Finite Group Databasebeta

← #25017895

Subgroups — #25017895

Order 11008.

2686 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2C2×#14582775C212yesmaximal
3C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
4C2×#95×D43C211yesmaximal, characteristic, complemented
5#19132832C211yesmaximal, characteristic, complemented
6#19132830C211yesmaximal, characteristic, complemented
7#19132828C211yesmaximal, characteristic, complemented
8#19132821C212yesmaximal, complemented
9#19132817C212yesmaximal, complemented
10(C2×D43)⋊#95C212yesmaximal, complemented
11C43×#1437C211yesmaximal, characteristic, complemented
12C23×C22⋊D43C2211yescharacteristic
13C24×Dic43C2211yescharacteristic
14C23×C4×D43C2212yes—
15C23×C4×D43C2211yescharacteristic
16C2×(C22⋊D43)⋊C4—24no—
17C2×(C22⋊D43)⋊C4—24no—
18C2×(C22⋊D43)⋊C4C418yescomplemented
19C22×Dic43⋊C4C2211yescharacteristic
20C22×C22⋊Dic43C2212yes—
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C22×(C2×D43)⋊C4C2212yes—
23C22×C4×Dic43C2211yescharacteristic
24C22×C4×Dic43C2211yescharacteristic
25#14582775C4116yescomplemented
26C4×(C2×D43)⋊C4—24no—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2211yescharacteristic
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35#95×D43—24no—
36C22×C22⋊C4×C43C2211yescharacteristic
37C22×C22⋊C4×C43C2212yes—
38C22×C42×C43C2211yescharacteristic
39C2×#95×C43C2211yescharacteristic
40C2×#95×C43C2212yes—
41C24×D43C2311yescharacteristic
42C22×C22⋊D43—22no—
43C22×C22⋊D43—22no—
44C22×C22⋊D43—24no—
45C22×C22⋊D43C2×C414yes—
46C22×C22⋊D43C2×C418yes—
47C23×Dic43—22no—
48C23×Dic43—22no—
49C23×Dic43—42no—
50C23×Dic43—42no—
51C23×Dic43C2×C414yescomplemented
52C23×Dic43C2312yes—
53C23×Dic43C2311yescharacteristic
54C23×Dic43C2312yes—
55C23×Dic43C2311yescharacteristic
56C23×Dic43C2311yescharacteristic
57C22×C4×D43—24no—
58C22×C4×D43—24no—
59C22×C4×D43—42no—
60C22×C4×D43—42no—
61C22×C4×D43—42no—
62C22×C4×D43—42no—
63C22×C4×D43—42no—
64C22×C4×D43—42no—
65C22×C4×D43C2×C414yes—
66C22×C4×D43C2×C418yescomplemented
67C22×C4×D43D414yes—
68C22×C4×D43D414yes—
69(C22⋊D43)⋊C4—232no—
70C2×Dic43⋊C4—22no—
71C2×Dic43⋊C4—22no—
72C2×Dic43⋊C4C2×C414yescomplemented
73C2×C22⋊Dic43—42no—
74C2×C22⋊Dic43—42no—
75C2×C22⋊Dic43C2×C418yescomplemented
76C2×(C2×D43)⋊C4—22no—
77C2×(C2×D43)⋊C4—22no—
78C2×(C2×D43)⋊C4—24no—
79C2×(C2×D43)⋊C4—24no—
80C2×(C2×D43)⋊C4C2×C414yes—
81C2×(C2×D43)⋊C4C2×C418yescomplemented
82C2×C4×Dic43—22no—
83C2×C4×Dic43—22no—
84C2×C4×Dic43—22no—
85C2×C4×Dic43—42no—
86C2×C4×Dic43C2×C414yescomplemented
87C43⋊#95—22no—
88C43⋊#95—24no—
89C43⋊#95—24no—
90C43⋊#95—42no—
91C43⋊#95—42no—
92C43⋊#95—42no—
93C43⋊#95C2×C418yescomplemented
94C43⋊#95C2×C418yescomplemented
95C25×C43C2311yescharacteristic
96C23×C4×C43C2312yes—
97C23×C4×C43C2311yescharacteristic
98C23×C4×C43C2312yes—
99C23×C4×C43C2311yescharacteristic
100C2×C22⋊C4×C43—22no—
101C2×C22⋊C4×C43—22no—
102C2×C22⋊C4×C43—42no—
103C2×C22⋊C4×C43—42no—
104C2×C22⋊C4×C43C2×C414yescomplemented
105C2×C22⋊C4×C43C2×C418yescomplemented
106C2×C42×C43—22no—
107C2×C42×C43—42no—
108#95×C43—22no—
109#95×C43—42no—
110C24×C43—21no—
111C24×C43—21no—
112C24×C43—22no—
113C24×C43—22no—
114C24×C43—22no—
115C24×C43—22no—
116C24×C43—22no—
117C24×C43C22×C414yes—
118C24×C43C22×C412yes—
119C24×C43C2411yescharacteristic
120C23×D43—22no—
121C23×D43—22no—
122C23×D43—22no—
123C23×D43—22no—
124C23×D43C22×C412yes—
125C23×D43C22×C414yes—
126C23×D43C2×D412yes—
127C23×D43C2×D412yes—
128C23×D43#4114yes—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43C22×C414yes—
148C22×C4×C43C22×C414yes—
149C22×C4×C43C22×C412yes—
150C22×C4×C43C22×C412yes—
151C22×C4×C43C2×D412yes—
152C22×C4×C43C2×D412yes—
153C2×C22⋊D43—28no—
154C2×C22⋊D43—28no—
155C2×C22⋊D43—216no—
156C2×C22⋊D43—216no—
157C2×C22⋊D43C42116yescomplemented
158C22×Dic43—28no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—22no—
166C22×Dic43—22no—
167C22×Dic43—22no—
168C22×Dic43—22no—
169C22×Dic43—22no—
170C22×Dic43—22no—
171C22×Dic43—22no—
172C22×Dic43—22no—
173C22×Dic43—22no—
174C22×Dic43—22no—
175C22×Dic43—22no—
176C22×Dic43—22no—
177C22×Dic43—22no—
178C22×Dic43—22no—
179C22×Dic43—22no—
180C22×Dic43—48no—
181C22×Dic43—48no—
182C22×Dic43—44no—
183C22×Dic43—44no—
184C22×Dic43C22×C414yes—
185C22×Dic43C22×C414yes—
186C22×Dic43C22×C412yes—
187C22×Dic43C22×C414yes—
188C22×Dic43C22×C412yes—
189C22×Dic43C22×C412yes—
190C22×Dic43C2×D412yes—
191C22×Dic43C2×D412yes—
192C2×C4×D43—216no—
193C2×C4×D43—48no—
194C2×C4×D43—48no—
195C2×C4×D43—48no—
196C2×C4×D43—48no—
197C2×C4×D43—44no—
198C2×C4×D43—44no—
199C2×C4×D43—48no—
200C2×C4×D43—48no—
201C2×C4×D43—48no—
202C2×C4×D43—48no—
203C2×C4×D43C22⋊C4116yescomplemented
204C22⋊C4×C43—28no—
205C22⋊C4×C43—48no—
206C42×C43—44no—
207C22⋊Dic43—48no—
208(C2×D43)⋊C4—28no—
209(C2×D43)⋊C4—216no—
210Dic43⋊C4—28no—
211C4×Dic43—28no—
212C4×Dic43—44no—
213C23×C43—22no—
214C23×C43—22no—
215C23×C43—24no—
216C23×C43—24no—
217C23×C43—24no—
218C23×C43—24no—
219C23×C43—24no—
220C23×C43—24no—
221C23×C43—24no—
222C23×C43—24no—
223C23×C43—42no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—42no—
229C23×C43—42no—
230C23×C43—42no—
231C23×C43—42no—
232C23×C43—42no—
233C23×C43C2×C4214yes—
234C23×C43C23×C411yescharacteristic
235C23×C43C23×C412yes—
236C23×C43C22×D411yescharacteristic
237C23×C43C22×D411yescharacteristic
238C23×C43C2×#4112yes—
239C23×C43H(5,𝔽2)12yes—
240C23×C43H(5,𝔽2)12yes—
241C23×C43H(5,𝔽2)12yes—
242C23×C432−1+412yes—
243C22×D43—24no—
244C22×D43—24no—
245C22×D43—24no—
246C22×D43—24no—
247C22×D43—24no—
248C22×D43—24no—
249C22×D43—24no—
250C22×D43—22no—
251C22×D43—22no—
252C22×D43—22no—
253C22×D43—22no—
254C22×D43—24no—
255C22×D43—24no—
256C22×D43—24no—
257C22×D43—24no—
258C22×D43—24no—
259C22×D43C2×C4214yes—
260C22×D43C2×C22⋊C414yes—
261C22×D43#11714yes—
262C22×D43C4×D418yes—
263C22×D43C4×D418yes—
264C2×C4×C43—24no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—24no—
268C2×C4×C43—22no—
269C2×C4×C43—24no—
270C2×C4×C43—24no—
271C2×C4×C43—24no—
272C2×C4×C43—24no—
273C2×C4×C43—24no—
274C2×C4×C43—24no—
275C2×C4×C43—24no—
276C2×C4×C43—42no—
277C2×C4×C43—42no—
278C2×C4×C43—42no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—42no—
282C2×C4×C43—42no—
283C2×C4×C43—42no—
284C2×C4×C43—42no—
285C2×C4×C43—42no—
286C2×C4×C43—42no—
287C2×C4×C43C2×C22⋊C414yes—
288C22⋊D43—232no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—24no—
292C2×Dic43—24no—
293C2×Dic43—24no—
294C2×Dic43—24no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—24no—
299C2×Dic43—24no—
300C2×Dic43—24no—
301C2×Dic43—24no—
302C2×Dic43—24no—
303C2×Dic43—24no—
304C2×Dic43—24no—
305C2×Dic43—416no—
306C2×Dic43—42no—
307C2×Dic43—42no—
308C2×Dic43—42no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43C2×C4214yes—
318C2×Dic43C2×C22⋊C414yes—
319C4×D43—416no—
320C4×D43—432no—
321#13784—431nomaximal, Sylow
322C22×C43—24no—
323C22×C43—28no—
324C22×C43—42no—
325C22×C43—42no—
326C22×C43—44no—
327C22×C43—44no—
328C22×C43—44no—
329C22×C43—44no—
330C22×C43—44no—
331C22×C43C22×C4211yescharacteristic
332C22×C43C22×C22⋊C411yescharacteristic
333C22×C43C2×#11711yescharacteristic
334C22×C43C2×C4×D412yes—
335C22×C43C2×C4×D412yes—
336C22×C43#51812yes—
337C22×C43#51812yes—
338C22×C43#51812yes—
339C22×C43#52012yes—
340C22×C43#52012yes—
341C22×C43#52012yes—
342C22×C43#53412yes—
343C22×C43#53411yescharacteristic
344C22×C43#53411yescharacteristic
345C22×C43#53511yescharacteristic
346C22×C43#53611yescharacteristic
347C22×C43#53712yes—
348C22×C43#53812yes—
349C22×C43#53812yes—
350C22×C43#53912yes—
351C22×C43#53912yes—
352C2×D43—24no—
353C2×D43—24no—
354C2×D43—28no—
355C2×D43—28no—
356C2×D43—28no—
357C2×D43—28no—
358C2×D43—28no—
359C2×D43—28no—
360C2×D43C4×C22⋊C418yes—
361C4×C43—24no—
362C4×C43—42no—
363C4×C43—44no—
364C4×C43—44no—
365Dic43—24no—
366Dic43—24no—
367Dic43—42no—
368Dic43—44no—
369Dic43—44no—
370C22×C4×D4—431no—
371C2×#386—432no—
372C2×C4×C22⋊C4—431no—
373C22×#95—431no—
374#1437—431no—
375#1437D4311yescharacteristic, complemented
376#1436—431no—
377#1436—431no—
378#1434—432no—
379C22⋊#95—432no—
380C22⋊#95—432no—
381C2×C43—44no—
382C2×C43C2×C4×C22⋊C411yescharacteristic
383C2×C43#227512yes—
384C2×C43#230811yescharacteristic
385C2×C43#231111yescharacteristic
386C2×C43#231812yes—
387C2×C43#232112yes—
388C2×C43#232212yes—
389C2×C43#232512yes—
390C2×C43#232512yes—
391D43—28no—
392C23×D4—431no—
393C24×C4—431no—
394C24×C4—431no—
395C24×C4—432no—
396C2×C4×D4—438no—
397C2×C4×D4—864no—
398C2×C4×D4—864no—
399C22×C4⋊C4—431no—
400C22×C22⋊C4—431no—
401C22×C22⋊C4—432no—
402C22×C22⋊C4—432no—
403C22×C22⋊C4C2×D4311yescharacteristic
404C22×C22⋊C4C2×D4312yes—
405C22×C42—431no—
406C22×C42—431no—
407C22×C42C2×D4311yescharacteristic
408#386—4316no—
409C4×C22⋊C4—864no—
410C2×#95—432no—
411C2×#95—432no—
412C2×#95—432no—
413C2×#95—432no—
414C2×#95—431no—
415C2×#95—432no—
416C2×#95—432no—
417C2×#95—432no—
418C2×#95—864no—
419C2×#95C2×D4311yescharacteristic
420C2×#95C2×D4312yes—
421C43#1378411yescharacteristic, complemented, Sylow
422C25—431no—
423C25C22×D4311yescharacteristic
424C22×D4—434no—
425C22×D4—438no—
426C22×D4—862no—
427C22×D4—862no—
428C22×D4—864no—
429C23×C4—431no—
430C23×C4—431no—
431C23×C4—434no—
432C23×C4—434no—
433C23×C4—434no—
434C23×C4—432no—
435C23×C4—431no—
436C23×C4—432no—
437C23×C4—434no—
438C23×C4—438no—
439C23×C4—864no—
440C23×C4—864no—
441C23×C4—862no—
442C23×C4—862no—
443C23×C4—1722no—
444C23×C4—1722no—
445C23×C4—1722no—
446C23×C4—1722no—
447C23×C4—1722no—
448C23×C4—1722no—
449C23×C4—1722no—
450C23×C4—1722no—
451C23×C4C22×D4312yes—
452C23×C4C22×D4311yescharacteristic
453C23×C4C22×D4312yes—
454C23×C4C22×D4311yescharacteristic
455C4×D4—8632no—
456C2×C4⋊C4—434no—
457C2×C4⋊C4—862no—
458C2×C4⋊C4—862no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—42no—
462C2×C22⋊C4—42no—
463C2×C22⋊C4—434no—
464C2×C22⋊C4—438no—
465C2×C22⋊C4—438no—
466C2×C22⋊C4—862no—
467C2×C22⋊C4—862no—
468C2×C22⋊C4—864no—
469C2×C22⋊C4—864no—
470C2×C22⋊C4—1722no—
471C2×C22⋊C4—1722no—
472C2×C22⋊C4C4×D4314yescomplemented
473C2×C22⋊C4C4×D4318yescomplemented
474C2×C42—22no—
475C2×C42—42no—
476C2×C42—434no—
477C2×C42—862no—
478C2×C42—862no—
479C2×C42—862no—
480C2×C42—1722no—
481#95—22no—
482#95—42no—
483#95—438no—
484#95—438no—
485#95—864no—
486#95—864no—
487#95—862no—
488#95—1722no—
489#95—1722no—
490#95—1722no—
491C24—21no—
492C24—21no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—432no—
499C24—434no—
500C24—432no—
501C24—432no—
502C24—434no—
503C24—862no—
504C24—862no—
505C24—862no—
506C24—862no—
507C24C2×C4×D4314yes—
508C24C2×C4×D4312yes—
509C24C23×D4311yescharacteristic
510C2×D4—4316no—
511C2×D4—868no—
512C2×D4—868no—
513C2×D4—8616no—
514C2×D4—8616no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—434no—
534C22×C4—432no—
535C22×C4—432no—
536C22×C4—432no—
537C22×C4—432no—
538C22×C4—4316no—
539C22×C4—434no—
540C22×C4—434no—
541C22×C4—432no—
542C22×C4—8616no—
543C22×C4—868no—
544C22×C4—861no—
545C22×C4—861no—
546C22×C4—862no—
547C22×C4—862no—
548C22×C4—862no—
549C22×C4—862no—
550C22×C4—862no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—862no—
554C22×C4—862no—
555C22×C4—862no—
556C22×C4—862no—
557C22×C4—862no—
558C22×C4—862no—
559C22×C4—862no—
560C22×C4—862no—
561C22×C4—862no—
562C22×C4—862no—
563C22×C4—862no—
564C22×C4—862no—
565C22×C4—1728no—
566C22×C4—1728no—
567C22×C4—1724no—
568C22×C4—1724no—
569C22×C4—1728no—
570C22×C4—1728no—
571C22×C4—1728no—
572C22×C4—1728no—
573C22×C4—1728no—
574C22×C4—1728no—
575C22×C4—1728no—
576C22×C4—1728no—
577C22×C4—1724no—
578C22×C4—1724no—
579C22×C4C2×C4×D4314yes—
580C22×C4C2×C4×D4314yes—
581C22×C4C2×C4×D4312yes—
582C22×C4C2×C4×D4312yes—
583C22×C4D4×D4312yes—
584C22×C4D4×D4312yes—
585C4⋊C4—868no—
586C22⋊C4—28no—
587C22⋊C4—48no—
588C22⋊C4—868no—
589C22⋊C4—8616no—
590C22⋊C4—1728no—
591C42—44no—
592C42—868no—
593C42—1724no—
594C23—22no—
595C23—22no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—42no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—434no—
615C23—434no—
616C23—434no—
617C23—438no—
618C23—438no—
619C23—864no—
620C23—864no—
621C23—864no—
622C23—864no—
623C23—864no—
624C23—864no—
625C23—864no—
626C23—862no—
627C23—862no—
628C23—862no—
629C23—862no—
630C23—864no—
631C23—864no—
632C23—864no—
633C23—864no—
634C23—864no—
635C23C42×D4314yes—
636C23C22×C4×D4311yescharacteristic
637C23C22×C4×D4312yes—
638C23C2×D4×D4311yescharacteristic
639C23C2×D4×D4311yescharacteristic
640C23#41×D4312yes—
641C23#1306337012yes—
642C23#1306337012yes—
643C23#1306337112yes—
644C23#1306337212yes—
645D4—8632no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—434no—
670C2×C4—434no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—864no—
674C2×C4—864no—
675C2×C4—864no—
676C2×C4—864no—
677C2×C4—862no—
678C2×C4—862no—
679C2×C4—862no—
680C2×C4—864no—
681C2×C4—864no—
682C2×C4—864no—
683C2×C4—864no—
684C2×C4—864no—
685C2×C4—864no—
686C2×C4—864no—
687C2×C4—17216no—
688C2×C4—17232no—
689C2×C4—17216no—
690C2×C4—1722no—
691C2×C4—1722no—
692C2×C4—1721no—
693C2×C4—1722no—
694C2×C4—1721no—
695C2×C4—1722no—
696C2×C4—1722no—
697C2×C4—1722no—
698C2×C4—1722no—
699C2×C4—1722no—
700C2×C4—1722no—
701C2×C4C22⋊C4×D4314yes—
702C22—24no—
703C22—28no—
704C22—44no—
705C22—44no—
706C22—42no—
707C22—42no—
708C22—44no—
709C22—44no—
710C22—44no—
711C22—438no—
712C22—868no—
713C22—868no—
714C22—864no—
715C22—864no—
716C22—868no—
717C22—868no—
718C22—868no—
719C22—868no—
720C22C2×C42×D4311yescharacteristic
721C22C2×C22⋊C4×D4311yescharacteristic
722C22#117×D4311yescharacteristic
723C22C4×D4×D4312yes—
724C22C4×D4×D4312yes—
725C22#1458337112yes—
726C22#1458337112yes—
727C22#1458337212yes—
728C22#1458337812yes—
729C22#1458337812yes—
730C22#1458337912yes—
731C22#1458345712yes—
732C22#1458345911yescharacteristic
733C22#1458346011yescharacteristic
734C22#1458346211yescharacteristic
735C22#1458346911yescharacteristic
736C22#1458347812yes—
737C22#1458348112yes—
738C22#1458348312yes—
739C22#1458349012yes—
740C22#1458349212yes—
741C4—24no—
742C4—44no—
743C4—42no—
744C4—44no—
745C4—864no—
746C4—864no—
747C4—1724no—
748C4—1722no—
749C4—1724no—
750C2—44no—
751C2—868no—
752C2C4×C22⋊C4×D4311yescharacteristic
753C2#1913695412yes—
754C2#1913716911yescharacteristic
755C2#1913718511yescharacteristic
756C2#1913722512yes—
757C2#1913725412yes—
758C2#1913726512yes—
759C2#1913729712yes—
760C2#1913729912yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC22×C43C22×C42
FittingC43×#1437C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenter#1437D43
hypocenterC43#13784
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
3. C2×C4×(C2×D43)⋊C4C2semidirect
4. C2×#95×D43C2semidirect
5. #19132832C2semidirect
6. #19132830C2semidirect
7. #19132828C2semidirect
8. #19132821C2semidirect
9. #19132817C2semidirect
10. (C2×D43)⋊#95C2semidirect
11. C43×#1437C2semidirect
18. C2×(C22⋊D43)⋊C4C4semidirect
25. #14582775C4semidirect
51. C23×Dic43C2×C4semidirect
66. C22×C4×D43C2×C4semidirect
72. C2×Dic43⋊C4C2×C4semidirect
75. C2×C22⋊Dic43C2×C4semidirect
81. C2×(C2×D43)⋊C4C2×C4semidirect
86. C2×C4×Dic43C2×C4semidirect
93. C43⋊#95C2×C4semidirect
94. C43⋊#95C2×C4semidirect
104. C2×C22⋊C4×C43C2×C4semidirect
105. C2×C22⋊C4×C43C2×C4semidirect
157. C2×C22⋊D43C42semidirect
203. C2×C4×D43C22⋊C4semidirect
375. #1437D43semidirect
421. C43#13784semidirect
472. C2×C22⋊C4C4×D43semidirect
473. C2×C22⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D43)⋊C42
C2×#145827752
C2×C4×(C2×D43)⋊C42
C2×#95×D432
#191328322
#191328302
#191328282
#191328212
#191328172
(C2×D43)⋊#952
C43×#14372
#1378443