Finite Group Databasebeta

← C4×#14583133 #25103089

Subgroups — C4×#14583133 #25103089

Order 11008.

1222 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583133C211yesmaximal, characteristic
2C2×C4×#10621882C211yesmaximal, characteristic, complemented
3C22×C4×C43⋊C8C211yesmaximal, characteristic, complemented
4C4×#13063299C211yesmaximal, characteristic, complemented
5#19135460C211yesmaximal, characteristic, complemented
6#19135325C211yesmaximal, characteristic, complemented
7#19135281C211yesmaximal, characteristic, complemented
8#19135277C211yesmaximal, characteristic, complemented
9#19135024C211yesmaximal, characteristic, complemented
10#19135021C211yesmaximal, characteristic, complemented
11#19134622C211yesmaximal, characteristic, complemented
12C4×#13063258C211yesmaximal, characteristic, complemented
13C4×#13063245C211yesmaximal, characteristic, complemented
14C4×#13063246C211yesmaximal, characteristic, complemented
15C4×#121×C43C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C23×C43⋊C8C2211yescharacteristic
18C23×C43⋊C8C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×C4×C22⋊D43—21no—
22#14583133C418yesdirect product factor
23C4×#10621882—24no—
24C2×#13063258C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×#13063258C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×C4×C43⋊C8—24no—
34C2×C4×C43⋊C8C2211yescharacteristic
35C2×C4×C43⋊C8C2211yescharacteristic
36C2×C4×C43⋊C8C2211yescharacteristic
37C2×C4×C43⋊C8C2211yescharacteristic
38#14582801C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582790—21no—
41#14582778—21no—
42#14582759C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44C4×(C2×D43)⋊C4—21no—
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51C2×#121×C43C2211yescharacteristic
52C2×C4×D4×C43—21no—
53C2×C4×D4×C43C2211yescharacteristic
54C22×C42×C43C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#388—21no—
58C43×#386—21no—
59C43×#380C2211yescharacteristic
60C4×C4⋊C4×C43C2211yescharacteristic
61C4×C22⋊C4×C43—21no—
62C22×D172C2311yescharacteristic
63C22×C22⋊D43—21no—
64C22×C4×D43—21no—
65C2×#10621882—22no—
66C2×#10621882—22no—
67C2×#10621882C2×C414yescomplemented
68C22×C43⋊C8—22no—
69C22×C43⋊C8—22no—
70C22×C43⋊C8—22no—
71C22×C43⋊C8—22no—
72C22×C43⋊C8—22no—
73C22×C43⋊C8C2×C414yescomplemented
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78#13063299—22no—
79#13063299C2×C414yescomplemented
80C4×D172—22no—
81C4×D172—22no—
82C4×C22⋊D43—44no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4—21no—
87C2×C22⋊Dic43—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×C4×Dic43—21no—
93#13063258—22no—
94#13063258—22no—
95#13063258C2×C414yescomplemented
96#13063246—22no—
97#13063246—22no—
98#13063246C2×C414yescomplemented
99#13063245—22no—
100#13063245—22no—
101#13063245C2×C414yescomplemented
102C4×C43⋊C8—22no—
103C4×C43⋊C8—22no—
104C4×C43⋊C8—22no—
105C4×C43⋊C8D414yescomplemented
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C22×D4×C43—21no—
110C22×D4×C43C2311yescharacteristic
111C23×C4×C43—21no—
112C23×C4×C43D411yescharacteristic
113C23×C4×C43D411yescharacteristic
114C23×C4×C43C2311yescharacteristic
115#121×C43—22no—
116#121×C43C2×C414yescomplemented
117C4×D4×C43—22no—
118C4×D4×C43—22no—
119C4×D4×C43—44no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C42×C43—22no—
130C2×C42×C43—22no—
131C2×C42×C43—21no—
132C2×C42×C43D411yescharacteristic
133C2×C42×C43D411yescharacteristic
134C2×C42×C43C2311yescharacteristic
135C2×C42×C43C2311yescharacteristic
136#95×C43—21no—
137#95×C43—21no—
138#95×C43—21no—
139C24×C43—21no—
140C24×C43C2×D411yescharacteristic
141C23×D43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—24no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—42no—
149C2×D4×C43—42no—
150C2×D4×C43C22×C412yes—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—22no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—42no—
164C22×C4×C43—42no—
165C22×C4×C43—42no—
166C22×C4×C43D814yescomplemented
167C22×C4×C43C22×C412yes—
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43#4112yes—
174C22×C4×C43C2411yescharacteristic
175C2×C22⋊D43—24no—
176C2×C22⋊D43—42no—
177C2×C22⋊D43—42no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172C22×C412yes—
187C2×C4×D43—42no—
188C2×C4×D43—42no—
189C2×C4×D43—42no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—42no—
196C4⋊C4×C43C22×C412yes—
197C22⋊C4×C43—24no—
198C22⋊C4×C43—42no—
199C22⋊C4×C43—42no—
200C22⋊C4×C43—42no—
201C22⋊C4×C43—42no—
202C42×C43—22no—
203C42×C43—22no—
204C42×C43—21no—
205C42×C43—21no—
206C42×C43—42no—
207C42×C43C2×D412yes—
208C42×C43#4112yes—
209C22⋊Dic43—42no—
210#10621882—28no—
211(C2×D43)⋊C4—24no—
212(C2×D43)⋊C4—42no—
213(C2×D43)⋊C4—42no—
214(C2×D43)⋊C4—42no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43C22×C412yes—
221Dic43⋊C4—42no—
222C4×Dic43—42no—
223C2×C43⋊C8—28no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—28no—
231C2×C43⋊C8C22×C412yes—
232C2×C43⋊C8C22×C412yes—
233C2×C43⋊C8C2×D412yes—
234C2×C43⋊C8C2×D412yes—
235C2×C43⋊C8#4112yes—
236C2×C43⋊C8#4112yes—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—22no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43C4×D412yes—
249C23×C43C2×D812yes—
250C23×C43#13512yes—
251C23×C43C22×D411yescharacteristic
252C22×D43—22no—
253C22×D43—41no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259D4×C43—22no—
260D4×C43—22no—
261D4×C43—48no—
262D4×C43—41no—
263D4×C43—41no—
264C2×C4×C43—28no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—28no—
278C2×C4×C43—22no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—84no—
288C2×C4×C43C4×D412yes—
289C2×C4×C43#12112yes—
290C2×C4×C43#12112yes—
291C2×C4×C43C2×D812yes—
292C2×C4×C43C2×D812yes—
293C2×C4×C43#13512yes—
294C2×C4×C43#13512yes—
295C2×C4×C43C23×C411yescharacteristic
296C2×C4×C43C22×D411yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C2×C4×C43C2×#4111yescharacteristic
299C2×C4×C43C2×#4111yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C22⋊D43—48no—
302C2×Dic43—22no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311D172—22no—
312D172—22no—
313D172—41no—
314D172—41no—
315C4×D43—84no—
316C43⋊C8—22no—
317C43⋊C8—22no—
318C43⋊C8—22no—
319C43⋊C8C4×D414yescomplemented
320C4×#466—431nomaximal, Sylow
321C22×C43—22no—
322C22×C43—22no—
323C22×C43—22no—
324C22×C43—22no—
325C22×C43—22no—
326C22×C43—22no—
327C22×C43—42no—
328C22×C43—42no—
329C22×C43—42no—
330C22×C43—81no—
331C22×C43—81no—
332C22×C43—81no—
333C22×C43—81no—
334C22×C43C4×D814yescomplemented
335C22×C43C2×C4×D411yescharacteristic
336C22×C43C2×#12111yescharacteristic
337C22×C43#53211yescharacteristic
338C22×C43C22×D811yescharacteristic
339C22×C43C2×#13511yescharacteristic
340C22×C43C2×#13511yescharacteristic
341C22×C43C2×#13511yescharacteristic
342C2×D43—42no—
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—81no—
346C2×D43—81no—
347C2×D43—81no—
348C2×D43—81no—
349C4×C43—22no—
350C4×C43—22no—
351C4×C43—22no—
352C4×C43—22no—
353C4×C43—42no—
354C4×C43—81no—
355C4×C43—81no—
356C4×C43#46614yescomplemented
357C4×C43C2×C4×D411yescharacteristic
358C4×C43C4×#4111yescharacteristic
359C4×C43#52511yescharacteristic
360C4×C43#52911yescharacteristic
361Dic43—42no—
362Dic43—81no—
363Dic43—81no—
364C2×#466—431no—
365C2×C4×D8—431no—
366C22×C4×C8—431no—
367C4×#121—431no—
368C4×#121D4311yescharacteristic, complemented
369#1970—431no—
370#1942—431no—
371#1934—431no—
372#1934—431no—
373#1893—431no—
374#1893—431no—
375#1808—431no—
376C4×#107—431no—
377C4×#102—431no—
378C4×#102—431no—
379C2×C43—24no—
380C2×C43—82no—
381C2×C43C4×#12111yescharacteristic
382C2×C43C2×C4×D811yescharacteristic
383C2×C43C4×#13511yescharacteristic
384C2×C43C2×#46611yescharacteristic
385C2×C43#305011yescharacteristic
386C2×C43#316811yescharacteristic
387C2×C43#316911yescharacteristic
388D43—82no—
389C22×D8—431no—
390C23×C8—431no—
391C23×C8—431no—
392C2×#121—431no—
393C2×#121C2×D4311yescharacteristic
394C2×C4×D4—21no—
395C2×C4×D4—431no—
396C2×C4×D4—861no—
397C2×C4×D4C2×D4311yescharacteristic
398C22×C42C2×D4311yescharacteristic
399#466—438no—
400C4×D8—864no—
401C2×#107—431no—
402C2×#107—431no—
403C2×#107—431no—
404C2×#102—431no—
405C2×#102—431no—
406C2×#102—431no—
407C2×#102—431no—
408C2×#102—431no—
409C2×#102—431no—
410C2×C4×C8—431no—
411C2×C4×C8—431no—
412C2×C4×C8—431no—
413C2×C4×C8—431no—
414C2×C4×C8—864no—
415#390—431no—
416#390C2×D4311yescharacteristic
417#389—431no—
418#389C2×D4311yescharacteristic
419#388—21no—
420#388—861no—
421#386—21no—
422#386—861no—
423#380—431no—
424#380C2×D4311yescharacteristic
425C4×C4⋊C4—431no—
426C4×C4⋊C4C2×D4311yescharacteristic
427C4×C22⋊C4—21no—
428C4×C22⋊C4—861no—
429#340—431no—
430#340—431no—
431#340—431no—
432#340—431no—
433#340—431no—
434#340—431no—
435C43C4×#46611yescharacteristic, complemented, Sylow
436C22×D4—21no—
437C22×D4—431no—
438C22×D4—861no—
439C22×D4C22×D4311yescharacteristic
440C23×C4—21no—
441C23×C4—861no—
442C23×C4C22⋊D4311yescharacteristic
443C23×C4C22⋊D4311yescharacteristic
444C23×C4C22×D4311yescharacteristic
445C2×D8—434no—
446C2×D8—862no—
447C2×D8—862no—
448C22×C8—431no—
449C22×C8—434no—
450C22×C8—431no—
451C22×C8—431no—
452C22×C8—431no—
453C22×C8—862no—
454C22×C8—862no—
455C22×C8—862no—
456C22×C8—862no—
457C22×C8—862no—
458#121—22no—
459#121—434no—
460#121—862no—
461#121C4×D4314yescomplemented
462C4×D4—22no—
463C4×D4—22no—
464C4×D4—44no—
465C4×D4—862no—
466C4×D4—862no—
467C4×D4—1724no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4C22×D4311yescharacteristic
474C2×C4⋊C4C22×D4311yescharacteristic
475C2×C4⋊C4C22×D4311yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—861no—
482C2×C22⋊C4—861no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C42—22no—
487C2×C42—22no—
488C2×C42—21no—
489C2×C42—861no—
490C2×C42C22⋊D4311yescharacteristic
491C2×C42C22⋊D4311yescharacteristic
492C2×C42C22×D4311yescharacteristic
493C2×C42C22×D4311yescharacteristic
494#107—434no—
495#107—862no—
496#107—862no—
497#102—434no—
498#102—434no—
499#102—862no—
500#102—862no—
501#102—862no—
502#102—862no—
503C4×C8—434no—
504C4×C8—862no—
505C4×C8—862no—
506C4×C8—862no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—861no—
511#95—861no—
512#95—861no—
513C24—21no—
514C24—861no—
515C24C2×C22⋊D4311yescharacteristic
516C2×D4—24no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—432no—
525C2×D4—864no—
526C2×D4—861no—
527C2×D4—861no—
528C2×D4—861no—
529C2×D4—861no—
530C2×D4—861no—
531C2×D4—1722no—
532C2×D4—1722no—
533C2×D4C2×C4×D4312yes—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—1722no—
553C22×C4—1722no—
554C22×C4—1722no—
555C22×C4#1062188214yescomplemented
556C22×C4C2×C4×D4312yes—
557C22×C4#1062189812yes—
558C22×C4C2×C22⋊D4311yescharacteristic
559C22×C4C2×C22⋊D4311yescharacteristic
560C22×C4C2×C22⋊D4311yescharacteristic
561C22×C4C2×C22⋊D4311yescharacteristic
562C22×C4C2×C22⋊D4311yescharacteristic
563C22×C4C23×D4311yescharacteristic
564D8—868no—
565C2×C8—432no—
566C2×C8—432no—
567C2×C8—432no—
568C2×C8—432no—
569C2×C8—432no—
570C2×C8—432no—
571C2×C8—868no—
572C2×C8—868no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—42no—
585C4⋊C4—432no—
586C4⋊C4—861no—
587C4⋊C4—861no—
588C4⋊C4—861no—
589C4⋊C4—861no—
590C4⋊C4—861no—
591C4⋊C4—1722no—
592C4⋊C4C2×C4×D4312yes—
593C22⋊C4—24no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—864no—
599C22⋊C4—1722no—
600C22⋊C4—1722no—
601C22⋊C4—1722no—
602C22⋊C4—1722no—
603C42—22no—
604C42—22no—
605C42—21no—
606C42—21no—
607C42—42no—
608C42—1722no—
609C42D4×D4312yes—
610C42#1062190012yes—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—22no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—862no—
623C23—1721no—
624C23—1721no—
625C23—1721no—
626C23—1721no—
627C23—1721no—
628C23—1721no—
629C23C4×C22⋊D4312yes—
630C23C2×#1062188212yes—
631C23#1306334512yes—
632C23C22×C22⋊D4311yescharacteristic
633D4—22no—
634D4—22no—
635D4—48no—
636D4—41no—
637D4—41no—
638D4—862no—
639D4—862no—
640D4—1728no—
641D4—1721no—
642D4—1721no—
643C2×C4—28no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—28no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—84no—
667C2×C4—862no—
668C2×C4—3444no—
669C2×C4—1721no—
670C2×C4—1721no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4C4×C22⋊D4312yes—
678C2×C4#1306329712yes—
679C2×C4#1306329712yes—
680C2×C4C2×#1062188212yes—
681C2×C4C2×#1062188212yes—
682C2×C4#1306334512yes—
683C2×C4#1306334512yes—
684C2×C4C22×C4×D4311yescharacteristic
685C2×C4C2×D4×D4311yescharacteristic
686C2×C4#41×D4311yescharacteristic
687C2×C4#41×D4311yescharacteristic
688C2×C4C2×#1062190011yescharacteristic
689C2×C4C2×#1062189811yescharacteristic
690C8—434no—
691C8—862no—
692C8—862no—
693C8—862no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—3441no—
708C22—3441no—
709C22—3441no—
710C22—3441no—
711C22—1722no—
712C22—1722no—
713C22—1722no—
714C22C4×#1062188214yescomplemented
715C22C2×C4×C22⋊D4311yescharacteristic
716C22C2×#1306329711yescharacteristic
717C22#1458344511yescharacteristic
718C22C22×#1062188211yescharacteristic
719C22C2×#1306334511yescharacteristic
720C22C2×#1306334511yescharacteristic
721C22C2×#1306334511yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—81no—
728C4—81no—
729C4—3441no—
730C4—3441no—
731C4—1722no—
732C4#1458313314yesdirect product factor
733C4C4×D4×D4311yescharacteristic
734C4C4×#1062190011yescharacteristic
735C4#1458340811yescharacteristic
736C4#1458342911yescharacteristic
737C2—24no—
738C2—82no—
739C2—3442no—
740C2C4×#1306329711yescharacteristic
741C2C2×C4×#1062188211yescharacteristic
742C2C4×#1306334511yescharacteristic
743C2C2×#1458313311yescharacteristic
744C2#1914417311yescharacteristic
745C2#1914515911yescharacteristic
746C2#1914517011yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#121×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583133C2
cosocleC22×C4×C43C24
hypercenterC4×#121D43
hypocenterC43C4×#466
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621882C2semidirect
3. C22×C4×C43⋊C8C2semidirect
4. C4×#13063299C2semidirect
5. #19135460C2semidirect
6. #19135325C2semidirect
7. #19135281C2semidirect
8. #19135277C2semidirect
9. #19135024C2semidirect
10. #19135021C2semidirect
11. #19134622C2semidirect
12. C4×#13063258C2semidirect
13. C4×#13063245C2semidirect
14. C4×#13063246C2semidirect
15. C4×#121×C43C2semidirect
22. #14583133C4direct (N × H)
67. C2×#10621882C2×C4semidirect
73. C22×C43⋊C8C2×C4semidirect
79. #13063299C2×C4semidirect
95. #13063258C2×C4semidirect
98. #13063246C2×C4semidirect
101. #13063245C2×C4semidirect
105. C4×C43⋊C8D4semidirect
116. #121×C43C2×C4semidirect
166. C22×C4×C43D8semidirect
319. C43⋊C8C4×D4semidirect
334. C22×C43C4×D8semidirect
356. C4×C43#466semidirect
368. C4×#121D43semidirect
435. C43C4×#466semidirect
461. #121C4×D43semidirect
555. C22×C4#10621882semidirect
714. C22C4×#10621882semidirect
732. C4#14583133direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145831332
C2×C4×#106218822
C22×C4×C43⋊C82
C4×#130632992
#191354602
#191353252
#191352812
#191352772
#191350242
#191350212
#191346222
C4×#130632582
C4×#130632452
C4×#130632462
C4×#121×C432
C4×#46643