Finite Group Databasebeta

← C2×#19146366 #25972784

Subgroups — C2×#19146366 #25972784

Order 11008.

2620 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583714C211yesmaximal, characteristic, complemented
2C2×#14583707C211yesmaximal, characteristic, complemented
3C2×#14583706C211yesmaximal, characteristic, complemented
4#19146366C2116yesmaximal, direct product factor
5C2×#14583292C211yesmaximal, characteristic, complemented
6C2×#14583172C211yesmaximal, characteristic, complemented
7C2×#14583171C211yesmaximal, characteristic, complemented
8C2×#14583164C211yesmaximal, characteristic, complemented
9C2×#14583162C211yesmaximal, characteristic, complemented
10C2×#14583082C211yesmaximal, characteristic, complemented
11C2×#14583080C211yesmaximal, characteristic, complemented
12C2×#14583072C211yesmaximal, characteristic, complemented
13C2×#14583075C211yesmaximal, characteristic, complemented
14C2×#14583021C211yesmaximal, characteristic, complemented
15C2×#14583019C211yesmaximal, characteristic, complemented
16C2×C43×#578C211yesmaximal, characteristic, complemented
17C2×#13063372C2211yescharacteristic
18C2×#13063371C2211yescharacteristic
19#14583714—24no—
20#14583714C2218yescomplemented
21#14583707—24no—
22#14583707C2218yescomplemented
23#14583706—24no—
24#14583706C2218yescomplemented
25C2×#13063357—21no—
26C2×#13063356—21no—
27C2×#13063356—21no—
28C2×#13063356C2211yescharacteristic
29C2×#13063356C2211yescharacteristic
30C2×#13063355—21no—
31C2×#13063355C2211yescharacteristic
32C2×#13063355C2211yescharacteristic, complemented
33C2×#13063350—21no—
34C2×#13063350C2211yescharacteristic
35C2×#13063350C2211yescharacteristic
36C2×#13063349—21no—
37C2×#13063346—21no—
38C2×#13063345—21no—
39C2×#13063345—21no—
40C2×#13063345C2211yescharacteristic
41C22×#10621885—21no—
42C22×#10621885C2211yescharacteristic, complemented
43C22×#10621873C2211yescharacteristic
44C22×#10621884—21no—
45C22×#10621884C2211yescharacteristic
46C2×SD16×D43—21no—
47C2×#13063332C2211yescharacteristic
48C2×#13063332C2211yescharacteristic, complemented
49C2×#13063331C2211yescharacteristic
50C2×#13063323C2211yescharacteristic, complemented
51C2×#13063314C2211yescharacteristic
52#14583292C2218yescomplemented
53#14583172C2218yescomplemented
54#14583171C2218yescomplemented
55#14583164C2218yescomplemented
56#14583162C2218yescomplemented
57#14583082C2218yescomplemented
58#14583080C2218yescomplemented
59#14583075C2218yescomplemented
60#14583072C2218yescomplemented
61#14583021C2218yescomplemented
62#14583019C2218yescomplemented
63C2×#13063261C2211yescharacteristic, complemented
64C2×#13063260C2211yescharacteristic, complemented
65C2×#13063252C2211yescharacteristic
66C2×#13063252C2211yescharacteristic, complemented
67C2×#13063252C2211yescharacteristic, complemented
68C2×#13063251C2211yescharacteristic
69C2×#13063244C2211yescharacteristic, complemented
70C2×#13063244C2211yescharacteristic, complemented
71C2×#13063243C2211yescharacteristic, complemented
72C2×#13063241C2211yescharacteristic
73C2×#13063235C2211yescharacteristic, complemented
74C2×2−1+4×C43C2211yescharacteristic
75C2×2−1+4×C43C2211yescharacteristic, complemented
76C43×#578—24no—
77C43×#578C2218yescomplemented
78C2×#137×C43—21no—
79C2×#137×C43—21no—
80C2×#137×C43C2211yescharacteristic
81C2×#137×C43C2211yescharacteristic, complemented
82C2×#135×C43—21no—
83C2×#135×C43C2211yescharacteristic
84C22×Q16×C43—21no—
85C22×Q16×C43C2211yescharacteristic, complemented
86C2×#131×C43C2211yescharacteristic, complemented
87#13063372—22no—
88#13063372—22no—
89#13063372—41no—
90#13063372C2314yes—
91#13063371—22no—
92#13063371—22no—
93#13063371—41no—
94#13063371C2314yes—
95C2×#10621902—21no—
96C2×#10621898—21no—
97C2×#10621898—21no—
98C2×#10621898C2311yescharacteristic
99C2×#10621900—21no—
100C2×#10621900—41no—
101C22×Dic86—21no—
102C22×Dic86C2311yescharacteristic
103C2×Q8×D43—21no—
104C22×D172—21no—
105C22×D172C2311yescharacteristic
106C2×D4×D43—21no—
107C2×D4×D43—41no—
108#13063357—28no—
109#13063356—22no—
110#13063356—22no—
111#13063356—28no—
112#13063356—28no—
113#13063356C2314yes—
114#13063356C2314yes—
115#13063355—22no—
116#13063355—22no—
117#13063355—28no—
118#13063355C2314yes—
119#13063355C2314yescomplemented
120#13063350—22no—
121#13063350—22no—
122#13063350—28no—
123#13063350C2314yes—
124#13063350C2314yes—
125#13063349—28no—
126#13063346—28no—
127#13063345—28no—
128#13063345—28no—
129#13063345D414yes—
130#13063345C2314yes—
131C2×#10621885—21no—
132C2×#10621885—21no—
133C2×#10621885—21no—
134C2×#10621885—21no—
135C2×#10621885—28no—
136C2×#10621885—21no—
137C2×#10621885—21no—
138C2×#10621885—22no—
139C2×#10621885D411yescharacteristic
140C2×#10621885C2314yescomplemented
141C2×#10621873—21no—
142C2×#10621873—21no—
143C2×#10621873—22no—
144C2×#10621873C2314yes—
145C2×#10621883—21no—
146C2×#10621883—21no—
147C2×#10621883D411yescharacteristic
148C2×#10621884—21no—
149C2×#10621884—21no—
150C2×#10621884—21no—
151C2×#10621884—21no—
152C2×#10621884—28no—
153C2×#10621884—21no—
154C2×#10621884—21no—
155C2×#10621884—22no—
156C2×#10621884D411yescharacteristic
157C2×#10621884C2314yes—
158SD16×D43—28no—
159C2×#10621882—21no—
160C2×#10621882—21no—
161C2×#10621882D411yescharacteristic
162#13063332—22no—
163#13063332—22no—
164#13063332C2314yes—
165#13063332C2314yescomplemented
166#13063331—22no—
167#13063331C2314yes—
168C2×#10621877—21no—
169C2×#10621877—21no—
170C2×#10621877C2311yescharacteristic
171C2×#10621877C2311yescharacteristic
172C2×#10621877C2311yescharacteristic
173C2×#10621872—21no—
174C22×C43⋊C8—21no—
175C22×C43⋊C8—21no—
176C22×C43⋊C8C2311yescharacteristic
177C2×C8×D43—21no—
178#13063323—41no—
179#13063323C2314yescomplemented
180#13063314—41no—
181#13063314C2314yes—
182C2×Dic43⋊C4—41no—
183C2×(C2×D43)⋊C4—41no—
184C2×C4×Dic43C2311yescharacteristic
185#13063261C2314yescomplemented
186#13063260C2314yescomplemented
187#13063252C2314yes—
188#13063252C2314yescomplemented
189#13063252C2314yescomplemented
190#13063251C2314yes—
191#13063244C2314yescomplemented
192#13063244C2314yescomplemented
193#13063243C2314yescomplemented
194#13063241C2314yes—
195#13063235C2314yescomplemented
1962−1+4×C43—22no—
1972−1+4×C43—22no—
1982−1+4×C43—22no—
1992−1+4×C43—22no—
2002−1+4×C43—41no—
2012−1+4×C43—41no—
2022−1+4×C43C2314yes—
2032−1+4×C43C2314yescomplemented
204C2×#41×C43—21no—
205C2×#41×C43—21no—
206C2×#41×C43—21no—
207C2×#41×C43—21no—
208C2×#41×C43—41no—
209C2×#41×C43—41no—
210C2×#41×C43C2311yescharacteristic
211C2×#41×C43C2311yescharacteristic
212C2×#41×C43C2311yescharacteristic
213C22×Q8×C43—21no—
214C22×Q8×C43—21no—
215C22×Q8×C43—21no—
216C22×Q8×C43—21no—
217C22×Q8×C43C2311yescharacteristic
218C22×Q8×C43C2311yescharacteristic
219#137×C43—22no—
220#137×C43—22no—
221#137×C43—28no—
222#137×C43—28no—
223#137×C43C2314yes—
224#137×C43C2314yescomplemented
225#135×C43—28no—
226#135×C43D414yes—
227#135×C43C2314yes—
228C2×Q16×C43—21no—
229C2×Q16×C43—21no—
230C2×Q16×C43—28no—
231C2×Q16×C43—21no—
232C2×Q16×C43—21no—
233C2×Q16×C43—22no—
234C2×Q16×C43D411yescharacteristic
235C2×Q16×C43C2314yescomplemented
236C2×SD16×C43—21no—
237C2×SD16×C43—21no—
238C2×SD16×C43D411yescharacteristic
239C2×SD16×C43D411yescharacteristic
240C2×D8×C43D411yescharacteristic
241#131×C43—22no—
242#131×C43C2314yescomplemented
243C2×M16×C43—21no—
244C2×M16×C43C2311yescharacteristic
245C22×C8×C43—21no—
246C22×C8×C43C2311yescharacteristic
247C23×D43—21no—
248C23×D43—41no—
249#41×C43—21no—
250#41×C43—21no—
251#41×C43—21no—
252#41×C43—21no—
253#41×C43—21no—
254#41×C43—21no—
255#41×C43—24no—
256#41×C43—24no—
257#41×C43—24no—
258#41×C43—24no—
259#41×C43—44no—
260#41×C43—44no—
261#41×C43—42no—
262#41×C43—42no—
263#41×C43—42no—
264#41×C43—42no—
265#41×C43—44no—
266#41×C43—44no—
267#41×C43C2×D412yes—
268#41×C43C2×D412yes—
269#41×C43C2×D412yes—
270#41×C43C2412yes—
271#41×C43C2412yes—
272#41×C43C2412yes—
273C2×Q8×C43—21no—
274C2×Q8×C43—21no—
275C2×Q8×C43—24no—
276C2×Q8×C43—24no—
277C2×Q8×C43—24no—
278C2×Q8×C43—24no—
279C2×Q8×C43—21no—
280C2×Q8×C43—21no—
281C2×Q8×C43—21no—
282C2×Q8×C43—21no—
283C2×Q8×C43—21no—
284C2×Q8×C43—21no—
285C2×Q8×C43—21no—
286C2×Q8×C43—21no—
287C2×Q8×C43—41no—
288C2×Q8×C43—41no—
289C2×Q8×C43—42no—
290C2×Q8×C43—42no—
291C2×Q8×C43—42no—
292C2×Q8×C43—42no—
293C2×Q8×C43C2×D411yescharacteristic
294C2×Q8×C43C2×D411yescharacteristic
295C2×Q8×C43C2×D411yescharacteristic
296C2×Q8×C43C2412yes—
297C2×Q8×C43C2412yes—
298C2×D4×C43—21no—
299C2×D4×C43—21no—
300C2×D4×C43—21no—
301C2×D4×C43—41no—
302C2×D4×C43—41no—
303C2×D4×C43C2×D411yescharacteristic
304C2×D4×C43C2×D411yescharacteristic
305C2×D4×C43C2×D411yescharacteristic
306C22×C4×C43—21no—
307C22×C4×C43—21no—
308C22×C4×C43—21no—
309C22×C4×C43—21no—
310C22×C4×C43—21no—
311C22×C4×C43—41no—
312C22×C4×C43—41no—
313C22×C4×C43—41no—
314C22×C4×C43—41no—
315C22×C4×C43C2411yescharacteristic
316C2×C22⋊D43—21no—
317C2×C22⋊D43—41no—
318C2×C22⋊D43—41no—
319C22×Dic43—21no—
320C22×Dic43—21no—
321C22×Dic43—41no—
322#10621902—24no—
323#10621902—42no—
324Q8×D43—24no—
325Q8×D43—42no—
326#10621900—24no—
327#10621900—42no—
328#10621900—44no—
329#10621900—44no—
330D4×D43—24no—
331D4×D43—44no—
332D4×D43—42no—
333D4×D43—44no—
334#10621898—21no—
335#10621898—21no—
336#10621898—24no—
337#10621898—24no—
338#10621898—42no—
339#10621898—42no—
340#10621898C2×D412yes—
341#10621898C2412yes—
342C2×D172—21no—
343C2×D172—21no—
344C2×D172—21no—
345C2×D172—21no—
346C2×D172—21no—
347C2×D172—24no—
348C2×D172—41no—
349C2×D172—42no—
350C2×D172C2×D411yescharacteristic
351C2×D172C2412yes—
352C2×C4×D43—21no—
353C2×C4×D43—41no—
354C2×C4×D43—41no—
355C2×Dic86—21no—
356C2×Dic86—21no—
357C2×Dic86—21no—
358C2×Dic86—21no—
359C2×Dic86—24no—
360C2×Dic86—21no—
361C2×Dic86—42no—
362C2×Dic86—41no—
363C2×Dic86C2×D411yescharacteristic
364C2×Dic86C2412yes—
365Q16×C43—24no—
366Q16×C43—24no—
367Q16×C43—24no—
368Q16×C43—24no—
369Q16×C43C2×D414yes—
370SD16×C43—24no—
371SD16×C43—24no—
372SD16×C43C2×D414yes—
373SD16×C43C2×D414yes—
374D8×C43C2×D414yes—
375M16×C43—21no—
376M16×C43—24no—
377M16×C43C2412yes—
378C2×C8×C43—21no—
379C2×C8×C43—24no—
380C2×C8×C43C2×D411yescharacteristic
381C2×C8×C43C2×D411yescharacteristic
382C2×C8×C43C2×D412yes—
383C2×C8×C43C2412yes—
384#10621885—24no—
385#10621885—24no—
386#10621885—24no—
387#10621885—24no—
388#10621885—24no—
389#10621885—24no—
390#10621885C2×D414yes—
391#10621884—24no—
392#10621884—24no—
393#10621884—24no—
394#10621884—24no—
395#10621884—24no—
396#10621884—24no—
397#10621884C2×D414yes—
398#10621883—24no—
399#10621883—24no—
400#10621883C2×D414yes—
401#10621882—24no—
402#10621882—24no—
403#10621882C2×D414yes—
404(C2×D43)⋊C4—44no—
405Dic43⋊C4—44no—
406C4×Dic43—21no—
407C4×Dic43C2412yes—
408#10621877—21no—
409#10621877—21no—
410#10621877—21no—
411#10621877—24no—
412#10621877—24no—
413#10621877C2412yes—
414#10621877C2412yes—
415#10621877C2412yes—
416C2×C43⋊C8—21no—
417C2×C43⋊C8—21no—
418C2×C43⋊C8—21no—
419C2×C43⋊C8—24no—
420C2×C43⋊C8—24no—
421C2×C43⋊C8C2×D411yescharacteristic
422C2×C43⋊C8C2×D411yescharacteristic
423C2×C43⋊C8C2×D412yes—
424C2×C43⋊C8C2412yes—
425#10621873—24no—
426#10621873—24no—
427#10621872—24no—
428C8×D43—24no—
429C23×C43—21no—
430C23×C43—21no—
431C23×C43—21no—
432C23×C43H(5,𝔽2)11yescharacteristic
433C22×D43—21no—
434C22×D43—22no—
435C22×D43—44no—
436C22×D43—41no—
437C22×D43—41no—
438C22×D43—82no—
439C22×D43—162no—
440Q8×C43—21no—
441Q8×C43—21no—
442Q8×C43—21no—
443Q8×C43—22no—
444Q8×C43—22no—
445Q8×C43—22no—
446Q8×C43—22no—
447Q8×C43—44no—
448Q8×C43—44no—
449Q8×C43—41no—
450Q8×C43—41no—
451Q8×C43—41no—
452Q8×C43—41no—
453Q8×C43C22×D412yes—
454Q8×C43C22×D412yes—
455Q8×C43C22×D412yes—
456D4×C43—22no—
457D4×C43—22no—
458D4×C43—22no—
459D4×C43—22no—
460D4×C43—22no—
461D4×C43—22no—
462D4×C43—21no—
463D4×C43—21no—
464D4×C43—21no—
465D4×C43—44no—
466D4×C43—44no—
467D4×C43C22×D412yes—
468D4×C43C22×D412yes—
469D4×C43C22×D412yes—
470C2×C4×C43—21no—
471C2×C4×C43—21no—
472C2×C4×C43—21no—
473C2×C4×C43—22no—
474C2×C4×C43—22no—
475C2×C4×C43—22no—
476C2×C4×C43—22no—
477C2×C4×C43—22no—
478C2×C4×C43—22no—
479C2×C4×C43—22no—
480C2×C4×C43—22no—
481C2×C4×C43—44no—
482C2×C4×C43—44no—
483C2×C4×C43—44no—
484C2×C4×C43—44no—
485C2×C4×C43—41no—
486C2×C4×C43—41no—
487C2×C4×C43—41no—
488C2×C4×C43—41no—
489C2×C4×C43C22×D411yescharacteristic
490C2×C4×C43C22×D411yescharacteristic
491C2×C4×C43C22×D411yescharacteristic
492C2×C4×C43C22×D411yescharacteristic
493C2×C4×C43H(5,𝔽2)11yescharacteristic
494C2×C4×C43C2511yescharacteristic
495C22⋊D43—22no—
496C22⋊D43—22no—
497C22⋊D43—44no—
498C22⋊D43—44no—
499C2×Dic43—21no—
500C2×Dic43—22no—
501C2×Dic43—22no—
502C2×Dic43—44no—
503C2×Dic43—42no—
504C2×Dic43—41no—
505C2×Dic43—41no—
506D172—21no—
507D172—22no—
508D172—22no—
509D172—44no—
510D172—41no—
511D172—41no—
512D172C22×D412yes—
513C4×D43—22no—
514C4×D43—22no—
515C4×D43—44no—
516C4×D43—44no—
517Dic86—21no—
518Dic86—22no—
519Dic86—22no—
520Dic86—44no—
521Dic86—41no—
522Dic86—41no—
523Dic86C22×D412yes—
524C8×C43—22no—
525C8×C43C22×D412yes—
526C8×C43C22×D412yes—
527C43⋊C8—22no—
528C43⋊C8—22no—
529C43⋊C8—22no—
530C43⋊C8C22×D412yes—
531C43⋊C8C22×D412yes—
532C2×#3289—431nomaximal, Sylow
533C22×C43—22no—
534C22×C43—22no—
535C22×C43—22no—
536C22×C43—22no—
537C22×C43—42no—
538C22×C43—42no—
539C22×C43—42no—
540C22×C43D4211yescharacteristic
541C22×C43D4211yescharacteristic
542C22×C43C2×H(5,𝔽2)11yescharacteristic
543C2×D43—22no—
544C2×D43—42no—
545C2×D43—42no—
546C2×D43—82no—
547C2×D43—82no—
548C2×D43—164no—
549C2×D43—161no—
550C4×C43—22no—
551C4×C43—22no—
552C4×C43—22no—
553C4×C43—42no—
554C4×C43—42no—
555C4×C43D4211yescharacteristic
556C4×C43D4211yescharacteristic
557C4×C43C23×D411yescharacteristic
558C4×C43C23×D411yescharacteristic
559Dic43—22no—
560Dic43—42no—
561Dic43—42no—
562C2×#578—431no—
563C2×#578D4311yescharacteristic, complemented
564C2×#577—431no—
565C2×#577—431no—
566#3289—4316no—
567C2×#497—431no—
568C2×#473—431no—
569C2×#473—431no—
570C2×#471—431no—
571C2×#471—431no—
572C2×#456—431no—
573C2×#456—431no—
574C2×#454—431no—
575C2×#455—431no—
576C2×#444—431no—
577C2×#444—431no—
578C2×C43—21no—
579C2×C43—21no—
580C2×C43—42no—
581C2×C43—42no—
582C2×C43—42no—
583C2×C43#328912yescomplemented
584C2×C43C2×D4211yescharacteristic
585D43—42no—
586D43—82no—
587C2×2−1+4—431no—
588C2×2−1+4C2×D4311yescharacteristic
589C2×2−1+4C2×D4311yescharacteristic, complemented
590C2×H(5,𝔽2)—431no—
591#578—24no—
592#578—438no—
593#578—864no—
594#578C2×D4318yescomplemented
595#577—438no—
596#577—438no—
597#577—864no—
598#577—864no—
599C2×#137—21no—
600C2×#137—21no—
601C2×#137—431no—
602C2×#137—431no—
603C2×#137—431no—
604C2×#137—431no—
605C2×#137—861no—
606C2×#137—861no—
607C2×#137—861no—
608C2×#137—861no—
609C2×#137C2×D4311yescharacteristic
610C2×#137C2×D4311yescharacteristic, complemented
611C2×AGL(1,ℤ/8)—431no—
612C2×AGL(1,ℤ/8)—431no—
613C2×AGL(1,ℤ/8)—861no—
614C2×AGL(1,ℤ/8)—861no—
615C2×#135—21no—
616C2×#135—431no—
617C2×#135—861no—
618C2×#135—861no—
619C2×#135—861no—
620C2×#135C2×D4311yescharacteristic
621C22×Q16—21no—
622C22×Q16—431no—
623C22×Q16—861no—
624C22×Q16C2×D4311yescharacteristic, complemented
625C22×SD16—431no—
626C22×SD16—431no—
627C22×SD16—861no—
628C22×SD16—861no—
629C2×#131—431no—
630C2×#131—431no—
631C2×#131—431no—
632C2×#131C2×D4311yescharacteristic, complemented
633C2×C4⋊Q8—431no—
634C2×#124—431no—
635#497—438no—
636#473—438no—
637#473—438no—
638#471—438no—
639#471—438no—
640#456—438no—
641#456—438no—
642#455—438no—
643#454—438no—
644#444—438no—
645#444—438no—
646C2×#108—431no—
647C2×#108—431no—
648C2×#104—431no—
649C2×#104—431no—
650C2×#104—431no—
651C2×#104—431no—
652C2×#101—431no—
653C2×#101—431no—
654C2×#101—431no—
655C2×#100—431no—
656C2×#97—431no—
657C43C2×#328911yescharacteristic, complemented, Sylow
6582−1+4—22no—
6592−1+4—22no—
6602−1+4—22no—
6612−1+4—22no—
6622−1+4—41no—
6632−1+4—41no—
6642−1+4—434no—
6652−1+4—862no—
6662−1+4—862no—
6672−1+4—1721no—
6682−1+4C22×D4314yes—
6692−1+4C22×D4314yescomplemented
670H(5,𝔽2)—434no—
671H(5,𝔽2)—862no—
672H(5,𝔽2)—862no—
673H(5,𝔽2)—1721no—
674C2×#41—21no—
675C2×#41—21no—
676C2×#41—21no—
677C2×#41—21no—
678C2×#41—41no—
679C2×#41—41no—
680C2×#41—431no—
681C2×#41—861no—
682C2×#41—861no—
683C2×#41—861no—
684C2×#41—861no—
685C2×#41—1721no—
686C2×#41C22×D4311yescharacteristic
687C2×#41C22×D4311yescharacteristic
688C2×#41C22×D4311yescharacteristic
689C22×Q8—21no—
690C22×Q8—21no—
691C22×Q8—21no—
692C22×Q8—21no—
693C22×Q8—431no—
694C22×Q8—861no—
695C22×Q8—861no—
696C22×Q8C22×D4311yescharacteristic
697C22×Q8C22×D4311yescharacteristic
698C22×D4—431no—
699C22×D4—861no—
700C22×D4—861no—
701C22×D4—1721no—
702#137—22no—
703#137—22no—
704#137—28no—
705#137—28no—
706#137—434no—
707#137—434no—
708#137—434no—
709#137—434no—
710#137—868no—
711#137—868no—
712#137—868no—
713#137—862no—
714#137—862no—
715#137—862no—
716#137—862no—
717#137—868no—
718#137C22×D4314yes—
719#137C22×D4314yescomplemented
720AGL(1,ℤ/8)—434no—
721AGL(1,ℤ/8)—434no—
722AGL(1,ℤ/8)—868no—
723AGL(1,ℤ/8)—862no—
724AGL(1,ℤ/8)—862no—
725AGL(1,ℤ/8)—868no—
726#135—28no—
727#135—434no—
728#135—434no—
729#135—868no—
730#135—868no—
731#135—868no—
732#135C22⋊D4314yes—
733#135C22×D4314yes—
734C2×Q16—21no—
735C2×Q16—21no—
736C2×Q16—28no—
737C2×Q16—21no—
738C2×Q16—21no—
739C2×Q16—22no—
740C2×Q16—431no—
741C2×Q16—434no—
742C2×Q16—861no—
743C2×Q16—861no—
744C2×Q16—862no—
745C2×Q16—868no—
746C2×Q16—861no—
747C2×Q16—861no—
748C2×Q16—861no—
749C2×Q16—861no—
750C2×Q16C22⋊D4311yescharacteristic
751C2×Q16C22×D4314yescomplemented
752C2×SD16—21no—
753C2×SD16—21no—
754C2×SD16—431no—
755C2×SD16—431no—
756C2×SD16—434no—
757C2×SD16—434no—
758C2×SD16—861no—
759C2×SD16—861no—
760C2×SD16—862no—
761C2×SD16—868no—
762C2×SD16—861no—
763C2×SD16—861no—
764C2×SD16—861no—
765C2×SD16—861no—
766C2×SD16—861no—
767C2×SD16—861no—
768C2×SD16—868no—
769C2×SD16—861no—
770C2×SD16—861no—
771C2×SD16—862no—
772C2×SD16C22⋊D4311yescharacteristic
773C2×SD16C22⋊D4311yescharacteristic
774C2×D8—431no—
775C2×D8—861no—
776C2×D8—861no—
777C2×D8C22⋊D4311yescharacteristic
778#131—22no—
779#131—434no—
780#131—434no—
781#131—434no—
782#131—862no—
783#131—862no—
784#131—862no—
785#131C22×D4314yescomplemented
786C2×M16—21no—
787C2×M16—431no—
788C2×M16—431no—
789C2×M16—431no—
790C2×M16—861no—
791C2×M16—861no—
792C2×M16—861no—
793C2×M16C22×D4311yescharacteristic
794C22×C8—21no—
795C22×C8—431no—
796C22×C8—861no—
797C22×C8—861no—
798C22×C8—861no—
799C22×C8C22×D4311yescharacteristic
800C4⋊Q8—434no—
801C4⋊Q8—1721no—
802#124—434no—
803#124—1721no—
804C2×C4⋊C4—1721no—
805C2×C22⋊C4—1721no—
806C2×C42—431no—
807#108—434no—
808#108—434no—
809#104—434no—
810#104—434no—
811#104—434no—
812#104—434no—
813#101—434no—
814#101—434no—
815#101—434no—
816#100—434no—
817#97—434no—
818C24—861no—
819C24—1721no—
820#41—21no—
821#41—21no—
822#41—21no—
823#41—21no—
824#41—21no—
825#41—21no—
826#41—24no—
827#41—24no—
828#41—24no—
829#41—24no—
830#41—44no—
831#41—44no—
832#41—42no—
833#41—42no—
834#41—42no—
835#41—42no—
836#41—44no—
837#41—44no—
838#41—432no—
839#41—432no—
840#41—864no—
841#41—864no—
842#41—861no—
843#41—861no—
844#41—864no—
845#41—864no—
846#41—1722no—
847#41—1722no—
848#41—1724no—
849#41—1722no—
850#41—1722no—
851#41—1724no—
852#41D4×D4312yes—
853#41C2×C22⋊D4312yes—
854#41C2×C22⋊D4312yes—
855#41C23×D4312yes—
856#41C23×D4312yes—
857#41C23×D4312yes—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—24no—
861C2×Q8—24no—
862C2×Q8—24no—
863C2×Q8—24no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—41no—
873C2×Q8—41no—
874C2×Q8—42no—
875C2×Q8—42no—
876C2×Q8—42no—
877C2×Q8—42no—
878C2×Q8—431no—
879C2×Q8—432no—
880C2×Q8—864no—
881C2×Q8—861no—
882C2×Q8—864no—
883C2×Q8—861no—
884C2×Q8—861no—
885C2×Q8—861no—
886C2×Q8—861no—
887C2×Q8—1721no—
888C2×Q8—1722no—
889C2×Q8—1722no—
890C2×Q8D4×D4311yescharacteristic
891C2×Q8C2×C22⋊D4311yescharacteristic
892C2×Q8C2×C22⋊D4311yescharacteristic
893C2×Q8C23×D4312yes—
894C2×Q8C23×D4312yes—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—41no—
899C2×D4—41no—
900C2×D4—431no—
901C2×D4—432no—
902C2×D4—864no—
903C2×D4—861no—
904C2×D4—864no—
905C2×D4—861no—
906C2×D4—861no—
907C2×D4—861no—
908C2×D4—861no—
909C2×D4—861no—
910C2×D4—1722no—
911C2×D4—1721no—
912C2×D4—1722no—
913C2×D4—1721no—
914C2×D4—1724no—
915C2×D4—1724no—
916C2×D4—1721no—
917C2×D4D4×D4311yescharacteristic
918C2×D4C2×C22⋊D4311yescharacteristic
919C2×D4C2×C22⋊D4311yescharacteristic
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—41no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4—861no—
930C22×C4—861no—
931C22×C4—861no—
932C22×C4—1721no—
933C22×C4—1721no—
934C22×C4—1721no—
935C22×C4C23×D4311yescharacteristic
936Q16—24no—
937Q16—24no—
938Q16—24no—
939Q16—24no—
940Q16—434no—
941Q16—864no—
942Q16—864no—
943Q16—864no—
944Q16—864no—
945Q16—864no—
946Q16—864no—
947Q16C2×C22⋊D4314yes—
948SD16—24no—
949SD16—24no—
950SD16—434no—
951SD16—434no—
952SD16—864no—
953SD16—864no—
954SD16—864no—
955SD16—864no—
956SD16—864no—
957SD16—864no—
958SD16—864no—
959SD16—864no—
960SD16—864no—
961SD16—864no—
962SD16C2×C22⋊D4314yes—
963SD16C2×C22⋊D4314yes—
964D8—434no—
965D8—864no—
966D8—864no—
967D8C2×C22⋊D4314yes—
968M16—21no—
969M16—24no—
970M16—432no—
971M16—432no—
972M16—432no—
973M16—864no—
974M16—864no—
975M16—861no—
976M16—861no—
977M16—861no—
978M16—864no—
979M16C23×D4312yes—
980C2×C8—21no—
981C2×C8—24no—
982C2×C8—431no—
983C2×C8—431no—
984C2×C8—432no—
985C2×C8—432no—
986C2×C8—864no—
987C2×C8—864no—
988C2×C8—861no—
989C2×C8—861no—
990C2×C8—861no—
991C2×C8—864no—
992C2×C8C2×C22⋊D4311yescharacteristic
993C2×C8C2×C22⋊D4311yescharacteristic
994C2×C8C2×C22⋊D4312yes—
995C2×C8C23×D4312yes—
996C4⋊C4—1724no—
997C22⋊C4—1724no—
998C42—432no—
999C42—861no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—861no—
1004C23—862no—
1005C23—3442no—
1006C23—1724no—
1007C23—1721no—
1008C23—1721no—
1009C23—6882no—
1010C23#1306337011yescharacteristic
1011Q8—21no—
1012Q8—21no—
1013Q8—21no—
1014Q8—22no—
1015Q8—22no—
1016Q8—22no—
1017Q8—22no—
1018Q8—44no—
1019Q8—44no—
1020Q8—41no—
1021Q8—41no—
1022Q8—41no—
1023Q8—41no—
1024Q8—432no—
1025Q8—861no—
1026Q8—862no—
1027Q8—862no—
1028Q8—1724no—
1029Q8—1721no—
1030Q8—1721no—
1031Q8C2×D4×D4312yes—
1032Q8C22×C22⋊D4312yes—
1033Q8C22×C22⋊D4312yes—
1034D4—22no—
1035D4—22no—
1036D4—22no—
1037D4—22no—
1038D4—22no—
1039D4—22no—
1040D4—21no—
1041D4—21no—
1042D4—21no—
1043D4—44no—
1044D4—44no—
1045D4—432no—
1046D4—862no—
1047D4—862no—
1048D4—862no—
1049D4—862no—
1050D4—861no—
1051D4—1724no—
1052D4—1724no—
1053D4—1724no—
1054D4—1721no—
1055D4—1721no—
1056D4C2×D4×D4312yes—
1057D4C22×C22⋊D4312yes—
1058D4C22×C22⋊D4312yes—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—44no—
1071C2×C4—44no—
1072C2×C4—44no—
1073C2×C4—44no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—861no—
1079C2×C4—862no—
1080C2×C4—862no—
1081C2×C4—862no—
1082C2×C4—862no—
1083C2×C4—1724no—
1084C2×C4—1724no—
1085C2×C4—1724no—
1086C2×C4—1722no—
1087C2×C4—1721no—
1088C2×C4—1721no—
1089C2×C4C2×D4×D4311yescharacteristic
1090C2×C4C2×D4×D4311yescharacteristic
1091C2×C4C22×C22⋊D4311yescharacteristic
1092C2×C4C22×C22⋊D4311yescharacteristic
1093C2×C4#1306337011yescharacteristic
1094C2×C4C24×D4311yescharacteristic
1095C8—22no—
1096C8—432no—
1097C8—432no—
1098C8—862no—
1099C8—862no—
1100C8—862no—
1101C8C22×C22⋊D4312yes—
1102C8C22×C22⋊D4312yes—
1103C22—22no—
1104C22—22no—
1105C22—22no—
1106C22—22no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—862no—
1111C22—3442no—
1112C22—3442no—
1113C22—1722no—
1114C22—1722no—
1115C22—6881no—
1116C22—6884no—
1117C22D4×C22⋊D4311yescharacteristic
1118C22D4×C22⋊D4311yescharacteristic
1119C22C2×#1306337011yescharacteristic
1120C4—22no—
1121C4—22no—
1122C4—22no—
1123C4—42no—
1124C4—42no—
1125C4—862no—
1126C4—1722no—
1127C4—1722no—
1128C4D4×C22⋊D4311yescharacteristic
1129C4D4×C22⋊D4311yescharacteristic
1130C4C22×D4×D4311yescharacteristic
1131C4C23×C22⋊D4311yescharacteristic
1132C2—21no—
1133C2—21no—
1134C2—42no—
1135C2—42no—
1136C2—42no—
1137C2—3442no—
1138C2—1722no—
1139C2#1914636612yesdirect product factor
1140C2C2×D4×C22⋊D4311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#578C2
socleC22×C43D42
hypercenterC2×#578D43
hypocenterC43C2×#3289
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#578

Complements

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

NH ≅ G/Ntype
1. C2×#14583714C2semidirect
2. C2×#14583707C2semidirect
3. C2×#14583706C2semidirect
4. #19146366C2direct (N × H)
5. C2×#14583292C2semidirect
6. C2×#14583172C2semidirect
7. C2×#14583171C2semidirect
8. C2×#14583164C2semidirect
9. C2×#14583162C2semidirect
10. C2×#14583082C2semidirect
11. C2×#14583080C2semidirect
12. C2×#14583072C2semidirect
13. C2×#14583075C2semidirect
14. C2×#14583021C2semidirect
15. C2×#14583019C2semidirect
16. C2×C43×#578C2semidirect
20. #14583714C22semidirect
22. #14583707C22semidirect
24. #14583706C22semidirect
32. C2×#13063355C22semidirect
42. C22×#10621885C22semidirect
48. C2×#13063332C22semidirect
50. C2×#13063323C22semidirect
52. #14583292C22semidirect
53. #14583172C22semidirect
54. #14583171C22semidirect
55. #14583164C22semidirect
56. #14583162C22semidirect
57. #14583082C22semidirect
58. #14583080C22semidirect
59. #14583075C22semidirect
60. #14583072C22semidirect
61. #14583021C22semidirect
62. #14583019C22semidirect
63. C2×#13063261C22semidirect
64. C2×#13063260C22semidirect
66. C2×#13063252C22semidirect
67. C2×#13063252C22semidirect
69. C2×#13063244C22semidirect
70. C2×#13063244C22semidirect
71. C2×#13063243C22semidirect
73. C2×#13063235C22semidirect
75. C2×2−1+4×C43C22semidirect
77. C43×#578C22semidirect
81. C2×#137×C43C22semidirect
85. C22×Q16×C43C22semidirect
86. C2×#131×C43C22semidirect
119. #13063355C23semidirect
140. C2×#10621885C23semidirect
165. #13063332C23semidirect
179. #13063323C23semidirect
185. #13063261C23semidirect
186. #13063260C23semidirect
188. #13063252C23semidirect
189. #13063252C23semidirect
191. #13063244C23semidirect
192. #13063244C23semidirect
193. #13063243C23semidirect
195. #13063235C23semidirect
203. 2−1+4×C43C23semidirect
224. #137×C43C23semidirect
235. C2×Q16×C43C23semidirect
242. #131×C43C23semidirect
563. C2×#578D43semidirect
583. C2×C43#3289semidirect
589. C2×2−1+4C2×D43semidirect
594. #578C2×D43semidirect
610. C2×#137C2×D43semidirect
624. C22×Q16C2×D43semidirect
632. C2×#131C2×D43semidirect
657. C43C2×#3289semidirect
669. 2−1+4C22×D43semidirect
719. #137C22×D43semidirect
751. C2×Q16C22×D43semidirect
785. #131C22×D43semidirect
1139. C2#19146366direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145837142
C2×#145837072
C2×#145837062
#191463662
C2×#145832922
C2×#145831722
C2×#145831712
C2×#145831642
C2×#145831622
C2×#145830822
C2×#145830802
C2×#145830722
C2×#145830752
C2×#145830212
C2×#145830192
C2×C43×#5782
C2×#328943