Finite Group Databasebeta

← #25965101

Subgroups — #25965101

Order 11008.

2002 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147987C211yesmaximal, characteristic
2C2×#14583375C211yesmaximal, characteristic, complemented
3#19144897C214yesmaximal, complemented
4#19144888C214yesmaximal, complemented
5#19144831C214yesmaximal, complemented
6#19144829C214yesmaximal, complemented
7#19144529C212yesmaximal, complemented
8#19144396C211yesmaximal, characteristic, complemented
9#19144069C211yesmaximal, characteristic, complemented
10#19144067C211yesmaximal, characteristic, complemented
11#19143831C212yesmaximal, complemented
12#19143413C212yesmaximal, complemented
13#19143410C212yesmaximal, complemented
14#19143232C211yesmaximal, characteristic, complemented
15C43×#3078C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C2×#13063358C2212yes—
18C2×#13063356C2212yes—
19#14583523C2212yes—
20#14583523C2212yes—
21#14583512C2212yes—
22#14583505C2212yes—
23#14583498—21no—
24#14583498—21no—
25#14583489—21no—
26#14583489—21no—
27#14583449C2211yescharacteristic
28#14583436—22no—
29#14583436—22no—
30#14583411C2212yes—
31#14583375—22no—
32#14583375—22no—
33#14583375C2214yes—
34#14583375C2214yes—
35#14583367C2212yes—
36C2×Q8×Dic43C2211yescharacteristic
37C2×C4×Dic86—21no—
38C2×C4×Dic86C2211yescharacteristic
39C2×#13063290—21no—
40C2×#13063290C2211yescharacteristic
41C2×#13063283—21no—
42C2×#13063283C2211yescharacteristic
43C2×#13063282—21no—
44C2×#13063282C2211yescharacteristic
45#14583243C2214yes—
46#14583242C2214yes—
47#14583226C2214yes—
48#14583225C2214yes—
49#14583203C2214yescomplemented
50#14583191C2212yescomplemented
51#14583181C2212yescomplemented
52#14583122C2214yescomplemented
53#14583121C2214yescomplemented
54#14583110C2212yescomplemented
55#14583109C2212yescomplemented
56#14583100C2212yescomplemented
57#14583099C2212yescomplemented
58#14583056C2214yes—
59#14583056C2214yes—
60#14583039C2214yes—
61#14583039C2214yes—
62#14583005C2214yescomplemented
63#14583003C2214yescomplemented
64#14583002C2214yescomplemented
65#14582998C2214yescomplemented
66#14582993C2214yescomplemented
67#14582991C2214yescomplemented
68#14582986C2214yescomplemented
69#14582984C2214yescomplemented
70#14582959C2214yes—
71#14582959C2214yes—
72#14582942C2212yes—
73#14582923C2211yescharacteristic
74#14582907C2212yes—
75#14582901C2212yes—
76#14582898C2212yes—
77#14582862C2212yes—
78M16×Dic43C2212yes—
79C43×#533C2211yescharacteristic
80C2×C4×Q8×C43C2211yescharacteristic
81C43×#479C2214yescomplemented
82C43×#477C2212yescomplemented
83C43×#475C2212yescomplemented
84C43×#428C2212yes—
85C43×#423C2211yescharacteristic
86C43×#419C2212yes—
87C2×#10621898C2312yes—
88C22×Dic86—21no—
89C22×Dic86C2311yescharacteristic
90C2×Q8×D43—24no—
91C2×Q8×D43—22no—
92C2×Q8×D43—24no—
93C2×Q8×D43C2314yes—
94C22×C4×D43—21no—
95C22×C4×D43C2311yescharacteristic
96#13063358—28no—
97#13063356—28no—
98C2×Dic172C2314yes—
99C2×#10621885C2314yes—
100C2×#10621873C2314yes—
101C2×#10621884C2314yes—
102C2×#10621877C2312yes—
103#13063325C2311yescharacteristic
104#13063322C2311yescharacteristic
105#13063320—22no—
106#13063320—22no—
107#13063320—22no—
108#13063320—22no—
109#13063316—22no—
110#13063316—22no—
111#13063314—22no—
112#13063314—22no—
113#13063313C2312yes—
114#13063310—22no—
115#13063310—22no—
116#13063310—22no—
117#13063310—22no—
118#13063309—22no—
119#13063305C2312yes—
120#13063305C2312yes—
121#13063301—22no—
122#13063301—22no—
123#13063300—22no—
124#13063300—22no—
125#13063300C2312yes—
126#13063300C2312yes—
127#13063299—21no—
128#13063299—21no—
129#13063295—22no—
130Q8×Dic43—22no—
131Q8×Dic43C2314yes—
132C4×Dic86—21no—
133C4×Dic86—21no—
134C4×Dic86—24no—
135C4×Dic86—24no—
136C4×Dic86C2312yes—
137C4×Dic86C2312yes—
138#13063290—24no—
139#13063290—24no—
140#13063290—22no—
141#13063290C2314yes—
142#13063290C2312yes—
143#13063290C2312yes—
144C4×D172—22no—
145C4×D172—22no—
146C4×D172—21no—
147C4×D172—21no—
148#13063287C2312yes—
149#13063287C2312yes—
150(C22⋊D43)⋊C4—22no—
151(C22⋊D43)⋊C4—22no—
152#13063283—22no—
153#13063283—24no—
154#13063283—24no—
155#13063283C2314yes—
156#13063282—24no—
157#13063282—24no—
158#13063282—22no—
159#13063282D412yes—
160#13063282D412yes—
161#13063282C2312yes—
162#13063282C2312yes—
163C2×C4⋊Dic43—21no—
164C2×C4⋊Dic43C2311yescharacteristic
165C2×Dic43⋊C4—21no—
166C2×Dic43⋊C4—21no—
167C2×Dic43⋊C4D411yescharacteristic
168C2×Dic43⋊C4D411yescharacteristic
169C2×(C2×D43)⋊C4—21no—
170C2×(C2×D43)⋊C4D411yescharacteristic
171C2×(C2×D43)⋊C4D411yescharacteristic
172C2×C4×Dic43—21no—
173C2×C4×Dic43—21no—
174C2×C4×Dic43—21no—
175C2×C4×Dic43—21no—
176C2×C4×Dic43C2311yescharacteristic
177C42×D43—22no—
178#13063258C2314yes—
179#13063256C2314yes—
180C4⋊(C43⋊C8)C2312yes—
181C4⋊(C43⋊C8)C2312yes—
182#13063250C2314yes—
183#13063248C2314yes—
184#13063248C2314yes—
185#13063248C2314yes—
186#13063247C2314yes—
187#13063245C2314yes—
188(C2×D43)⋊C8C2314yes—
189(C2×D43)⋊C8C2314yes—
190#13063235C2314yes—
191C8×Dic43C2314yes—
192C22×Q8×C43C2311yescharacteristic
193C2×M16×C43C2312yes—
194C4⋊Q8×C43C2311yescharacteristic
195C4⋊Q8×C43C2311yescharacteristic
196#125×C43C2312yes—
197C22⋊Q8×C43—21no—
198C22⋊Q8×C43—21no—
199C4×Q8×C43—21no—
200C4×Q8×C43—21no—
201C4×Q8×C43—21no—
202C4×Q8×C43—21no—
203C4×Q8×C43C2312yes—
204C4×Q8×C43C2312yes—
205#117×C43C2312yes—
206C2×C4⋊C4×C43—21no—
207C2×C4⋊C4×C43C2311yescharacteristic
208C2×C42×C43—21no—
209C2×C42×C43C2311yescharacteristic
210#107×C43C2314yes—
211#106×C43C2314yes—
212C4⋊C8×C43C2312yes—
213C4⋊C8×C43C2312yes—
214#103×C43C2314yes—
215#103×C43C2314yes—
216C23×D43C2×D411yescharacteristic
217C2×Q8×C43—21no—
218C2×Q8×C43—21no—
219C2×Q8×C43—21no—
220C2×Q8×C43—22no—
221C2×Q8×C43#4114yes—
222C2×Q8×C43C2412yes—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2411yescharacteristic
228C2×C22⋊D43—22no—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43C2×D411yescharacteristic
232C22×Dic43C2×D411yescharacteristic
233C22×Dic43C2×D411yescharacteristic
234Q8×D43—216no—
235Q8×D43—28no—
236Q8×D43—28no—
237#10621898—24no—
238#10621898—24no—
239C2×D172—21no—
240C2×D172—21no—
241C2×D172—22no—
242C2×D172—22no—
243C2×D172C2412yes—
244C2×C4×D43—28no—
245C2×C4×D43—22no—
246C2×C4×D43—22no—
247C2×C4×D43—22no—
248C2×C4×D43—22no—
249C2×C4×D43—22no—
250C2×C4×D43—24no—
251C2×C4×D43C2×D412yes—
252C2×C4×D43C2412yes—
253C2×Dic86—28no—
254C2×Dic86—21no—
255C2×Dic86—22no—
256C2×Dic86—24no—
257C2×Dic86#4114yes—
258C2×Dic86C2412yes—
259C2×Dic86C2412yes—
260M16×C43—24no—
261C2×C8×C43C2414yes—
262C4⋊C4×C43—22no—
263C4⋊C4×C43—22no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43—22no—
266C4⋊C4×C43—22no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43C2412yes—
270C4⋊C4×C43C2412yes—
271C4⋊C4×C43C2412yes—
272C22⋊C4×C43—22no—
273C42×C43—22no—
274C42×C43—22no—
275C42×C43—22no—
276C42×C43C2×D411yescharacteristic
277C42×C43C2×D411yescharacteristic
278C42×C43C2411yescharacteristic
279C42×C43C2411yescharacteristic
280#10621885—28no—
281#10621884—28no—
282(C2×D43)⋊C4—22no—
283(C2×D43)⋊C4—22no—
284(C2×D43)⋊C4—22no—
285(C2×D43)⋊C4—22no—
286(C2×D43)⋊C4—22no—
287(C2×D43)⋊C4—22no—
288(C2×D43)⋊C4—24no—
289(C2×D43)⋊C4—22no—
290(C2×D43)⋊C4—22no—
291(C2×D43)⋊C4C2×D412yes—
292(C2×D43)⋊C4C2×D412yes—
293(C2×D43)⋊C4C2×D412yes—
294(C2×D43)⋊C4C2×D412yes—
295C4⋊Dic43—21no—
296C4⋊Dic43—21no—
297C4⋊Dic43—21no—
298C4⋊Dic43—24no—
299C4⋊Dic43—22no—
300C4⋊Dic43—22no—
301C4⋊Dic43C2412yes—
302Dic43⋊C4—22no—
303Dic43⋊C4—22no—
304Dic43⋊C4—24no—
305Dic43⋊C4—22no—
306Dic43⋊C4—22no—
307Dic43⋊C4C2×D412yes—
308Dic43⋊C4C2×D412yes—
309Dic43⋊C4C2×D412yes—
310Dic43⋊C4C2×D412yes—
311C4×Dic43—22no—
312C4×Dic43—22no—
313C4×Dic43—22no—
314C4×Dic43—22no—
315C4×Dic43—24no—
316C4×Dic43—24no—
317C4×Dic43—24no—
318C4×Dic43C2×D412yes—
319C4×Dic43C2412yes—
320#10621877—24no—
321C2×C43⋊C8C2414yes—
322Dic172—28no—
323#10621873—28no—
324C23×C43C22×D411yescharacteristic
325C22×D43—22no—
326C22×D43—22no—
327C22×D43—41no—
328C22×D43—41no—
329C22×D43C22×D412yes—
330Q8×C43—24no—
331Q8×C43—22no—
332Q8×C43—81no—
333Q8×C43—81no—
334Q8×C43C2×#4114yes—
335C2×C4×C43—24no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—42no—
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C2×#4112yes—
349C2×C4×C43C2×#4112yes—
350C2×C4×C43C2511yescharacteristic
351C22⋊D43—44no—
352C2×Dic43—22no—
353C2×Dic43—24no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—22no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—42no—
360C2×Dic43C22×D412yes—
361C2×Dic43C22×D412yes—
362C2×Dic43C22×D412yes—
363D172—22no—
364D172—22no—
365D172—81no—
366D172—81no—
367D172—82no—
368D172—82no—
369C4×D43—216no—
370C4×D43—24no—
371C4×D43—22no—
372C4×D43—22no—
373C4×D43—44no—
374C4×D43—82no—
375C4×D43—82no—
376Dic86—216no—
377Dic86—24no—
378Dic86—22no—
379Dic86—22no—
380Dic86—22no—
381Dic86C2×#4114yes—
382C8×C43—24no—
383C43⋊C8—24no—
384#60566—431nomaximal, Sylow
385C22×C43—21no—
386C22×C43—21no—
387C22×C43#52512yes—
388C22×C43C23×D411yescharacteristic
389C2×D43—22no—
390C2×D43—22no—
391C2×D43—22no—
392C2×D43—44no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—42no—
396C4×C43—21no—
397C4×C43—21no—
398C4×C43—21no—
399C4×C43—21no—
400C4×C43—24no—
401C4×C43—42no—
402C4×C43—42no—
403C4×C43—42no—
404C4×C43#52512yes—
405C4×C43C22×#4111yescharacteristic
406C4×C43C22×#4111yescharacteristic
407Dic43—22no—
408Dic43—22no—
409Dic43—22no—
410Dic43—24no—
411Dic43—42no—
412Dic43—42no—
413#3455—431no—
414C2×#519—431no—
415#3127—434no—
416#3126—434no—
417#3121—434no—
418#3121—434no—
419#3093—432no—
420#3078—431no—
421#3078D4311yescharacteristic, complemented
422#3037—431no—
423#3037—431no—
424#3004—432no—
425C4×#137—432no—
426C4×#137—432no—
427#2921—431no—
428C2×C43—22no—
429C2×C43C2×#52511yescharacteristic
430C2×C43#358611yescharacteristic
431C2×C43#358611yescharacteristic
432D43—42no—
433D43—82no—
434C23×Q8—431no—
435C2×#137—432no—
436C2×#137—432no—
437#542—432no—
438#542—432no—
439#541—432no—
440#540—432no—
441#539—861no—
442#539—861no—
443#538—861no—
444#538—861no—
445#533C2×D4311yescharacteristic
446#532—431no—
447#529—862no—
448#529—862no—
449#525—432no—
450#519—434no—
451#519—434no—
452#519—862no—
453#519—862no—
454C4×#41—432no—
455C2×C4×Q8—431no—
456C2×C4×Q8—431no—
457C2×C4×Q8—431no—
458C2×C4×Q8—861no—
459C2×C4×Q8—861no—
460C2×C4×Q8C2×D4311yescharacteristic
461C2×#117—431no—
462C2×#117—431no—
463C2×#117—861no—
464C2×#117—861no—
465#485—434no—
466#485—434no—
467#482—434no—
468#482—434no—
469#479—434no—
470#479C2×D4314yescomplemented
471#477—432no—
472#477C2×D4312yescomplemented
473#475—432no—
474#475C2×D4312yescomplemented
475#464—434no—
476#464—434no—
477#462—432no—
478#462—432no—
479#460—432no—
480#460—432no—
481#451—434no—
482#451—434no—
483#448—434no—
484#448—434no—
485#441—434no—
486#441—434no—
487#440—434no—
488#440—434no—
489C4×Q16—434no—
490C4×Q16—434no—
491C4×SD16—434no—
492C4×SD16—434no—
493#433—434no—
494#433—434no—
495#428—432no—
496#428C2×D4312yes—
497#423—431no—
498#423C2×D4311yescharacteristic
499#419—432no—
500#419C2×D4312yes—
501#417—432no—
502#417—432no—
503#407—432no—
504C4×M16—432no—
505C43#6056611yescharacteristic, complemented, Sylow
506C2×#41—432no—
507C22×Q8—434no—
508C22×Q8—431no—
509C22×Q8—861no—
510C22×Q8—862no—
511C22×Q8—864no—
512C22×Q8—864no—
513C22×Q8C22×D4311yescharacteristic
514C23×C4—431no—
515C23×C4—861no—
516#137—868no—
517#137—868no—
518C2×Q16—434no—
519C2×Q16—434no—
520C2×SD16—434no—
521C2×SD16—434no—
522C2×M16—432no—
523C2×M16C22×D4312yes—
524C4⋊Q8—431no—
525C4⋊Q8C22×D4311yescharacteristic
526C4⋊Q8C22×D4311yescharacteristic
527#127—431no—
528#126—862no—
529#126—862no—
530#126—862no—
531#126—862no—
532#125—862no—
533#125—862no—
534#125C22×D4312yes—
535#124—432no—
536#124—862no—
537#124—862no—
538#123—862no—
539#123—862no—
540#123—862no—
541#123—862no—
542#123—862no—
543C22⋊Q8—21no—
544C22⋊Q8—21no—
545C22⋊Q8—432no—
546C22⋊Q8—432no—
547C22⋊Q8—862no—
548C22⋊Q8—862no—
549#121—432no—
550#121—432no—
551#121—862no—
552#121—862no—
553#121—861no—
554#121—861no—
555#120—862no—
556C4×Q8—21no—
557C4×Q8—21no—
558C4×Q8—21no—
559C4×Q8—21no—
560C4×Q8—434no—
561C4×Q8—434no—
562C4×Q8—432no—
563C4×Q8—432no—
564C4×Q8—432no—
565C4×Q8—432no—
566C4×Q8—864no—
567C4×Q8—864no—
568C4×Q8—862no—
569C4×Q8—862no—
570C4×Q8—864no—
571C4×Q8—864no—
572C4×Q8—861no—
573C4×Q8—861no—
574C4×Q8C22×D4312yes—
575C4×Q8C22×D4312yes—
576C4×D4—432no—
577C4×D4—432no—
578C4×D4—862no—
579C4×D4—862no—
580C4×D4—862no—
581C4×D4—862no—
582C4×D4—861no—
583C4×D4—861no—
584#117—432no—
585#117—432no—
586#117—432no—
587#117—432no—
588#117—434no—
589#117—862no—
590#117—864no—
591#117—864no—
592#117—864no—
593#117—864no—
594#117—862no—
595#117C22×D4312yes—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—431no—
598C2×C4⋊C4—431no—
599C2×C4⋊C4—431no—
600C2×C4⋊C4—861no—
601C2×C4⋊C4—861no—
602C2×C4⋊C4—861no—
603C2×C4⋊C4C22×D4311yescharacteristic
604C2×C22⋊C4—431no—
605C2×C22⋊C4—431no—
606C2×C22⋊C4—861no—
607C2×C42—21no—
608C2×C42—431no—
609C2×C42—862no—
610C2×C42—861no—
611C2×C42—861no—
612C2×C42—861no—
613C2×C42—861no—
614C2×C42C22×D4311yescharacteristic
615#107—434no—
616#107C22×D4314yes—
617#106—434no—
618#106C22×D4314yes—
619C4⋊C8—432no—
620C4⋊C8—432no—
621C4⋊C8C22×D4312yes—
622C4⋊C8C22×D4312yes—
623#103—434no—
624#103—434no—
625#103—434no—
626#103—434no—
627#103C22×D4314yes—
628#103C22×D4314yes—
629#102—434no—
630#102—434no—
631C22⋊C8—434no—
632C22⋊C8—434no—
633#97—434no—
634C4×C8—434no—
635C24—431no—
636#41—864no—
637#41—864no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—22no—
642C2×Q8—434no—
643C2×Q8—432no—
644C2×Q8—432no—
645C2×Q8—864no—
646C2×Q8—868no—
647C2×Q8—868no—
648C2×Q8—8616no—
649C2×Q8—868no—
650C2×Q8—861no—
651C2×Q8—862no—
652C2×Q8#1062190214yes—
653C2×Q8C23×D4312yes—
654C2×D4—432no—
655C2×D4—862no—
656C2×D4—862no—
657C2×D4—862no—
658C2×D4—861no—
659C2×D4—861no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—431no—
663C22×C4—431no—
664C22×C4—431no—
665C22×C4—432no—
666C22×C4—432no—
667C22×C4—862no—
668C22×C4—862no—
669C22×C4—864no—
670C22×C4—868no—
671C22×C4—861no—
672C22×C4—862no—
673C22×C4—862no—
674C22×C4—861no—
675C22×C4—862no—
676C22×C4D4×D4311yescharacteristic
677C22×C4D4×D4311yescharacteristic
678C22×C4C23×D4311yescharacteristic
679Q16—868no—
680Q16—868no—
681SD16—868no—
682SD16—868no—
683M16—24no—
684M16—864no—
685C2×C8—434no—
686C2×C8C23×D4314yes—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—21no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—432no—
695C4⋊C4—432no—
696C4⋊C4—432no—
697C4⋊C4—432no—
698C4⋊C4—432no—
699C4⋊C4—864no—
700C4⋊C4—864no—
701C4⋊C4—862no—
702C4⋊C4—862no—
703C4⋊C4—862no—
704C4⋊C4—862no—
705C4⋊C4—861no—
706C4⋊C4—862no—
707C4⋊C4—862no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4C23×D4312yes—
711C4⋊C4C23×D4312yes—
712C4⋊C4C23×D4312yes—
713C22⋊C4—22no—
714C22⋊C4—432no—
715C22⋊C4—432no—
716C22⋊C4—432no—
717C22⋊C4—432no—
718C22⋊C4—862no—
719C22⋊C4—862no—
720C22⋊C4—862no—
721C22⋊C4—862no—
722C22⋊C4—864no—
723C22⋊C4—862no—
724C22⋊C4—862no—
725C22⋊C4—862no—
726C22⋊C4—862no—
727C42—22no—
728C42—22no—
729C42—22no—
730C42—432no—
731C42—432no—
732C42—864no—
733C42—864no—
734C42—864no—
735C42—862no—
736C42—862no—
737C42—862no—
738C42—862no—
739C42D4×D4311yescharacteristic
740C42D4×D4311yescharacteristic
741C42C23×D4311yescharacteristic
742C42C23×D4311yescharacteristic
743C23—432no—
744C23—862no—
745C23—862no—
746C23—1721no—
747C23—1721no—
748C23C2×D4×D4311yescharacteristic
749Q8—24no—
750Q8—22no—
751Q8—81no—
752Q8—81no—
753Q8—434no—
754Q8—8616no—
755Q8—864no—
756Q8—862no—
757Q8—862no—
758Q8—862no—
759Q8C2×#1062190214yes—
760D4—862no—
761D4—862no—
762D4—3441no—
763D4—3441no—
764D4—3442no—
765D4—3442no—
766D4—1724no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—432no—
776C2×C4—432no—
777C2×C4—432no—
778C2×C4—8616no—
779C2×C4—862no—
780C2×C4—864no—
781C2×C4—862no—
782C2×C4—864no—
783C2×C4—862no—
784C2×C4—862no—
785C2×C4—862no—
786C2×C4—862no—
787C2×C4—3442no—
788C2×C4—3442no—
789C2×C4—1721no—
790C2×C4—1721no—
791C2×C4—1722no—
792C2×C4—1724no—
793C2×C4C2×D4×D4311yescharacteristic
794C2×C4C2×D4×D4311yescharacteristic
795C2×C4C2×D4×D4311yescharacteristic
796C2×C4C2×D4×D4311yescharacteristic
797C2×C4C2×D4×D4311yescharacteristic
798C2×C4#41×D4312yes—
799C2×C4C2×#1062190212yes—
800C2×C4C24×D4311yescharacteristic
801C8—24no—
802C8—864no—
803C22—21no—
804C22—21no—
805C22—862no—
806C22—862no—
807C22—862no—
808C22—1724no—
809C22—1722no—
810C22—1722no—
811C22—1722no—
812C22#1458341212yes—
813C22C22×D4×D4311yescharacteristic
814C4—24no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—862no—
823C4—864no—
824C4—862no—
825C4—862no—
826C4—1722no—
827C4—1722no—
828C4#1458341212yes—
829C4C2×#41×D4311yescharacteristic
830C4C22×#1062190211yescharacteristic
831C2—22no—
832C2—3442no—
833C2—1722no—
834C2C2×#1458341211yescharacteristic
835C2#1914937811yescharacteristic
836C2#1914937911yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3078C2
socleC22×C43C23×D4
prime radical#19147987C2
hypercenter#3078D43
hypocenterC43#60566
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
2. C2×#14583375C2semidirect
3. #19144897C2semidirect
4. #19144888C2semidirect
5. #19144831C2semidirect
6. #19144829C2semidirect
7. #19144529C2semidirect
8. #19144396C2semidirect
9. #19144069C2semidirect
10. #19144067C2semidirect
11. #19143831C2semidirect
12. #19143413C2semidirect
13. #19143410C2semidirect
14. #19143232C2semidirect
15. C43×#3078C2semidirect
49. #14583203C22semidirect
50. #14583191C22semidirect
51. #14583181C22semidirect
52. #14583122C22semidirect
53. #14583121C22semidirect
54. #14583110C22semidirect
55. #14583109C22semidirect
56. #14583100C22semidirect
57. #14583099C22semidirect
62. #14583005C22semidirect
63. #14583003C22semidirect
64. #14583002C22semidirect
65. #14582998C22semidirect
66. #14582993C22semidirect
67. #14582991C22semidirect
68. #14582986C22semidirect
69. #14582984C22semidirect
81. C43×#479C22semidirect
82. C43×#477C22semidirect
83. C43×#475C22semidirect
421. #3078D43semidirect
470. #479C2×D43semidirect
472. #477C2×D43semidirect
474. #475C2×D43semidirect
505. C43#60566semidirect

Maximal subgroups

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

subgroupindex
#191479872
C2×#145833752
#191448972
#191448882
#191448312
#191448292
#191445292
#191443962
#191440692
#191440672
#191438312
#191434132
#191434102
#191432322
C43×#30782
#6056643