Finite Group Databasebeta

← C2×#19146710 #25973191

Subgroups — C2×#19146710 #25973191

Order 11008.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583607C211yesmaximal, characteristic, complemented
2C2×#14583560C211yesmaximal, characteristic
3#19146710C2116yesmaximal, direct product factor
4C2×#14583260C211yesmaximal, characteristic, complemented
5C2×#14583218C211yesmaximal, characteristic, complemented
6C2×#14583228C211yesmaximal, characteristic, complemented
7C2×#14583182C211yesmaximal, characteristic, complemented
8C2×#14583154C211yesmaximal, characteristic, complemented
9C2×#14583130C211yesmaximal, characteristic, complemented
10C2×#14583123C211yesmaximal, characteristic, complemented
11C2×#14583060C211yesmaximal, characteristic, complemented
12C2×#14583006C211yesmaximal, characteristic, complemented
13C2×#14582967C211yesmaximal, characteristic, complemented
14C2×#14582899C211yesmaximal, characteristic, complemented
15C22×#13063249C211yesmaximal, characteristic, complemented
16C2×C43×#451C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C23×C43⋊C8C2211yescharacteristic
21#14583607—24no—
22#14583607C2218yescomplemented
23#14583560—24no—
24#14583560C2218yes—
25C2×#13063324C2211yescharacteristic
26C2×#13063315—21no—
27C2×#13063314—21no—
28C2×#13063314C2211yescharacteristic
29C2×#13063305—21no—
30C2×#13063302—21no—
31C2×#13063301—21no—
32C2×#13063301C2211yescharacteristic
33C2×#13063301C2211yescharacteristic
34C2×#13063299—21no—
35C2×#13063299C2211yescharacteristic
36C2×Q8×Dic43C2211yescharacteristic
37C2×Q8×Dic43C2211yescharacteristic
38C2×C4×C22⋊D43—21no—
39C2×C4×C22⋊D43C2211yescharacteristic
40C2×(C22⋊D43)⋊C4—21no—
41C22×C4⋊Dic43C2211yescharacteristic
42C2×C4⋊C4×D43C2211yescharacteristic
43#14583260C2218yescomplemented
44#14583228C2218yescomplemented
45#14583218C2218yescomplemented
46#14583182C2218yescomplemented
47#14583154C2218yescomplemented
48#14583130C2218yescomplemented
49#14583123C2218yescomplemented
50#14583060C2218yescomplemented
51#14583006C2218yescomplemented
52#14582967C2218yescomplemented
53C2×#13063257C2211yescharacteristic
54C2×#13063257C2211yescharacteristic
55C2×#13063256C2211yescharacteristic
56C2×Dic43⋊C8C2211yescharacteristic
57#14582899C2218yescomplemented
58C2×#13063249C2211yescharacteristic
59C2×#13063249C2211yescharacteristic
60C2×#13063249C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063249C2218yescomplemented
64C2×#13063247C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C23×Q8×C43C2211yescharacteristic
70C22×Q16×C43C2211yescharacteristic
71C22×Q16×C43C2211yescharacteristic
72C2×C22⋊Q8×C43C2211yescharacteristic
73C43×#451C2218yescomplemented
74C2×#103×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621902—22no—
78C2×#10621902—24no—
79C2×#10621902—42no—
80C2×#10621902C2314yes—
81C22×Dic86—21no—
82C22×D172—21no—
83C22×D172C2311yescharacteristic
84C22×C22⋊D43—21no—
85C22×C22⋊D43D411yescharacteristic
86C23×Dic43—21no—
87C22×C4×D43—21no—
88C22×C4×D43—21no—
89C22×C4×D43C2311yescharacteristic
90C2×#10621884—42no—
91C2×#10621884C2314yes—
92C2×#10621872—42no—
93C2×#10621872C2314yes—
94C22×C43⋊C8—42no—
95C22×C43⋊C8C2311yescharacteristic
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2314yes—
98#13063324—22no—
99#13063324C2314yes—
100#13063315—28no—
101#13063314—28no—
102#13063314—22no—
103#13063314C2314yes—
104#13063305—28no—
105#13063302—28no—
106#13063301—22no—
107#13063301—22no—
108#13063301—28no—
109#13063301C2314yes—
110#13063301C2314yes—
111#13063299—22no—
112#13063299—28no—
113#13063299C2314yes—
114Q8×Dic43—22no—
115Q8×Dic43—22no—
116Q8×Dic43C2314yes—
117Q8×Dic43C2314yes—
118C4×C22⋊D43—28no—
119C4×C22⋊D43D414yes—
120C4×C22⋊D43C2314yes—
121(C22⋊D43)⋊C4—28no—
122C2×C4⋊Dic43—22no—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43—21no—
125C2×C4⋊Dic43—21no—
126C2×C4⋊Dic43C2311yescharacteristic
127C2×C4⋊Dic43C2314yes—
128C2×C4⋊Dic43C2311yescharacteristic
129C2×C4⋊Dic43C2311yescharacteristic
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4D411yescharacteristic
135C4⋊C4×D43—22no—
136C4⋊C4×D43C2314yes—
137C2×C22⋊Dic43D411yescharacteristic
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4D411yescharacteristic
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43C2311yescharacteristic
147#13063257C2314yes—
148#13063257C2314yes—
149#13063256C2314yes—
150Dic43⋊C8C2314yes—
151#13063249C2314yes—
152#13063249C2314yes—
153#13063249C2314yes—
154#13063249C2314yes—
155#13063249C2314yes—
156#13063247C2314yes—
157#13063247C2314yes—
158#13063245C2314yes—
159(C2×D43)⋊C8C2314yes—
160#13063235C2314yes—
161C22×Q8×C43—22no—
162C22×Q8×C43—21no—
163C22×Q8×C43—24no—
164C22×Q8×C43—42no—
165C22×Q8×C43C2311yescharacteristic
166C22×Q8×C43C2311yescharacteristic
167C22×Q8×C43C2314yes—
168C22×Q8×C43C2311yescharacteristic
169C23×C4×C43—21no—
170C23×C4×C43C2311yescharacteristic
171C2×Q16×C43—24no—
172C2×Q16×C43—42no—
173C2×Q16×C43C2314yes—
174C2×Q16×C43C2314yes—
175C22×C8×C43C2311yescharacteristic
176C22×C8×C43C2311yescharacteristic
177C22⋊Q8×C43—22no—
178C22⋊Q8×C43C2314yes—
179C2×C4⋊C4×C43—21no—
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C22⋊C4×C43—21no—
182#103×C43C2314yes—
183#103×C43C2314yes—
184C22⋊C8×C43C2314yes—
185C24×C43C2×D411yescharacteristic
186C23×D43—21no—
187C23×D43C2×D411yescharacteristic
188C2×Q8×C43—21no—
189C2×Q8×C43—21no—
190C2×Q8×C43—24no—
191C2×Q8×C43—21no—
192C2×Q8×C43—22no—
193C2×Q8×C43—28no—
194C2×Q8×C43—22no—
195C2×Q8×C43—22no—
196C2×Q8×C43—22no—
197C2×Q8×C43—22no—
198C2×Q8×C43—44no—
199C2×Q8×C43—44no—
200C2×Q8×C43—48no—
201C2×Q8×C43#4114yes—
202C2×Q8×C43C2412yes—
203C2×Q8×C43C2412yes—
204C2×Q8×C43C2412yes—
205C22×C4×C43—22no—
206C22×C4×C43—22no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—24no—
212C22×C4×C43—44no—
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D412yes—
215C22×C4×C43C2412yes—
216C22×C4×C43C2411yescharacteristic
217C2×C22⋊D43—24no—
218C2×C22⋊D43—24no—
219C2×C22⋊D43—44no—
220C2×C22⋊D43C2×D414yes—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—21no—
224C22×Dic43—24no—
225C22×Dic43—82no—
226C22×Dic43C2×D411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228C22×Dic43C2×D411yescharacteristic
229#10621902—28no—
230#10621902—44no—
231#10621902—48no—
232C2×D172—21no—
233C2×D172—24no—
234C2×D172—22no—
235C2×D172—22no—
236C2×D172—44no—
237C2×D172C2412yes—
238C2×C4×D43—22no—
239C2×C4×D43—22no—
240C2×C4×D43—24no—
241C2×C4×D43—24no—
242C2×C4×D43—44no—
243C2×C4×D43—82no—
244C2×C4×D43C2×D412yes—
245C2×C4×D43C2412yes—
246C2×Dic86—24no—
247C2×Dic86—82no—
248Q16×C43—28no—
249Q16×C43—44no—
250C2×C8×C43—22no—
251C2×C8×C43—22no—
252C2×C8×C43C2412yes—
253C2×C8×C43C2412yes—
254C4⋊C4×C43—24no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43C2412yes—
257C22⋊C4×C43—24no—
258C22⋊Dic43C2×D414yes—
259#10621884—44no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—24no—
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4C2×D414yes—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—24no—
269C4⋊Dic43—21no—
270C4⋊Dic43—24no—
271C4⋊Dic43—24no—
272C4⋊Dic43C2412yes—
273C4⋊Dic43C2412yes—
274C4⋊Dic43C2412yes—
275Dic43⋊C4—24no—
276Dic43⋊C4—24no—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279Dic43⋊C4C2×D414yes—
280C4×Dic43—24no—
281C4×Dic43—24no—
282C4×Dic43C2×D412yes—
283C4×Dic43C2412yes—
284C2×C43⋊C8—22no—
285C2×C43⋊C8—22no—
286C2×C43⋊C8—44no—
287C2×C43⋊C8C2412yes—
288C2×C43⋊C8C2412yes—
289#10621872—44no—
290C23×C43—22no—
291C23×C43—22no—
292C23×C43#13714yes—
293C23×C43C22×D412yes—
294C23×C43C22×D411yescharacteristic
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—42no—
300C22×D43—42no—
301C22×D43—42no—
302C22×D43C22×D412yes—
303Q8×C43—24no—
304Q8×C43—22no—
305Q8×C43—22no—
306Q8×C43—22no—
307Q8×C43—22no—
308Q8×C43—22no—
309Q8×C43—48no—
310Q8×C43—42no—
311Q8×C43—42no—
312Q8×C43C2×#4114yes—
313C2×C4×C43—24no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—24no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—48no—
323C2×C4×C43—42no—
324C2×C4×C43—42no—
325C2×C4×C43—42no—
326C2×C4×C43C22×D412yes—
327C2×C4×C43C22×D411yescharacteristic
328C2×C4×C43C2×#4112yes—
329C2×C4×C43H(5,𝔽2)12yes—
330C2×C4×C43C2511yescharacteristic
331C22⋊D43—28no—
332C22⋊D43—48no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—42no—
340C2×Dic43—42no—
341C2×Dic43—42no—
342C2×Dic43—84no—
343C2×Dic43C22×D412yes—
344C2×Dic43C22×D412yes—
345C2×Dic43C22×D412yes—
346D172—22no—
347D172—22no—
348D172—48no—
349D172—42no—
350C4×D43—24no—
351C4×D43—22no—
352C4×D43—22no—
353C4×D43—48no—
354C4×D43—84no—
355Dic86—84no—
356C8×C43—22no—
357C8×C43—22no—
358C43⋊C8—22no—
359C43⋊C8—22no—
360C2×#3316—431nomaximal, Sylow
361C22×C43—22no—
362C22×C43—28no—
363C22×C43—22no—
364C22×C43#54612yes—
365C22×C43C2×#13714yes—
366C22×C43C2×#13712yes—
367C22×C43#57712yes—
368C22×C43C23×D411yescharacteristic
369C2×D43—22no—
370C2×D43—22no—
371C2×D43—22no—
372C2×D43—44no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—84no—
377C4×C43—24no—
378C4×C43—22no—
379C4×C43—42no—
380C4×C43—42no—
381C4×C43—42no—
382C4×C43#54612yes—
383C4×C43C22×#4111yescharacteristic
384C4×C43C2×H(5,𝔽2)11yescharacteristic
385Dic43—22no—
386Dic43—22no—
387Dic43—22no—
388Dic43—42no—
389Dic43—42no—
390Dic43—42no—
391C2×#554—431no—
392C2×#548—431no—
393#3316—4316no—
394C2×#489—431no—
395C2×#481—431no—
396C2×#483—431no—
397C2×#475—431no—
398C2×#470—431no—
399C2×#465—431no—
400C2×#464—431no—
401C2×#452—431no—
402C2×#451D4311yescharacteristic, complemented
403C2×#441—431no—
404C2×#435—431no—
405C2×#417—431no—
406C22×#103—431no—
407C2×C43—24no—
408C2×C43#331614yescomplemented
409C2×C43C2×#54611yescharacteristic
410C2×C43C22×#13711yescharacteristic
411C2×C43C2×#57711yescharacteristic
412D43—42no—
413D43—82no—
414C22×#41—431no—
415C23×Q8C2×D4311yescharacteristic
416C22×Q16C2×D4311yescharacteristic
417C22×Q16C2×D4311yescharacteristic
418C22×SD16—431no—
419C22×M16—431no—
420C23×C8—431no—
421#554—438no—
422#554—864no—
423#548—438no—
424#548—864no—
425C2×C4⋊Q8—431no—
426C2×#125—861no—
427C2×#124—431no—
428C2×#124—861no—
429C2×C22⋊Q8—431no—
430C2×C22⋊Q8—431no—
431C2×C22⋊Q8—861no—
432C2×C22⋊Q8—861no—
433C2×C22⋊Q8—861no—
434C2×C22⋊Q8C2×D4311yescharacteristic
435C2×#121—431no—
436C2×#121—861no—
437C2×C4×Q8—431no—
438C2×C4×Q8—431no—
439C2×C4×D4—431no—
440C2×C4×D4—861no—
441C2×C4×D4—861no—
442C22×C4⋊C4—431no—
443C22×C4⋊C4—431no—
444#489—438no—
445#483—438no—
446#481—438no—
447#475—438no—
448#470—438no—
449#465—438no—
450#464—438no—
451#452—438no—
452#451C2×D4318yescomplemented
453#441—438no—
454#435—438no—
455C2×#106—431no—
456C2×#106—431no—
457C2×#106—431no—
458C2×C4⋊C8—431no—
459#417—438no—
460C2×#103—431no—
461C2×#103—431no—
462C2×#103—431no—
463C2×#103—431no—
464C2×#103—438no—
465C2×#103—431no—
466C2×#103C2×D4311yescharacteristic
467C2×#103C2×D4311yescharacteristic
468C2×#102—431no—
469C2×#102—431no—
470C2×#102—431no—
471C2×C22⋊C8—431no—
472C2×C22⋊C8C2×D4311yescharacteristic
473C2×#97—431no—
474C43C2×#331611yescharacteristic, complemented, Sylow
475C2×#41—434no—
476C2×#41—862no—
477C2×#41—864no—
478C2×#41—1722no—
479C22×Q8—21no—
480C22×Q8—22no—
481C22×Q8—24no—
482C22×Q8—42no—
483C22×Q8—861no—
484C22×Q8C22×D4311yescharacteristic
485C22×Q8C22×D4311yescharacteristic
486C22×Q8C22×D4314yes—
487C22×Q8C22×D4311yescharacteristic
488C22×D4—431no—
489C22×D4—431no—
490C22×D4—861no—
491C22×D4—861no—
492C23×C4—21no—
493C23×C4—431no—
494C23×C4—861no—
495C23×C4—861no—
496C23×C4—861no—
497C23×C4C22×D4311yescharacteristic
498C2×Q16—24no—
499C2×Q16—42no—
500C2×Q16C22×D4314yes—
501C2×Q16C22×D4314yes—
502C2×SD16—434no—
503C2×SD16—1722no—
504C2×M16—434no—
505C2×M16—1722no—
506C22×C8—431no—
507C22×C8—431no—
508C22×C8—434no—
509C22×C8—1722no—
510C22×C8C22×D4311yescharacteristic
511C22×C8C22×D4311yescharacteristic
512C4⋊Q8—434no—
513C4⋊Q8—862no—
514#125—868no—
515#124—434no—
516#124—862no—
517#124—868no—
518C22⋊Q8—22no—
519C22⋊Q8—434no—
520C22⋊Q8—434no—
521C22⋊Q8—868no—
522C22⋊Q8—868no—
523C22⋊Q8—868no—
524C22⋊Q8—862no—
525C22⋊Q8—862no—
526C22⋊Q8C22×D4314yes—
527#121—434no—
528#121—868no—
529#121—862no—
530C4×Q8—434no—
531C4×Q8—434no—
532C4×Q8—862no—
533C4×Q8—862no—
534C4×D4—434no—
535C4×D4—434no—
536C4×D4—868no—
537C4×D4—868no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—431no—
540C2×C4⋊C4—431no—
541C2×C4⋊C4—431no—
542C2×C4⋊C4—434no—
543C2×C4⋊C4—431no—
544C2×C4⋊C4—434no—
545C2×C4⋊C4—862no—
546C2×C4⋊C4—861no—
547C2×C4⋊C4—861no—
548C2×C4⋊C4—861no—
549C2×C4⋊C4—861no—
550C2×C4⋊C4—861no—
551C2×C4⋊C4—861no—
552C2×C4⋊C4—861no—
553C2×C4⋊C4—862no—
554C2×C4⋊C4C22×D4311yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—431no—
557C2×C22⋊C4—431no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C42—431no—
564C2×C42—861no—
565C2×C42—861no—
566#106—434no—
567#106—434no—
568#106—434no—
569C4⋊C8—434no—
570#103—434no—
571#103—434no—
572#103—434no—
573#103—434no—
574#103—434no—
575#103C22×D4314yes—
576#103C22×D4314yes—
577#102—434no—
578#102—434no—
579#102—434no—
580C22⋊C8—434no—
581C22⋊C8C22×D4314yes—
582#97—434no—
583C24—431no—
584C24—861no—
585C24D4×D4311yescharacteristic
586#41—868no—
587#41—1724no—
588#41—1728no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—24no—
592C2×Q8—21no—
593C2×Q8—22no—
594C2×Q8—28no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8—22no—
598C2×Q8—22no—
599C2×Q8—44no—
600C2×Q8—44no—
601C2×Q8—48no—
602C2×Q8—864no—
603C2×Q8—3442no—
604C2×Q8#1062190014yes—
605C2×Q8C23×D4312yes—
606C2×Q8C23×D4312yes—
607C2×Q8C23×D4312yes—
608C2×D4—434no—
609C2×D4—432no—
610C2×D4—864no—
611C2×D4—864no—
612C2×D4—864no—
613C2×D4—861no—
614C2×D4—862no—
615C2×D4—862no—
616C2×D4—1724no—
617C2×D4—1724no—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—24no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—44no—
626C22×C4—431no—
627C22×C4—431no—
628C22×C4—431no—
629C22×C4—432no—
630C22×C4—432no—
631C22×C4—864no—
632C22×C4—864no—
633C22×C4—862no—
634C22×C4—862no—
635C22×C4—864no—
636C22×C4—861no—
637C22×C4—861no—
638C22×C4—861no—
639C22×C4—3442no—
640C22×C4—3442no—
641C22×C4—1724no—
642C22×C4D4×D4312yes—
643C22×C4D4×D4311yescharacteristic
644C22×C4C23×D4312yes—
645C22×C4C23×D4311yescharacteristic
646Q16—28no—
647Q16—44no—
648SD16—1724no—
649M16—1724no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—432no—
653C2×C8—432no—
654C2×C8—862no—
655C2×C8—862no—
656C2×C8—1724no—
657C2×C8C23×D4312yes—
658C2×C8C23×D4312yes—
659C4⋊C4—24no—
660C4⋊C4—21no—
661C4⋊C4—434no—
662C4⋊C4—432no—
663C4⋊C4—432no—
664C4⋊C4—432no—
665C4⋊C4—864no—
666C4⋊C4—864no—
667C4⋊C4—864no—
668C4⋊C4—864no—
669C4⋊C4—864no—
670C4⋊C4—864no—
671C4⋊C4—861no—
672C4⋊C4—864no—
673C4⋊C4—861no—
674C4⋊C4—861no—
675C4⋊C4C23×D4312yes—
676C22⋊C4—24no—
677C22⋊C4—434no—
678C22⋊C4—434no—
679C22⋊C4—864no—
680C22⋊C4—864no—
681C22⋊C4—864no—
682C22⋊C4—864no—
683C22⋊C4—864no—
684C42—432no—
685C42—432no—
686C42—864no—
687C42—864no—
688C23—22no—
689C23—22no—
690C23—432no—
691C23—862no—
692C23—862no—
693C23—862no—
694C23—862no—
695C23—1722no—
696C23—1722no—
697C23—1722no—
698C23#1306335714yes—
699C23C2×D4×D4312yes—
700C23C2×D4×D4311yescharacteristic
701Q8—22no—
702Q8—24no—
703Q8—22no—
704Q8—22no—
705Q8—22no—
706Q8—22no—
707Q8—48no—
708Q8—42no—
709Q8—42no—
710Q8—3444no—
711Q8C2×#1062190014yes—
712D4—868no—
713D4—862no—
714D4—862no—
715D4—1728no—
716D4—1728no—
717D4—1722no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—48no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—432no—
732C2×C4—432no—
733C2×C4—432no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—864no—
740C2×C4—862no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—3444no—
744C2×C4—3444no—
745C2×C4—1728no—
746C2×C4—1722no—
747C2×C4—1722no—
748C2×C4—1722no—
749C2×C4C2×D4×D4312yes—
750C2×C4C2×D4×D4311yescharacteristic
751C2×C4C2×#1062190012yes—
752C2×C4#1306337012yes—
753C2×C4C24×D4311yescharacteristic
754C8—22no—
755C8—22no—
756C8—862no—
757C8—862no—
758C22—22no—
759C22—22no—
760C22—28no—
761C22—862no—
762C22—862no—
763C22—862no—
764C22—3444no—
765C22—1722no—
766C22—1722no—
767C22—1722no—
768C22—1724no—
769C22#1458353612yes—
770C22C2×#1306335714yes—
771C22C2×#1306335712yes—
772C22#1458370812yes—
773C22C22×D4×D4311yescharacteristic
774C4—22no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—862no—
780C4—862no—
781C4—862no—
782C4—1722no—
783C4—1722no—
784C4—1722no—
785C4#1458353612yes—
786C4C22×#1062190011yescharacteristic
787C4C2×#1306337011yescharacteristic
788C2—24no—
789C2—3442no—
790C2—1722no—
791C2#1914671014yesdirect product factor
792C2C2×#1458353611yescharacteristic
793C2C22×#1306335711yescharacteristic
794C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#451C2
socleC23×C43C22×D4
prime radicalC2×#14583560C2
hypercenterC2×#451D43
hypocenterC43C2×#3316
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C2×#14583607C2semidirect
3. #19146710C2direct (N × H)
4. C2×#14583260C2semidirect
5. C2×#14583218C2semidirect
6. C2×#14583228C2semidirect
7. C2×#14583182C2semidirect
8. C2×#14583154C2semidirect
9. C2×#14583130C2semidirect
10. C2×#14583123C2semidirect
11. C2×#14583060C2semidirect
12. C2×#14583006C2semidirect
13. C2×#14582967C2semidirect
14. C2×#14582899C2semidirect
15. C22×#13063249C2semidirect
16. C2×C43×#451C2semidirect
22. #14583607C22semidirect
43. #14583260C22semidirect
44. #14583228C22semidirect
45. #14583218C22semidirect
46. #14583182C22semidirect
47. #14583154C22semidirect
48. #14583130C22semidirect
49. #14583123C22semidirect
50. #14583060C22semidirect
51. #14583006C22semidirect
52. #14582967C22semidirect
57. #14582899C22semidirect
63. C2×#13063249C22semidirect
73. C43×#451C22semidirect
402. C2×#451D43semidirect
408. C2×C43#3316semidirect
452. #451C2×D43semidirect
474. C43C2×#3316semidirect
791. C2#19146710direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836072
C2×#145835602
#191467102
C2×#145832602
C2×#145832182
C2×#145832282
C2×#145831822
C2×#145831542
C2×#145831302
C2×#145831232
C2×#145830602
C2×#145830062
C2×#145829672
C2×#145828992
C22×#130632492
C2×C43×#4512
C2×#331643