Finite Group Databasebeta

← C2×#19139906 #25267055

Subgroups — C2×#19139906 #25267055

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#19139906C2116yesmaximal, direct product factor
2C2×C43⋊#401C211yesmaximal, characteristic, complemented
3C2×#14582828C211yesmaximal, characteristic, complemented
4C2×#14582821C211yesmaximal, characteristic, complemented
5C2×#14582816C211yesmaximal, characteristic
6C2×#14582790C211yesmaximal, characteristic, complemented
7C2×#14582789C211yesmaximal, characteristic, complemented
8C2×#14582781C211yesmaximal, characteristic, complemented
9C2×#14582777C211yesmaximal, characteristic
10C2×#14582777C211yesmaximal, characteristic
11C2×#14582773C211yesmaximal, characteristic, complemented
12C2×#14582764C211yesmaximal, characteristic, complemented
13C2×#14582761C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
15C2×#14582746C211yesmaximal, characteristic, complemented
16C2×C43×#387C211yesmaximal, characteristic, complemented
17C23×D172C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35C43⋊#401C2218yescomplemented
36#14582828C2218yescomplemented
37#14582821C2218yescomplemented
38#14582816C2218yes—
39#14582790C2218yescomplemented
40#14582789C2218yescomplemented
41#14582781C2218yescomplemented
42#14582777C2218yes—
43#14582777C2218yes—
44#14582773C2218yescomplemented
45#14582764C2218yescomplemented
46#14582761C2218yescomplemented
47C4×(C2×D43)⋊C4C2218yescomplemented
48#14582746C2218yescomplemented
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
59C22×C4⋊C4×C43C2211yescharacteristic
60C22×C4⋊C4×C43C2211yescharacteristic
61C22×C42×C43C2211yescharacteristic
62C43×#387C2218yescomplemented
63C2×#95×C43C2211yescharacteristic
64C2×#95×C43C2211yescharacteristic
65C2×#95×C43C2211yescharacteristic
66C2×#95×C43C2211yescharacteristic
67C24×D43C2311yescharacteristic
68C24×D43C2311yescharacteristic
69C22×D172—24no—
70C22×D172—24no—
71C22×D172—42no—
72C22×D172C2314yes—
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C22×C4×D43—24no—
80C22×C4×D43—24no—
81C22×C4×D43—24no—
82C22×C4×D43—42no—
83C22×C4×D43—42no—
84C22×C4×D43—42no—
85C22×C4×D43C2314yes—
86C22×C4×D43C2314yes—
87C2×C4⋊Dic43—42no—
88C2×C4⋊Dic43C2314yes—
89C2×Dic43⋊C4—24no—
90C2×Dic43⋊C4—42no—
91C2×Dic43⋊C4C2314yes—
92C2×Dic43⋊C4C2314yes—
93C2×(C2×D43)⋊C4—24no—
94C2×(C2×D43)⋊C4—24no—
95C2×(C2×D43)⋊C4—24no—
96C2×(C2×D43)⋊C4—24no—
97C2×(C2×D43)⋊C4—24no—
98C2×(C2×D43)⋊C4—24no—
99C2×(C2×D43)⋊C4—24no—
100C2×(C2×D43)⋊C4—42no—
101C2×(C2×D43)⋊C4—42no—
102C2×(C2×D43)⋊C4—42no—
103C2×(C2×D43)⋊C4C2314yes—
104C2×(C2×D43)⋊C4C2314yes—
105C2×(C2×D43)⋊C4C2314yes—
106C2×(C2×D43)⋊C4C2314yes—
107C2×(C2×D43)⋊C4C2314yes—
108C2×(C2×D43)⋊C4C2314yes—
109C2×(C2×D43)⋊C4C2314yes—
110C2×(C2×D43)⋊C4C2314yes—
111C2×(C2×D43)⋊C4C2314yes—
112C2×(C2×D43)⋊C4C2314yes—
113C2×C4×Dic43—24no—
114C2×C4×Dic43—42no—
115C2×C4×Dic43C2314yes—
116C2×C4×Dic43C2314yes—
117C43⋊#95C2314yes—
118C43⋊#95C2314yes—
119C43⋊#95C2314yes—
120C43⋊#95C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C23×C4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43—24no—
135C2×C4⋊C4×C43—42no—
136C2×C4⋊C4×C43C2314yes—
137C2×C4⋊C4×C43C2314yes—
138C2×C42×C43—42no—
139C2×C42×C43C2314yes—
140#95×C43C2314yes—
141#95×C43C2314yes—
142#95×C43C2314yes—
143#95×C43C2314yes—
144C24×C43C2411yescharacteristic
145C23×D43—22no—
146C23×D43—22no—
147C23×D43—22no—
148C23×D43—22no—
149C23×D43—22no—
150C23×D43—22no—
151C23×D43—22no—
152C23×D43—22no—
153C23×D43—22no—
154C23×D43—22no—
155C23×D43—22no—
156C23×D43—22no—
157C23×D43#4114yes—
158C23×D43#4114yes—
159C23×D43C2412yes—
160C23×D43C2412yes—
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—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#4114yes—
181C22×C4×C43#4114yes—
182C22×C4×C43C2412yes—
183C22×C4×C43C2412yes—
184C22×C4×C43C2412yes—
185C22×C4×C43C2412yes—
186C22×C4×C43C2412yes—
187C22×C4×C43C2412yes—
188C22×C4×C43C2412yes—
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—22no—
201C22×Dic43—22no—
202C22×Dic43—22no—
203C22×Dic43—22no—
204C22×Dic43—22no—
205C22×Dic43—22no—
206C22×Dic43#4114yes—
207C22×Dic43C2412yes—
208C22×Dic43C2412yes—
209C22×Dic43C2412yes—
210C22×Dic43C2412yes—
211C22×Dic43C2412yes—
212C22×Dic43C2412yes—
213C2×D172—28no—
214C2×D172—28no—
215C2×D172—44no—
216C2×D172—416no—
217C2×C4×D43—28no—
218C2×C4×D43—28no—
219C2×C4×D43—28no—
220C2×C4×D43—44no—
221C2×C4×D43—44no—
222C2×C4×D43—44no—
223C2×C4×D43—416no—
224C2×C4×D43—416no—
225C4⋊C4×C43—28no—
226C4⋊C4×C43—44no—
227C42×C43—44no—
228(C2×D43)⋊C4—28no—
229(C2×D43)⋊C4—28no—
230(C2×D43)⋊C4—28no—
231(C2×D43)⋊C4—28no—
232(C2×D43)⋊C4—28no—
233(C2×D43)⋊C4—28no—
234(C2×D43)⋊C4—28no—
235(C2×D43)⋊C4—44no—
236(C2×D43)⋊C4—44no—
237(C2×D43)⋊C4—44no—
238C4⋊Dic43—44no—
239Dic43⋊C4—28no—
240Dic43⋊C4—44no—
241C4×Dic43—28no—
242C4×Dic43—44no—
243C23×C43C2×#4112yes—
244C23×C43C2×#4112yes—
245C23×C43C2×#4112yes—
246C23×C43C2×#4112yes—
247C23×C43C2×#4112yes—
248C23×C43H(5,𝔽2)12yes—
249C23×C43H(5,𝔽2)12yes—
250C23×C43C2511yescharacteristic
251C22×D43—28no—
252C22×D43—28no—
253C22×D43—28no—
254C22×D43—28no—
255C22×D43—28no—
256C22×D43—28no—
257C22×D43—22no—
258C22×D43—22no—
259C22×D43—22no—
260C22×D43—22no—
261C22×D43—22no—
262C22×D43—22no—
263C22×D43—22no—
264C22×D43—22no—
265C22×D43—22no—
266C22×D43—22no—
267C22×D43—22no—
268C22×D43—22no—
269C22×D43—44no—
270C22×D43—44no—
271C22×D43—44no—
272C22×D43—44no—
273C22×D43—44no—
274C22×D43—44no—
275C22×D43—44no—
276C22×D43—44no—
277C22×D43C2×#4114yes—
278C22×D43C2×#4114yes—
279C2×C4×C43—28no—
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—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—44no—
301C2×C4×C43—44no—
302C2×C4×C43—44no—
303C2×C4×C43—44no—
304C2×C4×C43—44no—
305C2×C4×C43C2×#4114yes—
306C2×C4×C43C2×#4114yes—
307C2×Dic43—28no—
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—44no—
326C2×Dic43—44no—
327C2×Dic43—44no—
328C2×Dic43—44no—
329C2×Dic43—44no—
330C2×Dic43C2×#4114yes—
331D172—416no—
332C4×D43—416no—
333C4×D43—416no—
334C2×#2576—431nomaximal, Sylow
335C22×C43#52914yes—
336C22×C43#52914yes—
337C22×C43#53814yes—
338C22×C43#55114yes—
339C22×C43#55114yes—
340C22×C43#55314yes—
341C22×C43#55314yes—
342C22×C43C22×#4111yescharacteristic
343C22×C43C22×#4111yescharacteristic
344C22×C43C22×#4111yescharacteristic
345C22×C43C22×#4111yescharacteristic
346C22×C43C22×#4111yescharacteristic
347C22×C43C2×H(5,𝔽2)11yescharacteristic
348C22×C43C2×H(5,𝔽2)11yescharacteristic
349C2×D43—24no—
350C2×D43—24no—
351C2×D43—24no—
352C2×D43—24no—
353C2×D43—24no—
354C2×D43—24no—
355C2×D43—416no—
356C2×D43—416no—
357C2×D43—42no—
358C2×D43—42no—
359C2×D43—42no—
360C2×D43—42no—
361C2×D43—42no—
362C2×D43—42no—
363C2×D43—42no—
364C2×D43—42no—
365C4×C43—24no—
366C4×C43—24no—
367C4×C43—42no—
368C4×C43—42no—
369C4×C43—42no—
370C4×C43—42no—
371C4×C43—42no—
372Dic43—24no—
373Dic43—42no—
374Dic43—42no—
375Dic43—42no—
376Dic43—42no—
377Dic43—42no—
378#2576—4316no—
379C2×#401—431no—
380C2×#397—431no—
381C2×#396—431no—
382C2×#394—431no—
383C2×#388—431no—
384C2×#388—431no—
385C2×#387—431no—
386C2×#387D4311yescharacteristic, complemented
387C2×#386—431no—
388C2×#386—431no—
389C2×#385—431no—
390C2×#382—431no—
391C2×#381—431no—
392C2×C4×C22⋊C4—431no—
393C2×C4×C22⋊C4—431no—
394C2×C43#257618yescomplemented
395C2×C43C2×#52911yescharacteristic
396C2×C43C2×#52911yescharacteristic
397C2×C43C2×#53811yescharacteristic
398C2×C43C2×#55111yescharacteristic
399C2×C43C2×#55111yescharacteristic
400C2×C43C2×#55311yescharacteristic
401C2×C43C2×#55311yescharacteristic
402D43—44no—
403D43—44no—
404C23×D4—431no—
405C24×C4—431no—
406C24×C4—431no—
407C22×C4⋊C4—431no—
408C22×C4⋊C4—431no—
409C22×C4⋊C4—431no—
410C22×C4⋊C4C2×D4311yescharacteristic
411C22×C4⋊C4C2×D4311yescharacteristic
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⋊C4—431no—
420C22×C22⋊C4—431no—
421C22×C22⋊C4—431no—
422C22×C42—431no—
423C22×C42—431no—
424C22×C42C2×D4311yescharacteristic
425#401—438no—
426#397—438no—
427#396—438no—
428#394—438no—
429#388—438no—
430#388—438no—
431#387—438no—
432#387C2×D4318yescomplemented
433#386—438no—
434#386—438no—
435#385—438no—
436#382—438no—
437#381—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×#95C2×D4311yescharacteristic
451C2×#95C2×D4311yescharacteristic
452C2×#95C2×D4311yescharacteristic
453C2×#95C2×D4311yescharacteristic
454C43C2×#257611yescharacteristic, complemented, Sylow
455C25—431no—
456C25—431no—
457C22×D4—434no—
458C22×D4—864no—
459C22×D4—864no—
460C22×D4—1722no—
461C23×C4—431no—
462C23×C4—431no—
463C23×C4—431no—
464C23×C4—431no—
465C23×C4—431no—
466C23×C4—431no—
467C23×C4—434no—
468C23×C4—434no—
469C23×C4—864no—
470C23×C4—864no—
471C23×C4—864no—
472C23×C4—1722no—
473C23×C4—1722no—
474C23×C4—1722no—
475C23×C4C22×D4311yescharacteristic
476C23×C4C22×D4311yescharacteristic
477C23×C4C22×D4311yescharacteristic
478C23×C4C22×D4311yescharacteristic
479C23×C4C22×D4311yescharacteristic
480C23×C4C22×D4311yescharacteristic
481C23×C4C22×D4311yescharacteristic
482C2×C4⋊C4—24no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—434no—
485C2×C4⋊C4—434no—
486C2×C4⋊C4—434no—
487C2×C4⋊C4—864no—
488C2×C4⋊C4—1722no—
489C2×C4⋊C4—1722no—
490C2×C4⋊C4C22×D4314yes—
491C2×C4⋊C4C22×D4314yes—
492C2×C22⋊C4—434no—
493C2×C22⋊C4—434no—
494C2×C22⋊C4—434no—
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—864no—
508C2×C22⋊C4—864no—
509C2×C22⋊C4—1722no—
510C2×C22⋊C4—1722no—
511C2×C22⋊C4—1722no—
512C2×C42—42no—
513C2×C42—434no—
514C2×C42—434no—
515C2×C42—864no—
516C2×C42—1722no—
517C2×C42C22×D4314yes—
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#95C22×D4314yes—
529#95C22×D4314yes—
530#95C22×D4314yes—
531#95C22×D4314yes—
532C24—434no—
533C24—434no—
534C24—432no—
535C24—432no—
536C24—862no—
537C24—862no—
538C24—862no—
539C24—862no—
540C24—862no—
541C24—862no—
542C24—862no—
543C24—862no—
544C24—862no—
545C24—862no—
546C24—862no—
547C24—862no—
548C24C23×D4311yescharacteristic
549C2×D4—868no—
550C2×D4—868no—
551C2×D4—1724no—
552C2×D4—17216no—
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—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—434no—
573C22×C4—432no—
574C22×C4—432no—
575C22×C4—432no—
576C22×C4—432no—
577C22×C4—432no—
578C22×C4—432no—
579C22×C4—868no—
580C22×C4—868no—
581C22×C4—862no—
582C22×C4—862no—
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—868no—
599C22×C4—1724no—
600C22×C4—1724no—
601C22×C4—1724no—
602C22×C4—17216no—
603C22×C4—17216no—
604C22×C4#1062189814yes—
605C22×C4#1062190214yes—
606C22×C4C23×D4312yes—
607C22×C4C23×D4312yes—
608C22×C4C23×D4312yes—
609C22×C4C23×D4312yes—
610C22×C4C23×D4312yes—
611C22×C4C23×D4312yes—
612C22×C4C23×D4312yes—
613C4⋊C4—28no—
614C4⋊C4—44no—
615C4⋊C4—868no—
616C4⋊C4—1724no—
617C4⋊C4—1724no—
618C22⋊C4—868no—
619C22⋊C4—868no—
620C22⋊C4—868no—
621C22⋊C4—868no—
622C22⋊C4—868no—
623C22⋊C4—868no—
624C22⋊C4—868no—
625C22⋊C4—1724no—
626C22⋊C4—1724no—
627C22⋊C4—1724no—
628C42—44no—
629C42—868no—
630C42—1724no—
631C23—434no—
632C23—434no—
633C23—868no—
634C23—868no—
635C23—868no—
636C23—868no—
637C23—868no—
638C23—868no—
639C23—862no—
640C23—862no—
641C23—862no—
642C23—862no—
643C23—862no—
644C23—862no—
645C23—862no—
646C23—862no—
647C23—862no—
648C23—862no—
649C23—862no—
650C23—862no—
651C23—1724no—
652C23—1724no—
653C23—1724no—
654C23—1724no—
655C23—1724no—
656C23—1724no—
657C23—1724no—
658C23—1724no—
659C23#41×D4312yes—
660C23#41×D4312yes—
661C23#41×D4312yes—
662C23C2×#1062189812yes—
663C23C2×#1062190212yes—
664C23#1306337012yes—
665C23#1306337112yes—
666C23C24×D4311yescharacteristic
667D4—17216no—
668C2×C4—28no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—28no—
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—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—434no—
695C2×C4—868no—
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—17216no—
714C2×C4—17216no—
715C2×C4—1724no—
716C2×C4—1724no—
717C2×C4—1724no—
718C2×C4—1724no—
719C2×C4—1724no—
720C2×C4C2×#1062189814yes—
721C2×C4C2×#1062190214yes—
722C22—864no—
723C22—864no—
724C22—864no—
725C22—864no—
726C22—864no—
727C22—864no—
728C22—1722no—
729C22—17216no—
730C22—17216no—
731C22—1722no—
732C22—1722no—
733C22—1722no—
734C22—1722no—
735C22—1722no—
736C22—1722no—
737C22—1722no—
738C22#1458343414yes—
739C22#1458343614yes—
740C22#1458348914yes—
741C22#1458357414yes—
742C22#1458357714yes—
743C22#1458359314yes—
744C22#1458359814yes—
745C22C2×#41×D4311yescharacteristic
746C22C2×#41×D4311yescharacteristic
747C22C2×#41×D4311yescharacteristic
748C22C22×#1062189811yescharacteristic
749C22C22×#1062190211yescharacteristic
750C22C2×#1306337011yescharacteristic
751C22C2×#1306337111yescharacteristic
752C4—24no—
753C4—24no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—42no—
759C4—864no—
760C4—1722no—
761C4—1722no—
762C4—1722no—
763C4—1722no—
764C4—1722no—
765C2—1724no—
766C2—1724no—
767C2#1913990618yesdirect product factor
768C2C2×#1458343411yescharacteristic
769C2C2×#1458343611yescharacteristic
770C2C2×#1458348911yescharacteristic
771C2C2×#1458357411yescharacteristic
772C2C2×#1458357711yescharacteristic
773C2C2×#1458359311yescharacteristic
774C2C2×#1458359811yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#387C2
socleC24×C43C24
prime radicalC23×D172C22
hypercenterC2×#387D43
hypocenterC43C2×#2576
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. #19139906C2direct (N × H)
2. C2×C43⋊#401C2semidirect
3. C2×#14582828C2semidirect
4. C2×#14582821C2semidirect
6. C2×#14582790C2semidirect
7. C2×#14582789C2semidirect
8. C2×#14582781C2semidirect
11. C2×#14582773C2semidirect
12. C2×#14582764C2semidirect
13. C2×#14582761C2semidirect
14. C2×C4×(C2×D43)⋊C4C2semidirect
15. C2×#14582746C2semidirect
16. C2×C43×#387C2semidirect
35. C43⋊#401C22semidirect
36. #14582828C22semidirect
37. #14582821C22semidirect
39. #14582790C22semidirect
40. #14582789C22semidirect
41. #14582781C22semidirect
44. #14582773C22semidirect
45. #14582764C22semidirect
46. #14582761C22semidirect
47. C4×(C2×D43)⋊C4C22semidirect
48. #14582746C22semidirect
62. C43×#387C22semidirect
386. C2×#387D43semidirect
394. C2×C43#2576semidirect
432. #387C2×D43semidirect
454. C43C2×#2576semidirect
767. C2#19139906direct (N × H)

Maximal subgroups

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

subgroupindex
#191399062
C2×C43⋊#4012
C2×#145828282
C2×#145828212
C2×#145828162
C2×#145827902
C2×#145827892
C2×#145827812
C2×#145827772
C2×#145827732
C2×#145827642
C2×#145827612
C2×C4×(C2×D43)⋊C42
C2×#145827462
C2×C43×#3872
C2×#257643