Finite Group Databasebeta

← #25969599

Subgroups — #25969599

Order 11008.

2168 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147891C211yesmaximal, characteristic, complemented
2C2×#14583449C211yesmaximal, characteristic, complemented
3#19145983C212yesmaximal, complemented
4#19145976C212yesmaximal, complemented
5#19145958C214yesmaximal, complemented
6#19145922C214yesmaximal, complemented
7#19145912C212yesmaximal, complemented
8#19145905C212yesmaximal, complemented
9#19144411C212yesmaximal, complemented
10#19144394C212yesmaximal, complemented
11#19144214C214yesmaximal, complemented
12#19144076C212yesmaximal, complemented
13#19144061C212yesmaximal, complemented
14C2×C43×#423C211yesmaximal, characteristic, complemented
15C22×#10621898—21no—
16C2×#13063353C2214yes—
17#14583456C2211yescharacteristic
18#14583456C2211yescharacteristic, complemented
19#14583456C2211yescharacteristic, complemented
20#14583449—21no—
21#14583449—21no—
22#14583449—21no—
23#14583449—21no—
24#14583449C2211yescharacteristic
25#14583449C2212yes—
26#14583449C2212yes—
27#14583449C2212yes—
28#14583449C2212yes—
29#14583449C2211yescharacteristic, complemented
30#14583449C2211yescharacteristic, complemented
31C2×#13063325C2211yescharacteristic
32C2×#13063322C2211yescharacteristic
33#14583433—21no—
34#14583433—21no—
35#14583433—21no—
36#14583433—21no—
37#14583433C2212yescomplemented
38#14583433C2212yescomplemented
39C2×#13063313—21no—
40#14583410—21no—
41#14583410—21no—
42#14583410C2212yes—
43C2×#13063299—21no—
44C2×#13063299C2212yes—
45C4×#10621898—21no—
46C4×#10621898—21no—
47C4×#10621898C2212yes—
48C2×C4×D172—21no—
49C2×C4×D172C2212yes—
50#14583200C2218yescomplemented
51#14583195C2214yescomplemented
52#14583190C2214yescomplemented
53#14583190C2214yescomplemented
54#14583185C2214yescomplemented
55#14583180C2214yescomplemented
56#14583180C2214yescomplemented
57#14583152C2218yescomplemented
58#14583145C2218yescomplemented
59#14583135C2218yescomplemented
60#14583128C2218yescomplemented
61#14583115C2218yescomplemented
62#14583105C2214yescomplemented
63#14583100C2214yescomplemented
64#14583100C2214yescomplemented
65#14583095C2214yescomplemented
66#14583095C2214yescomplemented
67#14583095C2214yescomplemented
68#14582941C2214yes—
69#14582905C2214yes—
70#14582901C2214yes—
71C22×M16×C43C2212yes—
72C22×C42×C43C2211yescharacteristic
73C43×#423C2212yes—
74C43×#423C2212yes—
75C43×#423C2212yescomplemented
76C43×#423C2212yescomplemented
77C2×C4⋊C8×C43C2212yescomplemented
78C2×C4⋊C8×C43C2212yescomplemented
79C2×#10621898—21no—
80C2×#10621898—21no—
81C2×#10621898—22no—
82C2×#10621898—22no—
83C2×#10621898—22no—
84C2×#10621898—22no—
85C2×#10621898—48no—
86C2×#10621898C2312yes—
87C22×Dic86—21no—
88C22×D172—21no—
89C22×D172—21no—
90C22×D172C2312yes—
91C22×C22⋊D43—22no—
92C22×C4×D43—22no—
93#13063353—48no—
94C2×#10621873C2318yes—
95C2×D344C2318yes—
96#13063325—21no—
97#13063325—21no—
98#13063325C2311yescharacteristic
99#13063325C2311yescharacteristic
100#13063325C2312yes—
101#13063325C2312yes—
102#13063325C2311yescharacteristic
103#13063322—21no—
104#13063322—21no—
105#13063322C2311yescharacteristic
106#13063322C2312yes—
107#13063322C2312yes—
108#13063319—22no—
109#13063319—22no—
110#13063317—21no—
111#13063317—21no—
112#13063317C2312yes—
113#13063313—22no—
114#13063313—22no—
115#13063313—22no—
116#13063313—22no—
117#13063313—21no—
118#13063313—21no—
119#13063313C2312yes—
120#13063308—22no—
121#13063308—22no—
122#13063308—22no—
123#13063304—21no—
124#13063304—21no—
125#13063304—21no—
126#13063304—21no—
127#13063304C2312yes—
128#13063304C2312yes—
129#13063299—22no—
130#13063299—22no—
131#13063299—22no—
132#13063299—22no—
133#13063299—22no—
134#13063299—22no—
135#13063299—21no—
136#13063299—21no—
137#13063299—21no—
138#13063299—21no—
139#13063299C2314yes—
140#13063299C2312yes—
141#13063299C2314yes—
142#13063299C2312yes—
143#13063294—22no—
144C4×Dic86—21no—
145C4×Dic86—21no—
146C4×Dic86—21no—
147C4×Dic86—21no—
148C4×Dic86C2312yes—
149C4×Dic86C2312yes—
150C4×D172—22no—
151C4×D172—22no—
152C4×D172—22no—
153C4×D172—22no—
154C4×D172—22no—
155C4×D172—22no—
156C4×D172—21no—
157C4×D172—21no—
158C4×D172—21no—
159C4×D172—21no—
160C4×D172C2312yes—
161C4×D172C2312yes—
162C4×D172C2314yes—
163C4×D172C2314yes—
164C4×C22⋊D43—22no—
165C4×C22⋊D43—22no—
166C4×C22⋊D43—22no—
167C4×C22⋊D43—22no—
168C4×C22⋊D43—22no—
169C4×C22⋊D43—22no—
170#13063284—21no—
171#13063284—21no—
172#13063284C2312yes—
173#13063282—22no—
174#13063282—22no—
175#13063282—22no—
176C2×C4⋊Dic43—21no—
177C2×C4⋊Dic43C2312yes—
178C2×(C2×D43)⋊C4—22no—
179C2×(C2×D43)⋊C4—22no—
180C42×D43—22no—
181#13063259C2318yes—
182#13063257C2318yes—
183#13063250C2318yes—
184#13063247C2318yes—
185#13063247C2318yes—
186#13063247C2318yes—
187C23×C4×C43D411yescharacteristic
188C23×C4×C43D411yescharacteristic
189C23×C4×C43C2311yescharacteristic
190C2×M16×C43—44no—
191C2×M16×C43C2314yes—
192C2×M16×C43C2314yes—
193C22×C8×C43C2314yes—
194C2×C42×C43D411yescharacteristic
195C2×C42×C43D411yescharacteristic
196C2×C42×C43D411yescharacteristic
197C2×C42×C43D411yescharacteristic
198C2×C42×C43D411yescharacteristic
199C2×C42×C43D411yescharacteristic
200C2×C42×C43C2311yescharacteristic
201C2×C42×C43C2311yescharacteristic
202C2×C42×C43C2311yescharacteristic
203C2×C42×C43C2311yescharacteristic
204C2×C42×C43C2311yescharacteristic
205C2×C42×C43C2311yescharacteristic
206C4⋊C8×C43C2314yes—
207C4⋊C8×C43C2314yes—
208C4⋊C8×C43C2314yes—
209C4⋊C8×C43C2314yes—
210C24×C43C2×D411yescharacteristic
211C23×D43—22no—
212C22×C4×C43—24no—
213C22×C4×C43—22no—
214C22×C4×C43—22no—
215C22×C4×C43—42no—
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2411yescharacteristic
232C22×C4×C43C2411yescharacteristic
233C22×C4×C43C2411yescharacteristic
234C2×C22⋊D43—22no—
235C2×C22⋊D43—22no—
236C2×C22⋊D43—22no—
237C2×C22⋊D43—24no—
238C2×C22⋊D43—24no—
239C2×C22⋊D43—48no—
240C22×Dic43—22no—
241#10621898—24no—
242#10621898—24no—
243#10621898—44no—
244#10621898—48no—
245#10621898—48no—
246#10621898—48no—
247#10621898—44no—
248#10621898—48no—
249C2×D172—21no—
250C2×D172—21no—
251C2×D172—22no—
252C2×D172—22no—
253C2×D172—22no—
254C2×D172—22no—
255C2×D172—22no—
256C2×D172—24no—
257C2×D172—24no—
258C2×D172—44no—
259C2×D172—44no—
260C2×D172C2412yes—
261C2×D172C2414yes—
262C2×C4×D43—22no—
263C2×C4×D43—22no—
264C2×C4×D43—22no—
265C2×C4×D43—24no—
266C2×C4×D43—24no—
267C2×C4×D43—48no—
268C2×Dic86—21no—
269C2×Dic86—21no—
270C2×Dic86—22no—
271C2×Dic86—22no—
272C2×Dic86—44no—
273C2×Dic86C2412yes—
274M16×C43—28no—
275M16×C43—44no—
276C2×C8×C43—44no—
277C2×C8×C43C2418yes—
278C42×C43C2×D411yescharacteristic
279C42×C43C2×D411yescharacteristic
280C42×C43C2×D411yescharacteristic
281C42×C43C2×D411yescharacteristic
282C42×C43C2×D411yescharacteristic
283C42×C43C2×D411yescharacteristic
284C42×C43C2×D411yescharacteristic
285C42×C43C2×D411yescharacteristic
286C42×C43C2×D411yescharacteristic
287C42×C43C2×D411yescharacteristic
288C42×C43C2×D411yescharacteristic
289C42×C43C2×D411yescharacteristic
290C42×C43C2411yescharacteristic
291C42×C43C2411yescharacteristic
292C42×C43C2411yescharacteristic
293C42×C43C2411yescharacteristic
294C22⋊Dic43—22no—
295C22⋊Dic43—22no—
296C22⋊Dic43—22no—
297(C2×D43)⋊C4—24no—
298(C2×D43)⋊C4—24no—
299(C2×D43)⋊C4—24no—
300(C2×D43)⋊C4—24no—
301(C2×D43)⋊C4—22no—
302(C2×D43)⋊C4—22no—
303(C2×D43)⋊C4—22no—
304(C2×D43)⋊C4—22no—
305(C2×D43)⋊C4—22no—
306(C2×D43)⋊C4—22no—
307C4⋊Dic43—22no—
308C4⋊Dic43—22no—
309C4⋊Dic43—22no—
310C4⋊Dic43—21no—
311C4⋊Dic43—21no—
312C4⋊Dic43—21no—
313C4⋊Dic43—21no—
314C4⋊Dic43C2412yes—
315C4⋊Dic43C2412yes—
316C4⋊Dic43C2414yes—
317Dic43⋊C4—22no—
318Dic43⋊C4—22no—
319Dic43⋊C4—22no—
320Dic43⋊C4—22no—
321Dic43⋊C4—22no—
322Dic43⋊C4—22no—
323C4×Dic43—22no—
324C4×Dic43—22no—
325C4×Dic43—22no—
326D344—48no—
327#10621873—48no—
328C23×C43—22no—
329C23×C43—22no—
330C23×C43—41no—
331C23×C43C22×D411yescharacteristic
332C23×C43C22×D411yescharacteristic
333C23×C43C22×D411yescharacteristic
334C22×D43—22no—
335C22×D43—24no—
336C22×D43—44no—
337C22×D43—44no—
338C22×D43—44no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—21no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43AGL(1,ℤ/8)14yescomplemented
358C2×C4×C43C22×D411yescharacteristic
359C2×C4×C43C22×D411yescharacteristic
360C2×C4×C43C22×D411yescharacteristic
361C2×C4×C43C22×D411yescharacteristic
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43C22×D411yescharacteristic
364C2×C4×C43C22×D411yescharacteristic
365C2×C4×C43C22×D411yescharacteristic
366C2×C4×C43C22×D411yescharacteristic
367C2×C4×C43C22×D411yescharacteristic
368C2×C4×C43C22×D411yescharacteristic
369C2×C4×C43H(5,𝔽2)12yes—
370C2×C4×C432−1+412yes—
371C2×C4×C43C2511yescharacteristic
372C22⋊D43—48no—
373C22⋊D43—44no—
374C22⋊D43—44no—
375C22⋊D43—48no—
376C22⋊D43—44no—
377C2×Dic43—22no—
378C2×Dic43—22no—
379C2×Dic43—22no—
380C2×Dic43—24no—
381C2×Dic43—44no—
382D172—24no—
383D172—22no—
384D172—24no—
385D172—22no—
386D172—44no—
387D172—44no—
388D172—42no—
389D172—44no—
390D172—44no—
391D172—42no—
392D172—44no—
393C4×D43—48no—
394C4×D43—44no—
395C4×D43—48no—
396C4×D43—44no—
397C4×D43—44no—
398Dic86—22no—
399Dic86—22no—
400Dic86—44no—
401Dic86—42no—
402Dic86—44no—
403Dic86—42no—
404C8×C43—28no—
405#60916—431nomaximal, Sylow
406C22×C43—21no—
407C22×C43—21no—
408C22×C43—21no—
409C22×C43—21no—
410C22×C43—21no—
411C22×C43—21no—
412C22×C43—21no—
413C22×C43—44no—
414C22×C43#53712yes—
415C22×C43C2×AGL(1,ℤ/8)12yes—
416C22×C43C23×D411yescharacteristic
417C2×D43—44no—
418C2×D43—42no—
419C2×D43—44no—
420C2×D43—42no—
421C2×D43—44no—
422C2×D43—42no—
423C2×D43—88no—
424C4×C43—21no—
425C4×C43—21no—
426C4×C43—21no—
427C4×C43—21no—
428C4×C43—21no—
429C4×C43—21no—
430C4×C43—21no—
431C4×C43#53712yes—
432C4×C43C2×AGL(1,ℤ/8)12yes—
433C4×C43C2×AGL(1,ℤ/8)12yes—
434C4×C43#57512yes—
435C4×C43C2×H(5,𝔽2)11yescharacteristic
436C4×C43C2×2−1+411yescharacteristic
437Dic43—42no—
438Dic43—44no—
439Dic43—42no—
440Dic43—42no—
441#3444—431no—
442C2×#532—431no—
443#3254—432no—
444#3253—432no—
445#3251—434no—
446#3247—434no—
447#3246—432no—
448#3245—432no—
449#3079—432no—
450#3077—432no—
451#3055—434no—
452#3038—432no—
453#3036—432no—
454C2×#423D4311yescharacteristic, complemented
455C2×C43—22no—
456C2×C43—22no—
457C2×C43—41no—
458C2×C43C2×#53711yescharacteristic
459C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
460C2×C43C2×#57511yescharacteristic
461D43—82no—
462D43—84no—
463C22×#41—861no—
464C2×AGL(1,ℤ/8)—434no—
465C22×M16C2×D4312yes—
466#533—431no—
467#533—431no—
468#533—431no—
469#532—432no—
470#532—432no—
471#532—432no—
472#532—432no—
473#532—431no—
474#532—431no—
475#532—431no—
476#532—861no—
477#532—861no—
478#532—861no—
479#532—861no—
480C2×C4⋊Q8—431no—
481C2×#127—431no—
482#529—432no—
483#529—432no—
484#529—861no—
485#529—861no—
486#529—861no—
487#529—861no—
488C2×#124—861no—
489#525—432no—
490#525—861no—
491#525—861no—
492C2×#121—432no—
493C2×#121—861no—
494C4×#41—432no—
495C4×#41—861no—
496C4×#41—861no—
497C2×C4×D4—432no—
498C2×C4×D4—861no—
499C22×C42C2×D4311yescharacteristic
500#478—438no—
501#477—434no—
502#476—434no—
503#476—434no—
504#475—434no—
505#474—434no—
506#474—434no—
507#469—438no—
508#468—438no—
509#466—438no—
510#465—438no—
511#463—438no—
512#461—434no—
513#460—434no—
514#460—434no—
515#459—434no—
516#459—434no—
517#459—434no—
518#428—434no—
519#423C2×D4312yes—
520#423C2×D4312yes—
521#423C2×D4312yescomplemented
522#423C2×D4312yescomplemented
523C2×C4⋊C8C2×D4312yescomplemented
524C2×C4⋊C8C2×D4312yescomplemented
525#418—434no—
526#417—434no—
527C43#6091611yescharacteristic, complemented, Sylow
528C2×#41—432no—
529C2×#41—861no—
530C2×#41—861no—
531C2×#41—862no—
532C2×#41—862no—
533C2×#41—862no—
534C2×#41—862no—
535C2×#41—1728no—
536C22×Q8—861no—
537C22×D4—432no—
538C22×D4—862no—
539C22×D4—861no—
540C22×D4—861no—
541C23×C4—862no—
542C23×C4D17211yescharacteristic
543C23×C4D17211yescharacteristic
544C23×C4C22×D4311yescharacteristic
545AGL(1,ℤ/8)—1728no—
546C2×SD16—438no—
547C2×D8—438no—
548C2×M16—44no—
549C2×M16C22×D4314yes—
550C2×M16C22×D4314yes—
551C22×C8C22×D4314yes—
552C4⋊Q8—432no—
553C4⋊Q8—432no—
554C4⋊Q8—431no—
555C4⋊Q8—431no—
556C4⋊Q8—431no—
557C4⋊Q8—861no—
558C4⋊Q8—861no—
559#127—432no—
560#127—432no—
561#127—431no—
562#127—861no—
563#127—861no—
564#126—862no—
565#126—862no—
566#125—432no—
567#125—861no—
568#125—861no—
569#124—432no—
570#124—862no—
571#124—862no—
572#124—862no—
573#124—862no—
574#124—861no—
575#124—861no—
576#123—862no—
577#123—862no—
578#123—862no—
579C22⋊Q8—432no—
580C22⋊Q8—432no—
581C22⋊Q8—861no—
582C22⋊Q8—861no—
583C22⋊Q8—861no—
584C22⋊Q8—861no—
585#121—434no—
586#121—434no—
587#121—432no—
588#121—432no—
589#121—862no—
590#121—862no—
591#121—862no—
592#121—862no—
593#121—862no—
594#121—862no—
595#121—861no—
596#121—861no—
597#121—861no—
598#121—861no—
599#120—862no—
600C4×Q8—432no—
601C4×Q8—432no—
602C4×Q8—861no—
603C4×Q8—861no—
604C4×Q8—861no—
605C4×Q8—861no—
606C4×D4—434no—
607C4×D4—434no—
608C4×D4—432no—
609C4×D4—432no—
610C4×D4—862no—
611C4×D4—862no—
612C4×D4—862no—
613C4×D4—862no—
614C4×D4—862no—
615C4×D4—862no—
616C4×D4—862no—
617C4×D4—862no—
618C4×D4—862no—
619C4×D4—862no—
620C4×D4—862no—
621C4×D4—862no—
622C4×D4—861no—
623C4×D4—861no—
624C4×D4—861no—
625C4×D4—861no—
626#117—432no—
627#117—861no—
628#117—861no—
629#117—862no—
630#117—862no—
631#117—862no—
632C2×C4⋊C4—432no—
633C2×C4⋊C4—861no—
634C2×C22⋊C4—862no—
635C2×C22⋊C4—862no—
636C2×C42—862no—
637C2×C42D17211yescharacteristic
638C2×C42D17211yescharacteristic
639C2×C42D17211yescharacteristic
640C2×C42D17211yescharacteristic
641C2×C42D17211yescharacteristic
642C2×C42D17211yescharacteristic
643C2×C42C22×D4311yescharacteristic
644C2×C42C22×D4311yescharacteristic
645C2×C42C22×D4311yescharacteristic
646C2×C42C22×D4311yescharacteristic
647C2×C42C22×D4311yescharacteristic
648C2×C42C22×D4311yescharacteristic
649#107—438no—
650#106—438no—
651C4⋊C8C22×D4314yes—
652C4⋊C8C22×D4314yes—
653C4⋊C8C22×D4314yes—
654C4⋊C8C22×D4314yes—
655#103—438no—
656#102—438no—
657#102—438no—
658#102—438no—
659C24—862no—
660C24C2×D17211yescharacteristic
661#41—864no—
662#41—864no—
663#41—1728no—
664#41—1728no—
665#41—1728no—
666#41—1724no—
667#41—1728no—
668#41—1724no—
669C2×Q8—432no—
670C2×Q8—861no—
671C2×Q8—861no—
672C2×Q8—862no—
673C2×Q8—862no—
674C2×Q8—1724no—
675C2×D4—432no—
676C2×D4—434no—
677C2×D4—862no—
678C2×D4—862no—
679C2×D4—862no—
680C2×D4—864no—
681C2×D4—864no—
682C2×D4—861no—
683C2×D4—861no—
684C2×D4—862no—
685C2×D4—862no—
686C2×D4—862no—
687C2×D4—862no—
688C2×D4—862no—
689C2×D4—864no—
690C2×D4—864no—
691C2×D4—1724no—
692C2×D4—1724no—
693C2×D4—1728no—
694C22×C4—24no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—42no—
698C22×C4—862no—
699C22×C4—862no—
700C22×C4—862no—
701C22×C4—862no—
702C22×C4—864no—
703C22×C4—864no—
704C22×C4—1728no—
705C22×C4C2×D17211yescharacteristic
706C22×C4C2×D17211yescharacteristic
707C22×C4C2×D17211yescharacteristic
708C22×C4C2×D17211yescharacteristic
709C22×C4C2×D17211yescharacteristic
710C22×C4C2×D17211yescharacteristic
711C22×C4C2×D17211yescharacteristic
712C22×C4C2×D17211yescharacteristic
713C22×C4C2×D17211yescharacteristic
714C22×C4C2×D17211yescharacteristic
715C22×C4C2×D17211yescharacteristic
716C22×C4C2×D17211yescharacteristic
717C22×C4C2×D17211yescharacteristic
718C22×C4C2×D17211yescharacteristic
719C22×C4C2×D17211yescharacteristic
720C22×C4C23×D4311yescharacteristic
721C22×C4C23×D4311yescharacteristic
722C22×C4C23×D4311yescharacteristic
723SD16—1728no—
724D8—1728no—
725M16—28no—
726M16—44no—
727C2×C8—44no—
728C2×C8C23×D4318yes—
729C4⋊C4—432no—
730C4⋊C4—432no—
731C4⋊C4—434no—
732C4⋊C4—862no—
733C4⋊C4—862no—
734C4⋊C4—862no—
735C4⋊C4—862no—
736C4⋊C4—862no—
737C4⋊C4—861no—
738C4⋊C4—861no—
739C4⋊C4—861no—
740C4⋊C4—861no—
741C4⋊C4—862no—
742C4⋊C4—862no—
743C4⋊C4—862no—
744C4⋊C4—862no—
745C22⋊C4—862no—
746C22⋊C4—862no—
747C22⋊C4—862no—
748C22⋊C4—864no—
749C22⋊C4—864no—
750C22⋊C4—864no—
751C22⋊C4—864no—
752C22⋊C4—862no—
753C22⋊C4—862no—
754C22⋊C4—862no—
755C22⋊C4—862no—
756C22⋊C4—862no—
757C22⋊C4—862no—
758C42—862no—
759C42—862no—
760C42—862no—
761C42C2×D17211yescharacteristic
762C42C2×D17211yescharacteristic
763C42C2×D17211yescharacteristic
764C42C2×D17211yescharacteristic
765C42C2×D17211yescharacteristic
766C42C2×D17211yescharacteristic
767C42C2×D17211yescharacteristic
768C42C2×D17211yescharacteristic
769C42C2×D17211yescharacteristic
770C42C2×D17211yescharacteristic
771C42C2×D17211yescharacteristic
772C42C2×D17211yescharacteristic
773C42C23×D4311yescharacteristic
774C42C23×D4311yescharacteristic
775C42C23×D4311yescharacteristic
776C42C23×D4311yescharacteristic
777C23—22no—
778C23—22no—
779C23—41no—
780C23—862no—
781C23—864no—
782C23—1724no—
783C23—1724no—
784C23—1724no—
785C23C22×D17211yescharacteristic
786C23C22×D17211yescharacteristic
787C23C22×D17211yescharacteristic
788Q8—862no—
789Q8—862no—
790Q8—1724no—
791Q8—1722no—
792Q8—1724no—
793Q8—1722no—
794D4—862no—
795D4—864no—
796D4—864no—
797D4—862no—
798D4—1724no—
799D4—1724no—
800D4—1722no—
801D4—1728no—
802D4—1724no—
803D4—1728no—
804D4—1724no—
805D4—1724no—
806D4—1724no—
807D4—1722no—
808D4—1724no—
809D4—1724no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—862no—
829C2×C4—862no—
830C2×C4—862no—
831C2×C4—864no—
832C2×C4—1728no—
833C2×C4—1724no—
834C2×C4—1728no—
835C2×C4—1724no—
836C2×C4—1724no—
837C2×C4—1724no—
838C2×C4#1306335314yescomplemented
839C2×C4C22×D17211yescharacteristic
840C2×C4C22×D17211yescharacteristic
841C2×C4C22×D17211yescharacteristic
842C2×C4C22×D17211yescharacteristic
843C2×C4C22×D17211yescharacteristic
844C2×C4C22×D17211yescharacteristic
845C2×C4C22×D17211yescharacteristic
846C2×C4C22×D17211yescharacteristic
847C2×C4C22×D17211yescharacteristic
848C2×C4C22×D17211yescharacteristic
849C2×C4C22×D17211yescharacteristic
850C2×C4#1306337012yes—
851C2×C4#1306337312yes—
852C2×C4C24×D4311yescharacteristic
853C8—28no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—44no—
862C22—3448no—
863C22—1724no—
864C22—1722no—
865C22—1722no—
866C22—1724no—
867C22—1722no—
868C22—1724no—
869C22#1458348012yes—
870C22C2×#1306335312yes—
871C22C23×D17211yescharacteristic
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—1724no—
880C4—1722no—
881C4—1722no—
882C4—1722no—
883C4#1458348012yes—
884C4C2×#1306335312yes—
885C4C2×#1306335312yes—
886C4#1458369912yes—
887C4C2×#1306337011yescharacteristic
888C4C2×#1306337311yescharacteristic
889C2—22no—
890C2—22no—
891C2—41no—
892C2—3444no—
893C2—3442no—
894C2C2×#1458348011yescharacteristic
895C2C22×#1306335311yescharacteristic
896C2C2×#1458369911yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#423C2
socleC22×C43C23×D4
hypercenterC2×#423D43
hypocenterC43#60916
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
1. #19147891C2semidirect
2. C2×#14583449C2semidirect
3. #19145983C2semidirect
4. #19145976C2semidirect
5. #19145958C2semidirect
6. #19145922C2semidirect
7. #19145912C2semidirect
8. #19145905C2semidirect
9. #19144411C2semidirect
10. #19144394C2semidirect
11. #19144214C2semidirect
12. #19144076C2semidirect
13. #19144061C2semidirect
14. C2×C43×#423C2semidirect
18. #14583456C22semidirect
19. #14583456C22semidirect
29. #14583449C22semidirect
30. #14583449C22semidirect
37. #14583433C22semidirect
38. #14583433C22semidirect
50. #14583200C22semidirect
51. #14583195C22semidirect
52. #14583190C22semidirect
53. #14583190C22semidirect
54. #14583185C22semidirect
55. #14583180C22semidirect
56. #14583180C22semidirect
57. #14583152C22semidirect
58. #14583145C22semidirect
59. #14583135C22semidirect
60. #14583128C22semidirect
61. #14583115C22semidirect
62. #14583105C22semidirect
63. #14583100C22semidirect
64. #14583100C22semidirect
65. #14583095C22semidirect
66. #14583095C22semidirect
67. #14583095C22semidirect
75. C43×#423C22semidirect
76. C43×#423C22semidirect
77. C2×C4⋊C8×C43C22semidirect
78. C2×C4⋊C8×C43C22semidirect
357. C2×C4×C43AGL(1,ℤ/8)semidirect
454. C2×#423D43semidirect
521. #423C2×D43semidirect
522. #423C2×D43semidirect
523. C2×C4⋊C8C2×D43semidirect
524. C2×C4⋊C8C2×D43semidirect
527. C43#60916semidirect
838. C2×C4#13063353semidirect

Maximal subgroups

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

subgroupindex
#191478912
C2×#145834492
#191459832
#191459762
#191459582
#191459222
#191459122
#191459052
#191444112
#191443942
#191442142
#191440762
#191440612
C2×C43×#4232
#6091643