C2×Dic43—42no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—42no—
304C2×Dic43—42no—
305C2×Dic43—42no—
306C2×Dic43—42no—
307C2×Dic43—42no—
308C2×Dic43—42no—
309C2×Dic43C2×C22⋊C411yescharacteristic
310C2×Dic43C2×C22⋊C411yescharacteristic
311C2×Dic43C2×C22⋊C411yescharacteristic
312C2×Dic43C2×C22⋊C412yes—
313C2×Dic43C2×C22⋊C412yes—
314C2×Dic43C2×C22⋊C411yescharacteristic
315C4×D43—42no—
316C4×D43—42no—
317Dic86—42no—
318Dic86—42no—
319#22478—431nomaximal, Sylow
320C22×C43—21no—
321C22×C43—22no—
322C22×C43—21no—
323C22×C43—22no—
324C22×C43—42no—
325C22×C43—41no—
326C22×C43—41no—
327C22×C43C22×C22⋊C411yescharacteristic
328C22×C43C4×#4111yescharacteristic
329C22×C43#52011yescharacteristic
330C22×C43#54612yes—
331C22×C43#54712yes—
332C2×D43—41no—
333C2×D43—41no—
334C2×D43—41no—
335C2×D43—81no—
336C2×D43—81no—
337C4×C43—21no—
338C4×C43—22no—
339C4×C43—21no—
340C4×C43—44no—
341C4×C43—41no—
342C4×C43—41no—
343C4×C43—41no—
344C4×C43—41no—
345C4×C43—82no—
346Dic43—21no—
347Dic43—22no—
348Dic43—21no—
349Dic43—21no—
350Dic43—22no—
351Dic43—41no—
352Dic43—41no—
353Dic43—41no—
354Dic43—82no—
355Dic43—82no—
356Dic43#41012yes—
357C2×#552—431no—
358#2344—432no—
359#1996—432no—
360#1899—432no—
361#1899—432no—
362#1820—431no—
363#1820—431no—
364#1799—431no—
365C4×#99—431no—
366#1740—431no—
367#1740D4311yescharacteristic, complemented
368C2×C43—22no—
369C2×C43—22no—
370C2×C43—21no—
371C2×C43—21no—
372C2×C43#233911yescharacteristic
373C2×C43C2×#41011yescharacteristic
374C2×C43#288411yescharacteristic
375D43—81no—
376#552—862no—
377#552—862no—
378#552—862no—
379#552—862no—
380C2×#126—431no—
381C2×#126—431no—
382C2×#125—431no—
383C2×#125—431no—
384C2×#125—431no—
385C2×#123—431no—
386C2×#123—431no—
387C2×C22⋊Q8—431no—
388C2×C22⋊Q8—431no—
389C2×C4×Q8—431no—
390C2×C4×D4—431no—
391C2×#117—431no—
392C2×#117—431no—
393C2×#117—432no—
394C2×#117C2×D4312yes—
395C2×#117C2×D4311yescharacteristic
396C22×C4⋊C4—431no—
397C2×#99—432no—
398C2×#99—432no—
399#389—862no—
400#387—862no—
401#387—862no—
402#381—432no—
403#381—432no—
404#380—432no—
405C4×C4⋊C4—862no—
406C4×C22⋊C4—432no—
407#342—431no—
408#342—431no—
409#342—432no—
410#342—432no—
411#342—432no—
412#342C2×D4311yescharacteristic
413#342C2×D4312yes—
414#342C2×D4311yescharacteristic
415C43#2247811yescharacteristic, complemented, Sylow
416C22×Q8—431no—
417C22×D4—431no—
418C23×C4—431no—
419C23×C4—431no—
420C23×C4—431no—
421C23×C4C22×D4311yescharacteristic
422#126—862no—
423#126—862no—
424#126—862no—
425#126—862no—
426#125—862no—
427#125—862no—
428#125—862no—
429#125—862no—
430#125—862no—
431#125—862no—
432#123—862no—
433#123—862no—
434#123—862no—
435#123—862no—
436C22⋊Q8—862no—
437C22⋊Q8—862no—
438C22⋊Q8—862no—
439C22⋊Q8—862no—
440C4×Q8—861no—
441C4×Q8—861no—
442C4×Q8—861no—
443C4×Q8—861no—
444C4×D4—862no—
445C4×D4—862no—
446#117—22no—
447#117—22no—
448#117—24no—
449#117—42no—
450#117—861no—
451#117—861no—
452#117—861no—
453#117—861no—
454#117—862no—
455#117—862no—
456#117—864no—
457#117—1722no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—431no—
460C2×C4⋊C4—431no—
461C2×C4⋊C4—431no—
462C2×C4⋊C4—431no—
463C2×C4⋊C4—432no—
464C2×C4⋊C4—432no—
465C2×C4⋊C4—432no—
466C2×C4⋊C4—432no—
467C2×C4⋊C4—431no—
468C2×C4⋊C4—431no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—862no—
478C2×C4⋊C4—862no—
479C2×C4⋊C4C4×D4311yescharacteristic
480C2×C4⋊C4C4×D4311yescharacteristic
481C2×C22⋊C4—431no—
482C2×C22⋊C4—431no—
483C2×C22⋊C4—431no—
484C2×C22⋊C4—431no—
485C2×C22⋊C4—431no—
486C2×C22⋊C4—431no—
487C2×C22⋊C4—432no—
488C2×C22⋊C4—432no—
489C2×C22⋊C4C22×D4312yes—
490C2×C22⋊C4C22×D4311yescharacteristic
491C2×C22⋊C4C22×D4311yescharacteristic
492C2×C22⋊C4C22×D4312yes—
493C2×C42—22no—
494C2×C42—431no—
495C2×C42—431no—
496C2×C42—431no—
497C2×C42—862no—
498C2×C42—862no—
499C2×C42C4×D4311yescharacteristic
500C2×C42C4×D4311yescharacteristic
501#99—864no—
502#99—1722no—
503#95—862no—
504#95—862no—
505#95—862no—
506#95—862no—
507#95—862no—
508#95—862no—
509C24—431no—
510C24C23×D4311yescharacteristic
511C2×Q8—861no—
512C2×Q8—861no—
513C2×Q8—1722no—
514C2×D4—862no—
515C2×D4—862no—
516C2×D4—861no—
517C2×D4—861no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—431no—
524C22×C4—431no—
525C22×C4—431no—
526C22×C4—432no—
527C22×C4—432no—
528C22×C4—432no—
529C22×C4—431no—
530C22×C4—432no—
531C22×C4—431no—
532C22×C4—431no—
533C22×C4—431no—
534C22×C4—861no—
535C22×C4—861no—
536C22×C4—862no—
537C22×C4—861no—
538C22×C4—861no—
539C22×C4—862no—
540C22×C4—862no—
541C22×C4—1722no—
542C22×C4—1722no—
543C22×C4C2×C4×D4311yescharacteristic
544C22×C4C2×C4×D4311yescharacteristic
545C22×C4C2×C4×D4311yescharacteristic
546C22×C4C2×C4×D4311yescharacteristic
547C22×C4C2×C4×D4311yescharacteristic
548C22×C4C2×C4×D4311yescharacteristic
549C22×C4D4×D4312yes—
550C22×C4D4×D4312yes—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—44no—
554C4⋊C4—431no—
555C4⋊C4—431no—
556C4⋊C4—431no—
557C4⋊C4—431no—
558C4⋊C4—432no—
559C4⋊C4—432no—
560C4⋊C4—432no—
561C4⋊C4—432no—
562C4⋊C4—432no—
563C4⋊C4—432no—
564C4⋊C4—862no—
565C4⋊C4—861no—
566C4⋊C4—861no—
567C4⋊C4—862no—
568C4⋊C4—862no—
569C4⋊C4—861no—
570C4⋊C4—861no—
571C4⋊C4—862no—
572C4⋊C4—862no—
573C4⋊C4—862no—
574C4⋊C4—861no—
575C4⋊C4—861no—
576C4⋊C4—862no—
577C4⋊C4—1724no—
578C4⋊C4—1724no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—861no—
585C22⋊C4—861no—
586C22⋊C4—862no—
587C22⋊C4—862no—
588C22⋊C4—862no—
589C22⋊C4—861no—
590C22⋊C4—861no—
591C22⋊C4—862no—
592C22⋊C4—862no—
593C22⋊C4—862no—
594C22⋊C4—862no—
595C22⋊C4—862no—
596C22⋊C4#1062189814yes—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—44no—
602C42—861no—
603C42—861no—
604C42—861no—
605C42—861no—
606C42—861no—
607C42—861no—
608C42—1724no—
609C42—1724no—
610C23—41no—
611C23—41no—
612C23—861no—
613C23—861no—
614C23—861no—
615C23—1721no—
616C23—1721no—
617C23C22×C4×D4311yescharacteristic
618C23C2×D4×D4312yes—
619C23C2×#1062189812yes—
620C23#1306337011yescharacteristic
621C23#1306337311yescharacteristic
622Q8—1722no—
623Q8—1722no—
624D4—1722no—
625D4—1722no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—24no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—431no—
649C2×C4—431no—
650C2×C4—431no—
651C2×C4—431no—
652C2×C4—432no—
653C2×C4—432no—
654C2×C4—864no—
655C2×C4—862no—
656C2×C4—861no—
657C2×C4—861no—
658C2×C4—861no—
659C2×C4—861no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—861no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—1722no—
670C2×C4—1722no—
671C2×C4—1722no—
672C2×C4—1721no—
673C2×C4—1722no—
674C2×C4—1722no—
675C2×C4—1722no—
676C2×C4—1722no—
677C2×C4—1722no—
678C2×C4—1722no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4C22⋊C4×D4311yescharacteristic
682C2×C4C22⋊C4×D4311yescharacteristic
683C2×C4C22⋊C4×D4312yes—
684C22—22no—
685C22—21no—
686C22—22no—
687C22—21no—
688C22—42no—
689C22—41no—
690C22—41no—
691C22—3441no—
692C22—3441no—
693C22—1721no—
694C22—1721no—
695C22—1721no—
696C22C2×C22⋊C4×D4311yescharacteristic
697C22C4×#1062189811yescharacteristic
698C22#1458338011yescharacteristic
699C22#1458353912yes—
700C22#1458355012yes—
701C4—21no—
702C4—22no—
703C4—21no—
704C4—44no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—82no—
710C4—432no—
711C4—861no—
712C4—862no—
713C4—861no—
714C4—861no—
715C4—862no—
716C4—3442no—
717C4—3442no—
718C4—1721no—
719C4—1721no—
720C4—1721no—
721C2—22no—
722C2—22no—
723C2—21no—
724C2—21no—
725C2—3441no—
726C2#1913742211yescharacteristic
727C2#410×D4311yescharacteristic
728C2#1914305711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1740C2
socleC22×C43C22×C22⋊C4
prime radicalC22×C22⋊D43C23
cosocleC24×C43C24
hypercenter#1740D43
hypocenterC43#22478
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1740

Complements

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

NH ≅ G/Ntype
2. #19137465C2semidirect
3. #19135578C2semidirect
6. #19134672C2semidirect
7. #19134671C2semidirect
10. #19134326C2semidirect
11. C43×#1740C2semidirect
16. C2×#13063320C4semidirect
17. C2×#13063319C4semidirect
18. C2×#13063317C4semidirect
19. C2×#13063315C4semidirect
20. C2×#13063315C4semidirect
23. C2×#13063303C4semidirect
25. C2×C4×Dic86C4semidirect
27. C2×#13063282C4semidirect
367. #1740D43semidirect
415. C43#22478semidirect

Maximal subgroups

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

subgroupindex
C2×#145835822
#191374652
#191355782
#191350532
#191350522
#191346722
#191346712
#191345822
#191343822
#191343262
C43×#17402
#2247843