Finite Group Databasebeta

← C2×#19145587 #25967879

Subgroups — C2×#19145587 #25967879

Order 11008.

2446 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583445C211yesmaximal, characteristic, complemented
2C2×#14583444C211yesmaximal, characteristic, complemented
3#19145587C2116yesmaximal, direct product factor
4C2×#14583287C211yesmaximal, characteristic, complemented
5C2×#14583285C211yesmaximal, characteristic, complemented
6C2×#14583260C211yesmaximal, characteristic, complemented
7C2×#14583257C211yesmaximal, characteristic, complemented
8C2×#14583103C211yesmaximal, characteristic, complemented
9C2×#14583102C211yesmaximal, characteristic, complemented
10C2×#14583093C211yesmaximal, characteristic, complemented
11C2×#14583092C211yesmaximal, characteristic, complemented
12C2×#14583046C211yesmaximal, characteristic, complemented
13C2×#14583044C211yesmaximal, characteristic, complemented
14C2×#14583042C211yesmaximal, characteristic, complemented
15C2×#14582953C211yesmaximal, characteristic, complemented
16C2×C43×#449C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×#10621900—21no—
19C22×#10621873C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21C22×#10621884C2211yescharacteristic
22C22×D344C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24C22×#10621882C2211yescharacteristic
25#14583445—24no—
26#14583445C2218yescomplemented
27#14583444—24no—
28#14583444C2218yescomplemented
29C2×#13063324C2211yescharacteristic
30C2×#13063323C2211yescharacteristic
31C2×#13063321C2211yescharacteristic
32C2×#13063321C2211yescharacteristic
33C2×#13063314C2211yescharacteristic
34C2×#13063312C2211yescharacteristic
35C2×#13063311—21no—
36C2×#13063299C2211yescharacteristic
37C2×#13063297—21no—
38C2×#13063297—21no—
39C2×#13063297—21no—
40C2×D4×Dic43C2211yescharacteristic
41C2×#13063287C2211yescharacteristic
42C2×C4×C22⋊D43—21no—
43C2×C4×C22⋊D43—21no—
44C2×(C22⋊D43)⋊C4—21no—
45C22×C4×Dic43C2211yescharacteristic
46#14583287C2218yescomplemented
47#14583285C2218yescomplemented
48#14583260C2218yescomplemented
49#14583257C2218yescomplemented
50#14583103C2218yescomplemented
51#14583102C2218yescomplemented
52#14583093C2218yescomplemented
53#14583092C2218yescomplemented
54#14583046C2218yescomplemented
55#14583044C2218yescomplemented
56#14583042C2218yescomplemented
57#14582953C2218yescomplemented
58C2×Dic43⋊C8C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C22×#41×C43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C22×D8×C43C2211yescharacteristic
72C2×#121×C43C2211yescharacteristic
73C43×#449C2218yescomplemented
74C2×#103×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621898—22no—
78C2×#10621898—42no—
79C2×#10621898—42no—
80C2×#10621898C2314yes—
81C2×#10621900—28no—
82C2×#10621900—48no—
83C22×Dic86—21no—
84C22×Dic86C2311yescharacteristic
85C22×D172C2311yescharacteristic
86C22×D172C2311yescharacteristic
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C23×Dic43—21no—
94C23×Dic43D411yescharacteristic
95C23×Dic43D411yescharacteristic
96C22×C4×D43—21no—
97C22×C4×D43—21no—
98C2×#10621873—42no—
99C2×#10621873C2314yes—
100C2×#10621883—42no—
101C2×#10621883C2314yes—
102C2×#10621884—42no—
103C2×#10621884C2314yes—
104C2×D344—42no—
105C2×D344C2314yes—
106C2×#10621882—42no—
107C2×#10621882—42no—
108C2×#10621882C2314yes—
109C2×#10621882C2314yes—
110C22×C43⋊C8C2311yescharacteristic
111C22×C43⋊C8C2311yescharacteristic
112#13063324—22no—
113#13063324C2314yes—
114#13063323—22no—
115#13063323C2314yes—
116#13063321—22no—
117#13063321—22no—
118#13063321C2314yes—
119#13063321C2314yes—
120#13063314—22no—
121#13063314C2314yes—
122#13063312—22no—
123#13063312C2314yes—
124#13063311—28no—
125#13063299—22no—
126#13063299C2314yes—
127#13063297—28no—
128#13063297—28no—
129#13063297—28no—
130D4×Dic43—22no—
131D4×Dic43C2314yes—
132#13063287—22no—
133#13063287C2314yes—
134C4×C22⋊D43—28no—
135C4×C22⋊D43—28no—
136(C22⋊D43)⋊C4—28no—
137C2×C4⋊Dic43C2311yescharacteristic
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×Dic43⋊C4—21no—
141C2×C22⋊Dic43—21no—
142C2×C22⋊Dic43—21no—
143C2×C22⋊Dic43—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×C4×Dic43D411yescharacteristic
149C2×C4×Dic43D411yescharacteristic
150C2×C4×Dic43D414yes—
151C2×C4×Dic43C2311yescharacteristic
152C2×C4×Dic43C2311yescharacteristic
153C2×C4×Dic43C2314yes—
154Dic43⋊C8C2314yes—
155Dic43⋊C8C2314yes—
156#13063250C2314yes—
157#13063249C2314yes—
158#13063248C2314yes—
159#13063247C2314yes—
160#13063246C2314yes—
161#13063245C2314yes—
162C22⋊(C43⋊C8)C2314yes—
163#13063235C2314yes—
164#13063235C2314yes—
165C2×#41×C43—22no—
166C2×#41×C43—42no—
167C2×#41×C43—42no—
168C2×#41×C43C2314yes—
169C22×Q8×C43C2311yescharacteristic
170C22×D4×C43—21no—
171C22×D4×C43—21no—
172C22×D4×C43C2311yescharacteristic
173C22×D4×C43C2311yescharacteristic
174C23×C4×C43—21no—
175C23×C4×C43C2311yescharacteristic
176C2×SD16×C43—42no—
177C2×SD16×C43C2314yes—
178C2×D8×C43—42no—
179C2×D8×C43C2314yes—
180C22×C8×C43C2311yescharacteristic
181C22×C8×C43C2311yescharacteristic
182#121×C43—22no—
183#121×C43C2314yes—
184C2×C4⋊C4×C43C2311yescharacteristic
185C2×C22⋊C4×C43—21no—
186#103×C43C2314yes—
187#102×C43C2314yes—
188C22⋊C8×C43C2314yes—
189C24×C43—21no—
190C24×C43—21no—
191C24×C43C2×D411yescharacteristic
192C23×D43—21no—
193C23×D43—21no—
194#41×C43—44no—
195#41×C43—44no—
196#41×C43—48no—
197C2×Q8×C43—21no—
198C2×Q8×C43—22no—
199C2×Q8×C43—22no—
200C2×Q8×C43C2412yes—
201C2×D4×C43—21no—
202C2×D4×C43—21no—
203C2×D4×C43—24no—
204C2×D4×C43—24no—
205C2×D4×C43—22no—
206C2×D4×C43—22no—
207C2×D4×C43—22no—
208C2×D4×C43—22no—
209C2×D4×C43—44no—
210C2×D4×C43—44no—
211C2×D4×C43C2412yes—
212C2×D4×C43C2412yes—
213C22×C4×C43—22no—
214C22×C4×C43—22no—
215C22×C4×C43—24no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—44no—
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D412yes—
221C22×C4×C43C2412yes—
222C22×C4×C43C2411yescharacteristic
223C2×C22⋊D43—24no—
224C2×C22⋊D43—24no—
225C2×C22⋊D43—24no—
226C2×C22⋊D43—24no—
227C2×C22⋊D43—24no—
228C2×C22⋊D43—24no—
229C2×C22⋊D43—44no—
230C2×C22⋊D43—44no—
231C2×C22⋊D43—44no—
232C2×C22⋊D43—44no—
233C2×C22⋊D43—44no—
234C2×C22⋊D43—44no—
235C22×Dic43—24no—
236C22×Dic43—24no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—42no—
240C22×Dic43—44no—
241C22×Dic43C2×D411yescharacteristic
242C22×Dic43C2×D411yescharacteristic
243C22×Dic43C2×D411yescharacteristic
244C22×Dic43C2×D414yes—
245C22×Dic43C2×D414yes—
246C22×Dic43C2×D411yescharacteristic
247#10621900—432no—
248#10621898—44no—
249#10621898—44no—
250#10621898—48no—
251C2×D172—21no—
252C2×D172—21no—
253C2×D172—22no—
254C2×D172—22no—
255C2×D172—22no—
256C2×D172—22no—
257C2×D172C2412yes—
258C2×D172C2412yes—
259C2×C4×D43—24no—
260C2×C4×D43—24no—
261C2×C4×D43—44no—
262C2×C4×D43—44no—
263C2×Dic86—22no—
264C2×Dic86—22no—
265C2×Dic86—21no—
266C2×Dic86—24no—
267C2×Dic86—44no—
268C2×Dic86C2412yes—
269SD16×C43—44no—
270D8×C43—44no—
271C2×C8×C43—22no—
272C2×C8×C43—22no—
273C2×C8×C43C2412yes—
274C2×C8×C43C2412yes—
275C4⋊C4×C43—21no—
276C4⋊C4×C43C2412yes—
277C22⋊C4×C43—24no—
278C22⋊Dic43—24no—
279C22⋊Dic43—24no—
280C22⋊Dic43—24no—
281#10621884—44no—
282#10621883—44no—
283#10621882—44no—
284#10621882—44no—
285(C2×D43)⋊C4—24no—
286(C2×D43)⋊C4—24no—
287(C2×D43)⋊C4—24no—
288(C2×D43)⋊C4—24no—
289C4⋊Dic43—21no—
290C4⋊Dic43C2412yes—
291Dic43⋊C4—24no—
292Dic43⋊C4—24no—
293Dic43⋊C4—24no—
294C4×Dic43C2×D414yes—
295C4×Dic43C2×D414yes—
296C4×Dic43C2×D412yes—
297C4×Dic43C2×D412yes—
298C4×Dic43C2412yes—
299C4×Dic43C2412yes—
300C2×C43⋊C8—22no—
301C2×C43⋊C8—22no—
302C2×C43⋊C8C2412yes—
303C2×C43⋊C8C2412yes—
304D344—44no—
305#10621873—44no—
306C23×C43—22no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—22no—
311C23×C43—42no—
312C23×C43—42no—
313C23×C43—42no—
314C23×C43—42no—
315C23×C43—42no—
316C23×C43—42no—
317C23×C43C22×D412yes—
318C23×C43C22×D411yescharacteristic
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—42no—
322C22×D43—42no—
323C22×D43—42no—
324C22×D43—42no—
325C22×D43—42no—
326C22×D43—42no—
327Q8×C43—22no—
328Q8×C43—22no—
329Q8×C43—42no—
330D4×C43—22no—
331D4×C43—22no—
332D4×C43—22no—
333D4×C43—22no—
334D4×C43—48no—
335D4×C43—48no—
336D4×C43—42no—
337D4×C43—42no—
338C2×C4×C43—22no—
339C2×C4×C43—24no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—48no—
345C2×C4×C43—42no—
346C2×C4×C43—42no—
347C2×C4×C43C22×D412yes—
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43H(5,𝔽2)12yes—
350C2×C4×C43H(5,𝔽2)12yes—
351C2×C4×C43C2511yescharacteristic
352C22⋊D43—48no—
353C22⋊D43—48no—
354C22⋊D43—48no—
355C22⋊D43—48no—
356C22⋊D43—48no—
357C22⋊D43—48no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—28no—
362C2×Dic43—22no—
363C2×Dic43—22no—
364C2×Dic43—44no—
365C2×Dic43—42no—
366C2×Dic43—42no—
367C2×Dic43—48no—
368C2×Dic43AGL(1,ℤ/8)14yes—
369C2×Dic43C22×D412yes—
370C2×Dic43C22×D412yes—
371C2×Dic43C22×D412yes—
372C2×Dic43C22×D412yes—
373D172—22no—
374D172—22no—
375D172—22no—
376D172—22no—
377D172—42no—
378D172—42no—
379C4×D43—48no—
380C4×D43—48no—
381Dic86—22no—
382Dic86—22no—
383Dic86—48no—
384Dic86—42no—
385C8×C43—22no—
386C8×C43—22no—
387C43⋊C8—22no—
388C43⋊C8—22no—
389C2×#3214—431nomaximal, Sylow
390C22×C43—22no—
391C22×C43—22no—
392C22×C43—22no—
393C22×C43—44no—
394C22×C43—42no—
395C22×C43—42no—
396C22×C43—42no—
397C22×C43—42no—
398C22×C43—42no—
399C22×C43—42no—
400C22×C43—84no—
401C22×C43—84no—
402C22×C43#53512yes—
403C22×C43C2×AGL(1,ℤ/8)12yes—
404C22×C43#57512yes—
405C22×C43C23×D411yescharacteristic
406C2×D43—42no—
407C2×D43—42no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—42no—
412C2×D43—84no—
413C2×D43—84no—
414C4×C43—22no—
415C4×C43—42no—
416C4×C43—42no—
417C4×C43#53512yes—
418C4×C43C2×H(5,𝔽2)11yescharacteristic
419C4×C43C2×H(5,𝔽2)11yescharacteristic
420Dic43—22no—
421Dic43—22no—
422Dic43—22no—
423Dic43—42no—
424Dic43—42no—
425Dic43C2×AGL(1,ℤ/8)14yes—
426C2×#532—431no—
427C2×#532—431no—
428#3214—4316no—
429C2×#496—431no—
430C2×#496—431no—
431C2×#489—431no—
432C2×#489—431no—
433C2×#461—431no—
434C2×#461—431no—
435C2×#459—431no—
436C2×#459—431no—
437C2×#449—431no—
438C2×#449—431no—
439C2×#449—431no—
440C2×#449D4311yescharacteristic, complemented
441C2×#432—431no—
442C2×C43—42no—
443C2×C43—82no—
444C2×C43—82no—
445C2×C43#321414yescomplemented
446C2×C43C2×#53511yescharacteristic
447C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
448C2×C43C2×#57511yescharacteristic
449D43—82no—
450D43—82no—
451C22×#41—431no—
452C22×#41—861no—
453C22×#41C2×D4311yescharacteristic
454C22×SD16—431no—
455C22×SD16—431no—
456C22×SD16—431no—
457C22×SD16C2×D4311yescharacteristic
458C22×D8—431no—
459C22×D8—431no—
460C22×D8—431no—
461C22×D8C2×D4311yescharacteristic
462#532—438no—
463#532—438no—
464#532—864no—
465#532—864no—
466C2×C4⋊Q8—431no—
467C2×C4⋊Q8—431no—
468C2×#127—431no—
469C2×#127—431no—
470C2×#124—431no—
471C2×#124—431no—
472C2×#124—861no—
473C2×#121—431no—
474C2×#121—861no—
475C2×#121—861no—
476C2×#121—861no—
477C2×#121C2×D4311yescharacteristic
478C2×C4×D4—431no—
479C2×C4×D4—431no—
480C2×C4×D4—861no—
481C2×C4×D4—861no—
482C2×C4×D4—861no—
483C22×C42—431no—
484#496—438no—
485#496—438no—
486#489—438no—
487#489—438no—
488#461—438no—
489#461—438no—
490#459—438no—
491#459—438no—
492#449—438no—
493#449—438no—
494#449—438no—
495#449C2×D4318yescomplemented
496#432—438no—
497C2×C4⋊C8—431no—
498C2×C4⋊C8—431no—
499C2×#103—431no—
500C2×#103—431no—
501C2×#103—431no—
502C2×#103C2×D4311yescharacteristic
503C2×#102—431no—
504C2×#102—431no—
505C2×#102—431no—
506C2×#102C2×D4311yescharacteristic
507C2×C22⋊C8—431no—
508C2×C22⋊C8C2×D4311yescharacteristic
509C2×#97—431no—
510C2×#97—431no—
511C43C2×#321411yescharacteristic, complemented, Sylow
512C2×#41—22no—
513C2×#41—42no—
514C2×#41—42no—
515C2×#41—434no—
516C2×#41—868no—
517C2×#41—862no—
518C2×#41—1722no—
519C2×#41—1722no—
520C2×#41—1728no—
521C2×#41C22×D4314yes—
522C22×Q8—431no—
523C22×Q8—861no—
524C22×Q8C22×D4311yescharacteristic
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—431no—
528C22×D4—431no—
529C22×D4—861no—
530C22×D4—861no—
531C22×D4—861no—
532C22×D4—861no—
533C22×D4—861no—
534C22×D4—861no—
535C22×D4C22×D4311yescharacteristic
536C22×D4C22×D4311yescharacteristic
537C23×C4—21no—
538C23×C4—431no—
539C23×C4—431no—
540C23×C4—861no—
541C23×C4—861no—
542C23×C4—861no—
543C23×C4C22×D4311yescharacteristic
544C2×SD16—42no—
545C2×SD16—434no—
546C2×SD16—434no—
547C2×SD16—434no—
548C2×SD16—1722no—
549C2×SD16—1722no—
550C2×SD16—1722no—
551C2×SD16C22×D4314yes—
552C2×D8—42no—
553C2×D8—434no—
554C2×D8—434no—
555C2×D8—434no—
556C2×D8—1722no—
557C2×D8—1722no—
558C2×D8—1722no—
559C2×D8C22×D4314yes—
560C22×C8—431no—
561C22×C8—431no—
562C22×C8C22×D4311yescharacteristic
563C22×C8C22×D4311yescharacteristic
564C4⋊Q8—434no—
565C4⋊Q8—434no—
566C4⋊Q8—862no—
567C4⋊Q8—862no—
568#127—434no—
569#127—434no—
570#127—862no—
571#127—862no—
572#124—434no—
573#124—434no—
574#124—868no—
575#124—862no—
576#124—862no—
577#121—22no—
578#121—434no—
579#121—868no—
580#121—868no—
581#121—868no—
582#121—862no—
583#121C22×D4314yes—
584C4×D4—434no—
585C4×D4—434no—
586C4×D4—868no—
587C4×D4—862no—
588C4×D4—868no—
589C4×D4—868no—
590C4×D4—862no—
591C2×C4⋊C4—431no—
592C2×C4⋊C4—861no—
593C2×C4⋊C4—861no—
594C2×C4⋊C4—861no—
595C2×C4⋊C4C22×D4311yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—861no—
598C2×C22⋊C4—861no—
599C2×C22⋊C4—861no—
600C2×C22⋊C4—861no—
601C2×C22⋊C4—861no—
602C2×C22⋊C4—861no—
603C2×C22⋊C4—861no—
604C2×C42—431no—
605C2×C42—431no—
606C2×C42—434no—
607C2×C42—431no—
608C2×C42—431no—
609C2×C42—434no—
610C4⋊C8—434no—
611C4⋊C8—434no—
612#103—434no—
613#103—434no—
614#103—434no—
615#103C22×D4314yes—
616#102—434no—
617#102—434no—
618#102—434no—
619#102C22×D4314yes—
620C22⋊C8—434no—
621C22⋊C8C22×D4314yes—
622#97—434no—
623#97—434no—
624C24—21no—
625C24—21no—
626C24—861no—
627C24—861no—
628C24D4×D4311yescharacteristic
629#41—44no—
630#41—44no—
631#41—48no—
632#41—1724no—
633#41—1724no—
634#41—1728no—
635#41—17232no—
636C2×Q8—21no—
637C2×Q8—22no—
638C2×Q8—22no—
639C2×Q8—432no—
640C2×Q8—864no—
641C2×Q8—861no—
642C2×Q8—862no—
643C2×Q8—862no—
644C2×Q8—1724no—
645C2×Q8C23×D4312yes—
646C2×D4—24no—
647C2×D4—24no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—44no—
655C2×D4—44no—
656C2×D4—432no—
657C2×D4—432no—
658C2×D4—864no—
659C2×D4—864no—
660C2×D4—864no—
661C2×D4—864no—
662C2×D4—864no—
663C2×D4—864no—
664C2×D4—861no—
665C2×D4—861no—
666C2×D4—862no—
667C2×D4—862no—
668C2×D4—862no—
669C2×D4—862no—
670C2×D4—1724no—
671C2×D4—1724no—
672C2×D4—1724no—
673C2×D4—1724no—
674C2×D4—1724no—
675C2×D4—1724no—
676C2×D4C23×D4312yes—
677C2×D4C23×D4312yes—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—24no—
683C22×C4—44no—
684C22×C4—431no—
685C22×C4—434no—
686C22×C4—431no—
687C22×C4—431no—
688C22×C4—431no—
689C22×C4—434no—
690C22×C4—864no—
691C22×C4—864no—
692C22×C4—864no—
693C22×C4—861no—
694C22×C4—861no—
695C22×C4—864no—
696C22×C4—1724no—
697C22×C4—1724no—
698C22×C4—1724no—
699C22×C4—1722no—
700C22×C4D4×D4312yes—
701C22×C4D4×D4311yescharacteristic
702C22×C4C23×D4312yes—
703C22×C4C23×D4311yescharacteristic
704SD16—44no—
705SD16—1724no—
706SD16—1724no—
707SD16—1724no—
708D8—44no—
709D8—1724no—
710D8—1724no—
711D8—1724no—
712C2×C8—22no—
713C2×C8—22no—
714C2×C8—432no—
715C2×C8—432no—
716C2×C8—862no—
717C2×C8—862no—
718C2×C8C23×D4312yes—
719C2×C8C23×D4312yes—
720C4⋊C4—21no—
721C4⋊C4—432no—
722C4⋊C4—864no—
723C4⋊C4—864no—
724C4⋊C4—864no—
725C4⋊C4—861no—
726C4⋊C4C23×D4312yes—
727C22⋊C4—24no—
728C22⋊C4—864no—
729C22⋊C4—864no—
730C22⋊C4—864no—
731C22⋊C4—864no—
732C22⋊C4—864no—
733C22⋊C4—864no—
734C22⋊C4—864no—
735C42—434no—
736C42—434no—
737C42—432no—
738C42—432no—
739C42—432no—
740C42—432no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—862no—
753C23—862no—
754C23—1722no—
755C23—1722no—
756C23—1722no—
757C23—1722no—
758C23—1722no—
759C23—1722no—
760C23C2×D4×D4312yes—
761C23C2×D4×D4311yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—42no—
765Q8—862no—
766Q8—862no—
767Q8—1728no—
768Q8—1722no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—22no—
773D4—48no—
774D4—48no—
775D4—42no—
776D4—42no—
777D4—862no—
778D4—862no—
779D4—862no—
780D4—862no—
781D4—1728no—
782D4—1728no—
783D4—1728no—
784D4—1728no—
785D4—1728no—
786D4—1728no—
787D4—1722no—
788D4—1722no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—48no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—434no—
799C2×C4—432no—
800C2×C4—432no—
801C2×C4—432no—
802C2×C4—432no—
803C2×C4—868no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—862no—
809C2×C4—1728no—
810C2×C4—1728no—
811C2×C4—1728no—
812C2×C4—1724no—
813C2×C4—1722no—
814C2×C4—1722no—
815C2×C4C2×D4×D4312yes—
816C2×C4C2×D4×D4311yescharacteristic
817C2×C4#1306337012yes—
818C2×C4#1306337012yes—
819C2×C4C24×D4311yescharacteristic
820C8—22no—
821C8—22no—
822C8—862no—
823C8—862no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—44no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—84no—
835C22—84no—
836C22—3444no—
837C22—3444no—
838C22—1722no—
839C22—1722no—
840C22—1722no—
841C22—1722no—
842C22—1722no—
843C22—1722no—
844C22#1458346412yes—
845C22AGL(1,ℤ/8)×D4312yes—
846C22#1458369612yes—
847C22C22×D4×D4311yescharacteristic
848C4—22no—
849C4—42no—
850C4—42no—
851C4—434no—
852C4—862no—
853C4—862no—
854C4—862no—
855C4—1722no—
856C4—1722no—
857C4#1458346412yes—
858C4C2×#1306337011yescharacteristic
859C4C2×#1306337011yescharacteristic
860C2—42no—
861C2—82no—
862C2—82no—
863C2—3442no—
864C2—3442no—
865C2#1914558714yesdirect product factor
866C2C2×#1458346411yescharacteristic
867C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
868C2C2×#1458369611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#449C2
socleC23×C43C22×D4
hypercenterC2×#449D43
hypocenterC43C2×#3214
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#14583445C2semidirect
2. C2×#14583444C2semidirect
3. #19145587C2direct (N × H)
4. C2×#14583287C2semidirect
5. C2×#14583285C2semidirect
6. C2×#14583260C2semidirect
7. C2×#14583257C2semidirect
8. C2×#14583103C2semidirect
9. C2×#14583102C2semidirect
10. C2×#14583093C2semidirect
11. C2×#14583092C2semidirect
12. C2×#14583046C2semidirect
13. C2×#14583044C2semidirect
14. C2×#14583042C2semidirect
15. C2×#14582953C2semidirect
16. C2×C43×#449C2semidirect
26. #14583445C22semidirect
28. #14583444C22semidirect
46. #14583287C22semidirect
47. #14583285C22semidirect
48. #14583260C22semidirect
49. #14583257C22semidirect
50. #14583103C22semidirect
51. #14583102C22semidirect
52. #14583093C22semidirect
53. #14583092C22semidirect
54. #14583046C22semidirect
55. #14583044C22semidirect
56. #14583042C22semidirect
57. #14582953C22semidirect
73. C43×#449C22semidirect
440. C2×#449D43semidirect
445. C2×C43#3214semidirect
495. #449C2×D43semidirect
511. C43C2×#3214semidirect
865. C2#19145587direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834452
C2×#145834442
#191455872
C2×#145832872
C2×#145832852
C2×#145832602
C2×#145832572
C2×#145831032
C2×#145831022
C2×#145830932
C2×#145830922
C2×#145830462
C2×#145830442
C2×#145830422
C2×#145829532
C2×C43×#4492
C2×#321443