Finite Group Databasebeta

← C2×#19149378 #26010442

Subgroups — C2×#19149378 #26010442

Order 11008.

10794 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583735C211yesmaximal, characteristic, complemented
2C22×#13063373C211yesmaximal, characteristic, complemented
3#19149378C2132yesmaximal, direct product factor
4C2×#14583715C214yesmaximal, complemented
5C2×#14583712C214yesmaximal, complemented
6C2×#14583708C214yesmaximal, complemented
7C2×#14583705C214yesmaximal, complemented
8C2×#14583699C211yesmaximal, characteristic, complemented
9C2×#14583698C214yesmaximal, complemented
10C2×#14583697C211yesmaximal, characteristic, complemented
11C22×#13063356C211yesmaximal, characteristic, complemented
12C2×#137×D43C214yesmaximal, complemented
13C2×#14583665C211yesmaximal, characteristic, complemented
14C22×#137×C43C211yesmaximal, characteristic, complemented
15#14583735—28no—
16#14583735C22116yescomplemented
17C2×#13063373—22no—
18C2×#13063373—22no—
19C2×#13063373—28no—
20C2×#13063373C2214yescomplemented
21C2×#13063373C2214yescomplemented
22C2×#13063373C2212yescomplemented
23C2×#13063373C22116yescomplemented
24C2×#13063372—21no—
25C2×#13063372C2212yescomplemented
26C2×#13063371—21no—
27C2×#13063371C2212yescomplemented
28C2×#13063370—22no—
29C2×#13063370C2212yescomplemented
30C22×#10621902—21no—
31C22×#10621902C2212yescomplemented
32C22×#10621898—22no—
33C22×#10621898—22no—
34C22×#10621898C2211yescharacteristic
35C22×#10621898C2211yescharacteristic
36C22×#10621898C2211yescharacteristic, complemented
37C2×#41×D43—22no—
38C2×#41×D43C2214yes—
39C22×Q8×D43—21no—
40C22×Q8×D43C2212yescomplemented
41#14583715C22164yescomplemented
42#14583712C22164yescomplemented
43#14583708C22164yescomplemented
44#14583705C22164yescomplemented
45#14583699C22116yescomplemented
46#14583698C22164yescomplemented
47#14583697C22116yescomplemented
48C2×#13063358C2212yescomplemented
49C2×#13063358C2212yescomplemented
50C2×#13063357C2218yescomplemented
51C2×#13063357C2218yescomplemented
52C2×#13063356C2214yescomplemented
53C2×#13063356C2214yescomplemented
54C2×#13063356C2212yescomplemented
55C2×#13063356C22116yescomplemented
56C2×#13063355C2212yescomplemented
57C2×#13063354C2218yescomplemented
58#137×D43C22164yescomplemented
59C2×#13063353C2212yescomplemented
60C2×#13063353C2212yescomplemented
61C2×#13063352C2218yescomplemented
62C2×#13063351C2212yescomplemented
63C2×#13063350C2212yescomplemented
64C2×#13063348C2218yescomplemented
65C2×#13063347C2214yescomplemented
66C2×#13063346C2218yescomplemented
67C2×#13063345C2214yescomplemented
68C22×#10621885C2212yescomplemented
69C2×Q16×D43C2218yescomplemented
70C22×#10621884C2212yescomplemented
71C2×SD16×D43C2218yescomplemented
72#14583665C22116yescomplemented
73C2×#13063333C2214yescomplemented
74C2×#13063331C2214yescomplemented
75C22×#10621877C2211yescharacteristic, complemented
76C2×M16×D43C2214yescomplemented
77C22×#41×C43C2211yescharacteristic
78C23×Q8×C43C2211yescharacteristic, complemented
79C2×#137×C43C2214yescomplemented
80C2×#137×C43C2214yescomplemented
81C2×#137×C43C22116yescomplemented
82C22×Q16×C43C2212yescomplemented
83C22×SD16×C43C2212yescomplemented
84C22×M16×C43C2211yescharacteristic, complemented
85#13063373—216no—
86#13063373—216no—
87#13063373—232no—
88#13063373—232no—
89#13063373—28no—
90#13063373C23132yescomplemented
91#13063373C23132yescomplemented
92#13063373C23116yescomplemented
93#13063372—28no—
94#13063372—216no—
95#13063372C23116yescomplemented
96#13063371—28no—
97#13063371—216no—
98#13063371C23116yescomplemented
99#13063370—232no—
100#13063370—28no—
101#13063370C23116yescomplemented
102C2×#10621902—22no—
103C2×#10621902—24no—
104C2×#10621902—24no—
105C2×#10621902—216no—
106C2×#10621902—24no—
107C2×#10621902—28no—
108C2×#10621902C2318yes—
109C2×#10621902C2314yes—
110C2×#10621902C23116yescomplemented
111C2×#10621898—21no—
112C2×#10621898—21no—
113C2×#10621898—24no—
114C2×#10621898—21no—
115C2×#10621898—21no—
116C2×#10621898—24no—
117C2×#10621898—24no—
118C2×#10621898—28no—
119C2×#10621898—28no—
120C2×#10621898—232no—
121C2×#10621898—232no—
122C2×#10621898—22no—
123C2×#10621898—24no—
124C2×#10621898—22no—
125C2×#10621898D412yes—
126C2×#10621898D412yes—
127C2×#10621898D418yes—
128C2×#10621898C2312yes—
129C2×#10621898C2312yes—
130C2×#10621898C2318yes—
131C2×#10621898C2312yes—
132C2×#10621898C2312yes—
133C2×#10621898C2312yes—
134C2×#10621898C2312yes—
135C2×#10621898C2318yes—
136C2×#10621898C2318yescomplemented
137C2×#10621900—24no—
138C2×#10621900—24no—
139C2×#10621900—22no—
140C2×#10621900C2314yes—
141#41×D43—232no—
142#41×D43—216no—
143#41×D43C23132yes—
144C22×Dic86—22no—
145C22×Dic86—22no—
146C22×Dic86D411yescharacteristic
147C22×Dic86C2311yescharacteristic
148C22×Dic86C2311yescharacteristic
149C2×Q8×D43—24no—
150C2×Q8×D43—28no—
151C2×Q8×D43—24no—
152C2×Q8×D43—24no—
153C2×Q8×D43—216no—
154C2×Q8×D43—22no—
155C2×Q8×D43C2318yes—
156C2×Q8×D43C2314yes—
157C2×Q8×D43C23116yescomplemented
158C22×D172—22no—
159C22×D172—22no—
160C22×D172D411yescharacteristic
161C22×D172C2311yescharacteristic
162C22×D172C2311yescharacteristic
163C22×C22⋊D43—21no—
164C22×C22⋊D43—21no—
165C22×C22⋊D43—24no—
166C22×C22⋊D43D412yes—
167C2×D4×D43—24no—
168C2×D4×D43—24no—
169C2×D4×D43—22no—
170C2×D4×D43C2314yes—
171C22×C4×D43—22no—
172C22×C4×D43—21no—
173C22×C4×D43—21no—
174C22×C4×D43—22no—
175C22×C4×D43—24no—
176C22×C4×D43C2312yes—
177#13063358C23116yescomplemented
178#13063358C23116yescomplemented
179#13063357C23164yescomplemented
180#13063357C23164yescomplemented
181#13063356C23132yescomplemented
182#13063356C23132yescomplemented
183#13063356C23116yescomplemented
184#13063355C23116yescomplemented
185#13063354C23164yescomplemented
186#13063353C23116yescomplemented
187#13063353C23116yescomplemented
188#13063352C23164yescomplemented
189#13063351C23116yescomplemented
190#13063350C23116yescomplemented
191#13063348C23164yescomplemented
192#13063347C23132yescomplemented
193#13063346C23164yescomplemented
194#13063345C23132yescomplemented
195C2×Dic172C2314yes—
196C2×#10621885C2314yes—
197C2×#10621885C2318yes—
198C2×#10621885C23116yescomplemented
199Q16×D43C23164yescomplemented
200C2×#10621873C2314yes—
201C2×#10621873C2314yes—
202C2×#10621883C2314yes—
203C2×#10621884C2318yes—
204C2×#10621884C2314yes—
205C2×#10621884C23116yescomplemented
206SD16×D43C23164yescomplemented
207C2×D344C2314yes—
208C2×#10621882C2314yes—
209#13063333C23132yescomplemented
210#13063331C23132yescomplemented
211C2×#10621877C2312yes—
212C2×#10621877C2312yes—
213C2×#10621877C2318yescomplemented
214C2×#10621872C2318yes—
215M16×D43C23132yescomplemented
216C22×C43⋊C8C2312yes—
217C2×C8×D43C2318yes—
218C2×#41×C43—21no—
219C2×#41×C43—21no—
220C2×#41×C43—24no—
221C2×#41×C43C2312yes—
222C2×#41×C43C2312yes—
223C2×#41×C43C2318yes—
224C22×Q8×C43—21no—
225C22×Q8×C43—21no—
226C22×Q8×C43—21no—
227C22×Q8×C43—24no—
228C22×Q8×C43C2312yes—
229C22×Q8×C43C2311yescharacteristic
230C22×Q8×C43C2312yes—
231C22×Q8×C43C2312yes—
232C22×Q8×C43C2318yescomplemented
233C22×D4×C43—21no—
234C22×D4×C43C2311yescharacteristic
235C23×C4×C43—21no—
236C23×C4×C43—21no—
237C23×C4×C43C2311yescharacteristic
238#137×C43C23132yescomplemented
239#137×C43C23132yescomplemented
240C2×Q16×C43C2318yes—
241C2×Q16×C43C23116yescomplemented
242C2×SD16×C43C2318yes—
243C2×SD16×C43C23116yescomplemented
244C2×M16×C43C2312yes—
245C2×M16×C43C2312yes—
246C2×M16×C43C2318yescomplemented
247C22×C8×C43C2312yes—
248C24×C43—21no—
249C24×C43C2×D411yescharacteristic
250C23×D43—21no—
251C23×D43—21no—
252C23×D43—24no—
253C23×D43C2×D412yes—
254#41×C43—24no—
255#41×C43—28no—
256#41×C43—24no—
257#41×C43—28no—
258#41×C43C2418yes—
259#41×C43C2418yes—
260C2×Q8×C43—22no—
261C2×Q8×C43—22no—
262C2×Q8×C43—24no—
263C2×Q8×C43—22no—
264C2×Q8×C43—24no—
265C2×Q8×C43—24no—
266C2×Q8×C43—28no—
267C2×Q8×C43—28no—
268C2×Q8×C43—28no—
269C2×Q8×C43—21no—
270C2×Q8×C43—22no—
271C2×Q8×C43C2414yes—
272C2×Q8×C43C2418yes—
273C2×Q8×C43C2412yes—
274C2×Q8×C43C2414yes—
275C2×Q8×C43C2418yes—
276C2×Q8×C43C2418yes—
277C2×D4×C43—21no—
278C2×D4×C43—22no—
279C2×D4×C43—22no—
280C2×D4×C43—22no—
281C2×D4×C43—28no—
282C2×D4×C43C2412yes—
283C2×D4×C43C2414yes—
284C22×C4×C43—22no—
285C22×C4×C43—22no—
286C22×C4×C43—28no—
287C22×C4×C43—21no—
288C22×C4×C43—22no—
289C22×C4×C43—22no—
290C22×C4×C43—22no—
291C22×C4×C43—28no—
292C22×C4×C43C2×D411yescharacteristic
293C22×C4×C43C2×D411yescharacteristic
294C22×C4×C43C2×D411yescharacteristic
295C22×C4×C43C2×D414yes—
296C22×C4×C43C2411yescharacteristic
297C22×C4×C43C2411yescharacteristic
298C22×C4×C43C2411yescharacteristic
299C22×C4×C43C2414yes—
300C2×C22⋊D43—232no—
301C2×C22⋊D43—24no—
302C2×C22⋊D43—22no—
303C2×C22⋊D43—22no—
304C2×C22⋊D43—22no—
305C2×C22⋊D43—22no—
306C2×C22⋊D43—28no—
307C2×C22⋊D43—28no—
308C2×C22⋊D43—24no—
309C2×C22⋊D43C2×D414yes—
310C2×C22⋊D43C2×D414yes—
311C2×C22⋊D43C2×D4116yes—
312C22×Dic43—24no—
313C22×Dic43—21no—
314C22×Dic43—21no—
315C22×Dic43C2×D412yes—
316#10621902—216no—
317#10621902—232no—
318#10621902—232no—
319#10621902—28no—
320#10621902—216no—
321#10621902—232no—
322#10621902C24132yes—
323#10621902C24116yes—
324Q8×D43—216no—
325Q8×D43—232no—
326Q8×D43—28no—
327Q8×D43—232no—
328Q8×D43—232no—
329Q8×D43—216no—
330Q8×D43C24132yes—
331Q8×D43C24116yes—
332#10621900—232no—
333#10621900—232no—
334#10621900—28no—
335#10621900—216no—
336#10621900C24116yes—
337D4×D43—232no—
338D4×D43—216no—
339D4×D43—28no—
340D4×D43—232no—
341D4×D43C24116yes—
342#10621898—24no—
343#10621898—28no—
344#10621898—24no—
345#10621898—28no—
346#10621898—24no—
347#10621898—24no—
348#10621898—28no—
349#10621898—28no—
350#10621898—232no—
351#10621898—264no—
352#10621898—264no—
353#10621898—216no—
354#10621898—232no—
355#10621898—216no—
356#10621898C2×D4116yes—
357#10621898C2×D4116yes—
358#10621898C2×D418yes—
359#10621898C2×D418yes—
360#10621898C2418yes—
361#10621898C2418yes—
362#10621898C2418yes—
363#10621898C2418yes—
364#10621898C2418yes—
365#10621898C2418yes—
366C2×D172—21no—
367C2×D172—21no—
368C2×D172—22no—
369C2×D172—22no—
370C2×D172—216no—
371C2×D172—24no—
372C2×D172—28no—
373C2×D172—216no—
374C2×D172C2×D412yes—
375C2×D172C2×D412yes—
376C2×D172C2×D418yes—
377C2×D172C2412yes—
378C2×D172C2412yes—
379C2×D172C2414yes—
380C2×D172C2414yes—
381C2×C4×D43—22no—
382C2×C4×D43—22no—
383C2×C4×D43—22no—
384C2×C4×D43—22no—
385C2×C4×D43—28no—
386C2×C4×D43—28no—
387C2×C4×D43—24no—
388C2×C4×D43—28no—
389C2×C4×D43—216no—
390C2×C4×D43—232no—
391C2×C4×D43—24no—
392C2×C4×D43—28no—
393C2×C4×D43—216no—
394C2×C4×D43C2×D414yes—
395C2×C4×D43C2×D418yes—
396C2×C4×D43C2414yes—
397C2×C4×D43C2418yes—
398C2×Dic86—21no—
399C2×Dic86—22no—
400C2×Dic86—21no—
401C2×Dic86—22no—
402C2×Dic86—28no—
403C2×Dic86—216no—
404C2×Dic86—24no—
405C2×Dic86—216no—
406C2×Dic86C2×D412yes—
407C2×Dic86C2×D412yes—
408C2×Dic86C2×D418yes—
409C2×Dic86C2412yes—
410C2×Dic86C2412yes—
411C2×Dic86C2414yes—
412C2×Dic86C2414yes—
413Q16×C43C24132yes—
414SD16×C43C24132yes—
415M16×C43C2418yes—
416M16×C43C2418yes—
417C2×C8×C43C2414yes—
418C2×C8×C43C2418yes—
419#10621885C24116yes—
420#10621885C24132yes—
421#10621884C24132yes—
422#10621884C24116yes—
423#10621883C24116yes—
424#10621882C24116yes—
425#10621877C2418yes—
426#10621877C2418yes—
427C2×C43⋊C8C2414yes—
428C2×C43⋊C8C2418yes—
429Dic172C24116yes—
430D344C24116yes—
431#10621873C24116yes—
432#10621873C24116yes—
433#10621872C24132yes—
434C8×D43C24132yes—
435C23×C43—22no—
436C23×C43—24no—
437C23×C43—42no—
438C23×C43—82no—
439C23×C43C22×D411yescharacteristic
440C23×C43C22×D411yescharacteristic
441C23×C43C22×D411yescharacteristic
442C23×C43C22×D414yes—
443C22×D43—24no—
444C22×D43—22no—
445C22×D43—22no—
446C22×D43—24no—
447C22×D43—216no—
448C22×D43—44no—
449C22×D43—44no—
450C22×D43—88no—
451C22×D43—82no—
452C22×D43C22×D414yes—
453C22×D43C22×D418yes—
454Q8×C43—24no—
455Q8×C43—28no—
456Q8×C43—28no—
457Q8×C43—28no—
458Q8×C43—22no—
459Q8×C43—24no—
460Q8×C43C2518yes—
461Q8×C43C2514yes—
462D4×C43—28no—
463D4×C43—28no—
464D4×C43—22no—
465D4×C43—24no—
466D4×C43C2514yes—
467C2×C4×C43—22no—
468C2×C4×C43—28no—
469C2×C4×C43—24no—
470C2×C4×C43—24no—
471C2×C4×C43—28no—
472C2×C4×C43—28no—
473C2×C4×C43—28no—
474C2×C4×C43—28no—
475C2×C4×C43C22×D411yescharacteristic
476C2×C4×C43C22×D411yescharacteristic
477C2×C4×C43C22×D412yes—
478C2×C4×C43C22×D412yes—
479C2×C4×C43C22×D411yescharacteristic
480C2×C4×C43C22×D414yes—
481C2×C4×C43C22×D414yes—
482C2×C4×C43C22×D414yes—
483C2×C4×C43C22×D412yes—
484C2×C4×C43C2511yescharacteristic
485C2×C4×C43C2512yes—
486C2×C4×C43C2512yes—
487C2×C4×C43C2512yes—
488C22⋊D43—28no—
489C22⋊D43—28no—
490C22⋊D43—28no—
491C22⋊D43—28no—
492C22⋊D43—216no—
493C22⋊D43—216no—
494C22⋊D43C22×D4116yes—
495C22⋊D43C22×D4116yes—
496C2×Dic43—24no—
497C2×Dic43—22no—
498C2×Dic43—22no—
499C2×Dic43—24no—
500C2×Dic43—216no—
501C2×Dic43C22×D414yes—
502C2×Dic43C22×D418yes—
503D172—216no—
504D172—232no—
505D172—24no—
506D172—22no—
507D172—22no—
508D172—24no—
509D172C22×D418yes—
510D172C22×D418yes—
511D172C2514yes—
512D172C2514yes—
513C4×D43—216no—
514C4×D43—232no—
515C4×D43—28no—
516C4×D43—28no—
517C4×D43—28no—
518C4×D43—28no—
519C4×D43—216no—
520C4×D43—232no—
521C4×D43C22×D4116yes—
522C4×D43C22×D418yes—
523C4×D43C2518yes—
524Dic86—24no—
525Dic86—22no—
526Dic86—22no—
527Dic86—24no—
528Dic86—216no—
529Dic86—232no—
530Dic86C22×D418yes—
531Dic86C22×D418yes—
532Dic86C2514yes—
533Dic86C2514yes—
534C8×C43C2518yes—
535C43⋊C8C2518yes—
536C2×#3586—431nomaximal, Sylow
537C22×C43—22no—
538C22×C43—22no—
539C22×C43—22no—
540C22×C43—24no—
541C22×C43—44no—
542C22×C43—44no—
543C22×C43—84no—
544C22×C43C23×D412yes—
545C22×C43C23×D412yes—
546C22×C43C23×D412yes—
547C22×C43C23×D411yescharacteristic
548C2×D43—28no—
549C2×D43—24no—
550C2×D43—24no—
551C2×D43—48no—
552C2×D43—48no—
553C2×D43—44no—
554C2×D43—44no—
555C2×D43—816no—
556C2×D43—84no—
557C2×D43C23×D418yes—
558C4×C43—24no—
559C4×C43—28no—
560C4×C43C23×D411yescharacteristic
561C4×C43C23×D412yes—
562C4×C43C23×D412yes—
563C4×C43C23×D412yes—
564C4×C43C2611yescharacteristic
565Dic43—24no—
566Dic43—24no—
567Dic43C23×D418yes—
568C2×#585—431no—
569C22×2−1+4—431no—
570#3586—4332no—
571C2×#578—434no—
572C2×#578—434no—
573C2×#577—434no—
574C2×#577—434no—
575C2×#575—431no—
576C2×#575—434no—
577C2×#575—431no—
578C22×#137—431no—
579C22×#137—434no—
580C22×#137D4311yescharacteristic, complemented
581C2×#568—431no—
582C2×C43—22no—
583C2×C43—22no—
584C2×C43—22no—
585C2×C43—44no—
586C2×C43#358612yescomplemented
587C2×C43C24×D411yescharacteristic
588D43—28no—
589D43—44no—
590D43—44no—
591#585—4316no—
592#585—868no—
593C2×2−1+4—432no—
594C2×2−1+4—434no—
595C2×2−1+4—434no—
596C2×2−1+4—432no—
597C2×2−1+4—4316no—
598C2×2−1+4—862no—
599C2×2−1+4—862no—
600C2×2−1+4—868no—
601C2×2−1+4—861no—
602C2×H(5,𝔽2)—432no—
603C2×H(5,𝔽2)—432no—
604C2×H(5,𝔽2)—862no—
605C2×H(5,𝔽2)—861no—
606C22×#41—431no—
607C22×#41—434no—
608C22×#41—432no—
609C22×#41—431no—
610C22×#41—431no—
611C22×#41—862no—
612C22×#41—862no—
613C22×#41—861no—
614C22×#41—862no—
615C22×#41C2×D4311yescharacteristic
616C23×Q8—432no—
617C23×Q8—861no—
618C23×Q8C2×D4311yescharacteristic, complemented
619#578—4364no—
620#578—4364no—
621#577—4364no—
622#577—4364no—
623#575—4316no—
624#575—4364no—
625#575—4316no—
626C2×#137—432no—
627C2×#137—434no—
628C2×#137—434no—
629C2×#137—432no—
630C2×#137—4316no—
631C2×#137—4364no—
632C2×#137—438no—
633C2×#137—438no—
634C2×#137—438no—
635C2×#137—432no—
636C2×#137—432no—
637C2×#137C2×D4314yescomplemented
638C2×#137C2×D4314yescomplemented
639C2×#137C2×D43116yescomplemented
640C2×AGL(1,ℤ/8)—432no—
641C2×AGL(1,ℤ/8)—432no—
642C2×AGL(1,ℤ/8)—438no—
643C2×AGL(1,ℤ/8)—432no—
644C2×AGL(1,ℤ/8)—432no—
645C2×#135—434no—
646C2×#135—438no—
647C2×#135—438no—
648C2×#135—434no—
649C22×Q16—432no—
650C22×Q16—438no—
651C22×Q16C2×D4312yescomplemented
652C22×SD16—432no—
653C22×SD16—438no—
654C22×SD16C2×D4312yescomplemented
655#568—4316no—
656C2×#131—434no—
657C2×#131—434no—
658C22×M16—431no—
659C22×M16—434no—
660C22×M16C2×D4311yescharacteristic, complemented
661C43C2×#358611yescharacteristic, complemented, Sylow
6622−1+4—4316no—
6632−1+4—4332no—
6642−1+4—4332no—
6652−1+4—4316no—
6662−1+4—8616no—
6672−1+4—8616no—
6682−1+4—8632no—
6692−1+4—8632no—
6702−1+4—868no—
6712−1+4—8616no—
6722−1+4—868no—
673H(5,𝔽2)—4316no—
674H(5,𝔽2)—4316no—
675H(5,𝔽2)—8632no—
676H(5,𝔽2)—868no—
677H(5,𝔽2)—8616no—
678H(5,𝔽2)—868no—
679C2×#41—21no—
680C2×#41—21no—
681C2×#41—24no—
682C2×#41—432no—
683C2×#41—432no—
684C2×#41—438no—
685C2×#41—432no—
686C2×#41—432no—
687C2×#41—438no—
688C2×#41—4332no—
689C2×#41—438no—
690C2×#41—434no—
691C2×#41—4316no—
692C2×#41—434no—
693C2×#41—432no—
694C2×#41—432no—
695C2×#41—432no—
696C2×#41—432no—
697C2×#41—438no—
698C2×#41—438no—
699C2×#41—864no—
700C2×#41—864no—
701C2×#41—862no—
702C2×#41—868no—
703C2×#41—868no—
704C2×#41—8632no—
705C2×#41—862no—
706C2×#41—8632no—
707C2×#41—864no—
708C2×#41—864no—
709C2×#41—868no—
710C2×#41—8616no—
711C2×#41—864no—
712C2×#41—862no—
713C2×#41—862no—
714C2×#41—864no—
715C2×#41—864no—
716C2×#41—8616no—
717C2×#41—8632no—
718C2×#41—861no—
719C2×#41—861no—
720C2×#41—861no—
721C2×#41—861no—
722C2×#41—864no—
723C2×#41—864no—
724C2×#41C22×D4312yes—
725C2×#41C22×D4312yes—
726C2×#41C22×D4318yes—
727C22×Q8—21no—
728C22×Q8—21no—
729C22×Q8—21no—
730C22×Q8—24no—
731C22×Q8—431no—
732C22×Q8—438no—
733C22×Q8—434no—
734C22×Q8—4316no—
735C22×Q8—431no—
736C22×Q8—431no—
737C22×Q8—862no—
738C22×Q8—862no—
739C22×Q8—864no—
740C22×Q8—868no—
741C22×Q8—864no—
742C22×Q8—864no—
743C22×Q8—8616no—
744C22×Q8—862no—
745C22×Q8C22×D4312yes—
746C22×Q8C22×D4312yes—
747C22×Q8C22×D4311yescharacteristic
748C22×Q8C22×D4312yes—
749C22×Q8C22×D4318yescomplemented
750C22×D4—21no—
751C22×D4—432no—
752C22×D4—434no—
753C22×D4—431no—
754C22×D4—431no—
755C22×D4—431no—
756C22×D4—862no—
757C22×D4—862no—
758C22×D4—864no—
759C22×D4—862no—
760C22×D4—864no—
761C22×D4—864no—
762C22×D4—861no—
763C22×D4—861no—
764C22×D4C22×D4311yescharacteristic
765C23×C4—21no—
766C23×C4—21no—
767C23×C4—432no—
768C23×C4—862no—
769C23×C4—864no—
770C23×C4—862no—
771C23×C4—861no—
772C23×C4—861no—
773C23×C4C22×D4311yescharacteristic
774#137—4316no—
775#137—4332no—
776#137—4332no—
777#137—4316no—
778#137—4364no—
779#137—4364no—
780#137—4364no—
781#137—4316no—
782#137—4316no—
783#137C22×D43132yescomplemented
784#137C22×D43132yescomplemented
785AGL(1,ℤ/8)—4316no—
786AGL(1,ℤ/8)—4316no—
787AGL(1,ℤ/8)—4364no—
788AGL(1,ℤ/8)—4316no—
789AGL(1,ℤ/8)—4316no—
790#135—4332no—
791#135—4364no—
792#135—4364no—
793#135—4332no—
794C2×Q16—434no—
795C2×Q16—438no—
796C2×Q16—4316no—
797C2×Q16—4364no—
798C2×Q16—434no—
799C2×Q16C22×D4318yes—
800C2×Q16C22×D43116yescomplemented
801C2×SD16—438no—
802C2×SD16—4316no—
803C2×SD16—434no—
804C2×SD16—434no—
805C2×SD16—4364no—
806C2×SD16—434no—
807C2×SD16—434no—
808C2×SD16C22×D4318yes—
809C2×SD16C22×D43116yescomplemented
810C2×D8—434no—
811C2×D8—434no—
812#131—4332no—
813#131—4332no—
814C2×M16—432no—
815C2×M16—432no—
816C2×M16—438no—
817C2×M16—4332no—
818C2×M16—438no—
819C2×M16C22×D4312yes—
820C2×M16C22×D4312yes—
821C2×M16C22×D4318yescomplemented
822C22×C8—432no—
823C22×C8—438no—
824C22×C8C22×D4312yes—
825C24—21no—
826C24—432no—
827C24—864no—
828C24—861no—
829C24—861no—
830C24D4×D4311yescharacteristic
831#41—24no—
832#41—28no—
833#41—28no—
834#41—24no—
835#41—4316no—
836#41—4316no—
837#41—438no—
838#41—438no—
839#41—438no—
840#41—438no—
841#41—4332no—
842#41—4316no—
843#41—4316no—
844#41—438no—
845#41—438no—
846#41—438no—
847#41—438no—
848#41—8632no—
849#41—8632no—
850#41—8616no—
851#41—8664no—
852#41—8664no—
853#41—8616no—
854#41—8632no—
855#41—868no—
856#41—868no—
857#41—8632no—
858#41—8616no—
859#41—8632no—
860#41—8616no—
861#41—8616no—
862#41—8632no—
863#41—8632no—
864#41—868no—
865#41—864no—
866#41—868no—
867#41—864no—
868#41—868no—
869#41—868no—
870#41—864no—
871#41—864no—
872#41C23×D4318yes—
873#41C23×D4318yes—
874C2×Q8—24no—
875C2×Q8—22no—
876C2×Q8—22no—
877C2×Q8—22no—
878C2×Q8—28no—
879C2×Q8—24no—
880C2×Q8—24no—
881C2×Q8—28no—
882C2×Q8—28no—
883C2×Q8—21no—
884C2×Q8—22no—
885C2×Q8—432no—
886C2×Q8—432no—
887C2×Q8—438no—
888C2×Q8—4332no—
889C2×Q8—4316no—
890C2×Q8—432no—
891C2×Q8—432no—
892C2×Q8—434no—
893C2×Q8—434no—
894C2×Q8—8616no—
895C2×Q8—868no—
896C2×Q8—864no—
897C2×Q8—8616no—
898C2×Q8—8632no—
899C2×Q8—8616no—
900C2×Q8—868no—
901C2×Q8—8632no—
902C2×Q8—8632no—
903C2×Q8—8616no—
904C2×Q8—862no—
905C2×Q8—861no—
906C2×Q8—861no—
907C2×Q8—862no—
908C2×Q8C23×D4314yes—
909C2×Q8C23×D4312yes—
910C2×Q8C23×D4318yes—
911C2×Q8C23×D4318yes—
912C2×Q8C23×D4314yes—
913C2×Q8C23×D4318yes—
914C2×D4—22no—
915C2×D4—22no—
916C2×D4—28no—
917C2×D4—21no—
918C2×D4—22no—
919C2×D4—434no—
920C2×D4—434no—
921C2×D4—4316no—
922C2×D4—4316no—
923C2×D4—432no—
924C2×D4—432no—
925C2×D4—438no—
926C2×D4—432no—
927C2×D4—432no—
928C2×D4—434no—
929C2×D4—434no—
930C2×D4—8616no—
931C2×D4—864no—
932C2×D4—8616no—
933C2×D4—868no—
934C2×D4—868no—
935C2×D4—864no—
936C2×D4—8632no—
937C2×D4—8616no—
938C2×D4—8632no—
939C2×D4—8632no—
940C2×D4—864no—
941C2×D4—862no—
942C2×D4—862no—
943C2×D4—868no—
944C2×D4—862no—
945C2×D4—862no—
946C2×D4—868no—
947C2×D4—861no—
948C2×D4—862no—
949C2×D4—861no—
950C2×D4—862no—
951C2×D4C23×D4312yes—
952C2×D4C23×D4314yes—
953C22×C4—22no—
954C22×C4—21no—
955C22×C4—22no—
956C22×C4—22no—
957C22×C4—28no—
958C22×C4—22no—
959C22×C4—22no—
960C22×C4—28no—
961C22×C4—432no—
962C22×C4—434no—
963C22×C4—438no—
964C22×C4—434no—
965C22×C4—438no—
966C22×C4—864no—
967C22×C4—8616no—
968C22×C4—868no—
969C22×C4—8632no—
970C22×C4—864no—
971C22×C4—8616no—
972C22×C4—868no—
973C22×C4—864no—
974C22×C4—861no—
975C22×C4—861no—
976C22×C4—862no—
977C22×C4—862no—
978C22×C4—868no—
979C22×C4—862no—
980C22×C4—862no—
981C22×C4—868no—
982C22×C4D4×D4311yescharacteristic
983C22×C4D4×D4311yescharacteristic
984C22×C4D4×D4311yescharacteristic
985C22×C4D4×D4314yes—
986C22×C4C23×D4311yescharacteristic
987C22×C4C23×D4311yescharacteristic
988C22×C4C23×D4311yescharacteristic
989C22×C4C23×D4314yes—
990Q16—4316no—
991Q16—4332no—
992Q16—4316no—
993Q16C23×D43132yes—
994SD16—4332no—
995SD16—4316no—
996SD16—4316no—
997SD16—4316no—
998SD16—4316no—
999SD16C23×D43132yes—
1000D8—4316no—
1001D8—4316no—
1002M16—438no—
1003M16—438no—
1004M16—4332no—
1005M16C23×D4318yes—
1006M16C23×D4318yes—
1007C2×C8—434no—
1008C2×C8—438no—
1009C2×C8—4332no—
1010C2×C8C23×D4314yes—
1011C2×C8C23×D4318yes—
1012C23—22no—
1013C23—24no—
1014C23—42no—
1015C23—82no—
1016C23—434no—
1017C23—438no—
1018C23—8616no—
1019C23—864no—
1020C23—864no—
1021C23—862no—
1022C23—862no—
1023C23—3442no—
1024C23—3448no—
1025C23—1724no—
1026C23—1724no—
1027C23C2×D4×D4311yescharacteristic
1028C23C2×D4×D4311yescharacteristic
1029C23C2×D4×D4311yescharacteristic
1030C23C2×D4×D4314yes—
1031Q8—28no—
1032Q8—28no—
1033Q8—24no—
1034Q8—28no—
1035Q8—22no—
1036Q8—24no—
1037Q8—438no—
1038Q8—438no—
1039Q8—434no—
1040Q8—434no—
1041Q8—8632no—
1042Q8—8616no—
1043Q8—864no—
1044Q8—862no—
1045Q8—864no—
1046Q8—862no—
1047Q8C24×D4318yes—
1048Q8C24×D4314yes—
1049D4—28no—
1050D4—28no—
1051D4—22no—
1052D4—24no—
1053D4—4316no—
1054D4—4316no—
1055D4—438no—
1056D4—438no—
1057D4—434no—
1058D4—434no—
1059D4—8616no—
1060D4—8632no—
1061D4—8616no—
1062D4—8616no—
1063D4—868no—
1064D4—868no—
1065D4—868no—
1066D4—868no—
1067D4—864no—
1068D4—862no—
1069D4—864no—
1070D4—862no—
1071D4C24×D4314yes—
1072C2×C4—28no—
1073C2×C4—24no—
1074C2×C4—28no—
1075C2×C4—28no—
1076C2×C4—22no—
1077C2×C4—24no—
1078C2×C4—28no—
1079C2×C4—28no—
1080C2×C4—438no—
1081C2×C4—434no—
1082C2×C4—4316no—
1083C2×C4—438no—
1084C2×C4—438no—
1085C2×C4—8616no—
1086C2×C4—8632no—
1087C2×C4—8616no—
1088C2×C4—8632no—
1089C2×C4—8616no—
1090C2×C4—864no—
1091C2×C4—864no—
1092C2×C4—862no—
1093C2×C4—862no—
1094C2×C4—868no—
1095C2×C4—868no—
1096C2×C4—868no—
1097C2×C4—868no—
1098C2×C4C2×D4×D4314yes—
1099C2×C4C2×D4×D4312yes—
1100C2×C4C2×D4×D4314yes—
1101C2×C4C2×D4×D4314yes—
1102C2×C4C2×D4×D4312yes—
1103C2×C4C2×D4×D4312yes—
1104C2×C4C2×D4×D4311yescharacteristic
1105C2×C4C2×D4×D4311yescharacteristic
1106C2×C4C2×D4×D4311yescharacteristic
1107C2×C4C24×D4312yes—
1108C2×C4C24×D4312yes—
1109C2×C4C24×D4312yes—
1110C2×C4C24×D4311yescharacteristic
1111C8—438no—
1112C8C24×D4318yes—
1113C22—22no—
1114C22—22no—
1115C22—22no—
1116C22—24no—
1117C22—44no—
1118C22—44no—
1119C22—84no—
1120C22—438no—
1121C22—868no—
1122C22—864no—
1123C22—864no—
1124C22—3444no—
1125C22—34416no—
1126C22—1728no—
1127C22—1728no—
1128C22—1724no—
1129C22—1724no—
1130C22C22×D4×D4312yes—
1131C22C22×D4×D4312yes—
1132C22C22×D4×D4312yes—
1133C22C22×D4×D4311yescharacteristic
1134C4—24no—
1135C4—28no—
1136C4—438no—
1137C4—864no—
1138C4—864no—
1139C4C22×D4×D4312yes—
1140C4C22×D4×D4312yes—
1141C4C22×D4×D4311yescharacteristic
1142C4C22×D4×D4312yes—
1143C4C25×D4311yescharacteristic
1144C2—22no—
1145C2—22no—
1146C2—22no—
1147C2—44no—
1148C2—868no—
1149C2—1724no—
1150C2—1724no—
1151C2#1914937812yesdirect product factor
1152C2C23×D4×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC4×C43C26
FrattiniC4C25×D43
FittingC22×#137×C43C2
socleC22×C43C23×D4
hypercenterC22×#137D43
hypocenterC43C2×#3586
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C2×#14583735C2semidirect
2. C22×#13063373C2semidirect
3. #19149378C2direct (N × H)
4. C2×#14583715C2semidirect
5. C2×#14583712C2semidirect
6. C2×#14583708C2semidirect
7. C2×#14583705C2semidirect
8. C2×#14583699C2semidirect
9. C2×#14583698C2semidirect
10. C2×#14583697C2semidirect
11. C22×#13063356C2semidirect
12. C2×#137×D43C2semidirect
13. C2×#14583665C2semidirect
14. C22×#137×C43C2semidirect
16. #14583735C22semidirect
20. C2×#13063373C22semidirect
21. C2×#13063373C22semidirect
22. C2×#13063373C22semidirect
23. C2×#13063373C22semidirect
25. C2×#13063372C22semidirect
27. C2×#13063371C22semidirect
29. C2×#13063370C22semidirect
31. C22×#10621902C22semidirect
36. C22×#10621898C22semidirect
40. C22×Q8×D43C22semidirect
41. #14583715C22semidirect
42. #14583712C22semidirect
43. #14583708C22semidirect
44. #14583705C22semidirect
45. #14583699C22semidirect
46. #14583698C22semidirect
47. #14583697C22semidirect
48. C2×#13063358C22semidirect
49. C2×#13063358C22semidirect
50. C2×#13063357C22semidirect
51. C2×#13063357C22semidirect
52. C2×#13063356C22semidirect
53. C2×#13063356C22semidirect
54. C2×#13063356C22semidirect
55. C2×#13063356C22semidirect
56. C2×#13063355C22semidirect
57. C2×#13063354C22semidirect
58. #137×D43C22semidirect
59. C2×#13063353C22semidirect
60. C2×#13063353C22semidirect
61. C2×#13063352C22semidirect
62. C2×#13063351C22semidirect
63. C2×#13063350C22semidirect
64. C2×#13063348C22semidirect
65. C2×#13063347C22semidirect
66. C2×#13063346C22semidirect
67. C2×#13063345C22semidirect
68. C22×#10621885C22semidirect
69. C2×Q16×D43C22semidirect
70. C22×#10621884C22semidirect
71. C2×SD16×D43C22semidirect
72. #14583665C22semidirect
73. C2×#13063333C22semidirect
74. C2×#13063331C22semidirect
75. C22×#10621877C22semidirect
76. C2×M16×D43C22semidirect
78. C23×Q8×C43C22semidirect
79. C2×#137×C43C22semidirect
80. C2×#137×C43C22semidirect
81. C2×#137×C43C22semidirect
82. C22×Q16×C43C22semidirect
83. C22×SD16×C43C22semidirect
84. C22×M16×C43C22semidirect
90. #13063373C23semidirect
91. #13063373C23semidirect
92. #13063373C23semidirect
95. #13063372C23semidirect
98. #13063371C23semidirect
101. #13063370C23semidirect
110. C2×#10621902C23semidirect
136. C2×#10621898C23semidirect
157. C2×Q8×D43C23semidirect
177. #13063358C23semidirect
178. #13063358C23semidirect
179. #13063357C23semidirect
180. #13063357C23semidirect
181. #13063356C23semidirect
182. #13063356C23semidirect
183. #13063356C23semidirect
184. #13063355C23semidirect
185. #13063354C23semidirect
186. #13063353C23semidirect
187. #13063353C23semidirect
188. #13063352C23semidirect
189. #13063351C23semidirect
190. #13063350C23semidirect
191. #13063348C23semidirect
192. #13063347C23semidirect
193. #13063346C23semidirect
194. #13063345C23semidirect
198. C2×#10621885C23semidirect
199. Q16×D43C23semidirect
205. C2×#10621884C23semidirect
206. SD16×D43C23semidirect
209. #13063333C23semidirect
210. #13063331C23semidirect
213. C2×#10621877C23semidirect
215. M16×D43C23semidirect
232. C22×Q8×C43C23semidirect
238. #137×C43C23semidirect
239. #137×C43C23semidirect
241. C2×Q16×C43C23semidirect
243. C2×SD16×C43C23semidirect
246. C2×M16×C43C23semidirect
580. C22×#137D43semidirect
586. C2×C43#3586semidirect
618. C23×Q8C2×D43semidirect
637. C2×#137C2×D43semidirect
638. C2×#137C2×D43semidirect
639. C2×#137C2×D43semidirect
651. C22×Q16C2×D43semidirect
654. C22×SD16C2×D43semidirect
660. C22×M16C2×D43semidirect
661. C43C2×#3586semidirect
749. C22×Q8C22×D43semidirect
783. #137C22×D43semidirect
784. #137C22×D43semidirect
800. C2×Q16C22×D43semidirect
809. C2×SD16C22×D43semidirect
821. C2×M16C22×D43semidirect
1151. C2#19149378direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145837352
C22×#130633732
#191493782
C2×#145837152
C2×#145837122
C2×#145837082
C2×#145837052
C2×#145836992
C2×#145836982
C2×#145836972
C22×#130633562
C2×#137×D432
C2×#145836652
C22×#137×C432
C2×#358643