Finite Group Databasebeta

← C2×#19147678 #25977622

Subgroups — C2×#19147678 #25977622

Order 11008.

2066 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583635C211yesmaximal, characteristic, complemented
2C2×#14583632C211yesmaximal, characteristic, complemented
3#19147678C2116yesmaximal, direct product factor
4C2×#14583287C211yesmaximal, characteristic, complemented
5C2×#14583286C211yesmaximal, characteristic, complemented
6C2×#14583282C211yesmaximal, characteristic, complemented
7C2×#14583122C211yesmaximal, characteristic, complemented
8C2×#14583120C211yesmaximal, characteristic, complemented
9C2×#14583113C211yesmaximal, characteristic, complemented
10C2×#14583112C211yesmaximal, characteristic, complemented
11C2×#14583092C211yesmaximal, characteristic, complemented
12C2×#14583028C211yesmaximal, characteristic, complemented
13C2×#14582999C211yesmaximal, characteristic, complemented
14C2×#14582996C211yesmaximal, characteristic, complemented
15C2×#14582979C211yesmaximal, characteristic, complemented
16C2×C43×#459C211yesmaximal, characteristic, complemented
17C22×Dic172C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C22×#10621883C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21C22×#10621883C2211yescharacteristic
22C22×#10621882C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24#14583635—24no—
25#14583635C2218yescomplemented
26#14583632—24no—
27#14583632C2218yescomplemented
28C2×#13063321C2211yescharacteristic
29C2×#13063313C2211yescharacteristic
30C2×#13063312—21no—
31C2×#13063312C2211yescharacteristic
32C2×#13063312C2211yescharacteristic
33C2×#13063312C2211yescharacteristic
34C2×#13063311—21no—
35C2×#13063308—21no—
36C2×#13063307—21no—
37C2×#13063306—21no—
38C2×#13063306—21no—
39C2×C4×Dic86C2211yescharacteristic
40C2×C4×Dic86C2211yescharacteristic
41C2×#13063290C2211yescharacteristic
42C2×D4×Dic43—21no—
43C2×D4×Dic43C2211yescharacteristic
44C2×D4×Dic43C2211yescharacteristic
45C2×#13063287C2211yescharacteristic
46C2×C4×C22⋊D43—21no—
47#14583287C2218yescomplemented
48#14583286C2218yescomplemented
49#14583282C2218yescomplemented
50#14583122C2218yescomplemented
51#14583120C2218yescomplemented
52#14583113C2218yescomplemented
53#14583112C2218yescomplemented
54#14583092C2218yescomplemented
55#14583028C2218yescomplemented
56#14582999C2218yescomplemented
57#14582996C2218yescomplemented
58#14582979C2218yescomplemented
59C2×#13063258C2211yescharacteristic
60C2×Dic43⋊C8C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×#13063250C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×#13063236C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×D8×C43C2211yescharacteristic
70C22×D8×C43C2211yescharacteristic
71C2×#127×C43C2211yescharacteristic
72C2×C4×D4×C43C2211yescharacteristic
73C43×#459C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C22×Dic86D411yescharacteristic
78C22×Dic86C2311yescharacteristic
79C22×Dic86C2311yescharacteristic
80C22×D172C2311yescharacteristic
81C22×C22⋊D43—21no—
82C22×C22⋊D43—21no—
83C23×Dic43—21no—
84C23×Dic43—21no—
85C22×C4×D43—21no—
86C2×Dic172—42no—
87C2×Dic172C2314yes—
88C2×#10621873—42no—
89C2×#10621873C2314yes—
90C2×#10621883—24no—
91C2×#10621883—24no—
92C2×#10621883—42no—
93C2×#10621883C2314yes—
94C2×#10621883C2314yes—
95C2×#10621883C2314yes—
96C2×#10621882—24no—
97C2×#10621882—42no—
98C2×#10621882C2314yes—
99C2×#10621882C2314yes—
100C22×C43⋊C8C2311yescharacteristic
101C22×C43⋊C8C2311yescharacteristic
102#13063321—22no—
103#13063321C2314yes—
104#13063313—22no—
105#13063313C2314yes—
106#13063312—28no—
107#13063312—22no—
108#13063312—22no—
109#13063312—22no—
110#13063312C2314yes—
111#13063312C2314yes—
112#13063312C2314yes—
113#13063311—28no—
114#13063308—28no—
115#13063307—28no—
116#13063306—28no—
117#13063306—28no—
118C4×Dic86—22no—
119C4×Dic86D414yes—
120C4×Dic86C2314yes—
121C4×Dic86C2314yes—
122#13063290—22no—
123#13063290C2314yes—
124D4×Dic43—28no—
125D4×Dic43—22no—
126D4×Dic43—22no—
127D4×Dic43C2314yes—
128D4×Dic43C2314yes—
129#13063287—22no—
130#13063287C2314yes—
131C4×C22⋊D43—28no—
132C2×C4⋊Dic43D411yescharacteristic
133C2×C4⋊Dic43C2311yescharacteristic
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4D411yescharacteristic
137C2×Dic43⋊C4D411yescharacteristic
138C2×C22⋊Dic43—21no—
139C2×C22⋊Dic43—21no—
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43—21no—
142C2×C22⋊Dic43—21no—
143C2×C22⋊Dic43—21no—
144C2×C22⋊Dic43—21no—
145C2×C22⋊Dic43—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×C4×Dic43—21no—
150C2×C4×Dic43—21no—
151C2×C4×Dic43C2311yescharacteristic
152C2×C4×Dic43C2311yescharacteristic
153#13063258C2314yes—
154Dic43⋊C8C2314yes—
155Dic43⋊C8C2314yes—
156#13063250C2314yes—
157#13063248C2314yes—
158#13063247C2314yes—
159#13063246C2314yes—
160#13063236C2314yes—
161#13063235C2314yes—
162C8×Dic43C2314yes—
163C22×D4×C43—21no—
164C22×D4×C43—21no—
165C22×D4×C43C2311yescharacteristic
166C22×D4×C43C2311yescharacteristic
167C22×D4×C43C2311yescharacteristic
168C23×C4×C43—21no—
169C2×D8×C43—42no—
170C2×D8×C43—42no—
171C2×D8×C43C2314yes—
172C2×D8×C43C2314yes—
173C22×C8×C43C2311yescharacteristic
174C22×C8×C43C2311yescharacteristic
175#127×C43—22no—
176#127×C43C2314yes—
177C4×D4×C43—22no—
178C4×D4×C43C2314yes—
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C22⋊C4×C43—21no—
181C2×C42×C43C2311yescharacteristic
182C4⋊C8×C43C2314yes—
183#102×C43C2314yes—
184#102×C43C2314yes—
185C24×C43—21no—
186C24×C43—21no—
187C24×C43—21no—
188C23×D43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—24no—
193C2×D4×C43—24no—
194C2×D4×C43—22no—
195C2×D4×C43—22no—
196C2×D4×C43—22no—
197C2×D4×C43—22no—
198C2×D4×C43—22no—
199C2×D4×C43—22no—
200C2×D4×C43—44no—
201C2×D4×C43—82no—
202C2×D4×C43C2412yes—
203C2×D4×C43C2412yes—
204C2×D4×C43C2412yes—
205C22×C4×C43—24no—
206C22×C4×C43—21no—
207C22×C4×C43—82no—
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2411yescharacteristic
211C2×C22⋊D43—24no—
212C2×C22⋊D43—24no—
213C2×C22⋊D43—44no—
214C2×C22⋊D43—82no—
215C22×Dic43—24no—
216C22×Dic43—24no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—82no—
221C22×Dic43—82no—
222C22×Dic43C2×D411yescharacteristic
223C22×Dic43C2×D411yescharacteristic
224C22×Dic43C2×D411yescharacteristic
225C22×Dic43C2×D411yescharacteristic
226C2×D172—21no—
227C2×D172—22no—
228C2×D172—22no—
229C2×D172C2412yes—
230C2×C4×D43—24no—
231C2×C4×D43—82no—
232C2×Dic86—22no—
233C2×Dic86—22no—
234C2×Dic86—22no—
235C2×Dic86—22no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—42no—
239C2×Dic86C2×D414yes—
240C2×Dic86C2412yes—
241C2×Dic86C2412yes—
242D8×C43—44no—
243D8×C43—44no—
244C2×C8×C43—22no—
245C2×C8×C43—22no—
246C2×C8×C43C2412yes—
247C2×C8×C43C2412yes—
248C4⋊C4×C43—21no—
249C4⋊C4×C43C2412yes—
250C22⋊C4×C43—24no—
251C42×C43C2×D412yes—
252C42×C43C2412yes—
253C22⋊Dic43—24no—
254C22⋊Dic43—24no—
255C22⋊Dic43—24no—
256C22⋊Dic43—24no—
257C22⋊Dic43—24no—
258C22⋊Dic43—24no—
259C22⋊Dic43—24no—
260C22⋊Dic43—24no—
261#10621883—28no—
262#10621883—28no—
263#10621883—44no—
264#10621882—28no—
265#10621882—44no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—24no—
269C4⋊Dic43—21no—
270C4⋊Dic43C2×D414yes—
271C4⋊Dic43C2412yes—
272Dic43⋊C4—24no—
273Dic43⋊C4—24no—
274Dic43⋊C4C2×D414yes—
275Dic43⋊C4C2×D414yes—
276C4×Dic43—24no—
277C4×Dic43—24no—
278C4×Dic43C2×D412yes—
279C4×Dic43C2×D412yes—
280C4×Dic43C2412yes—
281C4×Dic43C2412yes—
282C2×C43⋊C8—22no—
283C2×C43⋊C8#4114yes—
284C2×C43⋊C8C2412yes—
285C2×C43⋊C8C2412yes—
286Dic172—44no—
287#10621873—44no—
288C23×C43—22no—
289C23×C43—22no—
290C23×C43—22no—
291C23×C43—42no—
292C23×C43—42no—
293C23×C43—42no—
294C23×C43—42no—
295C23×C43—42no—
296C23×C43—42no—
297C23×C43—42no—
298C23×C43—42no—
299C23×C43—42no—
300C23×C43C22×D411yescharacteristic
301C22×D43—22no—
302C22×D43—42no—
303C22×D43—42no—
304C22×D43—42no—
305D4×C43—22no—
306D4×C43—22no—
307D4×C43—22no—
308D4×C43—22no—
309D4×C43—22no—
310D4×C43—22no—
311D4×C43—48no—
312D4×C43—42no—
313D4×C43—42no—
314D4×C43—42no—
315D4×C43—84no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—42no—
320C2×C4×C43—84no—
321C2×C4×C43C22×D412yes—
322C2×C4×C43C22×D412yes—
323C2×C4×C43C22×D411yescharacteristic
324C2×C4×C43C2×#4112yes—
325C2×C4×C43H(5,𝔽2)12yes—
326C2×C4×C43C2511yescharacteristic
327C22⋊D43—48no—
328C22⋊D43—84no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—42no—
337C2×Dic43—42no—
338C2×Dic43—42no—
339C2×Dic43—84no—
340C2×Dic43—84no—
341C2×Dic43C22×D412yes—
342C2×Dic43C22×D412yes—
343C2×Dic43C22×D412yes—
344C2×Dic43C22×D412yes—
345D172—22no—
346D172—22no—
347D172—42no—
348C4×D43—84no—
349Dic86—22no—
350Dic86—22no—
351Dic86—22no—
352Dic86—22no—
353Dic86—44no—
354Dic86—42no—
355Dic86—42no—
356C8×C43—22no—
357C8×C43—22no—
358C43⋊C8—22no—
359C43⋊C8C2×#4114yes—
360C2×#3403—431nomaximal, Sylow
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43—42no—
368C22×C43—42no—
369C22×C43—42no—
370C22×C43—84no—
371C22×C43—84no—
372C22×C43—84no—
373C22×C43#55012yes—
374C22×C43#57512yes—
375C22×C43#57612yes—
376C22×C43C23×D411yescharacteristic
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—84no—
381C4×C43—22no—
382C4×C43—22no—
383C4×C43—42no—
384C4×C43#55012yes—
385C4×C43C22×#4111yescharacteristic
386C4×C43C2×H(5,𝔽2)11yescharacteristic
387Dic43—22no—
388Dic43—22no—
389Dic43—22no—
390Dic43—22no—
391Dic43—42no—
392Dic43—42no—
393Dic43—42no—
394C2×#559—431no—
395C2×#559—431no—
396#3403—4316no—
397C2×#496—431no—
398C2×#496—431no—
399C2×#495—431no—
400C2×#464—431no—
401C2×#464—431no—
402C2×#463—431no—
403C2×#463—431no—
404C2×#459—431no—
405C2×#459D4311yescharacteristic, complemented
406C2×#446—431no—
407C2×#440—431no—
408C2×#440—431no—
409C2×C4×D8—431no—
410C2×C43—82no—
411C2×C43—82no—
412C2×C43—82no—
413C2×C43#340314yescomplemented
414C2×C43C2×#55011yescharacteristic
415C2×C43C2×#57511yescharacteristic
416C2×C43C2×#57611yescharacteristic
417D43—82no—
418C22×Q16—431no—
419C22×SD16—431no—
420C22×SD16—431no—
421C22×SD16—431no—
422C22×SD16—431no—
423C22×D8—431no—
424C22×D8—431no—
425C22×D8C2×D4311yescharacteristic
426C22×D8C2×D4311yescharacteristic
427#559—438no—
428#559—438no—
429#559—864no—
430#559—864no—
431C2×#127—431no—
432C2×#127C2×D4311yescharacteristic
433C2×#124—431no—
434C2×#124—431no—
435C2×#124—431no—
436C2×#124—431no—
437C2×#124—861no—
438C2×#124—861no—
439C2×#123—861no—
440C2×#123—861no—
441C2×#123—861no—
442C2×#123—861no—
443C2×C4×Q8—431no—
444C2×C4×Q8—431no—
445C2×C4×Q8—431no—
446C2×C4×D4—431no—
447C2×C4×D4—431no—
448C2×C4×D4—431no—
449C2×C4×D4—861no—
450C2×C4×D4—861no—
451C2×C4×D4C2×D4311yescharacteristic
452#496—438no—
453#496—438no—
454#495—438no—
455#464—438no—
456#464—438no—
457#463—438no—
458#463—438no—
459#459—438no—
460#459C2×D4318yescomplemented
461#446—438no—
462#440—438no—
463#440—438no—
464C4×D8—438no—
465C2×#107—431no—
466C2×C4⋊C8—431no—
467C2×C4⋊C8—431no—
468C2×C4⋊C8C2×D4311yescharacteristic
469C2×#103—431no—
470C2×#103—431no—
471C2×#102—431no—
472C2×#102—431no—
473C2×#102C2×D4311yescharacteristic
474C2×#102C2×D4311yescharacteristic
475C2×#97—431no—
476C2×#97—431no—
477C2×C4×C8—431no—
478C43C2×#340311yescharacteristic, complemented, Sylow
479C22×Q8—431no—
480C22×Q8—431no—
481C22×Q8—431no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—431no—
485C22×D4—861no—
486C22×D4—861no—
487C22×D4C22×D4311yescharacteristic
488C22×D4C22×D4311yescharacteristic
489C22×D4C22×D4311yescharacteristic
490C23×C4—21no—
491C23×C4—861no—
492C23×C4—861no—
493C23×C4—861no—
494C2×Q16—434no—
495C2×Q16—1722no—
496C2×SD16—434no—
497C2×SD16—434no—
498C2×SD16—434no—
499C2×SD16—434no—
500C2×SD16—864no—
501C2×SD16—864no—
502C2×SD16—1722no—
503C2×SD16—1722no—
504C2×D8—42no—
505C2×D8—42no—
506C2×D8—434no—
507C2×D8—434no—
508C2×D8—864no—
509C2×D8—1722no—
510C2×D8C22×D4314yes—
511C2×D8C22×D4314yes—
512C22×C8—431no—
513C22×C8—431no—
514C22×C8C22×D4311yescharacteristic
515C22×C8C22×D4311yescharacteristic
516#127—22no—
517#127—434no—
518#127—862no—
519#127C22×D4314yes—
520#124—434no—
521#124—434no—
522#124—434no—
523#124—434no—
524#124—862no—
525#124—862no—
526#124—862no—
527#124—868no—
528#124—868no—
529#124—862no—
530#123—868no—
531#123—868no—
532#123—868no—
533#123—868no—
534C4×Q8—434no—
535C4×Q8—434no—
536C4×Q8—434no—
537C4×Q8—434no—
538C4×Q8—862no—
539C4×Q8—862no—
540C4×D4—22no—
541C4×D4—434no—
542C4×D4—434no—
543C4×D4—434no—
544C4×D4—862no—
545C4×D4—862no—
546C4×D4—862no—
547C4×D4—868no—
548C4×D4—868no—
549C4×D4C22×D4314yes—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—861no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4C22×D4311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C22⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C42—431no—
570C2×C42—431no—
571C2×C42—861no—
572C2×C42—861no—
573C2×C42C22×D4311yescharacteristic
574#107—434no—
575C4⋊C8—434no—
576C4⋊C8—434no—
577C4⋊C8C22×D4314yes—
578#103—434no—
579#103—434no—
580#102—434no—
581#102—434no—
582#102C22×D4314yes—
583#102C22×D4314yes—
584#97—434no—
585#97—434no—
586C4×C8—434no—
587C24—21no—
588C24—21no—
589C24—21no—
590C24—861no—
591C2×Q8—434no—
592C2×Q8—432no—
593C2×Q8—432no—
594C2×Q8—861no—
595C2×Q8—861no—
596C2×Q8—862no—
597C2×Q8—862no—
598C2×Q8—862no—
599C2×Q8—862no—
600C2×Q8—1722no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—44no—
613C2×D4—82no—
614C2×D4—432no—
615C2×D4—864no—
616C2×D4—864no—
617C2×D4—861no—
618C2×D4—862no—
619C2×D4—862no—
620C2×D4—3442no—
621C2×D4—1724no—
622C2×D4C23×D4312yes—
623C2×D4C23×D4312yes—
624C2×D4C23×D4312yes—
625C22×C4—21no—
626C22×C4—24no—
627C22×C4—82no—
628C22×C4—431no—
629C22×C4—431no—
630C22×C4—431no—
631C22×C4—431no—
632C22×C4—864no—
633C22×C4—864no—
634C22×C4—864no—
635C22×C4—861no—
636C22×C4—861no—
637C22×C4—861no—
638C22×C4—3442no—
639C22×C4—3442no—
640C22×C4—3442no—
641C22×C4D4×D4311yescharacteristic
642C22×C4D4×D4311yescharacteristic
643C22×C4C23×D4311yescharacteristic
644Q16—1724no—
645SD16—868no—
646SD16—868no—
647SD16—1724no—
648SD16—1724no—
649D8—44no—
650D8—44no—
651D8—868no—
652D8—1724no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—434no—
656C2×C8—432no—
657C2×C8—432no—
658C2×C8—862no—
659C2×C8C23×D4312yes—
660C2×C8C23×D4312yes—
661C4⋊C4—21no—
662C4⋊C4—434no—
663C4⋊C4—434no—
664C4⋊C4—434no—
665C4⋊C4—432no—
666C4⋊C4—864no—
667C4⋊C4—861no—
668C4⋊C4—864no—
669C4⋊C4C23×D4312yes—
670C22⋊C4—24no—
671C22⋊C4—864no—
672C22⋊C4—864no—
673C22⋊C4—864no—
674C22⋊C4—864no—
675C22⋊C4—864no—
676C22⋊C4—864no—
677C22⋊C4—864no—
678C22⋊C4—864no—
679C22⋊C4—864no—
680C22⋊C4—864no—
681C22⋊C4—864no—
682C42—432no—
683C42—432no—
684C42—432no—
685C42—432no—
686C42—864no—
687C42—864no—
688C42D4×D4312yes—
689C42C23×D4312yes—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—862no—
703C23—1722no—
704C23—1722no—
705C23—1722no—
706C23C2×D4×D4311yescharacteristic
707Q8—862no—
708Q8—862no—
709Q8—862no—
710Q8—862no—
711Q8—1724no—
712Q8—1722no—
713Q8—1722no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—48no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—84no—
725D4—862no—
726D4—862no—
727D4—3444no—
728D4—1728no—
729D4—1722no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—42no—
734C2×C4—84no—
735C2×C4—432no—
736C2×C4—432no—
737C2×C4—432no—
738C2×C4—432no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—3444no—
747C2×C4—3444no—
748C2×C4—3444no—
749C2×C4—1722no—
750C2×C4—1722no—
751C2×C4—1722no—
752C2×C4C2×D4×D4312yes—
753C2×C4C2×D4×D4312yes—
754C2×C4C2×D4×D4311yescharacteristic
755C2×C4#41×D4312yes—
756C2×C4#1306337012yes—
757C2×C4C24×D4311yescharacteristic
758C8—22no—
759C8—22no—
760C8—434no—
761C8—862no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—84no—
772C22—84no—
773C22—84no—
774C22—3444no—
775C22—1722no—
776C22—1722no—
777C22—1722no—
778C22#1458356712yes—
779C22#1458369512yes—
780C22#1458370012yes—
781C22C22×D4×D4311yescharacteristic
782C4—22no—
783C4—22no—
784C4—42no—
785C4—862no—
786C4—862no—
787C4—862no—
788C4—862no—
789C4—1722no—
790C4—1722no—
791C4—1722no—
792C4#1458356712yes—
793C4C2×#41×D4311yescharacteristic
794C4C2×#1306337011yescharacteristic
795C2—82no—
796C2—82no—
797C2—82no—
798C2—3442no—
799C2#1914767814yesdirect product factor
800C2C2×#1458356711yescharacteristic
801C2C2×#1458369511yescharacteristic
802C2C2×#1458370011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#459C2
socleC23×C43C22×D4
hypercenterC2×#459D43
hypocenterC43C2×#3403
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#14583635C2semidirect
2. C2×#14583632C2semidirect
3. #19147678C2direct (N × H)
4. C2×#14583287C2semidirect
5. C2×#14583286C2semidirect
6. C2×#14583282C2semidirect
7. C2×#14583122C2semidirect
8. C2×#14583120C2semidirect
9. C2×#14583113C2semidirect
10. C2×#14583112C2semidirect
11. C2×#14583092C2semidirect
12. C2×#14583028C2semidirect
13. C2×#14582999C2semidirect
14. C2×#14582996C2semidirect
15. C2×#14582979C2semidirect
16. C2×C43×#459C2semidirect
25. #14583635C22semidirect
27. #14583632C22semidirect
47. #14583287C22semidirect
48. #14583286C22semidirect
49. #14583282C22semidirect
50. #14583122C22semidirect
51. #14583120C22semidirect
52. #14583113C22semidirect
53. #14583112C22semidirect
54. #14583092C22semidirect
55. #14583028C22semidirect
56. #14582999C22semidirect
57. #14582996C22semidirect
58. #14582979C22semidirect
73. C43×#459C22semidirect
405. C2×#459D43semidirect
413. C2×C43#3403semidirect
460. #459C2×D43semidirect
478. C43C2×#3403semidirect
799. C2#19147678direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836352
C2×#145836322
#191476782
C2×#145832872
C2×#145832862
C2×#145832822
C2×#145831222
C2×#145831202
C2×#145831132
C2×#145831122
C2×#145830922
C2×#145830282
C2×#145829992
C2×#145829962
C2×#145829792
C2×C43×#4592
C2×#340343