Finite Group Databasebeta

← C2×#19139870 #25266839

Subgroups — C2×#19139870 #25266839

Order 11008.

2334 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139870C2116yesmaximal, direct product factor
2C2×#14582833C211yesmaximal, characteristic, complemented
3C2×#14582822C211yesmaximal, characteristic
4C2×#14582818C211yesmaximal, characteristic, complemented
5C2×#14582806C211yesmaximal, characteristic, complemented
6C2×#14582793C211yesmaximal, characteristic
7C2×#14582787C211yesmaximal, characteristic
8C2×#14582781C211yesmaximal, characteristic, complemented
9C2×#14582781C211yesmaximal, characteristic, complemented
10C2×#14582781C211yesmaximal, characteristic, complemented
11C2×#14582771C211yesmaximal, characteristic
12C2×#14582763C211yesmaximal, characteristic, complemented
13C2×#14582757C211yesmaximal, characteristic
14C2×#14582750C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic43C211yesmaximal, characteristic
16C2×C43×#393C211yesmaximal, characteristic
17C24×Dic43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34#14582833C2218yescomplemented
35#14582822C2218yes—
36#14582818C2218yescomplemented
37#14582806C2218yescomplemented
38#14582793C2218yes—
39#14582787C2218yes—
40#14582781C2218yescomplemented
41#14582781C2218yescomplemented
42#14582781C2218yescomplemented
43#14582771C2218yes—
44#14582763C2218yescomplemented
45#14582757C2218yes—
46#14582750C2218yescomplemented
47C22⋊C4×Dic43C2218yes—
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C23×Q8×C43C2211yescharacteristic
60C22×C22⋊C4×C43C2211yescharacteristic
61C22×C22⋊C4×C43C2211yescharacteristic
62C22×C22⋊C4×C43C2211yescharacteristic
63C43×#393C2218yes—
64C2×#95×C43C2211yescharacteristic
65C2×#95×C43C2211yescharacteristic
66C2×#95×C43C2211yescharacteristic
67C23×Dic43—24no—
68C23×Dic43—24no—
69C23×Dic43—42no—
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2314yes—
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C2×C4⋊Dic43—42no—
80C2×C4⋊Dic43C2314yes—
81C2×Dic43⋊C4—24no—
82C2×Dic43⋊C4—24no—
83C2×Dic43⋊C4—24no—
84C2×Dic43⋊C4—24no—
85C2×Dic43⋊C4—24no—
86C2×Dic43⋊C4—42no—
87C2×Dic43⋊C4—42no—
88C2×Dic43⋊C4—42no—
89C2×Dic43⋊C4C2314yes—
90C2×Dic43⋊C4C2314yes—
91C2×Dic43⋊C4C2314yes—
92C2×Dic43⋊C4C2314yes—
93C2×Dic43⋊C4C2314yes—
94C2×Dic43⋊C4C2314yes—
95C2×Dic43⋊C4C2314yes—
96C2×Dic43⋊C4C2314yes—
97C2×C22⋊Dic43—24no—
98C2×C22⋊Dic43—42no—
99C2×C22⋊Dic43Q818yescomplemented
100C2×C22⋊Dic43C2314yes—
101C2×C22⋊Dic43C2314yes—
102C2×C22⋊Dic43C2314yes—
103C2×C4×Dic43—24no—
104C2×C4×Dic43—24no—
105C2×C4×Dic43—42no—
106C2×C4×Dic43—42no—
107C2×C4×Dic43C2314yes—
108C2×C4×Dic43C2314yes—
109C2×C4×Dic43C2314yes—
110C2×C4×Dic43C2314yes—
111C43⋊#95C2314yes—
112C43⋊#95C2314yes—
113C43⋊#95C2314yes—
114C43⋊#95C2314yes—
115C43⋊#95C2314yes—
116C43⋊#95C2314yes—
117C43⋊#95C2314yes—
118C43⋊#95C2314yes—
119C43⋊#95C2314yes—
120C43⋊#95C2314yes—
121C43⋊#95C2314yes—
122C25×C43C2311yescharacteristic
123C22×Q8×C43—24no—
124C22×Q8×C43—42no—
125C22×Q8×C43—42no—
126C22×Q8×C43C2314yes—
127C23×C4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C2×C22⋊C4×C43—24no—
134C2×C22⋊C4×C43—42no—
135C2×C22⋊C4×C43—42no—
136C2×C22⋊C4×C43C2314yes—
137C2×C22⋊C4×C43C2314yes—
138C2×C22⋊C4×C43C2314yes—
139#95×C43C2314yes—
140#95×C43C2314yes—
141#95×C43C2314yes—
142C24×C43—22no—
143C24×C43—22no—
144C24×C43—22no—
145C24×C43—22no—
146C24×C43—22no—
147C24×C43—22no—
148C24×C43C2×Q814yes—
149C24×C43C2412yes—
150C24×C43C2411yescharacteristic
151C2×Q8×C43—28no—
152C2×Q8×C43—44no—
153C2×Q8×C43—44no—
154C2×Q8×C43—416no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43#4114yes—
173C22×C4×C43C2412yes—
174C22×C4×C43C2412yes—
175C22×C4×C43C2412yes—
176C22×C4×C43C2412yes—
177C22×C4×C43C2412yes—
178C22×C4×C43C2412yes—
179C22×Dic43—28no—
180C22×Dic43—28no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—44no—
201C22×Dic43—416no—
202C22×Dic43C2×Q814yes—
203C22×Dic43C2×Q814yes—
204C22×Dic43#4114yes—
205C22×Dic43#4114yes—
206C22×Dic43#4114yes—
207C22×Dic43C2412yes—
208C22×Dic43C2412yes—
209C22×Dic43C2412yes—
210C22×Dic43C2412yes—
211C22×Dic43C2412yes—
212C22×Dic43C2412yes—
213C22×Dic43C2412yes—
214C22×Dic43C2412yes—
215C22⋊C4×C43—28no—
216C22⋊C4×C43—44no—
217C22⋊C4×C43—44no—
218C22⋊Dic43—28no—
219C22⋊Dic43—44no—
220C22⋊Dic43C2×Q8116yescomplemented
221C4⋊Dic43—44no—
222Dic43⋊C4—28no—
223Dic43⋊C4—28no—
224Dic43⋊C4—28no—
225Dic43⋊C4—28no—
226Dic43⋊C4—28no—
227Dic43⋊C4—44no—
228Dic43⋊C4—44no—
229Dic43⋊C4—44no—
230C4×Dic43—28no—
231C4×Dic43—28no—
232C4×Dic43—44no—
233C4×Dic43—44no—
234C23×C43—28no—
235C23×C43—28no—
236C23×C43—28no—
237C23×C43—22no—
238C23×C43—22no—
239C23×C43—22no—
240C23×C43—22no—
241C23×C43—22no—
242C23×C43—22no—
243C23×C43—44no—
244C23×C43—44no—
245C23×C43—44no—
246C23×C43—44no—
247C23×C43C22×Q814yes—
248C23×C43C22×Q812yes—
249C23×C43C2×#4112yes—
250C23×C43C2×#4112yes—
251C23×C43C2×#4112yes—
252C23×C43C2×#4112yes—
253C23×C43H(5,𝔽2)12yes—
254C23×C43H(5,𝔽2)12yes—
255C23×C43C2511yescharacteristic
256Q8×C43—416no—
257C2×C4×C43—28no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—44no—
276C2×C4×C43—44no—
277C2×C4×C43—44no—
278C2×C4×C43—44no—
279C2×C4×C43—44no—
280C2×C4×C43C2×#4114yes—
281C2×Dic43—28no—
282C2×Dic43—28no—
283C2×Dic43—28no—
284C2×Dic43—28no—
285C2×Dic43—28no—
286C2×Dic43—22no—
287C2×Dic43—22no—
288C2×Dic43—22no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—416no—
306C2×Dic43—44no—
307C2×Dic43—44no—
308C2×Dic43—44no—
309C2×Dic43C22×Q814yes—
310C2×Dic43C22×Q814yes—
311C2×Dic43C2×#4114yes—
312C2×Dic43C2×#4114yes—
313C2×Dic43C2×#4114yes—
314C2×#2574—431nomaximal, Sylow
315C22×C43—24no—
316C22×C43—24no—
317C22×C43—24no—
318C22×C43—416no—
319C22×C43—42no—
320C22×C43—42no—
321C22×C43—42no—
322C22×C43—42no—
323C22×C43#52914yes—
324C22×C43#53314yes—
325C22×C43#53814yes—
326C22×C43#55114yes—
327C22×C43#55414yes—
328C22×C43#55414yes—
329C22×C43#55514yes—
330C22×C43C23×Q811yescharacteristic
331C22×C43C22×#4111yescharacteristic
332C22×C43C22×#4111yescharacteristic
333C22×C43C22×#4111yescharacteristic
334C22×C43C22×#4111yescharacteristic
335C22×C43C2×H(5,𝔽2)11yescharacteristic
336C22×C43C2×H(5,𝔽2)11yescharacteristic
337C4×C43—24no—
338C4×C43—42no—
339C4×C43—42no—
340C4×C43—42no—
341C4×C43—42no—
342C4×C43—42no—
343Dic43—24no—
344Dic43—24no—
345Dic43—24no—
346Dic43—24no—
347Dic43—24no—
348Dic43—42no—
349Dic43—42no—
350Dic43—42no—
351#2574—4316no—
352C2×#398—431no—
353C2×#396—431no—
354C2×#395—431no—
355C2×#393D4311yescharacteristic
356C2×#391—431no—
357C2×#388—431no—
358C2×#388—431no—
359C2×#387—431no—
360C2×#387—431no—
361C2×#387—431no—
362C2×#385—431no—
363C2×#382—431no—
364C2×#380—431no—
365C2×C4×C4⋊C4—431no—
366C2×C4×C22⋊C4—431no—
367C2×C43—44no—
368C2×C43#257418yescomplemented
369C2×C43C2×#52911yescharacteristic
370C2×C43C2×#53311yescharacteristic
371C2×C43C2×#53811yescharacteristic
372C2×C43C2×#55111yescharacteristic
373C2×C43C2×#55411yescharacteristic
374C2×C43C2×#55411yescharacteristic
375C2×C43C2×#55511yescharacteristic
376C23×Q8C2×D4311yescharacteristic
377C24×C4—431no—
378C22×C4⋊C4—431no—
379C22×C4⋊C4—431no—
380C22×C4⋊C4—431no—
381C22×C4⋊C4—431no—
382C22×C4⋊C4—431no—
383C22×C4⋊C4—431no—
384C22×C4⋊C4—431no—
385C22×C4⋊C4—431no—
386C22×C4⋊C4—431no—
387C22×C22⋊C4—431no—
388C22×C22⋊C4—431no—
389C22×C22⋊C4—431no—
390C22×C22⋊C4C2×D4311yescharacteristic
391C22×C22⋊C4C2×D4311yescharacteristic
392C22×C22⋊C4C2×D4311yescharacteristic
393C22×C42—431no—
394C22×C42—431no—
395C22×C42—431no—
396C22×C42—431no—
397#398—438no—
398#396—438no—
399#395—438no—
400#393C2×D4318yes—
401#391—438no—
402#388—438no—
403#388—438no—
404#387—438no—
405#387—438no—
406#387—438no—
407#385—438no—
408#382—438no—
409#380—438no—
410C4×C4⋊C4—438no—
411C4×C22⋊C4—438no—
412C2×#95—431no—
413C2×#95—431no—
414C2×#95—431no—
415C2×#95—431no—
416C2×#95—431no—
417C2×#95—431no—
418C2×#95—431no—
419C2×#95—431no—
420C2×#95—431no—
421C2×#95—431no—
422C2×#95—431no—
423C2×#95C2×D4311yescharacteristic
424C2×#95C2×D4311yescharacteristic
425C2×#95C2×D4311yescharacteristic
426C43C2×#257411yescharacteristic, complemented, Sylow
427C25C22×D4311yescharacteristic
428C22×Q8—24no—
429C22×Q8—42no—
430C22×Q8—42no—
431C22×Q8C22×D4314yes—
432C23×C4—431no—
433C23×C4—431no—
434C23×C4—431no—
435C23×C4—431no—
436C23×C4—431no—
437C23×C4—431no—
438C23×C4—431no—
439C23×C4—431no—
440C23×C4—434no—
441C23×C4—864no—
442C23×C4—864no—
443C23×C4—1722no—
444C23×C4C22×D4311yescharacteristic
445C23×C4C22×D4311yescharacteristic
446C23×C4C22×D4311yescharacteristic
447C23×C4C22×D4311yescharacteristic
448C23×C4C22×D4311yescharacteristic
449C23×C4C22×D4311yescharacteristic
450C2×C4⋊C4—434no—
451C2×C4⋊C4—434no—
452C2×C4⋊C4—434no—
453C2×C4⋊C4—434no—
454C2×C4⋊C4—434no—
455C2×C4⋊C4—434no—
456C2×C4⋊C4—434no—
457C2×C4⋊C4—434no—
458C2×C4⋊C4—434no—
459C2×C4⋊C4—864no—
460C2×C4⋊C4—864no—
461C2×C4⋊C4—864no—
462C2×C4⋊C4—864no—
463C2×C4⋊C4—864no—
464C2×C4⋊C4—1722no—
465C2×C4⋊C4—1722no—
466C2×C4⋊C4—1722no—
467C2×C4⋊C4—1722no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4—42no—
471C2×C22⋊C4—438no—
472C2×C22⋊C4—434no—
473C2×C22⋊C4—434no—
474C2×C22⋊C4—434no—
475C2×C22⋊C4—864no—
476C2×C22⋊C4—1722no—
477C2×C22⋊C4C22×D4314yes—
478C2×C22⋊C4C22×D4314yes—
479C2×C22⋊C4C22×D4314yes—
480C2×C42—434no—
481C2×C42—434no—
482C2×C42—434no—
483C2×C42—434no—
484C2×C42—864no—
485C2×C42—864no—
486C2×C42—1722no—
487C2×C42—1722no—
488#95—434no—
489#95—434no—
490#95—434no—
491#95—434no—
492#95—434no—
493#95—434no—
494#95—434no—
495#95—434no—
496#95—434no—
497#95—434no—
498#95—434no—
499#95C22×D4314yes—
500#95C22×D4314yes—
501#95C22×D4314yes—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24Q8×D4314yes—
509C24C23×D4312yes—
510C24C23×D4311yescharacteristic
511C2×Q8—28no—
512C2×Q8—44no—
513C2×Q8—44no—
514C2×Q8—416no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
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—434no—
533C22×C4—434no—
534C22×C4—434no—
535C22×C4—434no—
536C22×C4—434no—
537C22×C4—432no—
538C22×C4—432no—
539C22×C4—432no—
540C22×C4—432no—
541C22×C4—432no—
542C22×C4—432no—
543C22×C4—432no—
544C22×C4—432no—
545C22×C4—868no—
546C22×C4—868no—
547C22×C4—862no—
548C22×C4—862no—
549C22×C4—862no—
550C22×C4—862no—
551C22×C4—862no—
552C22×C4—862no—
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—862no—
566C22×C4—1724no—
567C22×C4—17216no—
568C22×C4#1062190014yes—
569C22×C4C23×D4312yes—
570C22×C4C23×D4312yes—
571C22×C4C23×D4312yes—
572C22×C4C23×D4312yes—
573C22×C4C23×D4312yes—
574C22×C4C23×D4312yes—
575C4⋊C4—868no—
576C4⋊C4—868no—
577C4⋊C4—868no—
578C4⋊C4—868no—
579C4⋊C4—868no—
580C4⋊C4—1724no—
581C4⋊C4—1724no—
582C4⋊C4—1724no—
583C4⋊C4—1724no—
584C22⋊C4—28no—
585C22⋊C4—44no—
586C22⋊C4—44no—
587C22⋊C4—4316no—
588C22⋊C4—868no—
589C22⋊C4—1724no—
590C42—868no—
591C42—868no—
592C42—1724no—
593C42—1724no—
594C23—28no—
595C23—28no—
596C23—28no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—44no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23C2×Q8×D4314yes—
608C23C2×Q8×D4312yes—
609C23#41×D4312yes—
610C23#41×D4312yes—
611C23#41×D4312yes—
612C23C2×#1062190012yes—
613C23#1306337012yes—
614C23#1306337012yes—
615C23C24×D4311yescharacteristic
616Q8—416no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—28no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—44no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—434no—
641C2×C4—434no—
642C2×C4—434no—
643C2×C4—434no—
644C2×C4—434no—
645C2×C4—868no—
646C2×C4—868no—
647C2×C4—868no—
648C2×C4—868no—
649C2×C4—868no—
650C2×C4—862no—
651C2×C4—862no—
652C2×C4—862no—
653C2×C4—862no—
654C2×C4—862no—
655C2×C4—862no—
656C2×C4—862no—
657C2×C4—862no—
658C2×C4—862no—
659C2×C4—862no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—862no—
665C2×C4—862no—
666C2×C4—862no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—17216no—
670C2×C4—1724no—
671C2×C4—1724no—
672C2×C4—1724no—
673C2×C4C2×#1062190014yes—
674C22—24no—
675C22—24no—
676C22—24no—
677C22—416no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22#1458342814yes—
683C22#1458345114yes—
684C22#1458348414yes—
685C22#1458357914yes—
686C22#1458360314yes—
687C22#1458360314yes—
688C22#1458361114yes—
689C22C22×Q8×D4311yescharacteristic
690C22C2×#41×D4311yescharacteristic
691C22C2×#41×D4311yescharacteristic
692C22C2×#41×D4311yescharacteristic
693C22C22×#1062190011yescharacteristic
694C22C2×#1306337011yescharacteristic
695C22C2×#1306337011yescharacteristic
696C4—24no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—864no—
703C4—864no—
704C4—864no—
705C4—864no—
706C4—864no—
707C4—1722no—
708C4—1722no—
709C4—1722no—
710C2—44no—
711C2#1913987018yesdirect product factor
712C2C2×#1458342811yescharacteristic
713C2C2×#1458345111yescharacteristic
714C2C2×#1458348411yescharacteristic
715C2C2×#1458357911yescharacteristic
716C2C2×#1458360311yescharacteristic
717C2C2×#1458360311yescharacteristic
718C2C2×#1458361111yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#393C2
socleC24×C43C24
prime radicalC25×C43C23
hypercenterC2×#393D43
hypocenterC43C2×#2574
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. #19139870C2direct (N × H)
2. C2×#14582833C2semidirect
4. C2×#14582818C2semidirect
5. C2×#14582806C2semidirect
8. C2×#14582781C2semidirect
9. C2×#14582781C2semidirect
10. C2×#14582781C2semidirect
12. C2×#14582763C2semidirect
14. C2×#14582750C2semidirect
34. #14582833C22semidirect
36. #14582818C22semidirect
37. #14582806C22semidirect
40. #14582781C22semidirect
41. #14582781C22semidirect
42. #14582781C22semidirect
44. #14582763C22semidirect
46. #14582750C22semidirect
99. C2×C22⋊Dic43Q8semidirect
220. C22⋊Dic43C2×Q8semidirect
368. C2×C43#2574semidirect
426. C43C2×#2574semidirect
711. C2#19139870direct (N × H)

Maximal subgroups

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

subgroupindex
#191398702
C2×#145828332
C2×#145828222
C2×#145828182
C2×#145828062
C2×#145827932
C2×#145827872
C2×#145827812
C2×#145827712
C2×#145827632
C2×#145827572
C2×#145827502
C2×C22⋊C4×Dic432
C2×C43×#3932
C2×#257443