Finite Group Databasebeta

← C4×#14582871 #25094246

Subgroups — C4×#14582871 #25094246

Order 11008.

1666 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10621900C211yesmaximal, characteristic
2C2×#14582871C212yesmaximal
3C4×#13063281C212yesmaximal, complemented
4#99×Dic43C212yesmaximal, complemented
5C4×#13063239C212yesmaximal, complemented
6C4×#13063240C211yesmaximal, characteristic, complemented
7#19134382C212yesmaximal, complemented
8#19134326C212yesmaximal, complemented
9C4×#99×C43C211yesmaximal, characteristic, complemented
10C22×#10621900C2211yescharacteristic
11C4×#10621900—22no—
12C4×#10621900—22no—
13C4×#10621900—22no—
14C4×#10621900—22no—
15C2×C4×Dic86C411yescharacteristic, complemented
16C2×#13063290C411yescharacteristic, complemented
17C2×D4×Dic43C2211yescharacteristic
18C2×C4×C22⋊D43C411yescharacteristic, complemented
19C2×C4×C22⋊D43C2211yescharacteristic
20C2×(C22⋊D43)⋊C4C411yescharacteristic, complemented
21C2×(C22⋊D43)⋊C4C2211yescharacteristic
22C2×#13063283C411yescharacteristic, complemented
23C2×#13063281C411yescharacteristic, complemented
24C2×#13063281C2214yes—
25C2×#13063281C2211yescharacteristic
26C22×C4×Dic43C411yescharacteristic, complemented
27C22×C4×Dic43C2211yescharacteristic
28C2×C42×D43C411yescharacteristic, complemented
29#14582871C4116yesdirect product factor
30C2×#13063240C2212yes—
31C2×#13063239C2214yes—
32C4×Dic43⋊C4—22no—
33#14582750—22no—
34C22⋊C4×Dic43C2214yes—
35C4×C22⋊Dic43C2212yes—
36#14582744—22no—
37C42×Dic43—22no—
38#14582666C2212yes—
39#14582665C2214yes—
40C2×C4×D4×C43C2211yescharacteristic
41C2×#99×C43C2212yes—
42C4×C22⋊C4×C43C2212yes—
43C43×#342C2212yes—
44C2×#10621900—22no—
45C2×#10621900—22no—
46C2×#10621900—24no—
47C2×#10621900C2×C418yes—
48C22×Dic86C2×C411yescharacteristic
49C22×C22⋊D43C2×C411yescharacteristic
50C22×C22⋊D43C2311yescharacteristic
51C23×Dic43C2×C411yescharacteristic
52C23×Dic43C2×C411yescharacteristic
53C23×Dic43C2311yescharacteristic
54C23×Dic43C2311yescharacteristic
55C22×C4×D43C2×C411yescharacteristic
56C22×C4×D43C2×C411yescharacteristic
57C22×C4×D43C2×C411yescharacteristic
58C4×Dic86—22no—
59C4×Dic86—22no—
60#13063290—22no—
61#13063290—22no—
62D4×Dic43—22no—
63D4×Dic43—22no—
64C4×C22⋊D43—22no—
65C4×C22⋊D43—22no—
66C4×C22⋊D43—22no—
67C4×C22⋊D43—22no—
68(C22⋊D43)⋊C4—22no—
69(C22⋊D43)⋊C4—22no—
70(C22⋊D43)⋊C4—22no—
71(C22⋊D43)⋊C4—22no—
72#13063283—22no—
73#13063283—22no—
74#13063281—22no—
75#13063281—22no—
76#13063281—28no—
77#13063281—22no—
78#13063281—22no—
79#13063281C2×C4116yescomplemented
80C2×C4⋊Dic43C2×C411yescharacteristic
81C2×Dic43⋊C4—24no—
82C2×Dic43⋊C4C2×C411yescharacteristic
83C2×Dic43⋊C4C2×C411yescharacteristic
84C2×Dic43⋊C4C2×C411yescharacteristic
85C2×Dic43⋊C4C2×C411yescharacteristic
86C2×C22⋊Dic43C2×C411yescharacteristic
87C2×C22⋊Dic43C2311yescharacteristic
88C2×C22⋊Dic43C2314yes—
89C2×(C2×D43)⋊C4C2×C411yescharacteristic
90C2×(C2×D43)⋊C4C2×C411yescharacteristic
91C2×C4×Dic43—24no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—22no—
97C2×C4×Dic43—24no—
98C2×C4×Dic43C2×C411yescharacteristic
99C2×C4×Dic43C2×C411yescharacteristic
100C2×C4×Dic43C2×C411yescharacteristic
101C2×C4×Dic43C2×C411yescharacteristic
102C2×C4×Dic43C2×C411yescharacteristic
103C2×C4×Dic43C2×C411yescharacteristic
104C2×C4×Dic43C2×C411yescharacteristic
105C2×C4×Dic43C2×C411yescharacteristic
106C2×C4×Dic43C2×C411yescharacteristic
107C2×C4×Dic43D412yes—
108C2×C4×Dic43D412yes—
109C2×C4×Dic43D412yes—
110C2×C4×Dic43D412yes—
111C42×D43—21no—
112C42×D43—21no—
113C42×D43—21no—
114C42×D43—21no—
115#13063240C2×C418yescomplemented
116#13063239C2×C4116yescomplemented
117C43⋊#95—22no—
118C43⋊#95—24no—
119C22×D4×C43C2311yescharacteristic
120C23×C4×C43C2×C411yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C4×D4×C43—22no—
123C4×D4×C43—22no—
124C2×C4⋊C4×C43C2×C411yescharacteristic
125C2×C22⋊C4×C43C2×C411yescharacteristic
126C2×C22⋊C4×C43C2311yescharacteristic
127C2×C22⋊C4×C43C2314yes—
128C2×C42×C43—22no—
129C2×C42×C43C2×C411yescharacteristic
130#99×C43C2×C418yescomplemented
131#95×C43—22no—
132C24×C43C22×C411yescharacteristic
133C24×C43C2411yescharacteristic
134C23×D43C22×C411yescharacteristic
135C2×D4×C43—22no—
136C2×D4×C43—22no—
137C2×D4×C43C22×C414yes—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—24no—
141C22×C4×C43—42no—
142C22×C4×C43—42no—
143C22×C4×C43C22×C411yescharacteristic
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C22×C411yescharacteristic
146C22×C4×C43C22×C411yescharacteristic
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D412yes—
150C2×C22⋊D43—22no—
151C2×C22⋊D43—22no—
152C2×C22⋊D43—22no—
153C2×C22⋊D43—22no—
154C2×C22⋊D43C4214yescomplemented
155C2×C22⋊D43C22×C414yes—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—22no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—24no—
162C22×Dic43—42no—
163C22×Dic43—42no—
164C22×Dic43C4214yescomplemented
165C22×Dic43C22×C411yescharacteristic
166C22×Dic43C22×C411yescharacteristic
167C22×Dic43C22×C411yescharacteristic
168C22×Dic43C22×C411yescharacteristic
169C22×Dic43C22×C411yescharacteristic
170C22×Dic43C22×C411yescharacteristic
171C22×Dic43C22×C411yescharacteristic
172C22×Dic43C22×C414yes—
173C22×Dic43C2×D412yes—
174C22×Dic43C2×D412yes—
175C22×Dic43C2×D412yes—
176C22×Dic43C2×D412yes—
177C22×Dic43#4114yes—
178#10621900—216no—
179#10621900—216no—
180C2×C4×D43—21no—
181C2×C4×D43—21no—
182C2×C4×D43—22no—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×C4×D43—42no—
188C2×C4×D43—42no—
189C2×C4×D43C4214yescomplemented
190C2×Dic86—22no—
191C2×Dic86—22no—
192C2×Dic86C4214yescomplemented
193C4⋊C4×C43—22no—
194C22⋊C4×C43—22no—
195C22⋊C4×C43—22no—
196C22⋊C4×C43—24no—
197C22⋊C4×C43C22×C418yes—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43—44no—
201C22⋊Dic43—22no—
202C22⋊Dic43—22no—
203C22⋊Dic43—24no—
204C22⋊Dic43C22×C418yes—
205(C2×D43)⋊C4—22no—
206(C2×D43)⋊C4—22no—
207C4⋊Dic43—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212Dic43⋊C4—216no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C4×Dic43—21no—
219C4×Dic43—21no—
220C4×Dic43—21no—
221C4×Dic43—21no—
222C4×Dic43—21no—
223C4×Dic43—216no—
224C4×Dic43—48no—
225C4×Dic43—44no—
226C4×Dic43C22⋊C411yescharacteristic
227C4×Dic43C22⋊C411yescharacteristic
228C4×Dic43C22⋊C411yescharacteristic
229C4×Dic43C22⋊C411yescharacteristic
230C4×Dic43C22⋊C412yes—
231C4×Dic43C22⋊C412yes—
232C4×Dic43C22⋊C412yes—
233C4×Dic43C22⋊C412yes—
234C4×Dic43C22⋊C412yes—
235C4×Dic43C22⋊C412yes—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—41no—
239C23×C43—41no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43C2×C4212yes—
243C23×C43C23×C411yescharacteristic
244C23×C43C23×C412yes—
245C23×C43C22×D412yes—
246C23×C43C2×#4112yes—
247C22×D43—21no—
248C22×D43—21no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43C2×C4212yes—
252D4×C43—28no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—24no—
256C2×C4×C43—22no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—28no—
260C2×C4×C43—41no—
261C2×C4×C43—42no—
262C2×C4×C43—42no—
263C2×C4×C43—44no—
264C2×C4×C43—44no—
265C2×C4×C43—42no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43C2×C4212yes—
269C2×C4×C43C2×C22⋊C411yescharacteristic
270C2×C4×C43C2×C22⋊C412yes—
271C2×C4×C43C2×C22⋊C411yescharacteristic
272C22⋊D43—28no—
273C22⋊D43—28no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—24no—
277C2×Dic43—24no—
278C2×Dic43—24no—
279C2×Dic43—22no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—28no—
283C2×Dic43—41no—
284C2×Dic43—42no—
285C2×Dic43—42no—
286C2×Dic43—44no—
287C2×Dic43—44no—
288C2×Dic43—42no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43C2×C4212yes—
292C2×Dic43C2×C4212yes—
293C2×Dic43C2×C4212yes—
294C2×Dic43C2×C22⋊C411yescharacteristic
295C2×Dic43C2×C22⋊C412yes—
296C2×Dic43C2×C22⋊C411yescharacteristic
297C2×Dic43C2×C22⋊C411yescharacteristic
298C2×Dic43C2×C22⋊C412yes—
299C2×Dic43C2×C22⋊C411yescharacteristic
300C2×Dic43#11712yes—
301C2×Dic43#11712yes—
302C2×Dic43C4×D418yes—
303C2×Dic43C4×D418yes—
304C4×D43—24no—
305C4×D43—24no—
306C4×D43—42no—
307C4×D43—42no—
308C4×D43—42no—
309C4×D43—42no—
310Dic86—28no—
311C4×#410—431nomaximal, Sylow
312C22×C43—21no—
313C22×C43—21no—
314C22×C43—22no—
315C22×C43—22no—
316C22×C43—22no—
317C22×C43—42no—
318C22×C43—42no—
319C22×C43—42no—
320C22×C43—42no—
321C22×C43—41no—
322C22×C43—41no—
323C22×C43C22×C4211yescharacteristic
324C22×C43C22×C22⋊C411yescharacteristic
325C22×C43C2×#11711yescharacteristic
326C22×C43C2×C4×D414yes—
327C2×D43—22no—
328C2×D43—42no—
329C2×D43—41no—
330C2×D43—41no—
331C2×D43—42no—
332C4×C43—21no—
333C4×C43—22no—
334C4×C43—22no—
335C4×C43—48no—
336C4×C43—41no—
337C4×C43—41no—
338C4×C43#41012yescomplemented
339Dic43—21no—
340Dic43—22no—
341Dic43—22no—
342Dic43—48no—
343Dic43—41no—
344Dic43—41no—
345Dic43C4×C22⋊C414yes—
346Dic43C4×C22⋊C412yes—
347Dic43C4×C22⋊C412yes—
348Dic43#41012yescomplemented
349C2×C4×#41—431no—
350C2×#410—432no—
351C4×#117—432no—
352C4×#99—432no—
353C4×#99—432no—
354C4×#99—432no—
355C4×#99—431no—
356C4×#99D4311yescharacteristic, complemented
357#1740—432no—
358C2×C43—24no—
359C2×C43—21no—
360C2×C43—21no—
361C2×C43—42no—
362C2×C43C2×C4×C22⋊C411yescharacteristic
363C2×C43C2×#41011yescharacteristic
364C2×C43C2×#41011yescharacteristic
365D43—42no—
366C22×#41—431no—
367C4×#41—862no—
368C4×#41—862no—
369C4×#41—862no—
370C4×#41—862no—
371C2×C4×Q8—431no—
372C2×C4×Q8—431no—
373C2×C4×D4—431no—
374C2×C4×D4—431no—
375C2×C4×D4—431no—
376C2×C4×D4—431no—
377C2×C4×D4—431no—
378C2×C4×D4C2×D4311yescharacteristic
379C2×#117—431no—
380C2×#117—431no—
381C2×#117—431no—
382C2×#117—434no—
383C22×C42—431no—
384C22×C42—431no—
385C22×C42—431no—
386#410—4316no—
387C2×#99—432no—
388C2×#99—434no—
389C2×#99C2×D4312yes—
390C4×C4⋊C4—862no—
391C4×C4⋊C4—862no—
392C4×C22⋊C4—432no—
393C4×C22⋊C4—434no—
394C4×C22⋊C4C2×D4312yes—
395#376—862no—
396C43—862no—
397#342—434no—
398#342—432no—
399#342C2×D4312yes—
400C43C4×#41011yescharacteristic, complemented, Sylow
401C2×#41—438no—
402C2×#41—862no—
403C2×#41—862no—
404C2×#41—864no—
405C22×Q8—431no—
406C22×D4—431no—
407C22×D4—431no—
408C22×D4C22×D4311yescharacteristic
409C23×C4—431no—
410C23×C4—431no—
411C23×C4—431no—
412C23×C4—431no—
413C23×C4—431no—
414C23×C4—431no—
415C23×C4—431no—
416C23×C4C4×D4311yescharacteristic
417C23×C4C22×D4311yescharacteristic
418C4×Q8—862no—
419C4×Q8—862no—
420C4×Q8—862no—
421C4×Q8—862no—
422C4×D4—22no—
423C4×D4—22no—
424C4×D4—862no—
425C4×D4—862no—
426C4×D4—862no—
427C4×D4—862no—
428C4×D4—862no—
429C4×D4—862no—
430C4×D4—862no—
431C4×D4—862no—
432C4×D4—862no—
433C4×D4—862no—
434#117—4316no—
435#117—862no—
436#117—862no—
437#117—862no—
438#117—862no—
439#117—862no—
440#117—862no—
441#117—868no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—431no—
444C2×C4⋊C4—431no—
445C2×C4⋊C4—431no—
446C2×C4⋊C4—431no—
447C2×C4⋊C4—864no—
448C2×C4⋊C4C4×D4311yescharacteristic
449C2×C22⋊C4—434no—
450C2×C22⋊C4—431no—
451C2×C22⋊C4—431no—
452C2×C22⋊C4—431no—
453C2×C22⋊C4—431no—
454C2×C22⋊C4C4×D4311yescharacteristic
455C2×C22⋊C4C22×D4311yescharacteristic
456C2×C22⋊C4C22×D4314yes—
457C2×C42—22no—
458C2×C42—431no—
459C2×C42—431no—
460C2×C42—431no—
461C2×C42—431no—
462C2×C42—432no—
463C2×C42—432no—
464C2×C42—432no—
465C2×C42—432no—
466C2×C42—431no—
467C2×C42—431no—
468C2×C42—431no—
469C2×C42—431no—
470C2×C42—431no—
471C2×C42—861no—
472C2×C42—861no—
473C2×C42—861no—
474C2×C42—861no—
475C2×C42—861no—
476C2×C42—861no—
477C2×C42—861no—
478C2×C42—861no—
479C2×C42—864no—
480C2×C42—864no—
481C2×C42—862no—
482C2×C42C4×D4311yescharacteristic
483#99—438no—
484#99—4316no—
485#99C4×D4318yescomplemented
486#95—22no—
487#95—864no—
488#95—862no—
489C24—431no—
490C24C2×C4×D4311yescharacteristic
491C24C23×D4311yescharacteristic
492#41—8616no—
493#41—8616no—
494C2×Q8—434no—
495C2×Q8—862no—
496C2×Q8—862no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—434no—
500C2×D4—434no—
501C2×D4—862no—
502C2×D4—862no—
503C2×D4—862no—
504C2×D4—862no—
505C2×D4C2×C4×D4314yes—
506C22×C4—24no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—434no—
514C22×C4—432no—
515C22×C4—432no—
516C22×C4—434no—
517C22×C4—434no—
518C22×C4—431no—
519C22×C4—431no—
520C22×C4—432no—
521C22×C4—431no—
522C22×C4—432no—
523C22×C4—434no—
524C22×C4—431no—
525C22×C4—431no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4—862no—
529C22×C4—861no—
530C22×C4—861no—
531C22×C4—861no—
532C22×C4—861no—
533C22×C4—862no—
534C22×C4—861no—
535C22×C4—861no—
536C22×C4—864no—
537C22×C4—861no—
538C22×C4—861no—
539C22×C4—1722no—
540C22×C4—1722no—
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×C4D4×D4312yes—
549C22×C4D4×D4312yes—
550C4⋊C4—22no—
551C4⋊C4—862no—
552C4⋊C4—862no—
553C4⋊C4—862no—
554C4⋊C4—862no—
555C4⋊C4—8616no—
556C4⋊C4—862no—
557C22⋊C4—22no—
558C22⋊C4—24no—
559C22⋊C4—22no—
560C22⋊C4—438no—
561C22⋊C4—862no—
562C22⋊C4—862no—
563C22⋊C4—862no—
564C22⋊C4—864no—
565C22⋊C4—862no—
566C22⋊C4C2×C4×D4318yes—
567C42—21no—
568C42—21no—
569C42—44no—
570C42—431no—
571C42—431no—
572C42—432no—
573C42—432no—
574C42—432no—
575C42—432no—
576C42—432no—
577C42—431no—
578C42—431no—
579C42—432no—
580C42—861no—
581C42—861no—
582C42—861no—
583C42—861no—
584C42—861no—
585C42—861no—
586C42—861no—
587C42—861no—
588C42—8616no—
589C42—861no—
590C42—861no—
591C42—1724no—
592C42—1728no—
593C23—21no—
594C23—21no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—432no—
600C23—861no—
601C23—861no—
602C23—1721no—
603C23—1721no—
604C23C42×D4312yes—
605C23C22×C4×D4311yescharacteristic
606C23C22×C4×D4312yes—
607C23C2×D4×D4312yes—
608C23#41×D4312yes—
609Q8—868no—
610D4—28no—
611D4—868no—
612D4—868no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—28no—
620C2×C4—41no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—44no—
624C2×C4—44no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—432no—
629C2×C4—432no—
630C2×C4—431no—
631C2×C4—431no—
632C2×C4—431no—
633C2×C4—432no—
634C2×C4—432no—
635C2×C4—432no—
636C2×C4—438no—
637C2×C4—438no—
638C2×C4—432no—
639C2×C4—431no—
640C2×C4—432no—
641C2×C4—864no—
642C2×C4—864no—
643C2×C4—864no—
644C2×C4—864no—
645C2×C4—864no—
646C2×C4—862no—
647C2×C4—861no—
648C2×C4—861no—
649C2×C4—861no—
650C2×C4—861no—
651C2×C4—868no—
652C2×C4—1722no—
653C2×C4—1722no—
654C2×C4—1722no—
655C2×C4—1722no—
656C2×C4—1722no—
657C2×C4—1721no—
658C2×C4—1722no—
659C2×C4—1724no—
660C2×C4—1724no—
661C2×C4—1722no—
662C2×C4—1721no—
663C2×C4—1721no—
664C2×C4C42×D4312yes—
665C2×C4C22⋊C4×D4311yescharacteristic
666C2×C4C22⋊C4×D4312yes—
667C2×C4C22⋊C4×D4311yescharacteristic
668C22—22no—
669C22—21no—
670C22—22no—
671C22—21no—
672C22—22no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—41no—
678C22—41no—
679C22—862no—
680C22—1722no—
681C22—1722no—
682C22—1721no—
683C22—1721no—
684C22C2×C42×D4311yescharacteristic
685C22C2×C22⋊C4×D4311yescharacteristic
686C22#117×D4311yescharacteristic
687C22C4×D4×D4314yes—
688C4—21no—
689C4—22no—
690C4—22no—
691C4—48no—
692C4—41no—
693C4—41no—
694C4—432no—
695C4—432no—
696C4—432no—
697C4—434no—
698C4—861no—
699C4—862no—
700C4—862no—
701C4—1728no—
702C4—1721no—
703C4—1721no—
704C4#1458287112yesdirect product factor
705C2—24no—
706C2—21no—
707C2—21no—
708C2—42no—
709C2—1722no—
710C2C4×C22⋊C4×D4311yescharacteristic
711C2#410×D4311yescharacteristic
712C2C2×#1458287111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC22×C43C22×C42
FrattiniC24C23×D43
FittingC4×#99×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC22×#10621900C22
cosocleC24×C43C24
hypercenterC4×#99D43
hypocenterC43C4×#410
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. C4×#13063281C2semidirect
4. #99×Dic43C2semidirect
5. C4×#13063239C2semidirect
6. C4×#13063240C2semidirect
7. #19134382C2semidirect
8. #19134326C2semidirect
9. C4×#99×C43C2semidirect
15. C2×C4×Dic86C4semidirect
16. C2×#13063290C4semidirect
18. C2×C4×C22⋊D43C4semidirect
20. C2×(C22⋊D43)⋊C4C4semidirect
22. C2×#13063283C4semidirect
23. C2×#13063281C4semidirect
26. C22×C4×Dic43C4semidirect
28. C2×C42×D43C4semidirect
29. #14582871C4direct (N × H)
79. #13063281C2×C4semidirect
115. #13063240C2×C4semidirect
116. #13063239C2×C4semidirect
130. #99×C43C2×C4semidirect
154. C2×C22⋊D43C42semidirect
164. C22×Dic43C42semidirect
189. C2×C4×D43C42semidirect
192. C2×Dic86C42semidirect
338. C4×C43#410semidirect
348. Dic43#410semidirect
356. C4×#99D43semidirect
400. C43C4×#410semidirect
485. #99C4×D43semidirect
704. C4#14582871direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#106219002
C2×#145828712
C4×#130632812
#99×Dic432
C4×#130632392
C4×#130632402
#191343822
#191343262
C4×#99×C432
C4×#41043