Finite Group Databasebeta

← C2×#19144830 #25964882

Subgroups — C2×#19144830 #25964882

Order 11008.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583521C211yesmaximal, characteristic
2C2×#14583375C211yesmaximal, characteristic, complemented
3#19144830C2116yesmaximal, direct product factor
4C2×#14583238C211yesmaximal, characteristic, complemented
5C2×#14583226C211yesmaximal, characteristic
6C2×#14583193C211yesmaximal, characteristic, complemented
7C2×#14583182C211yesmaximal, characteristic, complemented
8C2×#14583124C211yesmaximal, characteristic, complemented
9C2×#14583123C211yesmaximal, characteristic, complemented
10C2×#14583053C211yesmaximal, characteristic, complemented
11C2×#14583039C211yesmaximal, characteristic
12C2×#14583004C211yesmaximal, characteristic, complemented
13C2×#14582997C211yesmaximal, characteristic, complemented
14C2×C4×#10621873C211yesmaximal, characteristic, complemented
15C2×#14582958C211yesmaximal, characteristic, complemented
16C2×C4×Q16×C43C211yesmaximal, characteristic, complemented
17C22×Q8×D43C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621884C2211yescharacteristic
21#14583521—24no—
22#14583521C2218yes—
23C2×#13063324C2211yescharacteristic
24C2×#13063319—21no—
25C2×#13063314C2211yescharacteristic
26C2×#13063313—21no—
27C2×#13063310—21no—
28C2×#13063303—21no—
29C2×#13063301C2211yescharacteristic
30C2×#13063300C2211yescharacteristic
31#14583375—24no—
32#14583375C2218yescomplemented
33C2×Q8×Dic43C2211yescharacteristic
34C2×C4×Dic86—21no—
35C2×C4×Dic86C2211yescharacteristic
36C2×#13063290—21no—
37C2×#13063290C2211yescharacteristic
38C2×C4×D172C2211yescharacteristic
39C2×#13063283—21no—
40C2×#13063283C2211yescharacteristic
41C2×#13063282—21no—
42C2×#13063282C2211yescharacteristic
43#14583238C2218yescomplemented
44#14583226C2218yes—
45#14583193C2218yescomplemented
46#14583182C2218yescomplemented
47#14583124C2218yescomplemented
48#14583123C2218yescomplemented
49#14583053C2218yescomplemented
50#14583039C2218yes—
51#14583004C2218yescomplemented
52#14582997C2218yescomplemented
53C4×#10621873C2218yescomplemented
54#14582958C2218yescomplemented
55C2×#13063258C2211yescharacteristic
56C2×#13063257C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063236C2211yescharacteristic
69C22×Q16×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C2×C4×Q8×C43C2211yescharacteristic
72C4×Q16×C43C2218yescomplemented
73C2×#107×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×C4×C8×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86—21no—
79C22×Dic86C2311yescharacteristic
80C2×Q8×D43—24no—
81C2×Q8×D43—22no—
82C2×Q8×D43—24no—
83C2×Q8×D43C2314yes—
84C22×D172—21no—
85C22×D172C2311yescharacteristic
86C22×C4×D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43C2311yescharacteristic
89C2×#10621885—24no—
90C2×#10621885C2314yes—
91C2×#10621873—24no—
92C2×#10621873C2314yes—
93C2×#10621884—24no—
94C2×#10621884C2314yes—
95C22×C43⋊C8C2311yescharacteristic
96C22×C43⋊C8C2311yescharacteristic
97#13063324—22no—
98#13063324C2314yes—
99#13063319—28no—
100#13063314—22no—
101#13063314C2314yes—
102#13063313—28no—
103#13063310—28no—
104#13063303—28no—
105#13063301—22no—
106#13063301C2314yes—
107#13063300—22no—
108#13063300C2314yes—
109Q8×Dic43—22no—
110Q8×Dic43C2314yes—
111C4×Dic86—22no—
112C4×Dic86—28no—
113C4×Dic86C2314yes—
114#13063290—28no—
115#13063290—22no—
116#13063290C2314yes—
117C4×D172—22no—
118C4×D172C2314yes—
119#13063283—22no—
120#13063283—28no—
121#13063283C2314yes—
122#13063282—28no—
123#13063282D414yes—
124#13063282C2314yes—
125C2×C4⋊Dic43—21no—
126C2×C4⋊Dic43C2311yescharacteristic
127C2×C4⋊Dic43C2311yescharacteristic
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4D411yescharacteristic
133C2×Dic43⋊C4D411yescharacteristic
134C2×(C2×D43)⋊C4—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4D411yescharacteristic
141C2×(C2×D43)⋊C4D411yescharacteristic
142C2×C4×Dic43—21no—
143C2×C4×Dic43—21no—
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43C2311yescharacteristic
147#13063258C2314yes—
148#13063257C2314yes—
149#13063256C2314yes—
150Dic43⋊C8C2314yes—
151Dic43⋊C8C2314yes—
152#13063250C2314yes—
153#13063249C2314yes—
154#13063249C2314yes—
155#13063248C2314yes—
156#13063247C2314yes—
157#13063245C2314yes—
158(C2×D43)⋊C8C2314yes—
159(C2×D43)⋊C8C2314yes—
160#13063236C2314yes—
161C22×Q8×C43C2311yescharacteristic
162C22×Q8×C43C2311yescharacteristic
163C2×Q16×C43—24no—
164C2×Q16×C43C2314yes—
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167C4×Q8×C43—22no—
168C4×Q8×C43—22no—
169C4×Q8×C43C2314yes—
170C4×Q8×C43C2314yes—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43—21no—
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C42×C43—21no—
176C2×C42×C43—21no—
177C2×C42×C43C2311yescharacteristic
178#107×C43C2314yes—
179#103×C43C2314yes—
180#103×C43C2314yes—
181C4×C8×C43C2314yes—
182C23×D43—21no—
183C23×D43C2×D411yescharacteristic
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—22no—
187C2×Q8×C43—22no—
188C2×Q8×C43—22no—
189C2×Q8×C43#4114yes—
190C2×Q8×C43C2412yes—
191C2×Q8×C43C2412yes—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2411yescharacteristic
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
204C22×Dic43C2×D411yescharacteristic
205Q8×D43—216no—
206Q8×D43—28no—
207Q8×D43—28no—
208C2×D172—21no—
209C2×D172—24no—
210C2×D172—22no—
211C2×D172—22no—
212C2×D172—82no—
213C2×D172C2412yes—
214C2×C4×D43—28no—
215C2×C4×D43—22no—
216C2×C4×D43—22no—
217C2×C4×D43—24no—
218C2×C4×D43—24no—
219C2×C4×D43—82no—
220C2×C4×D43C2×D412yes—
221C2×C4×D43C2412yes—
222C2×Dic86—28no—
223C2×Dic86—21no—
224C2×Dic86—22no—
225C2×Dic86—24no—
226C2×Dic86—24no—
227C2×Dic86—82no—
228C2×Dic86#4114yes—
229C2×Dic86C2412yes—
230Q16×C43—28no—
231C2×C8×C43—22no—
232C2×C8×C43—22no—
233C2×C8×C43C2412yes—
234C2×C8×C43C2412yes—
235C4⋊C4×C43—24no—
236C4⋊C4×C43—24no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43C2412yes—
240C4⋊C4×C43C2412yes—
241C42×C43—24no—
242C42×C43—24no—
243C42×C43C2×D412yes—
244C42×C43C2412yes—
245#10621885—28no—
246#10621884—28no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—24no—
251(C2×D43)⋊C4—24no—
252(C2×D43)⋊C4—24no—
253(C2×D43)⋊C4C2×D414yes—
254(C2×D43)⋊C4C2×D414yes—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43—24no—
258C4⋊Dic43C2412yes—
259C4⋊Dic43C2412yes—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263Dic43⋊C4—24no—
264Dic43⋊C4C2×D414yes—
265Dic43⋊C4C2×D414yes—
266C4×Dic43—24no—
267C4×Dic43—24no—
268C4×Dic43—24no—
269C4×Dic43—24no—
270C4×Dic43C2×D412yes—
271C4×Dic43C2412yes—
272C2×C43⋊C8—22no—
273C2×C43⋊C8—22no—
274C2×C43⋊C8C2412yes—
275C2×C43⋊C8C2412yes—
276#10621873—28no—
277C23×C43C22×D411yescharacteristic
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—42no—
283C22×D43—42no—
284C22×D43—42no—
285C22×D43C22×D412yes—
286Q8×C43—24no—
287Q8×C43—22no—
288Q8×C43—22no—
289Q8×C43—22no—
290Q8×C43—42no—
291Q8×C43C2×#4114yes—
292C2×C4×C43—24no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—42no—
300C2×C4×C43—42no—
301C2×C4×C43—42no—
302C2×C4×C43C22×D412yes—
303C2×C4×C43C22×D412yes—
304C2×C4×C43C22×D411yescharacteristic
305C2×C4×C43C2×#4112yes—
306C2×C4×C43C2×#4112yes—
307C2×C4×C43C2511yescharacteristic
308C2×Dic43—22no—
309C2×Dic43—24no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43C22×D412yes—
318C2×Dic43C22×D412yes—
319C2×Dic43C22×D412yes—
320D172—22no—
321D172—22no—
322D172—42no—
323D172—84no—
324C4×D43—216no—
325C4×D43—24no—
326C4×D43—22no—
327C4×D43—22no—
328C4×D43—84no—
329Dic86—216no—
330Dic86—24no—
331Dic86—22no—
332Dic86—84no—
333Dic86C2×#4114yes—
334C8×C43—22no—
335C8×C43—22no—
336C43⋊C8—22no—
337C43⋊C8—22no—
338C2×#3121—431nomaximal, Sylow
339C22×C43#52512yes—
340C22×C43#57712yes—
341C22×C43#57812yes—
342C22×C43C23×D411yescharacteristic
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—22no—
346C2×D43—44no—
347C2×D43—42no—
348C2×D43—42no—
349C2×D43—42no—
350C2×D43—84no—
351C4×C43—24no—
352C4×C43—22no—
353C4×C43—22no—
354C4×C43—42no—
355C4×C43—42no—
356C4×C43—42no—
357C4×C43#52512yes—
358C4×C43C22×#4111yescharacteristic
359C4×C43C22×#4111yescharacteristic
360Dic43—22no—
361Dic43—24no—
362Dic43—22no—
363Dic43—22no—
364Dic43—42no—
365Dic43—42no—
366C2×#542—431no—
367C2×#519—431no—
368#3121—4316no—
369C2×#485—431no—
370C2×#482—431no—
371C2×#477—431no—
372C2×#475—431no—
373C2×#464—431no—
374C2×#464—431no—
375C2×#451—431no—
376C2×#448—431no—
377C2×#441—431no—
378C2×#440—431no—
379C2×C4×Q16D4311yescharacteristic, complemented
380C2×C4×SD16—431no—
381C2×#433—431no—
382C2×C43#312114yescomplemented
383C2×C43C2×#52511yescharacteristic
384C2×C43C2×#57711yescharacteristic
385C2×C43C2×#57811yescharacteristic
386D43—42no—
387D43—82no—
388C23×Q8—431no—
389C22×Q16—431no—
390C22×Q16C2×D4311yescharacteristic
391C22×SD16—431no—
392C22×SD16—431no—
393#542—438no—
394#542—864no—
395C2×C4⋊Q8—431no—
396C2×#126—861no—
397C2×#124—431no—
398C2×#124—861no—
399C2×#123—861no—
400C2×C22⋊Q8—431no—
401C2×C22⋊Q8—861no—
402C2×#121—431no—
403#519—438no—
404#519—864no—
405C2×C4×Q8—431no—
406C2×C4×Q8—431no—
407C2×C4×Q8—431no—
408C2×C4×Q8—861no—
409C2×C4×Q8—861no—
410C2×C4×Q8C2×D4311yescharacteristic
411C2×C4×Q8C2×D4311yescharacteristic
412C2×C4×D4—431no—
413C2×#117—431no—
414C2×#117—431no—
415C2×#117—861no—
416C2×#117—861no—
417#485—438no—
418#482—438no—
419#477—438no—
420#475—438no—
421#464—438no—
422#464—438no—
423#451—438no—
424#448—438no—
425#441—438no—
426#440—438no—
427C4×Q16C2×D4318yescomplemented
428C4×SD16—438no—
429#433—438no—
430C2×#107—431no—
431C2×#107C2×D4311yescharacteristic
432C2×#106—431no—
433C2×#106—431no—
434C2×C4⋊C8—431no—
435C2×C4⋊C8—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#103—431no—
439C2×#103—431no—
440C2×#103C2×D4311yescharacteristic
441C2×#103C2×D4311yescharacteristic
442C2×#102—431no—
443C2×#102—431no—
444C2×C22⋊C8—431no—
445C2×C22⋊C8—431no—
446C2×#97—431no—
447C2×C4×C8C2×D4311yescharacteristic
448C43C2×#312111yescharacteristic, complemented, Sylow
449C22×Q8—434no—
450C22×Q8—431no—
451C22×Q8—861no—
452C22×Q8—861no—
453C22×Q8—862no—
454C22×Q8—864no—
455C22×Q8—864no—
456C22×Q8C22×D4311yescharacteristic
457C22×Q8C22×D4311yescharacteristic
458C22×D4—431no—
459C22×D4—861no—
460C23×C4—431no—
461C23×C4—861no—
462C23×C4—861no—
463C2×Q16—24no—
464C2×Q16—434no—
465C2×Q16—864no—
466C2×Q16C22×D4314yes—
467C2×SD16—434no—
468C2×SD16—434no—
469C2×SD16—864no—
470C2×SD16—864no—
471C22×C8—431no—
472C22×C8—431no—
473C22×C8C22×D4311yescharacteristic
474C22×C8C22×D4311yescharacteristic
475C4⋊Q8—434no—
476C4⋊Q8—862no—
477#126—868no—
478#124—434no—
479#124—868no—
480#124—862no—
481#123—868no—
482C22⋊Q8—434no—
483C22⋊Q8—868no—
484C22⋊Q8—862no—
485#121—434no—
486#121—862no—
487C4×Q8—22no—
488C4×Q8—22no—
489C4×Q8—434no—
490C4×Q8—434no—
491C4×Q8—434no—
492C4×Q8—868no—
493C4×Q8—862no—
494C4×Q8—862no—
495C4×Q8—868no—
496C4×Q8—862no—
497C4×Q8C22×D4314yes—
498C4×Q8C22×D4314yes—
499C4×D4—434no—
500C4×D4—862no—
501#117—434no—
502#117—434no—
503#117—434no—
504#117—868no—
505#117—868no—
506#117—862no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—431no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—431no—
512C2×C4⋊C4—431no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4C22×D4311yescharacteristic
519C2×C4⋊C4C22×D4311yescharacteristic
520C2×C22⋊C4—431no—
521C2×C22⋊C4—431no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—431no—
531C2×C42—861no—
532C2×C42—861no—
533C2×C42—861no—
534C2×C42—861no—
535C2×C42C22×D4311yescharacteristic
536#107—434no—
537#107C22×D4314yes—
538#106—434no—
539#106—434no—
540C4⋊C8—434no—
541C4⋊C8—434no—
542#103—434no—
543#103—434no—
544#103—434no—
545#103—434no—
546#103C22×D4314yes—
547#103C22×D4314yes—
548#102—434no—
549#102—434no—
550C22⋊C8—434no—
551C22⋊C8—434no—
552#97—434no—
553C4×C8C22×D4314yes—
554C24—431no—
555C24—861no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—434no—
562C2×Q8—432no—
563C2×Q8—864no—
564C2×Q8—864no—
565C2×Q8—868no—
566C2×Q8—868no—
567C2×Q8—8616no—
568C2×Q8—868no—
569C2×Q8—861no—
570C2×Q8—862no—
571C2×Q8—3442no—
572C2×Q8#1062189814yes—
573C2×Q8C23×D4312yes—
574C2×Q8C23×D4312yes—
575C2×D4—432no—
576C2×D4—864no—
577C2×D4—861no—
578C2×D4—862no—
579C2×D4—862no—
580C2×D4—3442no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—431no—
586C22×C4—431no—
587C22×C4—431no—
588C22×C4—432no—
589C22×C4—432no—
590C22×C4—864no—
591C22×C4—868no—
592C22×C4—861no—
593C22×C4—862no—
594C22×C4—862no—
595C22×C4—861no—
596C22×C4—861no—
597C22×C4—864no—
598C22×C4—3442no—
599C22×C4D4×D4311yescharacteristic
600C22×C4D4×D4311yescharacteristic
601C22×C4C23×D4311yescharacteristic
602Q16—28no—
603Q16—868no—
604SD16—868no—
605SD16—868no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—432no—
609C2×C8—432no—
610C2×C8—862no—
611C2×C8—862no—
612C2×C8C23×D4312yes—
613C2×C8C23×D4312yes—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—434no—
619C4⋊C4—434no—
620C4⋊C4—432no—
621C4⋊C4—432no—
622C4⋊C4—864no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C4⋊C4—864no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4—864no—
629C4⋊C4C23×D4312yes—
630C4⋊C4C23×D4312yes—
631C22⋊C4—434no—
632C22⋊C4—434no—
633C22⋊C4—864no—
634C22⋊C4—864no—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C22⋊C4—864no—
638C22⋊C4—864no—
639C42—24no—
640C42—24no—
641C42—432no—
642C42—432no—
643C42—864no—
644C42—864no—
645C42—864no—
646C42—864no—
647C42D4×D4312yes—
648C42C23×D4312yes—
649C23—432no—
650C23—862no—
651C23—862no—
652C23—862no—
653C23—862no—
654C23—1722no—
655C23—1722no—
656C23—1722no—
657C23C2×D4×D4311yescharacteristic
658Q8—24no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—434no—
664Q8—8616no—
665Q8—864no—
666Q8—862no—
667Q8—3444no—
668Q8C2×#1062189814yes—
669D4—862no—
670D4—862no—
671D4—3444no—
672D4—1722no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—432no—
684C2×C4—432no—
685C2×C4—432no—
686C2×C4—8616no—
687C2×C4—862no—
688C2×C4—864no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—864no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—3444no—
698C2×C4—1722no—
699C2×C4—1722no—
700C2×C4C2×D4×D4312yes—
701C2×C4C2×D4×D4312yes—
702C2×C4C2×D4×D4311yescharacteristic
703C2×C4#41×D4312yes—
704C2×C4C2×#1062189812yes—
705C2×C4C24×D4311yescharacteristic
706C8—22no—
707C8—22no—
708C8—862no—
709C8—862no—
710C22—862no—
711C22—862no—
712C22—862no—
713C22—3444no—
714C22—1722no—
715C22—1722no—
716C22—1722no—
717C22—1724no—
718C22#1458340812yes—
719C22#1458370612yes—
720C22#1458371212yes—
721C22C22×D4×D4311yescharacteristic
722C4—22no—
723C4—22no—
724C4—24no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—862no—
729C4—862no—
730C4—862no—
731C4—864no—
732C4—1722no—
733C4—1722no—
734C4#1458340812yes—
735C4C2×#41×D4311yescharacteristic
736C4C22×#1062189811yescharacteristic
737C2—3442no—
738C2—1722no—
739C2#1914483014yesdirect product factor
740C2C2×#1458340811yescharacteristic
741C2C2×#1458370611yescharacteristic
742C2C2×#1458371211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C4×Q16×C43C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenterC2×C4×Q16D43
hypocenterC43C2×#3121
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
2. C2×#14583375C2semidirect
3. #19144830C2direct (N × H)
4. C2×#14583238C2semidirect
6. C2×#14583193C2semidirect
7. C2×#14583182C2semidirect
8. C2×#14583124C2semidirect
9. C2×#14583123C2semidirect
10. C2×#14583053C2semidirect
12. C2×#14583004C2semidirect
13. C2×#14582997C2semidirect
14. C2×C4×#10621873C2semidirect
15. C2×#14582958C2semidirect
16. C2×C4×Q16×C43C2semidirect
32. #14583375C22semidirect
43. #14583238C22semidirect
45. #14583193C22semidirect
46. #14583182C22semidirect
47. #14583124C22semidirect
48. #14583123C22semidirect
49. #14583053C22semidirect
51. #14583004C22semidirect
52. #14582997C22semidirect
53. C4×#10621873C22semidirect
54. #14582958C22semidirect
72. C4×Q16×C43C22semidirect
379. C2×C4×Q16D43semidirect
382. C2×C43#3121semidirect
427. C4×Q16C2×D43semidirect
448. C43C2×#3121semidirect
739. C2#19144830direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835212
C2×#145833752
#191448302
C2×#145832382
C2×#145832262
C2×#145831932
C2×#145831822
C2×#145831242
C2×#145831232
C2×#145830532
C2×#145830392
C2×#145830042
C2×#145829972
C2×C4×#106218732
C2×#145829582
C2×C4×Q16×C432
C2×#312143