Finite Group Databasebeta

← C2×#19139926 #25267075

Subgroups — C2×#19139926 #25267075

Order 11008.

2550 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139926C2116yesmaximal, direct product factor
2C2×#14582840C211yesmaximal, characteristic, complemented
3C2×#14582827C211yesmaximal, characteristic, complemented
4C2×#14582824C211yesmaximal, characteristic, complemented
5C2×#14582813C211yesmaximal, characteristic
6C2×#14582793C211yesmaximal, characteristic, complemented
7C2×#14582792C211yesmaximal, characteristic, complemented
8C2×#14582786C211yesmaximal, characteristic, complemented
9C2×#14582781C211yesmaximal, characteristic, complemented
10C2×#14582779C211yesmaximal, characteristic
11C2×#14582772C211yesmaximal, characteristic, complemented
12C2×#14582766C211yesmaximal, characteristic, complemented
13C2×#14582757C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic43C211yesmaximal, characteristic, complemented
16C2×C43×#386C211yesmaximal, characteristic
17C24×Dic43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23C22×C22⋊Dic43C2211yescharacteristic
24C22×C22⋊Dic43C2211yescharacteristic
25C22×C22⋊Dic43C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33#14582840C2218yescomplemented
34#14582827C2218yescomplemented
35#14582824C2218yescomplemented
36#14582813C2218yes—
37#14582793C2218yescomplemented
38#14582792C2218yescomplemented
39#14582786C2218yescomplemented
40#14582781C2218yescomplemented
41#14582779C2218yes—
42#14582772C2218yescomplemented
43#14582766C2218yescomplemented
44#14582757C2218yescomplemented
45C22⋊C4×Dic43C2218yescomplemented
46C4×C22⋊Dic43C2218yescomplemented
47C2×C43⋊#95C2211yescharacteristic
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×D4×C43C2211yescharacteristic
60C24×C4×C43C2211yescharacteristic
61C22×C22⋊C4×C43C2211yescharacteristic
62C22×C22⋊C4×C43C2211yescharacteristic
63C22×C22⋊C4×C43C2211yescharacteristic
64C43×#386C2218yes—
65C2×#95×C43C2211yescharacteristic
66C2×#95×C43C2211yescharacteristic
67C23×Dic43—24no—
68C23×Dic43—24no—
69C23×Dic43—42no—
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2314yes—
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C2×C4⋊Dic43—42no—
80C2×C4⋊Dic43C2314yes—
81C2×Dic43⋊C4—24no—
82C2×Dic43⋊C4—24no—
83C2×Dic43⋊C4—42no—
84C2×Dic43⋊C4—42no—
85C2×Dic43⋊C4C2314yes—
86C2×Dic43⋊C4C2314yes—
87C2×Dic43⋊C4C2314yes—
88C2×Dic43⋊C4C2314yes—
89C2×C22⋊Dic43—24no—
90C2×C22⋊Dic43—24no—
91C2×C22⋊Dic43—24no—
92C2×C22⋊Dic43—24no—
93C2×C22⋊Dic43—24no—
94C2×C22⋊Dic43—42no—
95C2×C22⋊Dic43—42no—
96C2×C22⋊Dic43C2314yes—
97C2×C22⋊Dic43C2314yes—
98C2×C22⋊Dic43C2314yes—
99C2×C22⋊Dic43C2314yes—
100C2×C22⋊Dic43C2314yes—
101C2×C22⋊Dic43C2314yes—
102C2×C22⋊Dic43C2314yes—
103C2×C4×Dic43—24no—
104C2×C4×Dic43—42no—
105C2×C4×Dic43—42no—
106C2×C4×Dic43C2314yes—
107C2×C4×Dic43C2314yes—
108C2×C4×Dic43C2314yes—
109C43⋊#95C2314yes—
110C43⋊#95C2314yes—
111C43⋊#95C2314yes—
112C43⋊#95C2314yes—
113C43⋊#95C2314yes—
114C43⋊#95C2314yes—
115C43⋊#95C2314yes—
116C43⋊#95C2314yes—
117C43⋊#95C2314yes—
118C43⋊#95C2314yes—
119C43⋊#95C2314yes—
120C43⋊#95C2314yes—
121C25×C43C2311yescharacteristic
122C25×C43C2311yescharacteristic
123C22×D4×C43—24no—
124C22×D4×C43—24no—
125C22×D4×C43—42no—
126C22×D4×C43C2314yes—
127C23×C4×C43—24no—
128C23×C4×C43—42no—
129C23×C4×C43—42no—
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2314yes—
136C2×C22⋊C4×C43—24no—
137C2×C22⋊C4×C43—24no—
138C2×C22⋊C4×C43—42no—
139C2×C22⋊C4×C43C2314yes—
140C2×C22⋊C4×C43C2314yes—
141C2×C22⋊C4×C43C2314yes—
142#95×C43C2314yes—
143#95×C43C2314yes—
144C24×C43—22no—
145C24×C43—22no—
146C24×C43—22no—
147C24×C43—22no—
148C24×C43—22no—
149C24×C43—22no—
150C24×C43—22no—
151C24×C43—22no—
152C24×C43—22no—
153C24×C43—22no—
154C24×C43—22no—
155C24×C43—22no—
156C24×C43#4114yes—
157C24×C43#4114yes—
158C24×C43C2412yes—
159C24×C43C2412yes—
160C24×C43C2411yescharacteristic
161C2×D4×C43—28no—
162C2×D4×C43—28no—
163C2×D4×C43—44no—
164C2×D4×C43—416no—
165C22×C4×C43—28no—
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—22no—
173C22×C4×C43—22no—
174C22×C4×C43—22no—
175C22×C4×C43—22no—
176C22×C4×C43—22no—
177C22×C4×C43—22no—
178C22×C4×C43—22no—
179C22×C4×C43—22no—
180C22×C4×C43—44no—
181C22×C4×C43—44no—
182C22×C4×C43—416no—
183C22×C4×C43#4114yes—
184C22×C4×C43C2412yes—
185C22×C4×C43C2412yes—
186C22×C4×C43C2412yes—
187C22×C4×C43C2412yes—
188C22×C4×C43C2412yes—
189C22×Dic43—28no—
190C22×Dic43—28no—
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—22no—
201C22×Dic43—22no—
202C22×Dic43—22no—
203C22×Dic43—22no—
204C22×Dic43—22no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43—22no—
208C22×Dic43—22no—
209C22×Dic43—22no—
210C22×Dic43—22no—
211C22×Dic43—22no—
212C22×Dic43—22no—
213C22×Dic43—44no—
214C22×Dic43—416no—
215C22×Dic43#4114yes—
216C22×Dic43#4114yes—
217C22×Dic43C2412yes—
218C22×Dic43C2412yes—
219C22×Dic43C2412yes—
220C22×Dic43C2412yes—
221C22×Dic43C2412yes—
222C22×Dic43C2412yes—
223C22×Dic43C2412yes—
224C22×Dic43C2412yes—
225C22⋊C4×C43—28no—
226C22⋊C4×C43—28no—
227C22⋊C4×C43—44no—
228C22⋊Dic43—28no—
229C22⋊Dic43—28no—
230C22⋊Dic43—28no—
231C22⋊Dic43—28no—
232C22⋊Dic43—28no—
233C22⋊Dic43—44no—
234C22⋊Dic43—44no—
235C4⋊Dic43—44no—
236Dic43⋊C4—28no—
237Dic43⋊C4—28no—
238Dic43⋊C4—44no—
239Dic43⋊C4—44no—
240C4×Dic43—28no—
241C4×Dic43—44no—
242C4×Dic43—44no—
243C23×C43—28no—
244C23×C43—28no—
245C23×C43—28no—
246C23×C43—28no—
247C23×C43—28no—
248C23×C43—28no—
249C23×C43—22no—
250C23×C43—22no—
251C23×C43—22no—
252C23×C43—22no—
253C23×C43—22no—
254C23×C43—22no—
255C23×C43—22no—
256C23×C43—22no—
257C23×C43—22no—
258C23×C43—22no—
259C23×C43—22no—
260C23×C43—22no—
261C23×C43—44no—
262C23×C43—44no—
263C23×C43—44no—
264C23×C43—44no—
265C23×C43—44no—
266C23×C43—44no—
267C23×C43—44no—
268C23×C43—44no—
269C23×C43C2×#4112yes—
270C23×C43C2×#4112yes—
271C23×C43C2×#4114yes—
272C23×C43C2×#4112yes—
273C23×C43C2×#4112yes—
274C23×C43C2×#4114yes—
275C23×C43C2×#4112yes—
276C23×C43H(5,𝔽2)12yes—
277C23×C43H(5,𝔽2)12yes—
278C23×C43C2511yescharacteristic
279D4×C43—416no—
280C2×C4×C43—28no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—416no—
296C2×C4×C43—44no—
297C2×C4×C43—44no—
298C2×C4×C43—44no—
299C2×C4×C43—44no—
300C2×C4×C43C2×#4114yes—
301C2×Dic43—28no—
302C2×Dic43—28no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—416no—
326C2×Dic43—44no—
327C2×Dic43—44no—
328C2×Dic43—44no—
329C2×Dic43—44no—
330C2×Dic43—44no—
331C2×Dic43—44no—
332C2×Dic43C2×#4114yes—
333C2×Dic43C2×#4114yes—
334C2×#2578—431nomaximal, Sylow
335C22×C43—24no—
336C22×C43—24no—
337C22×C43—24no—
338C22×C43—24no—
339C22×C43—24no—
340C22×C43—24no—
341C22×C43—416no—
342C22×C43—416no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43#52914yes—
352C22×C43#52914yes—
353C22×C43#53814yes—
354C22×C43#55114yes—
355C22×C43#55114yes—
356C22×C43#55314yes—
357C22×C43#55314yes—
358C22×C43C22×#4111yescharacteristic
359C22×C43C22×#4111yescharacteristic
360C22×C43C22×#4111yescharacteristic
361C22×C43C22×#4111yescharacteristic
362C22×C43C22×#4111yescharacteristic
363C22×C43C2×H(5,𝔽2)11yescharacteristic
364C22×C43C2×H(5,𝔽2)11yescharacteristic
365C4×C43—24no—
366C4×C43—42no—
367C4×C43—42no—
368C4×C43—42no—
369C4×C43—42no—
370Dic43—24no—
371Dic43—24no—
372Dic43—42no—
373Dic43—42no—
374Dic43—42no—
375Dic43—42no—
376Dic43—42no—
377Dic43—42no—
378#2578—4316no—
379C2×#400—431no—
380C2×#397—431no—
381C2×#397—431no—
382C2×#394—431no—
383C2×#388—431no—
384C2×#388—431no—
385C2×#387—431no—
386C2×#387—431no—
387C2×#386—431no—
388C2×#386D4311yescharacteristic
389C2×#385—431no—
390C2×#383—431no—
391C2×#380—431no—
392C2×C4×C22⋊C4—431no—
393C2×C4×C22⋊C4—431no—
394C2×C43—44no—
395C2×C43—44no—
396C2×C43#257818yescomplemented
397C2×C43C2×#52911yescharacteristic
398C2×C43C2×#52911yescharacteristic
399C2×C43C2×#53811yescharacteristic
400C2×C43C2×#55111yescharacteristic
401C2×C43C2×#55111yescharacteristic
402C2×C43C2×#55311yescharacteristic
403C2×C43C2×#55311yescharacteristic
404C23×D4C2×D4311yescharacteristic
405C24×C4—431no—
406C24×C4C2×D4311yescharacteristic
407C22×C4⋊C4—431no—
408C22×C4⋊C4—431no—
409C22×C4⋊C4—431no—
410C22×C4⋊C4—431no—
411C22×C4⋊C4—431no—
412C22×C22⋊C4—431no—
413C22×C22⋊C4—431no—
414C22×C22⋊C4—431no—
415C22×C22⋊C4—431no—
416C22×C22⋊C4—431no—
417C22×C22⋊C4—431no—
418C22×C22⋊C4—431no—
419C22×C22⋊C4C2×D4311yescharacteristic
420C22×C22⋊C4C2×D4311yescharacteristic
421C22×C22⋊C4C2×D4311yescharacteristic
422C22×C42—431no—
423C22×C42—431no—
424C22×C42—431no—
425#400—438no—
426#397—438no—
427#397—438no—
428#394—438no—
429#388—438no—
430#388—438no—
431#387—438no—
432#387—438no—
433#386—438no—
434#386C2×D4318yes—
435#385—438no—
436#383—438no—
437#380—438no—
438C4×C22⋊C4—438no—
439C4×C22⋊C4—438no—
440C2×#95—431no—
441C2×#95—431no—
442C2×#95—431no—
443C2×#95—431no—
444C2×#95—431no—
445C2×#95—431no—
446C2×#95—431no—
447C2×#95—431no—
448C2×#95—431no—
449C2×#95—431no—
450C2×#95—431no—
451C2×#95—431no—
452C2×#95C2×D4311yescharacteristic
453C2×#95C2×D4311yescharacteristic
454C43C2×#257811yescharacteristic, complemented, Sylow
455C25C22×D4311yescharacteristic
456C25C22×D4311yescharacteristic
457C22×D4—24no—
458C22×D4—24no—
459C22×D4—42no—
460C22×D4C22×D4314yes—
461C23×C4—24no—
462C23×C4—42no—
463C23×C4—42no—
464C23×C4—431no—
465C23×C4—431no—
466C23×C4—431no—
467C23×C4—431no—
468C23×C4—431no—
469C23×C4—431no—
470C23×C4—431no—
471C23×C4—431no—
472C23×C4—434no—
473C23×C4—864no—
474C23×C4—864no—
475C23×C4—1722no—
476C23×C4C22×D4311yescharacteristic
477C23×C4C22×D4311yescharacteristic
478C23×C4C22×D4311yescharacteristic
479C23×C4C22×D4311yescharacteristic
480C23×C4C22×D4311yescharacteristic
481C23×C4C22×D4314yes—
482C2×C4⋊C4—434no—
483C2×C4⋊C4—434no—
484C2×C4⋊C4—434no—
485C2×C4⋊C4—434no—
486C2×C4⋊C4—434no—
487C2×C4⋊C4—864no—
488C2×C4⋊C4—864no—
489C2×C4⋊C4—1722no—
490C2×C4⋊C4—1722no—
491C2×C4⋊C4—1722no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—434no—
496C2×C22⋊C4—434no—
497C2×C22⋊C4—434no—
498C2×C22⋊C4—434no—
499C2×C22⋊C4—434no—
500C2×C22⋊C4—434no—
501C2×C22⋊C4—434no—
502C2×C22⋊C4—864no—
503C2×C22⋊C4—864no—
504C2×C22⋊C4—864no—
505C2×C22⋊C4—864no—
506C2×C22⋊C4—864no—
507C2×C22⋊C4—1722no—
508C2×C22⋊C4—1722no—
509C2×C22⋊C4C22×D4314yes—
510C2×C22⋊C4C22×D4314yes—
511C2×C22⋊C4C22×D4314yes—
512C2×C42—434no—
513C2×C42—434no—
514C2×C42—434no—
515C2×C42—864no—
516C2×C42—1722no—
517C2×C42—1722no—
518#95—434no—
519#95—434no—
520#95—434no—
521#95—434no—
522#95—434no—
523#95—434no—
524#95—434no—
525#95—434no—
526#95—434no—
527#95—434no—
528#95—434no—
529#95—434no—
530#95C22×D4314yes—
531#95C22×D4314yes—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24#1062189814yes—
545C24#1062190014yes—
546C24C23×D4312yes—
547C24C23×D4312yes—
548C24C23×D4311yescharacteristic
549C2×D4—28no—
550C2×D4—28no—
551C2×D4—44no—
552C2×D4—416no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—28no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—416no—
571C22×C4—434no—
572C22×C4—434no—
573C22×C4—432no—
574C22×C4—432no—
575C22×C4—432no—
576C22×C4—432no—
577C22×C4—432no—
578C22×C4—432no—
579C22×C4—432no—
580C22×C4—432no—
581C22×C4—868no—
582C22×C4—868no—
583C22×C4—862no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—862no—
591C22×C4—862no—
592C22×C4—862no—
593C22×C4—862no—
594C22×C4—862no—
595C22×C4—862no—
596C22×C4—862no—
597C22×C4—862no—
598C22×C4—862no—
599C22×C4—862no—
600C22×C4—862no—
601C22×C4—862no—
602C22×C4—862no—
603C22×C4—862no—
604C22×C4—862no—
605C22×C4—1724no—
606C22×C4—17216no—
607C22×C4#1062190014yes—
608C22×C4C23×D4312yes—
609C22×C4C23×D4312yes—
610C22×C4C23×D4312yes—
611C22×C4C23×D4312yes—
612C22×C4C23×D4312yes—
613C4⋊C4—868no—
614C4⋊C4—868no—
615C4⋊C4—1724no—
616C4⋊C4—1724no—
617C4⋊C4—1724no—
618C22⋊C4—28no—
619C22⋊C4—28no—
620C22⋊C4—44no—
621C22⋊C4—868no—
622C22⋊C4—868no—
623C22⋊C4—868no—
624C22⋊C4—868no—
625C22⋊C4—868no—
626C22⋊C4—1724no—
627C22⋊C4—1724no—
628C42—868no—
629C42—1724no—
630C42—1724no—
631C23—28no—
632C23—28no—
633C23—28no—
634C23—28no—
635C23—28no—
636C23—28no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23#41×D4312yes—
658C23#41×D4312yes—
659C23C2×#1062190014yes—
660C23C2×#1062190012yes—
661C23C2×#1062190012yes—
662C23C2×#1062189814yes—
663C23C2×#1062189812yes—
664C23#1306337012yes—
665C23#1306337012yes—
666C23C24×D4311yescharacteristic
667D4—416no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—28no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—416no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—434no—
689C2×C4—434no—
690C2×C4—868no—
691C2×C4—868no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—862no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—17216no—
715C2×C4—1724no—
716C2×C4—1724no—
717C2×C4—1724no—
718C2×C4—1724no—
719C2×C4—1724no—
720C2×C4—1724no—
721C2×C4C2×#1062190014yes—
722C22—24no—
723C22—24no—
724C22—24no—
725C22—24no—
726C22—24no—
727C22—24no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—416no—
735C22—416no—
736C22—42no—
737C22—42no—
738C22#1458342914yes—
739C22#1458343014yes—
740C22#1458348414yes—
741C22#1458357514yes—
742C22#1458357714yes—
743C22#1458359214yes—
744C22#1458359814yes—
745C22C2×#41×D4311yescharacteristic
746C22C2×#41×D4311yescharacteristic
747C22C22×#1062190011yescharacteristic
748C22C22×#1062190011yescharacteristic
749C22C22×#1062189811yescharacteristic
750C22C2×#1306337011yescharacteristic
751C22C2×#1306337011yescharacteristic
752C4—24no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—864no—
758C4—864no—
759C4—1722no—
760C4—1722no—
761C4—1722no—
762C4—1722no—
763C4—1722no—
764C4—1722no—
765C2—44no—
766C2—44no—
767C2#1913992618yesdirect product factor
768C2C2×#1458342911yescharacteristic
769C2C2×#1458343011yescharacteristic
770C2C2×#1458348411yescharacteristic
771C2C2×#1458357511yescharacteristic
772C2C2×#1458357711yescharacteristic
773C2C2×#1458359211yescharacteristic
774C2C2×#1458359811yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#386C2
socleC24×C43C24
prime radicalC23×D4×C43C22
hypercenterC2×#386D43
hypocenterC43C2×#2578
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. #19139926C2direct (N × H)
2. C2×#14582840C2semidirect
3. C2×#14582827C2semidirect
4. C2×#14582824C2semidirect
6. C2×#14582793C2semidirect
7. C2×#14582792C2semidirect
8. C2×#14582786C2semidirect
9. C2×#14582781C2semidirect
11. C2×#14582772C2semidirect
12. C2×#14582766C2semidirect
13. C2×#14582757C2semidirect
14. C2×C22⋊C4×Dic43C2semidirect
15. C2×C4×C22⋊Dic43C2semidirect
33. #14582840C22semidirect
34. #14582827C22semidirect
35. #14582824C22semidirect
37. #14582793C22semidirect
38. #14582792C22semidirect
39. #14582786C22semidirect
40. #14582781C22semidirect
42. #14582772C22semidirect
43. #14582766C22semidirect
44. #14582757C22semidirect
45. C22⋊C4×Dic43C22semidirect
46. C4×C22⋊Dic43C22semidirect
396. C2×C43#2578semidirect
454. C43C2×#2578semidirect
767. C2#19139926direct (N × H)

Maximal subgroups

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

subgroupindex
#191399262
C2×#145828402
C2×#145828272
C2×#145828242
C2×#145828132
C2×#145827932
C2×#145827922
C2×#145827862
C2×#145827812
C2×#145827792
C2×#145827722
C2×#145827662
C2×#145827572
C2×C22⋊C4×Dic432
C2×C4×C22⋊Dic432
C2×C43×#3862
C2×#257843