Finite Group Databasebeta

← C2×#19134896 #25097770

Subgroups — C2×#19134896 #25097770

Order 11008.

2050 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D43C211yesmaximal, characteristic, complemented
2C2×#14583411C211yesmaximal, characteristic
3C22×#13063253C211yesmaximal, characteristic, complemented
4C22×#13063251C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
6#19134896C218yesmaximal, direct product factor
7C2×#14582658C211yesmaximal, characteristic, complemented
8C2×C43×#339C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C23×C4×D43C2211yescharacteristic
11C22×#10621877C2211yescharacteristic
12C22×#10621872—21no—
13C2×M16×D43—22no—
14C2×M16×D43—24no—
15C2×M16×D43—24no—
16C2×M16×D43C2214yescomplemented
17C22×C8×D43—21no—
18#14583411—22no—
19#14583411—22no—
20#14583411C414yescomplemented
21#14583411C2214yes—
22C2×#13063309—21no—
23C2×#13063305C411yescharacteristic, complemented
24C2×#13063305C411yescharacteristic, complemented
25C2×#13063300C411yescharacteristic, complemented
26C2×#13063300C411yescharacteristic, complemented
27C2×#13063295—21no—
28C2×C4×D172—21no—
29C2×C4×D172—21no—
30C22×(C2×D43)⋊C4—21no—
31C22×C4×Dic43C2211yescharacteristic
32C2×#13063253—24no—
33C2×#13063253C2214yescomplemented
34C2×#13063251—24no—
35C2×#13063251C2214yescomplemented
36C4×(C2×D43)⋊C4—22no—
37C4×(C2×D43)⋊C4C2214yescomplemented
38C2×C43⋊#95—21no—
39#14582658C2214yescomplemented
40C22×M16×C43C2211yescharacteristic
41C2×#117×C43C2211yescharacteristic
42C22×C42×C43C2211yescharacteristic
43C43×#339C2214yescomplemented
44C24×D43D411yescharacteristic
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—22no—
48C2×#10621898—22no—
49C2×#10621898—22no—
50C2×#10621898—22no—
51C2×#10621898C2×C412yes—
52C2×#10621898C2312yes—
53C22×Dic86C2×C411yescharacteristic
54C22×D172—21no—
55C22×D172—21no—
56C22×D172C2×C411yescharacteristic
57C22×C22⋊D43—21no—
58C23×Dic43—21no—
59C23×Dic43D411yescharacteristic
60C22×C4×D43—22no—
61C22×C4×D43—22no—
62C22×C4×D43—22no—
63C22×C4×D43—22no—
64C22×C4×D43—21no—
65C22×C4×D43C2×C411yescharacteristic
66C22×C4×D43C2×C411yescharacteristic
67C22×C4×D43C2×C412yes—
68C22×C4×D43D412yes—
69C22×C4×D43D411yescharacteristic
70C22×C4×D43D411yescharacteristic
71C22×C4×D43D412yes—
72C22×C4×D43C2312yes—
73C2×#10621877—22no—
74C2×#10621877—21no—
75C2×#10621877D414yescomplemented
76C2×#10621877C2312yes—
77C2×#10621872—28no—
78C2×#10621872—24no—
79M16×D43—216no—
80M16×D43—28no—
81M16×D43—28no—
82C22×C43⋊C8—21no—
83C2×C8×D43—28no—
84C2×C8×D43—24no—
85#13063309—24no—
86#13063309—24no—
87#13063305—22no—
88#13063305—22no—
89#13063305C2×C414yescomplemented
90#13063305C2×C414yescomplemented
91#13063300—22no—
92#13063300—22no—
93#13063300C2×C414yescomplemented
94#13063300C2×C414yescomplemented
95#13063295—24no—
96#13063295—24no—
97C4×D172—24no—
98C4×D172—24no—
99C4×D172—24no—
100C4×D172—24no—
101C2×C4⋊Dic43—21no—
102C2×C4⋊Dic43—21no—
103C2×(C2×D43)⋊C4—28no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—24no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×C4×Dic43—22no—
110C2×C4×Dic43—22no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43C2312yes—
113#13063253—28no—
114#13063251—28no—
115C43⋊#95—24no—
116C23×C4×C43—21no—
117C23×C4×C43C2311yescharacteristic
118C2×M16×C43—22no—
119C2×M16×C43—21no—
120C2×M16×C43D414yescomplemented
121C2×M16×C43C2312yes—
122C22×C8×C43—21no—
123#117×C43—21no—
124#117×C43—21no—
125#117×C43C2×C412yes—
126#117×C43C2312yes—
127C2×C4⋊C4×C43C2×C411yescharacteristic
128C2×C4⋊C4×C43C2×C411yescharacteristic
129C2×C22⋊C4×C43—21no—
130C2×C42×C43—21no—
131C2×C42×C43—22no—
132C2×C42×C43—22no—
133C2×C42×C43—21no—
134C2×C42×C43C2312yes—
135C24×C43C2×D411yescharacteristic
136C23×D43—22no—
137C23×D43—22no—
138C23×D43—24no—
139C23×D43—21no—
140C23×D43—42no—
141C23×D43C22⋊C411yescharacteristic
142C23×D43C22⋊C412yes—
143C23×D43C22⋊C411yescharacteristic
144C23×D43C2×D412yes—
145C22×C4×C43—24no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—22no—
149C22×C4×C43—42no—
150C22×C4×C43—42no—
151C22×C4×C43C22×C411yescharacteristic
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D412yes—
156C22×C4×C43C2×D412yes—
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43#4112yes—
159C22×C4×C43#4112yes—
160C22×C4×C43C2411yescharacteristic
161C2×C22⋊D43—22no—
162C2×C22⋊D43—22no—
163C2×C22⋊D43—42no—
164C2×C22⋊D43—42no—
165C22×Dic43—24no—
166C22×Dic43—21no—
167C22×Dic43—22no—
168C22×Dic43—22no—
169C22×Dic43—22no—
170C22×Dic43—42no—
171C22×Dic43—42no—
172C22×Dic43C22⋊C411yescharacteristic
173C22×Dic43C22⋊C411yescharacteristic
174C22×Dic43C22⋊C412yes—
175C22×Dic43C2×D412yes—
176#10621898—24no—
177#10621898—24no—
178#10621898—22no—
179#10621898—22no—
180#10621898—22no—
181#10621898—22no—
182#10621898—42no—
183#10621898—42no—
184#10621898—42no—
185#10621898—42no—
186C2×D172—21no—
187C2×D172—24no—
188C2×D172—24no—
189C2×D172—22no—
190C2×D172—22no—
191C2×D172—44no—
192C2×D172—44no—
193C2×D172C22×C412yes—
194C2×C4×D43—22no—
195C2×C4×D43—22no—
196C2×C4×D43—22no—
197C2×C4×D43—24no—
198C2×C4×D43—22no—
199C2×C4×D43—24no—
200C2×C4×D43—22no—
201C2×C4×D43—24no—
202C2×C4×D43—22no—
203C2×C4×D43—24no—
204C2×C4×D43—24no—
205C2×C4×D43—22no—
206C2×C4×D43—22no—
207C2×C4×D43—24no—
208C2×C4×D43—22no—
209C2×C4×D43—22no—
210C2×C4×D43—22no—
211C2×C4×D43—22no—
212C2×C4×D43—22no—
213C2×C4×D43—22no—
214C2×C4×D43—42no—
215C2×C4×D43—42no—
216C2×C4×D43C22⋊C412yes—
217C2×C4×D43C22⋊C412yes—
218C2×C4×D43C22⋊C412yes—
219C2×C4×D43C22⋊C412yes—
220C2×C4×D43C22×C412yes—
221C2×C4×D43C22×C412yes—
222C2×C4×D43C2×D412yes—
223C2×C4×D43C2×D412yes—
224C2×Dic86—22no—
225C2×Dic86—22no—
226C2×Dic86—21no—
227C2×Dic86C22×C412yes—
228M16×C43—24no—
229M16×C43—22no—
230M16×C43C2×D414yescomplemented
231C2×C8×C43—24no—
232C2×C8×C43—22no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43C22×C412yes—
236C4⋊C4×C43C22×C412yes—
237C22⋊C4×C43—22no—
238C22⋊C4×C43—22no—
239C42×C43—22no—
240C42×C43—22no—
241C42×C43—22no—
242C42×C43—22no—
243C42×C43—42no—
244(C2×D43)⋊C4—216no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249C4⋊Dic43—24no—
250C4⋊Dic43—24no—
251C4×Dic43—22no—
252C4×Dic43—22no—
253C4×Dic43—42no—
254#10621877—24no—
255#10621877—22no—
256#10621877C2×D414yescomplemented
257C2×C43⋊C8—24no—
258C2×C43⋊C8—22no—
259#10621872—216no—
260C8×D43—216no—
261C23×C43—22no—
262C23×C43—22no—
263C23×C43C2×C22⋊C411yescharacteristic
264C23×C43C2×C22⋊C411yescharacteristic
265C23×C43#12112yes—
266C23×C43#12112yes—
267C23×C43C22×D411yescharacteristic
268C22×D43—22no—
269C22×D43—22no—
270C22×D43—22no—
271C22×D43—22no—
272C22×D43—24no—
273C22×D43—22no—
274C22×D43—22no—
275C22×D43—22no—
276C22×D43—24no—
277C22×D43—24no—
278C22×D43—22no—
279C22×D43—42no—
280C22×D43—42no—
281C22×D43—48no—
282C22×D43—48no—
283C22×D43—42no—
284C22×D43—42no—
285C22×D43—42no—
286C22×D43#10414yescomplemented
287C22×D43C2×C22⋊C412yes—
288C22×D43C2×C22⋊C412yes—
289C2×C4×C43—24no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—48no—
293C2×C4×C43—42no—
294C2×C4×C43—42no—
295C2×C4×C43—42no—
296C2×C4×C43—42no—
297C2×C4×C43C2×C22⋊C411yescharacteristic
298C2×C4×C43C2×C22⋊C411yescharacteristic
299C2×C4×C43C4×D412yes—
300C2×C4×C43C4×D412yes—
301C2×C4×C43C4×D412yes—
302C2×C4×C43C4×D412yes—
303C2×C4×C43#12012yes—
304C2×C4×C43#12012yes—
305C2×C4×C43#12112yes—
306C2×C4×C43#12112yes—
307C2×C4×C43#12312yes—
308C2×C4×C43#12312yes—
309C2×C4×C43C23×C411yescharacteristic
310C2×C4×C43C22×D411yescharacteristic
311C2×C4×C43C22×D411yescharacteristic
312C2×C4×C43C22×D411yescharacteristic
313C2×C4×C43C2×#4111yescharacteristic
314C2×C4×C43C2×#4111yescharacteristic
315C22⋊D43—42no—
316C22⋊D43—42no—
317C22⋊D43—44no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—24no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—24no—
324C2×Dic43—22no—
325C2×Dic43—48no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43—42no—
329C2×Dic43C2×C22⋊C412yes—
330C2×Dic43C2×C22⋊C412yes—
331D172—22no—
332D172—22no—
333D172—48no—
334D172—48no—
335D172—42no—
336C4×D43—22no—
337C4×D43—22no—
338C4×D43—22no—
339C4×D43—22no—
340C4×D43—22no—
341C4×D43—22no—
342C4×D43—22no—
343C4×D43—22no—
344C4×D43—24no—
345C4×D43—24no—
346C4×D43—24no—
347C4×D43—24no—
348C4×D43—42no—
349C4×D43—42no—
350C4×D43—44no—
351Dic86—22no—
352Dic86—22no—
353Dic86—42no—
354C8×C43—24no—
355C43⋊C8—24no—
356C2×#1871—431nomaximal, Sylow
357C22×C43—24no—
358C22×C43—24no—
359C22×C43—21no—
360C22×C43—21no—
361C22×C43—21no—
362C22×C43—21no—
363C22×C43#38612yes—
364C22×C43#38612yes—
365C22×C43C2×#10412yes—
366C22×C43#42112yes—
367C22×C43C22×C22⋊C411yescharacteristic
368C22×C43C2×#12111yescharacteristic
369C22×C43C2×#12111yescharacteristic
370C2×D43—28no—
371C2×D43—22no—
372C2×D43—22no—
373C2×D43—22no—
374C2×D43—22no—
375C2×D43—22no—
376C2×D43—44no—
377C2×D43—44no—
378C2×D43—48no—
379C2×D43—44no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—84no—
384C2×D43C2×#10414yescomplemented
385C4×C43—44no—
386C4×C43—42no—
387C4×C43—42no—
388C4×C43#38612yes—
389C4×C43#38612yes—
390C4×C43C2×C4×D411yescharacteristic
391C4×C43C2×C4×D411yescharacteristic
392C4×C43C2×#12011yescharacteristic
393C4×C43C2×#12311yescharacteristic
394Dic43—22no—
395Dic43—22no—
396Dic43—44no—
397Dic43—42no—
398C23×M16—431no—
399C2×#525—431no—
400C22×#104—431no—
401C22×#104—431no—
402C2×C4×C22⋊C4—431no—
403#1871—438no—
404C2×#339—431no—
405C2×#339D4311yescharacteristic, complemented
406C2×C43—21no—
407C2×C43—21no—
408C2×C43—22no—
409C2×C43#187114yescomplemented
410C2×C43C2×#38611yescharacteristic
411C2×C43C22×#10411yescharacteristic
412C2×C43C2×#42111yescharacteristic
413D43—24no—
414D43—42no—
415D43—82no—
416C22×#41—431no—
417C24×C4—431no—
418C22×M16—431no—
419C22×M16—434no—
420C22×M16—861no—
421C22×M16—864no—
422C22×M16—862no—
423C22×M16—864no—
424C22×M16C2×D4311yescharacteristic
425C23×C8—861no—
426#525—434no—
427#525—434no—
428#525—862no—
429#525—862no—
430C2×#123—861no—
431C2×C22⋊Q8—431no—
432C2×C22⋊Q8—431no—
433C2×#121—431no—
434C2×#121—431no—
435C2×#120—861no—
436C2×C4×D4—861no—
437C2×C4×D4—861no—
438C2×#117C2×D4311yescharacteristic
439C22×C22⋊C4—861no—
440C22×C42—431no—
441C22×C42C2×D4311yescharacteristic
442C2×#104—434no—
443C2×#104—434no—
444C2×#104—864no—
445C2×#104—864no—
446C4×C22⋊C4—434no—
447C4×C22⋊C4—862no—
448C2×#95—861no—
449#339—434no—
450#339C2×D4314yescomplemented
451C43C2×#187111yescharacteristic, complemented, Sylow
452C25—431no—
453C2×#41—432no—
454C2×#41—432no—
455C2×#41—861no—
456C2×#41—861no—
457C2×#41—862no—
458C2×#41—862no—
459C2×#41—862no—
460C2×#41—862no—
461C22×Q8—431no—
462C22×D4—431no—
463C22×D4—861no—
464C22×D4—861no—
465C22×D4—861no—
466C23×C4—21no—
467C23×C4—431no—
468C23×C4—431no—
469C23×C4—431no—
470C23×C4—432no—
471C23×C4—432no—
472C23×C4—432no—
473C23×C4—431no—
474C23×C4—431no—
475C23×C4—432no—
476C23×C4—862no—
477C23×C4—862no—
478C23×C4—862no—
479C23×C4—862no—
480C23×C4—861no—
481C23×C4—861no—
482C23×C4C22×D4311yescharacteristic
483C2×M16—22no—
484C2×M16—21no—
485C2×M16—434no—
486C2×M16—432no—
487C2×M16—864no—
488C2×M16—868no—
489C2×M16—868no—
490C2×M16—8616no—
491C2×M16—862no—
492C2×M16—861no—
493C2×M16—868no—
494C2×M16D17214yescomplemented
495C2×M16C22×D4312yes—
496C22×C8—21no—
497C22×C8—864no—
498C22×C8—868no—
499C22×C8—861no—
500#123—864no—
501#123—864no—
502C22⋊Q8—434no—
503C22⋊Q8—434no—
504C22⋊Q8—862no—
505C22⋊Q8—862no—
506#121—434no—
507#121—434no—
508#121—862no—
509#121—862no—
510#120—864no—
511#120—864no—
512C4×D4—864no—
513C4×D4—864no—
514C4×D4—864no—
515C4×D4—864no—
516#117—21no—
517#117—21no—
518#117C4×D4312yes—
519#117C22×D4312yes—
520C2×C4⋊C4—861no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4C4×D4311yescharacteristic
523C2×C4⋊C4C4×D4311yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—864no—
528C2×C22⋊C4—861no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4—868no—
531C2×C42—21no—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—21no—
535C2×C42—432no—
536C2×C42—862no—
537C2×C42—862no—
538C2×C42—861no—
539C2×C42C22×D4312yes—
540#104—868no—
541#104—868no—
542#95—864no—
543C24—431no—
544C24—431no—
545C24—432no—
546C24—432no—
547C24—864no—
548C24—862no—
549C24—862no—
550C24—861no—
551C24—1722no—
552C24D4×D4311yescharacteristic
553#41—864no—
554#41—864no—
555#41—862no—
556#41—862no—
557#41—862no—
558#41—862no—
559#41—1722no—
560#41—1722no—
561#41—1722no—
562#41—1722no—
563C2×Q8—432no—
564C2×Q8—861no—
565C2×Q8—862no—
566C2×Q8—862no—
567C2×D4—432no—
568C2×D4—864no—
569C2×D4—864no—
570C2×D4—862no—
571C2×D4—862no—
572C2×D4—861no—
573C2×D4—862no—
574C2×D4—862no—
575C2×D4—1724no—
576C2×D4—1724no—
577C2×D4—1722no—
578C2×D4—1722no—
579C22×C4—24no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—431no—
586C22×C4—431no—
587C22×C4—432no—
588C22×C4—432no—
589C22×C4—432no—
590C22×C4—432no—
591C22×C4—432no—
592C22×C4—432no—
593C22×C4—432no—
594C22×C4—432no—
595C22×C4—432no—
596C22×C4—432no—
597C22×C4—862no—
598C22×C4—862no—
599C22×C4—862no—
600C22×C4—862no—
601C22×C4—864no—
602C22×C4—862no—
603C22×C4—862no—
604C22×C4—864no—
605C22×C4—862no—
606C22×C4—864no—
607C22×C4—862no—
608C22×C4—864no—
609C22×C4—864no—
610C22×C4—862no—
611C22×C4—862no—
612C22×C4—864no—
613C22×C4—862no—
614C22×C4—862no—
615C22×C4—862no—
616C22×C4—862no—
617C22×C4—864no—
618C22×C4—861no—
619C22×C4—862no—
620C22×C4—862no—
621C22×C4—862no—
622C22×C4—1722no—
623C22×C4—1722no—
624C22×C4—1722no—
625C22×C4—1722no—
626C22×C4C2×C4×D4311yescharacteristic
627C22×C4C2×C4×D4311yescharacteristic
628C22×C4C2×D17212yes—
629C22×C4#1062189812yes—
630C22×C4D4×D4311yescharacteristic
631C22×C4D4×D4311yescharacteristic
632C22×C4D4×D4312yes—
633C22×C4D4×D4311yescharacteristic
634C22×C4#1062190212yes—
635C22×C4C23×D4311yescharacteristic
636M16—24no—
637M16—22no—
638M16—434no—
639M16—8616no—
640M16—864no—
641M16—862no—
642M16C2×D17214yescomplemented
643C2×C8—24no—
644C2×C8—22no—
645C2×C8—8616no—
646C2×C8—864no—
647C2×C8—862no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—864no—
651C4⋊C4—864no—
652C4⋊C4C2×C4×D4312yes—
653C4⋊C4C2×C4×D4312yes—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—864no—
657C22⋊C4—864no—
658C22⋊C4—864no—
659C22⋊C4—864no—
660C22⋊C4—8616no—
661C42—22no—
662C42—22no—
663C42—22no—
664C42—22no—
665C42—42no—
666C42—862no—
667C42—862no—
668C42—1722no—
669C23—22no—
670C23—22no—
671C23—432no—
672C23—434no—
673C23—432no—
674C23—864no—
675C23—864no—
676C23—862no—
677C23—862no—
678C23—862no—
679C23—862no—
680C23—862no—
681C23—862no—
682C23—864no—
683C23—862no—
684C23—862no—
685C23—1722no—
686C23—1722no—
687C23—1728no—
688C23—1728no—
689C23—1722no—
690C23—1722no—
691C23—1722no—
692C23C22⋊C4×D4311yescharacteristic
693C23C22⋊C4×D4311yescharacteristic
694C23#1306329812yes—
695C23#1306330012yes—
696C23C2×D4×D4311yescharacteristic
697Q8—862no—
698Q8—862no—
699Q8—1722no—
700D4—862no—
701D4—862no—
702D4—1728no—
703D4—1728no—
704D4—1722no—
705D4—1722no—
706D4—1724no—
707D4—1722no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—48no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—432no—
717C2×C4—432no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—864no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—864no—
732C2×C4—864no—
733C2×C4—864no—
734C2×C4—864no—
735C2×C4—864no—
736C2×C4—862no—
737C2×C4—1728no—
738C2×C4—1722no—
739C2×C4—1722no—
740C2×C4—1722no—
741C2×C4—1722no—
742C2×C4—1722no—
743C2×C4—1724no—
744C2×C4C22⋊C4×D4311yescharacteristic
745C2×C4C22⋊C4×D4311yescharacteristic
746C2×C4#1306328712yes—
747C2×C4#1306328712yes—
748C2×C4C4×D17212yes—
749C2×C4C4×D17212yes—
750C2×C4#1306329512yes—
751C2×C4#1306329512yes—
752C2×C4#1306329812yes—
753C2×C4#1306330012yes—
754C2×C4#1306331012yes—
755C2×C4#1306331012yes—
756C2×C4C22×C4×D4311yescharacteristic
757C2×C4C2×D4×D4311yescharacteristic
758C2×C4C2×D4×D4311yescharacteristic
759C2×C4C22×D17211yescharacteristic
760C2×C4C2×#1062189811yescharacteristic
761C2×C4C2×#1062190211yescharacteristic
762C8—24no—
763C8—864no—
764C22—24no—
765C22—24no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—434no—
771C22—868no—
772C22—862no—
773C22—862no—
774C22—862no—
775C22—862no—
776C22—862no—
777C22—3444no—
778C22—1724no—
779C22—1724no—
780C22—1728no—
781C22—1722no—
782C22—1722no—
783C22—1722no—
784C22—1724no—
785C22#1458277712yes—
786C22#1458277712yes—
787C22#104×D4312yes—
788C22#1458291412yes—
789C22C2×C22⋊C4×D4311yescharacteristic
790C22C2×#1306329811yescharacteristic
791C22C2×#1306330011yescharacteristic
792C4—44no—
793C4—42no—
794C4—42no—
795C4—862no—
796C4—862no—
797C4—1724no—
798C4—1722no—
799C4#1458277712yes—
800C4#1458277712yes—
801C4C2×#1306328711yescharacteristic
802C4C2×C4×D17211yescharacteristic
803C4C2×#1306329511yescharacteristic
804C4C2×#1306331011yescharacteristic
805C2—21no—
806C2—21no—
807C2—22no—
808C2—864no—
809C2—3442no—
810C2—1722no—
811C2#1913489614yesdirect product factor
812C2C2×#1458277711yescharacteristic
813C2C2×#104×D4311yescharacteristic
814C2C2×#1458291411yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#339C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#14583411C2
cosocleC22×C4×C43C24
hypercenterC2×#339D43
hypocenterC43C2×#1871
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
1. C22×M16×D43C2semidirect
3. C22×#13063253C2semidirect
4. C22×#13063251C2semidirect
5. C2×C4×(C2×D43)⋊C4C2semidirect
6. #19134896C2direct (N × H)
7. C2×#14582658C2semidirect
8. C2×C43×#339C2semidirect
16. C2×M16×D43C22semidirect
20. #14583411C4semidirect
23. C2×#13063305C4semidirect
24. C2×#13063305C4semidirect
25. C2×#13063300C4semidirect
26. C2×#13063300C4semidirect
33. C2×#13063253C22semidirect
35. C2×#13063251C22semidirect
37. C4×(C2×D43)⋊C4C22semidirect
39. #14582658C22semidirect
43. C43×#339C22semidirect
75. C2×#10621877D4semidirect
89. #13063305C2×C4semidirect
90. #13063305C2×C4semidirect
93. #13063300C2×C4semidirect
94. #13063300C2×C4semidirect
120. C2×M16×C43D4semidirect
230. M16×C43C2×D4semidirect
256. #10621877C2×D4semidirect
286. C22×D43#104semidirect
384. C2×D43C2×#104semidirect
405. C2×#339D43semidirect
409. C2×C43#1871semidirect
450. #339C2×D43semidirect
451. C43C2×#1871semidirect
494. C2×M16D172semidirect
642. M16C2×D172semidirect
811. C2#19134896direct (N × H)

Maximal subgroups

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

subgroupindex
C22×M16×D432
C2×#145834112
C22×#130632532
C22×#130632512
C2×C4×(C2×D43)⋊C42
#191348962
C2×#145826582
C2×C43×#3392
C2×#187143